Crystal Structure of the Disordered Non-Centrosymmetric Compound Fe_0.43Mo_2.56SbO_9.5

Abstract

Single crystals of Fe_0.43Mo_2.56SbO_9.5 were obtained by hydrothermal techniques at 230 °C. The crystal structure was determined from single crystal X-ray diffraction data. The compound crystallizes in the non-centrosymmetric space group Pc with unit cell parameters a = 4.0003(2) Å, b = 7.3355(3) Å, c = 12.6985(6) Å, β = 90°. The crystal structure comprises five crystallographically independent M atoms and one Sb³⁺ atom, M atoms are of two kinds of partially occupied sites Mo⁶⁺ and Fe³⁺. The building blocks consist of [SbO₃O_0.5O_0.5E] octahedra (E = lone electron pair) and [(Mo/Fe)O₆] octahedra. The M = (Mo, Fe) and O atoms are arranged in a distorted hexagonal 2D-net, not the Sb atoms. The distortion of the net and consequently the symmetry reduction results mainly from the location of the Sb atoms. Disorder manifests itself as a splitting of the metal sites and as a consequent shortening of the Mo–Fe distances. Six (Mo/Fe)O₆ octahedra are connected to form a pseudohexagonal channel. The Sb³⁺ atom is displaced from the pseudo-six-fold axis.

1. Introduction

The search for crystallographically non-centrosymmetric (NCS) materials is of current interest and of great importance due to the fact that such compounds may show interesting physical properties e.g., non-linear second harmonic generation, ferroelectricity etc. [1,2,3,4,5,6,7,8]. Involving cations having stereochemically active lone pairs e.g., Se⁴⁺, Te⁴⁺, Sb³⁺, As³⁺ and also d¹⁰ transition metal cations that are susceptible to second order Jahn–Teller distortion in the search for new compounds enhance the possibilities to form NCS materials [9,10].

A large variety of ternary oxides in the M–Sb–O system (M = Mn²⁺, Fe²⁺, Co²⁺, Ni²⁺, Zn²⁺, Mg²⁺) have previously been described in the literature [11,12,13,14,15]. The oxidation state of the Sbcations plays an important role when forming different kinds of crystal structures. MSb₂O₄ (M = Co, Ni, Fe, Mn) crystallizes in tetragonal symmetry with space group P4₂/mbc and forms schafarzikite type of crystal structures [11,14,15,16]. The crystal structure of MSb₂O₄ consists of rutile-type chains of edge-sharing MO₆ octahedra which are linked together by trigonal pyramidal Sb³⁺ cations. The Sb⁵⁺ cations have octahedral coordination and the example compounds crystallize with the trirutile crystal structure FeSbO₄, Fe₂Sb₂O₆, CoSb₂O₆, the pyrochlore-type Co₂Sb₂O₇ or the spinel-type compound Co_2.5Sb_0.5O₄ [12,17,18,19].

There are comparatively few quaternary compounds that have been investigated so far compared to the number of ternary compounds, especially in the M–Co–Sb–O (M= Mo, Ag, Na, Sr, Ba) system [13,20,21,22]. Some of these compounds exhibit interesting magnetic properties showing e.g., spin-glass transitions at low temperatures. Examples include the layered Ag₃Co₂SbO₆ and Sr₂CoSbO₆ and Sr₂CoSbO_5.63 (semiconductors) Na₃Co₂SbO₆ phases [13], the distorted Sr₃CoSb₂O₉ (insulator pervoskites [20] or the Ba₃CoSb₂O₉ and Ba₂Co_1.4Sb_0.6O_6−y phases [22]. However, there is only one such phase found in the [M–Fe–Sb–O] system; e.g., FeSb_2−xPb_xO₄ (x = 0.2–0.7) [23]. The replacement of Sb³⁺ by Pb²⁺ induces oxidation of Fe²⁺ to Fe³⁺. The substitution by Pb²⁺ leads to C-type antiferromagnetic orbital crystal structure compared to A-type antiferromagnetic orbital crystal structure for FeSb₂O₄. An example of disordered crystal structure in the [Fe–Mo–O] phase is observed e.g., Fe₂(MoO₄)₃. The disorder is mainly due to the Mo atom [24,25].

Compounds in the [M–Sb–O] and [M–Fe–Sb–O] systems have mainly been synthesized by solid state reactions that involve heating the constituents in a silica ampoule. The temperature varies from 500 °C to 1600 °C for different systems. In the present study we instead utilize a hydrothermal synthesis technique to grow single crystals of a new quaternary phase with the composition Fe_0.43Mo_2.56SbO_9.5. The crystals show diffuse scattering in addition to the Bragg reflections. After careful examination of many crystals by single crystal X-ray diffraction we concluded that the diffuse scattering, hence disorder, is intrinsic for this compound. The evidence is even more pronounced from the fact of lowering to non-centrosymmetric monoclinic symmetry with six-fold twinning instead of the higher hexagonal symmetry. Unfortunately it was not possible to synthesize phase-pure material for further characterization of the physical properties.

2. Materials and Methods

A mixture of FeF₂:MoO₃:Sb₂O₃=1:5:2 in 2 mL deionized water plus a few droplets of HF were sealed in an 18 mL teflon lined steel autoclave and heated to 230 °C at a rate of 1.6 °C/min. The plateau temperature was maintained for four days and thereafter the temperature was lowered to 30 °C with a rate 1.6 °C/min. The following starting chemicals were used: Sb₂O₃ (99.97%, Sigma-Aldrich, St. Louis, MO, USA), FeF₂ (99.8%, Sigma-Aldrich), and MoO₃ (99.5%, Sigma-Aldrich). The hydrothermal synthesis yielded green single crystals of Fe_0.43Mo_2.56SbO_9.5 that were washed using water and ethanol followed by drying at room temperature. An unidentified [Sb–Mo–O] phase was also found from the EDS analysis.

Single crystal X-ray diffraction data were collected using a Bruker D8 Venture diffractometer equipped with a PHOTON 100 detector. Data integration, including correction for oblique incidence, was performed with the software CrysAlis RED [26]. Absorption correction was applied with the computer program SADABS [27]. The crystal structure was solved using the program Superflip [28] and refined by using the program JANA2006 [29]. Fe, Mo, and Sb atoms were refined with anisotropic temperature parameters and oxygens were refined isotropically; the crystal refinement data is summarized in

Table 1. Crystallographic data for Fe_0.43Mo_2.56SbO_9.5.

	Fe0.43Mo2.56SbO9.5
formula weight/g mol−1	543.77
temperature/K	293
crystal system	Monoclinic
space group	Pc (no. 7)
a/Å	4.0003 (2)
b/Å	7.3355 (3)
C/Å	12.6985 (6)
β/°	90.0
V/Å3	372.6
ρ/g.cm−3	4.846
Z	2
crystal size/mm3	0.45 × 0.15 × 0.10
radiation type	Mo- Kα
wavelength/Å	0.71069
indices range	−8 ≤ h ≤ 8 −15 ≤ k ≤ 15 −26 ≤ l ≤ 26
No. of reflections
Measured/unique	18,904/13,739
observed [I >3 ϭ(I)]	9883
Rint	0.044
(sinθ/λ)max/Å−1	1.03
RF/wRF [F>3ϭ(F)] >
All reflections (%)	6.30/7.29
goodness of fit (all)	1.59

.

Chemical compositions were obtained by EDS using a Hitachi M3000 tabletop scanning electron microscope and a JEOL JSB-7000F. The content of heavy elements was found to be 10.6 at% Fe, 61.3at% Mo, and 28.1at% Sb, see Supplementary Materials. The expected values are 10at% Fe, 50at% Mo and 40at% Sb. An unidentified [Sb–Mo–O] phase was also found as byproduct with the composition 66at% Sb and 33 at% Mo respectively.

3. Results

Crystal Structure

The new compound Fe_0.43Mo_2.56SbO_9.5 crystallizes in the monoclinic non-centrosymmetric space group Pc with unit cell parameters a=4.0003(2) Å, b=7.3355(3) Å, c=12.6985(6) Å, β=90°. The refined β is 90.005 (3) which is within three times standard uncertainty. This is why we fixed the β to 90°, which showed convergence and good fit to data using space group Pc (monoclinic b-axis) compared to the possible space group in the higher symmetry of the orthorhombic cell. All crystallographic parameters from the refinement are summarized in Table 1. The structural units of Fe_0.43Mo_2.56SbO_9.5 with isotropic atomic displacement parameters and occupancies are summarized in the Supplementary Materials. Six fold twinning by fixing the volumes to one sixth was applied during the refinement. The twinning matrices are implied as follows: (100,0 −1/2 −3/2,01/2 −1/2); (100, 0 −1/23/2,0 −1/2 −1/2); (−100,010, 001); (−100, 0 −1/2 −3/2, 01/2 −1/2);(−100, 0 −1/23/2, 0 −1/2 −1/2). The unit cell contains one crystallographic independent Sb³⁺ atom and five sites by partially occupied Mo⁶⁺ and Fe³⁺ atoms. Mo/Fe sites are named either by a number or a number plus a letter. These five sites are Mo1/Fe1, Mo1a/Fe1a, Mo2/Fe2, Mo2a/Fe2a, and Mo3/Fe3. To make the description of the crystal structure simpler we introduced [Mo*/Fe*] to denote all [Mo/Fe] sites, [Mo1*/Fe1*] to denote the [Mo1/Fe1, Mo1a/Fe1a] sites and [Mo2*/Fe2*] to denote the [Mo2/Fe2, Mo2a/Fe2a] sites. The Mo1/Fe1 and Mo1a/Fe1a sites are present at a very short distance 0.71 Å and are actually split positions. Disorder manifests itself as a splitting of the metal sites and as a consequent shortening of the Fe–Mo distance. A similar trend has been found for the splitting of the Mo2/Fe2 and Mo2a/Fe2a sites. However, there is no split of the Mo3/Fe3 atom. Strong evidence for disorder is observed from the diffuse scattering found from the reconstructed image of the (hk2) layers, see Figure 1. The occupancy of Mo1 (0.72) is significantly higher than the occupancy of Fe1 (0.12), Mo1a (0.13), and Fe1a (0.02), however the overall occupancy is close to 1. Similarly, the occupancy of Mo2 (0.62) is significantly higher than for Fe2 (0.11), Mo2a (0.21) and Fe2a (0.04) and the overall occupancy is also close to 1. Mo3 (0.86) also has a higher occupancy than Fe3 (0.14) and together the occupancy is 1, see

Table 2. Occupancy factor of the partially occupied atoms in Fe_0.43Mo_2.56SbO₉.

Atom	Occ
Mo1	0.72
Fe1	0.12
Mo1a	0.13
Fe1a	0.02
Mo2 Fe2	0.64 0.11
Mo2a	0.21
Fe2a	0.04
Mo3	0.86
Fe3	0.14

. There are ten crystallographically independent oxygen atoms that have been refined isotropically and the O (10) atom is half occupied in a disordered manner.

The Sb atom is coordinated with five oxygen atoms to complete the distorted square pyramid [SbO₄]. The [SbO₄] units connected to each other by –Sb–O (10) –Sb–O (10) bridges to form a [Sb₂O₇]_n chain, see Figure 2a. The lone electron pair (E) sides opposite to the axial site of the pyramids to complete the distorted [SbO₃O_0.5O_0.5E] octahedras. The Sb–O distances vary from 1.95(2) Å to 2.443(7) Å, see

Table 3. Interatomic distances/Å in Fe_0.43Mo_2.56SbO_9.5.

Atoms	Atom–Oxygen (O) Distances
Sb1	1 × 2.146 (11); 1 × 2.063 (7); 1 × 2.09 (2); 1 × 1.95 (2); 1 × 2.443 (7)
Mo1/Fe1	1 × 2.326 (6); 1 × 1.680 (6); 1 × 1.904 (8); 1 × 1.927 (6); 1 × 2.010 (7); 1 × 1.942 (9)
Mo1a/Fe1a	1 × 1.620 (7); 1 × 2.391 (7); 1 × 1.946 (11); 1 × 1.912 (9); 1 × 2.014 (11); 1 × 1.941 (11)
Mo2/Fe2	1 × 1.720 (6); 1 × 2.286 (6); 1 × 1.930 (8); 1 × 1.859 (6); 1 × 2.012 (7); 1 × 2.020 (8)
Mo2a/Fe2a	1 × 2.329 (6); 1 × 1.675 (6); 1 × 1.868 (9); 1 × 1.809 (7); 1 × 2.031 (8); 1 × 2.066 (9)
Mo3/Fe3	1 × 1.739 (5); 1 × 2.273 (5); 1 × 1.838 (7); 1 × 2.037 (7); 1 × 1.874 (9); 1 × 2.023 (8)

. The Sb–O distances are comparable with the distances found in cubic Sb₂O₃ and monoclinic Sb₃O₄F [30,31]. Bond distances up to 2.76 Å for Sb–O are to be considered to belong to the primary coordination sphere according to the operative definition by Brown [32].

Both Mo1/Fe1 and Mo1a/Fe1a sites form distorted octahedral units of [(Mo1/Fe1)O₆] and [(Mo1a/Fe1a)O₆] respectively. The equatorial Mo/Fe–O distances are in the range 1.904(8)–2.014(11) Å. The axial Mo/Fe–O distances are 1.620(7)–2.391(7) Å. The short axial Mo/Fe–O distance is explained by the disorder present at the Mo1/Fe1, Mo1a/Fe1a sites. The [(Mo1*/Fe1*)O₆] octahedra are connected to each other by oxygen bridges to form a chain with the composition [(Mo1*/Fe1*)O₅]_n. Similarly, both Mo2/Fe2 and Mo2a/Fe2a sites forms distorted [(Mo2/Fe2)O₆] and [(Mo2a/Fe2a)O₆] octahedral and a similar chain; [(Mo2*/Fe2*)O₅]_n. The equatorial Mo/Fe–O distances are in the range 1.809(7)Å to 2.066(9) Å and the plane is shown in Figure 2b. The axial Mo/Fe–O distances are 1.675(6) Å and 2.329(6) Å respectively, see (Table 3). Mo3/Fe3 sites form distorted octahedra units of [(Mo3/Fe3)O₆]. The equatorial Mo3/Fe3–O distances are in the range 1.838(7)–2.023(8)Å and the axial Mo3/Fe3–O distances are in the range 1.739(5)–2.273(5)Å. The [(Mo3/Fe3)O₆] units are connected to each other by (Mo/Fe)–O–(Mo/Fe) bridges to form a [(Mo3/Fe3)O₅]_n chain along [1−1 0], see Figure 2a. The [(Mo1*/Fe1*)O₅]_n and [(Mo2*/Fe2*)O₅]_n chains connect to each other forming [(Mo1*/Fe1*)(Mo2*/Fe2*)O₈]_n layers, see Figure 3b,c. The [(Mo3/Fe3)O₅]_n and [SbO_3.5]_n chains connect via edge sharing to form [(Mo3/Fe3)SbO_6.5]_n chains, see Figure 3a. The [(Mo1*/Fe1*)(Mo2*/Fe2*)O₈]_n layers and the [(Mo3/Fe3)SbO_6.5]_n chains connect to each other by five different types of bridges, which are [(Mo1*/Fe1*)–O7–Sb1], [(Mo2*/Fe2*)–O7–Sb1], [(Mo2*/Fe2*)–O9–Sb1], [(Mo2*/Fe2*)–O9–(Mo3/Fe3)], [(Mo1*/Fe1*)–O8–(Mo3/Fe3)].

4. Discussion

The diffraction data suggests that a hexagonal crystal structure with space group P6/mmm would be a possible solution, but attempts to solve the crystals structure in this space group results in a very poor fit of the data. The solution is however sufficiently good to show the semblance of a hexagonal tungsten bronze type arrangement, the metal indicating a puckering of the layer. This, again, is a common structural response to the presence of a lone-pair element distorting the planar crystal structure and disrupting the mirror plane perpendicular to c.

There is no prescribed order for the modeling of this, but it is natural to first lower the symmetry from hexagonal P6/mmm to orthorhombic Cmmm and then to consider symmetry lowering compatible with the absence of a mirror plane perpendicular to c. This produces seven possible direct subgroups: Pmmn, Pman, Pbmn, Pban, Cmm2, C2/m11, C12/m1. The best result was found for Pbnm, but split positions caused by the symmetry remained and the symmetry was subsequently lowered through Pb2n to Pb11. No significant improvement was found on reducing the symmetry to P1. To control the veracity of this result, each of the other six maximal subgroups were taken as starting points for symmetry reduction, but these attempts verified the original result. The crystal structure in the orthorhombic group Pban could be reduced through the path Pban–Pb2n–Pb11 to yield the same result as before, as could Cmm2 via Cmm2–Cm11–Pb11 and Cmm2–Pba2–Pb11, but for the other orthorhombic starting points, the symmetry had to be reduced to P1 to yield a solution comparable to that in Pb11. The monoclinic group C2/m11 likewise could be reduced via C2/m11–Cm11–Pb11 and C2/m11–P2/b11–Pb11 to yield the same solution while C12/m1 yielded only the P1 solution.

The orientation of Mo*/Fe*atoms in the (bc) plane is shown in Figure 4. The cations Mo1*/Fe1*, Mo2*/Fe2*, and Mo3/Fe3 forms a pseudo-hexagonal channel, presented by a dotted line, see Figure 4. The distances in between the heavy atoms of the pseudo-hexagon vary from 3.616 Å to 3.837 Å and the angle varies from 114.55° to 125.69°. The antimony and oxygen atoms reside in the pseudo hexagons made up of six Mo*/Fe* and six O atoms. Inside the pseudohexagon there are two four-membered rings made of Mo*/Fe*, Sb and O atoms. Disorder manifests itself as a splitting of the metal sites on Mo*/Fe* in the pseudohexagons, which is why the symmetry is monoclinic instead of hexagonal. Sb is shifted away from the center of the pseudo 3-fold rotation axis, located in the pseudohexagonal channels.

5. Conclusions

The new compound Fe_0.43Mo_2.56SbO_9.5 crystallizes in the monoclinic non-centrosymmetric space group Pc with unit cell parameters a = 4.0003(2) Å, b = 7.3355(3) Å, c = 12.6985(6) Å, β = 90°. Five partially occupied sites with Mo⁶⁺/Fe³⁺ atoms and one Sb³⁺ atoms are present as crystallographically independent atoms. Several (Mo*/Fe*) sites sit at very short distances due to disorder in the crystal structure as evident from diffuse scattering. The lowering of symmetry confirms distortion in the crystal structure. The Sb atoms possess distorted octahedra of [SbO₄E] units with two half occupied oxygen atoms. The Mo*/Fe* forms distorted octahedral units of [(Mo*/Fe*)O₆]. Disorder manifests itself as a splitting of the metal sites on Mo*/Fe* in the pseudohexagonal channel, which is why lowering the symmetry to monoclinic from hexagonal is found. Sb is located in the pseudohexagonal channels and is shifted away from the center of the pseudo six-fold rotation axis6.