- Email: [email protected]
The crystal structure of Ni13Sn8P3 elucidated from HREM
Solid State Sciences 5 (2003) 205–217 www.elsevier.com/locate/ssscie
The crystal structure of Ni13Sn8 P3 elucidated from HREM F.J. García-García a , A.K. Larsson a,∗ , S. Furuseth b a Department of Inorganic Chemistry, Arrhenius Laboratory, Stockholm University, 106 91 Stockholm, Sweden b Department of Chemistry, University of Oslo, 0315 Oslo 3, Norway
Received 13 June 2002; accepted 27 June 2002 Dedicated to Sten Andersson for his scientific contribution to Solid State and Structural Chemistry
Abstract The crystal structure of Ni13 Sn8 P3 was elucidated from High Resolution Electron Microscopy Images. It was found to be a superstructure of the B8-type (NiAs-type) structure with Sn and P atoms ordered at the hexagonally closepacked array and Ni atoms in all octahedral and in two out of every eleven trigonal bipyramidal sites. The structure motif within a NiSn B8-type matrix comprises triangles of P atoms with two ¯ B8 zone axis so that the structure of the three edges capped by Ni atoms in trigonal bipyramidal sites. This motif is repeated along the [011] ¯ B8 . The reciprocal lattice (H) can can be envisaged as pairs of face-sharing Ni centered Edshammar polyhedra corner-connected along [011] ¯ B8 , be described as H = G + mq1 + nq2 (where G refers to the Bragg reflections of the underlying B8-type structure, q1 = 1/11 [1121] ¯ ¯ q2 = 1/22 [6515] B8 and m and n are integers. The resultant triclinic (P1) unit cell parameters are a = 6.456 Å, b = 21.291 Å, c = 13.247 Å, α = 81.052◦ , β = 56.260◦ and γ = 68.221◦ . 2003 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. Keywords: Crystal structure; B8-type structure; Ni–Sn–P system; Ni13 Sn8 P3 ; Edshammar polyhedron; Superstructure; Selected area electron diffraction; High resolution electron microscopy
1. Introduction A wide range non-stoichiometric B8-type (NiAs–Ni2 In) solid solution was detected in the ternary system Ni–Sn–P using X-ray and neutron diffraction methods [1]. The B8type phase field was found to be strongly temperature dependent with a maximum extent given by Ni1+m Sn1−x Px with 0.00 m 0.65 and 0.00 x 0.32 in samples annealed at high temperature (≈ 850 ◦ C). In samples annealed at low temperature (≈ 700 ◦ C) the B8-type phase field was reduced and separated into two regions centered around m = 0.5 and m = 0.1 at low phosphorous content. The studies showed indications of long-range order in the phases which subsequently led to electron diffraction studies of samples around the composition ≈ Ni1.1 Sn0.7 P0.3 [2]. In this first electron diffraction study of Ni–Sn–P B8-type phases an exceptionally complicated reciprocal space was found for samples annealed at high temperature (850 ◦ C) that comprised a collec* Corresponding author.
E-mail address: [email protected] (A.K. Larsson).
tion of sharp satellite reflections as well as highly structured diffuse scattering accompanying the strong Bragg reflections of the underlying B8-type structure (P 63 /mmc, a ≈ 3.82 Å, c ≈ 5.22 Å). In samples that were annealed at low temperature (700 ◦ C) an intriguing superstructure was found, the reciprocal lattice of which was described as “condensed out” from the short range ordered high temperature phase. Although the reciprocal lattice of this superstructure was quite complicated, all observed Bragg reflections could be indexed with an expression of the type H = G + mq1 + nq2 (where G refers to the Bragg reflections of the underlying B8-type ¯ B8 , q2 = 1/22 [6515] ¯ structure, q1 = 1/11 [1121] B8 and m and n are integers). A complete characterisation of the reciprocal lattice was done and a plausible real space model was suggested. The model was based on the assumption [2] that the trigonal bipyramids surrounding the additional Ni atoms had three P atoms in the base and two Sn atoms at the apical positions. The structural model for this so called α-phase was compatible with all the electron diffraction evidence, however it could not be verified because no direct information about the nature of the ordering in real space was available.
1293-2558/03/$ – see front matter 2003 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. doi:10.1016/S1293-2558(02)00095-X
206
F.J. García-García et al. / Solid State Sciences 5 (2003) 205–217
(a)
(b)
(c)
(d)
Fig. 1. The crystal structure of Ni10 Sn5 P3 with the structure motif used for the elucidation of the crystal structure of Ni13 Sn8 P3 circled. The matrix is Ni centered Sn octahedra. The triangles of P atoms forming top/bottom of octahedra are outlined as are the Ni atoms in trigonal bipyramidal sites capping these P-triangles. The solid lines and filled discs indicate atoms at the top of the octahedra layer and the dotted lines and the circles indicate atoms at the hidden ¯ B8 which is as indicated about side of the octahedral layer. In (a) the layer is viewed along [001]B8 and in (b) the structure is viewed along [100]β = [011] 35◦ off the [001]B8 axis if tilted around [120]B8 . (b), (c), and (d) all show roughly the same portion of the structure viewed along the same direction but with different features outlined; in (c) the octahedra are removed, the Sn atoms are the large discs, Ni atoms the medium discs and P atoms the small disks. In (d), the Edshammar polyhedra are outlined.
Recently, a second superstructure of the B8-type substructure has been found in the Ni–Sn–P system. The crystal structure of this phase, Ni10 Sn5 P3 (“the β-phase”), was determined and refined from twinned single crystal X-ray diffraction data [3]. As expected, the superstructure arose from ordering of P and Sn atoms at the hexagonally close packed (hcp) array coupled with ordered Ni occupancy in a portion of the trigonal bipyramidal sites. However, the earlier as-
sumed Ni–Sn2P3 trigonal bipyramids [1,2] were not found in the Ni10 Sn5 P3 structure. Instead, a rather peculiar structural motif was found in its crystal structure. The structural motif comprises triangles of P atoms forming the top/bottom of octahedra in the hcp array and Ni atoms capping two of the edges of these triangles (Fig. 1). With this information about the structure motif in Ni10 Sn5 P3 , the structure elucidation of the α-phase could be
F.J. García-García et al. / Solid State Sciences 5 (2003) 205–217
tackled. By examining the close relationship between the electron diffraction patterns of Ni10 Sn5 P3 to that of the α-phase and using HREM (high resolution electron microscopy) images for real space information, it has been possible to elucidate the crystal structure of the α-phase (which turned out to be Ni13 Sn8 P3 ). This structural elucidation is reported in this contribution.
2. Experimental Samples were prepared by heating weighed amounts of the elements (Ni: turnings from rods, 99.99%, Johnson, Matthey Laboratory Ltd., Sn: granules, 99.99%, Fluka AG, P: lumps, 99.99%, Koch-Light Laboratories, Ltd.) in evacuated and sealed silica glass ampoules at 800 ◦ C for a week. After the first treatment, the samples were crushed and annealed at 700 ◦ C for two months. They were quenched in ice water and analysed by powder X-ray diffraction using a Guinier–Hägg camera with CuKα1 radiation and Si as internal standard. Unit cell parameters refinements were performed by least-squares refinements using the PIRUM program [4]. Samples with different Sn/P ratios and Ni content were prepared around the composition Ni1.1 Sn0.7 P0.3 . The HREM images used for the elucidation of the structural model were recorded in a sample with nominal composition Ni1.091Sn0.727P0.273 as the best quality crystals for HREM were found in this sample. The nominal composition found for the α-phase is Ni1.182Sn0.727P0.273 and a sample with this composition was also prepared. A sample with nominal composition Ni1.5 Sn0.75P0.25 was additionally studied because of the highly disordered α-phase crystals present. The samples for transmission electron microscopy (TEM) were prepared by grinding the specimen under butanol and placing one drop of the resulting suspension onto a holey carbon film supported by a copper grid. A JEOL 2000FX electron microscope (double tilting ±45◦ holder) was used for the selected area electron diffraction (SAED) and convergent beam electron diffraction (CBED) studies. Crystals were analysed in the TEM by X-ray energy dispersive spectroscopy (XEDS) with a LINK AN10000 analysis system. The k values were checked by comparison with analysis carried out in crystals from Ni10 Sn5 P3 . For HREM experiments a JEM-3010 UHR microscope operating at 300 kV was used (structural resolution of 1.7 Å and Cs = 0.6 mm). For image processing of the observed experimental images CRISP software [5] was used. The negatives were digitalized by an 8 bit video-rate CCD camera. Image simulations were carried out with the NCEMSS program system [6] using multislice algorithms. Image simulations were always re-calculated using Block wave algorithms, using the EMS programs [7] but no appreciable difference between the two methods were noted.
207
3. Results No single crystals of sufficient quality for single crystal X-ray diffraction analysis were found in any of the samples. The electron diffraction studies showed that Ni2 SnP and Ni1±x Sn were present in all the samples and that small changes in the nominal compositions caused large differences in the fractions of Ni2 SnP and Ni1±x Sn present. The powder patterns were not used for detailed analysis since the B8-type sublattice reflections of Ni1±x Sn vary with composition and partly overlap with the reflections from the α-phase. In the samples with composition Ni1.091Sn0.727P0.273 and Ni1.182Sn0.727P0.273 , the α-phase was the major component while the sample with composition Ni1.5 Sn0.75 P0.25 comprised about 90% of Ni1±x Sn and 10% of the α-phase. The refined average B8-type subcell parameters for the α-phase are a = 3.824 and c = 5.229 Å. 3.1. Electron diffraction The reciprocal lattice of the α-phase and the consequences of this in real space were described by Furuseth et al. [2]. All observed reflections were indexed with an expression of the type H = G + mq1 + nq2 , where G refers to ¯ B8 , reflections of the B8-type substructure, q1 = 1/11 [1121] ¯ q2 = 1/22 [6515]B8 and n and m integers. The two modulation wave vectors are superfluous as the whole set of reflections can be indexed with the expression H = G + nq2 . However, using the two modulation wave vectors emphasises the two most important reciprocal directions. Furthermore, many binary superstructures of the B8-type structure ¯ ∗ [8– have a modulation wave vector of the form hh2hl 12] and stressing the modulation wave vector q1 = 1/11 ¯ B8 demonstrates the relationship to such structures. In [1121] an analogous manner, the reciprocal lattice of the β-phase, Ni10 Sn5 P3 , was indexed with two modulation wave vectors, ¯ B8 and q2 = 1/8 [3121] ¯ q1 = 1/4 [1121] B8 , although only q2 is required to index all observed reflections [3]. The elucidation of the crystal structure of the α-phase, Ni13 Sn8 P3 , was based on the similarities of its electron diffraction patterns to the electron diffraction patterns of the β-phase, Ni10 Sn5 P3 . The most important similarity between the two sets of electron diffraction data is that both superstructures have the two modulation wave vectors excited simultaneously when the crystals are aligned along ¯ B8 zone axis. The a axes of both superstructure cells the [011] were chosen along this axis and b∗α and c∗α were chosen as q1 and q2 , respectively. The corresponding real space unit cell vectors are then aα = −bB8 + cB8 , bα = 5aB8 − 6bB8 , cα = −2aB8 + 2bB8 . Note that these expressions are different to those given in [2] in order to emphasise that the major directions of the α-phase correspond to those in the β-phase. The resultant triclinic unit cell parameters are aα = 6.456 Å, bα = 21.291 Å, cα = 13.247 Å, αα = 81.052◦, βα = 56.260◦, γα = 68.221◦. In Figs. 2a and b typical electron diffraction patterns of the α-phase and the
208
F.J. García-García et al. / Solid State Sciences 5 (2003) 205–217
¯ B8 = [100]α , (c) [110] ¯ B8 = [001]α , (d) [101] ¯ B8 = [201] ¯ α, Fig. 2. Typical zone axis electron diffraction patterns of the α phase, Ni13 Sn8 P3 , along (a) [011] ¯ α , (f) [110]B8 = [041] ¯ α indexed according to the underlying B8-type substructure. The corresponding directions in the triclinic unit cell (e) [100]B8 = [013] ¯ B8 = [100]β of the β phase is presented for comparison. are also indicated. In (b) an EDP down [011]
¯ B8 are shown. β-phase, respectively, along [100]α,β = [011] The sublattice reflections, G, are circled and the remaining reflections are superstructure reflections. The similarities of the super cells might not be obvious at first glance, however only a small tilt of the modulation wave vector q2 (β) = ∗ is required to instead describe the reciprocal ¯ 1/8 [3121] lattice of the α-phase. To illustrate this the modulation wave vector for the α-phase can be chosen as q 2 = 1/22
∗ (instead of q = 1/22 [6515] ¯ ¯ [8353] 2 B8 ) and all observed B8 reflections can be indexed as H = G + nq 2 . The reflection ¯ α which is marked in nq 2 with n = 8 is the reflections 088 ¯ Fig. 2a as is the reflection 3121B8 . The difference between ¯ ∗ = [010]∗α . The the two reciprocal points is 1/11 [1121] B8 superstructure reflection described with 8q2 (β) and the superstructure reflection described with 8q 2 (α) are then ¯ ∗ = [010]∗α . The difference separated with 1/11 [1121] B8
F.J. García-García et al. / Solid State Sciences 5 (2003) 205–217
209
¯ B8 = [100]α . The fast Fourier transform is inset and indexation is with respect to the B8-type Fig. 3. High resolution micrograph of the α-phase along [011] substructure. The area used for the image processing is circled. This image was recorded in a crystal found in the sample with nominal composition Ni1.091 Sn0.727 P0.273 .
between the modulation wave vectors q2 (β) and q 2 (α) is ¯ ∗ = 1/8 [010]∗α . This means that the hence only 1/88 [1121] B8 whole set of reflections present in the diffraction patterns of the β-phase can be transformed into those of the α-phase just ∗ to q (α) = 1/8 ¯ by changing the vector q2 (β) = 1/8 [3121] 2 ∗ ∗ ¯ ¯ [3121] + 1/88 [1121]B8 . In Figs. 2c, d, e and f four typical electron diffraction patterns of the α-phase are presented. Indexation is with respect to the underlying hexagonal structure and with respect to the triclinic unit cell chosen for the α-phase. The quasi-extinction condition described in [2], important for the verification of the model is evident in the electron ¯ B8 = diffraction pattern recorded along the zone axis [110] [001]α (Fig. 2c). In Fig. 2d the crystal is oriented along the ¯ α zone axis. In a pure B8-type structure the ¯ B8 = [201] [101] ¯ B8 axes are symmetry related (see the ¯ [101]B8 and the [011] ¯ α , q1 is circled reflections in Figs. 2a and c). Along [201] excited but not q2 . Note the presence of extra reflections in (e) and (f) towards the edge of the patterns. These reflections are not in the corresponding reciprocal planes but they
belong to the FOLZ (First Order Laue Zone), and appear as a result of the very long projection axes. From these electron diffraction experiments we could confirm that all reciprocal peculiarities reported in [2] are present in the crystals of the α-phase found in the currently prepared samples. The presence of the two modulation wave vectors break all symmetry elements inherited from the P 63 /mmc sublat¯ tice and hence the only possible space groups are P1 or P1. The presence of an inversion center was assumed in [2] and this assumption was supported in the present investigation taking into account that in CBED patterns we could see projection symmetry ( 2 ) along all directions studied [13]. 3.2. High resolution electron microscopy HREM images were recorded along all reasonably major directions. Analysis of the symmetry in the images invariably gave the planar group p2 as the most likely which supports the assumption made from the electron diffraction data that the structure has a centre of symmetry.
210
F.J. García-García et al. / Solid State Sciences 5 (2003) 205–217
Fig. 4. In (a) the image obtained after image processing of the original image (see Fig. 3) is presented. The area marked in Fig. 3 was fast Fourier transformed and constrains in phases and amplitudes were applied to all reflections according to the planar group p2 before the inverse fast Fourier transform back to real space. The inset (b) is a simulated image of the B8-type substructure assuming a composition “NiSn”. The inset (c) is a simulated image with two nickel capped phosphorous triangles (as circled in Fig. 1c) placed in the unitcell. The inset (d) is a simulated image of the α phase, Ni13 Sn8 P3 . In all the cases the projected atomic positions are indicated, tin as white large discs, nickel as smaller grey discs and phosphorous as small dark grey disc. All parameters used for the simulations are given in Table 1.
The projected potential of the B8-type substructure along ¯ B8 is formed by atomic columns composed exclusively [011] by one kind of chemical element (see, for instance, Figs. 1b ¯ B8 = [100]α direction is also the zone axis and c). The [011] along which both modulation wave vectors of the α-phase are excited simultaneously (confer Fig. 2a). This means that if it is assumed that the superstructure results from compositional ordering, then the elucidation of the superstructure reduces to a two-dimensional problem. Thus, only images ¯ B8 = [100]α were used to deteralong the zone axis [011]
mine the ordering pattern of Sn/P atoms at the hcp array and Ni/vacancies at the trigonal bipyramidal sites. The image in Fig. 4a used to determine the superstructure was obtained after crystallographic processing of the experimental image presented in Fig. 3. The circled area in Fig. 3 was fast Fourier transformed and phases and amplitudes for all peaks were corrected using the symmetry constrains for the planar group p2 [14]. Subsequently, the inverse fast Fourier transform back to real space was performed and the image in Fig. 4a was obtained. This
F.J. García-García et al. / Solid State Sciences 5 (2003) 205–217
3.3. Structure description
Table 1 Parameters used for the image simulation Accelerating voltage Radius of the objective aperture Spherical aberration Focus spread Semi-angle of convergence Crystal thickness for one slice Thickness Value of defocus
300 kV 0.6 nm−1 0.6 mm 8 nm 1.0 mrad 3.2 Å 10 Å −400 Å
process also eliminates the noise present in the original image. The underlying B8-type substructure could be used to get an estimate of the defocus and thickness of the image since the contrast is easily recognised. The projected atomic positions of a NiSn B8-type matrix are indicated in the inset (b) of Fig. 4; tin as white large discs and nickel as smaller grey discs. The parameters used for the simulated image in the inset (b) of Fig. 4 are given in Table 1, and the same parameters are used for insets (c) and (d) of Fig. 4. The pair of tin atoms gives the black oval shaped contrast in the simulated image. In the image presented in Fig. 4 (a) these ovals are sometimes black and sometimes grey which is due to the exchange of tin for phosphorus. The structure was elucidated by comparing the variation in this contrast in the real image to the contrast in simulated images corresponding to different distributions of the structure motif extracted from the β-phase. The characteristic structural motif of the β-phase illustrated in Fig. 1 consists of triangles of P atoms capped by two Ni atoms as described in Fig. 1. The inset (c) of Fig. 4 is a simulated image where two nickel capped phosphorus triangles (as circled in Fig. 1) are placed into the unit cell of the α-phase while the remainder of the unit cell is a NiSn B8-type matrix. The elucidation of the full structure of the α-phase is now reduced to the fairly simple two-dimensional problem to fit this structure motif to the image (guided by the quasi extinction condition). The inset (d) of Fig. 4 shows a simulated image where two such units as in the inset (c) of Fig. 4 are placed into the unit cell of the α-phase. This simulation reproduces the contrast in the HREM image rather closely and represents the final structural model. The composition of the α-phase is taken from the structure; Z for a B8-type structure is 2, and the volume of the supercell is 22 times the volume of the subcell. There are four triangles of P in each unitcell, each capped with two trig Ni atoms. This gives the composition Nioct 44 Ni8 Sn32 P12 and the phase is referred to as Ni13 Sn8 P3 . The ideal atomic positions for the final structure as derived from (xyz)α = M(xyz)TB8 with 0 0 1 M = 1/11 1/11 1/11 −6/22 5/22 5/22 are listed in Table 2.
211
The structure of the α-phase, Ni13 Sn8 P3 , is hence a superstructure of the B8-type structure where Sn and P atoms are ordered at the hcp array and Ni atoms are in all the octahedral sites and ordered into two out of every eleventh of the trigonal bypiramidal sites. The structure motif of a triangle of P atoms capped with two Ni atoms (as described in Fig. 1) can also be described in terms of a pair of face sharing Edshammar polyhedra, each centered by a Ni atom in a trigonal bipyramidal site. These 11-vertex Edshammar polyhedra consist of the trigonal bipyramid (2 P atoms plus 3 Sn atoms) combined with the trigonal prism of 6 Ni atoms centering the closest octahedra (Fig. 5). The Edshammar polyhedron was first described by Edshammar [15] and have been found very useful to describe a range of structures since they can be closepacked in a space filling manner [16]. In particular, the NiAs type structure (or B81 ) can be described as an array of empty closepacked Edshammar polyhedra with both Ni and As atoms at the vertexes and the Ni2 In (or B82 ) type structure can be described as a close packed array of Ni filled Edshammar polyhedra with Ni and In at the vertexes. As a consequence, many superstructures found recently in the binary B81 –B82 type phase fields have been described in terms of different filling pattern of the Edshammar polyhedra. The crystal structures of Ni13 Sn8 P3 and Ni10 Sn5 P3 projected along [100]α,β are sketched in Figs. 6a and b, respectively. On the left side of each figure only the atomic positions in projection are shown while on the right side, the distribution of Edshammar polyhedra are indicated. The two structures are very similar, and the portion of the structures that are in common for the two structures is marked with broken lines. ¯ B8 (see Electron diffraction patterns along [001]α = [110] Fig. 2c), have a characteristic quasi extinction condition where the hk0α type reflections with h + k = 2n + l are weak. In terms of the modulation wave vector, reflections ¯ B8 are weak when m is odd described with q1 = 1/11 [1121] and strong when m is even. In Fig. 7a, the crystal structure of ¯ B8 Ni13 Sn8 P3 is sketched viewed along this [001]α = [110] zone axis in order to demonstrate the real space origin of this quasi extinction condition. Green circles correspond to Ni atoms in octahedra, yellow spheres to Sn atoms at the hcp array and red large circles to Ni atoms in trigonal bipyramids. The positions of the P atoms are emphasised by blue lines between P atoms at adjacent sites at the hcp array. The set of black lines with arrows pointing upwards ¯ B8 planes indicate (010)α planes, i.e., a set of 1/11 (1121) corresponding to the modulation wave vector q1 = b∗α = ¯ B8 . The planes are sketched as centred at the 1/11 [1121] structure motif of Edshammar polyhedra. The set of black lines with arrows pointing down correspond to another set ¯ B8 planes, also these sketched as centered of 1/11 (1121) at the planes of Edshammar polyhedra. These two sets of
212
F.J. García-García et al. / Solid State Sciences 5 (2003) 205–217
Table 2 Fractional atomic coordinates for the α phase Atoms Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni A Ni B
x
y
z
0.0000 0.0000 0.5000 0.0000 0.5000 0.0000 0.5000 0.5000 0.0000 0.5000 0.0000 0.5000 0.0000 0.5000 0.0000 0.5000 0.0000 0.5000 0.0000 0.5000 0.5000 0.0000 0.5000 0.7500 0.2500
0.5455 0.5455 0.5910 0.6364 0.6819 0.7273 0.5910 0.5000 0.6364 0.6819 0.7273 0.7728 0.8182 0.8637 0.9091 0.7728 0.8182 0.8637 0.9091 0.9546 0.9546 0.0000 0.5000 0.6591 0.7955
0.6136 0.1136 0.2272 0.3409 0.4545 0.5681 0.7272 0.5000 0.8409 0.9545 0.0681 0.1818 0.2954 0.4091 0.5227 0.6818 0.7954 0.9091 0.0227 0.1363 0.6363 0.7500 0.0000 0.5642 0.0721
(a)
Atoms Ni C Ni D Sn Sn Sn Sn Sn Sn Sn Sn Sn Sn Sn Sn Sn Sn Sn Sn P P P P P P
x
y
z
0.7500 0.2500 0.2500 0.2500 0.7500 0.2500 0.7500 0.7500 0.2500 0.7500 0.2500 0.7500 0.7500 0.2500 0.7500 0.2500 0.7500 0.2500 0.7500 0.2500 0.2500 0.7500 0.2500 0.7500
0.5682 0.8864 0.6137 0.5228 0.4773 0.4319 0.3864 0.6591 0.7046 0.7500 0.7955 0.8410 0.9319 0.9773 0.8410 0.8864 0.9319 0.9773 0.5682 0.8864 0.7955 0.7500 0.7046 0.6591
0.3369 0.2994 0.4506 0.2233 0.2766 0.9960 0.0494 0.7312 0.6778 0.9585 0.9051 0.1857 0.4130 0.3596 0.6857 0.6324 0.9130 0.8596 0.5039 0.1324 0.4051 0.4585 0.1778 0.2312
(b)
Fig. 5. In (a) an Edshammar polyhedron is drawn. The eleven-vertex polyhedron is composed of five atoms in a trigonal bipyramid (yellow discs) and 6 atoms in a triangular prism (green discs). In (b) the two face sharing Edshammar polyhedra constituting the structure motif in Ni13 Sn8 P3 and Ni10 Sn5 P3 are shown. The three P atoms forming the triangle are marked as blue spheres and the shared face is indicated with grey dashed lines. The Ni centering the Edshammar polyhedra are marked with red discs.
Edshammar polyhedra planes are very close to be out of phase, but not exactly, which explains the quasi extinction condition. Another piece of information from the reciprocal lattice pointed out by Furuseth et al. [2] was that the strongest superstructure reflection was the reflection 1/22 [1, 12, 13, 1]∗B8 . Traces of the corresponding planes are drawn in Fig. 7b
in order to demonstrate that the structure motif fall rather close to these planes causing this reflection to be strong. In our setting of the cell for the alpha phase these planes correspond to the 031¯ α planes. The contrast in HREM images of Ni13 Sn8 P3 is much closer to an ideal B8-type array than those of Ni10 Sn5 P3 . This indicates that the average distortion away from the ideal
F.J. García-García et al. / Solid State Sciences 5 (2003) 205–217
213
(a)
(b) Fig. 6. In (a) and (b) the structures of Ni13 Sn8 P3 and Ni10 Sn5 P3 , respectively, are shown projected down [100] of the triclinic superstructures. On the left side of each figure only the atomic positions are indicated (Sn as large black discs, Ni as medium grey discs and P as small white discs). On the right side the Edshammar polyhedra are indicated. The corresponding unit cells are outlined. The portion of the structure that are the same for both is indicated in the pictures.
214 F.J. García-García et al. / Solid State Sciences 5 (2003) 205–217
(a)
(b)
¯ B8 zoneaxis. Green circles correspond to Ni atoms in octahedra, yellow spheres to Sn atoms at the hcp array and red large circles to Fig. 7. (a) The crystal structure of Ni13 Sn8 P3 viewed along the [001]α = [110] Ni atoms in trigonalbipyramids. The positions of the P atoms are emphasised by drawing blue lines between P atoms at adjacent sites at the hcp array. The set of black lines with arrows pointing upwards indicate ¯ B8 planes centered at the structure motif. The set of black lines with arrows pointing down correspond to another set of (010)α = 1/11 (1121) ¯ B8 planes also centered at the structure motif. (010)α = 1/11 (1121) ¯ α planes are indicated order to demonstrate that the structure motif fall rather close to these planes These two sets of planes are almost out of phase which explains the quasi-extinction condition. In (b) the (031) causing the 031¯ reflection to be strong.
F.J. García-García et al. / Solid State Sciences 5 (2003) 205–217
215
(a) ¯ B8 = [001]α are presented. They are from different Fig. 8. Two high resolution micrographs (upper and lower) of a crystal belonging to the α-phase along [110] areas of the same crystal. In the upper image the experimental electron diffraction pattern is inset. The indexation is according to the B8-type substructure. The insets shown in the lower image correspond to the arrowed areas. (a) shows a twin boundary and (b) shows the presence of stacking faults. These pictures were recorded in a crystal found in the sample with nominal composition Ni1.5 Sn0.75 P0.25 .
atomic position given in Table 2 for Ni13 Sn8 P3 are smaller than the average distortion in Ni10 Sn5 P3 . This could result from that in β-Ni10Sn5 P3 all atoms belong to the Ni centered Edshammar polyhedra (Fig. 6b) while this is not the case for Ni13 Sn8 P3 which have regions in the structure where the B8-type structure is maintained in form of a NiSn array (Fig. 6a). The presence of areas of a maintained NiSn array in Ni13 Sn8 P3 will also help to understand why the distortions of the hexagonal subcell is very small for Ni13 Sn8 P3 while it is relatively large for Ni10 Sn5 P3 . Another consequence of these areas of a NiSn matrix is domain twinning. This was also observed in the HREM experiments, see bellow. 3.4. Structural defects In the sample with nominal composition Ni1.5 Sn0.75P0.25 rather disordered crystallites belonging to the α-phase were
usually found. In Fig. 8 two HREM images recorded in ¯ B8 = different areas of the same crystal oriented along [110] [001]α are shown. In Fig. 8a rather well defined twin boundary can be seen. The inset is the experimental zone axis electron diffraction pattern. It is clear that q1 = 1/11 ¯ B8 in one of the twins while the orientation of [1121] the modulation wave vector in the other domain is q1 = ¯ B8 (as indexed keeping the orientation of the 1/11 [112¯ 1] sublattice intact). In Fig. 8b, the fast Fourier transforms of different areas are inset. Note how the insets b and c in Fig. 8b have lines of diffuse scattering probably generated by the presence of stacking faults in the corresponding areas of the picture. In the area corresponding to inset c these defects are on the (010)α planes generating diffuse scattering along [010]∗α . This could correspond to stacking faults of (111)B8 type planes.
216
F.J. García-García et al. / Solid State Sciences 5 (2003) 205–217
(b) Fig. 8. (Continued).
In Fig. 9 a HREM image of a crystal oriented along ¯ B8 is presented. Four different domains could be 101 seen and the fast Fourier transformations obtained for each one are inset. In (a) only reflections that can be indexed as the basic B8-type structure are present. In (b) ¯ ∗ and commensurate superstructure satellites at 1/2 1101 B8 in (c) incommensurate satellites can be seen. In (d) all superlattice reflections can be indexed with the modulation ¯ wave vector q2 = 1/22 [6515] B8 which corresponds to the [100]α zone axis electron diffraction pattern (see Fig. 2a). The image can be directly interpreted in terms of a domain twinned crystallites where the superstructure reflections are ¯ progressing along different 6515 B8 directions with respect to the orientation of the underlying B8-type sublattice. The ¯ ∗ correspond commensurate reflections doubling 1101 B8 ¯ B8 = 062α , see Fig. 2a) or to the reflection 031α (1101 ¯ B8 = 26¯ 2¯ α ). The incommensurate reflections 13¯ 1¯ α (0111 that can be seen in the inset (c) presumably correspond to HOLZ reflections that due to the long projection axis of the superstructure appear in the corresponding fast Fourier transform along this direction.
4. Conclusions The crystal structure of Ni13 Sn8 P3 could be elucidated from HREM images by using structure a motif from Ni10 Sn5 P3 . This was justified by the very close relationship of the reciprocal lattices of the two structures and the similarity in composition. The structural model for Ni13 Sn8 P3 is totally compatible with all the reciprocal space evidences reported before [2]. The information about the crystal structures of Ni13 Sn8 P3 and Ni10 Sn5 P3 enable us to shed some light onto the peculiar superstructures found in this ternary system and as a result an interpretation of all detail observed in the reciprocal space of the high temperature (850 ◦ C) annealed samples is in progress and will be reported elsewhere.
Acknowledgements Financial support from the Swedish Science Council (Vetenskapsrådet) is gratefully acknowledged.
F.J. García-García et al. / Solid State Sciences 5 (2003) 205–217
217
¯ B8 ] = [100]α . Four different domains can be seen and the corresponding Fig. 9. High resolution micrograph of a crystal belonging to the α-phase along [011] fast Fourier transforms are inset. The presence of these domains is explained as due to a twinned domain structure (see text). This picture was recorded in a crystal found in the sample with nominal composition Ni1.5 Sn0.75 P0.25 .
References [1] S. Furuseth, H. Fjellvåg, Acta Chem. Scand. A 48 (1994) 134. [2] S. Furuseth, A.-K. Larsson, R.L. Withers, J. Solid State Chemistry 136 (1998) 125. [3] F.J. García-García, A.-K. Larsson, S. Furuseth, J. Solid State Chemistry (2002), in press. [4] P.E. Werner, Arkiv. Kemi. 31 (1969) 513. [5] S. Hovmöller, Ultramicroscopy 41 (1992) 121. [6] R. Kilaas, 45th Annual Proceedings of the Electron Microscopy Society of America, Baltimore, MD, 1987, p. 66. [7] P.A. Stadelman, Ultramicroscopy 21 (1987) 131. [8] A.C. Christy, A.-K. Larsson, J. Solid State Chemistry 140 (1998) 402.
[9] A.-K. Larsson, L. Stenberg, S. Lidin, Acta Crystallogr. B 50 (1994) 636. [10] A.-K. Larsson, L. Stenberg, S. Lidin, Z. Kristallogr. 210 (1995) 832. [11] M. Eldin-Ponten, L. Stenberg, A.-K. Larsson, S. Lidin, K. Ståhl, J. Solid State Chem. 129 (1997) 231. [12] A.-K. Larsson, R.L. Withers, J. Alloys, Compounds 264 (1998) 125. [13] J.P. Morniroli, J.W. Steeds, Ultramicroscopy 45 (1992) 219. [14] S. Hovmöller, A. Sjögren, G. Farrants, M. Sundberg, B.-O. Marinder, Nature 331 (1984) 238. [15] L.E. Edshammar, X-ray studies in Binary Alloys of Aluminium with platinum Matels, Thesis, Univ. Stockholm, Sweden, 1969. [16] B. Hyde, S. Andersson, Inorganic Crystal Structures, Wiley, New York, 1989.
The crystal structure of Ni13Sn8 P3 elucidated from HREM F.J. García-García a , A.K. Larsson a,∗ , S. Furuseth b a Department of Inorganic Chemistry, Arrhenius Laboratory, Stockholm University, 106 91 Stockholm, Sweden b Department of Chemistry, University of Oslo, 0315 Oslo 3, Norway
Received 13 June 2002; accepted 27 June 2002 Dedicated to Sten Andersson for his scientific contribution to Solid State and Structural Chemistry
Abstract The crystal structure of Ni13 Sn8 P3 was elucidated from High Resolution Electron Microscopy Images. It was found to be a superstructure of the B8-type (NiAs-type) structure with Sn and P atoms ordered at the hexagonally closepacked array and Ni atoms in all octahedral and in two out of every eleven trigonal bipyramidal sites. The structure motif within a NiSn B8-type matrix comprises triangles of P atoms with two ¯ B8 zone axis so that the structure of the three edges capped by Ni atoms in trigonal bipyramidal sites. This motif is repeated along the [011] ¯ B8 . The reciprocal lattice (H) can can be envisaged as pairs of face-sharing Ni centered Edshammar polyhedra corner-connected along [011] ¯ B8 , be described as H = G + mq1 + nq2 (where G refers to the Bragg reflections of the underlying B8-type structure, q1 = 1/11 [1121] ¯ ¯ q2 = 1/22 [6515] B8 and m and n are integers. The resultant triclinic (P1) unit cell parameters are a = 6.456 Å, b = 21.291 Å, c = 13.247 Å, α = 81.052◦ , β = 56.260◦ and γ = 68.221◦ . 2003 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. Keywords: Crystal structure; B8-type structure; Ni–Sn–P system; Ni13 Sn8 P3 ; Edshammar polyhedron; Superstructure; Selected area electron diffraction; High resolution electron microscopy
1. Introduction A wide range non-stoichiometric B8-type (NiAs–Ni2 In) solid solution was detected in the ternary system Ni–Sn–P using X-ray and neutron diffraction methods [1]. The B8type phase field was found to be strongly temperature dependent with a maximum extent given by Ni1+m Sn1−x Px with 0.00 m 0.65 and 0.00 x 0.32 in samples annealed at high temperature (≈ 850 ◦ C). In samples annealed at low temperature (≈ 700 ◦ C) the B8-type phase field was reduced and separated into two regions centered around m = 0.5 and m = 0.1 at low phosphorous content. The studies showed indications of long-range order in the phases which subsequently led to electron diffraction studies of samples around the composition ≈ Ni1.1 Sn0.7 P0.3 [2]. In this first electron diffraction study of Ni–Sn–P B8-type phases an exceptionally complicated reciprocal space was found for samples annealed at high temperature (850 ◦ C) that comprised a collec* Corresponding author.
E-mail address: [email protected] (A.K. Larsson).
tion of sharp satellite reflections as well as highly structured diffuse scattering accompanying the strong Bragg reflections of the underlying B8-type structure (P 63 /mmc, a ≈ 3.82 Å, c ≈ 5.22 Å). In samples that were annealed at low temperature (700 ◦ C) an intriguing superstructure was found, the reciprocal lattice of which was described as “condensed out” from the short range ordered high temperature phase. Although the reciprocal lattice of this superstructure was quite complicated, all observed Bragg reflections could be indexed with an expression of the type H = G + mq1 + nq2 (where G refers to the Bragg reflections of the underlying B8-type ¯ B8 , q2 = 1/22 [6515] ¯ structure, q1 = 1/11 [1121] B8 and m and n are integers). A complete characterisation of the reciprocal lattice was done and a plausible real space model was suggested. The model was based on the assumption [2] that the trigonal bipyramids surrounding the additional Ni atoms had three P atoms in the base and two Sn atoms at the apical positions. The structural model for this so called α-phase was compatible with all the electron diffraction evidence, however it could not be verified because no direct information about the nature of the ordering in real space was available.
1293-2558/03/$ – see front matter 2003 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. doi:10.1016/S1293-2558(02)00095-X
206
F.J. García-García et al. / Solid State Sciences 5 (2003) 205–217
(a)
(b)
(c)
(d)
Fig. 1. The crystal structure of Ni10 Sn5 P3 with the structure motif used for the elucidation of the crystal structure of Ni13 Sn8 P3 circled. The matrix is Ni centered Sn octahedra. The triangles of P atoms forming top/bottom of octahedra are outlined as are the Ni atoms in trigonal bipyramidal sites capping these P-triangles. The solid lines and filled discs indicate atoms at the top of the octahedra layer and the dotted lines and the circles indicate atoms at the hidden ¯ B8 which is as indicated about side of the octahedral layer. In (a) the layer is viewed along [001]B8 and in (b) the structure is viewed along [100]β = [011] 35◦ off the [001]B8 axis if tilted around [120]B8 . (b), (c), and (d) all show roughly the same portion of the structure viewed along the same direction but with different features outlined; in (c) the octahedra are removed, the Sn atoms are the large discs, Ni atoms the medium discs and P atoms the small disks. In (d), the Edshammar polyhedra are outlined.
Recently, a second superstructure of the B8-type substructure has been found in the Ni–Sn–P system. The crystal structure of this phase, Ni10 Sn5 P3 (“the β-phase”), was determined and refined from twinned single crystal X-ray diffraction data [3]. As expected, the superstructure arose from ordering of P and Sn atoms at the hexagonally close packed (hcp) array coupled with ordered Ni occupancy in a portion of the trigonal bipyramidal sites. However, the earlier as-
sumed Ni–Sn2P3 trigonal bipyramids [1,2] were not found in the Ni10 Sn5 P3 structure. Instead, a rather peculiar structural motif was found in its crystal structure. The structural motif comprises triangles of P atoms forming the top/bottom of octahedra in the hcp array and Ni atoms capping two of the edges of these triangles (Fig. 1). With this information about the structure motif in Ni10 Sn5 P3 , the structure elucidation of the α-phase could be
F.J. García-García et al. / Solid State Sciences 5 (2003) 205–217
tackled. By examining the close relationship between the electron diffraction patterns of Ni10 Sn5 P3 to that of the α-phase and using HREM (high resolution electron microscopy) images for real space information, it has been possible to elucidate the crystal structure of the α-phase (which turned out to be Ni13 Sn8 P3 ). This structural elucidation is reported in this contribution.
2. Experimental Samples were prepared by heating weighed amounts of the elements (Ni: turnings from rods, 99.99%, Johnson, Matthey Laboratory Ltd., Sn: granules, 99.99%, Fluka AG, P: lumps, 99.99%, Koch-Light Laboratories, Ltd.) in evacuated and sealed silica glass ampoules at 800 ◦ C for a week. After the first treatment, the samples were crushed and annealed at 700 ◦ C for two months. They were quenched in ice water and analysed by powder X-ray diffraction using a Guinier–Hägg camera with CuKα1 radiation and Si as internal standard. Unit cell parameters refinements were performed by least-squares refinements using the PIRUM program [4]. Samples with different Sn/P ratios and Ni content were prepared around the composition Ni1.1 Sn0.7 P0.3 . The HREM images used for the elucidation of the structural model were recorded in a sample with nominal composition Ni1.091Sn0.727P0.273 as the best quality crystals for HREM were found in this sample. The nominal composition found for the α-phase is Ni1.182Sn0.727P0.273 and a sample with this composition was also prepared. A sample with nominal composition Ni1.5 Sn0.75P0.25 was additionally studied because of the highly disordered α-phase crystals present. The samples for transmission electron microscopy (TEM) were prepared by grinding the specimen under butanol and placing one drop of the resulting suspension onto a holey carbon film supported by a copper grid. A JEOL 2000FX electron microscope (double tilting ±45◦ holder) was used for the selected area electron diffraction (SAED) and convergent beam electron diffraction (CBED) studies. Crystals were analysed in the TEM by X-ray energy dispersive spectroscopy (XEDS) with a LINK AN10000 analysis system. The k values were checked by comparison with analysis carried out in crystals from Ni10 Sn5 P3 . For HREM experiments a JEM-3010 UHR microscope operating at 300 kV was used (structural resolution of 1.7 Å and Cs = 0.6 mm). For image processing of the observed experimental images CRISP software [5] was used. The negatives were digitalized by an 8 bit video-rate CCD camera. Image simulations were carried out with the NCEMSS program system [6] using multislice algorithms. Image simulations were always re-calculated using Block wave algorithms, using the EMS programs [7] but no appreciable difference between the two methods were noted.
207
3. Results No single crystals of sufficient quality for single crystal X-ray diffraction analysis were found in any of the samples. The electron diffraction studies showed that Ni2 SnP and Ni1±x Sn were present in all the samples and that small changes in the nominal compositions caused large differences in the fractions of Ni2 SnP and Ni1±x Sn present. The powder patterns were not used for detailed analysis since the B8-type sublattice reflections of Ni1±x Sn vary with composition and partly overlap with the reflections from the α-phase. In the samples with composition Ni1.091Sn0.727P0.273 and Ni1.182Sn0.727P0.273 , the α-phase was the major component while the sample with composition Ni1.5 Sn0.75 P0.25 comprised about 90% of Ni1±x Sn and 10% of the α-phase. The refined average B8-type subcell parameters for the α-phase are a = 3.824 and c = 5.229 Å. 3.1. Electron diffraction The reciprocal lattice of the α-phase and the consequences of this in real space were described by Furuseth et al. [2]. All observed reflections were indexed with an expression of the type H = G + mq1 + nq2 , where G refers to ¯ B8 , reflections of the B8-type substructure, q1 = 1/11 [1121] ¯ q2 = 1/22 [6515]B8 and n and m integers. The two modulation wave vectors are superfluous as the whole set of reflections can be indexed with the expression H = G + nq2 . However, using the two modulation wave vectors emphasises the two most important reciprocal directions. Furthermore, many binary superstructures of the B8-type structure ¯ ∗ [8– have a modulation wave vector of the form hh2hl 12] and stressing the modulation wave vector q1 = 1/11 ¯ B8 demonstrates the relationship to such structures. In [1121] an analogous manner, the reciprocal lattice of the β-phase, Ni10 Sn5 P3 , was indexed with two modulation wave vectors, ¯ B8 and q2 = 1/8 [3121] ¯ q1 = 1/4 [1121] B8 , although only q2 is required to index all observed reflections [3]. The elucidation of the crystal structure of the α-phase, Ni13 Sn8 P3 , was based on the similarities of its electron diffraction patterns to the electron diffraction patterns of the β-phase, Ni10 Sn5 P3 . The most important similarity between the two sets of electron diffraction data is that both superstructures have the two modulation wave vectors excited simultaneously when the crystals are aligned along ¯ B8 zone axis. The a axes of both superstructure cells the [011] were chosen along this axis and b∗α and c∗α were chosen as q1 and q2 , respectively. The corresponding real space unit cell vectors are then aα = −bB8 + cB8 , bα = 5aB8 − 6bB8 , cα = −2aB8 + 2bB8 . Note that these expressions are different to those given in [2] in order to emphasise that the major directions of the α-phase correspond to those in the β-phase. The resultant triclinic unit cell parameters are aα = 6.456 Å, bα = 21.291 Å, cα = 13.247 Å, αα = 81.052◦, βα = 56.260◦, γα = 68.221◦. In Figs. 2a and b typical electron diffraction patterns of the α-phase and the
208
F.J. García-García et al. / Solid State Sciences 5 (2003) 205–217
¯ B8 = [100]α , (c) [110] ¯ B8 = [001]α , (d) [101] ¯ B8 = [201] ¯ α, Fig. 2. Typical zone axis electron diffraction patterns of the α phase, Ni13 Sn8 P3 , along (a) [011] ¯ α , (f) [110]B8 = [041] ¯ α indexed according to the underlying B8-type substructure. The corresponding directions in the triclinic unit cell (e) [100]B8 = [013] ¯ B8 = [100]β of the β phase is presented for comparison. are also indicated. In (b) an EDP down [011]
¯ B8 are shown. β-phase, respectively, along [100]α,β = [011] The sublattice reflections, G, are circled and the remaining reflections are superstructure reflections. The similarities of the super cells might not be obvious at first glance, however only a small tilt of the modulation wave vector q2 (β) = ∗ is required to instead describe the reciprocal ¯ 1/8 [3121] lattice of the α-phase. To illustrate this the modulation wave vector for the α-phase can be chosen as q 2 = 1/22
∗ (instead of q = 1/22 [6515] ¯ ¯ [8353] 2 B8 ) and all observed B8 reflections can be indexed as H = G + nq 2 . The reflection ¯ α which is marked in nq 2 with n = 8 is the reflections 088 ¯ Fig. 2a as is the reflection 3121B8 . The difference between ¯ ∗ = [010]∗α . The the two reciprocal points is 1/11 [1121] B8 superstructure reflection described with 8q2 (β) and the superstructure reflection described with 8q 2 (α) are then ¯ ∗ = [010]∗α . The difference separated with 1/11 [1121] B8
F.J. García-García et al. / Solid State Sciences 5 (2003) 205–217
209
¯ B8 = [100]α . The fast Fourier transform is inset and indexation is with respect to the B8-type Fig. 3. High resolution micrograph of the α-phase along [011] substructure. The area used for the image processing is circled. This image was recorded in a crystal found in the sample with nominal composition Ni1.091 Sn0.727 P0.273 .
between the modulation wave vectors q2 (β) and q 2 (α) is ¯ ∗ = 1/8 [010]∗α . This means that the hence only 1/88 [1121] B8 whole set of reflections present in the diffraction patterns of the β-phase can be transformed into those of the α-phase just ∗ to q (α) = 1/8 ¯ by changing the vector q2 (β) = 1/8 [3121] 2 ∗ ∗ ¯ ¯ [3121] + 1/88 [1121]B8 . In Figs. 2c, d, e and f four typical electron diffraction patterns of the α-phase are presented. Indexation is with respect to the underlying hexagonal structure and with respect to the triclinic unit cell chosen for the α-phase. The quasi-extinction condition described in [2], important for the verification of the model is evident in the electron ¯ B8 = diffraction pattern recorded along the zone axis [110] [001]α (Fig. 2c). In Fig. 2d the crystal is oriented along the ¯ α zone axis. In a pure B8-type structure the ¯ B8 = [201] [101] ¯ B8 axes are symmetry related (see the ¯ [101]B8 and the [011] ¯ α , q1 is circled reflections in Figs. 2a and c). Along [201] excited but not q2 . Note the presence of extra reflections in (e) and (f) towards the edge of the patterns. These reflections are not in the corresponding reciprocal planes but they
belong to the FOLZ (First Order Laue Zone), and appear as a result of the very long projection axes. From these electron diffraction experiments we could confirm that all reciprocal peculiarities reported in [2] are present in the crystals of the α-phase found in the currently prepared samples. The presence of the two modulation wave vectors break all symmetry elements inherited from the P 63 /mmc sublat¯ tice and hence the only possible space groups are P1 or P1. The presence of an inversion center was assumed in [2] and this assumption was supported in the present investigation taking into account that in CBED patterns we could see projection symmetry ( 2 ) along all directions studied [13]. 3.2. High resolution electron microscopy HREM images were recorded along all reasonably major directions. Analysis of the symmetry in the images invariably gave the planar group p2 as the most likely which supports the assumption made from the electron diffraction data that the structure has a centre of symmetry.
210
F.J. García-García et al. / Solid State Sciences 5 (2003) 205–217
Fig. 4. In (a) the image obtained after image processing of the original image (see Fig. 3) is presented. The area marked in Fig. 3 was fast Fourier transformed and constrains in phases and amplitudes were applied to all reflections according to the planar group p2 before the inverse fast Fourier transform back to real space. The inset (b) is a simulated image of the B8-type substructure assuming a composition “NiSn”. The inset (c) is a simulated image with two nickel capped phosphorous triangles (as circled in Fig. 1c) placed in the unitcell. The inset (d) is a simulated image of the α phase, Ni13 Sn8 P3 . In all the cases the projected atomic positions are indicated, tin as white large discs, nickel as smaller grey discs and phosphorous as small dark grey disc. All parameters used for the simulations are given in Table 1.
The projected potential of the B8-type substructure along ¯ B8 is formed by atomic columns composed exclusively [011] by one kind of chemical element (see, for instance, Figs. 1b ¯ B8 = [100]α direction is also the zone axis and c). The [011] along which both modulation wave vectors of the α-phase are excited simultaneously (confer Fig. 2a). This means that if it is assumed that the superstructure results from compositional ordering, then the elucidation of the superstructure reduces to a two-dimensional problem. Thus, only images ¯ B8 = [100]α were used to deteralong the zone axis [011]
mine the ordering pattern of Sn/P atoms at the hcp array and Ni/vacancies at the trigonal bipyramidal sites. The image in Fig. 4a used to determine the superstructure was obtained after crystallographic processing of the experimental image presented in Fig. 3. The circled area in Fig. 3 was fast Fourier transformed and phases and amplitudes for all peaks were corrected using the symmetry constrains for the planar group p2 [14]. Subsequently, the inverse fast Fourier transform back to real space was performed and the image in Fig. 4a was obtained. This
F.J. García-García et al. / Solid State Sciences 5 (2003) 205–217
3.3. Structure description
Table 1 Parameters used for the image simulation Accelerating voltage Radius of the objective aperture Spherical aberration Focus spread Semi-angle of convergence Crystal thickness for one slice Thickness Value of defocus
300 kV 0.6 nm−1 0.6 mm 8 nm 1.0 mrad 3.2 Å 10 Å −400 Å
process also eliminates the noise present in the original image. The underlying B8-type substructure could be used to get an estimate of the defocus and thickness of the image since the contrast is easily recognised. The projected atomic positions of a NiSn B8-type matrix are indicated in the inset (b) of Fig. 4; tin as white large discs and nickel as smaller grey discs. The parameters used for the simulated image in the inset (b) of Fig. 4 are given in Table 1, and the same parameters are used for insets (c) and (d) of Fig. 4. The pair of tin atoms gives the black oval shaped contrast in the simulated image. In the image presented in Fig. 4 (a) these ovals are sometimes black and sometimes grey which is due to the exchange of tin for phosphorus. The structure was elucidated by comparing the variation in this contrast in the real image to the contrast in simulated images corresponding to different distributions of the structure motif extracted from the β-phase. The characteristic structural motif of the β-phase illustrated in Fig. 1 consists of triangles of P atoms capped by two Ni atoms as described in Fig. 1. The inset (c) of Fig. 4 is a simulated image where two nickel capped phosphorus triangles (as circled in Fig. 1) are placed into the unit cell of the α-phase while the remainder of the unit cell is a NiSn B8-type matrix. The elucidation of the full structure of the α-phase is now reduced to the fairly simple two-dimensional problem to fit this structure motif to the image (guided by the quasi extinction condition). The inset (d) of Fig. 4 shows a simulated image where two such units as in the inset (c) of Fig. 4 are placed into the unit cell of the α-phase. This simulation reproduces the contrast in the HREM image rather closely and represents the final structural model. The composition of the α-phase is taken from the structure; Z for a B8-type structure is 2, and the volume of the supercell is 22 times the volume of the subcell. There are four triangles of P in each unitcell, each capped with two trig Ni atoms. This gives the composition Nioct 44 Ni8 Sn32 P12 and the phase is referred to as Ni13 Sn8 P3 . The ideal atomic positions for the final structure as derived from (xyz)α = M(xyz)TB8 with 0 0 1 M = 1/11 1/11 1/11 −6/22 5/22 5/22 are listed in Table 2.
211
The structure of the α-phase, Ni13 Sn8 P3 , is hence a superstructure of the B8-type structure where Sn and P atoms are ordered at the hcp array and Ni atoms are in all the octahedral sites and ordered into two out of every eleventh of the trigonal bypiramidal sites. The structure motif of a triangle of P atoms capped with two Ni atoms (as described in Fig. 1) can also be described in terms of a pair of face sharing Edshammar polyhedra, each centered by a Ni atom in a trigonal bipyramidal site. These 11-vertex Edshammar polyhedra consist of the trigonal bipyramid (2 P atoms plus 3 Sn atoms) combined with the trigonal prism of 6 Ni atoms centering the closest octahedra (Fig. 5). The Edshammar polyhedron was first described by Edshammar [15] and have been found very useful to describe a range of structures since they can be closepacked in a space filling manner [16]. In particular, the NiAs type structure (or B81 ) can be described as an array of empty closepacked Edshammar polyhedra with both Ni and As atoms at the vertexes and the Ni2 In (or B82 ) type structure can be described as a close packed array of Ni filled Edshammar polyhedra with Ni and In at the vertexes. As a consequence, many superstructures found recently in the binary B81 –B82 type phase fields have been described in terms of different filling pattern of the Edshammar polyhedra. The crystal structures of Ni13 Sn8 P3 and Ni10 Sn5 P3 projected along [100]α,β are sketched in Figs. 6a and b, respectively. On the left side of each figure only the atomic positions in projection are shown while on the right side, the distribution of Edshammar polyhedra are indicated. The two structures are very similar, and the portion of the structures that are in common for the two structures is marked with broken lines. ¯ B8 (see Electron diffraction patterns along [001]α = [110] Fig. 2c), have a characteristic quasi extinction condition where the hk0α type reflections with h + k = 2n + l are weak. In terms of the modulation wave vector, reflections ¯ B8 are weak when m is odd described with q1 = 1/11 [1121] and strong when m is even. In Fig. 7a, the crystal structure of ¯ B8 Ni13 Sn8 P3 is sketched viewed along this [001]α = [110] zone axis in order to demonstrate the real space origin of this quasi extinction condition. Green circles correspond to Ni atoms in octahedra, yellow spheres to Sn atoms at the hcp array and red large circles to Ni atoms in trigonal bipyramids. The positions of the P atoms are emphasised by blue lines between P atoms at adjacent sites at the hcp array. The set of black lines with arrows pointing upwards ¯ B8 planes indicate (010)α planes, i.e., a set of 1/11 (1121) corresponding to the modulation wave vector q1 = b∗α = ¯ B8 . The planes are sketched as centred at the 1/11 [1121] structure motif of Edshammar polyhedra. The set of black lines with arrows pointing down correspond to another set ¯ B8 planes, also these sketched as centered of 1/11 (1121) at the planes of Edshammar polyhedra. These two sets of
212
F.J. García-García et al. / Solid State Sciences 5 (2003) 205–217
Table 2 Fractional atomic coordinates for the α phase Atoms Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni A Ni B
x
y
z
0.0000 0.0000 0.5000 0.0000 0.5000 0.0000 0.5000 0.5000 0.0000 0.5000 0.0000 0.5000 0.0000 0.5000 0.0000 0.5000 0.0000 0.5000 0.0000 0.5000 0.5000 0.0000 0.5000 0.7500 0.2500
0.5455 0.5455 0.5910 0.6364 0.6819 0.7273 0.5910 0.5000 0.6364 0.6819 0.7273 0.7728 0.8182 0.8637 0.9091 0.7728 0.8182 0.8637 0.9091 0.9546 0.9546 0.0000 0.5000 0.6591 0.7955
0.6136 0.1136 0.2272 0.3409 0.4545 0.5681 0.7272 0.5000 0.8409 0.9545 0.0681 0.1818 0.2954 0.4091 0.5227 0.6818 0.7954 0.9091 0.0227 0.1363 0.6363 0.7500 0.0000 0.5642 0.0721
(a)
Atoms Ni C Ni D Sn Sn Sn Sn Sn Sn Sn Sn Sn Sn Sn Sn Sn Sn Sn Sn P P P P P P
x
y
z
0.7500 0.2500 0.2500 0.2500 0.7500 0.2500 0.7500 0.7500 0.2500 0.7500 0.2500 0.7500 0.7500 0.2500 0.7500 0.2500 0.7500 0.2500 0.7500 0.2500 0.2500 0.7500 0.2500 0.7500
0.5682 0.8864 0.6137 0.5228 0.4773 0.4319 0.3864 0.6591 0.7046 0.7500 0.7955 0.8410 0.9319 0.9773 0.8410 0.8864 0.9319 0.9773 0.5682 0.8864 0.7955 0.7500 0.7046 0.6591
0.3369 0.2994 0.4506 0.2233 0.2766 0.9960 0.0494 0.7312 0.6778 0.9585 0.9051 0.1857 0.4130 0.3596 0.6857 0.6324 0.9130 0.8596 0.5039 0.1324 0.4051 0.4585 0.1778 0.2312
(b)
Fig. 5. In (a) an Edshammar polyhedron is drawn. The eleven-vertex polyhedron is composed of five atoms in a trigonal bipyramid (yellow discs) and 6 atoms in a triangular prism (green discs). In (b) the two face sharing Edshammar polyhedra constituting the structure motif in Ni13 Sn8 P3 and Ni10 Sn5 P3 are shown. The three P atoms forming the triangle are marked as blue spheres and the shared face is indicated with grey dashed lines. The Ni centering the Edshammar polyhedra are marked with red discs.
Edshammar polyhedra planes are very close to be out of phase, but not exactly, which explains the quasi extinction condition. Another piece of information from the reciprocal lattice pointed out by Furuseth et al. [2] was that the strongest superstructure reflection was the reflection 1/22 [1, 12, 13, 1]∗B8 . Traces of the corresponding planes are drawn in Fig. 7b
in order to demonstrate that the structure motif fall rather close to these planes causing this reflection to be strong. In our setting of the cell for the alpha phase these planes correspond to the 031¯ α planes. The contrast in HREM images of Ni13 Sn8 P3 is much closer to an ideal B8-type array than those of Ni10 Sn5 P3 . This indicates that the average distortion away from the ideal
F.J. García-García et al. / Solid State Sciences 5 (2003) 205–217
213
(a)
(b) Fig. 6. In (a) and (b) the structures of Ni13 Sn8 P3 and Ni10 Sn5 P3 , respectively, are shown projected down [100] of the triclinic superstructures. On the left side of each figure only the atomic positions are indicated (Sn as large black discs, Ni as medium grey discs and P as small white discs). On the right side the Edshammar polyhedra are indicated. The corresponding unit cells are outlined. The portion of the structure that are the same for both is indicated in the pictures.
214 F.J. García-García et al. / Solid State Sciences 5 (2003) 205–217
(a)
(b)
¯ B8 zoneaxis. Green circles correspond to Ni atoms in octahedra, yellow spheres to Sn atoms at the hcp array and red large circles to Fig. 7. (a) The crystal structure of Ni13 Sn8 P3 viewed along the [001]α = [110] Ni atoms in trigonalbipyramids. The positions of the P atoms are emphasised by drawing blue lines between P atoms at adjacent sites at the hcp array. The set of black lines with arrows pointing upwards indicate ¯ B8 planes centered at the structure motif. The set of black lines with arrows pointing down correspond to another set of (010)α = 1/11 (1121) ¯ B8 planes also centered at the structure motif. (010)α = 1/11 (1121) ¯ α planes are indicated order to demonstrate that the structure motif fall rather close to these planes These two sets of planes are almost out of phase which explains the quasi-extinction condition. In (b) the (031) causing the 031¯ reflection to be strong.
F.J. García-García et al. / Solid State Sciences 5 (2003) 205–217
215
(a) ¯ B8 = [001]α are presented. They are from different Fig. 8. Two high resolution micrographs (upper and lower) of a crystal belonging to the α-phase along [110] areas of the same crystal. In the upper image the experimental electron diffraction pattern is inset. The indexation is according to the B8-type substructure. The insets shown in the lower image correspond to the arrowed areas. (a) shows a twin boundary and (b) shows the presence of stacking faults. These pictures were recorded in a crystal found in the sample with nominal composition Ni1.5 Sn0.75 P0.25 .
atomic position given in Table 2 for Ni13 Sn8 P3 are smaller than the average distortion in Ni10 Sn5 P3 . This could result from that in β-Ni10Sn5 P3 all atoms belong to the Ni centered Edshammar polyhedra (Fig. 6b) while this is not the case for Ni13 Sn8 P3 which have regions in the structure where the B8-type structure is maintained in form of a NiSn array (Fig. 6a). The presence of areas of a maintained NiSn array in Ni13 Sn8 P3 will also help to understand why the distortions of the hexagonal subcell is very small for Ni13 Sn8 P3 while it is relatively large for Ni10 Sn5 P3 . Another consequence of these areas of a NiSn matrix is domain twinning. This was also observed in the HREM experiments, see bellow. 3.4. Structural defects In the sample with nominal composition Ni1.5 Sn0.75P0.25 rather disordered crystallites belonging to the α-phase were
usually found. In Fig. 8 two HREM images recorded in ¯ B8 = different areas of the same crystal oriented along [110] [001]α are shown. In Fig. 8a rather well defined twin boundary can be seen. The inset is the experimental zone axis electron diffraction pattern. It is clear that q1 = 1/11 ¯ B8 in one of the twins while the orientation of [1121] the modulation wave vector in the other domain is q1 = ¯ B8 (as indexed keeping the orientation of the 1/11 [112¯ 1] sublattice intact). In Fig. 8b, the fast Fourier transforms of different areas are inset. Note how the insets b and c in Fig. 8b have lines of diffuse scattering probably generated by the presence of stacking faults in the corresponding areas of the picture. In the area corresponding to inset c these defects are on the (010)α planes generating diffuse scattering along [010]∗α . This could correspond to stacking faults of (111)B8 type planes.
216
F.J. García-García et al. / Solid State Sciences 5 (2003) 205–217
(b) Fig. 8. (Continued).
In Fig. 9 a HREM image of a crystal oriented along ¯ B8 is presented. Four different domains could be 101 seen and the fast Fourier transformations obtained for each one are inset. In (a) only reflections that can be indexed as the basic B8-type structure are present. In (b) ¯ ∗ and commensurate superstructure satellites at 1/2 1101 B8 in (c) incommensurate satellites can be seen. In (d) all superlattice reflections can be indexed with the modulation ¯ wave vector q2 = 1/22 [6515] B8 which corresponds to the [100]α zone axis electron diffraction pattern (see Fig. 2a). The image can be directly interpreted in terms of a domain twinned crystallites where the superstructure reflections are ¯ progressing along different 6515 B8 directions with respect to the orientation of the underlying B8-type sublattice. The ¯ ∗ correspond commensurate reflections doubling 1101 B8 ¯ B8 = 062α , see Fig. 2a) or to the reflection 031α (1101 ¯ B8 = 26¯ 2¯ α ). The incommensurate reflections 13¯ 1¯ α (0111 that can be seen in the inset (c) presumably correspond to HOLZ reflections that due to the long projection axis of the superstructure appear in the corresponding fast Fourier transform along this direction.
4. Conclusions The crystal structure of Ni13 Sn8 P3 could be elucidated from HREM images by using structure a motif from Ni10 Sn5 P3 . This was justified by the very close relationship of the reciprocal lattices of the two structures and the similarity in composition. The structural model for Ni13 Sn8 P3 is totally compatible with all the reciprocal space evidences reported before [2]. The information about the crystal structures of Ni13 Sn8 P3 and Ni10 Sn5 P3 enable us to shed some light onto the peculiar superstructures found in this ternary system and as a result an interpretation of all detail observed in the reciprocal space of the high temperature (850 ◦ C) annealed samples is in progress and will be reported elsewhere.
Acknowledgements Financial support from the Swedish Science Council (Vetenskapsrådet) is gratefully acknowledged.
F.J. García-García et al. / Solid State Sciences 5 (2003) 205–217
217
¯ B8 ] = [100]α . Four different domains can be seen and the corresponding Fig. 9. High resolution micrograph of a crystal belonging to the α-phase along [011] fast Fourier transforms are inset. The presence of these domains is explained as due to a twinned domain structure (see text). This picture was recorded in a crystal found in the sample with nominal composition Ni1.5 Sn0.75 P0.25 .
References [1] S. Furuseth, H. Fjellvåg, Acta Chem. Scand. A 48 (1994) 134. [2] S. Furuseth, A.-K. Larsson, R.L. Withers, J. Solid State Chemistry 136 (1998) 125. [3] F.J. García-García, A.-K. Larsson, S. Furuseth, J. Solid State Chemistry (2002), in press. [4] P.E. Werner, Arkiv. Kemi. 31 (1969) 513. [5] S. Hovmöller, Ultramicroscopy 41 (1992) 121. [6] R. Kilaas, 45th Annual Proceedings of the Electron Microscopy Society of America, Baltimore, MD, 1987, p. 66. [7] P.A. Stadelman, Ultramicroscopy 21 (1987) 131. [8] A.C. Christy, A.-K. Larsson, J. Solid State Chemistry 140 (1998) 402.
[9] A.-K. Larsson, L. Stenberg, S. Lidin, Acta Crystallogr. B 50 (1994) 636. [10] A.-K. Larsson, L. Stenberg, S. Lidin, Z. Kristallogr. 210 (1995) 832. [11] M. Eldin-Ponten, L. Stenberg, A.-K. Larsson, S. Lidin, K. Ståhl, J. Solid State Chem. 129 (1997) 231. [12] A.-K. Larsson, R.L. Withers, J. Alloys, Compounds 264 (1998) 125. [13] J.P. Morniroli, J.W. Steeds, Ultramicroscopy 45 (1992) 219. [14] S. Hovmöller, A. Sjögren, G. Farrants, M. Sundberg, B.-O. Marinder, Nature 331 (1984) 238. [15] L.E. Edshammar, X-ray studies in Binary Alloys of Aluminium with platinum Matels, Thesis, Univ. Stockholm, Sweden, 1969. [16] B. Hyde, S. Andersson, Inorganic Crystal Structures, Wiley, New York, 1989.