The incommensurately modulated structure of NiBi

Solid State Sciences 2 (2000) 353 – 363

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The incommensurately modulated structure of NiBi Sven Lidin a,*, Vaclav Petricek b, Lars Stenberg c, Sigrid Furuseth d, Helmer Fjellva˚g d, Ann-Kristin Larsson a a

Inorganic Chemistry, Arrhenius Laboratory, Stockholm Uni6ersity, Institute of Physics, Acad. Sci. Czech Rep., Cukro6arnicka 10, 162 c Inorganic Chemistry 2, Chemical Centre, Lund Uni6ersity, PO Box d Department of Chemistry, Uni6ersity of Oslo, N-0315

b

S-10691 Stockholm, Sweden 00 Prague 6, Czech Republic 124, S-221 00 Lund, Sweden Oslo 3, Norway

Received 24 September 1999; accepted 29 November 1999

Keywords: NiBi; X-ray diffraction; Incommensurately modulated

1. Introduction The close to equimolar compound NiBi was first reported by Ha¨gg and Funcke [2] as an NiAs type structure. Subsequent investigations have confirmed these findings [1], and established that the compound exists in a rather narrow composition range. Recent findings by Ruck [6] show the existence of a commensurate phase that may be grown by chemical transport techniques. As a part in a larger investigation into crystal structure modulations of B8 type intermetallics, the compound NiBi was synthesized from the elements. An incommensutately modulated phase was found which could be refined using a domain twinned four dimensional model. One of the approximants of this model presented here is closely related to the three dimensional model of Ruck [6]. Preliminary electron diffraction experiments showed incommensurate superstructure ordering of a rather complicated nature, but X-ray analysis on as-synthesized samples gave no useful information; extra reflections were measurable, but not indexable. The probable cause of this was badly defined twinning. Prolonged low temperature annealing (24 * Correspondence and reprints: Tel.: + 46-8-161256; fax; + 468-152187. E-mail address: [email protected] (S. Lidin)

months at 400°C) produced some needle-shaped crystal suitable for X-ray work.

2. Experimental Ni (powder, STREM) and Bi (coarse crystals, STREM) were mixed in equimolar ratios, pressed into pellets, arc melted, and sealed in quartz under argon. The quartz tubes were heated to 60°C for one week and subsequently annealed at 400°C for 24 months. The ingots had a silvery metallic luster, and contained some very thin needles that were used in the X-ray measurements. Specimens for the Transmission Electron Microscope (TEM) work were prepared by crushing and dispersing onto holey-carbon coated copper grids. Electron Diffraction Patterns (EDP’s) were recorded from several different samples with a JEOL 2000FX microscope.

3. Electron diffraction EDP’s from all crystallites investigated show extra scattering in addition to the Bragg reflections from the NiAs type (B8) P63/mmc sublattice (G). In the ensuing discussion all additional scattering will be

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S. Lidin et al. / Solid State Sciences 2 (2000) 353–363

indexed using additional lattice vectors q1 and q2. For instance, EDP’s along the zone axis B 001\ B8 often showed a commensurate doubling of all B 100\ B*8 directions (ql = B 1200 \ ). In Fig. 1a an EDP with apparent hexagonal symmetry, and a doubling of all B 100 \* B8 directions is shown. Upon moving the beam around on such crystallites, it was possible to record EDP’s where the superstructure is unbalanced, i.e. the intensities of the satellites deviate from hexagonal symmetry (Fig. 1b). The conclusion is that the apparent hexagonality is a product of mimetic twinning (all domains having a common

B 001\ B8 direction) of a lower symmetry superstructure enveloped in a hexagonal base lattice. The domain size is normally small, as judged by the apparently hexagonal intensity distribution in the B 001\ B8 EDP which indicate a large number of domains representing the three directions with equal frequency. In Fig. 1c and d, the EDP’s are recorded along theB100\ B8 zone axis. The different appearance of the patterns again suggests unbalanced twinning. In Fig. 1c the modulation q1 = B 1200\*, which was also present in the B001\ B8, zone EDP’s, is clearly observable together with q2 = B 12 0 0.26\ * while in the EDP in Fig. 1d q1 is absent. This means that the coplanar existence of q1 and q2 is an effect of twinning, and that the allowed combinations of the two in a single domain specimen are of the type q1 = − 12 120; q1 = 1200; q1 = 0120;

q2 {012g, 120g} q2 {− 12 12g, 012g} q2 (120g, − 12 120g}

This is confirmed by the EDP’s of Fig. 1e and f, where the zone axis is B 110\ B8. In Fig. 1e, all scattering can be explained by G+q1 +mq2 while in Fig. 1f, all scattering may be explained by G+q2. This suggests that the pure single domain reciprocal lattice is fully described by H= G+ q1 +mq2 where m is an integer, q1 = 1200 and q2 = 012g, g:0.26 (Fig. 2a). Mimetic twinning of such domains yield the hexagonal diffraction pattern from bulk samples. The 4D cell used in the refinements was derived in two steps by first considering the commensurate modulation wave vector q1 breaking the C-centering of the orthohexagonal setting of the B8 type cell. q2 describes the incommensurate modulation within this orthorhombic cell ao = 2aB8 bo = 2 3aB8 q2 : B 0 0 0.26\* Fig. 1. ED from the B8 B 001\ zone axis (a and b), the B8 B 100 \ zone axis (c and d) and the B8 B110\ zone axis (e and f). a, c and d are from domain twinned crystallites while b, d and f are dominated by scattering from one single domain. In e, the reflections 12 120 and 12 120.26 (B8 indexing) are both present. The 11 2 20hex corresponds to 11004D-ort and is forbidden by the W:Pmcm:ssg symmetry, and it originates from another twin orientation, where it may be indexed as 20004Dort while in f, reflections of type 12 120 are absent in accordance with the 4D symmetry (indicating that the pattern is a single crystalline fragment).

co = cB8 The relation of the 4D real and reciprocal lattices to the B8 type sublattices are sketched in Fig. 2. Unique atoms in the average Pmcm cell are indicated; Bi1 and Bi2 at the vertices of the octahedra, Ni1 and Ni2 at the octahedra centra and Ni3 at one of the trigonal bipyramidal sites (the other trigonal bipyramidal sites were found to be empty).

S. Lidin et al. / Solid State Sciences 2 (2000) 353–363

Fig. 2. (a) The reciprocal lattice of a B8 type structure with the modulation wave vectors of one single domain of NiBi indicated. (b) The B8 type structure with the P63/mmc unitcell and the stepwise transformation to the 4D spacegroup W:Pmcm:ssg indicated.

4. X-ray diffraction and structural solution A well defined needle was chosen for the X-ray experiment. The measurement was carried out on a STOE imaging plate system mounted on a Siemens rotating anode X-ray generator (Mo) operated at 50 kV, 90 mA. Details of the experiment are shown in Table 1. It is notable that the long axis of the needle coincides with the short orthohexagonal axis, not with the hexad of the sublattice, as might have been expected. This indicates the effect prolonged annealing has on domain size. The highest superspace group symmetry allowed was W:Pmcm:ssg based on group-subgroup relations and extinctions, and there was no indication of improvement on lowering the symmetry during the refinement. The starting positions for the refinement may be deduced from the group-subgroup relations as follows from Table 2 and Fig. 2.

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For the structural solution and refinement the JANA98 package [5] was used. Refinement of the Pmcm substructure was straight forward; Bi1 and Bi2 (forming a hexagonally close packed array) behave as expected as do the octahedral interstitial Ni positions (Ni1 and Ni2). Of the two positions for Ni in trigonal bipyramidal interstices, only one is occupied (Ni3) and to a rather small amount, ca. 20%. At this stage the agreement factor was about 16% (main reflections only). The introduction of first order harmonic displacement waves for Bi resulted in an R-value for first order satellites of 25% and a phasing of the satellite reflections that clearly showed all important features of the modulation; Bi1, Bi2 and Ni1 show displacive modulations while Ni2 and Ni3 show mainly occupational modulations. The latter behavior was modeled using crenel type functions. Finally modulations of thermal displacement parameters were introduced for Bi. The final values of all parameters are given in Table 2. From the non-overlapping reflections it was possible to get a rough estimate of the ratio between the different twin orientations. The twinning turned out to be unbalanced with an approximate volume ratio 3:1:1. This suggests a rather large domain size. This makes structural solution simpler, since a preferred domain orientation gives are more pronounced nonhexagonal behavior, but it complicates refinement, particularly in the way it influences absorption effects. A further complication is that the weak second order satellites, due to the almost commensurate nature of the modulation, partially overlap. This is treated as further twinning in the refinement. The final unweighted agreement factors for observed reflection were Rmain = 5.2, Rsat1 =11.9, Rsat2 = 13.6, a satisfactory result considering the nature of the specimen (unbalanced multiple twins cause severe difficulties in the absorption corrections). A major problem in the final stages of refinement was the occupational modulation of Ni2 and Ni3. These are largely crenel like, but the very large residual electron density (− 24 eA, − 3) on Ni3 indicates that it the electron density variation is not very well described. This may be caused either by actual deviations from the crenel behavior, or be truncation effects. Several attempts to model the occupational behavior with combinations of harmonic waves were made, but no improvement was possible. Electron density maps of the Ni3 position shows no unusual features (conf Fig. 3).

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Table 1

Data collection Diffractometer Data collection method Radiation type Wavelength Absorption correction Tmin, Tmax No of refls. No. of independent refls. Observed criterion No. of observed refls. u Range h, k, l, m limits

Rint Refinement Refinement on Weighting scheme Total R values Robs, Rwobs Rall, Rwall R values as functions of satellite index Rwall: R0, R1, R2 Robs: R0, R1, R2 Number of parameters Drmin, Drmax (D/s)max

BiNi0.92 293.0 Orthorhombic W:Pmcm:ss-1 8.1527 14.1209 5.3243 612.95 0 0 0.26 8 3.432 Grey metallic needle, 0.01×0.01×0.12 mm 66.55 Stoe IPDS Phi rotation scans, 0–200° X-ray, Mo–Ka 0.71073 Numerical, from shape 0.0297, 0.2909 12 318 3886 I\3s(I) 1092 2.9–30.4 −115h511 −195k519 −75l58 −25m52 13.9 F w =1/(s 2(F)+0.0001F 2 0.077, 0.078 0.265, 0.085 6.48, 13.42, 36.87 5.09, 11.98, 12.88 55 −24.0, 13.6 0.02

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Crystal data Chemical formula Formula weight Crystal system Superspace group a (A, ) b (A, ) c (A, ) V (A, 3) q Z r Crystal form and colour m

Table 1 (Continued) Atomic parameters

x

y

z

U11/Uiso

U22

U33

0.25

0.0892(1)

0.25

0.0096(4) 0.0126(6)

0.0108(5)

Bi2

0

0.1719(1)

0.75

0.0198(7) 0.0106(6)

0.0102(5)

Ni1 Ni2

0 0.25

0 0.25

0 0

0.012(2) 0.011(1) 0.0154(7)

0.010(2)

Ni3

0.25

0.0834(5)

0.75

Modulation parameters Occupational modulation of Ni2, Ni3 modelled by a crenel wave o(Ni2) = 1 for 0.17(4)BnB0.83(4) o(Ni3) = 1 for 0.4(1)BnB0.6(1) Positional modulation for Bi1, Bi2, Ni1, Ni2 are modelled by Á 2 à  c s Ãn = 1 U xn cos(2pnn)+U xn sin(2pnn) à 2 U( = Í  U cyn cos(2pnn)+U syn sin(2pnn) Ãn = 1 2 à  c s à n = 1 U zn cos(2pnn)+U zn sin(2pnn) Ä U cBi1y1 = 0.0090(2) U cBi1y2 = 0.0004(3) U sBi1z1 = −0.0008(4) U sBi1z2 = 0.0058(8)

U cBi2x1 =0.0229(3) U cBi2y2 =0.0035(3) U sBi2z2 =0.0009(7) U sNi2z2 =0.006(3)

U sNi1x1 =−0.0064(8) U sNi1y2 =0.0025(11) U sNi1z2 =−0.004(3)

U sNi2y1 = 0.0027(7) U sNi2y2 = 0.002(1) U sNi2z1 = 0.005(1)

−0.004(2)

S. Lidin et al. / Solid State Sciences 2 (2000) 353–363

Bi1

All other relevant terms are identically zero from symmetry constraints Thermal displacement modulations are modelled as DUij = 2n = 1 DU cij,n cos(2pnn)+DU sij,n sin(2pnn) DU sBi1 23,1 = 0.0002(9) DU cBi1 11,1 = 0.0000(7) DU cBi1 22,1 = 0.008(1) DU cBi1 33,1 = 0.0024(8) DU sBi1 23,2 = −0.003(1) DU cBi1 11,2 = 0.005(1)

DU sBi2 13,1 =−0.0020(7) DU cBi2 12,1 =0.0013(6) DU sBi2 23,2 =0.001(1) DU cBi2 11,2 =−0.010(1) DU cBi2 22,2 =−0.008(2) DU cBi2 33,2 =0.001(1)

DU cNi1 12,1 = 0.005(1) DU cNi1 13,1 = 0.000(1) DU cNi1 11,2 = −0.022(5) DU cNi1 22,2 = −0.003(6) DU cNi1 33,2 = −0.018(5) DU cNi1 23,2 = −0.004(5)

DU cBi1 22,2 = −0.001(2) DU cBi1 33,2 = −0.002(2) All other relevant terms are identically zero from symmetry constraints 357

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Fig. 3. Modulation electron density maps. The density is summarised over a 0.5 A, section.

S. Lidin et al. / Solid State Sciences 2 (2000) 353–363

5. Structural description Bi1 and Bi2 show only displacive modulations as does Ni1 (Fig. 3). This can be interpreted as a fully occupied NiBi2 sublattice. Ni2 at the other octahedral site showed mainly an occupational modulation which could be reasonably modeled with a crenel function and a small displasive modulation. Ni3 at the trigonal bipyramidal site was modeled with only a crenel function. (The other trigonal bipyramidal site is empty.) This gives a composition Ni0.925Bi. In Fig. 4, electron density maps are shown in cuts perpendicular to the a axis. In Fig. 4a, x= 0 and the electron density variations of Ni1 and Bi2 along t can be studied. Ni1Bi22Bi14 octahedra are indicated in yellow: In this cut all octahedra and no trigonal bipyramids are occupied. In Fig. 4b, the cut is through x =1/4 and the occupational modulations of Ni2 and Ni3 are showed. To help the eye, some Ni2 filled Bi12Bi24 octahedra are indicated with green and some Ni3 filled trigonal bipyramids are indicated as red E11 polyhedra. It is notable that the occupancies of Ni2 and Ni3 are coupled so that Ni3 (the trigonal bipyramidal position) is always surrounded by trigonal prisms of Ni1 and Ni2, giving a total coordination of 11 for Ni3 in the shape of an

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Edshammar polyhedron. Conversely, Ni2 is present only as vertices of these polyhedra. g= 0.26 is close to the commensurate value 1/4. If this value is chosen for commensurate approximations, it is possible to generate two high symmetry 3D approximants; The choice t0 = 0 (the origin of the c axis coincides with that of the modulation wave) generates a center of inversion in the commensurate super structure yielding the space group symmetry F2/m11 while t0 = 1/8 generates a mirror plane perpendicular to c and the 3D symmetry Fm2m. Compare the monoclinic F2/m11 structure of Fig. 5a with structure surrounding the local inversion center at the bottom part of Fig. 4b. The Fm2m structure approximant is in the same manner found surrounding the local mirror plane indicated in the top part of Fig. 4b. The Ni atoms are arranged in two types of slabs perpendicular to the hexagonal c-axis. In the type I slabs, all octahedra are filled giving a NiBi composition (green octahedra layers in Fig. 5), while in the type II slabs, 3/4 of the octahedra are filled in each layer and in addition 1/8 of the trigonal bipyramidal sites between such 3/4 octahedra layer (indicated by the red E11 polyhedra in Fig. 5). The width of these slabs are different in the two commensurate approximations but the composition

Table 2 Group-subgroup relations and atomic positions Substructure type Ni2In–NiAs Bi Nia Nib Orthorhombic setting, breaking of 3 Bi Nia Nib Primitive setting, breaking of C Bil Bi2 Ni1 Ni2 Ni3 Ni4 W centering, doubling the a and b axis Bi1 Bi2 Ni1 Ni2 Ni3 Ni4

P63/mmc

Cell

aB8 =4.1 A, bB8 =4.1 A, cB8 =5.3 A,

Cmcm

Cell

a%=aB8 b%= aB8+2bB8 c= cB8

Pmcm (Pmma)

Cell

No change

W:Pmcm:ssg

Cell

a%%= 2a% b%%=2b% c%%= c% q =0.26c%%

2c (l/3 2/3 1/4) 2a (0 0 0) 2d (2/3 1/3 1/4) 4c (12 0.167 1/4) 4a (0 0 0) 4c (0 0.333 1/4)

= 4.1 A, = 7.1 A, = 5.3 A,

2e (l12 0.167 1/4) 2f (0 0.333 3/4) 2a (0 0 0) 2b (12 12 0) 2e (1/4 0.167 3/4) 2f (0 0.333 1/4) 4*2e (l/4 0.083 1/4) 4*2f (0 0.167 3/4) 4*2a (0 0 0) 4*2b (l/4 1/4 0). 4*2e (l/4 0.083 3/4) 4*2f (0 0. 167 1/4)

=8.2 A, = 14.1 A, = 5.3 A,

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Fig. 4. T-maps of the 4D crystal structure of NiBi. The zone axis is [1001]. (a) A cut at x =0. This section shows the modulation of Ni1 and Bi2 along b and c. (b) A cut through x= 1/4. This section shows the modulations of Ni2, Ni3 and Bi1. The arrangement of octahedra and Edshammar polyhedra at the top of the figure corresponds to that of the orthorhombic commensurate approximant, while that at the bottom corresponds to the monoclinic approximant.

S. Lidin et al. / Solid State Sciences 2 (2000) 353–363

is not altered. However, the width of these slabs is possibly the origin of the incommensurate behavior which is then coupled to a small changes in composition. Modulation wave vectors of slightly different values have been observed in EDP’s as has occasionally diffuse scattering along c* indicating disorder of these slabs. The structural solution presented by Ruck [6] is largely the same as the F2/m11 approximant but with additional Ni atoms in E11 polyhedra. These positions are only half occupied in the Ruck model.

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This would correspond to a slightly wider crenel function on Ni3 in the 4D refinement. It is interesting to note that the structure of NiBi contains empty and occupied octahedral as well as trigonal bipyramidal interstices. This makes it rather special among the B8 type intermetallics that normally fall into two classes; those with c/a ratios B1.4 in which all octahedral interstices are occupied and the trigonal bipyramidal interstices are partially occupied, and those with c/a ratios \ 1.4 in which the octahedral interstices are partially occupied [3,4].

Fig. 5. Polyhedral model for the commensurate approximant in spacegroup F2/m11 (a) and in spacegroup Fm2m (b) and the commensurate model of Ruck [6] in space group F2/m11 (c). The structure models are shown in three perpendicular directions. Green octahedra in the structures projected along a indicate totally filled rows of octahedra. Green circles in the same projections indicate Ni octahedrally coordinated by Bi, but only every second octahedron along a is occupied. The red polyhedra are Edshammar 11 polyhedra formed by the trigonal bipyramid of Bi and the trigonal prism of Ni atoms surrounding these Ni atoms.

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Fig. 5. (Continued)

6. Conclusions Prolonged annealing produces a NiBi compound that is slightly Bi rich. This is a composition outside of that which has been established for the NiBi phase with powder methods. The very long annealing times may be the reason for this; the growth of this phase is slow, and the superstructure ordering may require the expulsion of Ni from the crystallites. As the crystallites are small, a substantial amount of Ni may be accommodated in the grain boundaries, and this Ni is then lost only upon prolonged annealing. The results of Ruck [6] indicate the same behavior for crystals grown by chemical transport-they are slightly Bi rich. The structure is unusual in that it features characteristics of typical NiAs–Ni2In phases

(c/a typically around 1.225, pseudo cubic) with extra Ni in trigonal bipyramidal positions, but also Ni deficiency in octahedral interstices, a phenomenon common in NiAs–CdI2 type systems that normally have a c/a ratio above 1.4 for the basic B8 type cell. The incommensurate NiBi structure has a c/a of 1.31 somewhere in between these values.

Acknowledgements Financial support is acknowledged from the Swedish Natural Science Research Council (A-KL, SL) and the Go¨ran Gustafsson Foundation (SL). VP thanks for the Grant Agency of the Czech Republic (grant no. 202/96/0085).

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Fig. 5. (Continued)

References [1] P. Feschotte, J.-M. Rosset, J. Less Common Metals 143 (1988) 31. [2] G. Ha¨gg, G. Funcke, Z. Phys. Chem. B Chemie der Elementarprozesse aulbau der materiale 6B (1929) 272.

.

[3] S. Lidin, Acta Cryst. B54 (1998) 97. [4] S. Lidin, A.-K. Larsson, J. Solid State Chem 118 (1995) 313. [5] Petricek V., Dusek M., JANA98 Crystallographic Computing System, Inst. Phys. Acad. Sci., Prague, Czech Republic, 1997. [6] M. Ruck, Z. Krist. 15 (1998) 54 Supplement.