Intermetallic rare-earth compounds

This article was downloaded by: [University of Sydney] On: 29 August 2014, At: 06:57 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Advances in Physics Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/tadp20 Intermetallic rare-earth compounds K.N.R. Taylor a a Physics Department , University of Durham , South Road, Durham Published online: 02 Jun 2006. To cite this article: K.N.R. Taylor (1971) Intermetallic rare-earth compounds, Advances in Physics, 20:87, 551-660 To link to this article: http://dx.doi.org/10.1080/00018737100101311 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. 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Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms- and-conditions http://www.tandfonline.com/loi/tadp20 http://dx.doi.org/10.1080/00018737100101311 http://www.tandfonline.com/page/terms-and-conditions http://www.tandfonline.com/page/terms-and-conditions [ 551 ] IntermetaUic Rare-earth Compounds By K. N. I~. TAYLOR Physics Department, University of Durham, South Road, Durham ABSTRACT The physical propert ies of m a n y of the rare-ear th intermetallic compounds have been collected together. They are discussed in t e rms of the role t ha t the magnetic exchange and crystal field interactions play in determining these properties. I t is pointed out t ha t in this vas t number of materials there is an ideal chance of establishing which of several second-order t e rms are effective in determining s t ruc tura l stability. CONTENTS PAGE 552 I:~,EFEHENCES. § 1. INTRODU-CTION. § 2. SOME BRIEF NOTES ON THE STABILITY OF INTEI~METALLIC SYSTEMS. 553 § 3. MAGNETIC INTERACTIONS AND THEIR CONSEQUENCES. 556 3.1. The Indirect I~KKiY Interact ion. 556 3.2. The Direct In teract ion. 560 § 4. ELECTROSTATIC CRYSTAL FIELD EFFECTS. 562 § 5. COMPOUNDS WITH NOlO-MAGNETIC ELEMENTS. 565 5.1. Aluminium and other I I I B Elements. 566 5.2. Compounds wi th E lements of Group IV B. 588 5.2.1. Silicon and Germanium. 588 5.2.2. Tin. 590 5.3. Compounds wi th Copper, Silver and Gold. 592 5.4. Discussion. 596 § 6. COMPOUNDS WITtt THE d-TRANSITION METALS. 598 6.1. The 3d Metals. 598 6.2. 4d and 5d Metals. 626 6.3. Discussion. 630 § 7. GENERAL CONCLUSIOI~S. 631 APPENDIX I. References to Phase Diagram Information. 633 ArPENDIX If. Crystallographic and Magnetic Data for the Compounds. 635 649 A.P. 2 P D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 552 K. N. g . Taylor o n § l. INTRODUCTIOI~ II~TERMETALLIC compounds can be satisfactorily described as mixtures of two or more metals which have a well-defined and simple stoichiometry. The properties of these compounds are often markedly different from those of either component element. The existence of intermetallic compounds has been known since 1839 (Karsten 1839), but little serious investigation of their physical properties was carried out for almost a century. During this time the number of known binary and ternary systems containing these compounds had been continuously increasing and considerable effort had gone into attempts to establish the rules relating to the stability of the different phases. Except for a few well-known exceptions, the reasons for the existence of compounds at certain preferred compositions in even a binary system is not well understood, and the detailed rules which govern the crystalline structure of each of these compounds are still unknown. During the last two decades the attention given to these metallic com- pounds by both pure and applied materials scientists has increased very rapidly, and the current literature suggests that this growth of interest is continuing. The experimental work being performed relates to all types of physical property and recently there have been some successful attempts at understanding the theory of quite complex systems. In spite of this attention, however, there are very few authoritative texts dealing speci- fically with either the metallurgy, physics or technical applications of these materials. The absence of such reviews of the subject may be due to the enormity of the task of classifying and discussing the very large number of possible compounds and the even larger number of pseudobinaries formed from mixtures of such compounds. The scale of the problem is not improved by the vast diversity of behaviour which all too often makes each closely related series of compounds, or even each member of the series, a separate subject for discussion. Fortunately, one does occasionally find reasonably large families of compounds for which the properties of at least one of the elements is understood and we are then in a position to contemplate a detailed investi- gation of the influence of the other component on the behaviour of the intermetallie system. This is the case for many of the rare-earth intermetallie compounds to be discussed in the following. In these, the deeply buried 4f shell and the trivalent state of most of the rare-earth ions allow us to study the variation of certain electronic properties almost independently of Fermi surface effects. The same is not true of 3d transition metal intermetallics, for which the ionic d states lie sufficiently close to the Fermi level that it is difficult to prevent the simultaneous variation of all the electronic characteristics in the study of a family of compounds which would be described as chemically related. The technical importance of intermetallic compounds has been well established in the past and they have been used in structural, magnetic, D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds 553 thermal-and electrical applications. I f we are to judge by the wealth of unusual and interesting properties which continuously appear in the literature, their use is still in its infancy and we must look forward to the increasing application of these materials. In the following article an at tempt is made to survey what is known of the physical properties of those intermetallies which have a rare-earth metal as one component. The bulk of the published work is concerned with their magnetic behaviour and consequently this emphasis is evident in what follows. In order to keep within a manageable length, little mention is given to behaviour which is associated with variable valence states of certain of the rare earths (notably cerium). These cases have been listed specifically by Wallace (1971). The early sections deal very briefly with some general points, including a few comments on the factors affecting structural stability (§ 2), the possible magnetic exchange interactions ( § 3) and the effects of the electro- static erystMline field on the electronic states of the ions in the compound (§ 4). Detailed discussion of the different types of materiM is given in § § 5 and 6, which deal with the compounds formed with non-transition and transition metal ions respectively. In order to be of as much value to the experimentalist as possible, I have listed the references to the latest phase diagram studies of many of the systems in Appendix I. Collected together in Appendix I I are the structural and magnetic characteristics of the compounds in the series of tables A1-A62. Reference is made to these repeatedly in the text and the format is kept as ' table A1 ', etc. so as to separate the material from data tabulated in the text. § 2. SOME BRIEF NOTES ON THE STABILITY OF INTEI~METALLIC SYSTEMS Numerous workers have been involved in an effort to establish general rules governing the existence of intermetMlic phases. This has been carried out using a wide variety of different approaches and Nevitt (1963) has suggested that two of the aims of research into the metallurgy of inter- metallic compounds should be to (a) at tempt to understand the factors influencing the stability of the various phases and (b) associate the structural properties with the bond distribution between the atoms. Both of these of course require the careful classification and characteriza- tion of the intermetallie phases. By and large, the research of the past years has shown tha t the problem is extremely complex and tha t many of the rules proposed to account for and predict the existence of intermediate phas~s are rather short-lived. Fortunately some notable exceptions have withstood the passage of time and these allow us to rationalize the observed behaviour of some groups of 2 P 2 D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 554 K . N . R . Taylor on compounds. These have been discussed at length in the book by Westbrook (1967) and only a few comments are required here. The first of these rules came from the work of Hume-l~othery (1926) in connection with the structure sequences observed in the phase diagrams of copper, silver and gold alloyed with other metals such as tin, zinc, cadmium and so on. Each of the observed structures was found to exist for a fixed ratio of valence electrons to atoms. We may t reat these phases as being intermetallic compounds having rather wide homogeneity ranges, and examination of the various phase diagrams shows that the Hume-Rothery electron-atom ratio rule applies in many systems and for widely differing stoichiometry. The origin of this ratio rule was shown to lie within the band theory of solids (Jones 1934 a, b) and arises from the different density of states curves which occur for the different structures in a given system. Exten- sive discussion of this point exists in standard metallurgical texts and it is sufficient here to reproduce the calculated curves for the f.c.c, and b.c.c. structures and the difference between the Fermi energies of the two structures as a function of electron concentration. These are shown in fig. 1, from which it is evident tha t as electrons are added to the band the Fermi energies of the structures are indistinguishable below A. Beyond z ÷ Fig. 1 Energy The calculated density of states curves for b.c.c, and f.c.c, structures showing the stability limits of the two phases. The inset shows the variation of AE F as a function of energy. A the higher N(E) associated with the f.c.c, structure (a) leads to a lower E F for this phase and hence its appearance as the stable phase. However at B the b.c.c. (fl) structure becomes stable as N(E)z becomes greater than N(E)~. The difference between the Fermi energies is shown in the inset. Rigorously B is the energy at which the areas under the two peaks are exactly equal. Perhaps the next most important contributions lie in the rules based on the role of atomic size and radius ratio. These were outlined by Laves (1935, D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Inter'metallic Rare-earth Compounds 555 1939) who extended the ideas of Goldschmidt (1921) on the importance of the radius ratio to structure determination. Laves examined the ease with which different types of atom may be stacked into different dense structures when the atomic radii are different. The AB 2 phases, called after Laves, are classic examples of these structures and are represented by three types, namely MgZn~(C14), MgCu~(C15) and MgNi2(C36 ). These phases occur for radius ratios between 1.10 and 1-30 (see, for example, Nevitt 1963) ; the ideal ratio for close packing being 1.225. The existence of compounds of this type is governed primarily by space- filling requirements, and it appears that the size ratios play little or no part in deciding which of the three Laves phases will be the most stable (Dwight 1961). Evidence does exist, however, to suggest that the struc- ture type goes through the sequence MgCu2-MgZne-MgCu e with increasing atomic number of the second element (Elliot 1961, Elliot and Rostoker 1958). The hexagonal structure (C14) also frequently occurs in an inter- mediate composition range in pseudobinaries formed from two C15 phases. From these and other observations (Laves and Witte 1936, Berry and l~aynor 1953, Lieser and Witte 1952, 1954, Witte 1952) it is now generally concluded that the electronic structure is the dominant factor determining the stable crystal structure. The parameter of importance is the valence electron concentration, as illustrated in table 1. Witte (1952) has calcu- lated the volumes of the Brillouin zones for the MgCu 2 and MgZn 2 struc- tures and finds that contact between the zone boundary and the Fermi surface first occurs at values of the valence electron concentration per atom equal to 1.83 (MgCu2) and 1.93 and 2.32 (MgZn2). The agreement of these values with the experimental data (Laves and Witte 1936) of table 1 is quite striking. The correctness of this approach is further supported by the magnetic susceptibility studies of Klee and Witte (1954) in Mg(Cu, Zn)~. The whole subject of the stability of these and other close-packed structures has recently been considered by Werniek (1967). Table 1. The valence electron concentrations occurring in the various stable Laves Phases in some ternary magnesium alloys. (Laves and ~Vitte 1936) System Mg(Cu, Zn)2 Mg(Cu, A1)2 Mg(Cu, Si)2 C15 1.33-1.75 1-33-1.73 1.33-1.71 C36 1.83-1.90 1-84-1.95 1.81-1.89 C14 1-98-2.00 2.03-2.05 1.81-2.01 The electrochemical factor has also been considered as a means of sys- tematically grouping compounds from those with ionic bonding to those which are typically metallic (Zintl and Kaiser 1933). The electrochemical factor is essentially a function of the relative electronegativities of the D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 556 K. N. R. Taylor on component metals in an alloy, and because of the uncertainties in the exact values of this quanti ty the technique is essentially a qualitative one. While each of the above terms is undoubtedly of importance in deciding which of the many possible structures will be stable for a given composition it must be remembered that the energy differences between many of these structures are small. Consequently the final decision between one phase and another can be made by second-order effects. These may be involved, for example, with the degree of filling of incomplete shells such as the 3d states in the transition metal compounds or with the presence of strong magnetic or electrostatic interactions between the ions. This being so, it requires that those workers concerned primarily with the investigation of the electronic properties of solids should be acutely aware of the possibility of observing factors influencing structural behaviour. § 3. ~/~AGNETIC INTERACTIONS AND THEIR CONSEQUENCES The vast majority of the rare-earth intermetallic compounds which have been examined exhibit magnetic ordering over some temperature range. In the compounds with non-magnetic elements such as aluminium, zinc, etc., the Curie temperatures are usually low (< 100°K) and the only interaction requiring consideration is that between the rare-earth ions. When the other component of the compound is a 3d transition metal, the magnetic ordering temperatures are frequently comparable to that of iron and in these cases it is also necessary to allow for the exchange interactions occurring between the transition metal ions and between the transition metal and rare-earth ions. The evidence suggests that the exchange mechanisms involving the 3d ions (usually due to overlap) depend very strongly on the moment of the transition metal ion, and that they rapidly become the dominant interaction. In the following sections the indirect exchange coupling between rare-earth ions and the direct coupling between transition metal ions is considered briefly. 3.1. The Indirect R K K Y Interaction I t is generally supposed that metallic rare-earth systems can be represented by an assembly of tripositive rare-earth ions embedded in a sea of conduction electrons. The mean radius of the 4f shell is small compared to the interionic spacing, and the relatively strong magnetic interactions between the ions are thought to arise fl'om an indirect ex- change involving the polarization of the conduction electrons. Inter- actions of this type are long-range and frequently oscillatory, and are therefore capable of giving rise to a wide variety of magnetic spin struc- tures. The theory, originally developed by Ruderman and Kittel (1954) in connection with nuclear magnetic resonance in metals, and subsequently adapted by Kasuya (1956) and Yosida (1957), now bears their name and is usually referred to as the RISKY theorv ~evet'al reviews of the theory D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds 557 and its consequences have appeared in the past (I~oeher 1962, de Gennes 1962, Kasuya 1966, Kittel 1968). The only other interaction requiring consideration is the electrostatic dipole term which is normally incor- porated in the crystalline electric field, the effects of which will be dis- cussed later (§ 4.). The exchange integral for the interaction between the localized f electrons and the conduction s electrons can be written e 2 A(k, k ) i , = ~ f f ¢(r', k)~Fa~(rz, r 2 , . . , r i . . . r~)}ri_ r ,----- ~ spins ¢(r~, k')~Faf(rz, r e . . . r' . . . r~)dr' dr 1 dr 2 . . . dry, (1) where ¢(r, k) represents the conduction electrons and ~F4c the electrons in the incomplete 4f shell. Because of the difficulties associated with evaluating eqn. (1) and the uncertainties introduced by the various approximations used in estimating A(k, k), the exchange integral has generally been assumed to be isotropie and a function of q( = I k ' - k l ) only. Further, within the I~KKY theory A(q) has been taken as constant, equal to F say. Writing the exchange integral in real space as A(r) leads to an exchange interaction between the conduction and f electrons of the form -5/~s: = - A ( r - R ) s . S , . (2) where s and S are the spins of the conduction electron and ion at r and R respectively. In an extended zone scheme, and for plane ' e l ec t ron ' w a v e s A(r) = ~ A(q) exp (iq. r). (3) q In the R K K Y approximation A ( r - R) = F ~ ( r - R). (4) Since 2/~t is spin dependent, the conduction electrons of different spin will respond differently to the interaction. For example, if A (r) < 0, the spin-up electrons have minimum energy in the vicinity of S and those of spin-down do not. This then leaves the conduction electrons polarized. The polarization P(r) is defined as the difference between the densities of spin-up and spin-down electrons and may be written P(r) = ~ f ( k ) [ I ¢+(r, k)12-I ¢_(r, k)]~], k (5) where f(k) is the occupancy of the states k and the ¢ ± are the electron wave functions in first-order perturbation theory. Assuming that the D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 558 K . N . R . Taylor on incident electrons may be represented by plane waves, P(r) may be written as T = 0°K (only states k < k I occupied) as 97r Z 2 f F(2/cilr- r'l)A(r' ) dr', (6) P(r) = ~ - ~ S z E-~ where Z is the number of conduction electrons per unit volume and ~ is the atomic volume. F(x) = (sin x - x cos x) /x ~. The R K K ¥ result, with A(r)= F3(r) is then long-range and oscillatory falling off approximately as 1/r a at large distances. For r-> O, F(x) diverges and the contact potential F~(r) is then not realistic. This divergence does not affect the calculation of the interaction energy between two spins, nor does it influence the oscillations in P(r) at large r. The introduction of more realistic exchange interactions A(q) to remove this divergence can result in a reversal of P(r) at r = 0, relative to that given by eqn. (6), as we shall see later. The polarization P(r) produced by an ionic spin Si at R i interacts with a second spin Sj at Rj through ~ / a n d the exchange interaction between the spins is written in second-order perturbation theory as ~ : _ ~ i Intermetallic _Rare-earth Compounds 559 The lattice sum ~ F(2kIIR ~- R3.1) varies for the different erystallo- R~R~ graphic structures and has been evaluated by several authors (Darby and Taylor 1965, Mattis 1965, Buschow et al. 1967) in connection with the interpretation of magnetic properties. Since F(x) depends upon the elec- tron density, through/c/, 0p is also an oscillatory function of the electron density and observed changes in the sign of 0p have been at tr ibuted to changes in conduction electron concentration across an alloy system. The effect of including the anisotropic terms in J/st have been examined for the pure metals (Specht 1967) but so far very few intermetallie systems justify this treatment. The non-infinite value of the mean free path A caused by both impurities and spin disorder, leads to a damping of the oscillations of the R K K Y interaction and for these conditions P(r) is usually written P(r)~=F(2k.~r) exp (-r /A). (11) Finally, at tempts have been made to improve on the gross assumption of the free-electron treatment in the above and several authors have con- sidered the changes in the R K K Y interaction caused by using non-spherical Fermi surfaces (goth et al. 1966, Blandin 1961 and de Silva 1968). Again, while these effects are unquestionably of relevance to the interpretation of the behaviour of intermetallic compound systems, there is presently insufficient unambiguous evidence to justify their use. The presence of the conduction electron polarization caused by a single ion produces an apparent increase in the experimentally determined ionic moment. The excess moment is trivially given by f 3ZF /~p =/~]~ P(r) dr=t~ B -~-~f ( g j - 1)J=txB(g J - I)JFN(E/) , (12) and in the pure metals it accounts for observed ionic moments in the ordered state which are almost 1 tLB greater than the g j J value for the ion. In the presence of a magnetic field the Zeeman energy per ion now becomes (g/~n +/~p)H and the apparent g value of the ion is shifted by an amount hg = (g j - 1)JFN(E/). . (13) This result has been compared with the experimental data for the rare- earth metals with reasonable satisfactory results (Liu 1960, 1961). The existence of the exchange interaction (eqn. (2)) leads to a spin- dependent electron-scattering mechanism which results in a spin-disorder contribution to the total resistivity. The form of this contribution has been examined by several authors (Kasuya 1956, 1966, De Gennes and Friedel 1958, Rocher 1962, van Peski-Tinbergen and Dekker 1963 and D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 560 K . N . R . Taylor on Dekker 1965). I t is generally accepted that above the magnetic ordering temperature the spin-disorder resistivity is constant and given by t~,k, (m'~r~ 2 PsPin = AvrZ \ - ~ ] (g J - 1)J (J+ 1). (14) This experimental value of P.~,in may be used along with the paramagnetic Curie temperature in eqns. (10) and (14) to make some estimate of F and m* provided tha t the function E F(2kll R i - Rjl ) has been evaluated for the structure in question. A general review of spin-disorder effects in metals and alloys has been given by Coles (1958) while Methfessel and Mattis (1968) have discussed the problem in connection with various rare-earth magnetic semi- conductors. 3.2. The Direct Interaction While the basic form of the rare-earth interaction, discussed in the previous section, can be represented quantitatively with some certainty, the same cannot be said of magnetic exchange interactions involving transition metal ions which carry an ionic moment. This is particularly true if the moment arises from a 3d band as is the case for the pure metals nickel, cobalt and iron. Since quite a large proportion of the intermetallic compounds to be discussed in the following contain 3d transition metals, it is appropriate to comment very briefly on certain features of the direct interaction which are of relevance to the understanding of the properties of these compounds. Detailed reviews of direct exchange have been given recently by Herring (1966a, b), Mort (1964) and in the book edited by Marshall (1967), while the extension of the usual band model by Friedel et al. (1961) has allowed for the existence of localized moments within a band picture. In the 3d transition metals the moment is associated with the electrons (or holes) in the unfilled 3d band. In the normal approach this band may be treated as being in a paramagnetic state in the absence of exchange and correlation effects. That is, we begin by considering two sub-bands equally populated with spin-up t and spin-down ~ electrons. In order for this band system to carry a moment, then n electrons per atom must be transferred from the ~ to the t states. This occurs with a displacement of one sub-band with respect to the other along the energy axis by a dis- tance AE (fig. 2). The energy necessary for the electron transfer may arise from an atomic exchange interaction or from the Coulomb correlation effect, both of which may be treated as a perturbation. Widely divergent opinions exist as to the relative importance of these two terms; see for example, Slater (1936), Friedel (1954), Mott (1964), Kanamori (1963), Hubbard (1963, 1964a, b) and Gutzwiller (1964): Beeby (1967) has recently discussed the two extremes in detail. For the present we shall assume that the correlation energy is small and that there is an exchange energy W per electron pair. Assuming that D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds Fig. 2 E E 561 A schematic representation of the splitting of the spin-up and spin-down sub- bands of an itinerant electron ferromagnet by the exchange interaction. there are n ~ and n 4 electrons in the two sub-bands, with n ~' - n ~ ( - n o say) initially, then once the electron t ransfer has t aken place as a resul t of the exchange interact ion we can write for the change in energy per a tom : A E ~ = n h E [ ( n t + n) ~ + (n $ - n ) 2 - 2(n0) 2] W = n [ A E - 2 n W ] . . . . . . (~5) Following Friedel et al. (1961) we ma y now let the dens i ty of s tates a t the Fermi energy be N(Ex) and obta in N(EF) =n/vAE, (16) where v is the atomic volume. F rom eqn. (15) it then follows immediate ly t h a t the fer romagnet ic s ta te is stable provided 2nW AE -2vWN(EF) > 1. (17) The quan t i ty nW/2 m a y be associated with the Weiss molecular field H w through nW/2=21~BH w or with the magnetic ordering t empera tu re 0 through nW/2 = 2k8. I t is well known tha t electron t ransfer f rom the $ to the ~ sub-band m ay not result in the filling of all the t states, i.e. we m a y be left with incomplete polarization. This is likely to be the case in iron (Wohlfar th 1949, Friedel 1954, Coles and Bit ler 1956, Mot t 1962, 1964). This lack of sa tura t ion m a y be associated with the t rapping of the $ Fermi level at a min imum in the d band, which arises because the molecular field is inadequate to provide the large excess energy necessary for E F to move through this region of low densi ty of states. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 562 K. N. R. Taylor on In this situation, in which both sub-bands are intersected by the Fermi level, then eqn. (17) becomes where 2W> 1/N(E)v, 1 i 'E~N(E) dE N ( E ) = n / A E = - - - ~ j E~ (is) is the average density of states between the positions of the Fermi level in the two sub-bands, i.e. between E 1 and E 2 respectively (AE = E 1 - E2). The result of experimental determination of the magnetic properties of an alloy system may be used along with eqns. (17) and (18) to calculate the approximate density of states curve for the system, assuming that there are no appreciable changes in its overall form for the range of speci- mens studied. Friedel et al. (1961) have shown, using a phase shift calculation, that within the band model it is possible to obtain a situation in which a local moment character may appear to be associated with an ion. They considered the spatial dependence of energy about a transition metal ion, when there is a local spin polarization in its neighbourhood which leaves the ~ population increased by n and the ~ population decreased by n. I t was then shown that such a polarization is stable for a condition given by eqn. (17) ; in other words, this is the condition for any spin polarization to occur spontaneously. In this model the excess ~ or deficit ~ population refers to the local populations of itinerant electrons, and the size of the polarization regions is comparable to the Fermi wavelength hf of these electrons ()~ = 2~r//CF). Surrounding the central region is a region of fringes of spin polarization of alternating sign, and it was proposed that the appearance of either ferromagnetic or antiferromagnetic states will depend upon the details of the overlap of these polarization regions. § 4. ELECTROSTATIC CRYSTAL FIELD EFFECTS Interactions between the rare-earth and transition metal moments are tikely to be even more complex since they undoubtedly depend on the electronic states associated with the 3d electrons of the transition ion. I f there is a 3d band of finite width then the f-d interaction may occur either through a direct process or via the polarized conduction electron cloud in the vicinity of the two ions. As yet there has been very little detailed treatment of this specific interaction. In contrast to the 3d transition metals, the interaction of the rare-earth ions with the crystalline electric field is known to be much less than that due to spin-orbit interactions within the ion. This arises as a consequence of the limited spatial extent of the 4f wave functions compared with those for the 3d electrons. The small values of (r ~} lead directly to a large D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds 563 reduction in the crystal field interaction and indirectly to a reduction through the screening effects of the outer electrons. As a result of the dominance of the spin-orbit interaction the total angular momentum J is a good quantum number in these ions and the effects of the crystal field may be taken as a small perturbation of the ( 2 J ÷ l ) fold-degenerate ground state of J . The number of new levels which arise as a result of this perturbation depends upon the symmetry of the electrostatic field Vo(r ) and is completely determined by group theo- retical methods (Bethe 1929). The lower the symmetry of Ve(r ) the greater the splitting and for a given symmetry the magnitude of the splitting depends upon the value of J . In order to calculate the eigenvalues and eigenveetors of these electron states one frequently uses a point-charge model in which the electrostatic potential is written at the origin : where Z i is the ionic valence and the R~ are the positions of the atoms in the crystal lattice about a typical ' reference ' ion at the origin. While this is a somewhat elementary picture it has been used successfully in the past to account for many of the properties of the rare-earth ions in non- conducting erystMline environments. Attempts to introduce a more realistic charge distribution become very complicated and are somewhat inflexible. The electric field at the position of the reference ion is found by the solution of Laplaee's equation and can be written in a spherical harmonic expansion. This has the general form + l where 47r Zj a m ( - 1)m Y/-m(0¢j). 2l+ 1 J The number of terms in this expansion is immediately reduced by the limitations imposed by crystal symmetry, and assuming initially that there is no configurationM mixing, further simplification occurs in the allowed matrix elements of V(r) : Vo(rO¢)=C+D4IYa°(O¢)+N/5 (Y44(0¢)+ Y~-4(0¢))] + D 6 ~ Y 6 ° ( O ¢ ) - ~ 7 (Y64(0¢) + Y0-4(0¢)) 1, (21) where C = constant, D 4 = (r4)a4 ° and D 6 = @6}a6°. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 564 K . N . R . Taylor on This is conveniently written Vo = V4°+ V44+ V6°+ V64. To calculate the crystal field splitting requires a knowledge of the matrix elements of Ve which involves the integrals of V c between the single particle wave functions for the 4f wave functions. Fortunately this is not necessary in practice, and the calculation may be simplified by introducing operator equivalents (Stevens 1952) which operate on the total I J, m j) . For a given J.~ the matrix elements of Vo are proportional to those of equivalent operators containing,Ix, Ju and Jz, hence we can replace operators in x, y, z by equivalent operators in Jx, J~j, J~. The equivalent operator for the cubic field, along a four-fold axis then becomes Vo = B4°(04 ° + 5044) + B6°(06 ° + 2].0G4), (22) where B4°=(-a4°fij(r4)/20) and B6°=(a6°~j(r6~/224) determine the magnitude of the crystal field splitting. Here fig and y j are tabulated constants and a4 ° and aG ° are lattice sums defined above. For other crystalline axes and structures the relevant operators are obtained from symmetry arguments. The 0n m have been listed in various review publications (see, for example, Hutcbings 1964) and it is a simple matter to set up the crystal field matrix for a given J state. Subsequent diagonalization to obtain the eigenvalues and eigenvectors is straightforward with standard computer programmes. For the case of cubic symmetry above, the level splitting of all the multiplet levels for J between 2 and 8 have been tabulated by Lea et al. (1962) for various ratios of B4 ° and B6 °. On evaluation of the ionic moment associated with the ground state it is generally found tha t these are appreciably less than the maximum possible moment corresponding to gJ. In the case of ions with an even number of electrons the ground state is a singlet with zero moment in accordance with Kramers' Theorem (Kramers 1930) and the Jahn-Teller effect (1937). However, the separation of the two lowest levels is frequently small and under these conditions they behave in many respects as a doublet. In calculating the susceptibility it is important to know the ground state in a given crystalline field, as it directly influences the magnitudes and hence the relative importance of the low and high frequency com- ponents of the Van Vleck susceptibility. Indeed, it is such effects which lead to the observation of temperature-independent susceptibility of Pr and Tm at low temperatures in some environments. With temperature increase and the resulting increase in population of the excited states of the multiplet, the moment increases towards its full gJ value and the sus- ceptibility becomes Curie-Weiss in form. In many solids this quenching of the ionic moment is opposed, even at low temperatures, by exchange interactions such as were discussed in the foregoing. The effect of the exchange field is to mix some of the excited D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 intermetallic Rare-earth Compounds 565 states into the ground state and so give a moment more nearly equal to the ionic value. The extent of this admixing may be crudely estimated by comparison of the splitting of the lower states with the Curie temperature (Bleaney 1963). In practice the exact moments and energy level structure may be evaluated for this ease, provided that the exchange field is known, by treating it in the Hamiltonian on an equal footing with the crystal field contribution. Rather surprisingly, there are relatively few instances for which this has been done, for tile intermetallic compounds. Trammell (1963), however, has explored the compounds with the group V elements using this approach. Because of the many approximations which are present in the point- charge model, it is rarely used to make ab initio calculations of electronic states even in insulating materials. Rather, experimental data are fitted by allowing a reasonable variation in the scaling constants in the Hamil- tonian (for example, B4 °, B6 ° and B~°/B6°). In the case of intermetallics the situation is almost certainly worse than in non-metallic solids and it is possible that only indications of the relative positions of the multiplet levels can be expected from the type or calculations outlined above; however, the predicted degeneracy of the various states will still be accurate. Again, it is expedient to allow considerable flexibility of the values of the scaling constants and fit to the experimental data,. This has been done with considerable success in several systems (Bleaney 1963, Bowden et al. 1968) for a crystal field situation and it should be possible to include Zeeman terms satisfactorily in a computer fit. In circumstances such as this, the best values of B4 °, B6 °, etc. for various systems probably provide useful ' exper imenta l ' data values :for correlation with para- meters such as electron concentration, structures, etc. Once such a correlation is achieved it may give us much more insight into the relevance and value of point-charge calculations in metallic systems. § 5. COMPOUNDS WITH NON-MAGNETIC ELEMENTS The extent of compound formation between the rare-earth elements and the remaining elements of the periodic table has been the subject of considerable work in the past. Gschneidner and Waber (1961) found that intermctallic compounds are formed with elements lying to the right of the chromium-molybdenum-tungsten column of the periodic table. Rigorously-, this generalization includes the pnictides, chalcogenides and halides which are best classified separately from intermetallic compounds. These have either been the subject of reviews in recent years or have been included in other survey papers dealing with various rare-earth systems (McMasters and Gschneidner 1964, Jones 1969, Methf~ssel and Mattis 1968, Taylor and Darby 1971). The remaining intermetallic compounds can readily be divided into two groups, namely those with elements such as aluminium, zinc, silver and D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 566 K. N. l~. Taylor on so on, whose ions have complete inner shells, and the transition metals, which have incomplete 3d, 4d or 5d electron shells and consequently possess an ionic moment which may take part in the magnetic behaviour of the compounds. In the following, these two classes of compounds are treated independently. In this section many of the compounds will be considered which are formed with a non-magnetic partner. The order in which the various systems are discussed is mainly a feature of the amount of published literature dealing with them ; however, the appearance of the group I I I B elements in the initial subsection (§ 5.1) is principally a feature of the role the aluminium compounds have played in our under- standing of the behaviour of many other systems. 5.1. A l u m i n i u m and other I I I B Elements A variety of compounds occur in the phase diagrams of the rare-earth- aluminium systems (Buschow and van Vucht 1967) and include the com- positions RA1, RA12 and RA1 a which are common to all the trivalent lanthanide elements. Other stoichiometries, such as RaA1, R2A1, RaA12 and RaAll~ are found in conjnnction with a limited number of elements. There are some anomalies ; for example, ytterbium appears to have an effective valence of three in YbA1 a and two in YbAI~, while the other normally divalent element europium forms only EuA12. Buschow and van Vucht (1967) have attempted a systematic arrange- ment of the rare-earth-aluminium compound systems and have shown that both the stability and observed compositions of the compounds are strongly dependent upon the atomic size of the rare-earth element. The reported crystallographic data for all the compounds is listed in tables A1-AT. ]n general, a single structure type persists across the series, but in the case of the I~A1 a compounds a succession of structures occurs which has been associated with the change in the R/A1 radius ratio, passing from predominantly hexagonal structures to cubic structures as the ratio decreases (van Vucht and Buschow 1966). The observed structures listed in table A6, are shown schematically in fig. 3 (a) and the changes in the percentage hexagonal stacking as a function of the rare-earth atomic radius are shown in fig. 3 (b), where the results for both pure and pseudo- binary compounds are included. Electron concentration effects are clearly important both from the point of view of the observed stable structures, e.g. the cubic Laves phase RAI~ series, and for the non-existence of many compositions with divalent europium and ytterbium. In discussing the physical properties of these compounds it is convenient to examine the RAI~ series first. This series has been well studied and provides a valuable basis for the consideration of many of the other inter- metallic compounds. The ordered magnetic behaviour of these materials was first investigated by Williams et al. (1962), although Jaccarino et al. (1960, 1961) had D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Fig. 3 cubic , ~ Rare ,ar th trial.minid¢s Oo O0 a+.om$ in (I120] plane rhombohcdral . ° - - ° ° Alumln;um .~o9.o.0~ qp o iql)l o . , :o :. o..o ~.,,o~o.a, ~ 0 , / l ~ , 1 o ,; ,,O~o oq q ~---~---] . , "o %}'% o. • o,i.~ • . - o LaA' 3 toGd AI~I I a''YA' 3, ThAI 3 ¢~'DyAI3 "V P DyAI~.~,HoAI31w-- Er Al3k.~ SC AI311F ~ - YAI 3 (ErAI 3) IOC 90 8C ec 5c ~ 4c .c $C & '~ ~c Q. IC La P¢ C¢ Nd Sm Gd -~-----~¢-Wn I i I NI3$n - t ype ,I I i I t i i I I y I I Tb I I I I I II I ,I o I f af I oy nl I , li I I P°3Ba-type I I I II I u I 21 II I I I V 1"86 1'82 FRO 1"79 1"78 1'77 m¢talllc radius in ~ I~ ~1 3Ti-typ¢ HoAI typ~z I t I I I I I let Yd Tm Sc I~,~L_ ,A . . , ~ . ~ v ~ i f . 1'76 1.70 1.60 (a) The change in s tructure of the RA1 s compounds with increasing radius of the R element. (b) The decrease in the percentage hexagonal stacking of these structures with decreasing metallic radius. A.P. 2 Q D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 568 K . N . R . Taylor on previously been able to determine both the magnitude and sign of the conduction electron polarization at the rare-earth site in a number o£ the compounds using nuclear and paramagnetic resonance techniques. The resonance results, which will be discussed in detail later, show an antiferro- magnetic coupling between the ionic spin S and the spin Se of the conduction electrons. Further, the results of the magnetization measurements show that the spin moments of the rare-earth ions couple ferromagnetically. I£ this interaction occurs by way of the conduction electrons then the net exchange will be independent of the sign of the rare-earth-conduction electron interaction. Consequently the magnetostatic results are not inconsistent with those of Jaccarino et al. The Curie temperatures and magnetic moments of both the para- magnetic and ferromagnetic states (Williams et al. 1962, Nereson et al. 1966, Buschow et al. 1967, Olsen et al. 1967) are listed in table AS. The com- pounds with lanthanum, lutetium and yt terbium do not appear to order, the absence of a magnetic moment in the latter compound being attr ibuted to yt terbium being divalent in YbAI 2 and consequently having a full 4f shell. This conclusion is supported by the lattice parameter studies of these compounds (Haszko 1960 b) which show that the atomic spacings in both EuA12 and ¥bA12 are larger than those predicted by extrapolation from the dialuminides of the trivalent elements (see table AS). CeA1 e has more recently been reported to be antiferromagnetic (Swift and Wallace 1968) with a Ndel temperature below 4°K, and a specific heat anomaly has been found at 3"4°K (Hill and da Silva 1969). The variation of the Curie temperatures of the compounds with the heavy rare-earth elements lies reasonably close to the prediction o£ the R K K ¥ theory (see fig. 4) and it is usually assumed that the magnetic exchange proceeds via the conduction electrons as implied earlier. The ordering temperatures of the compounds with the light elements do not Fig. 4 2 0 C I I I #~oc - 0 5 I 0 15 17 (9-17 J O-0 , The Curie temperatures of the RA12 compounds as a function of the de Genncs factor G = ( g - 1 ) 2 J ( J + I ) . Only the points for the heavy elements arc shown. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallie Rare-earth Compounds 569 fit so well into this general pattern, however. The magnetization results suggest that the ordered moments are appreciably less than the free ion values, while in the paramagnetic region the Curie constant is in good agreement with that corresponding to the theoretical g~ / [ J ( J+ 1)] value. The degree of quenching of the rare-earth moment in the ferromagnetic state is reported to be as large as 20% in some compounds and is normally attributed to crystal field effects, since in these materials the strength of this field is of the same order as the exchange interaction (Bleaney 1963). l~esults of the neutron diffraction studies of DyA12, NdAl~ and PrA12 (Nereson et al. 1966, Olsen et al. 1967) indicate that the magnetic moments of the ordered rare earth ions are appreciably greater than those obtained from magnetization studies, and it is suggested that the crystal field effects are not as large as those predicted by the theory of Bleaney. On the other hand, low temperature specific heat measurements (McDermott and Marklund 1969) are consistent with sizeable crystal field effects. Table 2. Crystal field quenched moments of the rare-earth ions in C15 Laves phase compounds, specifically RNi 2 Compound PrNie NdNi 2 SmNi 2 GdNi~ TbNi 2 DyNi2 HoNi~ ErNi 2 TmNi 2 Ground State moment 0 1.33 0.24 7.0 0 3.35 0 5-50 0 Maximum moment (~B) 2.07 3-25 0.71 7"0 5-62 8.02 10 6"23 4.37 Observed moment 1 "04 1"89 0"25 7"1 7"8 9"2 8"4 6"8 Low excited states (°~) 77 47 112 27 12 610 36 37 Curie temperature (°K) 15 16 21 85 45 30 22 21 12 The simple theory of the partial quenching of the rare-earth ionic moment, referred to above, was developed by Bleaney (1963) to account for the observed magnetic behaviour of the C15, rare-earth nickel compounds of basic formula l~Ni e. As a result of the crystal field interaction the ground state of the free I£ 3+ ion is split according to the zero-order crystal field level structure given by Lea et al. (1962). In the absence of appreci- able exchange interactions, the moment of the ground-state multiplet of these crystal field split levels provides a minimum possible value for the ionic moment. As discussed in the previous section, if the exchange interaction is comparable in magnitude to the crystalline electric field strength, then the lower excited states may be mixed into the ground- state level and a new limiting value of the ionic moment obtained. This was taken by Bleaney to be a ' maximum moment ' and arose from the 2Q2 D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 570 K. N. R. Taylor on ground and first excited states. I t is perhaps worth mentioning here that the theoretical values, listed in table 2, were derived for the RNi~ com- pounds but are usually transferred directly to the RA12 series because of the similarity of the observed lattice spacings. I t is also vital to the com- parison to note that the calculations of the zero-order pattern were based on a four-fold symmetry axis which may be incompatible with the direc- tion of easy magnetization. I t is this latter term which determines the detailed effects of the molecular field used to represent the exchange inter- action in the total Hamiltonian. Once the magnetic easy directions are known it will be more meaning.~511 to carry out a complete analysis of the problem rather than treating the exchange as a small perturbation. This is particularly true of some of the compounds formed with the light, rare earths, for which the exchange splitting is appreciably greater than the separation of the lower crystal field split levels. In addition to casting some doubt about the size of the erystM field effects on the ionic moment, the neutron diffraction studies of DyA12 (Nereson et al. 1966) were best interpreted in terms of a weak helical anti- ferromagnetic ordering in addition to the ferromagnetic spin structure. Similar results have also been reported for compounds in the RC% series (Moon et al. 1965) and for pseudobinary compounds formed between the Muminium and cobalt series (Oesterreicher et al. 1970). In the latter case, at tempts are made to associate the antiferromagnetic contribution with the valence electron concentration. These results will be discussed later. Magnetostatic measurements on pseudobinary compounds formed between the heavy and light rare-earth dialuminides (Williams et al. 1962) have confirmed that the rare-earth ions interact via a ferromagnetic spin coupling since the observed magnetization for eompolmds such as (Gd, Nd) A12 corresponds to the ferrimagnetie coupling of the two types of moment I t then follows directly that there is a parallel spin alignment since the ionic moment is proportional to the total angular momentum J and this in turn is given by J = L - S and J = L + S for the light and heavy elements respectively. Substitution of yttrium, lanthanum or thorium for the heavy rare-earth element in GdA12, TbA12 and ErA12 (Busehow et al. 1967) has been used to identify the exchange coupling with the R K K Y theory. Figure 5 shows the variation of the Curie temperature in the series (Gd, M)A12 (where M is Y, La or Th). The linear decrease observed for the yt tr ium substitution is to be expected on the basis of simple dilution effects in eqn. (10). In addition to the direct effects of dilution, substitu- tion of tetravalent thorium into the R sites changes the conduction electron concentration and hence the value of the Fermi momentum and Fermi energy in eqn. (10). The term F(2/cfR) contained in this expression for 0~ involves M1 the R - R distances, and has been evaluated tbr GdAi.) by Buschow et al. (1967), as shown in fig. 6. Using/of as a variable parameter, whose magnitude may be very different from the value obtained using a free-electron approximation/%, we know that with increasing thorium D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds Fig. 5 571 l t I a . u ° - t2 2 0 0 IOC adx Y,-x A,, O .-- ~P Gd,, t.oi_,, A, 2 A = ~e Gd x Th(_xAI 2 [ ] = ~}p e = 0 , v ) I I Q2 OA O.6 0 tD / / / I _ O.B Compo~,i~c~ x The effects of dilution on the GdAt 2 Curie temperature for b~th yttr ium and lanthanum addition, which retains the same electron concentration and thorium addition which simultaneously changes the electron concentra- tion. concentra t ion k~ must also increase. Comparison of the two sets of da ta indicates t ha t a 1% increase of k s causes a 60% decrease of 0p, and the most likely location of ~ in fig. 6 is at kf = 0.94ki0. / t - R A iur ther indicat ion of tile likely value of ~'~ comes fl'om the nuclear magnet ic resonancc Knigh t shift K, This effect arises from the enhanced Collduethm eie('tron polarization at the alumhlium ntl(']eus caused 1) 3- the exchange interact ion (g) : j~o = - F s . S = - j ~ , s . S. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 572 K. N. R. Taylor on Fig. 6 r f s O - 5 oIO I I I I I 0"7 0 8 C),9 I'O I'l 1"2 The lattice sum Z F(2kfR) evaluated in GdA12 for the Gd and A1 sites. This interaction leads to an additional hyperfine interaction A ' I . S4, where I is the nuclear spin. Since J is a good quantum number, S must be projected onto J, giving. A ' I . S = A ' I . J (S . l ) / J ( J + l ) , (23) and the Knight shift becomes, assuming a uniform conduction electron polarization : K = K o 1+ (24) gjg ,. 3 J j' where K 0 is the Knight shift in the absence of polarization effects, X~ the f electron susceptibility per rare earth ion and gj and gs are the 4f and con- duction electron g values respectively. Since (S . J} < 0 for J = L - S (light rare earths) and ( S . J } > 0 f o r J = L + S (heavy rare earths) the observed K values give both the sign and magnitude of Js~- Equation (24) reduces to I1 + Js~(gJ-- 1)X~ 1 K = K o A (25) and for a model in which the conduction electron polarization is non- uniform we may write - 6 . r z ( 2 6 ) R ~ R j D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 T a b le 3 . R = R A 1 R A Ia R A 1 a T h e e x c h a n g e c o n st a n ts a ~s f fo r th e r ar e e a rt h -a lu m in iu m c o m p o u n d s o b ta in e d f ro m K n ig h t sh if t o b se rv a ti o n s C e -0 .6 3 -0 .4 1 P r - 0. 48 - 0. 35 N d -0 .3 8 - 0- 22 S m -0 .2 1 G d -0 .1 6 -0 .3 1 -0 .2 3 T b -0 .1 5 -- 0 .2 8 -0 .2 2 D y - 0 - 1 5 - 0 .2 5 - 0 .2 4 H o -0 .1 6 -0 .3 8 - 0. 20 E r -0 .1 4 - 0. 30 -- 0 .1 8 ~ (a ) -0 .2 4 (~ ) T m - 0. 29 - 0 . 2 4 Y b - 0. 23 E rA 1 a ex is ts i n t w o m o d if ic at io n s. 5" 05 ~b O ~ ¢, O D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 574 K. N. I~. Taylor on where the sum over R is now for the R-A1 distances (see fig. 6). Experi- mental J~r values may then be used along with 0p values in eqns. (26) and (10), and a solution found with k~ and F as variables. This technique of determining the exchange constant Js i , is of course, the method employed by Jaccarino et al. (1960) in the work referred to earlier. There has been some discrepancy over the magnitudes of J s f reported in the literature, since they depend on K o, but the sign has been consistently negative. The values for all the dialuminides have recently been collected by Jones (1969) and are given here in table 3. The dangers of over-simplification of the interpretation were pointed out by Jaccarino (1961) where he discussed the non-uniform polarization model. Following the work of Yosida (1957), it is assumed that the f-s interaction leaves the polarization localized at the f ion and the field at the aluminium site is H(r) = ~ ~ A(q)f(q)Sn ~ cos q. ( r - R~), (27) q r where q ( = k - k ' ) is the wave vector difference between the incident and scattered electrons, A(q) is the momentum dependent exchange interac- tion (eqn. (3)) f(q) = 1 + \ 4]Crq ] log \2k---~-~-q] S,~ ~ is the mean spin polarization of the rare-earth ion at R n and kf is the Fermi momentum. H(r) vanishes for all q other than q = 0 or a reciprocal lattice vector K. Thus H(r)=E2J(O) + ~ J(K)f(K) cos (K . r)l (28) and the first term is the spatially uniform field implicit in eqn. (25). Evaluation of the second term is difficult and requires detailed knowledge of the band structure. However, it is found (Jaccarino 1961, Watson and Freeman (1966) that this term may be of importance for f(]c)=f(0), i.e. ]c~ > K (see fig. 7, where the dependence of f(q) on q is shown). In this vicinity the oscillatory contribution of cos (K. r) can make the net value of H(r) negative and hence reverse the sign of J ~ relative to that of the experimental Knight shift. Such an interpretation, however, places severe restrictions on the values of o¢~, making them extremely large ( = 2 ev for PrA12) and the simpler treatment is normally favoured. This view is also supported by the observation of electron spin resonance g shifts. The fractional change in the g value, arising as a result of the conduction electron polarization, has been given by eqn. (13) and may be written Ag 3ngfsr g 2ff.i Ec (29) D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 20 ~.5 f (~9 I'0 0"5 0 0 3.0 Intermetallic Rare-earth Compounds Fig. 7 ! I I I I I I 0.5 I.O 1.5 2.0 2.5 2Kr The variation off(q) with q. 575 This again provides direct evidence for the sign and magnitude of Js~- In this ease, however, the conduction electron polarization being con- sidered is that at the rare-earth ion, rather than at the aluminium site, as was the case for Knight shift calculations. Consequently, it is possible that the two values of J~f may not agree, although for GdAl~ there is reasonable agreement between tile two determinations. In contrast to the observations of most workers using pure compounds, Coles et al. (1970) have recently reported positive Ag values, and hence positive Js~ in gadolinium-doped LaAle. Other confirmatory evidence of the relative magnitudes of Jsf for the various compounds comes from the spin-disorder resistivity of the pure materials and from the depression of the superconducting transition temperature of materials such as LaA12 by the addition of the ' magnetic ' rare-earth elements. These two parameters are given by P~pin = (3~Nm/2hq2EF)F2(g- 1)2']( J + 1), (30 a) ATo = AnN(EF)F2Z ~ F(2/cfl R~ - R~. I) (3o b) ] h ~ R, (de Gennes and Friedel 1958, de Gennes 1962, Rocher 1962). Here A is a constant, n is the impurity concentration, N(E~) the density of states at the Fermi level and N the density of rare-earth ions. The remaining terms have their usual meaning. ,qince the exchange constant appears as the square in both of these expressions, these methods give no indica- tion of the si~'n of the eondllction electron polarization. Van Daal and D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 576 K . N . R . Taylor o n Fig. 8 8C l I i I ] ~. m DyAI i 3C [ I I [ o Ioo 200 300 ----"T ('K') The resistivity-temperature relations for the BAI 2 compounds, showing dearly the spin resistivity contributions. Buschow (1969 a, b) have measured the electrical resistivity of all the compounds and their results for the compounds with the heavy metals arc shown in fig. 8. Using the values of Ps obtained from this investigation, along with the known Curie temperatures, the value of m* and F were obtained and found to be in close agreement with those of other workers. Similarly the depression of the superconducting transition temperature by the addition of rare-earth impurities (Maple 1970) indicates a variation of the exchange constant across the series which is consistent with that obtained using the other techniques. This comparison is shown in fig. 9, in which ~s~ is plotted in arbitrary units as a function of atomic number. In addition to providing evidence about the exchange constants in these materials, the results described above provide some support for the use of the R K K Y interaction in attempting to understand their behaviour. The negative value of ./s~ (and hence F), however, is incompatible with the simple R K K Y theory, since this exchange integral is necessarily always positive. This difference has been interpreted in terms of an effective exchange constant (Watson et al. 1965, 1969) arising partially from the R K K Y theory and partially from the effects of interband mixing (Anderson and Clogston 1961) of electron states near to the Fermi surface. In this mechanism, considered by Watson et al. specifically for the S-state gadolinium ion, the highly localized spin-up f states are assumed to lie well below the Fermi energy. In turn the spin-down f states are virtual D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds Fig. 9 I I I I I I I I I I ! 577 • NIVIR in (RE~ AI 2 I. EPR of G d o (RE~)~nGdAI2 • Sp1n-dlsordel" Resistivity of (RE) AI 2 O Depression of T c "in L e t . x ~RE) x AI 2 2 m O l o 9, 1 8 | x × O 1 I I I i i I i I 1 i l I La C¢ Pc Nd Pm Sm Eu Gd Tb Dy No Er Trn Yb Lu The variation of the exchange parameter Js~ with the atomic number of the rare-earth element. The results shown have been obtained from a number of different types of measurement. states above the Fermi energy, the conduction band being assumed to be unpolarized. A spin-up f electron will then have a non-zero matrix element (¢4~lafl ~bk} with an unoccupied spin-up conduction electron state just above El, and mixing of the two wave functions can occur. Here is in principle the total Hamiltonian for the crystal. Similar]y, an occupied spin-down conduction electron state can mix with the unoccupied spin-down f states above the Fermi energy. The effects of this mixing, which may be looked upon as the virtual emission of bound f electrons into the conduction band and virtual absorption of conduction electrons by the empty f states, is to lower the energies of the spin-down conduction electrons with respect to the spin-up electrons. This situation is shown in fig. 10, and its effects are opposite to the effects of the conventional Js~ exchange. The exchange parameter Sin, rep- resenting this process is proportional to the square of the number of bound 4f electrons and, as for the R K K Y interaction, leads to spin density oscil- lations but in this case the local polarization is negative. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 578 K . N . R . Taylor on The effective exchange parameter J+s is then the sum of the two con- tributions and its sign depends upon their relative strengths. In the present case of the rare-earth dialuminides, the indication is that the interband mixing contribution is dominant (de Wijn et al. 1968). How much of the apparent quenching of the rare-earth moment can be attri- buted to this negative conduction electron polarization is uncertain, but it would seem that at least in some cases there may be no need to invoke Fig. 10 h J i A simple representation of the changes in the energy levels near to the Fermi level arising from interband mixing effects. crystal field effects to explain the observed magnetization. Levy (1969, 1970) has recently pointed out the inadequacy of the simple R K K Y theory to give a quantitative understanding of basic experimental parameters of rare-earth intermetallies such as Curie temperatures and has proposed that the effects of sp i~orbi t coupling of the conduction electrons should be included in the total indirect exchange by including pair interactions of the type ~fex = - (D2(RAB)JA • JB, (31) where (I) 2 is the interaction constant, and the J ' s are the angular momenta of the ions A and B separated by RAB. The Curie temperature is then given in tile molecular field approxima- tion by To = ( 1 / 3 k ) F , 2 J ( J + 1), (32) where F , 2 is a summation over the pair interactions considered. By using up to three pair terms in the analysis, Levy was able to obtain a satisfactory fit to the experimental data. In a more recent analysis (Levy 1971) of the observed depression of the superconducting transition temperature (Maple 1970) of LaA12 by rare-earth additions, it was again found that new pair terms were needed for accurate fitting of the experi- mental results. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetal l ic Rare-earth Compounds 579 In addition to the determination of Js~, the eTA1 Knight shift observa- tions may be used in conjunction with the paramagnetic susceptibility data to derive the strength of the 2~A1 hyperfine field below the Curie temperature. This is possible, since the Knight shift may be written K ( T) = K o + (gj - 1)x~( T ) H ~ J N g j f f B, (33) where Hh~( = A / ~ ) is the hyperfine field per unit spin S, A is the hyper- fine interaction constant, and ~ is the nuclear gyromagnetie ratio. Using the measured values of K(T), K 0 and x(T) for ~TA1 in GdA12, Jones and Budnick (1966) obtained a value for the 2VA1 hyperfine field at 4.2°I( of - 4 6 koe, in good agreement with the result of direct measurement (Budniek et aI. 1965 Dintelmann et al. 1970, Shamir et al. 1971). In contrast to the other authors, Shamir et al. observed two ~TAl resonances at 4.2°K, with frequencies of 49.5 and 60.5 M~Z respectively. Only the low frequency line had previously been reported. The appearance of two lines was interpreted in terms of two inequivalent sites for the A ions in Fig. 11 / O .A. ATOM O ' B ATOM (a) (b) (a) The atomic positions in the MgCu 2 Laves phase structure. (b) The orienta- tion of the cobalt ions about the [111] axial direction. GdAI~, with the Gd spins aligned along the [111 ] direction. This approach was first introduced to account for the M0ssbauer effect observations in ZrFe 2 and Tml% 2 (Wertheim et al. 1964) the difference in hyperfine field strength arising because of the spatial distribution of the B atoms in the AB 2 cubic Laves phase compounds. As fig. 11 shows, these are situated on the corners of tet,radhedra who,~e vertical axes coincide with tile [111 ] direction. The electric field gradient tensor at the 13 nuclei, due t.o the lattice charges is axially symmetric and directed along a three fi~l(l axis of the B tetrahedra. When the magnetization is parallel to a [111] direction, it will form an angle 0= 0 with the electric field gradient axis D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 580 K . N . R . Tay lor on at the B a tom on the [ l l l ] axis (see fig. 11) and an angle O= 70 ° 32' a t the three o ther B sites. These inequivalent sites result in the appearance of two nuclear resonances for this magnet iza t ion direction, whereas for a magnet ica l ly easy [100] direction all the sites are equivalent with an angle of 0 = 54o44 ' between the magnet iza t ion and electric field gradient directions (Bowden 1967, Bowden, B u n b u r y and Guimaraes ]968). The quadrupole in teract ion te rm e2qQ was also measured direct ly in the work of Shamir, f rom the large oscillations which were observed in the ampl i tude of the two-pulse spin echo signal, as a funct ion of pulse spacing. The frequencies of these echo oscillations are given by Abe et al. (t966) as f = 3e2qQ(3 cos ~ 0 - 1)/(4/(21 - ! )). F r o m the observed values o f f for the two lines it is tbund t h a t e~qQ = 3 . 4 7 + 0 - 3 M~,z (see fig. 12). The hyperfine fields at the rare-ear th nuclei have been found for some of the compounds (Ofer et al. 1965, Nowik et al. 1966, Wi d e ma n n and Zinn 1967, Zinn 1971) and lie ve ry close to the free ion values. The appearance of the hyperfine field a t the 2VA1 nuclei in the ordered s ta te of these compmmds arises because of the conduct ion electron polar izat ion caused by the neighbouring rare-ear th moments , and as such 5 & o & Fig. 12 2 C = ~ s ]C 7 2~ ~)=605MC/s 2C IC i _ _ i I0 15 2O I I I 25 3O 35 The changes in the echo amplitude observed in GdA12 at both resonance fre- quencies due to increasing the interpulse spacing r. The oscillations arise from quadrupole interaction effects. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds 58t will be dependent on ( g j - 1 ) J . At present there is insufficient evidence to confirm this variation although measurements on yt t r ium substituted GdA12 have been reported as showing a linear variation of the 27A1 hyper- fine field with composition, going to zero at YAI~ (Dintelmann et al. 1970). The magnetostatic properties of the RA13 compounds have been investi- gated by Busehow and Fast (1966a) and the observed Curie temperatures and moment values are given in table A6 along with the structural details discussed earlier. In contrast to the I~A12 compounds, only NdA13 and ErAI.~ are found to be ferromagnetic. The compounds with gadolinh, m, terbium, dysprosium and holmium are antiihrronmgnetie and the re- mainder show no evidence of ordering above 4.2°z. The understaH(ting of these resulf, s is eompliea.t.ed bv the ehtmges i1~ crvst.al st.rm~l m'e which (),~.ur across the series. The reduced moment in ErAI a and the absence of ordering in the structurally similar TmA13 samples were attributed to crystal field effects. In the latter case it was assumed further that any exchange interaction which exists is too weak to establish a cooperative effect for the singlet ground-state ions. The low transition temperatures of all the compounds suggest that the exchange interactions are always weak and probably smaller than the electrostatic interactions with the lattice. The only complete eMeulations of the crystal field effects to date have been for TmA13 (de Wijn et al. 1970), whieh erystMlizes in the cubic CuaAu structure. The contribution of the exchange to the final splitting was determined by introducing the exchange field 2'E~ as a perturbation on the crystal field solutions. Using the moieeuiar field approximation ~ e x ~--- ~ s f [(g -- 1)/2/~B](Jz)~verag o (34) then allows Js~ to be used as a fitting variable. Knight shift determinations are consistent with eqn. (25) and fig. 13 shows the observed linear dependence of K on the 4f electron susceptibility )/f in HoA13 (van Diepen et al. 1968 a). The values of . t~ derived from these mea.sm'ements are given in table 3 (van Diepen ~t al. I967, de Wijn et at. 1967). The only other compoum[ t.,oml~ositions which lnave been examim'd at all consistently are the tl, AI and RaAI.~ systems, which (,rystallize in the orthorhombie (DyA1) (van Vueht 1957, Busehow 1965) and tetragonM (ZraA12) structures (Beele and Lemaire 1967 a, b) respectively. The equiatomie materials were originaJly believed to possess the CsCi structure (Iandelli 1939, Baenziger and Moriarty 1961 a, b) but were later classified as orthorhombie, the CsC1 structure being unstable at room i~emperature. The structures of LaAI, CeA1 and PrAI are different from the rest, and have space group Cmem, while the NdA1 to TmA1 compounds have space group Pmma. The structures are closely related and consist of ehMns of aluminium atoms and trigonal prisms consisting of six rare- earth and three Muminium atoms. The prisms are similar to a half cell of the CsC1 structure as indicated in fig. 14. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 582 o -I c 5K -3 O K. N. R. Tay lor on :Fig. 13 Su~tibility 0 C53cma/mso~) i , r \ \ \ \ / \ I I I / Ioo 20O .3.OO 40O T_~p~a!ur~. (°k) The dependence of the susceptibility and Knight shi±t in HoA1 a o~ the temperature. Magnetic studies (Kissell and Wallace 1966, Barba ra et al. 1968, Becle, Lemaire and P a u t h e n e t 1968, Becle, Lemaire and Pacca rd 1970, van Diepen et al. 1968 b) indicate t ha t with the except ion of HoA1, the equi- a tomic compounds are ant i fen 'omagnet ic and t h a t m a n y of them show evidence of a metamagne t ic type of t ransi t ion at low temperatures . The magnet iza t ion curves of these compounds are shown in fig. 15. The critical field and t ransi t ion t empera tu re values for some of the compounds are given in table 4. Fig. 14 2 o / d P d ,o / • o// 0"~ ? o: b > , + o - . ~ D o + o + The crystallographic structure of the I~A1 compounds showing how it is derived from the CsC1 unit cell. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Table 4. Inter.metallic Rare-earth Compounds 583 Critical fields and Transition temperatures in the I~A1 compounds Gd Tb Dy Ho Er Tm Tc(°K) 42 72 20 7.1 13 10 Hc(koe ) 35 > 70 22 0 2/18 12 Unlike the two series of aluminium compounds discussed previously, the magnetic properties of the equiatomic materials show no systematic variation throughout the series. The transition temperatures, listed in table A4 along with other details of the crystallographic and magnetic properties, do not follow the simple predictions of tile I{KKY theory, and indeed are not any simple flmction of atomic number. •eutro!! diffraction studies (Beele et al. 1968~ 1970, Becle and Lemaire 1968, 1970) of all the compounds have heen interpreted in tee'ms ()i' the non-collinear structures shown in fig. 16. The existence and nature of these structures have been taken as evidence for anisotropie exehal~ge , - ,4 ~.~3 Pig. ! 5 i ~ I I I . - - / / / / A NdAI V HoAI • GdAI • Er AI I-1 ThAI O TmAI • DyA! ! I o wo 2o a'o 4o sb 6b magn2tic field strengt.h(kO¢) 70 The magnetization curves of the I~A1 compounds at 4"2°K, showing the critical field effects. A . P . 2 R D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 584 K. N. R. Taylor on Fig. 16 TbAI~ NdAI # # Er AI ¢ b HoAI Tm A! The non-collinear spin structures reported for the equiatomic heavy rare-earth- aluminium compounds. between the rare-earth ions, a feature which must necessarily be considered in connection with spin structures of this type and for materials of high magnetocrystalline anisotropy. The approach used for TbA1 (Becle, Lemaire and Parthe 1968) is as follows. The structure of fig. 16 contains two types of atomic site for the terbium ions, namely 1-4 (site I) and 5-8 (site II) and the moments of these ions are antiparallel to those in the next cell (1'-8') obtained using a propagation vector K = ½, 0, 0. This structure is then associated with the irreducible representation F~ of the basis vectors CaxCbxFayFb, for the two types of ion (a and b) (Bertaut 1963). D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 In termetal l ie Rare-earth Compounds 585 These basis vectors may be wri t ten in terms of the spin modulus S of the ion concerned, and the angle ¢ between the spins and the x axis. Thus Caz = S x + Sex - Sax - Sax = 4S cos Ca, - ) Cbx = Ssx - S6x + STx + Ssz = 4S cos Cb, F a y = S v + S e v + S 3 y + S 4 , = 4 S sin Ca, [ . (35) Fbu = Ssu + S6u + S7u + Ssu = 4S sin ¢~. J The magnetic energy due to the interactions between the atoms of the crystallographic cell is then expressed by means of the second-order invariants obtained from the basis vectors as W = a , C ~ ~ + a~CoJ + fi~Fbu 2 + aC~xC~, ~ + flFauFbu + 71CaxFay + ~2CbxFby + 7CazFby + ~'CbxFay. (36) Minimizing this energy with respect to ¢ then gives d W / d ¢ = ( i l l - a~) sin 2 ( ¢ - e)+ (fi2- %) sin 2 ( ¢ - ~)+ ( 8 - ~ ) sin 2¢ ÷~21 COS 2(¢--E) '~- ~/2 COS 2 ( ¢ - - E ) ~- (~2÷ ~/) cos 2 ¢ = 0 , (37) where the relations of eqn. (35) have been used in eqn. (36) and we have writ ten Ca = ¢ - E and ¢b = ¢ + ¢. Experimental ly ¢ = 56 °,. ¢ = 4 °, and this equation becomes 97(fl - ~a) + 87(f2 - a2) + 9 3 ( 8 - a) = 247~ + 5072 + 37(7 + y'). (38) In order to unders tand the meaning of these terms in brackets it is necessary to express the energy in the following equivalent form : A = ( ~ + fl)(Cax ~ + Fa~ e) + ( f ~ - ~x(F~2 - C~x e) + (~e + fe)(Cox e + F~, ~) + (fie - ~zz)(F~u ~ - Cvx e) + (~ + fi)(C~xF~u - C~Co~) + 27~C~F~u + 2CVebxFby ÷ ('F -- ~") (Caxl~W - CbyFbx) ÷ ( ' / ÷ "/ ')(Cax - CbxFay) . (39) On replacing the C's and F ' s by the linear spin combinations which they represent, we obtain the following specific terms which m a y be compared to those of eqn. (38) : (81 - ~ l ) ( f a u e - Cax e) = (f~ - ~ ) [ (Su + S2u + S3u + $4~) 2 - (Sx + Sex - S3x - S4x?], (Be - ~ ) ( F ~ , e - C~x e) = (f~ - ~ e ) [ ( S ~ + $6~ + S ~ , + $ 8 , ) e + (Ssx + S6x - STx - 88~)2], (Ssy + $6~ + $7~ + SsTj) + (Sx + $2~ - $3~ - S4x) × (Ssx + $6~ - $7~ - Ssx)], 2ylCaxFay = 27 ' (S x + Sex - Sax - S~x ) (S u + $2 u + S3y + S4u), 272CbxFbv = - 2~,2(S~x + S6x - STx - Ssx ) (S~ u + $6 u + $7 u + Ssu), ( ' / ÷ ~ ' ) ( S a x F b y -- CbxFay) = (7 - V') [(Sx + S2x - ~qax - Six) X (S5y ~- S6y "~ S7y "4- S8y ) -[- (t-~Sx ~- S6X -- SVX -- S8X ) × (Su + Sen + Sen + $4~)]. l (40) 1 1 2R2 D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 586 K. N. R. Taylor on The first three are of the same form as those on the left-hand side of eqn. (38) and may be identified with the sum of the isotropic Heisenberg exchange, and one and two-ion uniaxial anisotropy. The last three terms, i.e. the right-hand side of eqn. (38), may, in a similar way, be associated with an anisotropic DziMoshinskii interaction. The observed equilibrium structure is the result of a compromise between the Heisenberg and Dzialoshinskii interactions and in consequence implies the importance of anisotropic exchange in these materials. The origin of this anisotropy presumably stems from the low crystal symmetry of these materials and the interaction of the crystal field with the con- duction band. The wide variations in the transition temperatures across the series are also taken as an indication of this anisotropic exchange. In contrast, van Diepen et al. (1968 a, b) have discussed their Knight shift and susceptibility measurements in terms of the R K K Y theory as for the RA1 a and RA]2 compounds. This gives values of approximately - 0.15 ev and - 0.39 ev for Js~ and F respectively. The variation of the paramagnetic Curie temperatures across the scrms is understandable in terms of the/of and Js~ values, the latter term varying little, as shown in table 3 where the exchange constants for the gAl~(n = 1, 2 and 3) com- pounds are given. The change in magnitude of ~¢s~ with increasing aluminium concentration is taken to be the consequence of interband mixing effects, as will be discussed later. Finally, the observations of Barbara et al. (1968 b) and Barbara, Becle, Feron, Lemaire and Pauthenet (1968) on the R3A12 compounds, which are found only with the heavy rare earths, suggest that EraA12 and Tm3A1 ~ are antiferromagnetie at all temperatures below the ordering temperatures. Over a range of temperatures near to 4"2°K, but not extending to the ordering temperature, the magnetization curves of the compounds GdaA12, Tb3AI~, DyaAl~ and Ho~AI 2 show metamagnetic transitions similar to those of the I~A1 series. Originally these were thought to show evidence of a ferro- to antiferromagnetie transition with decreasing temperature. Buschow (1969), however, has shown tha t the 'meta- magnetic ' transitions in DysA12 are associated with the onset of a high magnetocrystalline anisotropy in a ferromagnetic material (see fig. 17). Subsequently Barbara et al. (1970) have re-interpreted their observations in terms of the motion of monatomic domain walls. Little information is available for the other compounds formed with the trivalent rare earths. Mader and Wallace (1968), however, have studied compounds based on EuA12 and EuA14 in order to determine the effects of electron concentration on magnetic structure. Their results suggest tha t on increasing the electron concentration by substituting lanthanum for europium, the coupling changes from predominantly antiferromagnetic to ferromagnetic, the change in sign of the interaction taking place at 8.4 electrons per magnetic ion. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds Fig. 17 15C - ~ ' ~ ~ ~ I DY3AI 2 O'lO C . 4"2°K | 5C - CTI o X o Jo 2o j 3o 0 IOO 200 300 TRmpCrm.ur{ (°K Single crystal data for the compou[~d Dy3A121 587 r ~ o Compounds with the other two group I I I ]B elements, indium and gallium, have been relatively little studied. A variety of compound compositions are known to exist (Palenzona 1986, Iandelli and Palenzona 1968) and the stabilities of several of these have been discussed in terms of atomic dimensions, although it has been shown that other factors require considering in compounds with 1 : 2 stoichiometry (Iande]li and Palenzona 1968). Structural studies have been made of most of the series of com- pounds with indium from R3In to l~In 3 but details of the physical pro- perties are limited to the magnetic behaviour of the extreme compositions and occasional compounds at other stoichiometries. The details of these properties are given in tables As-A13 for the systems which have been investigated. The paramagnetic Curie temperatures of the t~In 3 compounds studied by Busehow, Nastepaad and Westendorp (1969 b) lie very close to the values predicted on the basis of the I~KKY theory and the effective para- magnetic moments in several cases coincide with the theoretical ionic value. At low temperatures the magnetic behaviour of the compounds with Ce, Nd, Sm, Gd, Tb, Dy, t i c and Er is at tr ibuted to antiferro- magnetic ordering. In the case of Pr In 3 the susceptibility becomes roughly constant below about 30°~ and it is suggested that the magnetic exchange is too small to give rise to a cooperative state in the crystal field split FI ground state of the Pr 8+ ion. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 588 K. N. R. Taylor on Observations have also been of GdIn, TbIn and TbGa using magneto- static (Sekizawa and Yasukochi ]964, 1966) and neutron diffraction techniques (Cable et al. 1964). The results show that the indium com- pounds are antiferromagnetic, whilst the gallium compounds are ferro- magnetic. Further, the substitution of silver for indium in GdIn causes the paramagnetic Curie temperature to increase to a maximum at about 50% Ag before decreasing to a negative value at the GdAg composition. These changes have been interpreted as conduction electron density effects on the I~KKY exchange, rather than interatomic spacing effects. 5.2. Compounds with Elements of Group I V B 5.2.1. Silicon and germanium The rare-earth elements have been shown to form compounds of basic formula RsB 4 (Holtzberg et al. 1967) and RB 2 (Perri et al. 1959, Sekizawa and Yasukochi 1966, Sekizawa 1966) with both silicon and germanium and additional compositions RsB a (Gladyshevskii and Burnashova 1965) Fig. 18 3 0 0 P E U IOC i i I ] I I Gd l"b Dy Ho Ft. Tm IS "75 ,,2, N I O The variation of the paramagnetic Curie temperature of the RsSi a compounds and the de Gennes function with atomic number. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds 589 and RB (Baenziger and Moriarty 1961, Parthe et al. 1965, Buschow and Fast 1966 b) with germanium. As may be seen from tables A16-A21, in which are listed both crystallographic and magnetic data, not all the compounds are formed with all members of the rare-earth series. The RsB t silicon compounds with Gd, Tb, Dy, Ho and Er are ferro- magnetic (Holtzberg et al. 1967) with Curie temperatures being linearly proportional to G (see fig. 18) with a negative intercept on the 0 axis ( ~ - 40°K) at G = 0. In contrast, the compounds formed with germanium are antiferromagnetie (Holtzberg et al. 1967) with a maximum N~el temperature of 40°K for DysG %. The gadolinium compound shows some evidence of a second transition temperature at approximately 50°K, although the main transition is at much lower temperatures. In the paramagnetie region both series of compounds show Curie-Weiss be- haviour, with effective moments close to the theoretical value. Sur- prisingly the paramagnetie Curie temperatures of these antiferromagnetic compounds are large and positive. In the ordered state of the silicon compounds, however, the magnetization values at 4-2°K are appreciably less than those predicted by the ionic gJ value and it appears that this may arise from high magnetoel\~-stalline anisotropy value~. Solid ~oiubility is not observed across the system Gds((J%_xSi~), suggesting that the two orthorhombic structures (Smith et al. 1966, 1967) of the terminal compounds are not identical. The introduction of Si into GdsG % results in ferromagnetism occurring at low temperatures with the antiferromagnetie phase appearing with increasing temperature, the paramagnetie Curie temperature being positive at all compositions. The nature of these transition temperatures has been associated with the presence of several inequivMent sites and hence several interatomic inter- actions in these materials, after the discussions of Lotgering (1964) and Bozorth and Gambino (1966.) The RSi~ and RG% compounds have been studied by Sekizawa and ¥asukoehi (1966) and Sekizawa (1966), and again the structures of the two classes of compounds are different in most cases (see tables A17, A21). The magnetic properties show a change from ferromagnetic to antiferro- magnetic coupling with increasing atomic number of the rare-earth element. The variation of the transition temperatures across the series deviates appreciably from that expected from the R K K ¥ theory. The change in sign of the magnetie exchange interaction has been associated with the change in the radial extent, of the 4f wave function of the rare- earth ions. I t is assumed that this change is reflected directly into the indirect exchange expression for the paramagnetie Curie temperature through the constant ofproportionaii ty C. Very few measurements, other than those discussed above, appear to have been made on these compounds. However, electrical conductivity studies of Matthias et a[. (1958) and Henry (1962) show that ScG%, YG% LaG% and LaSi 2 are superconducting. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 590 K . N . R . Taylor on The series RsGe and RGe have been investigated by Buschow and Fast (1966, 1967) who report that the compounds are antiferromagnetic, with the exception of those formed with lanthanum, which are Pauli paramagnetic and PrGe and NdGe which are ferromagnetic. The antiferromagnetic exchange interaction appears to be relatively weak in many of the RsGe 3 compounds, and field-induced transitions to ferromagnetism at 4"2°K have been reported for R = Tb, Dy, Ho and Er. Field-induced transitions are also reported for HoGe at 4"2°K, at field strengths of approximately 12 and 26 koe. The variation of the transition temperatures of these materials as a function of the atomic number of the rare-earth element has been treated both in terms of the effect of the changing 4f wave function on the I%KK¥ interaction and also in terms of the exchange interactions which are present between the different magnetic sublattices. 5.2.2. T i n Compounds having the cubic Cu3Au structure are formed between tin and the light rare-earth elements (Iandelli 1960). The reported presence of a tin-rich phase in RSn 3 compounds (Gambino et al. 1968, Harris and l~aynor ]965 a ) h a s been attributed by Shenoy et al. (1970) to the hydrolysis of the sample, leaving free tin and a rare-earth hydroxide. In confirmation of this the MOssbauer spectra of stored samples were found to show evidence for/~-tin preciptiation. The lattice spacings reported by Iandelli (1959) are given in table A22. Also in this table are listed the 800 m , 6 0 0 ~400 2 0 0 Fig. 19 Ce Sn 3 N d S n 3 o ~ - - - ' - ~ I I I I | 0 0 2 0 0 3 0 0 T~rnp~ro~ure (°K) The variation of the susceptibility of some RSn 3 compounds with temperature. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds 591 details of the paramagnetic and ordered antiferromagnetic states of these materials (Ferro and Olcese 1964, Tsuchida and Wallace 1965 and Percheron et al. 1970). The magnetization-temperature curves between 4.2°I~ and 300°K are shown in fig. 19 for some of the compounds. In the cerium compound the anomaly at 130°t< has been attributed to a Ce a+ ~>Ce a+ promotion (Tsuchida and Wallace 1965) but the absence of any change in the electric field gradient and isomer shift at the 119 Sn nuclei (Shenoy et al. 1970) have been used to favour an interpretation involving crystal field effects. Several studies of the hyperfine interaction at the 119Sn nuclei have been made using both nuclear magnetic resonance and M6ssbauer studies above and below the ordering temperatures (Barnes et al. 1965, Rao and Vijayaraghavan 1965, Borsa et al. 1967, Kanekar et al. 1968 and Shenoy et al. 1970). The Knight shift observations in the paramagnetic region (Barnes et al. 1965, Rao and Vijayaraghavan ]965 and Borsa et al. 1967) have been used along with the evaluation of the lattice sum F(2]CFI R i - Rjl ) over both R - R and R-Sn spacings to give values of the exchange constant F for all the compounds. As was found for the aluminium compounds, these are all negative, a feature which may be associated with appreciable interband mixing in these materials (Borsa et al. 1967). In their M5ssbauer studies of these materials, Shenoy et al. (1970) have found magnetic hyperfine structure in the spectra of PrSn a and NdSn a, obtained below their N6el points. The results for PrSn~ were analysed on a two-site basis. At the first site there is only a quadrupole contribution, whereas at the second, there is an additional finite hyperfine magnetic field, lying parallel to the electric field gradient. The population of these two sites appear to be in the ratio of 2 : l, an observation which is believed to arise from an antiferromagnetic ordering of the first kind in these materials. In this magnetic structure the moments in the (100) planes are coupled ferromagnetically, while the planes are antiferromagnetic, and as a result the hyperfine fields at a Sn nucleus due to its Pr neighbours exactly balance to zero for two-thirds of the Sn nuclei, but leave a finite field for the remaining one-third. The NdSn a spectra have proved more difficult to interpret. The ngSn fields in the two materials are PrSn 3: 6 7 + l k o e , NdSn a: 35koe ; and the quadrupole interaction e2qQ has values CeSn a : 2.3+0.1 mm/sec, PrSn 3 : -2.2_+0-2 mm/sec. Resistivity measurements on LaSn 3 (in addition to the lanthanum compounds having the CuaAu structure formed with lead and thallium (Gambino et al. 1968)) have shown them to be superconducting with transition temperatures of LaSh a : 6-45°K, LaPb a : 4.05°I;, LaTe a : 1.57°K. The related compound La in 3 is not superconducting above I°K. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 592 K. N. R. Taylor on These transition temperatures were thought to be related to the valence of the non-rare-earth element, essentially through the relation (Bardeen et al. ]957) T~ _~ 0~) exp [ - 1/N(E~) VJ, where 0 D is the Debye temperature, N(E~) is the density of states at the Fermi energy and V the eleetron-phonon interaction strength. Three of these lanthanum compounds, namely LaSh3, LaPb3 and Lain3, have been reported (Toxen and Gambino 1.968) as having a susceptibility behaviour, indicating the presence of either narrow bands or even localized moments, and it is suggested tha t these arise from the partial occupation of the lanthanum 4flevels. In the ease of LaSn 3, for example, the Curie constant corresponds to an effective moment of about I ~B per formula unit. The effects of impurities were considered and it was thought that they may contribute to the low temperature behaviour, but not to the susceptibility above 77°K. 5.3. Compounds with Copper, Silver and Gold The equiatomic compounds are the only ones found for all combinations of the rare-earth metals with the elements of group I B, although the RB 2 stoichiometry is found for the majority of possible pairs of elements. The structures of all the RB compounds are cubic, CsC1 type (Chao et al. 1963, 1964, Walline and Wallace 1965), with the exception of compounds between the light rare earths and copper, For these an orthorhombic, FeB, structure has been reported (Larson and Cromer 1961). Structure changes are also observed in the RB~ compounds. The gCu 2 series is predomi- nantly cubic (CeCu~ structure), the only exception being LaCu 2, which has a hexagonal A1B~ structure. With increasing atomic weight of the group I B element the cubic phase becomes less favourable and is superseded by Table 5. Existence ranges of the various structures in the RB 2 com- pounds formed with copper, silver and gold La Ce Pr Nd Sm Eu Gd Tb Dy Ho Er Tm Yb Lu l~Cu2 A C RAg2 I C ? C M C M J. RAu2 / C ? C M [ A Hexagonal A1Bz. C Cubic CeCuz. M Tetragonal MoSi~. ? Unknown. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds 593 the tetragonal, MoSi 2 structure. Table 5 shows the existence ranges ibr the RB 2 compounds. The stability of these structures has been discussed at length, along with other intermetallic phases by various authors (Iandelli and Palenzona 1968, McMasters and Gschneidner 1964 and Nevitt 1967). In general it is concluded that the observed structure types are related mainly t o the radii of the two types of atom, but that electronegativity and valence should also be taken into consideration. The phases l~Ag 3 and RAu~ have been reported with the structural data given in tables A29, A32. The change from the hexagonal PuAg 3 to the orthorhombie TiCua structure reported for the gold system is not observed with silver (Sadagopan et al. 1968, Steeb et al. 1968, Donolato and Steeb 1969) and probably arises from size effects only. The copper-rich compounds do not include the RB~ phase but instead compositions of RCu 6 (Cromer et al. 1960, Buschow et al. 1970) and RCu 5 (Dwight 1961, Wernick and Geller 1959, Haszko 1960 a and Busehow, van der Goot and Birkhan 1969) have been reported. The former are observed for the elements cerium to gadolinium and the latter for gado- linium to thulium, indicating that again geometrical considerations are of prime importance in determining the stability of these phases, The structural and magnetic data for all the compounds are given in tables A23-A32. From tables A23, A27 and A30 it can be seen that with only two exceptions (CeAg and PrAg) the equiatomic compounds are all 200 ~oo ..~ 6c~ 5O 50 IO0 Fig. 20 J J A / o j f J J J J [3 ~ _ ~ . _~_~ • --5 - - / z5 m. f " ----~Au The variation of the Curie temperatures of the RAu, RAg and RCu compound~ with (g- 1)2J(J+ 1). D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 594 K. N. I~. Taylor on antiferromagnetic, and as fig. 20 shows, the N@I temperatures are approximately proportional to the de Gennes function G. This has been taken as an indication that the magnetic exchange is probably of the g K K Y type (Walline and Wallace 1964, 1965, Pierre 1970, Pierre and Pauthenet 1965, Kissell and Wallace 1966). The paramagnetic Curie temperatures of the copper and silver com- pounds are also proportional to G and always negative (note the exceptions given above). For the gold compounds, however, there is a change in sign of 0 at HoAu, going from positive to negative with increasing atomic number (Kissell and Wallace 1966). A change in sign of this type within the R K K Y framework can only occur through the F(2kfR) term and then only by a change in the density of carriers. Since the valence of the elements concerned will not change in the region of interest we must con- elude that the observations are associated with changes in the detailed energy band structure across the series, or alternatively with a changing magnitude of the conduction electron polarization due to interband mix- ing, relative to that due to the magnetic exchange interaction atf~f = F$ . s. Little can be said about the magnitude of the ordered moment in these antiferromagnetic compounds, although Kaneko (1968) has reported a metamagnetic transition at H~pp = 22 koe, T = 4-2°K, in DyAu with an extrapolated value for the moment on the dysprosium ion of 8 tLB. This value was thought to arise from crystal field quenching, but the published magnetization curve indicates that the material is far from saturation even at H~pp = 80 koe. In the paramagnetic region the effective moments are very close to the theoretical g ~ / [ J ( J + 1)] values. The magnetic structure has been determined using neutron diffraction techniques for several of the compounds : TbCu, ErCu and TbAg (Cable et al. 1964) and DyAg (Arnold et al. 1967). This is of type (TrTr0) formed from ferromagnetic coupling within a (110} plane but with antiparallel coupling between the planes. The magnetic parameters have been used along with the results of resistivity observations (Chao 1966) to obtain values of the exchange parameter F (Pierre 1970) using the I~KKY formalism. This theory has also been adopted by de Wijn et al. (1968) to interpret Knight shift measurements. These latter workers found that the data could best be fitted with an exchange constant . / - 0.2 ev for all the compounds studied. As in many of the other materials discussed to date, the results were consistent with the presence of an appreciable amount of interband mixing. The effects of conduction electron concentration on the magnetic properties of the compounds with a CsC1 structure have been studied by Sekizawa and Yasukoehi (1964, 1966) by means of the pseudobinary systems Gd(Ag, In) Gd(Ag, Cd, In) and Gd(Cu, Ag, Au). The results~ listed in table 6, indicate that with a continuous increase in the number of conduction electrons the magnetic ordering changes from antiferro- to ferro- to antiferromagnetic, with a corresponding change in the sign of the D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Table 6. Intermetallic Rare-earth Compounds 595 The magnetic properties of the pseudobinary compounds Gd(Agl_xInx) and GdCd x 0 0.1 0.2 0.3 0.5 GdCd 0.7 0.8 0.9 1-0 TN(°K) 145 132 77 155 28 Te(°K) 40 72 122 262 116 0p(°K) --82 - 2 8 42 80 126 105 63 - 8 - 6 6 ~(ffB) 1.1 45 6.6 5.9 3.9 t%~(ffB) 8-6 8.4 7.9 8.2 8.1 8.5 8.3 8.7 8.1 p~ramagnetic Curie temperature. The extremely low vMue of the ordered moment in the ferromagnetic compositions is somewhat surprising and has not yet been accounted for. Although the overall behaviour of the ex- change interaction can be interpreted in terms of the R K K Y model with a changing conduction electron concentration (and hence k~), it is worth while noting that the compounds GdCd, ~nd GdAgo.sIn0. 5 which h~ve similar structures and k~ values have magnetic properties which are markedly different. The RCu~ compounds, which crystallize in the orthorhombie CeCu 2 structure (Storm and Benson 1963) have been reported to be antiferro- magnetic with metamagnetic transitions to the ferromagnetic state at 4-2°K in applied fields of up to 80 koe (Sherwood gt al. 1964). The mag- netization-field curves for the compounds arc shown in fig. 21. The experimental N6el temperatures vary in a somewhat random manner with increasing atomic number and no paramagnetic Curie temperatures are available. As with other noble metal compounds the paramagnetic moment is sometimes in excess of the free ion value. Fig. 21 ~" ~ / " ' G d Cu2 2 T, 4'2°K I0 20 30 40 £0 60 70 80 Field .9.rcn.Oth (KOe~ The m~gnetization curves of the I~Cu 2 compounds showing the criticM field behaviour. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 596 K . N . 1%. Taylor on Magnetic data for the RB 2 compounds with silver and gold are incom- plete, as also are the experimental results for the RB s stoichiometry. The results for l~Ag 2 and I~Au 2 are limited to the neutron diffraction studies of the terbium, dysprosium and holmium compounds carried out by Atoji (1968 a, b, 1970) and the magnetic data of Miura et al. (1971) for DyAg 2 and DyAu 2. Finally the RCus's have been investigated by Buschow van der Goot and Birkhan (1969) and observed to form in the cubic AuBe 5 structure, although for the elements Gd-Dy a second hexagonal CaCu 5 phase is also observed. The stability of these phases appears to be related to atomic size. At the larger radius ratio compounds (R = La-Sm) the stable phase is in fact an orthorhombie structure (CeCu 6 type) as mentioned earlier (Busehow et al. 1970). The ordered magnetic properties of the t~Cu 5 compounds show a continuous change from antiferromagnetism in TbCu 5 to ferromagnetism in the eornpounds with holmium, erbium and thulium (Busehow et al. 1970). 5.4. Discussion In the foregoing sections we have considered in detail the experimental observations reported for the majority of the intermetallie compounds formed between rare-earth elements and non-magnetic metals. The available information is mainly associated with the crystallographic and magnetostatie properties of the various systems, although the M6ssbauer effect is beginning to produce a large amount of information which should ultimately assist in the interpretation of other properties. The structural investigations show that, as might have been anticipated, the stable crystal structure which forms for a given stoichiometry depends primarily on the resultant electron density of the compound. Other parameters, such as the effects of ionic size, become important in deter- mining the existence ranges of the observed structures within a single family of compounds, as is found for example in the compounds with copper, silver and gold. I t would appear that, providing the ionic dimensions do not grossly violate the geometric space-filling requirements, then the electronic structure may be used as a guide in predicting the stable structure. As the majority of the structural studies have been performed at or above room temperature, and since the ordering tempera- tures of the compounds are usually low, the effects of magnetic ordering on the various structures are unknown. The magnetic behaviour is generally consistent with an indirect ex- change interaction of the R K K Y type, occurring through the polarization of the conduction electrons. The situation is somewhat complicated, however, by the possibility of interband mixing taking place through the interaction of the 4f and conduction band electrons. This also causes a conduction electron polarization which opposes that due to the Heisenberg exchange interaction. The resultant polarization may then be either positive or negative at a given ionic site. The experimental sign and D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermel, allie Rare-earth Compounds 597 magnitude of the total conduction electron polarization have been mea- sured in many systems using electron spin resonance, or nuclear magnetic resonance techniques. De Wijn et al. (] 968) have shown that in general the effective exchange integral varies with the Fermi momentum /Q in the way shown in fig. 22. The change in sign occurring in the vicinity of]Q= 1.4 ~ results from the changes in the relative magnitude of the two components of the net conduction electron polarization. The values of /Q used in this figure were derived by fitting experimental data to relations of the type given in eqns. (10), (13), (14) and (25). Many of these involve Fig. 22 I 0 - ! Nd Pt 2 Gd Cu • h~ ~.. " 4 1 • ""M;,~ . ~ Gd A~S "~'f~$~" I 1 I I I 0 .75 ~ o o 1.2s 1.so t-~s Fermi wavcv,ctor k F ( ~ - ' ) ~. Dependence of the exchange constant on the Fermi momentum for a sequence of rare-earth compounds. the evaluation of the E F(2/cfR) term for a particular lattice. This has been done by using a free-electron model and consequently does not allow for Brillouin zone effects or for the related anisotropy of the Fermi surface, which will have an important effect on the final interpretation of the experi- mental data. The general form of the behaviour is encouraging, however, and it would seem that in the near future some effort is required in band structure calculations for the simpler materials. While the nature of the magnetic interaction appears to be at least qualitatively understood in terms of the R K K Y mechanism, the role of the electrostatic crystal field interaction is not so well established. Con- siderable variation of opinion exists concerning the magnitudes of the ordered magnetic moments associated with the ions. Since the crystal field calculations are of necessity performed using various fitting parameters, D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 598 K. N. R. Taylor on the final selection of these parameters to represent the experimental data may not be unique. I f one could have a reliable guide to the likely size of the antishielding or screening effects, then the derived crystal field parameters may be used with more confidence. As men- tioned earlier, it would seem that some feedback into these problems could come from the use of the derived values of the crystal field parameters as ' exper imenta l ' data for correlation with the ionic and electronic properties of the compounds. § 6. COMrOUNDS WIT~ THE d-TRAnSITiON METALS So far in the compounds which we have discussed the rare-earth ele- ments have been situated in a metallic lattice in combination with only non-magnetic partners. As we have seen, a broad understanding of these materials has been developed using an unsophisticated indirect exchange mechanism to provide the magnetic coupling. Once compounds are formed containing moment carrying ions, such as the transition metals, manganese, iron, cobalt, etc., then we can look for the development of much more complex magnetic behaviour resulting from the multiplicity of magnetic exchange interactions which become possible. In addition, structural transitions can be anticipated due to the changing electron concentration in the d states of the transition metal ions. By far the most extensively studied of these rare-earth transition metal compounds are those formed with the 3d elements from manganese to nickel. Much of the early stimulus originated from a search for better magnetic materials, which finally proved fruitful with the RC% materials. These will be discussed in the following section along with other compounds occurring in the phase diagrams of these systems. 6.1. The 3d Meta l s Investigation of the phase diagrams of the rare earths with the 3d transition metals has shown that compounds are only formed with elements to the right of chromium in the periodic table, i.e. with manganese, iron, cobalt and nickel. In spite of many similarities of these various systems, there is only one compound stoichiometry common to them all, namely, that represented by the basic formula RB 2, where B = M n , Fe, Co or Ni. The next most common are the RB 3 and t~B17 phases which are common to iron, cobalt and nickel, but as fig. 23 indicates, the major overlap occurs in the RCo-RNi series. The crystallographic structures, listed in tables A33-A53 increase in complexity with increasing or decreasing rare-earth concentration values relative to the cubic Laves phase AB 2 compounds. Metallurgical studies have shown (Cromer and Larson ]959, Bertaut et al. 1965), however, that at least three of these structures are related through atomic substitution and plane displacement. These are the stoichiometries A2B 7 (rhombohedral and hexagonal modifications) and AB 5 ; the relation between the structures is shown in fig. 24. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Compound Mn F e C o Intermetallic Rare-earth Compounds % ¢ i ~ J 11"I" ! I ! I ilii ! I i Ill Fig. 23 £ 4" II1 i I I I ! I ! ! I ! I I O ' S ,n 2 ¢-j j , * I I I I I "' I I [ [ [ I [ I O I 599 A P'rocl)onal Composlilon 8 The observed compound stoichiometries in the R-Mn, g-Fc, R-Co and R Ni phase diagrams. Fig. 24 A schematic view of the relation between some of the rare-earth transition metal compounds. The most extensively studied of all the compositions are the RBe com- pounds, the majority of which form in the cubic (C15) Laves phase struc- ture. As mentioned in § 2, the appearance of the Laves phases depends upon size-filling considerations, and the stable Laves phase (C14, C15, or C36) which eventually forms is controlled by valence electron concentra- tion effects. As the phase diagram for the gadolininm-cobalt system suggests (fig. 25), the I~B 2 compounds almost always form peritectically, and consider- able effort has to be made to obtain single phase materials. This has A . P . 2 S D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 600 K . N . 1~. Taylor on I- 150C %\ \ J O 0 0 5O0 0 Fig. 25 o o o . o'- ill J3ss~ | 3 0 0 ~ "\'\\ ,, ¢ I II I I I I I f I I I I i I I I IO 20 30 4 0 50 6 0 70 80 1 5 0 0 1 11OOO I 1500 9o loo at. % cobalt. The gadolinium-cobalt phase diagram. accounted for much of the variation in properties reported by tile earlier workers (Vogel 1947 Wucher 1952, Wernick and Geller 1960, Haszko 1960 b, Nassau et al. 1960, Baenziger and Moriarty 1961, Kripyakevich et al. 1965, Chechernikov et al. 1965, Harris et al. 1965, 1967). Pseudobinary studies by Mansey et al. (1968b) and Christopher et al. (1969), revealed an abrupt change in the lattice spacing variation with composition in the RNi2-RC%-RF % series. The results for the erbium series are shown in fig. 26, on which can be seen the marked expansion of the lattice caused by the addition of relatively small amounts of iron to the lattice. Attempts to prepare the series RNi~-gF% (Christopher et al. 1969) proved unsuccessful, two-phase specimens occurring over much of the range. Very little information is available concerning the stability of the more complex crystallographic lattices of the other compounds, although Poldy and Taylor (1971) have recently found some evidence for the influence of the 3d electron concentration on the occurrence of the R2B 7 and gaCo compounds, as also has Buschow (1970, 1971). The structural data for all the known compounds are now well documented, and the lattice D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds 601 Fig. 26 I | I ! ~25 \ ~,~.~ 7.20 \ \ \ \ ~ | I I I "~ 7"15 .J \ -1 7-10 ! ! 1 I I ! I ! 0 ~ r~2 O ErF% Er Co~. Er Ni~ Com po~'~.ion = The variation of the lattice parameters with composition in the Er(Fe, Co)2 and Er(Co, Ni)~ pseudobinaries. Fig. 27 I© Gd Co The composition dependence of the molecular moment in tile gadolinium-cobalt compounds. The deep minimum confirms the antiparallel moment alignment in these compounds. 2S2 D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 602 K. N. R. Taylor on parameters of the iron cobalt and nickel compounds are given in tables A33-A50. The manganese systems will be dealt with later. The results of early investigations of the magnetic properties of com- pounds in the gadolinium-iron (Vickery et al. 1960, Nesbitt et al. 1959, 1962) and gadolinium-cobalt (Nesbitt et al. 1959, Hubbard et al. 1960) systems showed the presence of a deep minimum in the saturation mag- netization-composition graph between 20 and 30% gadolinium. This is shown here in fig. 27 using more recent data for these series of compounds (Lemaire 1966 a, b). The appearance of this minimum and the nature of the magnetization studies of other heavy rare-earth-cobalt or iron com- pounds (Nesbitt et al. 1961, Nassau et al. 1960 b, Hubbard and Adams 1962, Wallace and Skrabek 1964, Mansmann and Wallace 1963, Ross and Crangle 1964 a, b and Poldy and Taylor 1971) were best understood in terms of a ferrimagnetic coupling of the two types of moment in these materials. Those investigators who also examined the compounds formed with the light rare earths (Nesbitt et al. 1961, 1.962) found evidence for ferromagnetic coupling of the moments. The saturation magnetization of the nickel compounds has generally been taken as indicating the absence of any moment associated with the nickel ions (Nesbitt et al. 1962, Skrabek and Wallace 1963, Farrell and Wallace 1966, Abrahams et al. 1964, Walline and WMlaee 1964), although more recently small moments have been detected in the YNia, Y2Ni7 and ¥~Ni17 compounds (Paecard and Pauthenet 1967, Lemaire et al. 1967, 1968, LaForest et al. 1967). The detailed studies of the magnetic properties have in general been made at a fixed composition and relatively few attempts have been made to obtain detailed comparisons of one stoichiometry with another. In discussing these materials this approach will be followed initially, begin- ning with the I~B~ compounds, since they occur with a wider range of elements than any of the other compositions and because many of the more important features of the magnetic behaviour can be found with these materials. The relatively simple structure makes them attractive for theoretical s tudy and the appearance of the same structure with aluminium and with the metals of the other d transition series produces a very large number of closely related materials for systematic study. The structural and magnetic characteristics of the RB 2 compounds formed with iron, cobalt and nickel are listed in tables A42, A48, A51. The lattice spacings (see fig. 28, for example) show the lanthanide con- traction in all eases except the cerium compounds (Mansey et aI. 1968 b) which have a lattice parameter far below that expected for the trivalent ion. This has been taken as an indication that in CeF%, CeCo 2 and CeNi 2 there has been a partial or total transfer of the 4f electron to the conduction band, leaving the cerium ion with an effective valence of between 3 + and 4+ . The anomalously large spacing of GdCo 2 is associated with the expansion of the lattice on ordering, since at the measuring temperature (20°c) GdCo 2 is magnetically ordered while the other cobalt compounds are D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds 603 o < E Fig. 28 7"2 7"22 r/•e / / I I "7.12 " Ce Pr Nd $rn Gd Tb Dy Ho Er l~m Element. The lattice parameters of the l~Co 2 compounds. not. The expansion curve shown in fig. 29 (Mansey et al. 1968 a) predicts a hypothetical non-magnetic GdC% room temperature lattice spacing of 7.233 kX which is closer to the value predicted using the lanthanide contraction. Measurements on various pseudobinary series also predict this value for the hypothetical 'non-magnet ic ' GdC% spacing (Piercy 1968, Christopher et al. 1969, Harris et al. 1970), and an expansion on ordering for the 1~C% compounds with the heavy rare earths has been observed by Chatterjee and Taylor (1971). Magnetic studies of the RNi 2 compounds (Farrell and Wallace 1966) show that in the paramagnetic state the susceptibility exhibits Curie-Weiss behaviour for all materials except CeNi2, LuNi 2 and SmNi 2. The former are Pauli paramagnetic and the behaviour of CeNi~ is undoubtedly asso- ciated with the quadripositive, non-magnetic, valence state of the Ce ion. Specific heat observations have been interpreted in terms of residual amounts of Ce 3+ in a Ce 4+ matrix (Dixon et al. 1970). The non-linear variation of the inverse susceptibility with temperature is frequently observed for samarium compounds and is probably due to electron excita- tion into the first excited J = 7/2 multiplet of the ion. The temperature-independent susceptibility of YNi 2 and LuNi~, for which the 4f shell is either empty or full, suggests that there is no magnetic moment associated with the nickel ions in these compounds. This conclusion is further supported by the molecular moment of GdNi2, which is very close to the free ion gJ value and by neutron diffraction observa- tions on TbNi~ (Felcher et al. 1965). Assuming that the nickel moment is D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 604 K. N. g . Taylor on Fig. 29 7"26 Q/ / /° Q.,Q / / / / e / 7"23 I I O Room IOO 200 300 ter~pcratur ¢ Temp¢ratur¢ ( ~ ) " ~ 7-25 X O .A 7-24 The lattice parameters of GdC% as a function of temperature, showing the marked expansion on ordering. also zero in the other compounds, both Bleaney (1963, 1964) and Wallace and Skrabek (1964) attributed the difference between the observed molecular moments and the tripositive ionic 9J value to the quenching of the orbital contribution to the total rare-earth moment by the crystal field. In this work, Bleaney used the fact that the twelve nearest-neighbour nickel ions surrounding a lanthanide ion have three-fold symmetry about the cubic three-fold axis and give rise to a cubic field at the lanthanide ion in the elaculation of the splitting of the J manifold. In doing this it was assumed that only the fourth degree component of the electrostatic field need be considered and that exchange effects could justifiably be neglected from the calculation. The moments of the true ground state and a com- pound ground state in which the first excited state is mixed into the ground state were compared with the experimental data (see table 2) to show that the observed moments could be accounted for, at least quali- tatively in this simple approach. Implicit to these calculations are D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds 605 assumptions concerning the direction of easy magnetization relative to the lattice and use was made of the tables of Lea et al. (1962) to evaluate the splittings and moment values. Recent measurements on the RFe 2 compounds using the M6ssbauer effect (Bowden 1967 and see later), however, have revealed that the magnetic easy axis is given reasonably reliably by the relative signs of the B 4 and B G crystal field terms and frequently predicts axes other than the four-fold [100] axis as the easy direction. Recent crystal field calculations along both the [100] and [111] directions in the RNi~ compounds using Ba/B 6 ~_ 1/50, and treating the exchange as part of the total Hamiltonian have shown that the ob- served moments and moment variation can be accounted for quantita- tively (Primavesi and Taylor 1971) using values of the exchange field given by the Weiss molecular field theory. The variation of the Curie temperatures with the de Gennes function G, follows two straight lines, one for the heavy and one for the light rare-earth compounds, and it is normally assumed that the exchange interaction is the simple I~KK¥ mechanism. I t would seem, however, that a mecha- nism involving pair interactions such as those considered by Levy for the dialuminides (Levy 1970) should be equally applicable to these materials. The molecular moments of the compounds GdCo 2 and GdF% are found to be 4.9/~B and 3"35/z B respectively (see tables A42 and A47), suggesting that the moment configuration is ferrimagnetic and in the simplest ease of antiparallel alignment the cobalt and iron ionic moment are approximately 1.1/x B and 1.8/~B" With the other rare earths (except for CeCo2, LuCoe and the related compound YCo~) the experimental magnetization values indicate a cobalt moment of about 1-0/~B, which for the heavy rare earths is coupled antiparallel to the rare-earth moment. The compounds PrCo2, NdCo 2 and SmCo 2 appear to be ferromagnetic, however, with parallel moment alignment. This reversal in the sign of the coupling is immediately understood in terms of an antiferromagnetic coupling of the spin angular momenta of the rare-earth and transition metals, since for the heavy and light elements we have J = L + S and J = L - S respectively (see fig. 30). The assignment of exact moment values in these compounds, for which both types of ion are magnetic, is of course extremely difficult, particularly in compounds such as those in which quite extensive quenching of either moment seems to be possible. Fortunately in a few instances the moment values have been confirmed during neutron diffraction investiga- tions (Moon et al. 1965, and Oesterreicher et al. 1970) and it has been shown that the quenching of the rare-earth moment is very much less than in the nickel compounds. I f we adopt the full rare-earth moment in the RF% compounds, as seems likely since the crystal field effects should be less than those for the RCo2's, the observed molecular moment values require that the iron moment varies from 1.45 ~B in YFe 2 to 2.2/x B in DyFe~. In UFeg, which also has the C15 structure, the moment value is 0.55/xB, while the magnetic ordering temperature (172°K) of this compound is very much less than the D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 606 K. N. 1~. Taylor o n Fig. 30 I. I I I I Light Rote Transition Hcevy lqlar¢ Transition Earth Metol Eorth Metal J - L - S J , L * S Porollel Mort~nt Antil~roll¢l Moment Alignrnent Alignment A simple view of the relative spin orientations in the rare-earth-transition metal compounds. ~ C OOC g ~= 4 0 0 - p_ O- r.) 200 -- Fig. 31 / / j • / J J f i • RFe~ - ~ " • RCo2 - - - Tc~ G Or G*Const. J J J J J j - 1:. J J o o ~ I I i o 5 ~o 15 G =~g- J)2J(J" 0 The dependence of the Curie temperatures of the RC% and RF% compounds on (g - 1)2J(J+ 1). D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds 607 RF%'s (Komura et al. 1961, Lin and Ogilvie 1963, Yessik 1969) (see table A47). As fig. 31 shows, in both the iron and the cobalt compounds the Curie temperatures are reasonably consistent with the R K K Y exchange interaction, as was the case for the RNi2's. This graph of T c versus G, however, shows that for the iron compounds in the limiting case of G = 0 (YF% and LuF%) there is a positive intercept on the temperature axis, while for both YNi~ and YCo~ the Curie temperatures are zero t Since the transition metal moment is not zero in YF%, the intercept (i.e. the Curie temperature of YF%) must be representative of the transition metal exchange interaction in these compounds. The experimental value of 550°K indicates further that these interactions are greater than those between the rare-earth ions. When both types of ion carry a moment, then the Curie temperature will-be further affected by the R-B interaction. The absence of a nickel moment in these compounds and the reduced moment values associated with the cobalt and iron atoms were originally attributed (Wallace and Skrabek 1964, Skrabek and Wallace 1963, Mansmann and Wallace 1963) to electron transfer from the rare-earth ions, resulting in the filling of localized 3d states. In the nickel compounds this left neutral nickel atoms with a configuration 3d ~°, and in. the cobalt systems a configuration intermediate between 3d s and 3d 1°. Some evidence for the localized nature of the transition metal moment was based on the hyperfine field observations of Wallace and Skrabek (1964) and Wallace (1964) which showed a linear dependence of the 57Fe field on the iron ion moment obtained from magnetostatie measurements. This interpretation assumed that the core polarization contribution to the total field was the only term requiring consideration, and all neighbour effects were disregarded. More recent studies show tha t this approach is not justifiable and that the hyperfine field is approximately independent of the moment of the iron ion (Bowden 1967, Bowden, Bunbury, Guimaraes and Snyder 1968, Guimaraes 1971). Studies of various pseudobinary systems by Piercy and Taylor (1968 a) and Taylor (1969) indicate a non-linear variation of the transition metal moment with composition in systems such as (Dyl_zY~)Fe 2 and Gd(Col_xNix) 2. In both these series the moment of the transition metal ions changes appreciably over a small composition range, a fact which is hard to justify on the basis of electron transfer to localized 3d states. In attempting to account for the observed behaviour Piercy and Taylor (1968 b) proposed tha t the 3d states of the iron, eobatt and nickel atoms in these compounds form a band which gives rise to an itinerant electroll moment. A~ ,;om~ m,m~+;,,-~.~,~ of this view, Pierev~ and Taylor (1968 b) carried out a series of experiments on the system Y(Fe l ,.Co)e which was There has been some variation of opinion concerning the magnetic state of YC%, but it now seems reasonably certain that it is a low moment compound which may not order. The observed behaviour is however sensitive to magnetic impurities. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 608 K. N. R. Taylor o n Fig. 32 4"0 3"O E 2"q ~ I ' 0 ~ 0 2.o YFe= ? d ~ s 4 s s f~SS \ , I , ] , I , I , | '6 1"2 0"8 0 ' 4 0 YCo~ Compos~ion. The change in the transition metal moment in the Y(Fe, Co)~ series of pseudo- binaries, with increasing 3d electron concentration. considered to be analogous to the classic Fe-Co system studied in the original work associated with collective electron ferromagnetism. The magnetization results, shown in fig. 32, can be interpreted in terms of the gradual filling of the 3d band as cobalt is added to the system. Similar results were obtained on the same system by Abel and Craig (1968) and by Kanematsu (1968) on Zr(Fel_xCox) 2. The sudden collapse at a composi- tion of about 20% iron is similar to that found in the middle of the Gd(Col_xNix)+: series Taylor (1969) and may be attributed to the disap- pearance of the splitting of the 3d sub-bands due to the combined effects of the increase in the 3d electron concentration and the variations of the rare-earth transition-metal and transition metal-transition metal exchange D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallie Rare-earth Compounds 609 interactions, both of which will depend upon the transition metal moment value. Further supporting evidence for an itinerant transition metal moment has come from other pseudobinary investigations by Buschow et al. (1970) and Slanicka et al. (1971). In this latter work, Slanicka observed a rapid decrease in the total moment of the heavy rare-earth pseudobinary compounds formed with iron, cobalt and nickel, in the vicinity of the pure RCo 2 composition. This occurred for decreasing 3d electron concentration and was accom- panied by a sudden rise in the Curie temperature (see fig. 33). The IC m 9 7 ~ 5 b 4 Fig. 33 ~3 ~2 I 0 P i 1 0 0 0 9 0 0 f ~ 5 0 0 2006 [ 0 0 '0 HoFe HoCo HoN i 2 2 2 The changes in the molecular moment and Curie temperature in the Ho(Fe, Co)~, Ho(Co, Ni)~ pseudobinaries, showing the rapid fall in F due to the increasing transition metal moment, and the associated increase in the ordering temperature. observed changes were interpreted in terms of the development of a 3d moment associated with the detailed band structure of the compound, and with the exchange field at the rare-earth ions in the lattice. Once this moment develops the net exchange is the sum of the t{-l~, I~-B and B-B interactions, of which the I{-B or B B is dominant. With the increase in the exchange field, the Zeeman splitting of the crystal field split levels of the rare-earth ion can no longer be treated as a perturbation and the magnitude of the 4f moment becomes comparable to the free ion gJ value. The form of these proposed changes has been investigated theoretically for the erbium and holmium compounds (Taylor 1971) and it is evident that good agreement is possible using reasonable values for the crystalline and exchange field strengths. Figure 34 shows the erbium moment variation with the exchange field strength for a specific fitting of the crystal field parameters in ErNi~. Bloeh and Lemaire (1970) have recently examined the paramagnetic behaviour of the l~Co 2 compounds in terms of an exchange enhanced susceptibility using a molecular field approach and have obtained a reasonably good fit to experimental data. A simple model of the antiferromagnetie coupling of the spins of the rare-earth and transition metal ions has been given by Wallace (1968) D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 610 K . N . 1~. Taylor on g 8 E O ~'~C- ,.%°_ 4 t~-6- -9 Fig. 34 f ~on fi~ld strength The variation of (a) the ground-state moment, and (b) the position of the lower energy levels in the erbium ion, as a function of the strength of the molecular field. and follows from the known sign of the interaction between the f and d electrons, of the two types of ions, with the conduction electrons. Following the work of Peter (1961), Gossard et al. (1962), Jacearino et al (1960) and Jaccarino (1961) on the rare-earth dialuminides (see § 5.1)we know that the conduction electron polarization due to a rare-earth ion is negative with respect to the spin of the ion at the ion site in the lattice, and also negative at the neighbouring aluminium sites. Since in these Laves phase compounds the R-B and t{-R distances are comparable we can assume that the polarization is also negative at the neighbouring rare- earth sites and will give rise to a ferromagnetic rare-earth sublattice. Wallace then goes on to take the s-3d interaction as positive, as Stearns (1965) has shown it to be for other systems involving iron. Under these conditions the spins of the iron or cobalt ions, which lie at sites equivalent to the aluminium ions in RA12, will be aligned antiparallel to the rare earth spins. This situation is shown in fig. 35 from which it is evident that this coupling mechanism will lead automatically to ferromagnetism in the light rare-earth compounds and ferrimagnetism in those formed with the heavy metals. No single crystal observations have yet been reported for these com- pounds, but as mentioned earlier hyperfine field observations have allowed the magnetic easy direction of the l~F% compounds to be determined (Wertheim et al. 1964, Bowden 1967, Bowden et al. 1968a, b). This is possible, as the distribution of the iron ions about the [ l l l ] axis of the structure (see fig. 11 b) can result in there being inequivalent sites for all but D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 N~_~pin Intermetallic Rare-earth Compounds Fig. 35 Lioht Ionthanides " (J= L - S) R Fe or Co Distanc~ / \ 611 (a) N¢t Spin Heavy Lanthanid~s. (d - L + S ) R F~ or Co ~ \ Distance (b) A pictorial view of the rare-earth-transit ion metal interaction occurring by way of the conduction electrons for (a) light rare earth elements and (b) heavy rare earth elements. e H(lll) Fig. 36 H (100) (a) (b) H(110~ (c) The location of the cobalt atoms in the MgCu 2 structure relative to the [111], [ l l0] and [100] axial directions. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 612 K . N . R . Taylor on the[100] magnetization direction, as had been discussed earlier. The two spectra corresponding to these inequivalent sites were first observed by Wertheim et al. (1964) using M0ssbauer observations in which two sets of six line spectra were obtained for TmFe 2 at 4.2°K, with an intensity ratio of 1 : 3. This intensity ratio is readily predicted from a consideration of the number of atoms occupying the equivalent sites. The derived values being (see fig. 36) [111] easy, two sites with three atoms in one and one in the other, intensity ratio 3 : 1 ; [110] easy, two pairs of inequivalent sites and consequently the spectral intensity ratios 1 : 1 ; [100] easy, all sites are equivalent and only one MOssbauer spectrum is found. Subsequent observations by Nevitt et al. (1964) and Bowden et al. ( 1968) showed tha t both [ 111 ] and [ 100] directions could be observed as the easy axis, and Bowden (1967) used a simple crystal field approach to show that these easy directions were primarily controlled by crystal field effects through the relative signs of the B 4 and B 6 terms. The agreement between this simple theory and experiment are listed in table 7. The spectra of both DyF%(100 easy) and TbF% (111 easy) are shown in fig. 37. in which the two types of spectra are clearly seen. Similar effects may also be observed in nuclear magnetic resonance observations, in which two resonant frequencies are found associated with a simple isotope. As already mentioned this has been observed in GdA12 (Shamir et al. 1971) and was found by Gegenworth et al. (1966) in GdFee. The hyperfine field values at the 57Fe nucleus, obtained from these measure- ments are also listed in table 7. Table 7. Hyperfine field parameters of RFe 2 compounds (Guimaraes 1971) Compound CeF% SmFe 2 GdF% TbFe 2 DyFe2 HoF% ErF% TmFe 2 LuFe 2 YFee B4 B6 0 + 0 + + + 0 0 Theoretical easy direction Experimental easy direction Complex /-/at 78°K (koe) 156 216 238 H at 78°K (koe) second site 190 224 (111> 226 197 228 221 228 204 216~ 202~ 207 203 221 211 Values from Wertheim et al. (1964). D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds Fig. 37 ~Veloclty ~- (a) 613 Velocity (b) M6ssbauer spectra of DyFe 2 and TbFe2 at 78°I( showing the two different types of spectra. The decomposition of the total hyperfine feld at the 57Fe nucleus is a difficult task, although it has been shown that the field direction is antiparallel to that of the magnetization (Cohen and Wernick 1964, Cohen ]964, Guimaraes 1971) as it is in metallic iron (Freeman and Watson 1965). The variation of the total field with (g - 1)J departs appreciably from linearity and it is not possible to give any reasonable estimate of the contribution arising from the rare-earth sublattice. Attempts have been made in GdCo 2 and various related pseudobinary compounds to account for the observed shifts of the nuclear resonance frequency with composition in terms of the self-and neighbour contributions to the field (Taylor and Christopher 1969). These measurements suggest a contribution to the 57Co field due to the neighbouring rare-earth ions of approximately 10 koe per Bohr magneton of the rare-earth ionic moment. Hyperfine field studies at the rare-earth nucleus are more restricted and in general have been obtained using Mossbauer observations (Ofer and Nowik 1967, Atzmony et al. ]966, Ofer et al. 1965, Cohen 1964) and are D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 614 K. N. R. Taylor on listed in table 8. Guimaraes (1971) has attempted to associate the differences between the hyperfine fields at the R nuclei in the g F % compounds and in the pure metal with the contributions due to the neighbouring ions about the rare earth ion. Table 8. The hyperfine field strength at the Rare Earth nucleus in g F e 2 compounds Free Ion (koe) Metal (koe) gF%(koe) Sm Gd Tb Dy Ho Er Tm 3390 316 3139 5700 7404 7640 6705 3430 --371 3068 5768 7344 7730 6420 3220 436 3800 6530 7900 8400 7220 Increasing the transition metal concentration leads to the g B a and R2B7 compounds with cobalt and nickel and to the RFe a and R~F%a compounds with iron. In many respects the behaviour of these materials may be understood in terms of the discussion of the RB 2 materials in the previous paragraphs. The structural and magnetic characteristics of these materials are given in tables A36, A37, A43, A44, A48, A49. Both the g B a compounds and the R2B 7 compounds with the heavy metals are rhombohedral and belong to the space group R 3 m (Virkhar and gaman 1969). In turn both are related to the structure of the I~B 5 compounds formed with cobalt or nickel, which are discussed later in this section. The RB 5 structure is isotypic with CaCu 5 (Wernick and Geller 1959, Haszko 1960 a) and may be considered as an alternate succession of two different layers of atoms, the first consisting of a hexagonal array of BII atoms and the second of R and B 1 atoms in the ratio of i : 2, the R atoms being located at the centre of the hexagon formed by the BI atoms (see fig. 38). The RB 3 (and g2B7) structures are then derived by the ordered replacement of BI atoms in every second (or third) cell by R atoms. These R atoms eventually lie both above and below the hexagonal planes to satisfy geometry requirements, and the original unit cell undergoes lateral rhombohedral transitions resulting in the RCo a and 1~2Co r struc- tures respectively (see fig. 38 b, c). These transitions were described briefly earlier and the form of the translation is shown in fig. 24. Examination of the magnetic data for the cobalt compounds (Lemaire 1966 a, b) indicates that an antiparallel spin coupling still occurs between the two types of ion. The observed molecular moments in the ordered state, however, correspond to increased values of the cobalt ionic moment compared to the RC% series. In YC% the cobalt moment is approxi- mately 0.5/~B/CO ion and in GdC% it has reached a value of 1.7/~B/ion, comparable to tha t in metallic cobalt. In these compounds accurate determination of the moments associated with the two types of ion is again D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds Fig. 38 (a) TCo 5 615 B'r (b) TCo3 / / C o , , I o r a r ~ earth atom .o. cobal t atom (c) T2Co7 The relation between the RB3, R~B 7 and RB 5 crystal structures. A.P. 2T D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 616 K. N. R. Taylor on difficult, except for the case of the yt t r ium compounds and to a lesser extent the gadolinium compounds. The results generally suggest, how- ever, that the lanthanide moments are appreciably lower than their theoretical gJ values, presumably as a result of crystal field interactions. Increased moments are also observed in the nickel compounds where the measurements of Paccard and Pauthenet (1967) and Lemaire et al. (1967) show that both YNi 3 and YeNi 7 are ferromagnetic with magnetizations corresponding to nickel moments of approximately 0.05 and 0.06/xB/ ion respectively. The results for the whole series of compounds suggests Fig. 39 Composition The transition metal moments in the pseudobinary compounds in the Y(Fe, Co) and Y(Co, Ni) systems. that the transition metal moment depends upon the rare-earth partner in the compounds, as also is the ease for the cobalt materiMs. This effect is probably associated with an itinerant nickel or cobalt moment. Poldy (1971) has recently examined the pseudobinary compounds in the (¥, Fe, Co) and (Y, Co, Ni) phase diagrams and has found eonsiderable evidence for the similarity of the moment behaviour in the compounds and in the Fe-Co-Ni metal Mloys as indicated in fig. 39. The magnetic ordering temperatures of both the cobalt and nickel compounds increase with increasing transition metal concentration D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds 617 relat ive to the RB 2 compounds. At a given concentra t ion these tempera- tures can be represented by Torao r = A + aG, where A and ~ are constants and G is the de Gennes funct ion defined earlier. This relation, which is also found in the RFe 2 materials, is more applicable to the compounds formed with the heavy metals t han to those formed wi th P r and Nd. This behaviour is shown in fig. 40 for the cobalt compounds, where the in tercept on the t empera tu re axis, corresponding to A, can be seen to increase from the RCo 3 to the R2Co1~ stoichiometry, and is re la ted to 125C I00( ~J u u5CX t_ O - - O Fig. 40 - - A w =--- . ~ y - RCo2 R . C % ~ , RaCo 5 I0 15 17 (g-'D(,J*~) The variation of the Curie temperatures of the rare earth-cobMt compounds with the de Gennes function. the t ransi t ion meta l - t rans i t ion metal interaction. The s t rength of the interact ion derived in this way will not be the same as its s t rength in the compounds formed wi th the ' magnet ic ' ra re-ear th ions, since the addi- t ional molecular field caused b y the rare-ear th sublatt iee leads to an increase in the t ransi t ion meta l momen t and hence to an increase in the magni tude of the B - B exchange interact ion. The strong dependence of the s t rength of the magnet ic coupling on the t ransi t ion meta l moment , is evident f rom fig. 41, in which the Curie t empera tu re and ordered mo me n t values of the y t t r ium-nicke l compounds are shown as a funct ion of the composition. 2 T 2 D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 618 200 K. N. g . Taylor o n Fig. 41 E O g E IOO O I 0'3 0.2 O.I O YNi l YNi YNi,I Y~4i, Y, Ni,, Ni Y2Ni7 The composition dependence of the Curie temperature and nickel ionic moment in the yttrium-nickel compounds. The magnetic spin structure of the RCo 3 compounds have been investi- gated by Schweizer and Yakinthos (1970) and are found to be parallel, or antiparallel, collinear moment arrangements for the light and heavy metals respectively. The easy direction of magnetization was found to be parallel to the c axis in PrC% and ErC% and perpendicular in the re- mainder except that in NdC% and HoC% it rotates into the c axis at approximately 300°x. The magnetic moments at the two cobalt sites were determined in this work and it was found that these depend strongly on tile site of the ion and on the rare-earth partner involved in the com- pound. The B 1 site moment was observed to reach a value of approxi- mately 2.0 t% per ion in the compounds with Tb, Ho and Er, as shown in fig. 42. The compounds with iron are still incompletely investigated, as may be seen from tables A48-AS0. The results indicate (Hoffer and Salmans 1968, Buschow and van der Goot 1969 a) that again the compounds involv- ing the heavy elements are ferrimagnetic with antiparallel spin coupling. In contrast to the cobalt and nickel materials, however, increasing the D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds 619 Fig. 42 +°pr 0 ._o ,,,o ',°I'~ 0 u o,s PB I I I C o x ~ C O = TCo 3 / / / / --7/- y / r T I I 1 I I / I "l I '1 I , Z The moment variation at the two cobalt sites as a function of the rare-earth element in the RCo s compounds. concentration of iron in the compounds, i.e. in going from l~F%-RFes- R6Fe23, the Curie temperature continuously decreases, a tendency which continues to the compounds richest in iron (see R2Fe17 later) for which the Curie temperatures have decreased to approximately half those in the RF% compounds. In these materials (RFe a and R6Fe23 ) the moment associated with the iron ion is appreciably less than the value in metallic iron, although it does appear to increase with increasing iron content. Because of their potential as permanent magnet materials the RCo s compounds have been the subject of numerous investigations over the past few years, and have recently been described in detail in reviews by Becker (1970), Nesbitt (1969) and Strnat (]970). The reader is referred to these papers for a bibliography on these specific materials. These compounds were originally studied metallurgically by several workers and shown to have the hexagonal CaCu 5 structure as described earlier (see fig. 38 a). Early magnetic measurements (Nassau et al. 1960, Cherry and Wallace 1960, Nesbitt et al. 1961, 1962) showed that they were difficult to saturate, and that the moment configuration was undoubtedly the result of a ferri- magnetic coupling of the spins as in the other compositions discussed previously. I t was not until the work of Strnat et al. (1967) and Hoffer D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 620 K. N. R. Taylor on and Strnat (1966, 1967), however, that their real value as possible per- manent magnet materials was first established. Their magnetization and anisotropy measurements on single crystal YCoa specimens showed that the first hexagonal anisotropy constant had a magnitude K I = 5.5 x 107 ergs/cm a. Along with the known magnetization values, this anisotropy figure was used to give a value for the coercive force and hence the maxi- mum energy storage. The maximum ( B H ) product obtained in this way was 28.1 Maoe, indicating that this material, at least, should be the basis for high performance permanent magnets. The magnetic and structural data are listed in table A45 and the parameters relevant to the use as permanent magnets are given separately in table 9. Of all these materials, most emphasis has been placed on SmCo 5 for its device potential, largely as it has been found to give a more reliable performance when processed into a magnet. Table 9. Properties of the RCo 5 permanent magnet materials YCo 5 LaCo a CeCos PrCo 5 SmCo 5 T c(°K) 4~rMJ(o) HA(koe) K( x 102erg/cm~) (BH)ma~(MGOe) 921 840 647 885 997 10600 9090 7700 12000 9650 ~30 ~ 175 170-210 145-210 210-290 5-5 6.3 5.2-6.4 6.9-10.0 8.1-11.2 28.1 18.9 31.3 22.5 The original at tempts at fine particle magnet production from these compounds simply employed a binder to cement together the ground particles (Strnat and IIoffer 1966). In practice however, the coercivity of all the RCos's, except SmCo 5, has been found to be very sensitive to grinding conditions (Decker 1970), and passes through a large maximum with decreasing particle size (i.e. increasing grinding time). The coercivity of the samarium compound rises to a large (10 koe) value and remains approximately constant. Unfortunately, the powders (SmCo 5 included) are sensitive to atmospheric conditions and deteriorate quite rapidly in the air. The peak in Ho is accompanied by an increasing difficulty in aligning the powders and it is thought that the grinding leads to a lattice deforma- tion and subsequent lowering of the local anisotropy (Strnat et al. 1967, Buschow and Velge 1969). The early magnets made from YCo 5 gave a poor performance compared to the potential of table 9, having energy products of only 1 NGOe (Strnat and I-Ioffer 1966). Other work, by numerous industrial and research laboratories (see the references in the reviews cited earlier) led to the use of mischmetal-Co5 systems, which could be prepared with better perfor- mance values. Another of the early problems lay in the low packing fractions which could be attained in the final magnet (Velge and Buschow D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds 621 1968~ Buschow and Velge 1969). After the development of special die pressings the workers at Philips were able to achieve (BHm~x) values in excess of 20 ~GOe (Buschow et al. 1968, 1969 a, Westendorp and Buschow 1969) without the use of binders. The precipitation of SmCo 5 in a copper matrix was achieved independently by Nesbitt et al. (1968) and Tawara and Senno (1968) by producing compositions in the Sm(Co, Cu)5 system. The coercive forces in these materials reached a value of 28 700 oe. Neutron diffraction studies of the magnetic structures of some t~Co 5 compounds (Bartholin et al. 1966, Lemaire and Schweizer 1967) indicates a general antiparallel spin configuration typical of all the materials discussed so far. The magnetic easy axis of CeCo 5, TbCo5 and NdCo~ is the e axis although in the latter two the hexagonal basal plane becomes easy on decreasing the temperature. The RNi 5 compounds are all ferromagnetic (Nesbitt et al. 1962, Abrahams et al. 1964, Buschow 1968) with low transition temperatures (see table A38) compared to those of the cobalt compounds (Salmans et al. 1968) which are almost constant and close to the cobalt metal value. The nickel moment again appears to be zero in the ordered phase an d the ionic moments associated with the rare-earth ion is appreciably less than that of the free ion. This strong dependence of the Curie temperature on the transition metal moment further emphasizes the importance of the transition metal ions in establishing the behaviour of all these compounds. The R2B17 compounds are the ones richest in the transition metal component and occur for iron, cobalt and nickel (Strnat et al. 1966, Bnschow 1966a and Ostertag and Strnat 1966), the structures being isotypic with either Th2Ni17 or Th2Zn~7. Tables A39, A46 and A50 give the lattice parameters for the various compounds. As with the I{Ba and R2B 7 materials, the R2B17 structure can be derived by atomic substitution and displacement from the RCo5 phase. Magnetic studies (Strnat et al. 1966, LaForcst et al. 1967) indicate a moment structure analogous to the other materials, in which antiparallel coupling of the rare-earth and transition metal spins takes place. In the case of nickel compounds the nickel moment is finite ( = 0-29/~B in Y2 Ni17) and undoubtedly has a marked effect on the increased Curie temperatures of these compounds (see fig. 44). The cobalt moment is again close to the metallic cobalt value and the ordering temperatures are all in excess of 1100°c (except C%Co17). The iron compounds are very markedly different, however, in tha t although the iron ion moment is of order 2/XB, the Curie temperatures are relatively low, suggesting a big reduction of the transition metal contribution to the total interaction in this case. I t might be of course that the 3d moment is more localized in these materials than in those formed with cobalt or nickel and may, in consequence, reduce the net exchange interaction energy. Alternatively we may be involved with complex band-filling features which affect those interactions involving the iron ions. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 622 K . N . 1~. Taylor on The high transition temperatures in the cobalt and nickel compounds are also close to those of the pure metals. Along with the observed changes in the transition metal moment shown in fig. 39 it would appear that in these systems the magnetic behaviour is governed by interactions and electron structures which are generally similar to those of the pure metals. To the rare earth rich side of the I~B 2 composition there is a composition RuB with both cobalt and nickel, having an orthorhombie (Fe3C) structure (Cromer and Larson 1961) and a stable compound l~Ni which is also orthorhombic and isotypic with either CrB(Ce-Tb) or FeB(Y, Dy-Tm) (Walline and Wallace 1964). The existence of these materials was dis- cussed in the original papers of Vogel et al. (1917, 1942, 1947) and Nassau et al. (1960) but little attention was given to them because of the difficulties of indexing the x-ray diffraction patterns. The g a b composition occurs with both cobalt and nickel but metal- lurgical studies show no evidence for an RaFe compound. The lattice parameters derived for these materials are listed in tables A33, A40 (Buschow and Van der Goot 1969b, c Buschow ]966b, and Lemaire and Paccard 1967). The magnetic properties of the pure compounds have been studied by Feron et al. (1968, 1970) and Strydom et al. (1970). Feron and his collaborators, working with magnetic field strengths of up to 70 koe between 1.5 and 300°K, find that both types of material are antiferro- magnetic with the paramagnetic Curie temperatures and N6el points given in tables A33, A40. In many cases it is found that the antiferromagnetie coupling may be destroyed by the application of relatively small field (see fig. 43) and the magnetization-field strength observations were discussed in terms of metamagnetic transitions at the critical fields listed in table 10, along with measured molecular moment at the highest field used. These latter values were observed by Taylor and Primavesi (1971 a) using pulsed fields. The critical fields observed during these measurements were greater than those Fig. 43 6 Er Co S I= r y/.z,,,, I 'PI/ YYY l 'r J I ~ / / / / / Pr.Ni l Mog..t,. ..,d .~..9~,. CKo,) Mog..ti. f,.,d .t . . .~,. (Ko.~ The magnetization curves in the RaNi and gaCo compounds. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 T ab le 1 0. T h e m ag n et ic c h ar ac te ri st ic s o f th e R aC o a n d R sN i co m p o u n d s /~ /R io n at 1 60 k o c T (° K ) H c ( st at ic ) k o e H c ( pu ls ed ) k o e N ic ke l co m p o u n d s P r N d G d T b D y H o E r T m 8. 1 6. 7 5. 7 7- 1 3- 5 10 0 62 33 20 9 5 28 42 45 38 15 0 51 97 76 50 0 C ob al t co m p o u n d s 15 55 P r 1Y d G d T b D y H o E r T m 1. 9 1. 3 8- 1 8 6. 4 7- 6 6. 9 3. 65 7 14 I4 3 76 45 23 13 12 -- 0 /1 6 t 4 10 15 2 0 0 7 10 9 63 52 2 0 5 ~ t N da C o m ag n et iz at io n i nc re as es i n tw o s te ps . M ea su re d in s ta ti c fi el ds o f 60 k oe . b~ D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 624 K. N. R. Taylor on found by Feron et al. (1970) and were discussed in terms of anisotropy effects (Taylor and Primavesi 1971 b). Poldy and Taylor (1971) find that in the pseudobinaries Gd a (Fe, Co), Gda(Co, Ni) the critical field strength under pulsed-field conditions decreases continuously from GdaNi as cobalt is added to the base compound and then further as iron is added to GdaCo. At approximately 10~o iron in GdaCo it becomes zero and interestingly this composition also marks the limit of solid solubility in the system. Neutron diffraction studies for some of the pure compounds have been reported by Gignoux et al. (1970). The magnetic structure for EraNi is found to be non-colinear as shown in fig. 44. Fig. 44 ) . . C . ~ T r ~ e ' 2 , ' ~ - I I /LI " f ' I Y ¢ ,,y ( i 4 - • a " • The m gnetm,structure of Er~Ni. Similar properties are also found for the equiatomic rare-earth-nickel compounds (Abrahams et al. 1964, Walline and Wallace 1964, Lemaire and Paceard 1970) with high initial coercivities being reported for several of the materials. The spin structures of both HoNi and ErNi were found to be non eollinear systems (Lemaire and Paccard 1.970). The form of these results showing magnetic transitions at 4"2°K in rather low fields is reminiscent of the observations on DyaA12 discussed earlier, for which the behaviour was eventually found to arise from a mechanism involving the magnetoerystalline anisotropy. The critical fields would appear to be a measure of the domain wall pinning and hence of the anistropy and exchange energy. Zijlstra (1971) has examined the dependence of the inertia of a domain wall under the conditions of high anisotropy and low exchange and has shown tha t it will be very sensitive to the ratio of the exchange and anisotropy. In the limit of a small value of this ratio the motion of a wall will be intrinsically pinned by the aniso- tropy energy and a critical field is necessary before the bulk magnetization can be increased. To explore this behaviour further we have recently examined the com- pounds in the Dy-Co system and have found tha t the initial coercivity D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds 625 (or critical field) depends directly on the magnetic ordering temperature and therefore on the exchange. Critical fields are observed in DyaCo , Dy4Co a and DyCo 2 but not in the remainder. This is generally consistent with an increase in the exchange energy (see table 11 for Tc values, etc.) and a decrease in the dysprosium concentration (it is anticipated that a decrease in the anisotropy may also occur). Table 11. The critical fields, transition temperatures and molecular moment values in some Dy-Co compounds Compound /* (/*B at 160 koe) To(°K) Hc(koe) DyaCo Dy4Co a DyCo~ DyC% 19-2 26"8 6"9 5"4 45 63 150 450 50 35 8 0 The manganese compounds were first investigated b y Werniek and Geller (1960), Nesbitt et al. (1963) and Nassau et al. (1960 a) who reported that the RMn~ compounds occurred in the C15 Laves phase structure and were antiferromagnetic. More recently Kirehmayr and his collaborators (see, for example, Kirehmayr 1965, 1966, 1968, Kirehmayr and Lihl 1967 and Kirchmayr and Steiner 1971) have carried out a large number of investigations on both the pure compounds and on pseudobinaries formed with RF% compounds. In addition to the I~B 2 composition, compounds are also found at I~,Mn~a and l~Mn12, and in all the eases studied the magnetic behaviour has been found to be typical of ferrimagnetie or anti- ferromagnetic coupling, with a manganese moment close to 0.5/*B (de Savage et al. 1965) although neutron diffraction results (Feleher et al. 1965) suggest that the manganese moment is zero in several of the compounds. Some measurements have been made by Oesterreicher et al. (1967, 1970, 1971) on psendobinary compositions formed between the I~A12 and RF% or gCo 2 compounds. These show a structure change to the hexagonal C14 phase in the centre of the composition range and this is ascribed to Brillouin zone-filling effects. This is taken as evidence supporting the concept of electron transfer from Gd, Er or A1 to the Fe or Co atoms. The variation of the magnetic properties, using magnetostatic and neutron diffraction techniques, have been examined by these workers and the results are thought to suggest a tendency towards antiferromagnetism for certain values of the vMenee electron concentration. A limited number of electrical resistivity measurements have been made on the t~B 2 systems (Kawatra et al. 1969, 1970, Smith and Harris 1967, Luo et al. 1968). The observed results for GdCo 2 and GdNi 2 have been discussed in terms of the molecular field theories of de Gennes andFriedel (1958) and Kim (1964). D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 626 K . N . R . Taylor on Fig. 45 I I i I i 1"5- g ~-~ ~o / # g 005 g_ 2 I I I I I I 7'160 7.]65 Lattice Parameter (~,') I I I \ 7.170 The dependence of the superconducting transition temperature in CeC% as a function of the compound lattice parameter. CeCo 2 has been reported (Smith and Harris 1967) to be a superconductor with a transition temperature at 0.84°K, whilst the related CeA12 and CeNi 2 compounds were found to remain normal to 0.34 and 0.015°K, respectively. The transition temperature was found to decrease rapidly on substitution of other transition elements. This was thought to be due to an increase in the 4f character of the cerium atoms as the cobalt ions were replaced by rhodium or nickel . Luo et al. (1968) have examined the properties of specimens across the homogeneity range of CeCo 2. This showed that the transition temperature was strongly dependent on lattice parameter as shown in fig. 45. The rather unexpected appearance of superconductivity in this compound appears to be associated with the cerium atoms losing their 4f electron to the cobalt 3d band. This transition leaves both types of ion in a non-magnetic state and in addition provides a favourable electron per atom ratio for the occurrence of superconductivity (Matthias 1955). 6.2. 4d and 5d Meta l s The rare-earth metals are known to form the cubic Laves phase RB 2 compounds with the 4d metals ruthenium and rhodium and the 5d metals osmium, iridium and platinum. In the case of the series RRu 2 and ROs 2, however, the C15 structure gives way to the hexagonal C14 (MgZne) phase part way along the series of compounds. McMasters and Gschneidner (1964) have at tr ibuted this change in the stable structure to a critical value D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds 627 of the radius ratio of 1.348 for these systems, beyond which the cubic phase is observed under normal conditions, this contradicts the observation made in § 2 concerning the relative roles of the size and electron concentration factors but in conditions where both factors are approaching a limiting value then it is likely that either one could be dominant. In the RMn 2 compounds, where a similar phenomena occurs, Wernick et al. (1962) have suggested that electron transfer is taking place between the Mn and rare- earth ions, which leads to Brillouin zone filling at ErMn 2, and hence to the change o f stable structure from the cubic to the hexagonal Laves phase. Other stoichiometries have also been reported for all but the R-Os and t~-I~u systems (see, for example, the details in Pearson (1967)). There has been little investigation of their physical properties however. The magnetic properties of the RB 2 materials appear to be relatively uncomplicated, and as tables A54-A59 show, they have all been reported to be" ferromagnetic with Curie temperatures usually very much less than 100°K. Bozorth et al. (1959) found that the transition temperatures were correlated with the de Gennes function and presumably the exchange interaction occurs through the polarization of the conduction electrons. The ordered moments are normally significantly lower than the theoretical ionic gJ value (Bozorth et al. 1959, Atoji 1961) and neutron diffraction studies of Feleher and Koehler (1963) have confirmed tha t this is the result of partial crystal field quenching of the ionic moment. M6ssbauer studies (Atzmony et al. 1967 and Henberger et al. 1967) of the hyperfine field at the 193Ir nucleus show that it is approximately pro- portional to (gj - 1) J as predicted by the Kasuya-Yosida model of conduc- tion electron polarization (Kasuya 1956, ¥osida 1957). The variation is shown in fig. 46, from which it can be seen that the results extrapolate to a hyperfine field strength of -170 koe at (g j - 1 ) J = 0. This can be interpreted in terms of other contributions to the total field, which are nearly independent of the ionic moment, or to the variation of the ex- change constant P describing the exchange interaction. Atzmony et al. attempted to fit the experimental data by allowing for a change in F using the relation for the paramagnetic Curie temperature (eqn. (10)). Eliminat- ing F from eqn. (10) and eqn. (6) modified to give an expression for the conduction electron polarization of the form 97rZ P(r) = - - - E~ ' leads to the relation P(r) = constant [OJ/(J + 1)]1/2. This was considered to represent the data more satisfactorily than did the simpler relation indicating a proportionality to (g j - 1)J. and assuming constant F. As in most of the other cases, however, the agreement is not outstanding and it may be tha t the origin of the hyperfine field is very much more complex than this simple approach would suggest. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 628 K . N . R . Taylor o n 3 0 0 0 ~ 2 0 0 cD I 00 --~ o i -IO0 - 2 0 6 - - Fig, 46 /( 2 s(~4j 4 The hyperfine field as a function of (g j - - 1)J in the RI r 2 compounds. c 300C 2000 -- I 0 0 0 -- 0 R Fig. 47 u ~ - I O O O - -2000 - ~ I I - 3 0 0 O - I 2 - B - 4 0 H~ Magnetic Field in (a) I I 4 8 Ki lo-oersteds. 3000 2000 -- ,ooo I .g o --1000 ¢m I I t ~ ' ~ 1 (b) I -3°°°~2 -B -4 0 4 B ,2 H ", Mognetlc Field in Kilo-0¢rsicd5. The magnetization hysteresis loops for tile (Gd, Ce) g u 2 compounds. (~) s%, (b) 4% D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetal l ic Rare-earth Compounds 629 In studying the properties of OdRu2-CeRu 2 pseudobinaries, Matthias et al. (1958) showed that some of the compounds were both ferromagnetic and superconducting. I t was subsequently found that the LaOs2-GdOs 2 system also showed this behaviour (Bozorth et al. 1960). In the former alloys, the overlap region occurred at about 7o/0 GdRu~, a composition which was later studied by Drautman et al. (1964). I 0 c 8 E ~ 4 P - P A R A M A G N E T I C I F - F E R R O M A G N E T I C - S U P E R C O N D U C T NG P o rTs o P, S Fig. 48 /;2 F,S [ I I [ I 2 4 6 8 I0 I 14 Mole Per C~nt GdRu 2in CeRu 2 The variation of the superconducting and magnetic transition temperatures with composition in the (Gd, Ce)I~u 2 system. One of the more interesting features of these materials is the appearance of the hysteresis loops. Figure 47 shows two loops, one for an 8~o GdRu 2 and one for a 4% GdRu 2 sample. As fig. 48 indicates, the former is both ferromagnetic and superconducting while the latter is only superconduct- ing. The negative susceptibility is clearly visible both in the initial magnetization and in the first quadrant of the loops. The reversal of the sign of the susceptibility occurs at the critical field and the remanence (difference between magnetizations at A and B) is taken as one of the indications of ferromagnetism. I t was suggested that the behaviour may result from the segregation of the specimen into superconducting and ferromagnetic domains. Drautman et al. (1964) found that the electrical resistance was not zero in the superconducting region and associated this with ' incipient superconductivity ' discovered by Webber and Reynolds (1948) in t i tanium and described theoretically by Koppe (1949) in terms of unconnected superconducting domains in a normal matrix. The RPd a phase forms for all of the rare earths and lattice parameter values suggest that the R ions are present in a trivalent state (Harris and Raynor 1965 b). This has been confirmed in the case of EuPd 3 by Mossbauer measurements (Wickman et al. 1968). Magnetization measurements have recently been carried out by Gardner et al. (1971) who find that magnetic ordering occurs in only two of the compounds, namely GdPd a (TN= 7"5°K) and TbPd a (T N-- 2.0°K). The observed behaviour in D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 630 K . N . R . Taylor on SmPd~, EuPd3, NdPd 3 and PrPd 8 was ascribed to crystal field effects and the energy levels of the former compounds have been deduced. 6.3. D i s c u s s i o n As might have been anticipated, the compounds formed with the 3d transition metals have provided (and are still providing) a wide variety of magnetic behaviour which is difficult to interpret. The magnetic moment of the rare-earth ions appears to be controlled by both crystal field and exchange field interactions. The latter occur partially through the rare- earth-transition metal interaction and are consequently dependent on the transition metal moment. The moment associated with the 3d electrons is variable and in certain conditions is extremely sensitive to the detailed composition of the material. The nickel moments are generally thought to be zero, and as the magnetic transition temperatures under these conditions are smM1, the indirect exchange interaction between the rare- earth ions in these compounds is also small. The rare-earth-transition metal and transition metal-transition metal interactions are undoubtedly responsible for the high transition temperatures found in the compounds with cobalt, and of the rapid increases in ordering temperature in (R, Co, Ni) pseudobinaries. I t is not yet completely clear, however, which of these interactions involving the 3d electrons is the more important. The behaviour of the transition metal moment as a function of composi- tion can best be understood, albeit qualitatively, in terms of an itinerant electron moment associated with a 3d band. The variation of the moment is then associated with a combination of band-filling and exchange effects in conjunction with the detailed form of the s-d bands of the materials. Very little is known of the electronic structure of this type of intermetallic compound, however, and as yet much of the interpretation is speculative. While this model appears to be satisfactory for the cobalt and nickel compounds, the decrease in the ordering temperatures of the iron com- pounds with increasing iron concentration is something of an anomaly. I t is possible that there is a change in character of the moment towards the iron compounds, and the degree of localization may increase. The pattern of behaviour is so similar to that in the Fe-Co alloy system that we appear to be dealing with the same problem in each ease. t~egardless of the origin of the 3d moment, the exchange interaction between the rare-earth and transition metal ions always favours the anti- parallel alignment of the spins of the two types of ion. There is also considerable evidence that the interaction between the rare-earth ions themselves occurs through the indirect R K K Y interaction which leads to the polarization of the conduction electron cloud. The problem of determining the sign of this polarization is more difficult than was the case for the compounds with non-magnetic elements discussed in § 5, but it is reasonably certain that the competing effect of interband mixing will be present in the total polarization. In addition, the mixing effects will D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds 631 include a contribution from the 3d states. Very few systems show complete agreement with the predictions of the R K K ¥ theory and it is undoubtedly necessary to allow for exchange anisotropy and magneto- crystalline anisotropy which is of the same order as the exchange in many c a s e s . § 7. GENERAL CONCLUSIONS From the metallurgical view-point, the structures of the rare-earth intermetallic compounds appear to be only slightly more attractive and capable of interpretation than other families of materials. There is undoubtedly evidence in the published work to show that atomic size and electron concentration effects are important in controlling crystal struc- tures. Unfortunately the problem is more subtle than this and it is likely that the contributions which finally determine the stable crystal structure may be second-order terms. I t is probably in this area that the collabora- tion of metallurgists and physicists can be most valuable through an examination of the correlation of structural and electronic properties. Even with well-established correlations, however, there is frequently the added problem of deciding which came first. Although the relatively simple t~KKY mechanism has enabled a considerable amount of general quantitative interpretation of the magnetic and related properties, it is clear that this is not sufficiently sophisticated to deal with the detailed behaviour. The complex spin structures of compounds such as the RA1 series can only be understood if we allow both the crystalline and exchange fields to be comparable in magnitude, and the implication in many cases is tha t the anisotropy effects may be dominant. The appearance of critical fields in a wide range of compounds is a relatively recent feature of the magnetic behaviour and again emphasizes the competitive nature of the two interactions. Whether all these transitions are ' metamagnetic ' is not yet certain, but the observation of characteristics which can only be related to time-dependent magnetization suggests that domain phenomena associated with wall nucleation and intrinsic pinning may be responsible for some of the observations. As a general rule critical field behaviour is observed in materials which crystal- lize in a lower symmetry structure and which have relatively low transition temperatures, and it is for such systems that the intrinsic pinning of narrow domain walls was originally envisaged. There can be no doubt that in many cases the rare-earth moment is quenched as a result of crystal field effects. The extent to which this occurs, however, is very much in doubt. The observation of reduced moments appears to be associated in some cases with rather complex spin structures and in others with negative conduction electron polarization. Consequently the magnitude of the effect which is being considered in connection with the electrostatic crystal field is uncertain and fitting to experimental data may prove unsatisfactory. A,P . 2 U D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 632 K. N. 1~. Taylor o n I f we could be sure of any one of these contributions to the overall behaviour, interpretation would be considerably simplified. I t is per- fectly clear however, tha t in order to achieve a full understanding of these materials future work will have to involve single crystal measurements and every effort should be made to achieve this end. ACKNOWLEDGMENTS Finally, I should like to thank Dr. M. I. Darby for his comments on the original manuscript, and the many other people with whom I have discussed the general problem of the rare-earth intermetallic compounds. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds 633 A P P E N D I X I ~EFEREbTCES TO PHASE DIAGRAM INFORMATIO~ The accounts of phase diagram studies are scattered through the literature, and there is considerable divergence of opinion concerning the details of many of them. In the list below is given some indication of the sources of the phase diagrams, although no system appears to have been completely studied (i.e. for all the rare-earth elements). The numbers following each system indicate the references in the table which follows. In some cases these refer to only one diagram while in others the reference contains several. Unfortunately the list is far fi'om complete but it is hoped that the information will be of value to the experimentalists for speci- men preparation. R-Aluminium 3 R-Copper 7, 12, 19 R-Indium 19 R-Silver 15, I9 R-Gallium 19 R-Gold 19 R-Silicon 12, 19 R-Zinc 10, l l , 18, 20 R- Germanium 16 R-Manganese ] 7 R-Tin 19, 24 R-Iron 6, 9, 12, 23 R-Lead 19 R-Cobalt 2, 5, 8, 22 R-Magnesium 1, 14, 19, 21 R-Nickel 4, 12, 13, 19 A great deal of older information is also available in Rare Earth Alloys, by K. A. Gschneidner, van Nostrand, 1961. 1. BuRov, I. Theory p. 116. 2. BUSCHOW, 13, 11. 3. Busc~ow, 233. 4. BuscI~OW, 5. Buscttow, 19, 153. 6. BuscHow, 515. 7. BuscHow, 8. BUSCHOW, 9. BUSCttOW, 231. V., TEREKHOVA, V. F., and SA¥ITSKY, E. M., 1964, Problems of and use of Rare Earth Metals (Moscow : Izdatelstvo ' Nauka '), K. H. J., and VELCE, W. A. J. 3., 1967, J. Less-common Metals, K. H. J., and VAN V~CHT, J. H. N., 1967, Philips, Res. Rep., 22, K. H. J. , 1968, J. Less-common Metals, 16, 45. K. H. J., and VAN DER GOOT, A. S., 1969, J. Less-common Metals, K. H. J., and VAN DER GOOT, A. S., 1969, Phys. Stat. Sol., 35, K. H. J., 1970, Philips Res. Rep., 25, 227. K. H. J. , 1970, Le8 Elements des Terms Rares, I, CNRS, p. 101. K. H. J., and VAN WIERING]~N, J. S., 1970, Phys. Star. Sol., 42, 10. CrrOITTI, P., and MASON, J. T., 1967, Trans. metall. Soc. A.I.M.E., 239, 547. 11. CttlOTTI, P., MASON, J. T., and GILL, K. J., 1963, Trans. metall. Soe. A.I.M.E., 227, 910. 12. COrELAND, M., and KATO, H., 1964, Physics and Material Problems of Reactor Control Rods (Vienna : IAEA), p. 295. 13. COt?ELAND, M., KRUG, M., ARMATROUT, C. E.~ and KATO, H., 1964, BM- R1-6566 (May). 14. DRITS, M. Y., S¥IDERSKAYA, Z. A., ROKHLIN, L. L., and BAYKOV, A. A., Met. Met. and Phys. Chem. Methods of Investigations, p. 143. 15. GEBHARDT, E., EttDBERG, M. V., and LuTY, U., 1964, IMD. Special Report No. 13, A.I.M.E., p. 303. 16. GLADYSHEVSXlI, E. I., and BURNASnOVA, V. V., 1965, Inorg. Mater., 1, 1374. 2U2 D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 634 K. N. R. Taylor on 17. KII~CHMAYR, H., 1965, 5th Rare Earth Conference. 18. LOTT, B. G., and CHIOTTI, P., 1966, Acta crystallogr., 20, 733. 19. LUNDIN, C. E., 1961, The Rare Earths edited by Spedding and Daane (Wiley), p. 224. 20. MAson, J. T., and CHIOTTI P., 1968, Trans. metall. Soc. A . I .M.E . , 242, 1167. 21. MUHLPFORDT, W.: and KLEMM, W., 1969, J. Less-common Metals, 17, 127. 22. PELLEG, J., and C~LsoN, O. I~., 1965, J. Less-common Metals, 9, 281. 23. SAVITSKY, E. M., TEREKHOVA, V. F., TORCHINOVA, R. S., MARKOVA, I. A., NAUMKI~, O. P., and KOLES~ICH~N~:O, V, E., Les Elements des Terres Rares,, I, CNRS, p. 47. 24. SCHM£DT, F. A., and McMASTERS, 0. D., 1968, J. Less-common Metals, 15, 1. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallie Rare-earth Compounds 635 A P P E N D I X I I CRYSTALLOGRAPHIC AND ~/[AGNETIC DATA FOR THE COM:POU~DS Table AO. Ionic propert ies of the rare ear ths of impor tance to theb. magnet ic behaviour Van Ion t rons La a÷ 0 Ce 3+ 1 Pr a+ 2 Nd 3+ 3 Pm a+ 4 Sm a+ 5 Eua+Sm 2+ 6 GdZ+Eu 2÷ 7 Tb ~+ 8 Dy 3+ 9 He a+ 10 Er a+ 11 Tm a+ 12 Yb a ~ 13 Lua+Yb 2÷ 14 No. of Vleck 4f elee- Ground and state S L J ff g~/J(J+l) Frank (g--1)2J(J+l) gJ 1S 0 0 0 0 0 0 0 0 0 ~Fs/2 0.5 3 2.5 0-86 2.54 2.56 0.17 2.14 3H~ 1 5 4 0"8 3"58 3.62 0-80 3-20 4Io/2 1.5 6 4.5 0.73 3"62 3"68 1.84 3-28 sI~ 2 6 4 0-6 2.68 2.83 3.2 2.40 ~Hs/2 2-5 5 2-5 0-286 0.84 1.6 4-54 0-72 7F 0 3 3 0 0 0.00 3-5 0 0 sST/2 "3.5 0 3.5 2 7.94 7.94 15.75 7 7 F 6 3 3 6 1.5 9-72 9.72 10-5 9 6I-Il5/2 2'5 5 7"5 1'33 10'63 10"6 7"08 10 aI s 1 6 8 1"25 10-6 10"6 4-5 10 HlS/~ 1"5 6 7-5 1'2 9"59 9"6 2-55 9 3H 6 1 5 6 1-17 7"57 7"6 1-17 7 2F7/2 0"5 3 3'5 1'14 4"54 4'5 0-32 4 1S 0 0 0 0 0 0 0 0 0 Table A1. RaA1 All compound data listed are for materials which have been stabilized into the cubic s t ructure by carbon addition. A3B only occurring natural ly for Ce, l~r and Nd Refs. St ructure Comp'd System Type a Ce3AI Cubic CuaAu 5.007 PraA1 Cubic CuaAu 5.040 Nd3AI Cubic CuaAu 5.003 SmaA1 Cubic CuaAu 4.940 Gd3AI Cubic Cu3Au 4.891 TbaA1 Cubic CuaAu 4.864 Dy3AI Cubic Cu3Au 4.842 tIoaAl Cubic CuaAu 4.809 EraAl Cubic CuaAu 4'783 YaA1 Cubic CuaAu 4-854 b c ~e~f Table A2. ]~4A1 CeaA1 Pr2A1 Ortho NiaSi 6.729 5'248 9.759 Nd2AI Ortho Ni2Si 6.716 5.235 9.650 SmaA1 Ortho Ni2Si 6.654 5.193 9-631 Gd2AI Ortho Ni2Si 6.606 5.146 9-531 Tb2AI Ortho Ni2Si 6.592 5.113 9-440 Dy2A1 Ortho Ni2Si 6.543 5-075 9.397 H%A1 Ortho Ni2Si 6-528 5-053 9.347 ErdA1 Ortho Ni2Si 6.516 5.015 9.279 Y2A1 Ortho NieSi 6.629 5.087 9.473 (listed at end of /~ Te TN Appendix II) 1 1 1 1 1 1 1 1 1 1 GdsAI 2 Tetrag Zr3A12 8.329 TbaA12 Tetrag Zr3A12 8.255 Dy3Al 2 Tetrag ZraA12 8.170 HoaA1 a Tetrag Zr3A12 8-182 EraA12 Tetrag ZraAI a 8.123 TmaA1 a YsA12 Tetrag ZraAl~ 8.222 Table A3. R~A12 7.578 8.2 285 7.1~ 282 3, 4 7.568 9-6 125 190 3, 4 7-523 10.8 31 76 3 ,4 7.525 10.9 l0 33 3, 4 7-484 9.6 --3 9 3, 4 7.8 -- 10 3 3, 4 7.620 3 t Per rare-ear th ion. D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 636 K . N . 1~. Taylor o n Table A4. RAI Structure Comp'd System Type LaAl Ortho CeAI CeAl Ortho CeAl PrAl Ortho ErAI NdAl Ortho ErAl SINAI Ortho ErAl GdAI Ortho ErAI TbAl Ortho ErAl DyAI Or~ho ErA1 I-IoAl Ortho ErAl ErAl Ortho ErAl 5.570 5.801 i1.272 10.1 TmAl 7.7 YA1 Ortho CrB 3-884 4'385 11.522 a b c ~e~ 0 5"809 7'734 9-531 5"670 7'680 9'270 2-34 4 5-745 5"964 11"771 3"58 ]1 5"729 5'940 11"728 3"53 -- 4 5'678 5-899 11"622 5"656 5"888 11'527 8'52 85 5.621 5.834 11.370 10.1 24 5.604 5.822 11-369 11.1 17 5.621 5.801 11.339 11.3 17 28 - - 2 l~efs. (listed at end of Tc T~ Appendix II) 3 9 3, 4 20 3, 4 29 3, 4 3 42 3, 4, 5 72 3, 4, 5 20 3, 4, 5 7'1 26 3, 4, 5 13 3, 4, 5 10 3 3 LaA1 e Cubic MgCu~ 8-131 CeA12 Cubic MgCu 2 8.047 I)rAl~ Cubic MgCu 2 8.015 NdAl~ Cubic MgCu 2 7.987 SmA12 Cubic MgCu 2 7-926 EuA12 Cubic MgCu 2 8"110 GdA12 Cubic MgCu~ 7.887 TbA12 Cubic MgCu e 7.850 DyA12 Cubic MgCu 2 7.821 H e A l 2 Cubic MgCu 2 7.802 ErA12 Cubic MgCu~ 7"780 TmA12 Cubic ]VigCu~ 7.760 Table A5. RA12 3-1 61 7.88 0 7.92 180 9.82 108 9.7 68 9.56 16 6 2.5 2 6 33 6 2.5 66 6, 8 123 6 15 6 7.0 170 6, 7 8.1 114 6, 7 9.1 58 6, 8 7-86 27 6 7.6 14 6, 7 4.69 8 6 Table A6. RA1 a LaA] s H e x NiaSn 6.662 CeA1 a H e x NiaSn 6-545 PrA1 a H e x NiaSn 6.504 NdA1 a H e x NiaSn 6.472 SmA1 a I-Iex NiaSn 6'380 GdA1 a H e x NiaSn 6"320 TbA1 a I-Iex B a P b a 6-175 DyA1 a R h o m b I:[oA1 a 6'080 (gex- index) H e A l a R h o m b H e A l 3 6-052 (I-Iex- index) ErA1 a Cubic CusAu 4.215 TmA18 Cubic CuaAu 4-200 YbA1 a Cubic CuaAu 4.202 LuA1 a YA1 a t t e x - NiaSn 6.28 R h o m b B a P b a 6.194 (Hex- index) 4.609 4.609 2.63 - -46 4-604 3.74 -- 14 4.606 4.11 + 5 4.597 4-592 8.29 -- 89 21.180 10.0 - -64 35.940 10.85 --51 35.930 10.89 - -26 9.87 + 6 7.88 -- 19 4.62 -- 300 6.2 21 9 9, 13 9 ,13 9, 13 l 0 17 10, 13 21 10,13 23 10 ,13 9 10, 13 11,13 12,13 1O, 13 aLa~A:lll Or tho LanAI11 4.431 13.142 10"132 1 aCe3Alll Or tho La3All l 4.395 13.025 10-090 2.4 - -24 0.6 9 1 aPraA1 n Ortho LaaAl l l 4.446 12.949 10"005 3'52 4 12 1 a N d a A l n O r t h o La3All l 4.359 12.924 10.017 3.62 --9 1 aSmaAl l lOr tho La3All l 4.333 12.81 9.97 1 Table A7. RaAl l l (low t e m p e r a t u r e modif ica t ion) 4"58 21"138 10 D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds Table A8. R a i n S t ruc tu re Comp 'd Sys t em Type a LaaIn Cubic CuaAu 5-07 Pr3In Cubic CuaAu NdaIn Cubic Cu3Au Gd3In Cubic Cu3Au Tb3In Cubic Cu3Au DyaIn Cubic Cu3Au b c t~ef~ 0 p, 3.48 9 0.7 62 3"4 10 1.1 l l 4 8.8 196 15.6 213 10.4 113 17.5 138 9.6 31 15-5 51 La~In H e x Ni~In 5.636 Ce2In H e x Ni2In 5-562 PrzIn H e x NieIn 5.534 Nd2In H e x Ni~In 5.505 Sm2In He): NiaIn 5.450 Gd2In t t e x NiaIn 5.413 TbaIn H e x Ni2Iu 5.367 Dy~In t t e x Ni~In 5.346 t to2In H e x Ni2In 5.319 Er2In H e x Ni2In 5.297 Tm2In He× Ni2L~ 5.274 Lu2In t t e x Ni2In 5.239 Table A9. R a i n 7"065 6"911 6'893 6"868 6"785 6'756 6-707 6"677 6'662 6'641 6-621 6"569 6 3 7 Refs. (listed at end of Te TN Appendix II) 14 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15 15 15 H % I n a Hex MnsSi 8 8-939 E r s I n 3 H e x MnBSi 8 8.889 T m s I n a H e x MnsSi 8 8.856 Lus In a t t e x MnsSi 3 8'800 G d I n Cubic CsC1 3.830 T b I n Te t r ag D y I n Cubic CsC[ 3-787 L a i n 2 EuIn~ H c x CaIn~ 4.975 Y b l n 2 H e x C a i n 2 4'889 L a i n a Cubic AuCu a CeIn a Cubic AuCu s 4.688 P r I n a Cubic AuCu a 4.671 N d I n a Cubic AuCu 3 4.653 S t a i n s Cubic AuCu 3 4.627 G d I n 3 Cubic AuCu 3 4.607 T b I n z Cubic AuCu 3 4.588 D y I n a Cubic AuCu a 4.579 t t o I n a Cubic AuCu z 4.573 E r I n 3 Cubic AuCu 8 4.564 T r a i n 8 Cubic AuCu 3 4-548 Y b I n a Cubic AuCu 3 4.611 L u I n 3 Cubic AuCu 8 4.544 ¥ I n 3 Cubic AuCu 8 4-592 Table A10. R~In~ 6.595 6.558 6.533 6.486 Tab le A11. R I n 8.1 --66 Table A12. R I n 2 7.869 7.630 Table A13. R I n 3 2.70 --62 2.70 2.54 --46 3.58 - -10 3.62 --17 8.20 --85 10-05 --62 10.78 --35 10.65 --18 9-75 --10 7-6 - -6 15 15 15 15 28 17, 18 190 16 17 19 19 10 20, 21 2O 7 20 2O 45 20 36 20 23 20, 22 11 20 6 2O 2O 23 23 23 D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 638 Structure Comp'd System Type PrGa Or tho CrB GdGa Ortho CrB TbGa Or tho CrB K. N. R. Taylor o n Table A14. l:~Ga a b c /~eff 4.452 11-331 4.195 4.34] 11'02 4.066 ~efs . (listed at end of Te T~ Appendix II) 24 24 155 24 Table A15. RGae LaGa 2 H e x A1B 2 4-320 4.416 CeGa~ H e x A1B 2 4.32 4.34 PrGa~ Hex A1B 2 4.272 4.298 NdGa~ H e x AIB 2 4-27 4.27 SmGa 2 H e x A1B~ 4.238 4.187 EuGa~ H e x A1B 2 4.35 4.511 GdGaz H e x A1B 2 4-219 4.135 TbGa~ Hex A1B 2 4.209 4.095 D y G a 2 t t e x A1B 2 4.199 4.066 H o G a , H e x A1B 2 4.192 4"044 E r G a 2 H e x AIB~ 4.186 4.018 Y b G a 2 Y b G a 2 4.456 7'187 25 25 25 25 25 19 25 25 25 25 25 19 Table A16. ]%Sia GdsSi ~ Ortho SmsGe 4 7.498 14.752 7.752 8.15 349 36-2 336 Tb~Si 4 Ortho Sm~Ge4 7-413 14.625 7-699 9-31 216 32.4 225 DysSi ~ Ortho SmsGe 4 7.373 14.536 7'675 10.3 133 35.4 ]40 HosSi ~ Or tho SmsGe 4 7.338 14.449 7.625 l l . 1 69 37-2 76 ErsSi 4 Ortho SmsGe 4 7.289 14,371 7-591 9.9 20 30-6 25 26, 27 26, 27 26, 27 26, 27 26, 27 Table A17. RSi~ LaSie Te t r ag ThSi 2 4.31 13- 80 CeSi 2 Te t r ag ThSi 2 4.27 13-88 PrSi,~ Te t r ag ThSi~ 4.20 13.76 NdSi 2 Or tho aThSi 2 4.18 4-15 13-56 SmSi~ Or tho aThSi~ 4'105 4'04 13"46 EuSi 2 Tetrag ThSi 2 4.29 13"66 GdSi 2 Or tho aThSi~ 4-09 4"01 13"42 7.8 TbSie Ortho aThSi 2 4"05 3-96 13"39 9'9 DySi~ Or tho aThSi 2 4'04 3'94 13'32 10.4 HoSi 2 Ortho aThSi 2 3.99 3.94 13-30 10.4 ErSi 2 I-Iex A1B~ 3-80 4"09 9.3 TmSi~ H e x A1B 2 3.773 4-070 YbSie H e x AIB2 3.771 4.098 LuSi 2 H e x A1Be 3.745 4.050 YSi 2 Or tho aThSi~ 4.04 3.95 13'33 aThSi 2 of ten referred to as G dSi H s t ruc ture . A t h igh t e m p e r a t u r e s th i s changes to the t e t r agona l ThSi 2. 28 28 28 28 28 29 27 29 17 29 17 29 18 29 29 29 29 29 29 Table A18. RsGe 4 GdsGe 4 Or tho SmsG % 7.701 14.832 7.787 8.1 94 Tb~Ge 4 Ortho SmsGe 4 7.634 14.701 7.707 9.61 80 Dy~Ge~ Or tho SmBGe 4 7.603 14.640 7.680 10.5 43 HosGe ~ Ortho StooGe4 7.565 14.582 7-635 10.7 16 EraGe 4 Or tho SmsGe 4 7.536 ]4 '506 7.600 9-75 ]0 15 26 30 26 40 26 21 26 7 26 D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds Table A19. RaGe s S t ruc tu re Comp'd Sys tem Type a LasGe a H e x Mn~Si 3 8-930 C%Ge s t I e x MnsSi 3 8-832 t)rsGes I-Iex MnsSi a 8.818 NdsGe s I t e x MnsSi s 8'772 SmaGe a H e x MnsSi a 8-653 GdsGe a H e x MnsSi a 8.548 TbsGe a H e x MnsSi 3 8-495 DysGe a H e x Mn~Si s 8"425 HoaGe a H e x MnsSi a 8-387 ErsGe a I-Iex Mn~Si a 8.346 YbsGe s H e x Mn~Si 3 8"360 Y~Ge a H e x MnaSi 3 8'458 b c ~eff 0 p. 6"874 6"653 2"66 - -50 --26 6-686 3"80 10 6"636 3"73 20 6"471 6"437 8"42 70 6"351 9"98 93 6"327 10'47 45 6"284 l l ' 1 0 l0 6"268 9"48 35 6"421 6'373 639 Refs. (listed at end of Tc TN Appendix II) 30 4"2 30 39 30 45 30 30 48 30 85 30 40 30 10 30 31 30 3O 3O LaGe Ortbo FeB CeGe Ortho FeB :PrGe Or tho CrB NdGe Or tho CrB SmGe Or tho CrB GdGe Or tho CrB TbGe Or tho CrB DyGe Or tho CrB HoGe Ortho CrB ErGe Ortho CrB YGe Ortho CrB Table A20. RGe 8.474 4.118 6.097 Pau l i para . 8.343 4.081 6-031 2.54 N0 4.479 11-083 4-050 3'85 30 4-444 10.99 4.027 3.62 18 4.376 10-87 3.995 Not C-W 4.318 10.77 3.966 7.94 - 1 3 4-285 10.70 3.942 9.72 --5 4.256 10'65 3.921 10'63 N0 4-235 10-60 3.911 10-60 - -5 4.208 10-58 3-897 9-60 --15 4.259 10.67 3-932 31 10 31 39 31 28 31 40 31 62 3] 48 31 36 31 18 3 l 7 31 31 Table A21. l~Ge 2 LaGe 2 Te t r ag aThSi~ 4.33 14.23 CeGe 2 Te t r ag aThSi 2 4'21 14-18 t)rG% Te t r ag aThSi~ 4"253 13-940 3"6 22 NdGe2 Te t r ag aThSiu 4.224 13.904 3.7 7 StaG% Te t r ag aThSi~ 4.183 13-810 EuGe 2 Tr igonaI 4-102 4.995 GdGe2 Or tho 8.047 8.270 14.98 8.1 --54 TbG% Or~ho 8-011 8.216 14.94 9'9 - -48 DyGe 2 Ortho 7-99 8.]2 14.89 10"9 --26 HoGe 2 Or tho 7.81 7.97 14-80 10-7 -- 4 2.18 19 3.6 33 33 32 32 32 33 28 32 42 32 28 32 l l 32 LaSh a Cubic CusAu 4-774 CeSn a Cubic CuaAu 4.721 PrSn s Cubic CusAu 4.714 NdSn a Cubic CusAu 4-705 SmSn 3 Cubic CuaAu GdSn a Cubic CuaAu CeCu Or tho FeB SmCu Cubic CsC1 GdCu Cubic CsC1 TbCu Cubic CsC1 DyCu Cubic CsC1 HoCu Cubic CsC1 ErCu Cubic CsC1 TmCu Cubic CsC1 LuCu Cubic CsC1 YCu Cubic CsC1 Table A22. RSn 8 34 2.70 --62 10 35 3.42 - 8 8.6 35 3.6 --22 4.7 35 No t C-W 12 35 8.0 - 73 No t 35 ordered Table A23. RCu 7.30 4.30 6-36 37 3.528 38 3.502 8.6 - 70 140 36 3.480 9.7 - 2 2 l l 7 37 3.461 10-7 --26 64 36 3-445 10.6 -- 18 28 36 3.432 9.6 - 12 15 36 3.414 7.5 - 5 9.5 36 3.390 39 3.477 40 D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 640 K. N. R. Taylor o n Table A24. RCU 2 S t ruc tu re Comp 'd Sys t em Type a b c t~eff LaCu 2 H e x A1B~ 4'348 3.818 CeCu 2 Ortho CeCu 2 4.435 7.057 7.475 PrCu~ Or tho CeCu 2 4-400 7.024 7'435 3.51 NdCu 2 Ortho CeCu 2 4.387 7'000 7.420 3.56 SmCu 2 Ortho CeCu~ 4.360 6.925 7-375 E u C u 2 Or tho CeCu 2 4.434 7.250 7.553 7.4 GdCu~ Or tho CeCu 2 4'320 6'858 7"330 8.4 TbCu 2 Ortho CeCu~ 4.310 6.825 7.320 9.8 DyCu 2 Ortho CeCu 2 4.300 6.792 7.300 10.75 HoCu 2 Or tho CeCu~ 4.280 6-759 7.290 10.5 E rCu , Or~ho CeCu 2 4.275 6.726 7.265 9.35 TmCu~ Or~ho CeCu 2 4.266 6.695 7.247 7.49 Y b C u 2 Or~ho CeCu 2 4-286 6.894 7-382 LuCu 2 Or tho CeCu 2 4.245 6.627 7.220 YCu~ Or tho CeCu~ 4-305 6.800 7.315 0 Refs. (listed at end of Tc TN Appendix II) 41 0"8 42, 43 2'3 42, 43 1"9 42, 43 0-1 42, 43 5"8 41, 43 6"0 41 42, 43 7-4 54 42, 43 8'7 24 42, 43 9"2 9 42, 43 5'6 I 1 42, 43 4'2 42, 43 41 42 42 GdCu 5 Cubic AuBe 5 7.06 TbCu s Cubic A u B e 5 7.041 D y C u 5 Cubic A u B e 5 7.027 HoCu 5 Cubic A u B e 5 7.016 ErCu 5 Cubic A u B e 5 7-003 T m C u 5 Cubic AuBe5 6.991 Table A25. RCu 6 44 9-6 2 15 44, 45 10.9 2 6.5 7 44, 45 10.8 ~ 0 7.6 ? 44, 45 9.7 ~ 0 7-3 ? 44, 45 7.4 ~ 0 4.9 ? 44, 45 Table A26. RCu 6 CeCu~ Ortho CeCu 6 8.108 5.102 10.160 P rCu 6 Or tho CeCu6 8.101 5.081 10.140 NdCu~ Or tho CeCu 6 8.092 5.062 10.105 SmCu~ Or~ho CeCu 6 8.060 5.034 10.049 GdCu 6 Or tho CeCu 6 8,040 5.009 9.995 YCu 6 Or tho CeCu~ 8.115 5.078 10.122 46 46 46 46 46 46 L a A g Cubic CsC1 3.768 CeAg Cubic CsC1 3.739 P r A g Cubic CsC1 3.739 N d A g Cubic CsC1 3.715 SmAg Cubic CsC1 3-673 GdAg Cubic CsC1 3.648 T b A g Cubic CsC1 3.625 D y A g Cubic CsC1 3.608 t t o A g Cubic CsC1 3-592 E r A g Cubic CsCl 3-574 T m A g Cubic CsC1 3.562 L u A g Cubic CsC1 3.541 Y A g Cubic CsC1 3.617 Table A27. R A g 2.51 - -20 0.95 3.44 2 1-55 14 3.53 - -3 8.2 - -70 10.15 --36 10.45 --23 10-3 --17 9.2 --9-5 7.15 --7 50 47, 48, 49 47, 48 22 47, 48, 49 150 47, 48 49, 50 106 47, 48, 49 63 47, 48, 49 33 47, 48, 49 21 47, 48, 49 9.5 47, 48, 49 D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds Table A28. l~Ag 2 S t ruc tu re Comp 'd Sys tem Type a b c /~err LaAg 2 Or tho CeCu 2 4.825 7.287 8.196 CeAg 2 Ortho CeCu 2 4.800 7-090 8.205 PrAga Or tho CeCu~ 4.781 7-084 8.196 :NdAg 2 Ortho CeCu~ 4.772 7.027 8.153 EuAg~ Ortho CeCu~ 4.785 7.534 8-215 GdAg 2 Te t r ag MoSi 2 3.728 9.296 TbAg 2 Te t r ag MoSi 2 3.709 9.251 DyAg~ Te~rag MoSi 2 3.696 9.213 ]toAg~ Te t r ag MoSi~ 3-681 9.181 E r A g 2 Te t r ag MoSi 2 3.668 9.159 TmAge Te t r ag MoSi 2 3.652 9.140 ¥ b A g 2 Or~ho CeCu 2 4.663 7.211 8.184 L u A g 2 Tet r~g MoSi 2 3.628 9.113 8-95 7.4 9"0 Table A29. l~Ag 8 LaAg a I-Iex P u A g a 12.848 9.487 CeAg a t t e x P u A g a 12.753 9.401 l°rAg3 I-Iex P u A g 3 12.719 9-401 N d A g 3 H e x P u A g 3 12.726 9.389 SmAg 8 H e x P u A g a 12.619 9-280 GdAg a H e x PuAga 12.613 9.226 TbAg 3 I-Iex 1)uAg3 12.628 9.272 D y A g 3 I-Iex PuAga 12.644 9-270 t I o A g a t t e x P u A g 8 12.554 9.210 E r A g 8 H e x P u A g a 12.463 9.155 T m A g a I-Iex P u A g a 12'553 9.203 YAg 3 I t e x P u A g a 12"526 9'190 Table A30. l~Au ]PrAu Cubic CsC1 3.68 N d A u Cubic CsC1 3.659 SmAu Cubic CsC1 3-621 GdAu Cubic CsC1 3-601 Ortho CrB 4.522 10-826 4.734 T b A u Cubic CsC1 3.576 D y A u Cubic CsC1 3.555 t t o A u Cubic CsC1 3.541 E r A u Cubic CsC1 3.527 T m A u Cubic CsC1 3.516 L u A u Cubic CsCI 3.497 Y A u Cubic CsC1 3.559 7.92 29 9.54 23 10-22 7 10.50 0 9.42 - -4 7.32 - -5 Tab le A31. RAu~ LaAu~ Ortho CeCu 2 4.700 7.295 8.155 CeAu 2 Or tho CeCu: 4.528 7.203 8-068 :EuAu 2 Ortho CeCu 2 4.67 7.33 8.14 GdAu 2 Te t r ag MoSi 2 3.728 9.020 T b A u 2 Te t r ag MoSi~ 3.705 8.989 I ) y A u 2 Te t r ag MoSi~ 3.691 8.961 I-IoAu 2 Te t r ag MoSi 2 3'677 8"940 E r A u 2 Te t r ag MoSi 2 3-662 8.920 T m A u 2 Te t r ag MoSi 2 3.644 8.900 YbAu~ Tet r~g MoSi 2 3.630 8.891 LuAu~ Te t r ag MoSi 2 3.624 8.883 641 Refs. (listed at end of Tc TN Appendix i[) 51 51 51 51 51 52 35 51, 54 15 52, 55 5.7 53, 56 53 53 51 53 57 57 59 59 57 57 58 57 57 57 58 57 -- 31 47, 60 40 47, 60 14 47, 60, 61 10 47, 60, 62 13-19 47, 60, 62 8-19 47, 60, 62 51 51 51 53 51 53 53 53 51 51 51 D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 642 K. N. 1~. Taylor o n Table A32. R A u 3 S t ruc tu re Comp 'd Sys tem Type a b c ~e~f L a A % H e x P u A g 3 12.83 9-25 CeAu a H e x P u A g 8 12'739 9.271 P r A u a H e x P u A g a 12.671 9-230 N d A u a H e x P u A g a 12.663 9-206 GdAu 3 Ortho TiCu 3 6.191 5.092 5.003 T b A u 3 Ortho TiCu 3 D y A u z Or tho TiCu a 6.094 5.086 4.976 H o A u 3 Ortho TiCu a 6"057 5'072 4.964 E r A u a Ortho TiCu a 6.029 5'079 4.949 TmAua Ortho TiCu a 6'030 5'068 4.930 Y b A u 3 Or tho TiCu 3 5.984 5-072 4.924 YAu a Ortho TiCu a 6'096 5.084 4.968 0 Refs. (listed at end of Tc TN Appendix I[) 63 63 63 63 63 63 63 63 63 63 63 63 Table A33. RaNi LaaNi Ortbo AlaNi 7.22 10.24 6.60 ~" PraNi Or tho AlaNi 7'07 9"96 6.49 3.7 -- 24 NdaNi Ortho AlaNi 7'04 9'86 6.43 3.6 0 Sm3Ni Or tho AlaNi 6"99 9-72 6.37 GdaNi Ortho AI3Ni 6"95 9.68 6'36 8-1 60 8.1 TbaNi Ortho AlaNi 6.88 9"61 6'29 10.0 -- 5 6.7 Dy3Ni Or tho AlaNi 6"85 9.60 6.26 10-6 29 5.7 t to3Ni Or tho AlaNi 6'83 9.54 6.25 l l . 1 - -6 7-1 EraNi Or tho AlaNi 6.79 9.45 6'23 9.8 - -5 7 1 TmzNi Ortho AlaNi 6'77 9.40 6.19 7.4 0 YaNi Ortho AlaNi 6"92 9'49 6"36 Obta ined a t 160 koe (per R ion). 64 2 64, 65, 66 15 64, 65, 66 64 100 64, 65, 66 62 64, 65, 66 35 64, 65, 66 20 64, 65, 66 9 64, 65, 66 12 64, 65, 66 64 L a N i Or tho CrB CeNi Ortho CrB P r N i Ortho CrB N d N i Ortho CrB SmNi Or tho CrB GdNi Ortho CrB TbNi Or tho CrB D y N i Ortho FeB HoNi Or tho CrB E r N i Or tho CrB T m N i Or tho CrB L u N i Ortho CrB YNi Ortho FeB Table A34. R N i 3-81 10'62 4'36 3'78 10"37 4"29 3'82 10"50 4.35 3-9 23 2'3 20 3-80 10.44 4.34 3"7 24 2.7 35 3'77 10-34 4-27 0-23 45 3.76 10 33 4-24 8.1 77 7.4 73 3.75 10-26 4"22 9-7 40 7.7 50 7.043 4.164 5.451 10.7 64 8.8 48 3"7] 10.11 4.20 ]0-7 36 8.7 31 3'69 10'09 4.18 9.8 13 8.1 l 0 3-68 10'04 4"16 5.2 4 3"67 9-99 4'17 7"151 4.124 5'513 67 67 67 67 67 67 67 67 67 67 67 67 67 LaNi~ Cubic MgCuo 7.350 CeNi 2 Cubic MgCue 7.2092 P r N i 2 Cubic MgCu~ 7-2748 NdNi~ Cubic MgCu 2 7.2560 SmNie Cubic MgCu 2 7.2180 GdNi 2 Cubic MgCu 2 7.1934 T b N i 2 Cubic ~¢IgCu 2 7.1631 D y N i 2 Cubic MgCu 2 7-1490 HoNi2 Cubic MgCu~ 7.1318 ErNi~ Cubic MgCu 2 7-1175 T m N i 2 Cubic MgCu 2 7.0943 YbNi~ Cubic MgCu~ YNi 2 Cubic MgCu~ Table A35. R N i 2 3.57 4 0.86 3.74 10 1.80 16 0.25 21 7.82 78 7.1 85 9.82 35 7'8 45 10'4 23 9.2 30 10'5 12 8.4 22 9-37 l l / 1 0 6.8 21 7'28 0 3.2 14 68 68 68, 69 68, 69 68, 69 68, 69 68, 69 68, 69 68, 69 68, 69 68, 69 68 68 D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds T a b l e A36. l:¢Ni a S t r u c t u r e C o m p ' d S y s t e m t y p e a b c L a N i a l~homb P u N i 3 5-086 25.01 CeNi 3 CeNi 3 4-95 16"48 P r N i 3 R h o m b P u N i a 5.03 25.01 N d N i a R h o m b P u N i 3 5.024 24.71 SmNi 3 l~homb P u N i 3 5.003 24-59 GdNi 3 R h o m b P u N i 3 4.99 24.5 TbNia I~homb P u N i 3 4.967 24.46 DyNia R h o m b P u N i a 4.964 24.16 H o N i a I { h o m b P u N i a 4.957 24.19 E r N i a R h o m b P u N i a 4.943 24.21 T m N i a R h o m b P u N i a 4.93 24-25 Y b N i a l g h o m b P u N i a 4.913 24.27 Y N i a l g h o m b P u N i 3 4.973 24"37 ~eff 0 p, 643 I{efs. (listed at end of Tc TN Appendix II) 70 7O 1'57 20 71 1"88 27 71 0"33 85 71 6"55 116 71 6 '84 98 71 7"0 69 71 7 '84 66 71 5"77 62 71 3"86 43 71 2"0 < 20 71 0-16 33 71 T a b l e A37. ~ N i 7 La2Ni 7 H e x C%Ni 7 5.053 24.62 C%Ni 7 t I e x Ce~Ni~ 4.93 24.19 0.26 48 Pr4Ni7~ t I e x Ce2Ni 7 5.01 24.23 4.36 85 R h o m b Gd2Co 7 36-36 Nd2Ni7~ H e x C%Ni 7 5.00 24.20 4.14 87 R h o m b Gd2Co: 36.31 Gd2Ni7~ H e x C%Ni 7 4.96 24-09 12.65 118 I~homb Gd2Co 7 36.14 T b 2 N i ~ I-Iex Ce2Ni 7 4-94 24.06 10.72 101 R h o m b Gd2Co 7 36.10 D y 2 N i ~ ~Iex Ce~Ni~ 4-93 24"05 13.30 81 R h o m b Gd2Co 7 36 '08 Ho2Ni 7 R h o m b Gd2Co 7 4"92 36.04 12.57 70 Er2Ni 7 I~homb Gd2C % 4.91 35"71 12.28 67 Y2Ni7 R h o m b Gd2Co 7 4.94 36-12 0'41 58 These c o m p o u n d s a re r e p o r t e d to cons is t of t w o coex i s t ing phases . 70 72 72 72 72 72 72 72 72 72 LaNis t t e x CcNi s t I e x P r N i 5 H e x N d N i s t t e x SmNi 5 t t e x G d N i 5 H e x T b N i 5 H e x D y N i 5 t t e x H o N i s H e x E r N i ~ H e x T m N i 5 t I e x Y b N i 5 H e x L u N i 5 H e x Y N i 5 H e x T a b l e A38. l~Ni 5 CaCu 5 5.013 3.984 CaCu~ 4.875 4-01 2.7 - 9 0 0-2 CaCu 5 4.958 3.980 C~Cu 5 4.948 3.977 CaCu 5 4 .924 3-974 CaCu 5 4.899 3.973 7.9 CaCu 5 4 .894 3.966 CooCu 5 4.869 3.969 9.3 CaCu 5 4.871 3.966 10.5 CaCu 5 4-856 3.966 CaCu 5 7"9 CaCus 4"841 3"965 CaCu~ CaCu 5 4.883 3"967 0.4 2.3 9 0.7 25 30 6.1 27 7.0 27 9-1 15 8 8.1 10 12 7.7 12 60 6.7 7 73 73, 74 14 73, 74 67, 73, 74 67, 73, 74 67, 73, 74 67, 73, 74 67, 73, 74 67, 73, 74 67, 73, 74 67, 74 67, 73 67 67, 73 Sm2Ni17 H e x Gd2Nil7 I-Iex Tb2Ni17 I-Iex Dy2Ni17 t I e x Ho2Ni17 H e x Er~Ni17 H e x Tm2Ni17 H e x Y2Nilv H e x T a b l e A39. R2Ni17 Th2Ni17 8.47 8-06 4.5 Th2Nir , 8.43 8.04 8.8 Th2Ni17 8.31 8.04 8 '5 Th2Ni17 8-29 8 '03 8 '05 Th2Ni17 8.29 8.02 12'2 ThgNi17 8.28 8.01 9.1 Th2Ni17 8.25 8.01 Th2Ni17 8-30 8.04 5 186 205 178 168 162 166 152 160 75 75 75 75 75 75 75 75 D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 644 Structure Comp'd System Type LasCo Ortho F%C PraCo Ortho FeaC NdaCo Ortho F%C SmaCo Ortho FcsC GdaCo Ortho F%C TbaCo Ortho F%C DyaCo Ortho FeaC HoaCo Or tho Fe3C ErsCo Or tho F%C YaCo 0rbho F%C K. N. R. Taylor o n Table A40. R3Co a b c /~eff 7"277 10'020 6"575 7'143 9"780 6"410 7"107 9'750 6'386 7'055 9'605 6"342 7-031 9"496 6"302 6'985 9'380 6"250 6"965 9'341 6'233 6"920 9-293 6-213 6-902 9"191 6"189 7-026 9"454 6"290 Measured a t 160 koe (per R ion). 0 1'9 19 1'3 30 8'1 145 8 102 6-4 7-1 27 6'9 7 Refs. (listed at end of Tc T~ Appendix II) 76 76, 77, 66 76, 77, 66 76, 77, 66 76, 77, 66 76, 77, 66 76, 77, 66 76, 77, 66 76, 77, 66 76 GdaCo a H e x HoaCo a 1t.61 Tb4Co a I~ex HoaCo a 11'49 Dy4Co 3 H e x I~o4Co a 11.48 Ho4Co s I-Iex Ho4Co a 11.40 Er4Co a ]-Iex Ho4Co a 11.32 Y~Co a H e x Ho~Co s 11.48 Table A41. R4Co a 4-048 242 6.5 230 4"005 3-994 62 5.2 55 3-980 50 7.4 44 3'967 28 5.75 25 4-O4 0.11 13 78, 79 78 78, 79 78, 79 78, 79 78, 79 CeCo 2 Cubic MgCu z 7.146 PrCo s Cubic MgCu~ 7.291 NdCo 2 Cubic MgCu~ 7.283 SmCo~ Cubic MgCu~ 7-248 GdCo~ Cubic MgCu 2 7.242 TbCo 2 Cubic MgCu~ 7.195 DyCo~ Cubic MgCu 2 7' 175 :HoC% Cubic MgCu~ 7.159 ErCo 2 Cubic MgCu 2 7' 139 TmCo 2 Cubic MgCu 2 7.121 LuCo 2 Cubic MgCu~ 7'06 YCo 2 Cubic MgCu 2 7.216 Table A42. RCo 2 3-2 50 107 3.8 116 2.0 259 4.9 409 228 6.7 256 129 7-6 159 7.8 85 28 7.0 36 4.7 18 8O 69, 80 69, 80 69, 80 69, 80 69, 80 69, 80 69, 80 69, 80 69, 80 8O 8O Table A43. l~,Co a CeCo a R h o m b P u N i a 4-955 24.75 PrCo s R h o m b P u ~ i a 5.062 24-81 NdCo 3 R h o m b P u N i a 5.060 24.78 SmCo a ]~homb P u N i s 5-050 24-59 GdCo a R h o m b P u N i a 5"039 24.52 TbCo 3 R h o m b P u N i 3 5.011 24.38 DyCo 3 R h o m b P u N i a 4.995 24.36 HoCo s :Rhomb P u N i 3 4.981 24-29 ErC% R h o m b P u N i 3 4'972 24.18 TraCe 3 R h o m b P u N i 3 YCo 3 l~homb P u N i a 5-005 24.27 0.2 78 3.8 349 5.6 395 2-2 612 3.4 506 4.3 450 5.6 418 3.9 401 3.0 370 1-4 301 81, 82 81, 82 81, 82 82 81, 82 81, 82 81, 82 81, 82 81, 82 81, 82 81, 82 D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds 645 St ruc tu re Comp 'd Sys tem Type a La~Co 7 R h o m b Gd2Co 7 5.101 I-Iex Ce2Ni 7 Ce~Co 7 l~homb GdeCo 7 4"940 t t e x Ce2Ni 7 Pr iCe 7 R h o m b Gd~Co 7 5.060 H e x Ce2Ni 7 NdeCo 7 R h o m b Gd~Co 7 5"059 Hex Ce~Ni, Sm2Co 7 R h o m b Gd2Co v 5.041 Hex Ce~Ni v Gd2Co 7 R h o m b Gd2Co 7 5.022 H e x Ce~Ni 7 Tb~Co 7 R h o m b Gd2Co 7 5.008 Dy2Co 7 R h o m b Gd~Co 7 4.992 Ho~Co 7 R h o m b Gd2Co 7 4.977 Er~Co 7 R h o m b Gd2Co v 4.960 Lu~Co 7 Y~Co 7 l~hornb Gd~Co 7 5.002 Table A44. R2Co 7 b c ~ef~ 0 36.69 24.51 36-52 24.46 36.52 24.43 36.43 24.39 36.31 24-33 36.24 24-19 36.18 36.13 36.10 36.07 36.15 Table A45. t~Co 5 LaCe 5 Hex CaCu 5 5-105 3-966 CeCo 5 H e x CaCu 5 4.926 4-020 PrCo 5 I-Iex CaCu 5 5-024 3.988 l~dCo 5 Hex CaCu 5 5.012 3-978 SmCo 5 I-Iex CaCu 5 4.989 3-981 GdCo5 H e x CaCu 5 4.976 3.973 TbCo 5 I t e x CaCu 5 4.946 3-980 DyCo~ t t e x CaCu 5 4.933 3.983 HoCo 5 I-Icx CaCu~ 4.911 3.993 ErCo~ H e x CaCu 5 4-883 4.007 TraCe 5 Hex CaCu~ 4-863 4.017 YCo~ I-Iex CaCu 5 4.937 3.978 T~ble A46. i~2Co~7 Ce2C017 t t e x Th2Nilv 8.335 8.102 R h o m b Th2Zn17 8.335 12.153 Pr~Co17 Rhomb Th2Zn17 8.415 12.170 Nd2Co17 Rhomb Th2Znl: 8-441 12.181 Sm2C017 R h o m b Th2Zn17 8-402 12.172 Gd~Co17 R h o m b Th2Zn17 8.361 12.159 Tb2Colv l~homb Th2Zn17 8.341 12.152 Dy~Co17 R h o m b Th2Zn17 8.335 12"153 I-Iex Th2Ni17 8.335 8.102 tto2C017 H e x Th2Ni17 8.335 8.101 Er2COl7 I~ex Th2Ni17 8'301 8-100 Tm2Co17 H e x Th~Nii7 8.285 8.095 Lu~Co17 H e x Th~Ni17 8'247 8"093 Y2C017 LaFe~ Cubic MgCu 2 CeFe 2 Cubic MgCu 2 7.286 SmFe 2 Cubic MgCu 2 7.401 GdFe~ Cubic MgCu 2 7.376 TbFe 2 Cubic MgCu 2 7.341 Dyl% 2 Cubic MgCu~ 7.309 I-IoFe 2 Cubic MgCu~ 7.287 ErFe 2 Cubic MgCu 2 7.260 TmFe 2 Cubic MgCu 2 7-247 LuFe~ Cubic MgCu 2 7.217 YFo 2 Cubic MgCu 2 7"363 Refs. (listed at end of Te TN Appendix II) 6'6 490 81 123 81 574 81 609 81 713 81 2"4 775 81 5'3 717 81 647 81 6.0 670 81 644 81 453 81 7.4 639 81 7.1 840 84 5'7 737 83 9.9 912 83 9.5 910 83 6'0 1020 83 1.2 1008 83 0.57 980 83 0"70 966 83 1"1 1000 83 0-46 986 83 1.9 1020 83 6'8 977 83 26.1 1083 31.10 1171 30.5 1150 20.1 1190 14.4 1209 10.7 1180 8.3 ]152 7.7 1173 ]0.1 1186 I1.3 1182 27.8 1167 81, 85 81, 85 81, 85 81, 85 81, 85 81, 85 81, 85 81, 85 81, 85 81, 85 85 81 Table A47. I~Fe~ 2.38 235/ 878 2.5 700 2.80 785 4.72 711 5.50 635 5-50 612 4.80 590 2.52 610 2.97 610 2.91 550 68, 89 68, 89 68, 86 68, 86 68, 86 68, 86 68, 87 88, 89 87, 89 86 D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 646 Structure Comp'd System Type a SmFea Rhomb PuNia GdF% l~homb PuNi~ 5.165 TbFe 3 Rhomb PuNia 5.11 DyFca l~homb PuNic I-IoFe s l~homb PuNi a 5'110 ErF% l%homb PuNia TmF% R h e m b PuNia l~d~F%a Th6Mn2a Gd~Fe2 a Th6Mn~a Tb6F%a Th~Mnza Dy~F%~ Th6Mn~ Ho6Fe~a Th~Mn2a Er~Fe2~ Th~Mn~s Tm~Fe2a Th6Mn~a Lu~Fe2a ThyMus3 Y6F%~ Th~Mn~a K. N. 1~. Taylor o n Table A48. RFe a b c ~eff 24.71 24.42 24.53 Table A49. R6Fe2a. 15'3 220 7"0 P~efs. (listed at end of Tc TN Appendix II) 651 90, 91 1'6 728 90, 91, 93 3"6 648 90, 91, 94 4"6 600 90, 91 4'6 567 90, 91, 93 3-5 553 90, 91, 92 1'6 539 90, 91 492 90 65~ 90,91 574 90 524 90 501 90 7.2 493 90, 92 475 90 471 90 37.8 484 91 C%Felv Hcx Th2Ni17 8.490 l~homb Th~Zni~ 8.490 Pr2Fel: Hex Th~Ni17 Gd2Fe17 Hex Th2NilT Tb2F%7 Hex Th2Ni17 Dy~Fel~ Hex Th2Nil~ H%Fe~7 Hex Th~Nil~ Er2Fer~ Hex Th~Ni17 LufFed7 Hex Th2Nii7 Y2F%7 I iex Th~Ni17 NdMn 2 Cubic MgCu 2 GdMn 2 Cubic MgCu 2 7.750 TbMn~ DyMn 2 Cubic 1KgCu 2 7'602 HoMn~ Cubic MgCu~ 7.592 I-Iex MgZn2 5.368 ErMn 2 t t ex MgZn~ 5"307 T m M n 2 YMn 2 Cubic MgCu 2 7-692 Table A50. R2Fe17 8.281 12.42 Table A51. R m n 2. 4.9 -- 90 8.86 45 10.9 -- 15 8.764 8-702 10.1 --90 30.6 270 96 282 21.2 466 16.8 408 15.6 363 15 325 299 33.8 34-2 244 7.86 7.72 5.44 90, 95 90, 95 90, 95 90,95 90, 95 90 95 90, 95 97 86 98,99 40 99 98, 99 10] 98,100 101 100 101 Nd6Mn2s Cubic Th6Mn2a I2.663 Sm~Mn2a Cabic Th6Mn~ 12'572 Gd~Mn2a Cubic ThyMus3 12.519 Tb~Mn~a Dy6Mn~8 Cubic Th6Mna~ 12"358 Ho6Mn2a Cubic Th6Mn2a 12-331 Er6Mn2a Cubic Th6Mn~a 12-285 TmeMn2a Yb6Mn2a Lu~Mnea Y6Mn~3 Cubic ThGMn2a 12.457 Table A52. I~6Mn23 9-6 5.05 85 3.0 439 10.04 --90 50.2 473 45 11-47 25 51.6 443 11.83 --5 49.8 434 10.56 30 46.2 415 31.8 2-35 4.75 12-4 9-2 102 98, 102 98,102 102 98,102 102 98, 102, 102 486 98,103 102 102 D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds T a b l e A 5 3 . RMn12 S t r u c b u r e C o m p ' d S y s t e m T y p e a Ndl~lnl~ T e t r a g T h M n l ~ 8 . 6 6 0 GdMl112 T e t r a g ThMn12 8 . 6 2 4 D y M n I ~ T e t r a g ThMn12 8 . 5 7 9 H o M n 1 2 T e t r a g ThMn12 8 . 5 7 0 ErMn12 T e t r a g T h M n l ~ 8 . 5 4 0 YnMI~ T e t r a g ThMn12 8 . 5 9 5 b c t~e~ ~ 4 ' 8 1 0 4"728 17"2 - - 2 5 4 ' 7 6 3 16"3 - 3 9 8 4 ' 7 4 7 4 ' 7 4 0 13"2 - - 6 5 4"773 647 l~efs. (listed a t end of T c T N Appendix II) 101 98, 101 98, 101 101 98, 101 t 0 1 L a R u 2 C u b i c MgCu~ 7-702 C e R u 2 C u b i c MgCu~ 7 . 5 3 5 P r l ~ u 2 C u b i c M g C u 2 7 . 6 2 4 N d R u 2 C u b i c M g C u 2 7 . 6 1 4 S m g u 2 C u b i c M g C u 2 7 . 5 8 0 Gdl%u 2 C u b i c MgCu~ 7 ' 5 6 ] t e x M g Z n 2 5"271 T b R u 2 H e x M g Z n 2 5 . 2 6 3 D y R u 2 H e x M g Z n 2 5 . 2 5 5 t Io l~u~ H e x M g Z n ~ 5 -244 E r l ~ u 2 t I e x M g Z n ~ 5 . 2 2 7 T m R u 2 I t e x M g Z n 2 5 . 2 4 6 Y b l ~ u 2 H e x M g Z n e 5 .211 Y1%u~ H e x M g Z n 2 5"256 T a b l e A 5 4 . l ~ R u 2 8 -904 8 . 8 6 9 8 . 8 3 4 8 . 8 1 0 8 . 7 8 0 8"790 8 -744 8-792 0.61 38 6 .35 83 13 105 105 104, 105 105 108 104, 105 107 106 106 106 105 109 105 105 T a b l e A 5 5 . R R h e L a R h 2 C u b i c M g C u 2 7"646 C e R h 2 C u b i c M g C u 2 7 . 5 3 8 1)rl~h2 C u b i c M g C u 2 7 -575 N d l ~ h 2 C u b i c M g C u 2 7 -564 S m R h 2 G d R h ~ C u b i c M g C u 7 . 5 1 4 T b l ~ h 2 C u b i c M g C u 2 7 . 4 9 2 D y R h 2 C u b i c M g C u 2 7 .483 H o 1 ~ h 2 C u b i c MgCu~ 7 . 4 2 6 E r l ~ h e C u b i c M g C u 2 7 . 4 4 4 T m R h 2 C u b i c M g C u 2 7-417 Y b R h 2 C u b i c M g C u 2 7 . 4 3 2 L u l ~ h 2 C u b i c M g C u 2 7 -422 Y R h 2 C u b i c M g C u 2 7 459 2 .24 8 .6 1.67 ~ 6 0 .53 ~ 2 2 6 .80 75 7 .07 4 0 8-16 35 7 .74 16 7 .26 7 105 105 105, 110 105, 110 110 105, 110 106, 110 108, 110 108, 1 ] 0 108, 110 109 109 105 E u P d 2 C u b i c M g C u 2 T a b l e A 5 6 . ICPd 2 7.8 80 111 L a P d a C u b i c A u C u a 4 . 2 3 5 C e P d a C u b i c A u C u a 4 . 1 3 6 P r P d a C u b i c A u O u a 4 . 1 3 8 N d P d a C u b i c A u C u a 4 . 1 3 0 S m P d a C u b i c A u C u a 4 -105 E u P d a C u b i c A u C u a 4"095 G d P d a C u b i c A u C u a 4 -090 T b F d a C u b i c A u C u a 4 ' 0 7 7 D y P d a C u b i c A u C u s 4"068 t t o P d a C u b i c A u C u 8 4 . 0 6 4 E r P d a C u b i c A u C u a 4 . 0 5 6 T m P d a C u b i c A u C u 3 4 . 0 4 0 Y b P d a C u b i c A u C u a 4 . 0 4 0 L u P d a C u b i c A u C u a 4"022 Y P d a C u b i c A u C u 8 4 - 0 7 4 A.P. T a b l e A 5 7 . l ~ P d a 3-4 - - 7 3 ' 4 1 8-6 19 5"4 10 '1 2 5-2 108 106 112 106 112 112 7"5 113 2"0 112, 113 112 108 106 112 106 108 2 X D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 648 K. N. 1~. Taylor o n Table A58. ROs 2 S t ruc tu re Comlo'd Sys t em Type a LaOs~ Cubic MgCu 2 7.737 CeOs 2 Cubic MgCu 2 7.593 PrOs 2 Cubic MgCu 2 7.663 I4ex MgZn 2 5.368 NdOs~ H e x MgZn 2 5.368 SmOs~ H e x MgZn 2 5.336 GdOs 2 I-Icx MgZn 2 5-319 TbOs 2 H e x MgZn 2 5.31 DyOs2 H e x MgZn~ 5.303 HoOs~ H c x MgZn 2 5.30 ErOs 2 H e x MgZn 2 5-284 Y b O s 2 H e x MgZn 2 5.244 Y0s~ Hcx MgZn 2 5.307 b 6 ~eff 8-945 8.926 8.879 8"838 8"80 8"779 8.76 8.732 8.626 8-786 Refs. (listed at end of Tc TN Appendix II) 105 0 47, 105 1.46 28 104, 105 1.34 23 104,105 105 6.71 66 104,105 7-31 34 104,109 6.73 15 104,106 6.0 9 104,109 5.31 3 104,106 105 105 L a i r 2 Cubic MgCu 2 7.688 CcIr 2 Cubic MgCu~ 7.571 P r I r 2 Cubic MgCu~ 7.621 N d I r 2 Cubic MgCu 2 7-605 S m I r 2 E u I r 2 Cubic MgCu 2 7-566 G d I r 2 Cubic MgCu 2 7.550 TbIr~ Cubic MgCu 2 7-532 D y I r 2 Cubic MgCu 2 7.517 t t o I r 2 Cubic MgCu 2 7-490 ErIr~ Cubic MgCu 2 7.473 T m I r 2 Cubic MgCu 2 7.460 Y b I r 2 Cubic MgCu~ 7.477 L u I r 2 Cubic MgCu 2 7"460 Y I r 2 Cubic MgCu 2 7"500 Table A59. R I r 2 6.8 0 47 ,105 1-76 16 104,105 1.47 11.8 104,105 0-24 37 104, 105 6-83 90 104, 105 6.95 45 104, 105 7-65 23 104, 109 7.45 12 104, 108 6-10 3 104, 108 2.92 1 104, 109 1-70 ~ 0 47, 109 109 ]O5 L a P t 2 Cubic MgCu~ 7.774 CcPte Cubic MgCu 2 7.723 P r P t 2 Cubic MgCu 2 7"709 NdPt~ Cubic MgCu 2 7"694 SmPt~ Cubic MgCu 2 7"662 E u P t 2 Cubic MgCu 2 7"731 G d P t 2 Cubic MgCu 2 7"637 T b P t 2 Cubic MgCu 2 7-613 D y P t 2 Cubic MgCu 2 7"597 HoPt 2 Cubic MgCu 2 7.586 ErP t~ Cubic MgCu 2 7.570 YPt~ Cubic MgCu 2 7.590 Table A60. l%Pt 2 3.43 0 1.67 13-5 3.60 0 2.11 10 7.9 105 8.]0 32 6-77 50 9.61 17 7.08 26 10.58 7 7-34 25 10-60 2 8.88 19 9.50 1 7.48 15 108 110, 114 105 110, 114 105 109 111,109 110, 114 105 110, 114 109 110, 114 17 110, 114 109 110, 114 109 105 D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4 Intermetallic Rare-earth Compounds Table A61. LaZn Structure Comp'd System Type a LaZn Cubic CsC1 3.759 CeZn Cubic CsC1 3-704 PrZn Cubic CsC1 3.678 NdZn Cubic CsC1 3.667 SmZb Cubic CsC1 3.627 GdZn Cubic CsC1 3' 602 TbZu Cubic CsC1 3-576 DyZn Cubic CsC1 3.563 HoZn Cubic CsC1 3-547 ErZn Cubic CsC1 3.532 TmZn Cubic CsC1 3" 516 b c ~eff 0 ~ Tc 2-14 -- 18 3.26 10 3-28 45 0.07 125 6-7 270 9-2 190 6 206 10.2 l l 0 4.9 144 10.2 80 4.7 80 9.2 5 2.3 50 649 l%efs. (listed at end of TN Appendix II) 116 36 115 116 115 116 148 115 117 115 117 115117 115 117 1t5 117 ]15 117 115 117 l l7 Table A62. RZn~ LaZn 2 Ortho CeCu 2 4.689 7.638 7.593 118 CeZn e Ortho CeCu~ 4.461 7"539 7.501 2'25 24 7 119, 122 PrZn 2 Ortho CeCu~ 4-619 7.474 7.533 3.56 14 118, 122 NdZn 2 Ortho CeCu 2 4.599 7"409 7.566 3"40 28 1.82 24 118, 122 SmZn 2 Ortho CeCu 2 4.552 7.299 7.590 45 118, 122 EuZn 2 Ortho CeCu 2 4-728 7.650 7.655 45 23 120, 122 20 111 GdZn 2 Ortho CeCu 2 4-513 7.214 7'606 8.48 70 68 118, 122 TbZn 2 Ortho CeCu~ 4.492 7.142 7.595 9-62 58 55 118, 122 25 DyZn 2 Ortho CeCu 2 4-477 7"090 7.600 118 ttoZn~ Ortho CeCu 2 4.460 7.042 7.612 9.71 26 12 118, 122 ErZn~ Ortho CeCu 2 4-448 6.984 7-610 118 TmZn 2 Ortho CeCu 2 4-433 6-944 7.604 118 YbZn~ Ortho CeCu 2 4-573 7"325 7.569 121 LuZn~ Ortho CeCu 2 4.416 6.866 7"600 118 ~EFERENCES 1. B u s c ~ o w , K . H. J . , a n d VAn VUCHT, J . H. N. , 1967, Philips Res. Rep., 22, 233. 2. BUSCHOW, K . H. J . , a n d VAN ])ER GOOT, A. S., 1971, J. Less-common Metals, 24, 117. 3. B u s c ~ o w , K . H . J . , 1965, J. Less-common Metals, 8, 209. 4. 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[The Editors do not hold themselves responsible for the views expressed by their eorresrondents. ] D ow nl oa de d by [ U ni ve rs ity o f Sy dn ey ] at 0 6: 57 2 9 A ug us t 2 01 4