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Crystal structures of some Ln3Rh, Ln7Rh3 and LnRh3 Phases
199
JOURNAL OF THE LESS-COMMON METALS Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands
CRYSTAL STRUCTURES
OF SOME Ln,Rh, Ln,Rh,
AND LnRh, PHASES*
A. RAMAN Materials Group, Department of Engineering Science, Louisiana State University, Baton Rouge, La. 70803 (U.S.A.) (Received
June 9th, 1971)
SUMMARY
The Fe&-type structure occurs in the phases Nd,Rh, Gd,Rh, Y,Rh and Er,Rh. The atomic positional parameters in the Pnma space group are: 4Er in 4(c) 8Er in 8(d) 4Rh in 4(c)
0.021,0.250,0.138 0.180, 0.061,0.667 0.389, 0.250,0.937
B, =2.0 A2 B, = 2.0 A2 B, = 0.5 A2
Phases with the Ln,Rh, stoichiometry in the Gd-Rh,Y-Rh and Er-Rh systems possess the Th,Fe,-type structure. The same structure occurs in the alloys of the light rare earths, La, Ce and Nd at the Ln,Rh stoichiometry. Unlike LaRh, and NdRh,, CeRh, crystallizes in the Cu,Au-type structure. It is shown that electronic factors rather than the size factor play prominent roles in stabilizing these structures in the rare-earth alloys.
INTRODUCTION
The crystal structures of several alloy phases of the La-Rh and Nd-Rh systems were described in earlier papers by the author’-3. While an Fe,C-type phase was encountered in the Nd-Rh system3 at off-stoichiometric composition, near Nd,, Rh,,, an analogous phase was not encountered in La-Rh alloys’. The study was extended to determine whether the Fe,C-type structure occurs in other rare earthhrhodium systems. Also it was of interest to see whether the phases which occur at Ln,Rh and LnRh, stoichiometries in the La-Rh and Nd-Rh systems occur in other Ln-Rh systems. The results of this study are described in this paper. EXPERIMENTAL
Suitable alloys at and near the Ln,Rh, Ln,Rh, and LnRh3 stoichiometries were melted from reactor grade rare earths (La, Ce, Nd, Gd, Y and Er-99.9 + % by weight, supplied by Lunex Company, Pleasant Valley. Iowa) and rhodium (99.92 + %, supplied by Engelhard Industries, Inc., Newark, New Jersey) in an arc-melting furnace * Ln
represents
a lanthanide,
La Ce, Nd, Cd. Y or Er. J. Less-Common Metals, 26 (1972) 199-206
A. RAMAN
200
under argon atmosphere. The alloys were wrapped in molybdenum foils and homogenized at suitable high temperatures in evacuated quartz tubes. The crystal structural data of phases present in the alloys were evaluated from Guinier X-ray diffraction photographs taken with CuKa radiations. The relative intensities in the powder patterns of selected alloy phases were calculated using a computer program written by Yvon, Jeitschko and ParthC4. The atomic positional parameters in an Fe,C-type phase were relined using a full matrix least-square refinement program written by Stewart’. The needed atomic scattering factors for X-rays were taken from International Tables for X-ray Crystallography6. RFSJLTS
Ln,Rh phases
Phases with the Fe&-type crystal structure’** were encountered at Ln,Rh stoichiometry in the systems Gd-Rh, Y-Rh and Er-Rh. Unlike as in Nd-Rh alloys, no shift in composition was observed. An analogous phase was not obtained in the Ce-Rh system in the alloys containing 20-30 at. % Rh. The relative intensities of the lines in the X-ray diffraction photographs of Er,Rh (Fe&-type; Space Group Prima) were calculated assuming the atomic positional parameters as in La&o (Fe,C-type)‘. The calculated relative intensities of diffraction lines did not match well with the observed relative intensities of several linesandtheresidualindex,R=~~F,~-IF,II/IF,I, was 0.22. The structure was improved using 35 well-defined, single reflections in the powder diffraction pattern whose relative intensities were judged visually with a calibrated intensity scale. After one cycle of refinement, the R-index dropped to 0.12 and it did not vary by more than +0.003 in five subsequent cycles. In this attempt, the isotropic temperature factors for the erbium and rhodium atoms were maintained constant at 2.0 and 0.5 A’, respectively. When the temperature factors were allowed to vary from 1 A2 for all atoms along with the variable positional parameters, those of the Er atoms rose to 2.84 and 4.1 A’ for the 4-fold and 8-fold positions, respectively, while that of the Rh atoms became - 4.57 A2, and the R-index obtained was 0.11. The improved atomic positional parameters and the observed and calculated structure factors for the 35 reflections are listed in Table I along with the data from the powder X-ray diffraction pattern of Er,Rh. Ln7Rh, phases
Intermediate phases of Ln,Rh, stoichiometry were encountered in the Gd-Rh, Y-Rh and Er-Rh systems. Their powder patterns resembled the patterns of La,Rh and Nd,Rh, already reported in the literature ‘v3. Since similar structures as in La,Rh and Nd,Rh occurred at the Ln,Rh, stoichiometry in the alloys of the heavy rare earths, it was felt that the structure could be isotypic to a known structure occurring at the A,B, stoichiometry. A literature survey yielded a few structure types prevalent at this stoichiometry, of which the Th,Fe,-type” (Space Group P6,mc) was striking since Ce,Ni, is known to crystallize with this structure”. The powder X-ray diffraction patterns of Gd7Rh3, Y,Rh,, and Er,Rh, resembled the pattern of Ce,Ni,, and could be indexed with the hexagonal unit cell of the Th,Fe,-type structure. The patterns of La,Rh and Nd,Rh, which had been originally indexed with an orthorhomJ. Less-Common
Metuls,
26 (1972)
IN-206
CRYSTAL STRUCTURES OF SOME TABLE
Ln,Rh, Ln,Rh,,
LnRh,
PHASES
201
I
POWDER X-RAY
DI~RAC~ON
PATTERN OF
Er,Rh
Material : Alloy Er,,Rh,,, annealed for 7 days at 900’ C in vacuum and the container cooled in air. Method : Powder X-ray diffraction in a Guinier-de Wolff camera with CuKu X-rays. Structural Data : Er,Rh, Fe&-type, orthorhombic a,=7.075; b,=9.235; c,=6.218 8, Space Group : D:,6-Pnma. Atomic Positional Parameters: 4Er in4fc) x,~.z(.x=O.O21,.~=0.138); B=2.0,&’ 8Er in 8(d) x, y, 2 (x=0.180, y=O.O61, z=O.667); B=2.0 AZ 4Rh in 4(c) x, 4, z (x=0.389. z=O.937); B=O.S A’ Fo*s.
103sin2 0
VI) (101) (020) (111) (2W ~~~~
WI) (104 (220) (031) (112) (022) (131) (221) (122) (202) (230) (040) (212) (301) (231) (311) (113) (240) (123) (213) (322) (401) (250) (332) (251) (060) (143) (252)
obs.
cafe.
22.3 1 27.03 28.01 34.05 47.44 61.24 62.86 69.69 73.11 75.46 78.10 80.20 89.00 89.80 90.90 101.00 108.75 110.14 111.68 115.72 122.00 125.56 128.94 156.74 159.13 177.56 192.40 195.95 205.19 221.90 230.60 237.48 251.42 261.23 283.60 _-
22.35 27.25 27.88 34.22 47.48 61.52 62.86 69.83 73.39 75.36 78.11 80.36 89.40 89.98 90.74 101.27 109.00 110.21 111.52 115.97 122.21 125.59 129.18 157.26 159.00 178.17 192.87 196.23 205.30 221.73 231.08 237.1 I 250.92 261.81 283.25
I: talc
29.50 80.17 74.06 86.39 30.94 141.53 167.79 238.81 309.90 480.96 447.10 351.38 242.32 271.77 272.92 223.34 47.29 380.42 382.79 195.04 346.63 25.34 229.8 1 138.01 169.76 266.13 30.84 43.85 357.10 112.74 295.34 266.78 543.47 108.97 172.78
34.05 65.29 58.08 34.30 51.01 161.39 $86.43 244.93 307.48 434.49 451.77 344.98 207.13 278.00 297.15 263.33 109.18 354.98 344.56 161.62 360.37 65.72 178.92 131.47 191.51 293.36 56.06 53.49 373.29 162.21 344.46 273.78 477.55 161.50 187.04 _..J. Less-Common Metals, 26 (1972) 199-206
TABLE Material: Method Structural Data :
II
:
annealed diffraction
Rel. Int.
103sin% obs.
w (210) 0334 W)
(211)
1::; (301) (202) (220) (212) IA/ (401) (321) (410) (203) 1 (411) (402) (213) (303) (322) (501) (330) 1 (412) (421) (313) 1
24.55 59.66 64.31 73.02 76.00 76.72 90.10 92.90 98.60 102.25 124.20 127.00 136.16 152.50 178.47 179.20 195.40 201.00 205.05 222.04 226.50 229.70 243.93 255.78 258.05 278.08
I!:; 1
;::j
1
for 7 days at 900” C in vacuum and the container cooled in air. in a GuinierAe Wolff camera with CuKa X-rays.
Er,Rh,, Th,Fe,-type, hexagonal a, = 9.643, c0 = 6.070 8, Space Group : C&-P6,mc. Atomic Positional Parameters (as in Ce,Ni,“): 2Er in 2(b) f, 4, z (z=O.789) 6Er in 6(c) x,51;z(x=O.l25, z=O) 6Er in 6(c) x,sI; 2(x=0.539, z=O.801) 6Rh in 6(c) x,Y, z(x=O.812, z=O.OSO) B=O for all positions.
(hkl)
[:;:;
Er,Rh,
POWDERX-RAYDIFFRACTIONPA~NOF
Alloy Er,,Rh,,, Powder X-ray
(601) (413) 1 (512) (431) (520) 1 (521) (224) (432) J. Less-Common
281.68 307.22 324.10 328.76 332.30 348.97 361.01 381.04
Metals,
talc. 24.65 59.64 64.52 73.04 75.77 76.68 90.08 92.81 98.60 102.24 124.16 126.89 136.32 152.45 178.01 178.92 179.25 195.05 200.84 204.81 221.85 226.52 229.13 230.04 243.44 254.69 255.93 258.08 277.52 280.25 281.49 306.72 307.17 322.85 324.09 328.64 331.37 332.28 348.41 360.32 379.76
obs. VW
st vvw
vst vvst st W
vst vst vst st st vvw W
st st st vvw VW
vst vst vst vvw vvw W VW VW
vvw VW
vvw VW VW VW
vvw
26 (1972) 199-206
talc. 39.4 145.0 32.5 467.6 1000.0 171.1 87.7 534.9 478.1 398.5 102.9 99.8 22.2 79.2 100.7 5.3 89.4 99.4 39.2 53.7 265.6 238.1 228.1 172.6 1 32.6 11.1 32.5 1 78.7 49.4 25.2 33.3 1 0.0 33.5 1 35.8 67.1 1 32.4 57.0 21.5 97.4 84.9 61.3
CRYSTAL STRUCTURES OF SOME Ln,Rh,
Ln,Rh3, LnRh,
203
PHASES
bit unit cell related in dimensions to the unit cell of the Fe&-type structure, were reindexedwiththesmallerhexagonalunitcelloftheTh,Fe,-typestructure.Ananalogous phase occurred in the Ce-Rh system in the alloy Ce,Rh. Alloys Ln,,Rh,, in the La-Rh, Ce-Rh and Nd-Rh systems were heterogeneous and contained the Th,Fe,-type phases with appreciable amounts of the immediately next Rh-rich phases. Alloys Ln,5Rh25 (Ln = La, Ce, Nd) were single phase, and since there-was negligible weight loss during melting and annealing of these alloys, it could only be concluded that the Th,Fe,type structure occurs possibly as a defect structure in the alloys of the light rare earths with rhodium. The previous finding that the Fe,C-type structure occurs as a defect structure in the Nd-Rh system3 favours this hypothesis. An average vacancy.content oft Ln-atom and l+Rh-atoms per unit cell was assumed, which shifts the stoichiometry from A,B, (14A+6B atoms per unit cell) to A,B (139A+4+ B atoms per unit cell). The relative intensities of X-ray diffraction lines were calculated using the atomic positional parameters as in Ce,Ni, lo . The caiculated and observed relative intensities for Er,Rh, matched quite well and indicated no serious necessity for parameter refinement. The powderx-ray diffraction pattern of Er,Rh, (Th,Fe,-type) is given in Table II. The relative intensities calculated for La,Rh (Th,Fe,-type) with TABLE III CRYSTALSTRUCTURALDATAOFSOME
Ln,Rb,Ln,Rh,
Phase
Lattice parameters ._
Structure type
Nd,Rh3 Gd,Rh Y,Rh Er,Rh La,Rh La,Rh, Ce,Rh Nd,Rh Gd,Rh,
16
Y,Rh, Y,Rh3i6 Er,Rh, LaRh,(l)’ fh)’ CeRh, NdRh, Nd,Co3i4*** La,Ir,i6 Ce,Ni,” Y,Pt,= Yb,Au,‘=
Fe& Fe& Fe& Fe,C Th,Fe, Th,Fe, Th,Fe, Th,Fe, Th,Fe, Th,Fe, Th,Fe, Th,Fe, CeNi, PuNi, Cu,Au CeNi, Th,Fe, Th,Fe, Th,Fe, Th,Fe, Th,Fe, Th,Fe,
AND
LnRh,
PHASES
(A)
Unit cell volume
a0
bo
co
co/b,
(A-')
Meam atomic oolume (A3/atom)
7.258 7.195 7.138 7.075 10.200 10.145 10.005 10.030 9.840 9.775 9.793 9.643 5.305 5.326 4.012 5.282 9.888 10.235 9.92 9.910 9.864 10.372
9.840 9.540 9.438 9.235
6.43 1 6.328 6.319 6.218 6.500 6.434 6.356 6.336 6.210 6.190 6.196 6.070 17.59 26.46
0.654 0.663 0.669 0.673 0.637 0.634 0.635 0.632 0.631 0.633
459.4 434.2 425.7 406.2 586.3 573.3 558.6 552.0 520.4 512.0
32.80* 27.f4 26.61 25.39 32.57** 28.67 31.03** 30.67** 26.02 25.60
0.630 3.315 4.968
17.52 5.937 6.473 6.33 6.293 6.299 6.514
3.317
488.8 428.7 649.9 64.55 423.9
24.44 17.86 18.05 16.14 17.66
0.638 0.635
535.0
26.75
+ (1) and (h) stand for the low and high temperature modification, respectively. * Calculated with 14 atoms per unit cell. (i Nd-atom and li Rh-atom vacancies.) ** Calculated with 18 atoms per unit cell. (8 La, Ce or Nd-atom and 11 Rh-atom vacancies.) l ** Possibly impurity-stabilized, J. L~~~-Commo~ Metals,
26 (1972) 199-206
204
A. RAh4AN
similar atomic positional parameters and different vacancy schemes (( 1) No vacancies in the La and Rh positions. (2) No vacancy in the La-positions, 16.67 ‘A vacancy in the Rh-position ; 26.3 at. % Rh. (3) 3.57 % Vacancy in the La-positions and 25 % vacancy in the Rh-positions ; 25 at. % Rh) yielded nearly similar results. The agreement between the relative observed and calculated intensities was fairly good except for three or four weak lines. It appears that further work in X-ray diffraction and electron microprobe analysis with single crystals will be needed to learn more precisely about the crystal structure of the La,Rh, etc. phases. LnRh, phases
The structures of LaRh, (CeNi, and PuNi,-types) and NdRh, (CeNi,-type) were reported in earlier papers 1,3. In the present work it was found that CeRh, crystallizes in the Cu&.t-type structure with a lattice parameter a,=4.012 A. The lattice parameter did not vary with composition, indicating fixed stoichiometry. An intermediate phase of the LnRh, stoichiometry was not encountered in the Er-Rh system. The alloy, E,,Rh,,, was two-phase and contained ErRh, (MgCu,-type) in equilibrium with Rh(Er) f.c.c. solid solution phase. The lattice parameters and other characteristics of some Ln,Rh, Ln,Rh, and LnRh, phases are given in Table III. DISCUSSION
The Fe,C-type structure occurs in the Nd-Rh, Gd-Rh, Y-Rh and Er-Rh systems, but it does not occur in the Ce-Rh and La-Rh systems. In the Ln-Rh alloys in which the Fe,C-type structure occurs, the radius ratio rA/rB, varies between 1.355 (rNJrRh) and 1.303 (rEr/rRh). When the radius ratio increases to 1.394 (rLa/rRh) the structure does not occur. The Fe,C-type structure is known to occur also in Ln,Ni” and Ln,Co’ 3 phases. In the systems with Ni or Co, the structure occurs in all the lanthanide (La-Lu) systems, and the radius ratio varies between 1.504 (rr,/r& and 1.397 (rLu/rNi). If the size ratio is the determining factor for the occurrence of the structure, the Fe,C-type should have been encountered also in the La-Rh and Ce-Rh systems since the radius ratios are favourable. The non-occurrence of this structure in these and in Ln-Fe systems’ 3, and the shift in its stoichiometry in the Nd-Rh system toward rare-earth-richer composition indicate that the electronic structure of the atoms play the dominant role in stabilizing this structure. A few phases of the Fe,C-type in which the atomic positional parameters have been determined and reported in the literature are given in Table IV. The radius ratios, r,&,, of the phases vary between 1.15 (as in Al,Ni) and 1.504 (as in La,Ni). The Fe,C-type structure has representatives which can be grouped into two branches as is the case with several crystal structures. Except in AI,Ni, both components are transition elements in the phases of Branch I. The A-component comes from Group III while the B-component comes from Group VIII, excluding possibly all the Fe-group elements. (Whether Ru or OS can act as B-components and stabilize this structure is not known.) Both component atoms are strongly metallic in their elemental states. Branch II has isotypic phases in which only the A-component is a transition element which comes from Group VIII, while the B-component is a non-transition element in which strong covalent type bonding prevails in the elemental state. J. Less-Common Metals, 26 (1972) 199-206
CRYSTAL STRUCTURES OF SOME Ln,Rh,
Ln,Rh,,
LnRh,
205
PHASES
The atomic positional parameters of some of the isotype phases listed in Table IV can be analyzed to see whether any deductions can be made regarding their variations with variations in sizes of the component atoms. All the shown positional parameters except the Z-parameter of the B-component atom decrease with a decrease in the size ratio, rA/rs, in phases of Branch I. This decrease is relatively large for the parameters of the A-component atom in the 4-fold position. Z, of the B-component atom appears to increase slightly. In phases of Branch II, X,, Z, and Y, decrease with a decrease of rJrB. X2, Z, and Z, oscillate, while X3 shows a definite increase. Since X, and Z, refer to the positional parameters of light atoms like carbon and boron in Fe,C and Ni,B, respectively, it is possible that they might not have been determined very accurately and no genuine conclusions on their variations can be drawn. It can, hence, be postulated that most of the parameters of the chosen atoms in the structure (shown in the Table) decrease with a decrease in the radius ratio rJrg. TABLE IV ATOMIC POSITIONAL PARAMETERSIN SOMEFe,C-TYPE PHASES(SETTING Pnma ) Isotypic phases
Atomic positional parameters
Branch I La,Co*
Brunch I1 Ho3Co**
Er,Rh**
Al,Ni*f
Fe,C**
Ni,S*
Pd,Si*
4A atoms in 4(c) x1, a, z1 Xl 0.0461 ZI 0.1434
0.033 0.135
0.021 0.138
0.011 0.085
0.040 0.167
0.028 0.136
0.0053 0.0964
8A atoms in 8(d) x2, y,, z2 X2 0.1688 YZ 0.0685 =z 0.6727
0.180 0.064 0.680
0.180 0.061 0.667
0.174 0.053 0.644
0.183 0.065 0.667
0.178 0.061 0.653
0.1810 0.0508 0.6783
4B atoms in 4(c) xj, a, z3 x3 0.3829
0.391
0.389
0.369
:: (A) rg (A)
0.9396 1.871 1.252
0.936 1.761 1.252
0.937 1.748 1.342
0.945 1.429 1.244
0.360 0.970 1.260 0.914
0.390 0.933 1.244 0.980
0.3976 0.9696 1.373 1.173
1.494
1.407
1.303
1.150
1.38
1.270
1.170
rA Ze f.
9
* Parameters determined ** Parameters determined
13
PW
from X-ray diffraction
19
8
20
21
data of single crystals.
from Powder X-ray diffraction
photographs.
A few rare earth-noble metal alloy phases which possess the Th,Fe,-type structure are described in the literature 14- l6 This structure is now found to occur in all the chosen Ln-Rh systems. In the La-Rh, Ce-Rh and Nd-Rh systems, the structure occurs at the Ln,Rh stoichiometry, while in the investigated systems of the heavy rare earths, the regular Ln,Rh, stoichiometry is preferred. It is inferred that the shift in the stoichiometry in the systems of the light rare earths can be due to J. Less-Common
Metals, 26 (1972) 199-206
206
A. RAMAN
electronic effects. It is also likely that the phase La,Rh possesses a small range of homogeneity. A look at the table of representatives of this structure provided by Schubert I7 shows that this structure also has two branches as elucidated for the Fe&J-type. Unlike LaRh, and NdRh,, CeRh, possesses the relatively simple Cu,Au-type structure. The interatomic distance between a Ce atom and a Rh atom in the 1Zfold coordination polyhedron of CeRh, (Cu,Au-type) is 2.837 A. Assuming that the Rh atom does not undergo any contraction in the structure, that isassumingr~~ (CN 12)= 1.342& the radius of the Ce atom in the structure is 1.495 .& Using Pauling’s relationship” for computing the number of bonding electrons of the Ce atom, R(l)- R(n) = 0.300 log n, where “n” is the number of resonant electrons in bond, it becomes 3.2. Conversely, the radius of the Ce atom calculated using only three resonant electrons is 1.503 A, whereas the observed value is 1.495 A. Pauling states that “there is some evidence that the constant (taken as 0.3~} varies with the kind of atom and with the type of bond’“18, and with this uncertainty it can be assumed that the Ce atom contributes three resonant electrons, as is the general case with most of the rare earth atoms, to the Ce-Rh bonds in CeRh,. The interatomic bonding in this phase can be considered to be metallic.
Thanks are due to Professor S. F. Watkins of the Chemistry Department at LSU, Baton Rouge for kindly allowing the author to use the X-ray 67 full matrix least-square-refinement computer program. REFERENCES I 2 3 4
5 6 7
8 9 10 11
P. P. SINGH AND A. RAMAN, Trans. AIM& 245 (1969) 1561. A. V. VIRKAR, P. P. SIHG~~AND A. RAMAN, Inory. Chem., 9 (1970) 353. P. P. SINGH AND A. RAMAN, Met. Trans., 1 (1970) 233. K. YVON, W. JEKXHKO ANU E. PART&, A Fortran IV Program for Intensity Calculation of Powder Patterns (1969 Version), Univ. Penn., Lab. for Research on the Structure of Matter, Philadelphia, Penn. 19104, U.S.A. J. M. STEWART,X-R~y67, A Full Matrix Leust SquczresRefmement ~~puter Program, Univ. Maryland. College Park, Md., U.S.A. International Tablesfor X-ray Crystallography, Vol. 3, The Kynoch Press, Birmingham, England, 1959. A. WESTOREN, Jernkontorets Ann., 87 (1932) 451; Strukturbericht, 2 (1928-32) 33. H. LIMIN AND N. J. PETCW,J. Iron Steel Inst., 142 (1940) 95. D. T. CROMERAND A. C. LARSON, Acra Crysf., 14 (1961) 1226. J. V. FLORIO, N. C. BAENZIGERANU R. E. Rwmra, Acta Cry.@., 9 (1956) 367. R. B. ROOF, JR., A. C. LARWN AND D. T. CROMER,Acia Cryst., I4 (1961) 1084.
12 R. LEXAIREAND D. PACCARD. Buli. Sm. Frune. Mine& Crist., 90 (1967) 311. 13 K. H. J. BUSCHOWAND A. S. VAN DERGoor, J. Less-Common Metals, 18 (1969) 309. 14 P. P. SINGH AKD A. RAMAX, Mater. Res. BUN., 3 (1968) 843. 15 A. IANDELLIAND A. PALENZONA,J. Less-Common Metals, 18 (1969) 221. 16 T. H. GEBALLE,B. T. MAIT~IAS, V. B. COXFTON, E. CORENZWET,G. W. HULL, Jn. AND L. D. LONGINOTTI, Phy.r. Ret’., 137A (1965) 119. 17 K. SCIIUBE~T, Kr~stalI~t~4~iure~ Zweikom~~ntiger Phasen, Springer Verlag, Berlin, 1964. p. 264. 18 L. PAULING.J. Am. Chem. Sot., 69 (1947) 542. 19 A. J. BRADLEYAND A. TAYLOR, Phil. Mug., 23 (1937) 1049. 20 S. RUMIQUIST, Acta Chem. Stand., I2 (1958) 658. 21 B. ARON~N AND A. LYLUND,Acta Chem. Scar& 14 (1960) 1011.
J. Less-~ommoo Met&,
26 (1972) 199-206
JOURNAL OF THE LESS-COMMON METALS Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands
CRYSTAL STRUCTURES
OF SOME Ln,Rh, Ln,Rh,
AND LnRh, PHASES*
A. RAMAN Materials Group, Department of Engineering Science, Louisiana State University, Baton Rouge, La. 70803 (U.S.A.) (Received
June 9th, 1971)
SUMMARY
The Fe&-type structure occurs in the phases Nd,Rh, Gd,Rh, Y,Rh and Er,Rh. The atomic positional parameters in the Pnma space group are: 4Er in 4(c) 8Er in 8(d) 4Rh in 4(c)
0.021,0.250,0.138 0.180, 0.061,0.667 0.389, 0.250,0.937
B, =2.0 A2 B, = 2.0 A2 B, = 0.5 A2
Phases with the Ln,Rh, stoichiometry in the Gd-Rh,Y-Rh and Er-Rh systems possess the Th,Fe,-type structure. The same structure occurs in the alloys of the light rare earths, La, Ce and Nd at the Ln,Rh stoichiometry. Unlike LaRh, and NdRh,, CeRh, crystallizes in the Cu,Au-type structure. It is shown that electronic factors rather than the size factor play prominent roles in stabilizing these structures in the rare-earth alloys.
INTRODUCTION
The crystal structures of several alloy phases of the La-Rh and Nd-Rh systems were described in earlier papers by the author’-3. While an Fe,C-type phase was encountered in the Nd-Rh system3 at off-stoichiometric composition, near Nd,, Rh,,, an analogous phase was not encountered in La-Rh alloys’. The study was extended to determine whether the Fe,C-type structure occurs in other rare earthhrhodium systems. Also it was of interest to see whether the phases which occur at Ln,Rh and LnRh, stoichiometries in the La-Rh and Nd-Rh systems occur in other Ln-Rh systems. The results of this study are described in this paper. EXPERIMENTAL
Suitable alloys at and near the Ln,Rh, Ln,Rh, and LnRh3 stoichiometries were melted from reactor grade rare earths (La, Ce, Nd, Gd, Y and Er-99.9 + % by weight, supplied by Lunex Company, Pleasant Valley. Iowa) and rhodium (99.92 + %, supplied by Engelhard Industries, Inc., Newark, New Jersey) in an arc-melting furnace * Ln
represents
a lanthanide,
La Ce, Nd, Cd. Y or Er. J. Less-Common Metals, 26 (1972) 199-206
A. RAMAN
200
under argon atmosphere. The alloys were wrapped in molybdenum foils and homogenized at suitable high temperatures in evacuated quartz tubes. The crystal structural data of phases present in the alloys were evaluated from Guinier X-ray diffraction photographs taken with CuKa radiations. The relative intensities in the powder patterns of selected alloy phases were calculated using a computer program written by Yvon, Jeitschko and ParthC4. The atomic positional parameters in an Fe,C-type phase were relined using a full matrix least-square refinement program written by Stewart’. The needed atomic scattering factors for X-rays were taken from International Tables for X-ray Crystallography6. RFSJLTS
Ln,Rh phases
Phases with the Fe&-type crystal structure’** were encountered at Ln,Rh stoichiometry in the systems Gd-Rh, Y-Rh and Er-Rh. Unlike as in Nd-Rh alloys, no shift in composition was observed. An analogous phase was not obtained in the Ce-Rh system in the alloys containing 20-30 at. % Rh. The relative intensities of the lines in the X-ray diffraction photographs of Er,Rh (Fe&-type; Space Group Prima) were calculated assuming the atomic positional parameters as in La&o (Fe,C-type)‘. The calculated relative intensities of diffraction lines did not match well with the observed relative intensities of several linesandtheresidualindex,R=~~F,~-IF,II/IF,I, was 0.22. The structure was improved using 35 well-defined, single reflections in the powder diffraction pattern whose relative intensities were judged visually with a calibrated intensity scale. After one cycle of refinement, the R-index dropped to 0.12 and it did not vary by more than +0.003 in five subsequent cycles. In this attempt, the isotropic temperature factors for the erbium and rhodium atoms were maintained constant at 2.0 and 0.5 A’, respectively. When the temperature factors were allowed to vary from 1 A2 for all atoms along with the variable positional parameters, those of the Er atoms rose to 2.84 and 4.1 A’ for the 4-fold and 8-fold positions, respectively, while that of the Rh atoms became - 4.57 A2, and the R-index obtained was 0.11. The improved atomic positional parameters and the observed and calculated structure factors for the 35 reflections are listed in Table I along with the data from the powder X-ray diffraction pattern of Er,Rh. Ln7Rh, phases
Intermediate phases of Ln,Rh, stoichiometry were encountered in the Gd-Rh, Y-Rh and Er-Rh systems. Their powder patterns resembled the patterns of La,Rh and Nd,Rh, already reported in the literature ‘v3. Since similar structures as in La,Rh and Nd,Rh occurred at the Ln,Rh, stoichiometry in the alloys of the heavy rare earths, it was felt that the structure could be isotypic to a known structure occurring at the A,B, stoichiometry. A literature survey yielded a few structure types prevalent at this stoichiometry, of which the Th,Fe,-type” (Space Group P6,mc) was striking since Ce,Ni, is known to crystallize with this structure”. The powder X-ray diffraction patterns of Gd7Rh3, Y,Rh,, and Er,Rh, resembled the pattern of Ce,Ni,, and could be indexed with the hexagonal unit cell of the Th,Fe,-type structure. The patterns of La,Rh and Nd,Rh, which had been originally indexed with an orthorhomJ. Less-Common
Metuls,
26 (1972)
IN-206
CRYSTAL STRUCTURES OF SOME TABLE
Ln,Rh, Ln,Rh,,
LnRh,
PHASES
201
I
POWDER X-RAY
DI~RAC~ON
PATTERN OF
Er,Rh
Material : Alloy Er,,Rh,,, annealed for 7 days at 900’ C in vacuum and the container cooled in air. Method : Powder X-ray diffraction in a Guinier-de Wolff camera with CuKu X-rays. Structural Data : Er,Rh, Fe&-type, orthorhombic a,=7.075; b,=9.235; c,=6.218 8, Space Group : D:,6-Pnma. Atomic Positional Parameters: 4Er in4fc) x,~.z(.x=O.O21,.~=0.138); B=2.0,&’ 8Er in 8(d) x, y, 2 (x=0.180, y=O.O61, z=O.667); B=2.0 AZ 4Rh in 4(c) x, 4, z (x=0.389. z=O.937); B=O.S A’ Fo*s.
103sin2 0
VI) (101) (020) (111) (2W ~~~~
WI) (104 (220) (031) (112) (022) (131) (221) (122) (202) (230) (040) (212) (301) (231) (311) (113) (240) (123) (213) (322) (401) (250) (332) (251) (060) (143) (252)
obs.
cafe.
22.3 1 27.03 28.01 34.05 47.44 61.24 62.86 69.69 73.11 75.46 78.10 80.20 89.00 89.80 90.90 101.00 108.75 110.14 111.68 115.72 122.00 125.56 128.94 156.74 159.13 177.56 192.40 195.95 205.19 221.90 230.60 237.48 251.42 261.23 283.60 _-
22.35 27.25 27.88 34.22 47.48 61.52 62.86 69.83 73.39 75.36 78.11 80.36 89.40 89.98 90.74 101.27 109.00 110.21 111.52 115.97 122.21 125.59 129.18 157.26 159.00 178.17 192.87 196.23 205.30 221.73 231.08 237.1 I 250.92 261.81 283.25
I: talc
29.50 80.17 74.06 86.39 30.94 141.53 167.79 238.81 309.90 480.96 447.10 351.38 242.32 271.77 272.92 223.34 47.29 380.42 382.79 195.04 346.63 25.34 229.8 1 138.01 169.76 266.13 30.84 43.85 357.10 112.74 295.34 266.78 543.47 108.97 172.78
34.05 65.29 58.08 34.30 51.01 161.39 $86.43 244.93 307.48 434.49 451.77 344.98 207.13 278.00 297.15 263.33 109.18 354.98 344.56 161.62 360.37 65.72 178.92 131.47 191.51 293.36 56.06 53.49 373.29 162.21 344.46 273.78 477.55 161.50 187.04 _..J. Less-Common Metals, 26 (1972) 199-206
TABLE Material: Method Structural Data :
II
:
annealed diffraction
Rel. Int.
103sin% obs.
w (210) 0334 W)
(211)
1::; (301) (202) (220) (212) IA/ (401) (321) (410) (203) 1 (411) (402) (213) (303) (322) (501) (330) 1 (412) (421) (313) 1
24.55 59.66 64.31 73.02 76.00 76.72 90.10 92.90 98.60 102.25 124.20 127.00 136.16 152.50 178.47 179.20 195.40 201.00 205.05 222.04 226.50 229.70 243.93 255.78 258.05 278.08
I!:; 1
;::j
1
for 7 days at 900” C in vacuum and the container cooled in air. in a GuinierAe Wolff camera with CuKa X-rays.
Er,Rh,, Th,Fe,-type, hexagonal a, = 9.643, c0 = 6.070 8, Space Group : C&-P6,mc. Atomic Positional Parameters (as in Ce,Ni,“): 2Er in 2(b) f, 4, z (z=O.789) 6Er in 6(c) x,51;z(x=O.l25, z=O) 6Er in 6(c) x,sI; 2(x=0.539, z=O.801) 6Rh in 6(c) x,Y, z(x=O.812, z=O.OSO) B=O for all positions.
(hkl)
[:;:;
Er,Rh,
POWDERX-RAYDIFFRACTIONPA~NOF
Alloy Er,,Rh,,, Powder X-ray
(601) (413) 1 (512) (431) (520) 1 (521) (224) (432) J. Less-Common
281.68 307.22 324.10 328.76 332.30 348.97 361.01 381.04
Metals,
talc. 24.65 59.64 64.52 73.04 75.77 76.68 90.08 92.81 98.60 102.24 124.16 126.89 136.32 152.45 178.01 178.92 179.25 195.05 200.84 204.81 221.85 226.52 229.13 230.04 243.44 254.69 255.93 258.08 277.52 280.25 281.49 306.72 307.17 322.85 324.09 328.64 331.37 332.28 348.41 360.32 379.76
obs. VW
st vvw
vst vvst st W
vst vst vst st st vvw W
st st st vvw VW
vst vst vst vvw vvw W VW VW
vvw VW
vvw VW VW VW
vvw
26 (1972) 199-206
talc. 39.4 145.0 32.5 467.6 1000.0 171.1 87.7 534.9 478.1 398.5 102.9 99.8 22.2 79.2 100.7 5.3 89.4 99.4 39.2 53.7 265.6 238.1 228.1 172.6 1 32.6 11.1 32.5 1 78.7 49.4 25.2 33.3 1 0.0 33.5 1 35.8 67.1 1 32.4 57.0 21.5 97.4 84.9 61.3
CRYSTAL STRUCTURES OF SOME Ln,Rh,
Ln,Rh3, LnRh,
203
PHASES
bit unit cell related in dimensions to the unit cell of the Fe&-type structure, were reindexedwiththesmallerhexagonalunitcelloftheTh,Fe,-typestructure.Ananalogous phase occurred in the Ce-Rh system in the alloy Ce,Rh. Alloys Ln,,Rh,, in the La-Rh, Ce-Rh and Nd-Rh systems were heterogeneous and contained the Th,Fe,-type phases with appreciable amounts of the immediately next Rh-rich phases. Alloys Ln,5Rh25 (Ln = La, Ce, Nd) were single phase, and since there-was negligible weight loss during melting and annealing of these alloys, it could only be concluded that the Th,Fe,type structure occurs possibly as a defect structure in the alloys of the light rare earths with rhodium. The previous finding that the Fe,C-type structure occurs as a defect structure in the Nd-Rh system3 favours this hypothesis. An average vacancy.content oft Ln-atom and l+Rh-atoms per unit cell was assumed, which shifts the stoichiometry from A,B, (14A+6B atoms per unit cell) to A,B (139A+4+ B atoms per unit cell). The relative intensities of X-ray diffraction lines were calculated using the atomic positional parameters as in Ce,Ni, lo . The caiculated and observed relative intensities for Er,Rh, matched quite well and indicated no serious necessity for parameter refinement. The powderx-ray diffraction pattern of Er,Rh, (Th,Fe,-type) is given in Table II. The relative intensities calculated for La,Rh (Th,Fe,-type) with TABLE III CRYSTALSTRUCTURALDATAOFSOME
Ln,Rb,Ln,Rh,
Phase
Lattice parameters ._
Structure type
Nd,Rh3 Gd,Rh Y,Rh Er,Rh La,Rh La,Rh, Ce,Rh Nd,Rh Gd,Rh,
16
Y,Rh, Y,Rh3i6 Er,Rh, LaRh,(l)’ fh)’ CeRh, NdRh, Nd,Co3i4*** La,Ir,i6 Ce,Ni,” Y,Pt,= Yb,Au,‘=
Fe& Fe& Fe& Fe,C Th,Fe, Th,Fe, Th,Fe, Th,Fe, Th,Fe, Th,Fe, Th,Fe, Th,Fe, CeNi, PuNi, Cu,Au CeNi, Th,Fe, Th,Fe, Th,Fe, Th,Fe, Th,Fe, Th,Fe,
AND
LnRh,
PHASES
(A)
Unit cell volume
a0
bo
co
co/b,
(A-')
Meam atomic oolume (A3/atom)
7.258 7.195 7.138 7.075 10.200 10.145 10.005 10.030 9.840 9.775 9.793 9.643 5.305 5.326 4.012 5.282 9.888 10.235 9.92 9.910 9.864 10.372
9.840 9.540 9.438 9.235
6.43 1 6.328 6.319 6.218 6.500 6.434 6.356 6.336 6.210 6.190 6.196 6.070 17.59 26.46
0.654 0.663 0.669 0.673 0.637 0.634 0.635 0.632 0.631 0.633
459.4 434.2 425.7 406.2 586.3 573.3 558.6 552.0 520.4 512.0
32.80* 27.f4 26.61 25.39 32.57** 28.67 31.03** 30.67** 26.02 25.60
0.630 3.315 4.968
17.52 5.937 6.473 6.33 6.293 6.299 6.514
3.317
488.8 428.7 649.9 64.55 423.9
24.44 17.86 18.05 16.14 17.66
0.638 0.635
535.0
26.75
+ (1) and (h) stand for the low and high temperature modification, respectively. * Calculated with 14 atoms per unit cell. (i Nd-atom and li Rh-atom vacancies.) ** Calculated with 18 atoms per unit cell. (8 La, Ce or Nd-atom and 11 Rh-atom vacancies.) l ** Possibly impurity-stabilized, J. L~~~-Commo~ Metals,
26 (1972) 199-206
204
A. RAh4AN
similar atomic positional parameters and different vacancy schemes (( 1) No vacancies in the La and Rh positions. (2) No vacancy in the La-positions, 16.67 ‘A vacancy in the Rh-position ; 26.3 at. % Rh. (3) 3.57 % Vacancy in the La-positions and 25 % vacancy in the Rh-positions ; 25 at. % Rh) yielded nearly similar results. The agreement between the relative observed and calculated intensities was fairly good except for three or four weak lines. It appears that further work in X-ray diffraction and electron microprobe analysis with single crystals will be needed to learn more precisely about the crystal structure of the La,Rh, etc. phases. LnRh, phases
The structures of LaRh, (CeNi, and PuNi,-types) and NdRh, (CeNi,-type) were reported in earlier papers 1,3. In the present work it was found that CeRh, crystallizes in the Cu&.t-type structure with a lattice parameter a,=4.012 A. The lattice parameter did not vary with composition, indicating fixed stoichiometry. An intermediate phase of the LnRh, stoichiometry was not encountered in the Er-Rh system. The alloy, E,,Rh,,, was two-phase and contained ErRh, (MgCu,-type) in equilibrium with Rh(Er) f.c.c. solid solution phase. The lattice parameters and other characteristics of some Ln,Rh, Ln,Rh, and LnRh, phases are given in Table III. DISCUSSION
The Fe,C-type structure occurs in the Nd-Rh, Gd-Rh, Y-Rh and Er-Rh systems, but it does not occur in the Ce-Rh and La-Rh systems. In the Ln-Rh alloys in which the Fe,C-type structure occurs, the radius ratio rA/rB, varies between 1.355 (rNJrRh) and 1.303 (rEr/rRh). When the radius ratio increases to 1.394 (rLa/rRh) the structure does not occur. The Fe,C-type structure is known to occur also in Ln,Ni” and Ln,Co’ 3 phases. In the systems with Ni or Co, the structure occurs in all the lanthanide (La-Lu) systems, and the radius ratio varies between 1.504 (rr,/r& and 1.397 (rLu/rNi). If the size ratio is the determining factor for the occurrence of the structure, the Fe,C-type should have been encountered also in the La-Rh and Ce-Rh systems since the radius ratios are favourable. The non-occurrence of this structure in these and in Ln-Fe systems’ 3, and the shift in its stoichiometry in the Nd-Rh system toward rare-earth-richer composition indicate that the electronic structure of the atoms play the dominant role in stabilizing this structure. A few phases of the Fe,C-type in which the atomic positional parameters have been determined and reported in the literature are given in Table IV. The radius ratios, r,&,, of the phases vary between 1.15 (as in Al,Ni) and 1.504 (as in La,Ni). The Fe,C-type structure has representatives which can be grouped into two branches as is the case with several crystal structures. Except in AI,Ni, both components are transition elements in the phases of Branch I. The A-component comes from Group III while the B-component comes from Group VIII, excluding possibly all the Fe-group elements. (Whether Ru or OS can act as B-components and stabilize this structure is not known.) Both component atoms are strongly metallic in their elemental states. Branch II has isotypic phases in which only the A-component is a transition element which comes from Group VIII, while the B-component is a non-transition element in which strong covalent type bonding prevails in the elemental state. J. Less-Common Metals, 26 (1972) 199-206
CRYSTAL STRUCTURES OF SOME Ln,Rh,
Ln,Rh,,
LnRh,
205
PHASES
The atomic positional parameters of some of the isotype phases listed in Table IV can be analyzed to see whether any deductions can be made regarding their variations with variations in sizes of the component atoms. All the shown positional parameters except the Z-parameter of the B-component atom decrease with a decrease in the size ratio, rA/rs, in phases of Branch I. This decrease is relatively large for the parameters of the A-component atom in the 4-fold position. Z, of the B-component atom appears to increase slightly. In phases of Branch II, X,, Z, and Y, decrease with a decrease of rJrB. X2, Z, and Z, oscillate, while X3 shows a definite increase. Since X, and Z, refer to the positional parameters of light atoms like carbon and boron in Fe,C and Ni,B, respectively, it is possible that they might not have been determined very accurately and no genuine conclusions on their variations can be drawn. It can, hence, be postulated that most of the parameters of the chosen atoms in the structure (shown in the Table) decrease with a decrease in the radius ratio rJrg. TABLE IV ATOMIC POSITIONAL PARAMETERSIN SOMEFe,C-TYPE PHASES(SETTING Pnma ) Isotypic phases
Atomic positional parameters
Branch I La,Co*
Brunch I1 Ho3Co**
Er,Rh**
Al,Ni*f
Fe,C**
Ni,S*
Pd,Si*
4A atoms in 4(c) x1, a, z1 Xl 0.0461 ZI 0.1434
0.033 0.135
0.021 0.138
0.011 0.085
0.040 0.167
0.028 0.136
0.0053 0.0964
8A atoms in 8(d) x2, y,, z2 X2 0.1688 YZ 0.0685 =z 0.6727
0.180 0.064 0.680
0.180 0.061 0.667
0.174 0.053 0.644
0.183 0.065 0.667
0.178 0.061 0.653
0.1810 0.0508 0.6783
4B atoms in 4(c) xj, a, z3 x3 0.3829
0.391
0.389
0.369
:: (A) rg (A)
0.9396 1.871 1.252
0.936 1.761 1.252
0.937 1.748 1.342
0.945 1.429 1.244
0.360 0.970 1.260 0.914
0.390 0.933 1.244 0.980
0.3976 0.9696 1.373 1.173
1.494
1.407
1.303
1.150
1.38
1.270
1.170
rA Ze f.
9
* Parameters determined ** Parameters determined
13
PW
from X-ray diffraction
19
8
20
21
data of single crystals.
from Powder X-ray diffraction
photographs.
A few rare earth-noble metal alloy phases which possess the Th,Fe,-type structure are described in the literature 14- l6 This structure is now found to occur in all the chosen Ln-Rh systems. In the La-Rh, Ce-Rh and Nd-Rh systems, the structure occurs at the Ln,Rh stoichiometry, while in the investigated systems of the heavy rare earths, the regular Ln,Rh, stoichiometry is preferred. It is inferred that the shift in the stoichiometry in the systems of the light rare earths can be due to J. Less-Common
Metals, 26 (1972) 199-206
206
A. RAMAN
electronic effects. It is also likely that the phase La,Rh possesses a small range of homogeneity. A look at the table of representatives of this structure provided by Schubert I7 shows that this structure also has two branches as elucidated for the Fe&J-type. Unlike LaRh, and NdRh,, CeRh, possesses the relatively simple Cu,Au-type structure. The interatomic distance between a Ce atom and a Rh atom in the 1Zfold coordination polyhedron of CeRh, (Cu,Au-type) is 2.837 A. Assuming that the Rh atom does not undergo any contraction in the structure, that isassumingr~~ (CN 12)= 1.342& the radius of the Ce atom in the structure is 1.495 .& Using Pauling’s relationship” for computing the number of bonding electrons of the Ce atom, R(l)- R(n) = 0.300 log n, where “n” is the number of resonant electrons in bond, it becomes 3.2. Conversely, the radius of the Ce atom calculated using only three resonant electrons is 1.503 A, whereas the observed value is 1.495 A. Pauling states that “there is some evidence that the constant (taken as 0.3~} varies with the kind of atom and with the type of bond’“18, and with this uncertainty it can be assumed that the Ce atom contributes three resonant electrons, as is the general case with most of the rare earth atoms, to the Ce-Rh bonds in CeRh,. The interatomic bonding in this phase can be considered to be metallic.
Thanks are due to Professor S. F. Watkins of the Chemistry Department at LSU, Baton Rouge for kindly allowing the author to use the X-ray 67 full matrix least-square-refinement computer program. REFERENCES I 2 3 4
5 6 7
8 9 10 11
P. P. SINGH AND A. RAMAN, Trans. AIM& 245 (1969) 1561. A. V. VIRKAR, P. P. SIHG~~AND A. RAMAN, Inory. Chem., 9 (1970) 353. P. P. SINGH AND A. RAMAN, Met. Trans., 1 (1970) 233. K. YVON, W. JEKXHKO ANU E. PART&, A Fortran IV Program for Intensity Calculation of Powder Patterns (1969 Version), Univ. Penn., Lab. for Research on the Structure of Matter, Philadelphia, Penn. 19104, U.S.A. J. M. STEWART,X-R~y67, A Full Matrix Leust SquczresRefmement ~~puter Program, Univ. Maryland. College Park, Md., U.S.A. International Tablesfor X-ray Crystallography, Vol. 3, The Kynoch Press, Birmingham, England, 1959. A. WESTOREN, Jernkontorets Ann., 87 (1932) 451; Strukturbericht, 2 (1928-32) 33. H. LIMIN AND N. J. PETCW,J. Iron Steel Inst., 142 (1940) 95. D. T. CROMERAND A. C. LARSON, Acra Crysf., 14 (1961) 1226. J. V. FLORIO, N. C. BAENZIGERANU R. E. Rwmra, Acta Cry.@., 9 (1956) 367. R. B. ROOF, JR., A. C. LARWN AND D. T. CROMER,Acia Cryst., I4 (1961) 1084.
12 R. LEXAIREAND D. PACCARD. Buli. Sm. Frune. Mine& Crist., 90 (1967) 311. 13 K. H. J. BUSCHOWAND A. S. VAN DERGoor, J. Less-Common Metals, 18 (1969) 309. 14 P. P. SINGH AKD A. RAMAX, Mater. Res. BUN., 3 (1968) 843. 15 A. IANDELLIAND A. PALENZONA,J. Less-Common Metals, 18 (1969) 221. 16 T. H. GEBALLE,B. T. MAIT~IAS, V. B. COXFTON, E. CORENZWET,G. W. HULL, Jn. AND L. D. LONGINOTTI, Phy.r. Ret’., 137A (1965) 119. 17 K. SCIIUBE~T, Kr~stalI~t~4~iure~ Zweikom~~ntiger Phasen, Springer Verlag, Berlin, 1964. p. 264. 18 L. PAULING.J. Am. Chem. Sot., 69 (1947) 542. 19 A. J. BRADLEYAND A. TAYLOR, Phil. Mug., 23 (1937) 1049. 20 S. RUMIQUIST, Acta Chem. Stand., I2 (1958) 658. 21 B. ARON~N AND A. LYLUND,Acta Chem. Scar& 14 (1960) 1011.
J. Less-~ommoo Met&,
26 (1972) 199-206