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Magnetic properties and structural chemistry of ternary silicides (RE, Th, U)Ru2Si2 (RE = RARE EARTH)
Journal of Magnetism North-Holland
and Magnetic
Materials
37 (1983) 287-296
MAGNETIC PROPERTIES AND STRUCTURAL Th, U)Ru,Si, (RE = RARE EARTH) K. HIEBL, Institut
C. HORVATH,
fiir Physikalische
287
CHEMISTRY
OF TERNARY SILICIDES (RE,
P. ROGL
Chemie, Unioersitiit
Wien, A- 1090 Vienna, Austria
and M.J. SIENKO Baker Laboratory Received
of Chemistry, Cornell University, Ithaca, NY 14853, USA
7 February
1983
Ternary silicides (RE, Th, U)Ru,Si, have been synthesized from the elements. All the compounds (RE = Y, La, Ce, Pr, Nd, Sm. Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu) were found to be isotypic and to crystallize with the structure type of ThCr,Si, (ordered derivative of the BaAl,-type). The magnetic behavior of these alloys was studied in the temperature range 1.5 K < T c 1100 K. Magnetic susceptibilities at temperatures T > 300 K closely follow a typical Van Vleck paramagnetism of free RE3+-ions. In the case of CeRu,Si, susceptibilities are well described for 20 K < T < 1100 K by a Van Vleck paramagnetism of widely spaced multiplets; the observed effective paramagnetic moment /+r = 2.12 BM indicates a high percentage (85%) of Ce3+. SmRu,Si, yields an effective moment p,rt = 0.54 BM, which compares reasonably well with the Hund’s rule J = 5/2 ground level for free Sm’ and a low-lying excited level with J= 7/2. For temperatures T> 15 K the magnetic susceptibility as a ferromagnetic ordering was function of temperature follows the “Van Vleck behavior” for free Sm3+. At low temperatures whereas antiferromagnetic ordering was observed for (Sm, Gd, Tb, Dy)Ru,Si2. encountered for (Pr, Nd, Ho, Er, Tm)Ru,Si,, The ordering temperatures are generally below 55 K. No superconductivity was found for temperatures as low as 1.8 K.
1. Introduction Based on a comprehensive review [1] on phase equilibria and compound formation in ternary and higher-order phase diagrams containing rare earth elements and silicon, we have started a systematic investigation of the thermodynamic phase equilibria and crystal chemistry in ternary rare earth silicide systems containing platinum metals such as ruthenium and osmium. Although a series of papers has been published on the constitution and compound formation in iron metal-rare earth-silicon systems, (see, e.g., review articles [ 1,2]), Barz [3] and Ballestracci [4] were the only ones reporting on RE-ruthenium-silicides. From X-ray powder analysis, ref. [4] observed the compounds (La, Ce, Nd, Sm, Tb, Dy, Er, Yb)Ru,Si, to adopt a ThCr,Si, type of structure. However, no detailed and systematic investigation of the crystal chemistry and physical (magnetic and/or 0304-8853/83/0000-0000/$03.00
0 1983 North-Holland
superconducting) properties of RERu ,Si 2-compounds is yet available; it thus became the subject of the present paper. During the course of our work, Slazki and Szytda [5] published their study of the magnetic properties of the compounds (Gd, Dy, Ho, Er)Ru,Si 2; their magnetic data were recorded in a rather restricted temperature region, 100-600 K, and in some cases are not compatible with our findings (see discussion).
2. Experimental All compounds were prepared from commercially available high purity elements: Ru (powder 99.9%, Engelhard Ind. Div., USA); rare earth elements (filings from ingots, 99.98, Rare Earth Ltd., Great Britain); uranium (platelets, nuclear grade, E. Merck, Darmstadt, FRG; surface cleaned in dilute HNO, prior to use); thorium (powder, 99.8%,
288
K. Hiebl et al. / Properties
of ternary silicides (RE,
Cerac Inc. USA); and silicon (crystalline, 99.95%, Alfa Ventron, FRG). Specimens with a total weight of 0.5-l g and a nominal composition RERu,Si, were compacted in steel dies without the use of binder materials and were then arc-melted on a water-cooled copper heath using a nonconsumable tungsten electrode in a Ti/Zr-gettered argon atmosphere. Weight losses due to the arc-melting process generally were less than 1 wt%. A part of each of the alloy buttons was wrapped in Ta foil and sealed in evacuated silica tubes for long-time heat treatment at 500°C (600 hrs) and finally quenched in water. To minimize ytterbium vapor losses, the ytterbium-containing specimens were prepared by sintering powder mixtures of prereacted YbSi, (Yb, Si-powder compacts at 600°C for 24 h followed by 950°C for 100 h in evacuated quartz capsules) with ruthenium. After a first short reaction in evacuated quartz tubes at 9OO’C for 24 h, the obtained sinteralloys were crushed and reground, recompacted again, wrapped in Ta-foil, and subjected to a final heat treatment at 9OO’C for 120 h. No significant differences could be detected from X-ray powder diffraction analysis of the as-cast and the annealed specimens and a metallographic inspection proved the alloys to be homogeneous. The only exception was YbRu ,Si 2, which contained some extra amounts of secondary phases. Lattice parameters and standard deviations were evaluated by a least squares extrapolation method [6] from room temperature Guinier powder photographs using monochromated CuKa, radiation with an internal standard of 99.9999% pure Ge. Intensities were recorded by means of a KD-530 microdensitometer. For the susceptibility measurements in the temperature range 80 K < T < 1100 K, a pendulum susceptibility meter was employed, using a Faraday compensation method [7] under high purity helium (T < 300 K); to reduce temperature losses, argon was used for temperatures higher than 300 K. For low temperature susceptibility data (1.5 K < T < 80 K), a Faraday balance [8] with Spectrosil quartz buckets and Cahn-electrobalance recording was used under helium. The determination of the superconducting critical temperatures was
Th, U)Ru,Si,
performed by use of ac-induction equipment as described in ref. [9]. No Eu- or Pm-containing samples were prepared.
3. Results and discussion 3.1. Structural
chemistry
Powder X-ray analysis of the prepared alloys, with nominal composition RERu,Si,, revealed a close resemblance to the powder pattern of CeOs,Si,, the crystal structure of which has quite recently [lo] been refined from single crystal counter data (reliability value R = 0.027) to be isotypic with the structure type of ThCr,Si,. In all the cases, (RE, Th, U)Ru,Si *, indexing was complete on the basis of a body-centered tetragonal cell (see table 1). The extension of a possible homogeneous region has not been examined for all RE-members; however, from a more detailed investigation of the phase equilibria in the Y-Ru-Si system, a rather narrow homogeneity region can be inferred for the complete series RERu,Si *. Thus, composition, lattice parameters and c/a ratio, and X-ray intensities as well as crystal symmetry prove structural identity with the crystal structure of ThCr,Si,. An X-ray study was done to examine possible vacancy formation on the RE-sublattice and, independently, possible Ru/Si substitution. X-ray powder intensity calculations were simulated for 90% occupation of the RE-metal site as well for 10% statistical distribution of Ru/Si on their sublattices. In all cases, a significant deviation from our observations was obvious and excludes vacancy formation or a statistical distribution. By use of the Si-parameter, as recently derived for the isotypic CeOs,Si, by Horvath and Rogl [lo], excellent agreement is obtained between observed and calculated powder X-ray intensities for the REmembers and U, Th. Proof is given in the case of PrRu,Si, in table 2. (Ho, Er)Ru,Si, are an exception insofar as the ratio of their (114) : (211) reflections appears slightly increased with respect to the calculated value of 1 : 3. Similarly, we have monitored the structural behavior of all RERu,Si,-type
I
9.5371 (34) 9.9506 (45) 9.93 9.7972 (48) 9.78 9.7779 (37) 9.7342 (5 1) 9.75 9.6601 (59) 9.71 9.6102 (49) 9.605 (2) 9.5726 (22) 9.54 9.5363 (59) 9.5 1 9.483 (3) 9.5 158 (30) 9.506 (4) 9.4899 (46) 9.45 9.495 (6) 9.4692 (49) 9.4695 (33) 9.44 9.4169 (31) 9.7456 (71) 9.5701 (69)
2.295 2.358 2.356 2.334 2.333 2.33 1 2.326 2.329 2.316 2.324 2.308 2.307 2.303 2.299 2.297 2.294 2.292 2.294 2.305 2.290 2.282 2.266 2.286 2.290 2.280 2.277 2.324 2.318 164.70 177.17 176.42 172.56 171.86 172.03 170.56 170.85 168.06 169.49 166.58 166.48 165.34 164.30 164.41 163.39 162.30 163.75 161.69 162.98 162.05 166.77 162.51 162.00 161.72 161.06 171.36 163.14
(A)
4.1557 (6) 4.2196 (3) 4.215 4.1968 (8) 4.192 4.1945 (4) 4.1859 (6) 4.186 4.1710 (5) 4.178 4.1634 (4) 4.163 (1) 4.1560 (4) 4.150 4.1521 (3) 4.145 4.137 (1) 4.1482 (3) 4.124 (2) 4.1442 (2) 4.141 4.191 (8) 4.1427 (4) 4.1361 (8) 4.139 4.1357 (4) 4.1932 (7) 4.1288 (10)
V (A’ )
a
6.7 7.38 (3.54)
(66) (9) (9)
7.55 4.54
9.59
10.58
10.63
9.72
7.94
0.84
3.58 3.62
2.54
25
100.0
18)
- 33.0 65.7
4.5
6.4
55
- 18.0 47.0 - 12.0 39.6
(-
7
17.8 17.4
31
*
type
temp. (K),
AF
AF
AF
AF
F F
*
139,z = 2)
Ordering
no.
54.7 12.0 100.0
14.4
46.8 29.9
0.5
cm3
Asymp. Curie temp.
D~~.l4/mmm,
K) = 0.00020 mol-’ K) = 0.00020
theor. (RE”)
space group:
x,, (300 K) = O.OCW8 mol- ’ cm’ x,,, (300 K) = 0.00011 x,,, (300 K) = 0.00317
6.3 10.60 9.9 9.66
(7) (6) (20) (8)
(6) (31) (32)
10.59
8.02 7.9 9.65
0.54
3.49 3.54
2.12
~~(300 x,(300
exp.
Pcrr (Pe)
of structure,
(10)
(9) (5) (5)
(I 1)
(7) (10)
(11)
(7) (9)
(ThCr,Si,-type
* Ordering at very low temperatures ( < 4 K), type of order undetermined. ** This work. F Ferromagnetic ordering; AF means antiferromagnetic ordering.
LuRu2Si, ThRu2Si, URu,Si,
TmRu,Si, YbRuZSi,
ErRu,Si,
HoRu,Si,
DyRu s Si a
TbRu*Si,
GdRu*Si,
SmRuaSi,
PrRu 2Si a NdRu,Sia
CeRu,Si,
YRu,Si, LaRu,Si,
Compound
Crystallographicad magnetic data of the ternary silicides RERuaSi,
Table
;;1 ** ** **
;;1 141 **
zl
;;1 I41
;;1
;4;
;;1
;;1
**
[31 **
** **
Ref.
290
K. Hiebl et al. / Properties
Table 2 Powder diffraction
(h k 1)
data for PrRuaSi,
x lo4 obs.
(0 0 2) (1 0 1) (1 10)
249 400 *
(103) (1 12) (0 0 4) (2 0 0) (2 0 2) (1 14) (2 1 1) (1 05) (0 0 6) (2 1 3) (2 0 4) (2 2 0) (1 16) (2 2 2) (3 0 1) (2 1 5) (3 1 0)
899 921 997 1356 1605 1675 1757 1899 *
(107) (2 0 6) (3 0 3) (3 1 2) (2 2 4) (0 0 8) (3 1 4) (32 1) (3 0 5) (1 18) (2 1 7) (2 2 6) (3 2 3) (2 0 8) (109) (4 0 0) (3 1 6) 1
a)
2257 2354 2713 2923 * 3112 3254 l
* * 3612 3639 3709 3992 4388 4469 4610 * 4749 * 4968 5347 1 542 1 5634
sin* talc. 249 401 678 900 927 998 1356 1605 1616 1757 1898 2245 2256 2354 2711 2923 2961 3113 3256 3389 3395 3601 3612 3639 3709 3992 4387 4468 4609 4669 4751 4957 4967 5347 5391 5423 5634
(ThCr,Si,-type)
of ternary srlicides (RE, Th, lJ)Ru$i,
a)
Intensity obs. 7 26 * 31 100 18 40 3 6 8 11 * 19 21 16 19 * 2 9 * * * 6 27 9 4 3 3 2 * 2 * 6 9 * 5 15
Table 3 Interatomic
Not observed Material: Pr(20) Ru(40) Si(40), arc melted; method: powder X-ray diffraction in a Guinier-camera, CuKa,-radiation (99.9999% Ge standard). Lattice parameters: a = 4.1945 (4) c = 9.7779 (37). The intensity is normalized to the strongest reflection I = 100. The space group is I4/mmm (Dll - no. 139); Two Pr in (2a) 0, 0, 0; four Ru in (4d) 0, l/2, l/4; four silicon in (4e) 0, 0, z = 0.37128.
compounds at lower temperatures (samples annealed at 500°C for 600 h); except for the above mentioned enhanced discrepancies in case of (Ho, Er)Ru ,Si *, no significant deviations from
( < 4 A) in PrRu2Si2
8 Ru 8 Si 2 Si
3.2209 (07) 3.2220 (03) 3.6303 (14)
Ru
4 Pr 4 Ru 4 Si
3.2209 (07) 2.9660 (02) 2.4093 (03)
Si
4 Pr 1 Pr 4Ru 1 Si
3.2220 3.6303 2.4093 2.5172
talc. 5.3 24.4 0.0 29.8 100.0 16.1 40.3 1.7 5.2 7.3 9.5 0.2 16.1 18.8 14.6 20.2 0.6 1.6 8.7 0.0 1.2 0.3 4.1 27.7 9.6 4.1 2.4 1.9 2.7 0.0 1.6 0.2 5.4 11.6 0.9 5.7 17.2
distances
Pr
(03) (14) (03) (10)
ThCr, Si ,-crystal symmetry or atom order could be observed. The interatomic distances obtained in the case of PrRu,Si, (table 3) agree with the general characteristics of the bond type in ThCr,Si,-silicides and in a wider sense with the BaAl,-type phases [2,10,11]. Si-Si and Si-Ru contacts are shorter than the sum of their radii by approximately 5-lo%;, whereas transition metal distances (Ru-Ru) are larger by approximately the same amount, indicating the formation of a tightly bonded Ru-Si layer. The rather long RE-RE distances corresponding to the unit cell dimension a imply a rather weak direct magnetic interaction (see magnetic properties). A nice linear dependence of the lattice parameters, volume and c/a values versus the corresponding RE3+ ionic radii is obvious from fig. 1, and, by this, trivalency of the rare earth constituent is indicated, especially also in the case of (Ce, Sm, Yb)Ru,Si, (see also magnetic properties). So far as the size factor is concerned, and according to the similar alloying behavior of 4f and 5f elements, it is not surprising that URu,Si, and ThRu,Si, do form isotypic compounds (see table 1). From comparison of their crystal data in fig. 1, the general behavior of Th (comparable to one of the larger RE elements) and U (comparable to the smaller RE-members) becomes obvious. The crystallographic data derived by us confirm the earlier findings by Ballestracci and Astier [4] concerning the compounds (La, Ce, Nd, Sm, Tb, Dy, Er, Yb)Ru,Si,. The lattice parameters and magnetic data for (Gd, Dy, Ho, Er)Ru,Si,, published recently by Slasky [5] during the course of
K. Hiebl et al. / Properties of ternary silicides (RE, Th, U)Ru,&,
291
RE Ru,Si,
0 This work m Ballestracci, 1978 0 Slaski, 1982
Ci 1.10
1.05 4
Fig. 1. Lattice
parameters
Pr Nd Pm Sm
and volumes
Eu Gd 1.00
RADIUS, RE3: of (RE, Th, U)Ru,Si,-silicides
the present paper, reveal however, remarkable discrepancies from our data (see table 1 and fig. 1); especially, the volume of ErRu,Si, appears to be inconceivably high, whereas the values for the Dy and Ho members appear much smaller than ours (for differences in the magnetic data. see below). 3.2. Magnetic properties The magnetic properties of the RERu,Si,-silitides are summarized in table 1 and in figs. 2-6 presenting the reciprocal magnetic susceptibility -I (cme3 g’) as a function of temperature. A X&G
Tb
Y Oy HO
I
Er
Tm Yb Lu
095
1
090
A versus the radius R,,l+.
practically temperature-independent magnetic susceptibility over a wide range of temperatures was observed for the compounds (Y, La, Lu, Th, U)Ru,Si, (see table 1 for characteristic molar susceptibility values at 300 K). The susceptibility data of the nonzero-moment RE-alloys in all cases reveal a typical Van Vleck type of paramagnetism [ 121 for temperatures higher than 200-300 K. The magnetic parameters as shown in table 1 were thus obtained from a least squares fit to the general formula: Nut*, XM = 3k,(~6) + xO9
K. Hiebl et al. / Properties of ternary silicides (RE, Th, U)Ru,Si,
292
-calculated
I
I
I
I
200
0
I
I
1
I
I
I
-
2. Reciprocal gram susceptibility versus temperature for (Ce, Sm)Ru,Si, theoretical values (Van Vleck) for free Sm’+ are shown by the dashed curve.
I
I
I
200 Fig. 3. Reciprocal
gram susceptibility
I
I
I
600 coo -TEHPERATURE.K versus temperature
I
1000
800
coo 600 -TEMPERATURE,K
I
1
and calculated
I
I
800 -
1000
for (Pr, Nd)Ru,Si,
and calculated
least squares
I
least squares
fit.
fit. For comparison
the
1
I
I
50-
I
I
I
I
I
I
I
I
I
I
293
0 GdRu,Si,
m
0 TbRuzSiz
‘0
-calculated
T+O-
XM
1.O 0 .6 0.2 0
20
40
60 T.K
20
0 I
Fig. 4. Reciprocal gram susceptibility versus temperature dependency and antiferromagnetic ordering for GdRu2Si,
I
l
0
60
80 T.K I
J
I
1000
800 600 TEMPERAT'URE,K-
-
30
A0 I
I
_I
for (Gd, Tb)Ru,Si, and calculated least squares (upper left) and TbRu,Si, (lower right).
fit; insets show field
1.18 1.05 Tesla
1.0 XM
20
0.6 0.2
0 DyRu2Si2 o HoRu2Si2 -calculated
I
200
I
I
coo
I
I
Fig. 5. Reciprocal gram susceptibility versus temperature dependency and antiferromagnetic ordering for DyRu,Si,.
I
I
600 TEMPERATURE,K for (Dy, Ho)Ru,Si,
I
800
I
I
1000
and calculated
least squares
fit; inset shows
field
294
K. Hiebl et al. / Properties of ternary silicides (RE, Th, lJ)Ru,Si2
60
-
0
ErRu,Si,
0
TmRuzSiz(e)
A
YbRu,Si,(C)
(A)
calculated
-1
-3
-2
-1
i Fig. 6. Reciprocal
gram susceptibility
TEMPERATURE ,K -
versus temperature
for (Er, Tm, Yb)Ru,Si*
where N is the Avogadro number, k, is Boltzmann’s constant, 8 is the asymptotic Curie temperature, and x0 is the temperature-independent part of the magnetism including the diamagnetic core correction xdia, the Pauli susceptibility of the elecand the Van Vleck temperature-intron gas XPau]i? dependent paramagnetism Na. With the exception the correction term x0 is relatively of SmRu,Si,, small, viz., of the order of 200 X 10p6, as is observed with the diamagnetic ions in LaRu,Si,, and LuRu,Si,. (In the case of YRu,Si,, SmRu,Si,, x0 is 960 X 10d6; the excess over 200 X 10e6, if all attributed to Nq leads to a calcula-
and calculated
least squares
fit.
tion of J = 5/2 to J = 7/2 separation that almost exactly matches the known spacing of these levels.) In all the cases, the obtained effective paramagnetic moments as presented in table 1 are in good agreement with a Hund’s rule ground state for the free RE3+ ions. The effective moment obtained for CeRu,Si, appears slightly reduced from the free Ce3+-ion value with its F5,2 base term. In view of the general ambivalent behavior of cerium, the obtained p.,rt = 2.12~~ would correspond to only a small fraction of Ce4+ (15%) in good accord with the unit cell dimensions relative to the
K. Hiebl et al. / Properties of ternary silicides (RE, Th, U)Ru2Si,
RE3+Ru,Si, members as shown in fig. 1. The paramagnetic values (table 1) derived for YbRu ZSi, are given in parenthesis in view of the inhomogeneity of the alloys used. The reciprocal magnetic susceptibility, however, closely follows a Curie-Weiss law, yielding a slightly smaller moment as compared to free Yb3+ and, on extrapolation, a slightly negative asymptotic Curie temperature. Except for Gd and Yb slight departures from Curie-Weiss behavior appear at low temperatures due to crystal field splitting of the Hund’s state in the tetragonal symmetry. At very low temperatures (T -G 100 K), there is also magnetic ordering of the RE-sublattice. The type of magnetic order was found to be ferromagnetic for (Pr, Nd, Ho, Er, Tm)Ru,Si, but appears to be antiferromagnetic for the RE-members in the middle of the RE-sequence (RE = Sm, Gd, Tb, Dy). The magnetic ordering temperatures do not follow a simple de Gennes scaling. Field dependences and NCel temperatures are presented as insets in each case. It is interesting to note, however, that in all cases exthe extrapolated asymptotic Curie cept YbRu,Si,, temperatures appear to be positive, which is particularly true for those alloys which exhibit antiferromagnetic ordering. In comparison with the recently derived magnetic data of Slaski [5] for (Gd, Tb, Ho, Er)Ru *Si,, a rather large discrepancy with our data is obvious from table 1. Whereas we have studied the magnetic behavior over a large temperature range, 1.5 K < T < 1100 K, Slaski’s data are based on a limited section (100 K < T < 600 K). As seen from our data in figs. 4, 5 and 6, the slopes of the reciprocal susceptibilities start to change at T < 300 K due to magnetic ordering at lower temperatures. Thus, taking data from a limited region only will invariably introduce deviations from the general Van Vleck type of paramagnetism of free RE3+ions. This reasoning, however, does not completely explain the lack of agreement. It may, in part, arise from observed discrepancies of the unit cell volumes, which might be due to RE-vacancy formation or to zero-moment impurities. As shown in the inset of fig. 5, there is a pronounced field-dependence of the susceptibility of the dysprosium compound below 25 K. It is not
295
unknown to find slight field-dependence of the susceptibility for antiferromagnetic materials below the Neel temperature, especially if there is anisotropy in the orientation energy, but the present effect is considerably greater than normal. It is not due to the large moment of the Dy3+ (10.6 BM) since the same effect is not observed for Ho3’ (10.6 BM). Nor is it due to field-uncoupling of the exchange energy, as the field used is orders of magnitude less than that corresponding to the thermal energy at the Neel temperature. Rather, it appears to be attributable to weak crystal-field splitting of the lowest spin-orbit level of Dy3+, which, although weak (of the order of 10 cm-‘), may be comparable to the anisotropy energy. Low-temperature ESR studies would be informative.
Acknowledgements This investigation was supported by the Science Foundation (Fonds zur Austrian Forderung der Wissenschaftlichen Forschung in Gsterreich) through grant No. 4605 and by the US Air Force Office of Scientific Research through grant no. 80-0009. It was assisted in part by the NSF and the Materials Science Center at Cornell University. P.R. expresses his gratitude to the Hochschuljubilaumsstiftung der Stadt Wien for the KD-530 type microdensitometer. Thanks are also due to the Austrian Science Foundation for the use of the SUS-10 under grant No. 4820.
References 111P. Rogl, Phase Equilibria
in Ternary and Higher Order Systems containing Rare Earth Elements and Silicon, in: Handbook on the Physics and Chemistry of the Rare Earths vol. 7, eds. K.A. Gschneidner, Jr. and L. Eyring (North-Holland, Amsterdam) to be published. I21 E. Partht and B. Chabot, Crystal Structures and Crystal Chemistry of Ternary Rare Earth Transition MetalBorides, Silicides and Homologs, in: Handbook on the Physics and Chemistry of the Rare Earths, vol. 6, eds. K.A. Gschneidner, Jr. and L. Eyring (North-Holland, Amsterdam, 1983) chap. 48, in press. [31 H. Barz, Mater. Res. Bull. 15 (1980) 1489, 1493. [41 M.R. Ballestracci and G. Astier, C.R. Acad. Sci. (Paris) Ser. B. 286 (1978) 109.
296
K. Hiebl et al. / Properties of ternmy silicides (RE, Th, U)Ru2Si,
[S] M. Slaski and A. Szytuta, J. Less Common Metals 87 (1982) LI. [6] M. Holocher-Ertl, Program Gitter, Adapted Version by H. Boller, University of Vienna (1976). [7] SUS-10, Susceptibility Measuring Device, A. Paar-KG., Graz, Austria. [8] J.E. Young, Jr., Ph.D. Thesis, Cornell University (1971).
[9] W.G. Fisher, Ph.D. Thesis, Cornell University (1978). [IO] C. Horvath and P. Rogl, Mater. Res. Bull. to be published. [ 1 l] R. Marazza, R. Ferro, G. Rimbaldi and G. Zanicchi, J. Less Common Metals 53 (1977) 193. [ 121 J.H. Van Vleck, The Theory of Electric and Magnetic Susceptibilities (Clarendon, Oxford, 1932) p. 232.
and Magnetic
Materials
37 (1983) 287-296
MAGNETIC PROPERTIES AND STRUCTURAL Th, U)Ru,Si, (RE = RARE EARTH) K. HIEBL, Institut
C. HORVATH,
fiir Physikalische
287
CHEMISTRY
OF TERNARY SILICIDES (RE,
P. ROGL
Chemie, Unioersitiit
Wien, A- 1090 Vienna, Austria
and M.J. SIENKO Baker Laboratory Received
of Chemistry, Cornell University, Ithaca, NY 14853, USA
7 February
1983
Ternary silicides (RE, Th, U)Ru,Si, have been synthesized from the elements. All the compounds (RE = Y, La, Ce, Pr, Nd, Sm. Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu) were found to be isotypic and to crystallize with the structure type of ThCr,Si, (ordered derivative of the BaAl,-type). The magnetic behavior of these alloys was studied in the temperature range 1.5 K < T c 1100 K. Magnetic susceptibilities at temperatures T > 300 K closely follow a typical Van Vleck paramagnetism of free RE3+-ions. In the case of CeRu,Si, susceptibilities are well described for 20 K < T < 1100 K by a Van Vleck paramagnetism of widely spaced multiplets; the observed effective paramagnetic moment /+r = 2.12 BM indicates a high percentage (85%) of Ce3+. SmRu,Si, yields an effective moment p,rt = 0.54 BM, which compares reasonably well with the Hund’s rule J = 5/2 ground level for free Sm’ and a low-lying excited level with J= 7/2. For temperatures T> 15 K the magnetic susceptibility as a ferromagnetic ordering was function of temperature follows the “Van Vleck behavior” for free Sm3+. At low temperatures whereas antiferromagnetic ordering was observed for (Sm, Gd, Tb, Dy)Ru,Si2. encountered for (Pr, Nd, Ho, Er, Tm)Ru,Si,, The ordering temperatures are generally below 55 K. No superconductivity was found for temperatures as low as 1.8 K.
1. Introduction Based on a comprehensive review [1] on phase equilibria and compound formation in ternary and higher-order phase diagrams containing rare earth elements and silicon, we have started a systematic investigation of the thermodynamic phase equilibria and crystal chemistry in ternary rare earth silicide systems containing platinum metals such as ruthenium and osmium. Although a series of papers has been published on the constitution and compound formation in iron metal-rare earth-silicon systems, (see, e.g., review articles [ 1,2]), Barz [3] and Ballestracci [4] were the only ones reporting on RE-ruthenium-silicides. From X-ray powder analysis, ref. [4] observed the compounds (La, Ce, Nd, Sm, Tb, Dy, Er, Yb)Ru,Si, to adopt a ThCr,Si, type of structure. However, no detailed and systematic investigation of the crystal chemistry and physical (magnetic and/or 0304-8853/83/0000-0000/$03.00
0 1983 North-Holland
superconducting) properties of RERu ,Si 2-compounds is yet available; it thus became the subject of the present paper. During the course of our work, Slazki and Szytda [5] published their study of the magnetic properties of the compounds (Gd, Dy, Ho, Er)Ru,Si 2; their magnetic data were recorded in a rather restricted temperature region, 100-600 K, and in some cases are not compatible with our findings (see discussion).
2. Experimental All compounds were prepared from commercially available high purity elements: Ru (powder 99.9%, Engelhard Ind. Div., USA); rare earth elements (filings from ingots, 99.98, Rare Earth Ltd., Great Britain); uranium (platelets, nuclear grade, E. Merck, Darmstadt, FRG; surface cleaned in dilute HNO, prior to use); thorium (powder, 99.8%,
288
K. Hiebl et al. / Properties
of ternary silicides (RE,
Cerac Inc. USA); and silicon (crystalline, 99.95%, Alfa Ventron, FRG). Specimens with a total weight of 0.5-l g and a nominal composition RERu,Si, were compacted in steel dies without the use of binder materials and were then arc-melted on a water-cooled copper heath using a nonconsumable tungsten electrode in a Ti/Zr-gettered argon atmosphere. Weight losses due to the arc-melting process generally were less than 1 wt%. A part of each of the alloy buttons was wrapped in Ta foil and sealed in evacuated silica tubes for long-time heat treatment at 500°C (600 hrs) and finally quenched in water. To minimize ytterbium vapor losses, the ytterbium-containing specimens were prepared by sintering powder mixtures of prereacted YbSi, (Yb, Si-powder compacts at 600°C for 24 h followed by 950°C for 100 h in evacuated quartz capsules) with ruthenium. After a first short reaction in evacuated quartz tubes at 9OO’C for 24 h, the obtained sinteralloys were crushed and reground, recompacted again, wrapped in Ta-foil, and subjected to a final heat treatment at 9OO’C for 120 h. No significant differences could be detected from X-ray powder diffraction analysis of the as-cast and the annealed specimens and a metallographic inspection proved the alloys to be homogeneous. The only exception was YbRu ,Si 2, which contained some extra amounts of secondary phases. Lattice parameters and standard deviations were evaluated by a least squares extrapolation method [6] from room temperature Guinier powder photographs using monochromated CuKa, radiation with an internal standard of 99.9999% pure Ge. Intensities were recorded by means of a KD-530 microdensitometer. For the susceptibility measurements in the temperature range 80 K < T < 1100 K, a pendulum susceptibility meter was employed, using a Faraday compensation method [7] under high purity helium (T < 300 K); to reduce temperature losses, argon was used for temperatures higher than 300 K. For low temperature susceptibility data (1.5 K < T < 80 K), a Faraday balance [8] with Spectrosil quartz buckets and Cahn-electrobalance recording was used under helium. The determination of the superconducting critical temperatures was
Th, U)Ru,Si,
performed by use of ac-induction equipment as described in ref. [9]. No Eu- or Pm-containing samples were prepared.
3. Results and discussion 3.1. Structural
chemistry
Powder X-ray analysis of the prepared alloys, with nominal composition RERu,Si,, revealed a close resemblance to the powder pattern of CeOs,Si,, the crystal structure of which has quite recently [lo] been refined from single crystal counter data (reliability value R = 0.027) to be isotypic with the structure type of ThCr,Si,. In all the cases, (RE, Th, U)Ru,Si *, indexing was complete on the basis of a body-centered tetragonal cell (see table 1). The extension of a possible homogeneous region has not been examined for all RE-members; however, from a more detailed investigation of the phase equilibria in the Y-Ru-Si system, a rather narrow homogeneity region can be inferred for the complete series RERu,Si *. Thus, composition, lattice parameters and c/a ratio, and X-ray intensities as well as crystal symmetry prove structural identity with the crystal structure of ThCr,Si,. An X-ray study was done to examine possible vacancy formation on the RE-sublattice and, independently, possible Ru/Si substitution. X-ray powder intensity calculations were simulated for 90% occupation of the RE-metal site as well for 10% statistical distribution of Ru/Si on their sublattices. In all cases, a significant deviation from our observations was obvious and excludes vacancy formation or a statistical distribution. By use of the Si-parameter, as recently derived for the isotypic CeOs,Si, by Horvath and Rogl [lo], excellent agreement is obtained between observed and calculated powder X-ray intensities for the REmembers and U, Th. Proof is given in the case of PrRu,Si, in table 2. (Ho, Er)Ru,Si, are an exception insofar as the ratio of their (114) : (211) reflections appears slightly increased with respect to the calculated value of 1 : 3. Similarly, we have monitored the structural behavior of all RERu,Si,-type
I
9.5371 (34) 9.9506 (45) 9.93 9.7972 (48) 9.78 9.7779 (37) 9.7342 (5 1) 9.75 9.6601 (59) 9.71 9.6102 (49) 9.605 (2) 9.5726 (22) 9.54 9.5363 (59) 9.5 1 9.483 (3) 9.5 158 (30) 9.506 (4) 9.4899 (46) 9.45 9.495 (6) 9.4692 (49) 9.4695 (33) 9.44 9.4169 (31) 9.7456 (71) 9.5701 (69)
2.295 2.358 2.356 2.334 2.333 2.33 1 2.326 2.329 2.316 2.324 2.308 2.307 2.303 2.299 2.297 2.294 2.292 2.294 2.305 2.290 2.282 2.266 2.286 2.290 2.280 2.277 2.324 2.318 164.70 177.17 176.42 172.56 171.86 172.03 170.56 170.85 168.06 169.49 166.58 166.48 165.34 164.30 164.41 163.39 162.30 163.75 161.69 162.98 162.05 166.77 162.51 162.00 161.72 161.06 171.36 163.14
(A)
4.1557 (6) 4.2196 (3) 4.215 4.1968 (8) 4.192 4.1945 (4) 4.1859 (6) 4.186 4.1710 (5) 4.178 4.1634 (4) 4.163 (1) 4.1560 (4) 4.150 4.1521 (3) 4.145 4.137 (1) 4.1482 (3) 4.124 (2) 4.1442 (2) 4.141 4.191 (8) 4.1427 (4) 4.1361 (8) 4.139 4.1357 (4) 4.1932 (7) 4.1288 (10)
V (A’ )
a
6.7 7.38 (3.54)
(66) (9) (9)
7.55 4.54
9.59
10.58
10.63
9.72
7.94
0.84
3.58 3.62
2.54
25
100.0
18)
- 33.0 65.7
4.5
6.4
55
- 18.0 47.0 - 12.0 39.6
(-
7
17.8 17.4
31
*
type
temp. (K),
AF
AF
AF
AF
F F
*
139,z = 2)
Ordering
no.
54.7 12.0 100.0
14.4
46.8 29.9
0.5
cm3
Asymp. Curie temp.
D~~.l4/mmm,
K) = 0.00020 mol-’ K) = 0.00020
theor. (RE”)
space group:
x,, (300 K) = O.OCW8 mol- ’ cm’ x,,, (300 K) = 0.00011 x,,, (300 K) = 0.00317
6.3 10.60 9.9 9.66
(7) (6) (20) (8)
(6) (31) (32)
10.59
8.02 7.9 9.65
0.54
3.49 3.54
2.12
~~(300 x,(300
exp.
Pcrr (Pe)
of structure,
(10)
(9) (5) (5)
(I 1)
(7) (10)
(11)
(7) (9)
(ThCr,Si,-type
* Ordering at very low temperatures ( < 4 K), type of order undetermined. ** This work. F Ferromagnetic ordering; AF means antiferromagnetic ordering.
LuRu2Si, ThRu2Si, URu,Si,
TmRu,Si, YbRuZSi,
ErRu,Si,
HoRu,Si,
DyRu s Si a
TbRu*Si,
GdRu*Si,
SmRuaSi,
PrRu 2Si a NdRu,Sia
CeRu,Si,
YRu,Si, LaRu,Si,
Compound
Crystallographicad magnetic data of the ternary silicides RERuaSi,
Table
;;1 ** ** **
;;1 141 **
zl
;;1 I41
;;1
;4;
;;1
;;1
**
[31 **
** **
Ref.
290
K. Hiebl et al. / Properties
Table 2 Powder diffraction
(h k 1)
data for PrRuaSi,
x lo4 obs.
(0 0 2) (1 0 1) (1 10)
249 400 *
(103) (1 12) (0 0 4) (2 0 0) (2 0 2) (1 14) (2 1 1) (1 05) (0 0 6) (2 1 3) (2 0 4) (2 2 0) (1 16) (2 2 2) (3 0 1) (2 1 5) (3 1 0)
899 921 997 1356 1605 1675 1757 1899 *
(107) (2 0 6) (3 0 3) (3 1 2) (2 2 4) (0 0 8) (3 1 4) (32 1) (3 0 5) (1 18) (2 1 7) (2 2 6) (3 2 3) (2 0 8) (109) (4 0 0) (3 1 6) 1
a)
2257 2354 2713 2923 * 3112 3254 l
* * 3612 3639 3709 3992 4388 4469 4610 * 4749 * 4968 5347 1 542 1 5634
sin* talc. 249 401 678 900 927 998 1356 1605 1616 1757 1898 2245 2256 2354 2711 2923 2961 3113 3256 3389 3395 3601 3612 3639 3709 3992 4387 4468 4609 4669 4751 4957 4967 5347 5391 5423 5634
(ThCr,Si,-type)
of ternary srlicides (RE, Th, lJ)Ru$i,
a)
Intensity obs. 7 26 * 31 100 18 40 3 6 8 11 * 19 21 16 19 * 2 9 * * * 6 27 9 4 3 3 2 * 2 * 6 9 * 5 15
Table 3 Interatomic
Not observed Material: Pr(20) Ru(40) Si(40), arc melted; method: powder X-ray diffraction in a Guinier-camera, CuKa,-radiation (99.9999% Ge standard). Lattice parameters: a = 4.1945 (4) c = 9.7779 (37). The intensity is normalized to the strongest reflection I = 100. The space group is I4/mmm (Dll - no. 139); Two Pr in (2a) 0, 0, 0; four Ru in (4d) 0, l/2, l/4; four silicon in (4e) 0, 0, z = 0.37128.
compounds at lower temperatures (samples annealed at 500°C for 600 h); except for the above mentioned enhanced discrepancies in case of (Ho, Er)Ru ,Si *, no significant deviations from
( < 4 A) in PrRu2Si2
8 Ru 8 Si 2 Si
3.2209 (07) 3.2220 (03) 3.6303 (14)
Ru
4 Pr 4 Ru 4 Si
3.2209 (07) 2.9660 (02) 2.4093 (03)
Si
4 Pr 1 Pr 4Ru 1 Si
3.2220 3.6303 2.4093 2.5172
talc. 5.3 24.4 0.0 29.8 100.0 16.1 40.3 1.7 5.2 7.3 9.5 0.2 16.1 18.8 14.6 20.2 0.6 1.6 8.7 0.0 1.2 0.3 4.1 27.7 9.6 4.1 2.4 1.9 2.7 0.0 1.6 0.2 5.4 11.6 0.9 5.7 17.2
distances
Pr
(03) (14) (03) (10)
ThCr, Si ,-crystal symmetry or atom order could be observed. The interatomic distances obtained in the case of PrRu,Si, (table 3) agree with the general characteristics of the bond type in ThCr,Si,-silicides and in a wider sense with the BaAl,-type phases [2,10,11]. Si-Si and Si-Ru contacts are shorter than the sum of their radii by approximately 5-lo%;, whereas transition metal distances (Ru-Ru) are larger by approximately the same amount, indicating the formation of a tightly bonded Ru-Si layer. The rather long RE-RE distances corresponding to the unit cell dimension a imply a rather weak direct magnetic interaction (see magnetic properties). A nice linear dependence of the lattice parameters, volume and c/a values versus the corresponding RE3+ ionic radii is obvious from fig. 1, and, by this, trivalency of the rare earth constituent is indicated, especially also in the case of (Ce, Sm, Yb)Ru,Si, (see also magnetic properties). So far as the size factor is concerned, and according to the similar alloying behavior of 4f and 5f elements, it is not surprising that URu,Si, and ThRu,Si, do form isotypic compounds (see table 1). From comparison of their crystal data in fig. 1, the general behavior of Th (comparable to one of the larger RE elements) and U (comparable to the smaller RE-members) becomes obvious. The crystallographic data derived by us confirm the earlier findings by Ballestracci and Astier [4] concerning the compounds (La, Ce, Nd, Sm, Tb, Dy, Er, Yb)Ru,Si,. The lattice parameters and magnetic data for (Gd, Dy, Ho, Er)Ru,Si,, published recently by Slasky [5] during the course of
K. Hiebl et al. / Properties of ternary silicides (RE, Th, U)Ru,&,
291
RE Ru,Si,
0 This work m Ballestracci, 1978 0 Slaski, 1982
Ci 1.10
1.05 4
Fig. 1. Lattice
parameters
Pr Nd Pm Sm
and volumes
Eu Gd 1.00
RADIUS, RE3: of (RE, Th, U)Ru,Si,-silicides
the present paper, reveal however, remarkable discrepancies from our data (see table 1 and fig. 1); especially, the volume of ErRu,Si, appears to be inconceivably high, whereas the values for the Dy and Ho members appear much smaller than ours (for differences in the magnetic data. see below). 3.2. Magnetic properties The magnetic properties of the RERu,Si,-silitides are summarized in table 1 and in figs. 2-6 presenting the reciprocal magnetic susceptibility -I (cme3 g’) as a function of temperature. A X&G
Tb
Y Oy HO
I
Er
Tm Yb Lu
095
1
090
A versus the radius R,,l+.
practically temperature-independent magnetic susceptibility over a wide range of temperatures was observed for the compounds (Y, La, Lu, Th, U)Ru,Si, (see table 1 for characteristic molar susceptibility values at 300 K). The susceptibility data of the nonzero-moment RE-alloys in all cases reveal a typical Van Vleck type of paramagnetism [ 121 for temperatures higher than 200-300 K. The magnetic parameters as shown in table 1 were thus obtained from a least squares fit to the general formula: Nut*, XM = 3k,(~6) + xO9
K. Hiebl et al. / Properties of ternary silicides (RE, Th, U)Ru,Si,
292
-calculated
I
I
I
I
200
0
I
I
1
I
I
I
-
2. Reciprocal gram susceptibility versus temperature for (Ce, Sm)Ru,Si, theoretical values (Van Vleck) for free Sm’+ are shown by the dashed curve.
I
I
I
200 Fig. 3. Reciprocal
gram susceptibility
I
I
I
600 coo -TEHPERATURE.K versus temperature
I
1000
800
coo 600 -TEMPERATURE,K
I
1
and calculated
I
I
800 -
1000
for (Pr, Nd)Ru,Si,
and calculated
least squares
I
least squares
fit.
fit. For comparison
the
1
I
I
50-
I
I
I
I
I
I
I
I
I
I
293
0 GdRu,Si,
m
0 TbRuzSiz
‘0
-calculated
T+O-
XM
1.O 0 .6 0.2 0
20
40
60 T.K
20
0 I
Fig. 4. Reciprocal gram susceptibility versus temperature dependency and antiferromagnetic ordering for GdRu2Si,
I
l
0
60
80 T.K I
J
I
1000
800 600 TEMPERAT'URE,K-
-
30
A0 I
I
_I
for (Gd, Tb)Ru,Si, and calculated least squares (upper left) and TbRu,Si, (lower right).
fit; insets show field
1.18 1.05 Tesla
1.0 XM
20
0.6 0.2
0 DyRu2Si2 o HoRu2Si2 -calculated
I
200
I
I
coo
I
I
Fig. 5. Reciprocal gram susceptibility versus temperature dependency and antiferromagnetic ordering for DyRu,Si,.
I
I
600 TEMPERATURE,K for (Dy, Ho)Ru,Si,
I
800
I
I
1000
and calculated
least squares
fit; inset shows
field
294
K. Hiebl et al. / Properties of ternary silicides (RE, Th, lJ)Ru,Si2
60
-
0
ErRu,Si,
0
TmRuzSiz(e)
A
YbRu,Si,(C)
(A)
calculated
-1
-3
-2
-1
i Fig. 6. Reciprocal
gram susceptibility
TEMPERATURE ,K -
versus temperature
for (Er, Tm, Yb)Ru,Si*
where N is the Avogadro number, k, is Boltzmann’s constant, 8 is the asymptotic Curie temperature, and x0 is the temperature-independent part of the magnetism including the diamagnetic core correction xdia, the Pauli susceptibility of the elecand the Van Vleck temperature-intron gas XPau]i? dependent paramagnetism Na. With the exception the correction term x0 is relatively of SmRu,Si,, small, viz., of the order of 200 X 10p6, as is observed with the diamagnetic ions in LaRu,Si,, and LuRu,Si,. (In the case of YRu,Si,, SmRu,Si,, x0 is 960 X 10d6; the excess over 200 X 10e6, if all attributed to Nq leads to a calcula-
and calculated
least squares
fit.
tion of J = 5/2 to J = 7/2 separation that almost exactly matches the known spacing of these levels.) In all the cases, the obtained effective paramagnetic moments as presented in table 1 are in good agreement with a Hund’s rule ground state for the free RE3+ ions. The effective moment obtained for CeRu,Si, appears slightly reduced from the free Ce3+-ion value with its F5,2 base term. In view of the general ambivalent behavior of cerium, the obtained p.,rt = 2.12~~ would correspond to only a small fraction of Ce4+ (15%) in good accord with the unit cell dimensions relative to the
K. Hiebl et al. / Properties of ternary silicides (RE, Th, U)Ru2Si,
RE3+Ru,Si, members as shown in fig. 1. The paramagnetic values (table 1) derived for YbRu ZSi, are given in parenthesis in view of the inhomogeneity of the alloys used. The reciprocal magnetic susceptibility, however, closely follows a Curie-Weiss law, yielding a slightly smaller moment as compared to free Yb3+ and, on extrapolation, a slightly negative asymptotic Curie temperature. Except for Gd and Yb slight departures from Curie-Weiss behavior appear at low temperatures due to crystal field splitting of the Hund’s state in the tetragonal symmetry. At very low temperatures (T -G 100 K), there is also magnetic ordering of the RE-sublattice. The type of magnetic order was found to be ferromagnetic for (Pr, Nd, Ho, Er, Tm)Ru,Si, but appears to be antiferromagnetic for the RE-members in the middle of the RE-sequence (RE = Sm, Gd, Tb, Dy). The magnetic ordering temperatures do not follow a simple de Gennes scaling. Field dependences and NCel temperatures are presented as insets in each case. It is interesting to note, however, that in all cases exthe extrapolated asymptotic Curie cept YbRu,Si,, temperatures appear to be positive, which is particularly true for those alloys which exhibit antiferromagnetic ordering. In comparison with the recently derived magnetic data of Slaski [5] for (Gd, Tb, Ho, Er)Ru *Si,, a rather large discrepancy with our data is obvious from table 1. Whereas we have studied the magnetic behavior over a large temperature range, 1.5 K < T < 1100 K, Slaski’s data are based on a limited section (100 K < T < 600 K). As seen from our data in figs. 4, 5 and 6, the slopes of the reciprocal susceptibilities start to change at T < 300 K due to magnetic ordering at lower temperatures. Thus, taking data from a limited region only will invariably introduce deviations from the general Van Vleck type of paramagnetism of free RE3+ions. This reasoning, however, does not completely explain the lack of agreement. It may, in part, arise from observed discrepancies of the unit cell volumes, which might be due to RE-vacancy formation or to zero-moment impurities. As shown in the inset of fig. 5, there is a pronounced field-dependence of the susceptibility of the dysprosium compound below 25 K. It is not
295
unknown to find slight field-dependence of the susceptibility for antiferromagnetic materials below the Neel temperature, especially if there is anisotropy in the orientation energy, but the present effect is considerably greater than normal. It is not due to the large moment of the Dy3+ (10.6 BM) since the same effect is not observed for Ho3’ (10.6 BM). Nor is it due to field-uncoupling of the exchange energy, as the field used is orders of magnitude less than that corresponding to the thermal energy at the Neel temperature. Rather, it appears to be attributable to weak crystal-field splitting of the lowest spin-orbit level of Dy3+, which, although weak (of the order of 10 cm-‘), may be comparable to the anisotropy energy. Low-temperature ESR studies would be informative.
Acknowledgements This investigation was supported by the Science Foundation (Fonds zur Austrian Forderung der Wissenschaftlichen Forschung in Gsterreich) through grant No. 4605 and by the US Air Force Office of Scientific Research through grant no. 80-0009. It was assisted in part by the NSF and the Materials Science Center at Cornell University. P.R. expresses his gratitude to the Hochschuljubilaumsstiftung der Stadt Wien for the KD-530 type microdensitometer. Thanks are also due to the Austrian Science Foundation for the use of the SUS-10 under grant No. 4820.
References 111P. Rogl, Phase Equilibria
in Ternary and Higher Order Systems containing Rare Earth Elements and Silicon, in: Handbook on the Physics and Chemistry of the Rare Earths vol. 7, eds. K.A. Gschneidner, Jr. and L. Eyring (North-Holland, Amsterdam) to be published. I21 E. Partht and B. Chabot, Crystal Structures and Crystal Chemistry of Ternary Rare Earth Transition MetalBorides, Silicides and Homologs, in: Handbook on the Physics and Chemistry of the Rare Earths, vol. 6, eds. K.A. Gschneidner, Jr. and L. Eyring (North-Holland, Amsterdam, 1983) chap. 48, in press. [31 H. Barz, Mater. Res. Bull. 15 (1980) 1489, 1493. [41 M.R. Ballestracci and G. Astier, C.R. Acad. Sci. (Paris) Ser. B. 286 (1978) 109.
296
K. Hiebl et al. / Properties of ternmy silicides (RE, Th, U)Ru2Si,
[S] M. Slaski and A. Szytuta, J. Less Common Metals 87 (1982) LI. [6] M. Holocher-Ertl, Program Gitter, Adapted Version by H. Boller, University of Vienna (1976). [7] SUS-10, Susceptibility Measuring Device, A. Paar-KG., Graz, Austria. [8] J.E. Young, Jr., Ph.D. Thesis, Cornell University (1971).
[9] W.G. Fisher, Ph.D. Thesis, Cornell University (1978). [IO] C. Horvath and P. Rogl, Mater. Res. Bull. to be published. [ 1 l] R. Marazza, R. Ferro, G. Rimbaldi and G. Zanicchi, J. Less Common Metals 53 (1977) 193. [ 121 J.H. Van Vleck, The Theory of Electric and Magnetic Susceptibilities (Clarendon, Oxford, 1932) p. 232.