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Crystal structure of phases of the YbGa system in the range 20–32 at.% Yb
331
Journal of the Less-Common Metals, 163 (1990) 331-338
CRYSTAL STRUCTURE OF PHASES OF THE Yb-Ga SYSTEM IN THE RANGE 20-32 AT.% Yb S. CIRAFICI and M. L. FORNASINI Istituto di Chimica Fisica, Universitri di Genova, Corso Europa 26, 16132 Genova (Italy) (Received April 4,199O)
Summary The region 20-32 at.% Yb of the Yb-Ga system was re-examined by X-ray and metallographic methods. Two new phases were identified: Yb,Ga, (Eu,Ga, type), 0122, space group Zmmm, a = 4.225(2) A, b = 4.340( 1) A, c = 25.665(g) A, which exists in a limited range of temperature estimated between 830 and 870 “C, and YbGa,_, with 0
1. Introduction In the Yb-Ga phase diagram [l] four phases have been identified: Yb,Ga (PbCl, type), YbGa (AuCu type), YbGa, (Cain, type) and YbGa, with unknown structure but probably isotypic with the phase CaGa,. Later another phase, YbGa, (PuGa, type), was found to form peritectically at 282 “C [2]. More recently, in a reexamination of the Ca-Ga system [3], the crystal structure of CaGa, was found to be a monoclinic distortion of the BaAl, type, and a new phase Ca,Ga, with a pseudo-tetragonal cell was identified as being isotypic with EqGas, a binary variant of the UsNi,Si, structure. Owing to the similarity between the Ca-Ga and Yb-Ga systems, it seemed interesting to re-investigate the part found between the Y bGa, andY bGa, compositions. 2. Experimental details The samples were prepared using elements supplied by Koch-Light Laboratories (Colnbrook, U.K.) with a stated purity of 99.8 wt.% for ytterbium and 0022-5088/90/$3.50
0 Elsevier Sequoia/Printed
in The Netherlands
332
99.999 wt.% for gallium. Hydrogen in the ytterbium metal was removed as described in ref. 4. For each sample of approximate mass 3 g stoichiometric amounts of the two metals were blended and pressed in tantalum crucibles, which were sealed by arc welding under pure argon. To ensure complete homogenization the mixtures were melted and shaken two or three times in a high frequency furnace under vacuum and cooled to room temperature. For each alloy several thermal treatments were applied, namely slow cooling, rapid quench and annealing at different temperatures: this procedure seemed reliable to identify the stability range of the compounds. Micrographic examination was carried out using standard techniques. No etching agent was used, as exposure to air was sufficient to ensure appropriate etching. X-ray analysis was performed with a Guinier-de Wolff camera or a powder diffractometer on powders mixed with silicon as an internal standard (a, = 5.43083 A). A single crystal of the phase YbGa,_, measuring 0.02 x 0.05 x 0.09 mm3, sealed under vacuum in a thin glass capillary, was mounted on an Enraf-Nonius CAD-4 automatic diffractometer, using graphite monochromated MO Ka radiation. The lattice constants were determined from 25 high angle reflections. In total 2166 intensities were collected in the o scan mode up to sin 0/n = 0.7 A- l, -18~h~18,O~k~18,0~1~11 with]h]>]k].Bothasemi-empiricalabsorption correction based on azimuthal scan data of the two top reflections and a spherical correction were applied, the linear absorption coefficient and ratio between the maximum and minimum transmission factors being 5 1.8 mrr- l and 4.9 respectively, and 757 independent reflections were obtained (R,, = 0.13). The principal programs used were LAZY PULVERIX [5] for calculating the powder pattern data, SHELX-76 [6] for structure refinement and SHELXS-86 [7] for structure solution. Atomic scattering factors and anomalous dispersion corrections were taken from international Tables forX-ray Crystallography [8].
3. Results
Crystal data of the compounds studied in this work are reported in Table 1 together with data from the literature for the other Yb-Ga phases. Alloys in the range 22-32 at.% Yb that were melted and slowly cooled were heterogeneous and their powder patterns contained the reflections of four phases, two of which are already known in the phase diagram, YbGa, (Cain, type) and YbGa,, and two new phases which were identified to be Yb,Ga, and YbGa, _-x.All these samples were microcrystalline, indicating that the primary crystals undergo several other reactions during cooling. 3.1. The Yb, Ga, and YbGa, phases It was impossible to obtain Yb,Ga, as a single phase, in spite of several trials on samples with this composition annealed at different temperatures. However, there are strong indications that this phase exists in a very narrow temperature range, since it was absent in the as-cast alloys, in an alloy quenched from 900 “C and in alloys annealed at 600 and 800 “C, but was present in an alloy annealed at
333
TABLE
1
Crystal data of the phases present in the Yb-Ga
system
type
Pearson symbol and space group
PbCl, AuCu Cain, Eu,Ga,
oP12-Pnma tP4-P4/mmm hP6-P6Jmmc oI22-Immm
YbGa,_. x=0.36(5) Y bGa,
-
hP54.3-P6/mmm
13.025( 2)
CaGa,
mSlO-C2/m
Y bGa,
PuGa,
tP14-P4/nbm
6.148( 1) p= 118.86(l) 5.849
Phase
Yb,Ga YbGa Y bGa, Yb,Ga,
Structure
a (A)
7.063 4.83 4.455 4.225(2)
b(A)
c(A)
Reference
5.050
9.427 3.94 7.199 25.665(g)
1 1 1 Present work Present work Present work
4.340( 1)
8.360( 1) 6.106(2)
6.084(2) 7.601
2
850 “C. It is reasonable to propose therefore that Yb,Ga, forms by peritectic reaction and decomposes by metatectic reaction at most 20 degrees above and below 850 “C respectively. This hypothesis is further confirmed by the powder data of the sample annealed at 800 “C and quenched in water, which showed only reflections of the YbGa, and YbGa, phases., By comparison with the powder patterns of Eu,Ga, [9] and Ca,Ga, [3], most reflections in the powder pattern of the sample annealed at 850 “C were indexed on the basis of the same orthorhombic structure. The remaining lines could be assigned to the neighbouring YbGa, and YbGa, phases. The lattice constants of Yb,Ga, listed in Table 1 are similar to those derived from single crystals by Palenzona and Cirafici [l], Q = b =4.32 A, c= 25.85 A, and attributed by these authors to the compound YbGa,. It is probable that primary crystals of the phase Yb,Ga,, formed by cooling from melts with a YbGa, composition, remain in a metastable condition and are easily picked out during the search for single crystals. On the other hand, a cell of such sizes does not match the powder pattern of the YbGa, phase, which is indexed instead on the basis of the monoclinic CaGa, structure [3]. The corresponding lattice parameters are given in Table 1. A pseudobinary compound Cq.,Yb,,,Ga, was also prepared as a single phase, crystallizing in the same monoclinic structure. The lattice constants a =6.162( 1) A, b=6.117(1) A, c=6.104(1) A, /3=118.87(l) are intermediate between those of the CaGa, and YbGa, phases. 3.2. The YbGa,_,pha.se A 25.0 at.% Yb alloy annealed at 600 “C was microscopically homogeneous and its powder pattern showed reflections of a new phase, here called YbGa,_ x. Although the strongest reflections correspond to a hexagonal cell with lattice periods close to those of the AlB, structure, the different composition and the numerous unindexed lines require a larger cell and an atomic arrangement only related to the AlB, type. In fact, single crystal X-ray analysis led to a hexagonal cell
334
with periods three and two times respectively greater than the a and c constants of the AlE$ subcell, namely a = 13.02.5( 2) A, c = 8.360( 1) A. The structure was determined to be in the space group P6/mmm by employing Patterson methods and isotropically refining with unit weights using 204 reflections with F0 > 3a(F0). Since the thermal parameters of three atoms, Yb(4), Ga(2) and Ga( 5), showed values higher than the other atoms, the occupation factors of the corresponding sites were allowed to vary, while the occupation of the Ga(4) site for which a full filling would give too short a Ga-Ga distance was fixed at 50%. At convergence R = 0.080, the maximum and minimum height in difference Fourier synthesis were 10.5 and - 10.6 e A- 3, and the final composition was Owing to the low number of observed intensities, no anisotropic Yb14.9(1p39.4(7). refinement was applied. The atomic coordinates and thermal parameters are reported in Table 2, while interatomic distances are given in Table 3.
TABLE 2 Atomic coordinates and thermal isotropic parameters for Yb,,,,,IGa,,,,C,,.
Wl) W2) Yb(3) W4) Wl) GaG’) G43) W4) Gab)
6(k) 6(j) 2(d) l(a) 12(o) 12(o) 12(o) 6(m) 6(l)
ESDs are in parentheses
x
Y
Z
Occupation (%)
U(K)
0.3367( 10) 3.3480( 7) l/3 0.0 0.1118(6) 0.223(2) 0.445( 1) 0.067( 2) 0.397( 2)
0.0 0.0 213 0.0 2x 2x 2x 2x 2x
0.5 0.0 0.5 0.0
100 100 100 86( 12) 100 62(6) 100 50 84(8)
0.01 l(2) 0.001(2) O.OOl(3) 0.026( 15) 0.003(2) 0.008(9) 0.013(7) 0.001(7) 0.019(8)
0.201(2) 0.244(4) 0.265(3) 0.5 0.0
The presence of the YbGa,_ x phase was confirmed in other samples prepared in the range 22.2-27.4 at.% Yb and annealed at 600 “C. Except for the extreme compositions, where some reflections were assigned to the neighbouring phases YbGa, and YbGa,, all powder patterns could be indexed according to the large hexagonal cell. The lattice constants were very close to those obtained from the crystal. The incomplete filling of some ytterbium and gallium sites in this structure may be responsible for the existence of a range of homogeneity. Moreover, decreasing the ytterbium and increasing the gallium content while changing the composition did not alter the cell dimensions. To estimate approximately the temperature of formation of the YbGa,_ x phase, two 27.3 at.% Yb alloys were particularly significant: one of them, annealed at 800 “C, showed in its powder pattern only reflections of the compounds YbGa, and YbGa,, while the other, annealed at 730 “C, a few degrees below the peritectic arrest of YbGa,, gave YbGa,_, as the main phase and weaker reflections of the YbGa, phase. Therefore, the formation of YbGa,_, by peritectoid reaction can be proposed to occur at a temperature between 730 and 755 “C.
335 TABLE
3
Interatomic distances (A) in Yb,,,Ga
3y,4up to d/D = 1.13. ESDs are in parentheses
Yb(l)-4Ga(3) -Ga( 4) -4Ga( 2) -4Ga( 1) -2Yb(2) -Yb(l) -2Yb(3) -2Yb( 1) Ga(l)-2Ga( 1) -Ga( 2) -Ga( 4) -Yb(4) -2Yb(2) -2Yb( 1) Ga(4)-2Ga(4) -2Ga( 1) -2Yb( 1)
Yb(2)-2Ga(5) -4Ga( -4Ga( -4Ga( -Yb(2) -2Yb(
3.15(2) 3.17(3) 3.30( 2) 3.56( 1) 4.18( 1) 4.25( 3) 4.32( 1) 4.39( 1) 2.52( 1) 2.53( 5) 2.70( 2) 3.03( 1) 3.15( 1) 3.56( 1) 2.62(7) 2.70(2) 3.17(3)
Yb( 3)-6Ga( 3) -6Ga( 2) -6Yb( 1)
3.19(3) 3.28(4) 4.32( 1)
1)
3.05(3) 3.15( 1) 3.22( 2) 3.24( 2) 3.96( 2) 4.18( 1)
Yb(4)-12Ga(l)
3.03( 1)
Ga(2)-2Ga(3) -Ga( 1) -2Ga(5) -2Yb(2) -Yb(3) -2Yb( 1) Ga( 5)-2Ga(3) -2Ga(5) -4Ga( 2) -2Yb(2)
2.51( 1) 2.53(5) 2.97(3) 3.24(2) 3.28(4) 3.30( 2) 2.47( 3) 2.49(6) 2.97( 3) 3.05( 3)
Ga( 3)-Ga( 5) -Ga( 3) -2Ga( 2) -2Yb( 1) -Yb(3) -2Yb( 2)
2.47( 3) 2.48( 6) 2.51( 1) 3.15(2) 3.19(3) 3.22(2)
1) 3) 2)
“The multiplicity of this distance depends on the occupancy of the Ga( 4) position.
4. Discussion
In Fig. 1 the Yb-Ga diagram is redrawn on the basis of ref. 1 and taking into account the results of the present work. The two new compounds, YbGa,_. and Yb,Ga,, are now adjoined but, since no further thermal analysis has been carried out, their formation temperature and stability.range can be assigned only tentatively, as indicated by the broken lines. A solid solution range between 25.0 and 27.4 at.% Yb is proposed for YbGa, --x, which is formed at - 740 “C by peritectoid reaction from the two phases YbGa, and YbGa,, while Yb,Ga, exists only in a narrow range of temperatures estimated to be between 830 and 870 “C. Another compound, YbG%, formed by peritectic reaction at 282 “C [2], was also inserted. A certain resemblance can be noted between the Yb-Ga and the Ca-Ga [3] phase diagrams in the gallium-rich side, as in these systems the phases MGa, (&In, type), M,Ga, (Eu,Ga, type) and MGa, (CaGa, type) are present and the maximum congruent melting temperature is always shown by the MGa, phase. The two compounds CaGa, + x and YbGa, _ x are both closely related to the AlB, structure. YbGa,_, crystallizes in a superstructure of the AlB, type maintaining the same space group P6/mmm with a and c three and two times respectively greater than the lattice constants of the parent structure. In the basic AlB, lattice 36 nets of ytterbium atoms alternate along the c axis with 63 nets of gallium atoms. In YbGa,_. the gallium layers remain practically identical, whilst in the ytterbium layers part of the ytterbium atoms are replaced in an ordered manner by a triad of gallium. Such a substitution mechanism allows the same symmetry of the sublattice
336
1
1 650
/
d!
620 765
605
J 50 at. % Yb
I
I loo
Fig. 1. Revised form of the Yb-Ga phase diagram.
to be maintained, but with larger lattice constants. The Ga( l), Ga( 2) and Ga( 3) atoms occupy the same positions as in the AlB, lattice and have similar coordinations. Ga( 1) and Ga( 3) are surrounded by trigonal prisms of 5Yb + 1Ga tricapped by three gallium atoms. In Ga( 2) a ytterbium atom of the trigonal prism is replaced by a pair of gallium atoms. The Ga(4) and Ga(5) atoms are of a new type. They are surrounded by a tetrahedron of gallium and have two other ytterbium atom neighbours. In Ga( 5) four gallium atoms at a larger distance complete the coordination. The YbGa, phase is isotypic with CaGa,, the structure of which was already described as a monoclinic distortion of the BaAl, type [3]. These two phases, probably form a complete solid solution following the Vegard’s law, as can be seen from the lattice constants values of the compound Cq,5Yb,,5Ga,, being exactly intermediate between those of the two binary phases. The structure of Yb,Ga,, isotypic with Eu,Gas [9] and Ca,Ga, [3], is a binary variant of the type U3Ni4Si4, in which AlB, and BaAl, segments are stacked along the c axis. Also Yb,Ga,, like Eu,Ga, and Ca3Gas, is composed of structural fragments present in the two compounds adjacent to it in the phase diagram. In fact,
337
the binary phases M,Ga, are formed in systems in which compounds with AlB, type or related structures also occur: the high temperature phase EuGa, with AlB, structure (a = 4.359 A, c= 4.494 A) [lo], CaGa,+. with a structure derived from the AlB, type (a = 4.32 A, c = 4.33 A) [3], and YbGa,_. with a superstructure of the AlB, type (mean subcell constants a = 4.34 A, c = 4.18 A). These values correspond respectively to the base edge and height of the trigonal prisms formed by the M atoms and centred by gallium. Interestingly enough, the same prism sizes are found in the AlB, segments of the M,Ga, phases, where they regulate respectively the b and a lattice constants: Eu,Ga, (b = 4.375 A, a = 4.408 A) [9], Ca,Ga, (b = a = 4.323 A) [3], and Yb,Ga, (b = 4.340 A, a = 4.225 A). Thus the structural fragments used in the description of the 3:s structure here have not only a geometrical but also a crystal chemical significance. The volumes per atom for the phases in the Yb-Ga, Eu-Ga and Eu-In systems are plotted vs. the composition in Fig. 2. The crystal structure of two phases in the Eu-Ga system and of three phases in the Eu-In system were determined recently [ 1 l]. These values, obtained by dividing the cell volume by the total number of atoms, show large negative deviations from the ideal straight line of Vegard’s or Zen’s laws (broken line in the figure). A formula was derived by Merlo [12] to represent the experimental trend of binary phases formed by the alkaline earths, europium and ytterbium, in terms of the composition of the phase, the composition of the phase with the maximum volume contraction in the system and the difference between the charge transfer parameter of the two atoms. The calculated trends, represented by solid lines in Fig. 2, show a good agreement with the experimental data and confirm the validity of the proposed formula.
0
50
100
at. % Ga. ln
Fig. 2. Volume per atom of the Yb-Ga, Eu-Ga and Eu-In phases vs. composition. The broken line refers to a Vegard-like trend; the solid curve is calculated according to ref. 12.
338
References 1 2 3 4 5 6 7 8 9 10 11 12
A. Palenzona and S. Cirafici, J. Less-Common Met., 63 (1979) 105. J. Pelleg, G. Kimmel and D. Dayan, J. Less-Common Met., 81(1981) 33. G. Bmzzone, M. L. Fomasini and F. Merlo, J. Less-Common Met., 1.54(1989) 67. 0. D. McMasters and K. A. Gschneidner, Jr., J. Less-Common Met., 8 (1965) 289. K. Yvon, W. Jeitschko and E. Partbe, J. Appl. Crystallogr., 10 (1977) 73. G. M. Sheldrick, SHELX-76, Program for Ctystal Structure Determination, University of Cambridge, U.K., 1976. G. M. Sheldrick, in G. M. Sheldrick, C. Kruger and R. Goddard (eds.), Crystallographic Computing 3, Clarendon, Oxford, 1985, p. 175. J. A. Ibers and W. C. Hamilton (eds.), International Tables for X-ray Crystallography, Vol. 4, Kynoch, Birmingham, 1974, pp. 7 1 and 148. D. B. de Mooij and K. H. J. Buschow, J. Less-Common Met., 109( 1985) 117. K. H. J. Buschow and D. B. de Mooij, J. Less-Common Mer., 97( 1984) L5. M. L. Fomasini and S. Cirafici, Z. Krisfallogr., 190 (1990) 295. F.Merlo,J. Phys.F, 18(1988)1905.
Journal of the Less-Common Metals, 163 (1990) 331-338
CRYSTAL STRUCTURE OF PHASES OF THE Yb-Ga SYSTEM IN THE RANGE 20-32 AT.% Yb S. CIRAFICI and M. L. FORNASINI Istituto di Chimica Fisica, Universitri di Genova, Corso Europa 26, 16132 Genova (Italy) (Received April 4,199O)
Summary The region 20-32 at.% Yb of the Yb-Ga system was re-examined by X-ray and metallographic methods. Two new phases were identified: Yb,Ga, (Eu,Ga, type), 0122, space group Zmmm, a = 4.225(2) A, b = 4.340( 1) A, c = 25.665(g) A, which exists in a limited range of temperature estimated between 830 and 870 “C, and YbGa,_, with 0
1. Introduction In the Yb-Ga phase diagram [l] four phases have been identified: Yb,Ga (PbCl, type), YbGa (AuCu type), YbGa, (Cain, type) and YbGa, with unknown structure but probably isotypic with the phase CaGa,. Later another phase, YbGa, (PuGa, type), was found to form peritectically at 282 “C [2]. More recently, in a reexamination of the Ca-Ga system [3], the crystal structure of CaGa, was found to be a monoclinic distortion of the BaAl, type, and a new phase Ca,Ga, with a pseudo-tetragonal cell was identified as being isotypic with EqGas, a binary variant of the UsNi,Si, structure. Owing to the similarity between the Ca-Ga and Yb-Ga systems, it seemed interesting to re-investigate the part found between the Y bGa, andY bGa, compositions. 2. Experimental details The samples were prepared using elements supplied by Koch-Light Laboratories (Colnbrook, U.K.) with a stated purity of 99.8 wt.% for ytterbium and 0022-5088/90/$3.50
0 Elsevier Sequoia/Printed
in The Netherlands
332
99.999 wt.% for gallium. Hydrogen in the ytterbium metal was removed as described in ref. 4. For each sample of approximate mass 3 g stoichiometric amounts of the two metals were blended and pressed in tantalum crucibles, which were sealed by arc welding under pure argon. To ensure complete homogenization the mixtures were melted and shaken two or three times in a high frequency furnace under vacuum and cooled to room temperature. For each alloy several thermal treatments were applied, namely slow cooling, rapid quench and annealing at different temperatures: this procedure seemed reliable to identify the stability range of the compounds. Micrographic examination was carried out using standard techniques. No etching agent was used, as exposure to air was sufficient to ensure appropriate etching. X-ray analysis was performed with a Guinier-de Wolff camera or a powder diffractometer on powders mixed with silicon as an internal standard (a, = 5.43083 A). A single crystal of the phase YbGa,_, measuring 0.02 x 0.05 x 0.09 mm3, sealed under vacuum in a thin glass capillary, was mounted on an Enraf-Nonius CAD-4 automatic diffractometer, using graphite monochromated MO Ka radiation. The lattice constants were determined from 25 high angle reflections. In total 2166 intensities were collected in the o scan mode up to sin 0/n = 0.7 A- l, -18~h~18,O~k~18,0~1~11 with]h]>]k].Bothasemi-empiricalabsorption correction based on azimuthal scan data of the two top reflections and a spherical correction were applied, the linear absorption coefficient and ratio between the maximum and minimum transmission factors being 5 1.8 mrr- l and 4.9 respectively, and 757 independent reflections were obtained (R,, = 0.13). The principal programs used were LAZY PULVERIX [5] for calculating the powder pattern data, SHELX-76 [6] for structure refinement and SHELXS-86 [7] for structure solution. Atomic scattering factors and anomalous dispersion corrections were taken from international Tables forX-ray Crystallography [8].
3. Results
Crystal data of the compounds studied in this work are reported in Table 1 together with data from the literature for the other Yb-Ga phases. Alloys in the range 22-32 at.% Yb that were melted and slowly cooled were heterogeneous and their powder patterns contained the reflections of four phases, two of which are already known in the phase diagram, YbGa, (Cain, type) and YbGa,, and two new phases which were identified to be Yb,Ga, and YbGa, _-x.All these samples were microcrystalline, indicating that the primary crystals undergo several other reactions during cooling. 3.1. The Yb, Ga, and YbGa, phases It was impossible to obtain Yb,Ga, as a single phase, in spite of several trials on samples with this composition annealed at different temperatures. However, there are strong indications that this phase exists in a very narrow temperature range, since it was absent in the as-cast alloys, in an alloy quenched from 900 “C and in alloys annealed at 600 and 800 “C, but was present in an alloy annealed at
333
TABLE
1
Crystal data of the phases present in the Yb-Ga
system
type
Pearson symbol and space group
PbCl, AuCu Cain, Eu,Ga,
oP12-Pnma tP4-P4/mmm hP6-P6Jmmc oI22-Immm
YbGa,_. x=0.36(5) Y bGa,
-
hP54.3-P6/mmm
13.025( 2)
CaGa,
mSlO-C2/m
Y bGa,
PuGa,
tP14-P4/nbm
6.148( 1) p= 118.86(l) 5.849
Phase
Yb,Ga YbGa Y bGa, Yb,Ga,
Structure
a (A)
7.063 4.83 4.455 4.225(2)
b(A)
c(A)
Reference
5.050
9.427 3.94 7.199 25.665(g)
1 1 1 Present work Present work Present work
4.340( 1)
8.360( 1) 6.106(2)
6.084(2) 7.601
2
850 “C. It is reasonable to propose therefore that Yb,Ga, forms by peritectic reaction and decomposes by metatectic reaction at most 20 degrees above and below 850 “C respectively. This hypothesis is further confirmed by the powder data of the sample annealed at 800 “C and quenched in water, which showed only reflections of the YbGa, and YbGa, phases., By comparison with the powder patterns of Eu,Ga, [9] and Ca,Ga, [3], most reflections in the powder pattern of the sample annealed at 850 “C were indexed on the basis of the same orthorhombic structure. The remaining lines could be assigned to the neighbouring YbGa, and YbGa, phases. The lattice constants of Yb,Ga, listed in Table 1 are similar to those derived from single crystals by Palenzona and Cirafici [l], Q = b =4.32 A, c= 25.85 A, and attributed by these authors to the compound YbGa,. It is probable that primary crystals of the phase Yb,Ga,, formed by cooling from melts with a YbGa, composition, remain in a metastable condition and are easily picked out during the search for single crystals. On the other hand, a cell of such sizes does not match the powder pattern of the YbGa, phase, which is indexed instead on the basis of the monoclinic CaGa, structure [3]. The corresponding lattice parameters are given in Table 1. A pseudobinary compound Cq.,Yb,,,Ga, was also prepared as a single phase, crystallizing in the same monoclinic structure. The lattice constants a =6.162( 1) A, b=6.117(1) A, c=6.104(1) A, /3=118.87(l) are intermediate between those of the CaGa, and YbGa, phases. 3.2. The YbGa,_,pha.se A 25.0 at.% Yb alloy annealed at 600 “C was microscopically homogeneous and its powder pattern showed reflections of a new phase, here called YbGa,_ x. Although the strongest reflections correspond to a hexagonal cell with lattice periods close to those of the AlB, structure, the different composition and the numerous unindexed lines require a larger cell and an atomic arrangement only related to the AlB, type. In fact, single crystal X-ray analysis led to a hexagonal cell
334
with periods three and two times respectively greater than the a and c constants of the AlE$ subcell, namely a = 13.02.5( 2) A, c = 8.360( 1) A. The structure was determined to be in the space group P6/mmm by employing Patterson methods and isotropically refining with unit weights using 204 reflections with F0 > 3a(F0). Since the thermal parameters of three atoms, Yb(4), Ga(2) and Ga( 5), showed values higher than the other atoms, the occupation factors of the corresponding sites were allowed to vary, while the occupation of the Ga(4) site for which a full filling would give too short a Ga-Ga distance was fixed at 50%. At convergence R = 0.080, the maximum and minimum height in difference Fourier synthesis were 10.5 and - 10.6 e A- 3, and the final composition was Owing to the low number of observed intensities, no anisotropic Yb14.9(1p39.4(7). refinement was applied. The atomic coordinates and thermal parameters are reported in Table 2, while interatomic distances are given in Table 3.
TABLE 2 Atomic coordinates and thermal isotropic parameters for Yb,,,,,IGa,,,,C,,.
Wl) W2) Yb(3) W4) Wl) GaG’) G43) W4) Gab)
6(k) 6(j) 2(d) l(a) 12(o) 12(o) 12(o) 6(m) 6(l)
ESDs are in parentheses
x
Y
Z
Occupation (%)
U(K)
0.3367( 10) 3.3480( 7) l/3 0.0 0.1118(6) 0.223(2) 0.445( 1) 0.067( 2) 0.397( 2)
0.0 0.0 213 0.0 2x 2x 2x 2x 2x
0.5 0.0 0.5 0.0
100 100 100 86( 12) 100 62(6) 100 50 84(8)
0.01 l(2) 0.001(2) O.OOl(3) 0.026( 15) 0.003(2) 0.008(9) 0.013(7) 0.001(7) 0.019(8)
0.201(2) 0.244(4) 0.265(3) 0.5 0.0
The presence of the YbGa,_ x phase was confirmed in other samples prepared in the range 22.2-27.4 at.% Yb and annealed at 600 “C. Except for the extreme compositions, where some reflections were assigned to the neighbouring phases YbGa, and YbGa,, all powder patterns could be indexed according to the large hexagonal cell. The lattice constants were very close to those obtained from the crystal. The incomplete filling of some ytterbium and gallium sites in this structure may be responsible for the existence of a range of homogeneity. Moreover, decreasing the ytterbium and increasing the gallium content while changing the composition did not alter the cell dimensions. To estimate approximately the temperature of formation of the YbGa,_ x phase, two 27.3 at.% Yb alloys were particularly significant: one of them, annealed at 800 “C, showed in its powder pattern only reflections of the compounds YbGa, and YbGa,, while the other, annealed at 730 “C, a few degrees below the peritectic arrest of YbGa,, gave YbGa,_, as the main phase and weaker reflections of the YbGa, phase. Therefore, the formation of YbGa,_, by peritectoid reaction can be proposed to occur at a temperature between 730 and 755 “C.
335 TABLE
3
Interatomic distances (A) in Yb,,,Ga
3y,4up to d/D = 1.13. ESDs are in parentheses
Yb(l)-4Ga(3) -Ga( 4) -4Ga( 2) -4Ga( 1) -2Yb(2) -Yb(l) -2Yb(3) -2Yb( 1) Ga(l)-2Ga( 1) -Ga( 2) -Ga( 4) -Yb(4) -2Yb(2) -2Yb( 1) Ga(4)-2Ga(4) -2Ga( 1) -2Yb( 1)
Yb(2)-2Ga(5) -4Ga( -4Ga( -4Ga( -Yb(2) -2Yb(
3.15(2) 3.17(3) 3.30( 2) 3.56( 1) 4.18( 1) 4.25( 3) 4.32( 1) 4.39( 1) 2.52( 1) 2.53( 5) 2.70( 2) 3.03( 1) 3.15( 1) 3.56( 1) 2.62(7) 2.70(2) 3.17(3)
Yb( 3)-6Ga( 3) -6Ga( 2) -6Yb( 1)
3.19(3) 3.28(4) 4.32( 1)
1)
3.05(3) 3.15( 1) 3.22( 2) 3.24( 2) 3.96( 2) 4.18( 1)
Yb(4)-12Ga(l)
3.03( 1)
Ga(2)-2Ga(3) -Ga( 1) -2Ga(5) -2Yb(2) -Yb(3) -2Yb( 1) Ga( 5)-2Ga(3) -2Ga(5) -4Ga( 2) -2Yb(2)
2.51( 1) 2.53(5) 2.97(3) 3.24(2) 3.28(4) 3.30( 2) 2.47( 3) 2.49(6) 2.97( 3) 3.05( 3)
Ga( 3)-Ga( 5) -Ga( 3) -2Ga( 2) -2Yb( 1) -Yb(3) -2Yb( 2)
2.47( 3) 2.48( 6) 2.51( 1) 3.15(2) 3.19(3) 3.22(2)
1) 3) 2)
“The multiplicity of this distance depends on the occupancy of the Ga( 4) position.
4. Discussion
In Fig. 1 the Yb-Ga diagram is redrawn on the basis of ref. 1 and taking into account the results of the present work. The two new compounds, YbGa,_. and Yb,Ga,, are now adjoined but, since no further thermal analysis has been carried out, their formation temperature and stability.range can be assigned only tentatively, as indicated by the broken lines. A solid solution range between 25.0 and 27.4 at.% Yb is proposed for YbGa, --x, which is formed at - 740 “C by peritectoid reaction from the two phases YbGa, and YbGa,, while Yb,Ga, exists only in a narrow range of temperatures estimated to be between 830 and 870 “C. Another compound, YbG%, formed by peritectic reaction at 282 “C [2], was also inserted. A certain resemblance can be noted between the Yb-Ga and the Ca-Ga [3] phase diagrams in the gallium-rich side, as in these systems the phases MGa, (&In, type), M,Ga, (Eu,Ga, type) and MGa, (CaGa, type) are present and the maximum congruent melting temperature is always shown by the MGa, phase. The two compounds CaGa, + x and YbGa, _ x are both closely related to the AlB, structure. YbGa,_, crystallizes in a superstructure of the AlB, type maintaining the same space group P6/mmm with a and c three and two times respectively greater than the lattice constants of the parent structure. In the basic AlB, lattice 36 nets of ytterbium atoms alternate along the c axis with 63 nets of gallium atoms. In YbGa,_. the gallium layers remain practically identical, whilst in the ytterbium layers part of the ytterbium atoms are replaced in an ordered manner by a triad of gallium. Such a substitution mechanism allows the same symmetry of the sublattice
336
1
1 650
/
d!
620 765
605
J 50 at. % Yb
I
I loo
Fig. 1. Revised form of the Yb-Ga phase diagram.
to be maintained, but with larger lattice constants. The Ga( l), Ga( 2) and Ga( 3) atoms occupy the same positions as in the AlB, lattice and have similar coordinations. Ga( 1) and Ga( 3) are surrounded by trigonal prisms of 5Yb + 1Ga tricapped by three gallium atoms. In Ga( 2) a ytterbium atom of the trigonal prism is replaced by a pair of gallium atoms. The Ga(4) and Ga(5) atoms are of a new type. They are surrounded by a tetrahedron of gallium and have two other ytterbium atom neighbours. In Ga( 5) four gallium atoms at a larger distance complete the coordination. The YbGa, phase is isotypic with CaGa,, the structure of which was already described as a monoclinic distortion of the BaAl, type [3]. These two phases, probably form a complete solid solution following the Vegard’s law, as can be seen from the lattice constants values of the compound Cq,5Yb,,5Ga,, being exactly intermediate between those of the two binary phases. The structure of Yb,Ga,, isotypic with Eu,Gas [9] and Ca,Ga, [3], is a binary variant of the type U3Ni4Si4, in which AlB, and BaAl, segments are stacked along the c axis. Also Yb,Ga,, like Eu,Ga, and Ca3Gas, is composed of structural fragments present in the two compounds adjacent to it in the phase diagram. In fact,
337
the binary phases M,Ga, are formed in systems in which compounds with AlB, type or related structures also occur: the high temperature phase EuGa, with AlB, structure (a = 4.359 A, c= 4.494 A) [lo], CaGa,+. with a structure derived from the AlB, type (a = 4.32 A, c = 4.33 A) [3], and YbGa,_. with a superstructure of the AlB, type (mean subcell constants a = 4.34 A, c = 4.18 A). These values correspond respectively to the base edge and height of the trigonal prisms formed by the M atoms and centred by gallium. Interestingly enough, the same prism sizes are found in the AlB, segments of the M,Ga, phases, where they regulate respectively the b and a lattice constants: Eu,Ga, (b = 4.375 A, a = 4.408 A) [9], Ca,Ga, (b = a = 4.323 A) [3], and Yb,Ga, (b = 4.340 A, a = 4.225 A). Thus the structural fragments used in the description of the 3:s structure here have not only a geometrical but also a crystal chemical significance. The volumes per atom for the phases in the Yb-Ga, Eu-Ga and Eu-In systems are plotted vs. the composition in Fig. 2. The crystal structure of two phases in the Eu-Ga system and of three phases in the Eu-In system were determined recently [ 1 l]. These values, obtained by dividing the cell volume by the total number of atoms, show large negative deviations from the ideal straight line of Vegard’s or Zen’s laws (broken line in the figure). A formula was derived by Merlo [12] to represent the experimental trend of binary phases formed by the alkaline earths, europium and ytterbium, in terms of the composition of the phase, the composition of the phase with the maximum volume contraction in the system and the difference between the charge transfer parameter of the two atoms. The calculated trends, represented by solid lines in Fig. 2, show a good agreement with the experimental data and confirm the validity of the proposed formula.
0
50
100
at. % Ga. ln
Fig. 2. Volume per atom of the Yb-Ga, Eu-Ga and Eu-In phases vs. composition. The broken line refers to a Vegard-like trend; the solid curve is calculated according to ref. 12.
338
References 1 2 3 4 5 6 7 8 9 10 11 12
A. Palenzona and S. Cirafici, J. Less-Common Met., 63 (1979) 105. J. Pelleg, G. Kimmel and D. Dayan, J. Less-Common Met., 81(1981) 33. G. Bmzzone, M. L. Fomasini and F. Merlo, J. Less-Common Met., 1.54(1989) 67. 0. D. McMasters and K. A. Gschneidner, Jr., J. Less-Common Met., 8 (1965) 289. K. Yvon, W. Jeitschko and E. Partbe, J. Appl. Crystallogr., 10 (1977) 73. G. M. Sheldrick, SHELX-76, Program for Ctystal Structure Determination, University of Cambridge, U.K., 1976. G. M. Sheldrick, in G. M. Sheldrick, C. Kruger and R. Goddard (eds.), Crystallographic Computing 3, Clarendon, Oxford, 1985, p. 175. J. A. Ibers and W. C. Hamilton (eds.), International Tables for X-ray Crystallography, Vol. 4, Kynoch, Birmingham, 1974, pp. 7 1 and 148. D. B. de Mooij and K. H. J. Buschow, J. Less-Common Met., 109( 1985) 117. K. H. J. Buschow and D. B. de Mooij, J. Less-Common Mer., 97( 1984) L5. M. L. Fomasini and S. Cirafici, Z. Krisfallogr., 190 (1990) 295. F.Merlo,J. Phys.F, 18(1988)1905.