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Single crystal structure refinement and high-pressure properties of CoSn
Journal of ALLOYS
AND COMPOUNDS ELSEVIER
Journal of Alloys and Compounds 240 (1996) 79-84
Single crystal structure refinement and high-pressure properties of CoSn A. K. Larssona'', M. Haeberleinb, S. Lidina, U. Schwarzc'* University of Lund, Inorganic Chemistry 2, Box 124, S-22100 Lund, Sweden `Royal Institute of Technology, Department of Chemistry, Physical Chemistry, S-10044 Stockholm, Sweden `Max-Planck-Institut für Festkörperforschung, Heisenbergstraße 1, D-70569 Stuttgart, Germany Received 9 November 1995
Abstract Using singled A, P6/mmm, in 5.2790(7) CoSn data have the crystal structure of crystal refined space group a= we c=4.2597(10) A with Sn1 at Wyckoff position la, Sn2 at 2d, and Co at 3f. The space group used for the structure refinement was confirmed by beam electron diffraction investigation. The crystal structure contains graphite-like a convergent subsequent 6 nets of Sn2 atoms and Kagome nets of Co centred by the Snl atoms. An unusual feature for a crystal structure of an intermetallic compound is a 20-atom void which is located between the Kagome nets. Powder diffraction experiments under high hydrostatic that - despite a space filling of only 55% - the ambient pressure modification is stable up to pressures show 26 GPa. Extended Mickel computations revealed significant overlap populations of Co and Snl orbitals in the Kagome nets and of Sn2 forming the graphite nets. The layers are connected by bonding interactions between Co and Sn2. Calculations of the electron localization function showed no indications of localized electron pairs within the 20-atom void. Keywords:
CoSn; Single crystal; Structure determination; High pressure; Intermetallic compound; Electron localization function
1. Introduction Graphite-like nets are a common feature in crystal structures of TB intermetallic phases (T: transition metal, B: tin compounds [1). main group e. g. metal), Several phases with 1:1 stoichiometry [2-8] and variants thereof, like NiInt_xSnx [9], (x=0-0.6) Fe2GaGe [10] and (Feo. Cr0.2,Nio. [11], crys2)Sn 6, tallize in the CoSn-type structure [12]; the corresPonding 1:2 composition crystallize compounds with in the CuA12-type structure [2,3,7-16]. Variations of stacking sequence [6,7,16,17] and intergrowth of segments [8,18] in a variety of new compositions. result The
number of isotypic phases indicates that CoSn [12] represents an important example of intermetallic compounds. According to the results of a crystal structure determination [12], by powder methods COSn can be described as consisting of two segments. In Fig. l(a) the 3636 Kagomenet of Co atoms is Corresponding author. Present
Research School of Chemistry, address: National University, Canberra ACT 0200, Australia.
Australian
0925-8388/96/$15.00 © 1996 Elsevier Science S.A. All rights reserved SSDI0925-8388(95)02189-2
emphasized. This net at z=0 is centred by Sn1 atoms, i. e. Co and Snl atoms together form a close packed hexagonal 36 net. Sn2 atoms at z =112 form a graphitic 63 net. A projection of the crystal structure along the [001] direction shown in Fig. 1(b) stresses that the graphite-like nets of Sn2 contain half the total number of atoms compared with the close packed Co3Sn1 nets. The layers are alternately stacked along the c-axis; this configuration leaves a 20-atom void around the centre of each hexagon in the graphite net, which is an extremely large empty space for an intermetallic structure. Since intermetallic phases are normally characterized by close packing and homogeneous coordination, the 20-atom void and the highly nonspherical coordination of the Sn1 atoms in CoSn are unusual and prompted the investigations presented here. A series of studies was performed to gather information on the nature of the crystal structure in general and the empty polyhedron in particular. It is tempting to speculate whether localized electrons in the voids could provide a reason for the stability of this intermetallic crystal structure. In the crystal structure of
80
A. K. Larsson
er al. / Journal
oJ Alloys
Adik
and Compuuunds 240 (/9%)
Adlk
79--84 AIL
0
. 0 0 VVV Ah
Ah
Ah
0
0
(h)
ww1 Fig. 1. The crystal strurturc ul ('uSn. (; I) Willi emphasis on the Kagu iuc net eil aihall anum Sn_' ,Aunt" runncct the lieu . Co, Sn2, polyhedra. (h) A projection along the 10OI ] direction stresses the centring ut the cobalt lets by Snt at urns.
Ni, Sn4 the stereochemical lone electron activity of 4 for the pairs has been suggested as an explanation nonspherical coordination of tin [19]. In the case of CoSn a stereochemically active electron pair connected to one of the tin atoms would lower the symmetry of the crystal structure. Hence, a single beam crystal structure refinement and convergent (('BED) electron diffraction experiments were performed to look for deviations from hln: nun symmetry. Large voids in a crystal structure he found in as can CoSn - normally indicate the possibility of a pressure-induced structural phase transition into a polymorph of higher density. Thus, we performed highto pressure X-ray powder diffraction experiments determine the stability range of the ambient pressure Finally, extended Hückel calculations modification. including the electron localization-function (ELF) are used to elucidate the bonding situation in this intermetallic structure.
I, v lurining
the lila iit
2. Experiments CoSn crystals were grown from a tin smelt. Sn and Co were mixed in it ratio 3.5: 1, scaled in a silica tuhe. heated to 650°C for 2 hours and cooled at it rate of* '. The ingot h 1()(1"(' approximately was then etched in 6M hydrochloric acid for 2 days to remove the tin matrix. The crystals, up to 3 mm in length, had irregular surfaces, and sonic of them were hollow due to the rough etching. A set of single crystal diffraction data was collected diffractºmmeter. Since the on a C'AD4 Enraf-Nonius surfaces of the crystals had poorly developed facets and were damaged by etching while removing the tin matrix, some crystals were ground. The crystal used for shape and, after corrections was of ellipsoidal absorption effects 1201, the crystal structure was refined [21] using standard atomic scattering factors [22] and assuming Lorentzian [23]. For mosaicity
81
A. K. Larsson et al. l Journal of Alloys and Compounds 240 (1996) 79-84
CBED experiments a Jeol 2000FX electron microscope was used [24]. High pressures were generated in gasketed diamond anvil cells with holes of typically 0.25 mm diameter using a 4:1 mixture of methanol-ethanol as a pressure transmitting medium. The ruby luminescence method was used as a pressure calibration [25]. Powder diagrams in transmission geometry were recorded on a two-circle diffractometer operated with Zr-filtered Mo Ka radiation detector. sensitive a and position 3. Results Since the crystal structure of CoSn has been investigated by powder methods only [12], a refinement using single crystal diffraction data was performed. Experimental details of data collection and refinement are shown in Table 1. The results confirm that Co is coordinated by a ten polyhedron consisting of a combination of a hexagon (4Co + 2Snl) with d(CoCo) = d(Co-Sn1) A, and a rectangle of 2.6395(3) = A. four Sn2 2.6189(4) with distances d(Co-Sn2) = Around Sn2, six Co atoms form a trigonal prism with d(Sn2-Co) 2.6189(4) A Sn2 three additional and = contacts d(Sn2-Sn2) = 3.0478(3) A cap the edges. The coordination polyhedron around Snl is highly nonspherical. Snl is coordinated by a hexagon of Co atoms with distances d(Co-Snl) = 2.6395(3) A.
Table 2 Atomic displacement parameters (Äz) of CoSn. The atomic posiand Co at tions are Sn1 at la(0,0,0), Sn2 at 2d(1/3,2/3,1/2), 3f(1 /2,0,0). For all occupied positions U, 3 = U2, =0 Atom
U,
U
U22
0.0053(1) 0.0064(1) 0.0065(1)
U U 0.0045(1)
U33
s0
Snl Sn2 Co
0.0068(1) 0.0056(1) 0.0059(1)
0.0099(1) 0.0041(1) 0.0059(1)
on the single crystal X-ray diffraction experiment: crystal data, intensity measurement and data refinement of CoSn Formula 177.6 weight (gmol-') Crystal habit metallic ellipsoid (ground) Half axis (mm3) 0.075 x 0.075 x 0.132
a a(A)
(A)
D--IC (g
25; 17-38 P6/mmm (191) 5.2790(7)
4.2597(10)
ý(Aj)
102.8(3)
3 cm-')
Intensity measurements Scan type; (deg) scan width 20 R90; No. x; reflections total, unique µ(Mo KI) (cm"'); F(000)
Transmission factor; extinction coefficient Structure refinements Weighting function No, observations (1>2o, ) No, variables; ratio Residuals R; Rý Goodness fit; max shift/error of MA, min Op (e A-')
1/2U 1/2U11 1/2U22
Atomic displacement parameters are shown in Table 2. Careful inspection of the displacement paSn1 the the that atom ellipsoid of shows rameters appears to be elongated along the c axis. According to the CBED study (vide infra) this is not due to lower symmetry. Taking into consideration the atomic packing of the crystal structure, the anisotropy can be explained as a result of the unusual coordination of Sn1 with all six short interatomic distances within the (001) plane. Thus, the amplitude of vibration is maxidisplacethe to and contacts, short mal perpendicular [0011 direction in Sn1 the corresponds to a ment of in direction the plane packed close of movement out 20-atom the large void. the within space empty of Unrecognized twinning usually shows up in signifi(which displacement might ellipsoids cantly anisotropic be restricted to one crystallographic site) owing to the fact that single crystal X-ray structure refinement incorrect if in an structure results an averaged crystal
Table 1 Details
Unit cell determination No. reflections; 20-range (deg) Space group
U12
8.606
w-2 ©; 0.60 + 0.50 tan 19 0.033 5513,307 296.43; 234
0.055-0.126;0.5642x 10-3
w' =QjýF2+(0.01Fä)2+1.0 306 8; 38 0.018; 0.024 1.06; 0.014 8.4, -4.4
82
A. K. Lamson
et at. / Journal
of Alluvs
and ('umpouuids
240 (1996)
79-84
of a minimum of eight reflections in the range 4.6 > A. Fig. 3(a) deterd>1.4 shows the experimentally mined volumes at pressures up to 26 GYa. The pressure-volume relation of CoSn was determined by fitting a Murnaghan-type equation of state [27] to the experimental data:
space group is chosen. Since the crystal structure of CoSn is peculiar for an intermetallic phase, and we indeed find a pronounced anisotropy of thermal diswas placement, an electron microscopy examination to detect any (possibly local) deviation undertaken from the symmetry of space group P6/mmm. By conventional electron diffraction no diffuse scattering or satellite reflection was detected. By using CBED the diffraction symmetry of an area about 100 A in diameter can be determined. This means that even small domains of lower symmetry can be detected. Along the zone axis (001) the whole pattern symmetry is 6mvrnv' (Fig. 2(a)). The diffraction group is then either 6mm or 6mm IR corresponding to point group 6mm and 61mmm respectively [26]. The whole pattern symmetry along (110) is 2mvmv' (Fig. 2(h)) which is compatible with the diffraction group 2mun IR only. Thus, 6mni can be excluded and 6/mmm is the only possible point group candidate. Lack of systematic extinctions of the (001) reflection confirms the space group (Fig. 2(b)) unambiguously group P61rnmm, consistent with earlier results from powder diffraction data [ 12 J. Lattice constants at various pressures were determined by least squares calculations using the d-values
where V is the volume at zero pressure, B the hulk modulus and B its pressure derivative. The solid line in; Fig. 3(a) was calculated using the values V = 102.8 A, B =4 and B = 127(8) GPa. The value of the hulk modulus compares well with a B of 160 GPa reported for the intermetallic PdZn [28]. PdZn compound in the CuAu-type crystallizes structure, an intermediate between a binary variety of a cubic close packing and a (`sCO structure. Fig. 3(h) shows the pressure dependence of the c/a-ratio. A decrease of about 1% over the investigated pressure range indiof CoSn is only slightly cates that the compressibility anisotropic and the pressure-induced alteration of the c/a ratio for CoSn is of the same order as the change found for PdZn [28].
(a)
(h)
Bo CPB
images of (oSn. (a) The symmetry of patterns taken along inne axis (()01) is fimi, mi' is 21n'niv' (acceleration voltage 2(H) kV). of images recorded along zone axis (lit))
Fig. 2. ('BED symmetry
/I3
(acceleration
voltage
IN) kV).
(h) The
A. K. Larsson et a!. / Journal of Alloys and Compounds 240 (1996) 79-84
83
35 M'
0.810
CoSn
c
0
a33 75
a cc
E L
0.805
Ll.
31 Q. au E m
0.800
> 29
05
15
10 Pressure
ýaý
20
25
UD
(GPa)
lU Pressure
15 (GPa)
"LU
(b)
Fig. 3. (a) Pressure-volume CoSn at pressures up to 26 Gpa. The solid line corresponds to a least squares fit of a Murnaghan-type of relation function to the experimental data. (b) cla ratio of CoSn at pressures up to 26 GPa. The solid line is a guide to the eye. Open symbols, single crystal data; filled symbols, powder diffraction data.
4" Calculations The ELF [29] has been found to be a useful tool for visualization of localized electrons which characterize chemical bonds, lone atomic shells and regions pair (30,31]. ELF is based on the probability of finding an electron with a spin parallel to that of a reference electron. The this probability is, the more smaller localized is the reference electron. ELF is defined to have the range 0< ELF <1 where ELF =1 correSPondsto perfect localization. The electronic density required for the ELF calculations was computed within the extended Mickel method using the program ehmacc [32]. The Mickel parameters are extended listed in Table 3. For the transition metal we take parameters from Ref. [33] the matrix elements where 11;,were determined by using charge iteration on bulk metals. The for tin are taken from Ref. parameters (34]. The k-point sets used were chosen according to the geometrical Ramirez and Böhm [35]. method of Fig. 4 shows the results of an ELF calculation, in Table 3 Parameters used for the extendedMickel calculations --" Co
S°
Orbital 4s 4P 3d 5s SP Contraction
(eV) _H -7.8 -3.8 -9.7 -16.16 -8.32
cz 2.00 2.00 5.55 2.12 1.82
1.90
0.5550
coefficients used in the double-ý expansion.
0.6678
Fig. 4. A contour map of the ELF in the (002) plane of the CoSn unit cell. The figure clearly shows two maxima between the Sn2 atoms. The centres of the empty polyhedra are located at the corners of the plot. No evidence is found for increased electron localization within the large voids.
which there are no indications of electron pairs in the centre of the large 20-atom void. Areas of increased electron localization are found in the honeycomb layer between the Sn2 atoms, but since we find two maxima of the ELF between the Sn2 atoms we have to rule out covalent bonding here [36]. On the basis of the presented data it is not clear whether the overall low ELF values indicate metallic bonding character of CoSn or are caused by the presence of Co(d) electrons. For further analysis of the bonding we calculated the overlap population of CoSn. The dominating bonding interactions are those between Co and Sn(1) within the (001) plane. Additionally, there is significant
84
A. K. Larsson et at. / Journal of Alloys and Compounds 240 (1996) 79-84
orbital overlap between the Sn2 atoms in the (002) plane. Co-Sn2 interactions of comparable magnitude connect the slices. These results of the calculations are consistent with the experimental finding of a small change in the c/a ratio with pressure.
5. Conclusion The crystal structure of CoSn was characterized by single crystal X-ray structure determination. The refinement reveals that the thermal displacement parameter of Sn1 is markedly anisotropic. Since the CBED experiments do not bear any evidence for a deviation from P6/mmm symmetry, the anisotropy of the thermal displacement is assigned to the unusual coordination of Snl. Thus, our findings concerning the crystal structure are in agreement with earlier results [12] from powder diffraction experiments. Within the investigated pressure range, the compressibility of CoSn is only slightly anisotropic. Furthermore, the bulk modulus of CoSn is in the range of values found for close packed elements and intermetallic structures. The findings of the extended Mickel calculations confirm the experimental evidence for a homogeneous network. Despite the occurrence of segments which are reminiscent of graphite nets, CoSn is a material with homodesmic bonding. Two descriptions of the CoSn structure are compatible with our theoretical and experimental findings. Firstly, CoSn can be viewed as a framework of condensed trigonal bipyramids Co3,2Sn22,2. The cobalt atoms forming a triangle connect each polyhedron within the (001) plane via vertex-sharing to three neighbours. The two capping tin atoms link adjacent slabs by corner-sharing along the [001] direction. In the resulting channels we find Sn1 hexagonally coordinated by cobalt corresponding to Sn1Cobl2 [11]. Alternatively, CoSn can be described as a Sn array isopointal to w-Ti [37] (c/a increased from 0.6 to 0.8) with elongated Sn1216Sn24/6octahedra occupied by Co. Four short distances d(Co-Co) = 2.6395(3) A result from the face sharing of these octahedra. In ionic compounds this short distance would result in a strong coulomb repulsion. In an intermetallic compound, however, the quasi-free conduction electrons cause an effective shielding of the core's net charge.
References [1] [2]
A. K. Larsson and S. Lidin, J. Alloys Comp., 221 (1995) 136. A. M. van der Kraan and K. H. J. ßuschow, Physica B&C, 138 (1986) 55.
[3] [4] [5] [6) [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20) [21] [22] [23] [24] [25] [26] [27] [28] [29) [30]
[31]
[32]
[33] [34] [35] [36] [37]
M. Richardson, Acta Chem. Scand., 21 (1967) 2305. E. Hellner and F. Laves, Z. Naturforsch. Teil A:, 2 (1947) 177. E. Hellner, Z. Metallkde., 41 (1950) 401. S. Bahn, T. Gödecke, P.K. Panday and K. Schubert, J. LessCommon Met., 16 (1968) 415. S. Bahn and K. Schubert, J. Less-Common Met., 17(1969) 73. M. El-Boragy, K. C. Jain, H. W. Mayer and K. Schubert, Z. Metallkde., 63 (1972) 751. M. K. Bhargava and K. Schubert, Z. Metallkde., 67(1976) 318. K. Schubert, M. Balk, S. Bhan, H. Breimer, P. Esslinger and E. Stolz, Naturwissenschaften, 46 (1959) 647. A. K. Larsson and S. Lidin, Acta Crystallogr. Sect. C:, 50 (1994) 13. O. Nial, Z. Anorg. Allg. Chem., 238 (1938) 287. E. E. Havinga, H. Damsma and P. Hokkeling, J. Less-Common Met., 27 (1972) 169. J. Wallbaum, Z. Metallkde., 35 (1943) 218. E. Kren and P. Szabo, Phys. Lett., 11 (1964) 215. K. Schubert, S. Bahn, T. K. Biswas, K. Frank and P.K. Panday, Naturwissenschaften, 55 (1968) 542. B. Malaman, B. Roques, A. Courtois and J. Protas, Acta Crystallogr. Sect. B:, 32 (1976) 1348. H. W. Mayer and K. Schubert, J. Less-Common Met., 33 (1973) 91. W. Jeitschko and B. Jaberg, Acta Crystallogr. Sect. B:, 38 (1982) 598. S. Lidin, A. Fogden and A. K. Larsson, Z. Kristallogr., 209 (1994) 930. J.-O. Lundgren, Crystallographic computer programs, Rep. No. UUIC-B13-4-05,1983 (University of Uppsala). International Tables for X-Ray Crystallography, Vol. IV, Kynoch Press, Birmingham, 1974. P.J. Becker and P. Coppens, Acta Crystallogr. Sect. A.; 30 (1974) 129. M. Tanaka and M. Terauchi, in Convergent-Beam Electron Diffraction, Jeol-Maruzen, Tokyo, 1985. G. J. Piermarini, S. Block, J.D. Barnett and R. A. Forman, J. Appl. Phys., 46 (1975) 2774. B. F. Buxton, J.A. Eades, J.W. Steeds and G. M. Rackham, Philos. Trans. R. Soc. London, 281 (1976) 171. F.D. Murnaghan, Proc. Natl. Acad. Sci. USA, 50 (1944) 244. H. Iwasaki, Acta Crystallogr. Sect. A:, 36 (1980) 299. A. D. Becke and K. E. Edgecombe, J. Chem. Phys., 92 (1990) 5397. A. Savin, A. D. Recke, J. Flad, R. Nesper, H. Preuss and H. G. von Schnering, Angew. Chem., 103 (1991) 421; Angew. Chem. Int. Ed. Engl., 30 (1991) 409. A. Savin, O. Jepsen, J. Flad, O. K. Andersen, H. Preuss, and H. G. von Schnering, Angew. Chem., 104 (1992) 186; Angew. Chem. Int. Ed. Eng!., 31 (1992) 187. M: H. Whangbo, M. Evain, T. Hughbanks, M. Kertesz, S. Wijeyesekera, C. Wilker, C. Zheng and R. Hoffmann, Program ehmacc; U. Häussermann, ELF routines. J: Y. Saillard and R. Hoffmann, J. Am. Chem. Soc., 106 (1984) 2006. J. Bernstein and R. Hoffmann, Inorg. Chem., 24 (1985) 4100. R. Ramirez and M. C. Böhm, Int. J. Quantum Chem., 34 (1988) 571. B. Silvi and A. Savin, Nature, 371 (1994) 683. B. G. Hyde and S. Andersson, in Inorganic Crystal Structures, Wiley, New York, 1989, pp. 138-140.
AND COMPOUNDS ELSEVIER
Journal of Alloys and Compounds 240 (1996) 79-84
Single crystal structure refinement and high-pressure properties of CoSn A. K. Larssona'', M. Haeberleinb, S. Lidina, U. Schwarzc'* University of Lund, Inorganic Chemistry 2, Box 124, S-22100 Lund, Sweden `Royal Institute of Technology, Department of Chemistry, Physical Chemistry, S-10044 Stockholm, Sweden `Max-Planck-Institut für Festkörperforschung, Heisenbergstraße 1, D-70569 Stuttgart, Germany Received 9 November 1995
Abstract Using singled A, P6/mmm, in 5.2790(7) CoSn data have the crystal structure of crystal refined space group a= we c=4.2597(10) A with Sn1 at Wyckoff position la, Sn2 at 2d, and Co at 3f. The space group used for the structure refinement was confirmed by beam electron diffraction investigation. The crystal structure contains graphite-like a convergent subsequent 6 nets of Sn2 atoms and Kagome nets of Co centred by the Snl atoms. An unusual feature for a crystal structure of an intermetallic compound is a 20-atom void which is located between the Kagome nets. Powder diffraction experiments under high hydrostatic that - despite a space filling of only 55% - the ambient pressure modification is stable up to pressures show 26 GPa. Extended Mickel computations revealed significant overlap populations of Co and Snl orbitals in the Kagome nets and of Sn2 forming the graphite nets. The layers are connected by bonding interactions between Co and Sn2. Calculations of the electron localization function showed no indications of localized electron pairs within the 20-atom void. Keywords:
CoSn; Single crystal; Structure determination; High pressure; Intermetallic compound; Electron localization function
1. Introduction Graphite-like nets are a common feature in crystal structures of TB intermetallic phases (T: transition metal, B: tin compounds [1). main group e. g. metal), Several phases with 1:1 stoichiometry [2-8] and variants thereof, like NiInt_xSnx [9], (x=0-0.6) Fe2GaGe [10] and (Feo. Cr0.2,Nio. [11], crys2)Sn 6, tallize in the CoSn-type structure [12]; the corresPonding 1:2 composition crystallize compounds with in the CuA12-type structure [2,3,7-16]. Variations of stacking sequence [6,7,16,17] and intergrowth of segments [8,18] in a variety of new compositions. result The
number of isotypic phases indicates that CoSn [12] represents an important example of intermetallic compounds. According to the results of a crystal structure determination [12], by powder methods COSn can be described as consisting of two segments. In Fig. l(a) the 3636 Kagomenet of Co atoms is Corresponding author. Present
Research School of Chemistry, address: National University, Canberra ACT 0200, Australia.
Australian
0925-8388/96/$15.00 © 1996 Elsevier Science S.A. All rights reserved SSDI0925-8388(95)02189-2
emphasized. This net at z=0 is centred by Sn1 atoms, i. e. Co and Snl atoms together form a close packed hexagonal 36 net. Sn2 atoms at z =112 form a graphitic 63 net. A projection of the crystal structure along the [001] direction shown in Fig. 1(b) stresses that the graphite-like nets of Sn2 contain half the total number of atoms compared with the close packed Co3Sn1 nets. The layers are alternately stacked along the c-axis; this configuration leaves a 20-atom void around the centre of each hexagon in the graphite net, which is an extremely large empty space for an intermetallic structure. Since intermetallic phases are normally characterized by close packing and homogeneous coordination, the 20-atom void and the highly nonspherical coordination of the Sn1 atoms in CoSn are unusual and prompted the investigations presented here. A series of studies was performed to gather information on the nature of the crystal structure in general and the empty polyhedron in particular. It is tempting to speculate whether localized electrons in the voids could provide a reason for the stability of this intermetallic crystal structure. In the crystal structure of
80
A. K. Larsson
er al. / Journal
oJ Alloys
Adik
and Compuuunds 240 (/9%)
Adlk
79--84 AIL
0
. 0 0 VVV Ah
Ah
Ah
0
0
(h)
ww1 Fig. 1. The crystal strurturc ul ('uSn. (; I) Willi emphasis on the Kagu iuc net eil aihall anum Sn_' ,Aunt" runncct the lieu . Co, Sn2, polyhedra. (h) A projection along the 10OI ] direction stresses the centring ut the cobalt lets by Snt at urns.
Ni, Sn4 the stereochemical lone electron activity of 4 for the pairs has been suggested as an explanation nonspherical coordination of tin [19]. In the case of CoSn a stereochemically active electron pair connected to one of the tin atoms would lower the symmetry of the crystal structure. Hence, a single beam crystal structure refinement and convergent (('BED) electron diffraction experiments were performed to look for deviations from hln: nun symmetry. Large voids in a crystal structure he found in as can CoSn - normally indicate the possibility of a pressure-induced structural phase transition into a polymorph of higher density. Thus, we performed highto pressure X-ray powder diffraction experiments determine the stability range of the ambient pressure Finally, extended Hückel calculations modification. including the electron localization-function (ELF) are used to elucidate the bonding situation in this intermetallic structure.
I, v lurining
the lila iit
2. Experiments CoSn crystals were grown from a tin smelt. Sn and Co were mixed in it ratio 3.5: 1, scaled in a silica tuhe. heated to 650°C for 2 hours and cooled at it rate of* '. The ingot h 1()(1"(' approximately was then etched in 6M hydrochloric acid for 2 days to remove the tin matrix. The crystals, up to 3 mm in length, had irregular surfaces, and sonic of them were hollow due to the rough etching. A set of single crystal diffraction data was collected diffractºmmeter. Since the on a C'AD4 Enraf-Nonius surfaces of the crystals had poorly developed facets and were damaged by etching while removing the tin matrix, some crystals were ground. The crystal used for shape and, after corrections was of ellipsoidal absorption effects 1201, the crystal structure was refined [21] using standard atomic scattering factors [22] and assuming Lorentzian [23]. For mosaicity
81
A. K. Larsson et al. l Journal of Alloys and Compounds 240 (1996) 79-84
CBED experiments a Jeol 2000FX electron microscope was used [24]. High pressures were generated in gasketed diamond anvil cells with holes of typically 0.25 mm diameter using a 4:1 mixture of methanol-ethanol as a pressure transmitting medium. The ruby luminescence method was used as a pressure calibration [25]. Powder diagrams in transmission geometry were recorded on a two-circle diffractometer operated with Zr-filtered Mo Ka radiation detector. sensitive a and position 3. Results Since the crystal structure of CoSn has been investigated by powder methods only [12], a refinement using single crystal diffraction data was performed. Experimental details of data collection and refinement are shown in Table 1. The results confirm that Co is coordinated by a ten polyhedron consisting of a combination of a hexagon (4Co + 2Snl) with d(CoCo) = d(Co-Sn1) A, and a rectangle of 2.6395(3) = A. four Sn2 2.6189(4) with distances d(Co-Sn2) = Around Sn2, six Co atoms form a trigonal prism with d(Sn2-Co) 2.6189(4) A Sn2 three additional and = contacts d(Sn2-Sn2) = 3.0478(3) A cap the edges. The coordination polyhedron around Snl is highly nonspherical. Snl is coordinated by a hexagon of Co atoms with distances d(Co-Snl) = 2.6395(3) A.
Table 2 Atomic displacement parameters (Äz) of CoSn. The atomic posiand Co at tions are Sn1 at la(0,0,0), Sn2 at 2d(1/3,2/3,1/2), 3f(1 /2,0,0). For all occupied positions U, 3 = U2, =0 Atom
U,
U
U22
0.0053(1) 0.0064(1) 0.0065(1)
U U 0.0045(1)
U33
s0
Snl Sn2 Co
0.0068(1) 0.0056(1) 0.0059(1)
0.0099(1) 0.0041(1) 0.0059(1)
on the single crystal X-ray diffraction experiment: crystal data, intensity measurement and data refinement of CoSn Formula 177.6 weight (gmol-') Crystal habit metallic ellipsoid (ground) Half axis (mm3) 0.075 x 0.075 x 0.132
a a(A)
(A)
D--IC (g
25; 17-38 P6/mmm (191) 5.2790(7)
4.2597(10)
ý(Aj)
102.8(3)
3 cm-')
Intensity measurements Scan type; (deg) scan width 20 R90; No. x; reflections total, unique µ(Mo KI) (cm"'); F(000)
Transmission factor; extinction coefficient Structure refinements Weighting function No, observations (1>2o, ) No, variables; ratio Residuals R; Rý Goodness fit; max shift/error of MA, min Op (e A-')
1/2U 1/2U11 1/2U22
Atomic displacement parameters are shown in Table 2. Careful inspection of the displacement paSn1 the the that atom ellipsoid of shows rameters appears to be elongated along the c axis. According to the CBED study (vide infra) this is not due to lower symmetry. Taking into consideration the atomic packing of the crystal structure, the anisotropy can be explained as a result of the unusual coordination of Sn1 with all six short interatomic distances within the (001) plane. Thus, the amplitude of vibration is maxidisplacethe to and contacts, short mal perpendicular [0011 direction in Sn1 the corresponds to a ment of in direction the plane packed close of movement out 20-atom the large void. the within space empty of Unrecognized twinning usually shows up in signifi(which displacement might ellipsoids cantly anisotropic be restricted to one crystallographic site) owing to the fact that single crystal X-ray structure refinement incorrect if in an structure results an averaged crystal
Table 1 Details
Unit cell determination No. reflections; 20-range (deg) Space group
U12
8.606
w-2 ©; 0.60 + 0.50 tan 19 0.033 5513,307 296.43; 234
0.055-0.126;0.5642x 10-3
w' =QjýF2+(0.01Fä)2+1.0 306 8; 38 0.018; 0.024 1.06; 0.014 8.4, -4.4
82
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et at. / Journal
of Alluvs
and ('umpouuids
240 (1996)
79-84
of a minimum of eight reflections in the range 4.6 > A. Fig. 3(a) deterd>1.4 shows the experimentally mined volumes at pressures up to 26 GYa. The pressure-volume relation of CoSn was determined by fitting a Murnaghan-type equation of state [27] to the experimental data:
space group is chosen. Since the crystal structure of CoSn is peculiar for an intermetallic phase, and we indeed find a pronounced anisotropy of thermal diswas placement, an electron microscopy examination to detect any (possibly local) deviation undertaken from the symmetry of space group P6/mmm. By conventional electron diffraction no diffuse scattering or satellite reflection was detected. By using CBED the diffraction symmetry of an area about 100 A in diameter can be determined. This means that even small domains of lower symmetry can be detected. Along the zone axis (001) the whole pattern symmetry is 6mvrnv' (Fig. 2(a)). The diffraction group is then either 6mm or 6mm IR corresponding to point group 6mm and 61mmm respectively [26]. The whole pattern symmetry along (110) is 2mvmv' (Fig. 2(h)) which is compatible with the diffraction group 2mun IR only. Thus, 6mni can be excluded and 6/mmm is the only possible point group candidate. Lack of systematic extinctions of the (001) reflection confirms the space group (Fig. 2(b)) unambiguously group P61rnmm, consistent with earlier results from powder diffraction data [ 12 J. Lattice constants at various pressures were determined by least squares calculations using the d-values
where V is the volume at zero pressure, B the hulk modulus and B its pressure derivative. The solid line in; Fig. 3(a) was calculated using the values V = 102.8 A, B =4 and B = 127(8) GPa. The value of the hulk modulus compares well with a B of 160 GPa reported for the intermetallic PdZn [28]. PdZn compound in the CuAu-type crystallizes structure, an intermediate between a binary variety of a cubic close packing and a (`sCO structure. Fig. 3(h) shows the pressure dependence of the c/a-ratio. A decrease of about 1% over the investigated pressure range indiof CoSn is only slightly cates that the compressibility anisotropic and the pressure-induced alteration of the c/a ratio for CoSn is of the same order as the change found for PdZn [28].
(a)
(h)
Bo CPB
images of (oSn. (a) The symmetry of patterns taken along inne axis (()01) is fimi, mi' is 21n'niv' (acceleration voltage 2(H) kV). of images recorded along zone axis (lit))
Fig. 2. ('BED symmetry
/I3
(acceleration
voltage
IN) kV).
(h) The
A. K. Larsson et a!. / Journal of Alloys and Compounds 240 (1996) 79-84
83
35 M'
0.810
CoSn
c
0
a33 75
a cc
E L
0.805
Ll.
31 Q. au E m
0.800
> 29
05
15
10 Pressure
ýaý
20
25
UD
(GPa)
lU Pressure
15 (GPa)
"LU
(b)
Fig. 3. (a) Pressure-volume CoSn at pressures up to 26 Gpa. The solid line corresponds to a least squares fit of a Murnaghan-type of relation function to the experimental data. (b) cla ratio of CoSn at pressures up to 26 GPa. The solid line is a guide to the eye. Open symbols, single crystal data; filled symbols, powder diffraction data.
4" Calculations The ELF [29] has been found to be a useful tool for visualization of localized electrons which characterize chemical bonds, lone atomic shells and regions pair (30,31]. ELF is based on the probability of finding an electron with a spin parallel to that of a reference electron. The this probability is, the more smaller localized is the reference electron. ELF is defined to have the range 0< ELF <1 where ELF =1 correSPondsto perfect localization. The electronic density required for the ELF calculations was computed within the extended Mickel method using the program ehmacc [32]. The Mickel parameters are extended listed in Table 3. For the transition metal we take parameters from Ref. [33] the matrix elements where 11;,were determined by using charge iteration on bulk metals. The for tin are taken from Ref. parameters (34]. The k-point sets used were chosen according to the geometrical Ramirez and Böhm [35]. method of Fig. 4 shows the results of an ELF calculation, in Table 3 Parameters used for the extendedMickel calculations --" Co
S°
Orbital 4s 4P 3d 5s SP Contraction
(eV) _H -7.8 -3.8 -9.7 -16.16 -8.32
cz 2.00 2.00 5.55 2.12 1.82
1.90
0.5550
coefficients used in the double-ý expansion.
0.6678
Fig. 4. A contour map of the ELF in the (002) plane of the CoSn unit cell. The figure clearly shows two maxima between the Sn2 atoms. The centres of the empty polyhedra are located at the corners of the plot. No evidence is found for increased electron localization within the large voids.
which there are no indications of electron pairs in the centre of the large 20-atom void. Areas of increased electron localization are found in the honeycomb layer between the Sn2 atoms, but since we find two maxima of the ELF between the Sn2 atoms we have to rule out covalent bonding here [36]. On the basis of the presented data it is not clear whether the overall low ELF values indicate metallic bonding character of CoSn or are caused by the presence of Co(d) electrons. For further analysis of the bonding we calculated the overlap population of CoSn. The dominating bonding interactions are those between Co and Sn(1) within the (001) plane. Additionally, there is significant
84
A. K. Larsson et at. / Journal of Alloys and Compounds 240 (1996) 79-84
orbital overlap between the Sn2 atoms in the (002) plane. Co-Sn2 interactions of comparable magnitude connect the slices. These results of the calculations are consistent with the experimental finding of a small change in the c/a ratio with pressure.
5. Conclusion The crystal structure of CoSn was characterized by single crystal X-ray structure determination. The refinement reveals that the thermal displacement parameter of Sn1 is markedly anisotropic. Since the CBED experiments do not bear any evidence for a deviation from P6/mmm symmetry, the anisotropy of the thermal displacement is assigned to the unusual coordination of Snl. Thus, our findings concerning the crystal structure are in agreement with earlier results [12] from powder diffraction experiments. Within the investigated pressure range, the compressibility of CoSn is only slightly anisotropic. Furthermore, the bulk modulus of CoSn is in the range of values found for close packed elements and intermetallic structures. The findings of the extended Mickel calculations confirm the experimental evidence for a homogeneous network. Despite the occurrence of segments which are reminiscent of graphite nets, CoSn is a material with homodesmic bonding. Two descriptions of the CoSn structure are compatible with our theoretical and experimental findings. Firstly, CoSn can be viewed as a framework of condensed trigonal bipyramids Co3,2Sn22,2. The cobalt atoms forming a triangle connect each polyhedron within the (001) plane via vertex-sharing to three neighbours. The two capping tin atoms link adjacent slabs by corner-sharing along the [001] direction. In the resulting channels we find Sn1 hexagonally coordinated by cobalt corresponding to Sn1Cobl2 [11]. Alternatively, CoSn can be described as a Sn array isopointal to w-Ti [37] (c/a increased from 0.6 to 0.8) with elongated Sn1216Sn24/6octahedra occupied by Co. Four short distances d(Co-Co) = 2.6395(3) A result from the face sharing of these octahedra. In ionic compounds this short distance would result in a strong coulomb repulsion. In an intermetallic compound, however, the quasi-free conduction electrons cause an effective shielding of the core's net charge.
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