- Email: [email protected]
The structure and bonding of Ni3Sn
Journal of Alloys and Compounds 340 (2002) 167–172
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The structure and bonding of Ni 3 Sn a b c c, a Andrei L. Lyubimtsev , Alexey I. Baranov , Andreas Fischer , Lars Kloo *, Boris A. Popovkin a
Inorganic Chemistry Division, Chemistry Department, Moscow State University, Vorob’ evy Gory, Moscow 119899, Russia b Materials Science Department, Moscow State University, Vorob’ evy Gory, Moscow 119899, Russia c Inorganic Chemistry, Royal Institute of Technology, Stockholm S 100 44, Sweden Received 14 December 2001; accepted 7 January 2002
Abstract The electronic structure of Ni 3 Sn was calculated at ab initio levels for the crystal structure of the low-temperature modification of ˚ R50.0288). The calculations Ni 3 Sn refined upon data of single-crystal X-ray diffractometry (P63 /mmc, a55.2950(7), c54.247(1) A, were made with the use of fixed Gaussian (CRYSTAL98 software) and energy-dependent (Stuttgart TB-LMTO-ASA software) basis sets. Difference electron charge density maps were analysed and compared with that of a hypothetical hcp Ni in order to understand bonding in Ni 3 Sn. It was found that bonding in Ni 3 Sn has multicentre character with Ni–Sn interaction stronger than Ni–Ni one. 2002 Elsevier Science B.V. All rights reserved. Keywords: Transition metal compound; Crystal structure; Electronic band structure; X-ray diffraction
1. Introduction The features of chemical bonding in intermetallics are one of the most interesting problems in modern chemistry. It is highly desirable to understand chemical bonding and to derive the principles of heterometallic bond formation because common bond models often can not provide consistent explanations of the bonding in intermetallics. Earlier studies of bonds between metal atoms recognize that intermetallic bonds should be multicentre because of the small number of available valence electrons per-metalatom [1]. However, it was difficult to distinguish between multicentre and covalent bonding without having a technique allowing a ‘look inside’ the compound. The only model was simple electron counting rules for example used by King to explain the bonding in gold intermetallics [2]. Recently, powerful theoretical tools such as ELF (electron localization function [3]) or AIM (Atoms in Molecules [4]) were applied in the analysis of the electronic structure of metals, leading to deeper understanding of the classical concept of the metallic bond [5]. Also, intermetallics have been studied by the use of ELF [6,7]. Some difficulties may occur in the interpretation of d-states because of their *Corresponding author. Fax: 146-8-790-9349. E-mail address: [email protected] (L. Kloo).
low ELF values. In such cases, valence charge densities were shown to be an appropriate tool to characterise the bonding properties involving d-states [7]. The crystal structure of Ni 3 Sn has not previously been explicitly determined and as a consequence, is absent in the ICSD Karlsruhe database [8]. It is known that Ni 3 Sn is isostructural with some other intermetallics (e.g. Fe 3 Sn [9], Fe 3 Ge [10] and Sc 3 In [11]), for which the crystal structures were reported at several levels of confidence. One reports [12,13] the existence of low- and high-temperature (T .1250 K) modifications of Ni 3 Sn. The ICDD PDF2 database [14] reports only one low-temperature modification of Ni 3 Sn, which crystallizes in the hexagonal ˚ c54.248 A). ˚ system (P63 /mmc (No. 194), a55.296 A, Earlier tight-binding calculations of Ni 3 Sn were carried out for a non-refined crystal structure [15], thus making an accurate analysis of bonding and electronic structure dubious. Only the band structure and density of states without any detailed analysis of orbital composition were reported. Also, no detailed analysis aimed at the understanding of the bonding in Ni 3 Sn was performed. The adequate description of the electronic structure of intermetallics and their properties is completely dependent on accurate knowledge about the crystal structure including potential superstructures, disorder or defects, such as vacancies [16]. This work presents a quantum chemical
0925-8388 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 02 )00047-6
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investigation of the electronic structure and bonding properties of the refined crystal structure of Ni 3 Sn.
2. Experimental
2.1. Synthesis and X-ray crystallography The crystals of Ni 3 Sn were obtained unexpectedly during an attempt to grow the crystals of new ternary nickel–tin telluride by the chemical transport reaction technique with the use of I 2 as a transport agent. An initial sample for crystal growth was synthesized by annealing the mixture of the elements (73.33% mol. Ni, 13.33% mol. Sn and 13.33% mol. Te) at 873 K during 280 h followed by grinding and further annealing at the same conditions. X-ray phase analysis showed that sample to be a mixture of Ni 3 Sn and new ternary nickel–tin telluride, which is under study now. The sample (0.2536 g) was mixed with I 2 (0.01 g) in a silica tube (203100 mm), evacuated and sealed off. A horizontal 2-zone furnace with the temperatures 893 K (sample region) and 823 K were used to perform crystal growth during 240 h. A brick-shaped, dark crystal of Ni 3 Sn was taken from the ‘cold’ part of the ampoule. The crystal structure was refined from singlecrystal X-ray data recorded at room temperature on a KappaCCD (Nonius) diffractometer 1 . Further details of the crystal structure investigation can be obtained from the Fachinformationszentrum Karlsruhe, 76344 Eggenstein– Leopoldshafen, Germany, (fax: (149)7247-808-666; email: [email protected]) on quoting the depositary number CSD-411928.
2.2. Calculation details 2.2.1. General The electronic structure of Ni 3 Sn was calculated by the use of CRYSTAL98 [17] and TB-LMTO-ASA [18] (ab initio) program packages. Modified Hay–Wadt effective core potential (ECP) basis sets [19] (see below), were used in the calculations (B3LYP hybrid exchange–correlation potential) made with CRYSTAL98. In order to investigate the dependence on the choice of ECP and basis set, modified Stuttgart–Dresden ECPs and basis sets [20] were used as well. Also, Hartree–Fock and DFT [local density approximation (LDA) using the Vosko–Wilk–Nusair ex1 Emp. formula: Ni 3 Sn, crystal size—0.07530.02530.025 mm; hexa˚ 3; gonal, sp.gr. P63 /mmc; a55.2950(7), c54.247(1), V5103.12(3) A 23 21 Z52, d calc 59.495 g cm , m 520.112 mm , radiation: AgK a , l 5 ˚ temperature: 298 K, u range: 3.518 u 25.118, 27,h,8, 0.56090 A, 24,k,3, 25,l ,6, total reflections: 124, independent reflections: 91, of which 85 have I . 2s (I), semiempirical absorption correction; SHELX-97, direct methods, full-matrix least squares, extinction correction, 8 parameters, R50.0288, wR250.0867, [w 5 1 / [s 2 (F 2o ) 1 (0.0528P)2 1 0.3518P] where P 5 [max(F 2o ) 1 2F 2c ] / 3, GoF51.162, re˚ 23 . sidual electron density (min. / max.)5 22.11 / 2.87 eA
change correlation potential (VWN)] Hamiltonians were used in order to check the reliability of the results obtained. The VWN correlation potential with nonlocal gradientcorrected Perdew–Wang exchange term was used in the LMTO calculations. No interstitials for that type of calculations were added, since the structure of Ni 3 Sn is closely packed. Hereafter, calculations performed with the use of CRYSTAL98 are referred to as B3 LYP/HW and with TB-LMTO-ASA as PW-VWN /LMTO. Average properties were calculated using a mesh of 28 k-points in the irreducible wedge of the Brillouin zone in the B3 LYP/HW calculations and of 270 k-points in the PW-VWN /LMTO one. The electronic structure of paramagnetic hcp nickel, calculated for sake of comparison, was computed with the use of the CRYSTAL98 package (B3LYP hybrid exchange–correlation potential and modified Hay–Wadt basis set). The mesh of 28 k-points was used in this case.
2.2.2. Basis set for B3 LYP/HW Several modifications were made in accordance with the CRYSTAL98 manual [17] in order to make the basis sets applicable for extended system calculations. Diffuse exponents (,0.1) of the contracted Gaussians in the Sn basis set [19] were removed and the contractions were completely split. The test calculation of bulk b -tin showed the modified basis set to be suitable and calculation results were in agreement with Ref. [21]. Test calculations with the use of the Hay–Wadt smallcore basis set [22] showed fcc Ni to be an insulator so that an additional d-exponent of value 0.20 was added to correct this discouraging fact. After the modification, the electronic structure of bulk fcc nickel (both para- and ferromagnetic) was well represented and in good agreement with the results of Ref. [23]. The Stuttgart–Dresden basis sets were modified by removal of the too diffuse exponents and tested to provide the proper conductivity properties of bulk fcc Ni and b -tin, as well.
2.2.3. Relaxation of the Ni3 Sn structure In order to validate the results of PW-VWN /LMTO calculations, the unit cell parameters of Ni 3 Sn were varied independently and equilibrium a and c were obtained via approximation of 2nd order polynomial. They occur to be ˚ longer than the experimental ones. Re-calculaabout 0.2 A tion of the electronic structure with equilibrium parameters showed that the band structure does not differ significantly from that obtained with the experimental unit cell parameters. The results for Ni 3 Sn presented in this work all originate from calculations performed with the experimentally determined crystal structure.
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2.2.4. The analysis of the difference charge density The difference charge density (Dr -defined as calculated electron charge density minus the superposition of atomic electron charge densities, using the density from B3 LYP/ HW for Ni 3 Sn) was analyzed in order to visualise a real-space representation of the bonding in Ni 3 Sn. The maxima of the difference charge density can be observed as isosurfaces. Such maxima may be interpreted as centers of regions, where the chemical bonds are located. In terms of the topology of the difference charge density gradient field, they can be called attractors; in accordance with the terminology usually employed in the analysis of charge densities [4]. The difference charge density was proposed to be a pictorial representation of the bond density [4], i.e. the higher the value of the Dr, the stronger the interaction it provides. The analysis and visualization of difference electronic charge densities were performed with the use of the TOPOND98 [24] and gOpenMol [25] program packages. Fig. 1. The crystal structure of Ni 3 Sn in terms of [Ni 6 ] octahedra.
3. Results and discussion We confirmed that Ni 3 Sn crystallizes in the hexagonal ˚ crystal system (P63 /mmc, a55.2950(7), c54.247(1) A). The Sn atomic positions (2c) are the same as those reported for Fe 3 Ge [10], whereas the Ni and Fe positions (6h) are quite close [Ni(0.8392, 0.6784, 0.25) in Ni 3 Sn vs. Fe(0.839, 0.678, 0.25) in Fe 3 Ge]. Traditionally, the Ni 3 Sn crystal structure is considered in terms of hexagonal close packing of Ni and Sn atoms [26]. Alternatively one can observe the 1D chains of opposite face-sharing [Ni 6 ] octahedra running parallel to the crystallographic c axis (Fig. 1). Therefore, d-electrons appear to be confined to only one dimension. ˚ Typical shortest interatomic distances are 2.6480(4) A ˚ for Ni–Ni. The for Ni–Sn and 2.555(2)–2.5854(7) A Ni–Ni distances are longer than in fcc metallic nickel [8] ˚ The Sn–Sn distances are about 3.72 A. ˚ Such (2.492 A). distances are very long as compared to the shortest Sn–Sn ˚ and they are close to noncontacts in b -Sn (3.023 A), ˚ [8]. bonding Sn–Sn distances in b -Sn (3.768 A) The high coordination number of Sn in this structure, which is equal to 12, points on the absence of Te atoms (potentially captured during the synthesis) in the Sn positions, since such high coordination numbers are very uncommon for tellurium. According both B3 LYP/HW and PW-VWN /LMTO calculations, Ni 3 Sn has metallic conductivity (Fig. 2). An analysis of the density of states (DOS) and orbital composition of the states (so-called ‘fat bands’) near the Fermi level shows that the main contribution is Ni–d and Sn–p. No dominant angular component (i.e. px , py or d xz , d xy etc.) can be chosen among them and consequently 3D metallic conductivity is apparent. These results are in agreement with those of Ref. [15].
The analysis of the electronic configurations of Ni and Sn based on both B3 LYP/HW and PW-VWN /LMTO, shows that Ni is of negative charge (approx. 20.1), and hence Sn of positive charge (approx. 10.3). The Ni d-orbitals are almost fully occupied, while the Sn s- and p-orbitals only are approximately half-filled. The Ni s- and p-orbitals are essentially non-occupied. Since essentially all Ni d-states are occupied, the confinement of the d-electrons in only one dimension by the tin atoms in Ni 3 Sn do not cause any anisotropy of the band structure near the Fermi level. ELF cannot be efficiently used for the analysis of bonding in Ni 3 Sn due to the reasons mentioned in the introduction. In fact, the regions with ELF $0.5 are localized only near Sn and seem to be almost spherically symmetric tin lone pairs. Thus, the difference charge density was utilized instead to visualize bonding in Ni 3 Sn. In order to make such an analysis more descriptive, the hypothetical structure of hcp Ni was used as a reference. The crystal structure of Ni 3 Sn can be viewed as a kind of hexagonal packing of two unequivalent atoms in the ratio 1:3 [26]. Nickel is known to crystallize with an fcc packing and a direct comparison of their crystal structures is impossible. However, one can calculate the electronic structure of hcp Ni and use it as a reference for Ni 3 Sn. It has been reported that hcp Ni can be stabilised as a thin film [27] and bulk hcp modification should be metallic [28]. The difference charge density map of the hcp Ni electronic structure is presented in Fig. 3. In hcp nickel such maxima are located inside the tetrahedral (marked as T ) and octahedral (marked as O) voids of the hcp packing, thus providing 4- and 6-centre interactions. If the level (i.e. Dr value) of the isosurface is increased, the T-type maxima will split. Also, spherically
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Fig. 2. Density of states and band structure of Ni 3 Sn (B3 LYP/HW ).
Fig. 3. Isosurfaces of the difference charge density of a hypothetical hcp Ni [Dr 5 10.0134 e 2 ?(a.u.)23 ]. Only the shortest Ni–Ni contacts of one chain of [Ni 6 ] face-sharing octahedra are shown.
shaped maxima surrounding the Ni atoms, which correspond to the core not active in bond formation, can be observed. Thus, in the case of a typical metallic system such as hcp Ni, the bonding is best characterised as multicentre. Both T and O maxima have approximately the same Dr values. Therefore, the electron charge density is distributed uniformly upon different types of voids. This picture of the metallic bond obtained with the difference charge density looks similar to that for a number of metals based on ELF [5]. In Ni 3 Sn one can distinguish voids inside [Ni 6 ] and [Ni 4 Sn 2 ] octahedra (corresponding to O1 and O2 in Fig. 4). Some Ni–Ni distances surrounding the O2 voids are ˚ In addition, the [Ni 3 Sn] tetrahedral quite long (2.74 A). voids in Ni 3 Sn are of two types: T1 and T2. All Ni–Ni ˚ distances, surrounding the T2 voids, are long (2.74 A). The difference charge density distribution in Ni 3 Sn visualized as isosurfaces, where Dr 5 10.0148 e 2 ?(a.u.)23 and Dr 5 10.0162 e 2 ?(a.u.)23 are shown in Fig. 5. The level of Dr was chosen to clearly present all maxima of difference charge density (left picture of Fig. 5, marked by T1, O1 and T2). In general, the distribution of the difference charge density is similar in Ni 3 Sn and hcp Ni. However, some differences can be noted. In hcp Ni maxima of the difference charge density can be found in all octahedral voids, while the maxima inside the [Ni 6 ] octahedra (of type O1) in Ni 3 Sn are much smaller than in hcp Ni. Moreover, no such maxima can be found for the O2 void in Ni 3 Sn. Thus, 6-centre Ni–Ni interaction is weaker in Ni 3 Sn than in hcp Ni. The size and shape of the O1-type isosurface strongly depends on the
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171
Fig. 4. Voids in Ni 3 Sn.
Dr level chosen (i.e. electron charge density is nearly constant), as it was noted earlier for metallic bonds [5]. The size and shape of maxima corresponding to the Ni–Sn interaction (types T1, T2 in Ni 3 Sn) do not depend so strongly on the Dr level. The maxima located inside the distorted [Ni 3 Sn] tetrahedra (i.e. inside the T1 tetrahedral voids), form a body of type T1 (Fig. 5, left). An increase of the isosurface level to
about 10.0162 e 2 ?(a.u.)23 (right picture, Fig. 5) splits the T1 maximum into two pairs (simultaneously, the O1 type of maxima disappears). Similar maxima can be found in hcp Ni as well. Every maximum of difference charge density has a smoothed tetrahedral shape. They correspond to a 4-centre Ni–Sn interaction. Here, Ni–Sn bonding seem to be stronger than Ni–Ni since the maxima of the difference charge density are placed outside the [Ni 6 ]
Fig. 5. Isosurfaces of difference charge density in Ni 3 Sn. White balls represent Sn atoms and dark ‘bonds’ the shortest Ni–Ni interatomic distances.
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octahedra. Compared with the maxima of the 6-centre Ni–Ni bond located in the octahedral voids, the former maxima are much bigger. In hcp Ni, in contrast, they are of similar size. This may be interpreted in terms of a Ni–Sn interaction in tetrahedral voids stronger than Ni–Ni in Ni 3 Sn. Maxima, for which the difference charge density is even higher than for T1 and O1, are located at the position (1 / 3, 2 / 3, 3 / 4); just halfway from one Sn atom to another along the crystallographic c axis, on the common face of two face-sharing [Ni 3 Sn] tetrahedra, corresponding to the T2 voids (Fig. 4). That type of maxima corresponds to a 5-centre Ni–Ni and Ni–Sn interaction involving Ni atoms from neighbouring chains of [Ni 6 ] octahedra. The Ni ˚ atoms form a perfect triangle [d(Ni–Ni)52.740 A]. It is known that the presence, the position of the attractor and the shape of its isosurface can depend strongly on the basis set chosen [5]. In our calculations, we noted that with the use of the Stuttgart–Dresden basis sets some maxima change in shape and position, but still, the general picture is highly similar to the one obtained with Hay–Wadt basis set. The Hamiltonian used also has an influence. For instance, HF calculations lead to a less pronounced multicentre character (a set of 3-centre Ni–Sn interactions instead of a 4-centre). However, we believe DFT calculations to be more suitable for metallic systems than conventional Hartree–Fock involving no correlation corrections 2 . In conclusion, both basis sets and level of theory are impacting factors, but the differences observed in this work are not significant. In summary, the bonding in Ni 3 Sn is provided by similar multicentre interactions observed in hypothetical hcp Ni. However, the presence of two different metal components in the crystal structure leads to a non-uniform distribution of the electron ‘gluemaking’ Ni–Sn interactions stronger than the Ni–Ni ones.
Acknowledgements ¨ The authors gratefully thank Dr U. Haussermann (Stockholm University) for fruitful discussion of the calculation results. The Natural Science Research Council (Sweden) is acknowledged for the financial support of the diffractome-
2
Because of the exchange potential used in the DFT Hamiltonian has been taken from uniform homogeneous electron gas model, which appears adequate for metallic systems.
ter. This work was supported by INTAS project No 991672 and Russian Foundation for Basic Research (RFBR) grant No. 00-03-32647a.
References [1] R.S. Nyholm, Adv. Sci. 23 (115) (1967) 421. [2] R.B. King, Inorg. Chim. Acta 277 (1998) 202. [3] (a) A.D. Becke, N.E. Edgecombe, J. Chem. Phys. 92 (1990) 5397; ¨ (b) A. Savin, R. Nesper, S. Wengert, T.F. Fassler, Angew. Chem., Int. Ed. Engl. 36 (1997) 1808, review on ELF application. [4] R.W.F. Bader, Atoms in Molecules. A Quantum Theory, Clarendon Press, Oxford, 1990. [5] B. Silvi, C. Gatti, J. Phys. Chem. A 104 (2000) 947. [6] Yu. Grin, U. Wedig, F. Wagner, H.G. von Schnering, A. Savin, J. Alloys Comp. 255 (1997) 203. [7] Y. Grin, U. Wedig, H.G. von Schnering, Angew. Chem., Int. Ed. Engl. 34 (11) (1995) 1204. [8] ICSD database. Karlsruhe 1999. [9] O. Nial, Sven. Kem. Tidskr. 9 (1947) 165. [10] J.P. Turbil, Y. Bulliet, A. Michel, Comptes Rendus Hebd. Seances de l’Acad, Sci. Ser. C Sci. Chim. 269 (1969) 309. [11] V.B. Compton, B.T. Matthias, Acta Crystallogr. 15 (1962) 94. [12] H. Massalski, Binary Alloy Phase Diagrams, 2nd Edition, ASN International, 1990. [13] P. Nash, A. Nash, Bull. Alloy Phase Diagrams 6 (4) (1985) 350. [14] JCPDS-ICDD 1996 PCPDF2 database. ˇ Phys. Status Solidi (b) 173 (1992) K13. [15] M. Divis, [16] H. Nakamura, D. Nguyen–Manh, D.G. Pettifor, J. Alloys Comp. 281 (1998) 81. ` N.M. Harrison, R. [17] V.R. Saunders, R. Dovesi, C. Roetti, M. Causa, Orlando, C.M. Zicovich–Wilson, CRYSTAL98 User’s Manual, University of Torino, Torino, 1998. [18] O. Jepsen, O.K. Andersen, The Stuttgart TB-LMTO-ASA program. ¨ Festkorperforschung, ¨ Version 4.7, Max-Planck-Institut fur Stuttgart, Aug. 2000. [19] P.J. Hay, W.R. Wadt, J. Chem. Phys. 82 (1) (1985) 270. [20] (a) M. Dolg, U. Wedig, H. Stoll, H. Preuss, J. Chem. Phys. 86 (1987) 866, for Ni; (b) G. Igel–Mann, H. Stoll, H. Preuss, Mol. Phys. 65 (1988) 1321, for Sn. [21] A. Svane, E. Antoncik, Solid State Commun. 58 (8) (1986) 541. [22] F. Freyria–Fava, Thesis Turin, 1997. [23] T. Jarlborg, A.J. Freeman, J. Magn. Magn. Mater. 22 (1980) 6. [24] C. Gatti, TOPOND 98 User’s Manual, CNR-CSRSRC, Milano, 1999. [25] L. Laaksonen, gOpenMol v.1.4, http: / / www.csc.fi / |laaksone / gopenmol / gIntro.html [26] A.F. Wells, Structural Inorganic Chemistry, 5th Edition, Clarendon Press, Oxford, 1984. [27] H. Weik, P. Hemenger, Bull. Am. Phys. Soc. 10 (1965) 1140. [28] D.A. Papaconstantopoulos, J.L. Fry, N.E. Brener, Phys. Rev. B 39 (4) (1989) 2526.
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The structure and bonding of Ni 3 Sn a b c c, a Andrei L. Lyubimtsev , Alexey I. Baranov , Andreas Fischer , Lars Kloo *, Boris A. Popovkin a
Inorganic Chemistry Division, Chemistry Department, Moscow State University, Vorob’ evy Gory, Moscow 119899, Russia b Materials Science Department, Moscow State University, Vorob’ evy Gory, Moscow 119899, Russia c Inorganic Chemistry, Royal Institute of Technology, Stockholm S 100 44, Sweden Received 14 December 2001; accepted 7 January 2002
Abstract The electronic structure of Ni 3 Sn was calculated at ab initio levels for the crystal structure of the low-temperature modification of ˚ R50.0288). The calculations Ni 3 Sn refined upon data of single-crystal X-ray diffractometry (P63 /mmc, a55.2950(7), c54.247(1) A, were made with the use of fixed Gaussian (CRYSTAL98 software) and energy-dependent (Stuttgart TB-LMTO-ASA software) basis sets. Difference electron charge density maps were analysed and compared with that of a hypothetical hcp Ni in order to understand bonding in Ni 3 Sn. It was found that bonding in Ni 3 Sn has multicentre character with Ni–Sn interaction stronger than Ni–Ni one. 2002 Elsevier Science B.V. All rights reserved. Keywords: Transition metal compound; Crystal structure; Electronic band structure; X-ray diffraction
1. Introduction The features of chemical bonding in intermetallics are one of the most interesting problems in modern chemistry. It is highly desirable to understand chemical bonding and to derive the principles of heterometallic bond formation because common bond models often can not provide consistent explanations of the bonding in intermetallics. Earlier studies of bonds between metal atoms recognize that intermetallic bonds should be multicentre because of the small number of available valence electrons per-metalatom [1]. However, it was difficult to distinguish between multicentre and covalent bonding without having a technique allowing a ‘look inside’ the compound. The only model was simple electron counting rules for example used by King to explain the bonding in gold intermetallics [2]. Recently, powerful theoretical tools such as ELF (electron localization function [3]) or AIM (Atoms in Molecules [4]) were applied in the analysis of the electronic structure of metals, leading to deeper understanding of the classical concept of the metallic bond [5]. Also, intermetallics have been studied by the use of ELF [6,7]. Some difficulties may occur in the interpretation of d-states because of their *Corresponding author. Fax: 146-8-790-9349. E-mail address: [email protected] (L. Kloo).
low ELF values. In such cases, valence charge densities were shown to be an appropriate tool to characterise the bonding properties involving d-states [7]. The crystal structure of Ni 3 Sn has not previously been explicitly determined and as a consequence, is absent in the ICSD Karlsruhe database [8]. It is known that Ni 3 Sn is isostructural with some other intermetallics (e.g. Fe 3 Sn [9], Fe 3 Ge [10] and Sc 3 In [11]), for which the crystal structures were reported at several levels of confidence. One reports [12,13] the existence of low- and high-temperature (T .1250 K) modifications of Ni 3 Sn. The ICDD PDF2 database [14] reports only one low-temperature modification of Ni 3 Sn, which crystallizes in the hexagonal ˚ c54.248 A). ˚ system (P63 /mmc (No. 194), a55.296 A, Earlier tight-binding calculations of Ni 3 Sn were carried out for a non-refined crystal structure [15], thus making an accurate analysis of bonding and electronic structure dubious. Only the band structure and density of states without any detailed analysis of orbital composition were reported. Also, no detailed analysis aimed at the understanding of the bonding in Ni 3 Sn was performed. The adequate description of the electronic structure of intermetallics and their properties is completely dependent on accurate knowledge about the crystal structure including potential superstructures, disorder or defects, such as vacancies [16]. This work presents a quantum chemical
0925-8388 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 02 )00047-6
168
A.L. Lyubimtsev et al. / Journal of Alloys and Compounds 340 (2002) 167 – 172
investigation of the electronic structure and bonding properties of the refined crystal structure of Ni 3 Sn.
2. Experimental
2.1. Synthesis and X-ray crystallography The crystals of Ni 3 Sn were obtained unexpectedly during an attempt to grow the crystals of new ternary nickel–tin telluride by the chemical transport reaction technique with the use of I 2 as a transport agent. An initial sample for crystal growth was synthesized by annealing the mixture of the elements (73.33% mol. Ni, 13.33% mol. Sn and 13.33% mol. Te) at 873 K during 280 h followed by grinding and further annealing at the same conditions. X-ray phase analysis showed that sample to be a mixture of Ni 3 Sn and new ternary nickel–tin telluride, which is under study now. The sample (0.2536 g) was mixed with I 2 (0.01 g) in a silica tube (203100 mm), evacuated and sealed off. A horizontal 2-zone furnace with the temperatures 893 K (sample region) and 823 K were used to perform crystal growth during 240 h. A brick-shaped, dark crystal of Ni 3 Sn was taken from the ‘cold’ part of the ampoule. The crystal structure was refined from singlecrystal X-ray data recorded at room temperature on a KappaCCD (Nonius) diffractometer 1 . Further details of the crystal structure investigation can be obtained from the Fachinformationszentrum Karlsruhe, 76344 Eggenstein– Leopoldshafen, Germany, (fax: (149)7247-808-666; email: [email protected]) on quoting the depositary number CSD-411928.
2.2. Calculation details 2.2.1. General The electronic structure of Ni 3 Sn was calculated by the use of CRYSTAL98 [17] and TB-LMTO-ASA [18] (ab initio) program packages. Modified Hay–Wadt effective core potential (ECP) basis sets [19] (see below), were used in the calculations (B3LYP hybrid exchange–correlation potential) made with CRYSTAL98. In order to investigate the dependence on the choice of ECP and basis set, modified Stuttgart–Dresden ECPs and basis sets [20] were used as well. Also, Hartree–Fock and DFT [local density approximation (LDA) using the Vosko–Wilk–Nusair ex1 Emp. formula: Ni 3 Sn, crystal size—0.07530.02530.025 mm; hexa˚ 3; gonal, sp.gr. P63 /mmc; a55.2950(7), c54.247(1), V5103.12(3) A 23 21 Z52, d calc 59.495 g cm , m 520.112 mm , radiation: AgK a , l 5 ˚ temperature: 298 K, u range: 3.518 u 25.118, 27,h,8, 0.56090 A, 24,k,3, 25,l ,6, total reflections: 124, independent reflections: 91, of which 85 have I . 2s (I), semiempirical absorption correction; SHELX-97, direct methods, full-matrix least squares, extinction correction, 8 parameters, R50.0288, wR250.0867, [w 5 1 / [s 2 (F 2o ) 1 (0.0528P)2 1 0.3518P] where P 5 [max(F 2o ) 1 2F 2c ] / 3, GoF51.162, re˚ 23 . sidual electron density (min. / max.)5 22.11 / 2.87 eA
change correlation potential (VWN)] Hamiltonians were used in order to check the reliability of the results obtained. The VWN correlation potential with nonlocal gradientcorrected Perdew–Wang exchange term was used in the LMTO calculations. No interstitials for that type of calculations were added, since the structure of Ni 3 Sn is closely packed. Hereafter, calculations performed with the use of CRYSTAL98 are referred to as B3 LYP/HW and with TB-LMTO-ASA as PW-VWN /LMTO. Average properties were calculated using a mesh of 28 k-points in the irreducible wedge of the Brillouin zone in the B3 LYP/HW calculations and of 270 k-points in the PW-VWN /LMTO one. The electronic structure of paramagnetic hcp nickel, calculated for sake of comparison, was computed with the use of the CRYSTAL98 package (B3LYP hybrid exchange–correlation potential and modified Hay–Wadt basis set). The mesh of 28 k-points was used in this case.
2.2.2. Basis set for B3 LYP/HW Several modifications were made in accordance with the CRYSTAL98 manual [17] in order to make the basis sets applicable for extended system calculations. Diffuse exponents (,0.1) of the contracted Gaussians in the Sn basis set [19] were removed and the contractions were completely split. The test calculation of bulk b -tin showed the modified basis set to be suitable and calculation results were in agreement with Ref. [21]. Test calculations with the use of the Hay–Wadt smallcore basis set [22] showed fcc Ni to be an insulator so that an additional d-exponent of value 0.20 was added to correct this discouraging fact. After the modification, the electronic structure of bulk fcc nickel (both para- and ferromagnetic) was well represented and in good agreement with the results of Ref. [23]. The Stuttgart–Dresden basis sets were modified by removal of the too diffuse exponents and tested to provide the proper conductivity properties of bulk fcc Ni and b -tin, as well.
2.2.3. Relaxation of the Ni3 Sn structure In order to validate the results of PW-VWN /LMTO calculations, the unit cell parameters of Ni 3 Sn were varied independently and equilibrium a and c were obtained via approximation of 2nd order polynomial. They occur to be ˚ longer than the experimental ones. Re-calculaabout 0.2 A tion of the electronic structure with equilibrium parameters showed that the band structure does not differ significantly from that obtained with the experimental unit cell parameters. The results for Ni 3 Sn presented in this work all originate from calculations performed with the experimentally determined crystal structure.
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2.2.4. The analysis of the difference charge density The difference charge density (Dr -defined as calculated electron charge density minus the superposition of atomic electron charge densities, using the density from B3 LYP/ HW for Ni 3 Sn) was analyzed in order to visualise a real-space representation of the bonding in Ni 3 Sn. The maxima of the difference charge density can be observed as isosurfaces. Such maxima may be interpreted as centers of regions, where the chemical bonds are located. In terms of the topology of the difference charge density gradient field, they can be called attractors; in accordance with the terminology usually employed in the analysis of charge densities [4]. The difference charge density was proposed to be a pictorial representation of the bond density [4], i.e. the higher the value of the Dr, the stronger the interaction it provides. The analysis and visualization of difference electronic charge densities were performed with the use of the TOPOND98 [24] and gOpenMol [25] program packages. Fig. 1. The crystal structure of Ni 3 Sn in terms of [Ni 6 ] octahedra.
3. Results and discussion We confirmed that Ni 3 Sn crystallizes in the hexagonal ˚ crystal system (P63 /mmc, a55.2950(7), c54.247(1) A). The Sn atomic positions (2c) are the same as those reported for Fe 3 Ge [10], whereas the Ni and Fe positions (6h) are quite close [Ni(0.8392, 0.6784, 0.25) in Ni 3 Sn vs. Fe(0.839, 0.678, 0.25) in Fe 3 Ge]. Traditionally, the Ni 3 Sn crystal structure is considered in terms of hexagonal close packing of Ni and Sn atoms [26]. Alternatively one can observe the 1D chains of opposite face-sharing [Ni 6 ] octahedra running parallel to the crystallographic c axis (Fig. 1). Therefore, d-electrons appear to be confined to only one dimension. ˚ Typical shortest interatomic distances are 2.6480(4) A ˚ for Ni–Ni. The for Ni–Sn and 2.555(2)–2.5854(7) A Ni–Ni distances are longer than in fcc metallic nickel [8] ˚ The Sn–Sn distances are about 3.72 A. ˚ Such (2.492 A). distances are very long as compared to the shortest Sn–Sn ˚ and they are close to noncontacts in b -Sn (3.023 A), ˚ [8]. bonding Sn–Sn distances in b -Sn (3.768 A) The high coordination number of Sn in this structure, which is equal to 12, points on the absence of Te atoms (potentially captured during the synthesis) in the Sn positions, since such high coordination numbers are very uncommon for tellurium. According both B3 LYP/HW and PW-VWN /LMTO calculations, Ni 3 Sn has metallic conductivity (Fig. 2). An analysis of the density of states (DOS) and orbital composition of the states (so-called ‘fat bands’) near the Fermi level shows that the main contribution is Ni–d and Sn–p. No dominant angular component (i.e. px , py or d xz , d xy etc.) can be chosen among them and consequently 3D metallic conductivity is apparent. These results are in agreement with those of Ref. [15].
The analysis of the electronic configurations of Ni and Sn based on both B3 LYP/HW and PW-VWN /LMTO, shows that Ni is of negative charge (approx. 20.1), and hence Sn of positive charge (approx. 10.3). The Ni d-orbitals are almost fully occupied, while the Sn s- and p-orbitals only are approximately half-filled. The Ni s- and p-orbitals are essentially non-occupied. Since essentially all Ni d-states are occupied, the confinement of the d-electrons in only one dimension by the tin atoms in Ni 3 Sn do not cause any anisotropy of the band structure near the Fermi level. ELF cannot be efficiently used for the analysis of bonding in Ni 3 Sn due to the reasons mentioned in the introduction. In fact, the regions with ELF $0.5 are localized only near Sn and seem to be almost spherically symmetric tin lone pairs. Thus, the difference charge density was utilized instead to visualize bonding in Ni 3 Sn. In order to make such an analysis more descriptive, the hypothetical structure of hcp Ni was used as a reference. The crystal structure of Ni 3 Sn can be viewed as a kind of hexagonal packing of two unequivalent atoms in the ratio 1:3 [26]. Nickel is known to crystallize with an fcc packing and a direct comparison of their crystal structures is impossible. However, one can calculate the electronic structure of hcp Ni and use it as a reference for Ni 3 Sn. It has been reported that hcp Ni can be stabilised as a thin film [27] and bulk hcp modification should be metallic [28]. The difference charge density map of the hcp Ni electronic structure is presented in Fig. 3. In hcp nickel such maxima are located inside the tetrahedral (marked as T ) and octahedral (marked as O) voids of the hcp packing, thus providing 4- and 6-centre interactions. If the level (i.e. Dr value) of the isosurface is increased, the T-type maxima will split. Also, spherically
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Fig. 2. Density of states and band structure of Ni 3 Sn (B3 LYP/HW ).
Fig. 3. Isosurfaces of the difference charge density of a hypothetical hcp Ni [Dr 5 10.0134 e 2 ?(a.u.)23 ]. Only the shortest Ni–Ni contacts of one chain of [Ni 6 ] face-sharing octahedra are shown.
shaped maxima surrounding the Ni atoms, which correspond to the core not active in bond formation, can be observed. Thus, in the case of a typical metallic system such as hcp Ni, the bonding is best characterised as multicentre. Both T and O maxima have approximately the same Dr values. Therefore, the electron charge density is distributed uniformly upon different types of voids. This picture of the metallic bond obtained with the difference charge density looks similar to that for a number of metals based on ELF [5]. In Ni 3 Sn one can distinguish voids inside [Ni 6 ] and [Ni 4 Sn 2 ] octahedra (corresponding to O1 and O2 in Fig. 4). Some Ni–Ni distances surrounding the O2 voids are ˚ In addition, the [Ni 3 Sn] tetrahedral quite long (2.74 A). voids in Ni 3 Sn are of two types: T1 and T2. All Ni–Ni ˚ distances, surrounding the T2 voids, are long (2.74 A). The difference charge density distribution in Ni 3 Sn visualized as isosurfaces, where Dr 5 10.0148 e 2 ?(a.u.)23 and Dr 5 10.0162 e 2 ?(a.u.)23 are shown in Fig. 5. The level of Dr was chosen to clearly present all maxima of difference charge density (left picture of Fig. 5, marked by T1, O1 and T2). In general, the distribution of the difference charge density is similar in Ni 3 Sn and hcp Ni. However, some differences can be noted. In hcp Ni maxima of the difference charge density can be found in all octahedral voids, while the maxima inside the [Ni 6 ] octahedra (of type O1) in Ni 3 Sn are much smaller than in hcp Ni. Moreover, no such maxima can be found for the O2 void in Ni 3 Sn. Thus, 6-centre Ni–Ni interaction is weaker in Ni 3 Sn than in hcp Ni. The size and shape of the O1-type isosurface strongly depends on the
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Fig. 4. Voids in Ni 3 Sn.
Dr level chosen (i.e. electron charge density is nearly constant), as it was noted earlier for metallic bonds [5]. The size and shape of maxima corresponding to the Ni–Sn interaction (types T1, T2 in Ni 3 Sn) do not depend so strongly on the Dr level. The maxima located inside the distorted [Ni 3 Sn] tetrahedra (i.e. inside the T1 tetrahedral voids), form a body of type T1 (Fig. 5, left). An increase of the isosurface level to
about 10.0162 e 2 ?(a.u.)23 (right picture, Fig. 5) splits the T1 maximum into two pairs (simultaneously, the O1 type of maxima disappears). Similar maxima can be found in hcp Ni as well. Every maximum of difference charge density has a smoothed tetrahedral shape. They correspond to a 4-centre Ni–Sn interaction. Here, Ni–Sn bonding seem to be stronger than Ni–Ni since the maxima of the difference charge density are placed outside the [Ni 6 ]
Fig. 5. Isosurfaces of difference charge density in Ni 3 Sn. White balls represent Sn atoms and dark ‘bonds’ the shortest Ni–Ni interatomic distances.
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octahedra. Compared with the maxima of the 6-centre Ni–Ni bond located in the octahedral voids, the former maxima are much bigger. In hcp Ni, in contrast, they are of similar size. This may be interpreted in terms of a Ni–Sn interaction in tetrahedral voids stronger than Ni–Ni in Ni 3 Sn. Maxima, for which the difference charge density is even higher than for T1 and O1, are located at the position (1 / 3, 2 / 3, 3 / 4); just halfway from one Sn atom to another along the crystallographic c axis, on the common face of two face-sharing [Ni 3 Sn] tetrahedra, corresponding to the T2 voids (Fig. 4). That type of maxima corresponds to a 5-centre Ni–Ni and Ni–Sn interaction involving Ni atoms from neighbouring chains of [Ni 6 ] octahedra. The Ni ˚ atoms form a perfect triangle [d(Ni–Ni)52.740 A]. It is known that the presence, the position of the attractor and the shape of its isosurface can depend strongly on the basis set chosen [5]. In our calculations, we noted that with the use of the Stuttgart–Dresden basis sets some maxima change in shape and position, but still, the general picture is highly similar to the one obtained with Hay–Wadt basis set. The Hamiltonian used also has an influence. For instance, HF calculations lead to a less pronounced multicentre character (a set of 3-centre Ni–Sn interactions instead of a 4-centre). However, we believe DFT calculations to be more suitable for metallic systems than conventional Hartree–Fock involving no correlation corrections 2 . In conclusion, both basis sets and level of theory are impacting factors, but the differences observed in this work are not significant. In summary, the bonding in Ni 3 Sn is provided by similar multicentre interactions observed in hypothetical hcp Ni. However, the presence of two different metal components in the crystal structure leads to a non-uniform distribution of the electron ‘gluemaking’ Ni–Sn interactions stronger than the Ni–Ni ones.
Acknowledgements ¨ The authors gratefully thank Dr U. Haussermann (Stockholm University) for fruitful discussion of the calculation results. The Natural Science Research Council (Sweden) is acknowledged for the financial support of the diffractome-
2
Because of the exchange potential used in the DFT Hamiltonian has been taken from uniform homogeneous electron gas model, which appears adequate for metallic systems.
ter. This work was supported by INTAS project No 991672 and Russian Foundation for Basic Research (RFBR) grant No. 00-03-32647a.
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