Crystal structures of PrAlxGe2−x compounds

Journal of Alloys and Compounds 296 (2000) 265–271

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Crystal structures of PrAl x Ge 22x compounds q a, a b a,c c E.I. Gladyshevskii *, N.Z. Nakonechna , K. Cenzual , R.E. Gladyshevskii , J.-L. Jorda b

a Department of Inorganic Chemistry, Ivan Franko L’ viv State University, 6, vul. Kyryla i Mefodiya, UA-290005 L’ viv, Ukraine ´ ´ ´ , Universite´ de Geneve ` , 30, quai Ernest Ansermet, CH-1211 Geneva, Switzerland , Analytique et Appliquee Departement de Chimie Minerale c ´ d’ Annecy, Universite´ de Savoie, 41, av. de la Plaine, F-74016 Annecy, France Laboratoire d’ Instrumentation et de Materiaux

Received 24 June 1999; accepted 29 July 1999

Abstract The PrAl x Ge 22x cross-section of the Pr–Al–Ge system at 1073 K was studied. The homogeneity ranges of two ternary praseodymium alumogermanides, PrAl 1.55 – 1.48 Ge 0.45 – 0.52 and PrAl 1.42 – 0.98 Ge 0.58 – 1.02 , were determined and their crystal structures refined from X-ray ˚ for single-crystal diffraction data. The former has a hexagonal structure of the AlB 2 type (hP3, P6 /mmm, a54.3223(3), c54.2585(4) A ˚ for x51). For both x51.476(2)) and the latter a tetragonal structure of the LaPtSi type (tI12, I4 1 md, a54.2534(5), c514.641(2) A structures, the Al–Ge interatomic distances are close to the sum of the covalent radii, whereas the Pr–Al(Ge) distances agree well with the sum of the metallic radii. The solubility of Ge in the cubic Laves phase PrAl 2 was found to be less than 2 at.%, that of Al in off-stoichiometric PrGe 22x less than 8 at.%. Al(Ge)-centered R 6 trigonal prisms constitute a common geometrical feature of the structures of the germanides RGe 22x and alumogermanides RAl x Ge 22x formed by the light rare-earth elements. Substitution of Ge for Al, or replacement of a large rare-earth element by a smaller one, leads to a reduction of the prism volume.  2000 Elsevier Science S.A. All rights reserved. Keywords: Praseodymium germanium aluminides; Crystal structure; Rare earth intermetallics

1. Introduction The R–Al–Ge systems, where R is a light rare-earth element, have been partly investigated [1–3]. Phase equilibria have been established for R5La, Ce [4] or Gd [5], however, only in the range 0–33.3 at.% R. On the RAl x Ge 22x cross-section of these systems and of the corresponding systems with Pr, Nd, Sm or Eu, alumogermanides and digermanides crystallizing with the AlB 2 , a-ThSi 2 , EuGe 2 , LaPtSi or YAlGe structure types were found [4–11]. For some of them, homogeneity ranges were established. The crystal structures of five compounds were found to belong to the AlB 2 type (hP3, P6 /mmm): LaAl x Ge 22x (x51.75–1.25 [5], x51.8–1.5 [6–8]), CeAl x Ge 22x (x5 1.6–1.5 [4–6]), NdAl x Ge 22x (x51.6–1.5 [6]), SmAl x Ge 22x (x51.25–1.4) [12]) and EuAl x Ge 22x (x5 1.2–1.25) [12]). The homogeneity ranges of the first three phases include the ‘stoichiometric’ composition RAl 1.5 Ge 0.5 (R 2 Al 3 Ge). Seven RAl x Ge 22x compounds, q

In memory of our colleague and friend Roman Skolozdra, who died on January, 24, 1999. *Corresponding author.

where R5La, Ce, Pr, Nd, Sm, Eu or Gd (high-temperature modification) crystallize with a-ThSi 2 -type structures (tI12, I4 1 /amd). For two of them, relatively large homogeneity ranges were established: LaAl x Ge 22x (x50.75– 0.20 at 1423 K [8], x51.2–0.9 at 773 K [4]) and CeAl x Ge 22x (x51.2–0.7 at 773 K [4]). All R–Al–Ge systems (except Pm–Al–Ge), were investigated at the equiatomic composition RAlGe [9,10]. The a-ThSi 2 type was confirmed for the compounds mentioned above, whereas the heavy rare-earth metals were found to adopt a different structure type, refined on YAlGe (oS12, Cmcm) [9]. A reinvestigation of the alumogermanide LaAlGe showed that it adopts a structure of the LaPtSi type (tI12, I4 1 md) [8], which is an ordered substitution variant of the a-ThSi 2 type. Ordering is still to be tested for other equiatomic compounds reported with the a-ThSi 2 type. Equiatomic GdAlGe forms an a-ThSi 2 -type structure at high temperature and a YAlGe-type structure at low temperature. A series of R 2 AlGe 3 compounds with a heavy rare-earth element (R5Dy, Ho, Er or Tm) were found to crystallize with an orthorhombic structure type determined on Y 2 AlGe 3 [13]. For the compounds with AlB 2 - or a-ThSi 2 -type structures, replacement of Al by Ge leads to a decrease of the

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cell volume. The solubility of Ge in CeAl 2 (MgCu 2 -type structure, cF24, Fd-3m) does not exceed 2 at.% at 1273 K but produces a decrease of the unit-cell parameter from ˚ [6]. Up to 8.7 at.% Ge can be dissolved 8.057 to 8.034 A in isotypic GdAl 2 , the a-parameter decreasing from 7.901 ˚ [6]. The solubility of aluminum in off-stoichioto 7.860 A metric LaGe 22x and CeGe 22x with structures of the orthorhombic a-GdSi 2 type (oI12, Imma) reaches about 10 at.% at 773 K and which corresponds to an increase of the ˚ 3 and from 262.5 to cell volumes from 270.6 to 276.5 A 3 ˚ , respectively [4]. 270.0 A We report here on the structure determination of the compounds on the PrAl x Ge 22x cross section in the corresponding ternary system. Preliminary results were reported in [11].

2. Experimental Samples of nominal composition PrAl x Ge 22x (x50–2) were prepared by arc melting under an argon atmosphere and annealed at 873 K in evacuated quartz tubes for 2 months. Starting components were: Pr.99.9, Al.99.99 and Ge.99.999%; the weight loss was less than 0.2%. Phase analysis and determination of the unit-cell parameters were based on X-ray diffraction data from polycrystalline samples, recorded on a diffractometer DRON˚ internal silicon stan2.0 (FeKa radiation, l51.9374 A,

˚ The programs LAZY PULVERIX [14] and dard, a55.4308 A). [15] were used for calculations and refinements. Single crystals were found in alloys of nominal compositions PrAl 1.5 Ge 0.5 and PrAlGe, annealed at 1073 K for 2 months. Their crystal structures were investigated using X-ray single-crystal data collected on an Enraf–Nonius CAD-4 automatic four-circle diffractometer. Experimental details are presented in Table 1; the programs used to refine the structures were all from the MOLEN system [16].

LATCON

3. Results

3.1. Phase equilibria in the PrAlx Ge22 x cross-section Four single-phase regions were found in the PrAl x Ge 22x cross-section in the Pr–Al–Ge system: a solid solution of Ge in binary PrAl 2 , ternary PrAl 1.5 Ge 0.5 with a narrow homogeneity range, ternary PrAlGe with a wide homogeneity range (Fig. 1) and a solid solution of Al in off-stoichiometric PrGe 22x . The solubility of Ge in PrAl 2 is less than 2 at.% and leads to a small decrease of the ˚ The cubic unit-cell parameter from 8.030(1) to 8.027(1) A. homogeneity range of the PrAl 1.5 Ge 0.5 phase with constant 33.3 at.% Pr ranges from 15.0 to 17.2 at.% Ge (PrAl 1.55 – 1.48 Ge 0.45 – 0.52 ). Upon replacement of Al by Ge, the hexagonal unit-cell parameters decrease slightly: a5

Fig. 1. Lattice parameters of PrAl x Ge 22x compounds with MgCu 2 (A), AlB 2 (B) and LaPtSi-type (C) structures as a function of the Ge content.

E.I. Gladyshevskii et al. / Journal of Alloys and Compounds 296 (2000) 265 – 271

˚ The 4.328(2)–4.327(3) and c54.267(2)–4.255(1) A. homogeneity range of the other ternary compound, PrAlGe, extends from 19.5 to 34.0 at.% Ge (PrAl 1.42 – 0.98 Ge 0.58 – 1.02 ). Replacement of Al by Ge leads to the following change in the tetragonal unit-cell parameters: a54.291(1)–4.254(2) and c514.929(8)–14.642(6) ˚ At high Ge content, this phase is found to be in A. equilibrium with the solid solution of Al in the germanide PrGe 22x . The binary compound dissolves up to about 8 at.% aluminum. A significant decrease of the melting point was observed for ternary alloys containing 35–60 at.% Ge, with respect to the binary compounds (1753 K for PrAl 2 , 1779 K PrGe 22x ). The eutectic PrAlGe1PrGe 22x formed already

267

at 1073 K and resulted in the formation of relatively large PrGe 22x single crystals. Structural studies showed that PrGe 1.75 adopts a new structure which is a deformation variant of the a-ThSi 2 type with an ordered distribution of vacancies. The superstructure and the phase equilibria in the Ge-rich region of the Pr–Al–Ge system are the subject of a separate work [17].

3.2. Crystal structure of PrAl1.5 Ge0.5 and PrAlGe The results of the structural refinements are compared in Table 1. PrAl 1.5 Ge 0.5 was found to crystallize with a hexagonal AlB 2 -type structure, the Al and Ge atoms being statistically mixed in the site 2(d) (space group P6 /mmm).

Table 1 Experimental details Crystal data Refined composition Mr Space group ˚ a (A) ˚ c (A) ˚ 3) V (A Z Dx (Mg m 23 ) ˚ Radiation type, wavelength (A) No. of reflections for cell parameters u range (8) m (mm 21 ) Temperature (K) Crystal shape Crystal size (mm) Colour

PrAl 1.476( 2 ) Ge 0.524 218.77 P6 /mmm 4.3223(3) 4.2585(4) 68.900(8) 1 5.79 MoKa, 0.71073 8 7–21 28.14 293 Plate 0.0730.0630.03 Metallic gray

PrAlGe 240.48 I4 1 md 4.2534(5) 14.641(2) 264.87(6) 4 6.03 MoKa, 0.71073 9 6–20 29.28 293 Plate 0.0630.0430.02 Metallic gray

Data collection Data collection method Absorption correction T min 2T max No. of measured reflections No. of independent reflections No. of reflections with F .3s (F ) R int umax (8) Range of h, k, l No. of standard reflections Frequency of standard reflections (min) Intensity decay (%)

v 22u Empirical (c scans) 0.548–1.000 766 58 58 0.014 30 26→6, 26→6, 26→6 3 120 0.4

v 22u Empirical (c scans) 0.437–0.999 1528 146 103 0.020 30 25→5, 25→5, 220→20 3 120 0.5

Refinement Refinement on R wR S No. of reflections used in refinement No. of parameters refined Weighting scheme (D /s ) max ˚ 23 ) Drmax (e A 23 ˚ Drmin (e A ) Correction for secondary extinction Extinction coefficient Scattering factors from

F F 0.009 0.015 0.012 0.026 0.66 1.01 58 103 7 13 w51 /s (F )2 w51 /s (F )2 23 0.1310 0.2310 23 0.50 1.91 0.79 0.90 Isotropic Isotropic 3.9(4)310 26 0.9(2)310 26 International Tables for X-ray Crystallography (1974, Vol. IV)

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Table 2 Fractional atomic coordinates and equivalent displacement parameters ˚ 2 ) for Pr Al 1.476( 2 ) Ge 0.524 (AlB 2 type, P6 /mmm, a54.3223(3), c5 (A ˚ Beq 5(8p 2 / 3)S i S jUij a *i a *j a i a j a 4.2585(4) A) Site

Wyckoff position

x

y

z

Beq

Pr Al 0.738( 1 ) Ge 0.262

1(a) 2(d)

0 1/3

0 2/3

0 1/2

0.497(4) 0.75(1)

a

Table 6 Anisotropic displacement parameters for PrAlGe Site

U11

U22

U33

U12

U13

U23

Pr Al Ge

0.0018(3) 0.016(2) 0.0027(7)

0.0102(3) 0.017(2) 0.0162(9)

0.0048(2) 0.005(2) 0.0064(7)

0 0 0

0 0 0

0 0 0

Constraints: PP(Al)1PP(Ge)51.

The atomic positional and displacement parameters, and the interatomic distances are given in Tables 2, 3 and 4, respectively. A model with a partly ordered distribution of Al and Ge atoms, corresponding to the hexagonal LiBaSi type (space group P-6m2), was tested but no tendency toward ordering was detected and the Al / Ge ratios for both positions (1(e) and 1(a)) refined to similar values (0.764 / 0.236(9) and 0.711 / 0.289(9)). Isotypism with the hexagonal U 2 RuSi 3 (double a-parameter) or Lu 2 CoGa 3 (double a- and c-parameter) types, which have the same ratio of the corresponding elements and are substitution derivatives of the AlB 2 type, was excluded since no superstructure reflections were observed. The structure of PrAlGe belongs to the tetragonal LaPtSi type (space group I4 1 md), which is a ternary substitution variant of the tetragonal a-ThSi 2 type (space group I4 1 /amd). Crystallographic parameters for this compound are given in Tables 5, 6 and 7, and the structure is shown in Fig. 2. The Al and Ge atoms are coordinated by tri-capped trigonal prisms of composition Pr 6 Ge 3 and Pr 6 Al 3 , respectively, whereas the Pr atoms center hexagonal Al 6 Ge 4 Pr 2 prisms, the faces of which are capped by two Ge and six Pr atoms. In the AlB 2 -type structure of PrAl 1.5 Ge 0.5 with statistical distribution of Al and Ge, the

atoms are characterized by the same coordination numbers and polyhedra. However, the hexagonal prism around the Pr site is built up exclusively by atoms from the Al / Ge site, the faces being capped by Pr atoms. Thus, both structures belong to class 10 (trigonal-prismatic coordination for the smaller atoms) according to the systematic developed by Kripyakevich [18]. For PrAlGe, the model with statistical distribution of Al and Ge atoms in a single site (8(e), space group I4 1 /amd), corresponding to the a-ThSi 2 type, was tested. The Al / Ge ratio refined close to unity (0.558(7) / 0.442), but the reliability factors were significantly higher (R50.037, wR50.037, S51.19) than those obtained for the ordered variant. As mentioned Table 7 ˚ in PrAlGe a Interatomic distances (A) Pr–Al –Ge –Pr a

233.211 433.259 233.241 433.243 434.233 434.253

Al–Pr –Ge

233.211 433.259 232.438 132.468

Ge–Pr –Al

233.241 433.243 232.438 132.468

E.s.d.s are ,6 on the last digit.

Table 3 Anisotropic displacement parameters for PrAl 1.476( 2 ) Ge 0.524 Site

U11

U22

U33

U12

U13

U23

Pr Al 0.738( 1 ) Ge 0.262

0.0071(1) 0.0065(3)

0.0071 0.0065

0.0047(1) 0.0154(4)

0.0036 0.0032

0 0

0 0

Table 4 ˚ in PrAl 1.476( 2 ) Ge 0.524 Interatomic distances (A) Pr–(Al,Ge) –Pr

123 3.280 234.259 634.322

(Al,Ge)–Pr –(Al,Ge)

633.280 332.495

Table 5 Fractional atomic coordinates and equivalent displacement parameters ˚ 2 ) for PrAlGe (LaPtSi type, I4 1 md, a54.2534(5), c514.641(2) A) ˚ (A Beq 5(8p 2 / 3)Si SjUij a *i a *j a i a j Site

Wyckoff position

x

y

z

Beq

Pr Al Ge

4(a) 4(a) 4(a)

0 0 0

0 0 0

0.5829(2) 0.1686(5) 0.0

0.44(1) 0.98(9) 0.66(3)

Fig. 2. Structure of PrAlGe (LaPtSi type) in a projection along [100] and coordination polyhedra: Pr(Al 6 Ge 6 Pr 8 ), Al(Pr 6 Ge 3 ) and Ge(Pr 6 Al 3 ).

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above, the limiting Al content in this phase is 47.2 at.%, which would correspond to a Ge /Al ratio on the Ge site of about 1.4, if the Al site is occupied exclusively by aluminum. Several works have emphasized the strong amount of localized bonding existing within the substructure formed by the smaller atoms in compounds crystallizing with AlB 2 - or a-ThSi 2 -type structures [8,19,20]. In both AX 2 structures, the X atoms are coordinated by three other X atoms forming a planar triangle, i.e. a coordination typical for an atom in sp 2 hybridization. In the AlB 2 type, such units share atoms to form infinite graphite-like planar nets. These nets allow strong interactions between the p z orbitals. Beyond a certain valence electron concentration per X atom, antibonding orbitals become populated, destabilizing the structure in favor of, for instance, an aThSi 2 -type structure with a less conjugated substructure [19]. In the a-ThSi 2 (LaPtSi) type, the X atoms also have trigonal coordination, however, neighboring units are sometimes rotated by 908. Infinite chains of corner-sharing units, running parallel to a or b of the tetragonal unit cell, are interconnected to form a 3D-framework. It has been emphasized that a partly localized bonding scheme is not contrary to the metallic behavior observed for some isotypic compounds where the Fermi level passes through bands with a large amount of d-character at higher energy. Puckering of the graphite-like layers constitutes another mean to stabilize a compound at a high valence electron concentration. Puckered hexagon-mesh layers are observed in many structure types, among which the EuGe 2 type (hP3, P-3m1) [21]. PrAlGe can be considered as a Zintl compound, with the crystal chemical formula

269

Pr 31 Al 22[3l ] Ge 2[3l ] . This viewpoint was supported by band calculations for LaAlGe [8]. The structure types formed by the heavy rare-earth elements, YAlGe and Y 2 AlGe 3 , are not characterized by planar trigonal coordination, but localized bonding was also evidenced within the Al–Ge framework of the latter [13]. As can be seen from Tables 4 and 7, the (Al,Ge)– (Al,Ge) distances in PrAl 1.5 Ge 0.5 and PrAlGe are close to ˚ for Al and 1.18 A ˚ for Ge. the sum of covalent radii, 1.22 A The unique distance in the AlB 2 -type structure is only slightly longer than the average distance for an Al / Ge ratio of 1.5 / 0.5. The LaPtSi-type structure contains two independent Al–Ge distances. The distances within the chains of conjugated trigonal units are close to the sum of covalent radii, whereas the distances between the chains (bonds parallel to c) are slightly longer. The angles inside the trigonal units differ little from the ideal value (13 121.468, 23119.278). The interatomic distances between Pr and Al or Ge atoms are close (61.5%) to the sum of ˚ The metallic radii (r Pr 51.82, rAl 51.43 and r Ge 51.37 A). AlPr 6 trigonal prisms are slightly irregular in the LaPtSitype structure (two shorter and four longer Al–Pr distances), whereas the GePr 6 prisms are regular, as in the AlB 2 -type structure. The Pr–Pr distances in both structures are longer by about 16% than twice the atom radius of metallic praseodymium. Fig. 1 shows that the a-parameter of the AlB 2 -type structure remains approximately constant within the homogeneity range, whereas the c-parameter decreases with increasing Ge content. Also for the LaPtSi-type structure, the c-parameter decreases more rapidly than the a-parameter for higher Ge concentrations.

Fig. 3. RAl x Ge 22x cross-section of the systems with R5La, Ce, Pr, Nd, Sm and Eu: MgCu 2 (A), AlB 2 (B), LaPtSi (C), a-ThSi 2 (D), a-GdSi 2 (E) and EuGe 2 -type (F) structures.

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Fig. 4. Arrangements of trigonal XR 6 prisms in the structures of AlB 2 (a) and a-ThSi 2 (b).

4. Discussion The PrAl 2 –PrGe 22x cross-section of the Pr–Al–Ge system is similar to the corresponding cross-sections in the ternary systems with La, Ce, Nd, Sm and Eu (Fig. 3). In all these systems solid solutions of Ge in RAl 2 are in phase equilibrium with R(Al,Ge) 2 compounds of the AlB 2 -type. It can be seen, that the homogeneity range for the Lacontaining AlB 2 -type phase is larger (from 6 to 25 at.% Ge) than those observed for the other compounds (up to 3 at.% Ge). The La-, Ce- and Pr-containing compounds reported with a-ThSi 2 - or LaPtSi-type structures are also characterized by large homogeneity ranges. It should be noted, that the compounds with Nd, Sm and Eu were studied only at the equiatomic composition. LaAlGe and PrAlGe crystallize with LaPtSi-type structures, whereas structures of the other RAlGe compounds were reported to belong to the a-ThSi 2 type, however, possible ordering

was not tested. The exact solubility ranges of Al in the binary phases RGe 22x (R5Pr or Nd) are also still to be determined. A large number of rare-earth alumogermanides RAl x Ge 22x and digermanides crystallize with structures which are built up by face-sharing trigonal prisms. In the structures of AlB 2 , a-ThSi 2 (LaPtSi), a-GdSi 2 and EuGe 2 types, the R atoms, which have large radius, are situated at the vertices of trigonal XR 6 prisms [22,23]. In the hexagonal or trigonal structures (AlB 2 and EuGe 2 ) the prism axes are all parallel, i.e. the base planes of the prisms are situated in parallel planes. The trigonal prisms are arranged in slabs which are stacked along the 6- or 3-fold axes (Fig. 4). In the structure of the a-ThSi 2 (LaPtSi) type, the prism axes of the neighboring slabs are rotated by 908, which leads to an overall tetragonal symmetry. In the ideal case ] the c /a ratio is equal 2Œ3. The structure of the orthorhombic a-GdSi 2 type can be obtained by deformation along one of the short cell vectors of the tetragonal structure. As expected, the trigonal prism volume (V6p ) decreases with decreasing ionic radius R 31 of the rare-earth element. The prism volumes, plotted in Fig. 5, were calculated based on data from references [1–12]. Higher V6p values observed for the compounds with R5Eu and Yb can be explained by a lower oxidation state of the rare-earth elements. The trigonal prism volumes in the PrAlx Ge 22x compounds with AlB 2 - and LaPtSi-type structures also decrease with increasing Ge content (Fig. 6), without any discontinuity at the change in structure type. The V6p values for the praseodymium digermanides called Q 1 and Q 2 [24], the structures of which contain vacancies on the

Fig. 5. Average trigonal prism volumes for RAl x Ge 22x compounds as a function of the ionic radii R 31 : AlB 2 (B: binary, B9: ternary compounds), LaPtSi (C), a-ThSi 2 (D: binary, D9: ternary compounds) and EuGe 2 -type (F) structures.

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271

Fig. 6. Average trigonal prism volumes for RAl x Ge 22x compounds as a function of the Ge content: AlB 2 (B), LaPtSi (C) and a-ThSi 2 -type (D) structures.

Ge site, increase when decreasing the number of vacancies in the average a-ThSi 2 -type structure. The lines illustrating the dependence of V6p on the Ge content for PrAl x Ge 22x and PrGe 22x would cross at the approximate composition PrGe 1.7 .

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