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Two for the price of one – Resolvable polymorphism in a ‘single crystal’ of α- and β-Sb3O4I
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Solid State Sciences 11 (2009) 24e28 www.elsevier.com/locate/ssscie
Two for the price of one e Resolvable polymorphism in a ‘single crystal’ of a- and b-Sb3O4I Zuzana Hugonin1, Mats Johnsson2, Sven Lidin* Department of Inorganic Chemistry, Stockholm University, Svante Arrhenius 12, S-106 91 Stockholm, Sweden Received 12 November 2007; received in revised form 21 April 2008; accepted 26 April 2008 Available online 24 May 2008
Abstract The title compound forms as biphasic single crystals containing the a- and b-polymorphs. The structure of both polymorphs was solved and refined from single crystal X-ray data in a simultaneous refinement. The structures consist of rods of composition Sb3O4 separated by isolated iodine ions. The two phases differ only in the next nearest neighbour arrangement. The orthorhombic a-phase crystallizes in space group Pbn21, and the monoclinic b-phase in space group P21/n. Ó 2008 Elsevier Masson SAS. All rights reserved. Keywords: Stereochemically active lone pair; Multiphase crystal; Oxo-halide
1. Introduction The compound Sb3O4I has been known since the work of Kra¨mer et al. [1] but unlike the Cl-analogue, Sb3O4Cl [2], its structure has so far not been elucidated. The reason for this may well be inherent polymorphism. The only structurally characterized compound in the SbeOeI system is Sb5O7I, which exists in three different polymorphs [3,4] characterized by sheets or rods of Sb5O7 surrounding the isolated iodine positions in hexagonal, or pseudo-hexagonal arrangements. By repeating previous synthetic procedures we produced long thin needles of the target compound only to find that the Xray diffraction pattern exhibits the perfect non-crystallographic extinction conditions often associated with twinning. We could, however, not identify any twinning operation that would reconcile the diffraction pattern with any simple superstructure of the obvious orthorhombic sub-cell, and in the end we had to take recourse to the unusual procedure of considering the compound to exist in two polymorphs that intergrow to
* Corresponding author. Tel.: þ46 8 16 12 56; fax: þ46 8 15 21 87. E-mail address: [email protected] (S. Lidin). 1 Tel.: þ46 8 16 12 59; fax: þ46 8 15 21 87. E-mail: [email protected]. 2 Tel.: þ46 8 16 21 69; fax: þ46 8 15 21 87. E-mail: [email protected]. 1293-2558/$ - see front matter Ó 2008 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.solidstatesciences.2008.04.028
form large domains in contiguous ‘single’ crystals much like low symmetry twins in a high symmetry host lattice. 2. Results 2.1. Structural solution The diffraction pattern suggests an orthorhombic sub-cell ˚ with a distinct douof approximately 4.51 9.41 15.68 A bling of the b- and c-directions. All a priori attempts to solve the structure failed. It was observed that some non-crystallographic reflection conditions were very consistently obeyed in the quadrupled super-cell. Thus reflections of the type hkl, k ¼ 2n, l ¼ 2n þ 1 were systematically absent (see Fig. 1). Several different crystals were measured, but the phenomenon was present in all of them. This condition is not only noncrystallographic, but further it cannot be explained by any conceivable superstructure twin law. It was therefore suspected that the diffraction pattern may be composed of contributions from two different superstructure individuals sharing the same basic structure. Casual inspection did not reveal any relative intensity differences between different crystals, as might be expected if the relative volumes of the two phases differ from crystal to crystal. As a first step the sub-cell structure
Z. Hugonin et al. / Solid State Sciences 11 (2009) 24e28
Fig. 1. Reconstructed reciprocal lattice (1kl section, b* horizontal, c* vertical) from the X-ray diffraction experiment. Note the presence of a prominent subcell of strong reflections indicated to the left in white (with indexing) and to the right in red. The natural choice of 1 2 2 superstructure cell is indicated on the right in yellow, and here the non-crystallographic absences are evident. All reflections of the form hkl, k ¼ 2n, l ¼ 2n þ 1 are absent. The solution to the indexing problem is to introduce two superstructure cells, one orthorhombic and one monoclinic. These are shown in blue and green on the right-hand side of the pattern. On the left-hand side of the diffraction pattern, the union of the orthorhombic and monoclinic superstructure cells is shown. Note that all non-absent reflections are indexed by one or both of the cells and that all the systematic absences from the yellow superstructure cell are unindexed by the blue/green union. This is a strong indication that the blue/green indexing is correct.
was solved by considering the systematic absences in the ˚ sub-cell (k0 ¼ 2k, l0 ¼ 2l; h0l0 : 4.51 9.41 15.68 A h þ l0 ¼ 2; hk0 0, k0 ¼ 2n) and assigning this subset of reflections to a structure in the space group Pmnb. This subset of reflections was used as input to Charge Flipping and the solution was straight-forward. The structure is composed by Sb3O4
25
units forming infinite tubes along the a-direction. The tubes are separated by isolated I ions, as can be seen in the overview (Fig. 2). In the Pmnb setting, the mirror planes perpendicular to a (the direction of projection) impose very short SbeSb distances, and this must be resolved in the superstructures. Next, different superstructuring alternatives were considered. The simplest solution that will account for all satellite reflections is the superposition of a superstructure doubling the b-axis and one doubling the bc-diagonal. Let us consider each of these in turn. Doubling only the b-axis in a Pmnb cell must be preceded by a symmetry reduction since neither the b-glide perpendicular to c or the 21-axis along b is compatible with this operation. Thus the symmetry is first reduced to Pmn21 (assuming to retain orthorhombic symmetry, P21/m is the monoclinic alternative) in the original cell, and the doubling of b then allows for two different possibilities: Pmn21 and Pbn21. Keeping in mind the short distances generated by the mirror plane perpendicular to a, the latter solution is much more probable. Reducing the symmetry to Pbn21 in ˚ unit cell and seeding the symmetry a 4.51 18.82 15.68 A reduction in the structure by simply removing one Sb atom provided a starting model for a refinement. Proceeding cautiously with damping of the first cycles of the refinement, and periodically checking the resulting structure for atoms with large isotropic thermal displacement parameters to identify candidates for removal produced a very reasonable structure with normal interatomic distances, but a rather high agreement parameter R, around 12%, and some non-physical thermal displacement parameters. If the diffraction pattern indeed is the result of two overlapping structures, the common main reflections are expected to be overrepresented, and so finally reflections obeying the condition hkl, k ¼ 2n þ 1 were
Fig. 2. The two polymorphs of Sb3O4I viewed down the a-axis. Antimony atoms are shown in grey, oxygen in red and iodine in green. Lone pair positions are depicted as black spheres. Blue and orange spheres indicate different heights for the Sb3O4 columns. The relative positions of the Sb3O4 columns in (a) orthorhombic a-Sb3O4I and (b) the monoclinic b-Sb3O4I.
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Z. Hugonin et al. / Solid State Sciences 11 (2009) 24e28
given a different scale factor from those obeying hkl, k ¼ 2n. This reduced the R value to about 2%, and all thermal displacement parameters reverted to normal (and quite isotropic) values. The structure produced in this refinement is shown in Fig. 2a. This treatment is of course a gross simplification. If two crystals have partially overlapping lattices, the intensities of individual overlapping reflections are not retrieved by the simple reduction of their intensities by a constant factor. Instead each reflection must be decomposed into its constituent contributions according to the structure factor for each structure. This is, however, only possible once the structures have been solved, and as a first step, rescaling works reasonably well. The problem is the same as that for structural solution of twins by direct methods, or indeed for Rietveld profile refinement for structures with overlapping reflections. The second part of the satellite reflections constitutes a simultaneous doubling of the b- and the c-axes. This may be described as a (non-standard) centred orthorhombic cell or as a monoclinic cell. Considering first the centred orthorhombic alternative, doubling the b- and the c-axes brings about the destruction of much of the original symmetry of the basic Pmnb cell. As for the previous case, the b-glide perpendicular to c and the 21-axis along b must be annihilated prior to the doubling of b and likewise, prior to the doubling of c, the nglide perpendicular to b and the 21-axis along c must both be destroyed. This leaves only the (monoclinic) P21/m11 as maximum subgroup alternative prior to cell doubling. An analysis of the monoclinic setting yields the same result. Doubling b and c may now result in four different (maximal) space groups, P21/m11, P21/b11, P21/c11 and P21/n11. The systematic absences favour the choice P21/n11, which is equivalent to P21/b11 (a unique) in monoclinic setting. This is the cell used in the subsequent work. The symmetry of the basic structure was reduced accordingly, pseudo-merohedral monoclinic twinning was assumed, the cell was enlarged, and the symmetry breaking was seeded by the removal of a single Sb atom. As before, some progress was made, but final R values for a model without split atoms stopped at an unsatisfying 20%. Examination of the residual electron density map revealed pronounced maxima corresponding to the application of a mirror plane perpendicular to a. This phenomenon is not uncommon in superstructures refined from the basic precursors. It may be a signal that further symmetry reduction is required, but it may equally well be the result of an unfortunate choice of origin. Whenever a superstructure is generated, there are as many choices of origin as the number of copies of the basic structure contained in the superstructure. The difference does not become apparent until the translational symmetry of the underlying structure is broken. To remove the possible problem of an offending origin choice, the symmetry was reduced to Pb (monoclinic setting) and the refinement not rapidly converged to about 12%. The resulting structure was inspected for higher symmetry which was indeed shown to be present, and the centro-symmetric space group was reinstated. Different scale factors were introduced for satellites and main reflections, as for the orthorhombic case, and final refinements converged at an R value of about 2%.
Finally, the two structural models were converted to the ˚ yielding nonsmallest common cell, 4.51 18.81 31.36 A standard settings for both structures, but facilitating their simultaneous refinement as a single, multiphase crystal. In this model, there are three scale factors to refine corresponding to the orthorhombic phase and two monoclinic domains of different orientation. For each of the phases there are two iodine positions, six antimony positions and eight oxygen positions. All oxygen atoms were constrained to the same isotropic thermal displacement parameter. The positions are pair-wise related in such a way that the two-fold axes from the orthorhombic symmetry are pseudo-symmetries in the monoclinic cell, and the centre of symmetry from the monoclinic symmetry is a pseudo-symmetry of the orthorhombic cell. By choosing a common origin for the two phases, this pseudo-symmetry becomes even more apparent. In Table 1 the details of the X-ray experiment are summarized, and in Table 2 all parameters for the two phases are given. Note Table 1 Crystal data for a-Sb3O4I and b-Sb3O4I Phase a-Sb3O4I Formula weight Temperature (K) ˚) Wavelength (A Crystal system Space group generators
556.2 293 ˚ 0.71069 A Orthorhombic xyz, 1/2 þ x 1/4 y 1/4 þ z, 1/2 x 1/2 þ yz, x 3/4 y 1/4 þ z, þ (0 0 0), (0 0 1/2)
Unit cell ˚) dimensions (A
a ¼ 4.5166(5) b ¼ 18.820(2) c ¼ 31.365(4) 2666.1(6) 16 5.54 16.636
˚ 3) Volume (A Z Density (calc) (g/cm3) Adsorption coefficient (mm1) Absorption correction F(0 0 0) Crystal color Crystal habit Crystal size (mm3) q range for data collection ( ) Index range Reflections collected Independent reflections Completeness to q Refinement method Data/restraints/ parameters Goodness-of-fit on F Final R indices [I > 3s(I )] R indices (all data) Largest difference of peak and hole
Empirical 952 Colorless Rod-like 0.05 0.05 0.12 3.9e45.6 5 h 8, 27 k 37 52 46 16 955 4757 0.95 Full-matrix least squares on F 4757/0/99 0.42 R ¼ 0.0365 Rw ¼ 0.0450 R ¼ 0.1344 Rw ¼ 0.0530 ˚ 3) 0.98 and 0.54 (e A
b-Sb3O4I
Monoclinic xyz, 1/2 þ x y 1/2 z, x y z, 1/2 x y 1/2 þ z, þ (0 0 0), (0 1/2 1/2)
Z. Hugonin et al. / Solid State Sciences 11 (2009) 24e28
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Table 2 Atomic coordinates and equivalent isotropic displacement parameters
I1 I2 Sb1 Sb2 Sb3 Sb4 Sb5 Sb6 O1 O2 O3 O4 O5 O6 O7 O8 a
xort
yort
zort
Ueqa,ort
xmon
ymon
zmon
Ueq,amon
0.7570(2) 0.2640(2) 0.1669(3) 0.8223(3) 0.3727(2) 0.6355(2) 0.6535(2) 0.3391(3) 0.248(2) 0.744(2) 0.237(2) 0.245(2) 0.740(2) 0.375(2) 0.620(2) 0.757(2)
0.0532(1) 0.0577(1) 0.88561(6) 0.38438(7) 0.75360(5) 0.74753(5) 0.91648(5) 0.41524(5) 0.924(1) 0.415(1) 0.366(1) 0.7846(9) 0.284(1) 0.6908(5) 0.1898(5) 0.128(1)
0.1693 0.3308(1) 0.1603(1) 0.3391(1) 0.1985(1) 0.3008(1) 0.2416(1) 0.2579(1) 0.2151(5) 0.2804(8) 0.3139(7) 0.1837(4) 0.3242(9) 0.2441(3) 0.2541(3) 0.1801(6)
0.0169(8) 0.0169(6) 0.0131(3) 0.0138(3) 0.0113(3) 0.0115(3) 0.0115(3) 0.0118(3) 0.0115(4) 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115
0.7456(2) 0.2659(2) 0.1807(3) 0.8109(4) 0.8671(3) 0.3571(3) 0.8350(4) 0.3266(4) 0.248(2) 0.741(2) 0.738(2) 0.238(2) 0.248(2) 0.750(2) 0.385(2) 0.638(2)
0.0541(2) 0.6970(2) 0.88495(8) 0.13434(9) 0.25347(6) 0.00266(5) 0.41594(6) 0.16545(6) 0.420(1) 0.174(1) 0.368(1) 0.118(1) 0.286(1) 0.036(1) 0.6916(5) 0.0591(5)
0.16955(9) 0.08069(9) 0.33909(4) 0.58953(5) 0.30128(4) 0.55100(4) 0.25811(4) 0.50811(4) 0.2792(6) 0.5282(6) 0.3177(6) 0.5647(6) 0.1773(7) 0.5754(7) 0.2547(3) 0.5058(3)
0.025(2) 0.024(1) 0.0162(6) 0.0178(6) 0.0220(6) 0.0242(6) 0.0173(6) 0.0184(6) 0.0115(4) 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115
U(eq) is defined as one-third of the trace of the orthogonalized U tensor.
that the structural parameters are given in the setting of the combined refinement, which is in concordance with Table 1 and while the setting used in the Supplementary material is that of the conventional settings for the two space groups. The refinement converges to an R value of 3.6 for a model with 99 refinable parameters and 4757 unique reflections. Refinement was carried out on F, treating negative intensities as zero. While this is a principally questionable procedure, the
negative values were generally below 0.1 s(F2) and always below 0.2 s(F2). The volume ratio of orthorhombic to monoclinic is close to 50% indicating that the twinning may well be balanced. This in turn indicates that the domains are quite small, yielding a statistical distribution of the two phases. 2.2. Structural description The two structures are very similar, both being built from infinite rods of Sb3O4, with Sb in the 3 or 3 þ 1 coordination typical for Sb3þ (Fig. 3). The loci of the Sb3O4 rods form a triangular 36 net [5] in projection along the short axis. The hexagonal symmetry is broken by the elliptic cross-section of the rods, and rods with the same ellipse orientation form lines in the plane creating a herringbone pattern. Within such a line of equal orientation, the rods are out-of-step in height. Neighbouring herringbone line can only be arranged in one unique way, but for next nearest neighbours there are two possibilities where the loci of in-step rods form either straight lines or zigzag lines. Straight line arrangements lead to monoclinic symmetry and zigzag line arrangements lead to orthorhombic symmetry. The energy difference between the two arrangements is expected to be small, explaining the two-phase behaviour of the crystals. Between the Sb3O4 rods, the iodine ions form a graphene type 63 net, each I being loosely associated to six Sb atoms. The local arrangement of Sb around I depends only on nearest neighbours, and is hence the same for the monoclinic and the orthorhombic phases. The SbeI distances are all longer ˚. than 3.3 A 3. Conclusions
Fig. 3. Relative arrangement of two columns of Sb3O4. Note how the blue and orange spheres marking difference in position along a (vertical) are positioned. The image is created from the monoclinic polymorph, but the corresponding image from the orthorhombic polymorph is indistinguishable.
The two phases of Sb3O4I behave rather as expected structurally. The Sb3O4 substructure consists of infinite, one dimensional, rods that couple only weakly via the I ions. A complication in the elucidation of the structure is the biphasic
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Z. Hugonin et al. / Solid State Sciences 11 (2009) 24e28
nature of the crystals. This behaviour is not wholly unprecedented, but still unusual for a single crystal material. The similarities between the structures of the compound do, however, afford a hint at the underlying reasons for this effect. The energy difference between the two polymorphs must be minute, and since the molecular units are large, one would expect that restructuring is kinetically difficult. Thus, the multiphase behaviour is not unexpected, and the surprise is really that the compound orders at all. The possibility to simultaneously refine two structures from one set of single crystal data is very appealing. The main problem involved is solving the structures when both are unknown. This requires that the structures involved are not too different so that the intensity distribution of the overlapping reflections is relatively similar for the two structures. The present study deals with such a case and then the discrepancy between intensities of overlapping and nonoverlapping reflections can be handled relatively easily. Further, the phasing of the overlapping reflections is expected to be quite similar for similar structures, and this again facilitates structural solution. Finally, it should be emphasized that two structures that intergrow seamlessly as those in this study are expected to be quite similar, or else the intergrowth would be difficult to understand. This means that the restriction that only similar structures can be treated by the procedure is a mild one. 4. Experimental Single crystals of Sb3O4I were obtained from Sb2O3 and SbI3 mixed in the stoichiometric molar ratio 4:1. The starting mixture was sealed in an evacuated silica tube and heat treated in a muffle furnace at 320 C for 192 h. As starting materials Sb2O3 (Acros Organics, 99.999%) and SbI3 (Acros Organics, 98%) were used. The synthesis product was a mixture of an orange powder of undetermined composition and colorless needle-like Sb3O4I single crystals. The crystals subject to analyses were selected manually based on color and morphology. Analysis of the powder X-ray pattern revealed the presence of the target Sb3O4I phase in the orange powder. Some of the remaining peaks were identified as belonging to starting materials. However, the powder pattern is complex and some peaks remain unidentified. The chemical composition of the Sb3O4I was characterized with a scanning electron microscope (SEM, JEOL 820) equipped with an energy-dispersive spectrometer (EDS, LINK AN10000). EDS based on five different
crystals confirmed the presence and the stoichiometry of the heavy elements to be 75.7 1.7 at% Sb, and 24.2 1.6 at% I. The silicon content is below the detection limit of the instrument indicating that there was no substantial reaction with the silica tubes. The values are in good agreement with the structural refinement that gives 75 at% Sb, and 25 at% I. Single crystal X-ray diffraction data were collected by use of an Oxford Xcalibur 3 system, mounted with a Mo Ka source. Integration of the reflection intensities and absorption correction were made using the software provided by the diffractometer manufacturer [6]. Initial phasing of the structures was achieved using Charge Flipping [7] as implemented in the program Superflip [8] and refined using full matrix least squares on jFj using the program JANA2000 [9]. All illustrations were made with the program DIAMOND [10]. Acknowledgement This work has been carried out through the financial support from the European Union (HPHN-CT-2002-00193) and the Swedish Research Council. Supplementary material has been sent to Fachinformationszentrum Karlsruhe, Abt. PROKA, 76344 Eggenstein-Leopoldshafen, Germany (fax: þ49 7247 808 666; e-mail: [email protected]), and can be obtained on quoting the deposit numbers 418722 and 418723, respectively. References [1] V. Kra¨mer, M. Schumacher, R. Nitsche, Mater. Res. Bull. 8 (1973) 65e74. [2] H. Katzke, Y. Oka, Y. Kanke, K. Kato, T. Yao, Z. Kristallogr. 214 (1999) 284e289. [3] V. Kra¨mer, Acta Crystallogr. B31 (1975) 234e237. [4] W. Altenburger, W. Hiller, I.R. Jahn, Z. Kristallogr. 181 (1987) 227e234. [5] B. Gru¨nbaum, G.C. Shephard, Tilings and Patterns, W.H. Freeman and company, New York, 1987. [6] CrysalisRED, software for the integration of the reflection intensities and absorption correction, Oxford diffraction, Poland, 2007. [7] G. Oszla´nyi, A. Su¨to, Acta Crystallogr. A60 (2) (2004) 134e141. [8] L. Palatinus, G. Chapuis, Superflip, a computer program for the solution of crystal structures by charge flipping in arbitrary dimensions, J. Appl. Crystallogr. 40 (2007) 786e790. [9] V. Petricek, M. Dusek, L. Palatinus, Jana2000, the Crystallographic Computing System, Institute of Physics, Praha, Czech Republic, 2000. [10] G. Bergerhoff, DIAMOND, visual crystal information system, Bonn, 1999.
Solid State Sciences 11 (2009) 24e28 www.elsevier.com/locate/ssscie
Two for the price of one e Resolvable polymorphism in a ‘single crystal’ of a- and b-Sb3O4I Zuzana Hugonin1, Mats Johnsson2, Sven Lidin* Department of Inorganic Chemistry, Stockholm University, Svante Arrhenius 12, S-106 91 Stockholm, Sweden Received 12 November 2007; received in revised form 21 April 2008; accepted 26 April 2008 Available online 24 May 2008
Abstract The title compound forms as biphasic single crystals containing the a- and b-polymorphs. The structure of both polymorphs was solved and refined from single crystal X-ray data in a simultaneous refinement. The structures consist of rods of composition Sb3O4 separated by isolated iodine ions. The two phases differ only in the next nearest neighbour arrangement. The orthorhombic a-phase crystallizes in space group Pbn21, and the monoclinic b-phase in space group P21/n. Ó 2008 Elsevier Masson SAS. All rights reserved. Keywords: Stereochemically active lone pair; Multiphase crystal; Oxo-halide
1. Introduction The compound Sb3O4I has been known since the work of Kra¨mer et al. [1] but unlike the Cl-analogue, Sb3O4Cl [2], its structure has so far not been elucidated. The reason for this may well be inherent polymorphism. The only structurally characterized compound in the SbeOeI system is Sb5O7I, which exists in three different polymorphs [3,4] characterized by sheets or rods of Sb5O7 surrounding the isolated iodine positions in hexagonal, or pseudo-hexagonal arrangements. By repeating previous synthetic procedures we produced long thin needles of the target compound only to find that the Xray diffraction pattern exhibits the perfect non-crystallographic extinction conditions often associated with twinning. We could, however, not identify any twinning operation that would reconcile the diffraction pattern with any simple superstructure of the obvious orthorhombic sub-cell, and in the end we had to take recourse to the unusual procedure of considering the compound to exist in two polymorphs that intergrow to
* Corresponding author. Tel.: þ46 8 16 12 56; fax: þ46 8 15 21 87. E-mail address: [email protected] (S. Lidin). 1 Tel.: þ46 8 16 12 59; fax: þ46 8 15 21 87. E-mail: [email protected]. 2 Tel.: þ46 8 16 21 69; fax: þ46 8 15 21 87. E-mail: [email protected]. 1293-2558/$ - see front matter Ó 2008 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.solidstatesciences.2008.04.028
form large domains in contiguous ‘single’ crystals much like low symmetry twins in a high symmetry host lattice. 2. Results 2.1. Structural solution The diffraction pattern suggests an orthorhombic sub-cell ˚ with a distinct douof approximately 4.51 9.41 15.68 A bling of the b- and c-directions. All a priori attempts to solve the structure failed. It was observed that some non-crystallographic reflection conditions were very consistently obeyed in the quadrupled super-cell. Thus reflections of the type hkl, k ¼ 2n, l ¼ 2n þ 1 were systematically absent (see Fig. 1). Several different crystals were measured, but the phenomenon was present in all of them. This condition is not only noncrystallographic, but further it cannot be explained by any conceivable superstructure twin law. It was therefore suspected that the diffraction pattern may be composed of contributions from two different superstructure individuals sharing the same basic structure. Casual inspection did not reveal any relative intensity differences between different crystals, as might be expected if the relative volumes of the two phases differ from crystal to crystal. As a first step the sub-cell structure
Z. Hugonin et al. / Solid State Sciences 11 (2009) 24e28
Fig. 1. Reconstructed reciprocal lattice (1kl section, b* horizontal, c* vertical) from the X-ray diffraction experiment. Note the presence of a prominent subcell of strong reflections indicated to the left in white (with indexing) and to the right in red. The natural choice of 1 2 2 superstructure cell is indicated on the right in yellow, and here the non-crystallographic absences are evident. All reflections of the form hkl, k ¼ 2n, l ¼ 2n þ 1 are absent. The solution to the indexing problem is to introduce two superstructure cells, one orthorhombic and one monoclinic. These are shown in blue and green on the right-hand side of the pattern. On the left-hand side of the diffraction pattern, the union of the orthorhombic and monoclinic superstructure cells is shown. Note that all non-absent reflections are indexed by one or both of the cells and that all the systematic absences from the yellow superstructure cell are unindexed by the blue/green union. This is a strong indication that the blue/green indexing is correct.
was solved by considering the systematic absences in the ˚ sub-cell (k0 ¼ 2k, l0 ¼ 2l; h0l0 : 4.51 9.41 15.68 A h þ l0 ¼ 2; hk0 0, k0 ¼ 2n) and assigning this subset of reflections to a structure in the space group Pmnb. This subset of reflections was used as input to Charge Flipping and the solution was straight-forward. The structure is composed by Sb3O4
25
units forming infinite tubes along the a-direction. The tubes are separated by isolated I ions, as can be seen in the overview (Fig. 2). In the Pmnb setting, the mirror planes perpendicular to a (the direction of projection) impose very short SbeSb distances, and this must be resolved in the superstructures. Next, different superstructuring alternatives were considered. The simplest solution that will account for all satellite reflections is the superposition of a superstructure doubling the b-axis and one doubling the bc-diagonal. Let us consider each of these in turn. Doubling only the b-axis in a Pmnb cell must be preceded by a symmetry reduction since neither the b-glide perpendicular to c or the 21-axis along b is compatible with this operation. Thus the symmetry is first reduced to Pmn21 (assuming to retain orthorhombic symmetry, P21/m is the monoclinic alternative) in the original cell, and the doubling of b then allows for two different possibilities: Pmn21 and Pbn21. Keeping in mind the short distances generated by the mirror plane perpendicular to a, the latter solution is much more probable. Reducing the symmetry to Pbn21 in ˚ unit cell and seeding the symmetry a 4.51 18.82 15.68 A reduction in the structure by simply removing one Sb atom provided a starting model for a refinement. Proceeding cautiously with damping of the first cycles of the refinement, and periodically checking the resulting structure for atoms with large isotropic thermal displacement parameters to identify candidates for removal produced a very reasonable structure with normal interatomic distances, but a rather high agreement parameter R, around 12%, and some non-physical thermal displacement parameters. If the diffraction pattern indeed is the result of two overlapping structures, the common main reflections are expected to be overrepresented, and so finally reflections obeying the condition hkl, k ¼ 2n þ 1 were
Fig. 2. The two polymorphs of Sb3O4I viewed down the a-axis. Antimony atoms are shown in grey, oxygen in red and iodine in green. Lone pair positions are depicted as black spheres. Blue and orange spheres indicate different heights for the Sb3O4 columns. The relative positions of the Sb3O4 columns in (a) orthorhombic a-Sb3O4I and (b) the monoclinic b-Sb3O4I.
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Z. Hugonin et al. / Solid State Sciences 11 (2009) 24e28
given a different scale factor from those obeying hkl, k ¼ 2n. This reduced the R value to about 2%, and all thermal displacement parameters reverted to normal (and quite isotropic) values. The structure produced in this refinement is shown in Fig. 2a. This treatment is of course a gross simplification. If two crystals have partially overlapping lattices, the intensities of individual overlapping reflections are not retrieved by the simple reduction of their intensities by a constant factor. Instead each reflection must be decomposed into its constituent contributions according to the structure factor for each structure. This is, however, only possible once the structures have been solved, and as a first step, rescaling works reasonably well. The problem is the same as that for structural solution of twins by direct methods, or indeed for Rietveld profile refinement for structures with overlapping reflections. The second part of the satellite reflections constitutes a simultaneous doubling of the b- and the c-axes. This may be described as a (non-standard) centred orthorhombic cell or as a monoclinic cell. Considering first the centred orthorhombic alternative, doubling the b- and the c-axes brings about the destruction of much of the original symmetry of the basic Pmnb cell. As for the previous case, the b-glide perpendicular to c and the 21-axis along b must be annihilated prior to the doubling of b and likewise, prior to the doubling of c, the nglide perpendicular to b and the 21-axis along c must both be destroyed. This leaves only the (monoclinic) P21/m11 as maximum subgroup alternative prior to cell doubling. An analysis of the monoclinic setting yields the same result. Doubling b and c may now result in four different (maximal) space groups, P21/m11, P21/b11, P21/c11 and P21/n11. The systematic absences favour the choice P21/n11, which is equivalent to P21/b11 (a unique) in monoclinic setting. This is the cell used in the subsequent work. The symmetry of the basic structure was reduced accordingly, pseudo-merohedral monoclinic twinning was assumed, the cell was enlarged, and the symmetry breaking was seeded by the removal of a single Sb atom. As before, some progress was made, but final R values for a model without split atoms stopped at an unsatisfying 20%. Examination of the residual electron density map revealed pronounced maxima corresponding to the application of a mirror plane perpendicular to a. This phenomenon is not uncommon in superstructures refined from the basic precursors. It may be a signal that further symmetry reduction is required, but it may equally well be the result of an unfortunate choice of origin. Whenever a superstructure is generated, there are as many choices of origin as the number of copies of the basic structure contained in the superstructure. The difference does not become apparent until the translational symmetry of the underlying structure is broken. To remove the possible problem of an offending origin choice, the symmetry was reduced to Pb (monoclinic setting) and the refinement not rapidly converged to about 12%. The resulting structure was inspected for higher symmetry which was indeed shown to be present, and the centro-symmetric space group was reinstated. Different scale factors were introduced for satellites and main reflections, as for the orthorhombic case, and final refinements converged at an R value of about 2%.
Finally, the two structural models were converted to the ˚ yielding nonsmallest common cell, 4.51 18.81 31.36 A standard settings for both structures, but facilitating their simultaneous refinement as a single, multiphase crystal. In this model, there are three scale factors to refine corresponding to the orthorhombic phase and two monoclinic domains of different orientation. For each of the phases there are two iodine positions, six antimony positions and eight oxygen positions. All oxygen atoms were constrained to the same isotropic thermal displacement parameter. The positions are pair-wise related in such a way that the two-fold axes from the orthorhombic symmetry are pseudo-symmetries in the monoclinic cell, and the centre of symmetry from the monoclinic symmetry is a pseudo-symmetry of the orthorhombic cell. By choosing a common origin for the two phases, this pseudo-symmetry becomes even more apparent. In Table 1 the details of the X-ray experiment are summarized, and in Table 2 all parameters for the two phases are given. Note Table 1 Crystal data for a-Sb3O4I and b-Sb3O4I Phase a-Sb3O4I Formula weight Temperature (K) ˚) Wavelength (A Crystal system Space group generators
556.2 293 ˚ 0.71069 A Orthorhombic xyz, 1/2 þ x 1/4 y 1/4 þ z, 1/2 x 1/2 þ yz, x 3/4 y 1/4 þ z, þ (0 0 0), (0 0 1/2)
Unit cell ˚) dimensions (A
a ¼ 4.5166(5) b ¼ 18.820(2) c ¼ 31.365(4) 2666.1(6) 16 5.54 16.636
˚ 3) Volume (A Z Density (calc) (g/cm3) Adsorption coefficient (mm1) Absorption correction F(0 0 0) Crystal color Crystal habit Crystal size (mm3) q range for data collection ( ) Index range Reflections collected Independent reflections Completeness to q Refinement method Data/restraints/ parameters Goodness-of-fit on F Final R indices [I > 3s(I )] R indices (all data) Largest difference of peak and hole
Empirical 952 Colorless Rod-like 0.05 0.05 0.12 3.9e45.6 5 h 8, 27 k 37 52 46 16 955 4757 0.95 Full-matrix least squares on F 4757/0/99 0.42 R ¼ 0.0365 Rw ¼ 0.0450 R ¼ 0.1344 Rw ¼ 0.0530 ˚ 3) 0.98 and 0.54 (e A
b-Sb3O4I
Monoclinic xyz, 1/2 þ x y 1/2 z, x y z, 1/2 x y 1/2 þ z, þ (0 0 0), (0 1/2 1/2)
Z. Hugonin et al. / Solid State Sciences 11 (2009) 24e28
27
Table 2 Atomic coordinates and equivalent isotropic displacement parameters
I1 I2 Sb1 Sb2 Sb3 Sb4 Sb5 Sb6 O1 O2 O3 O4 O5 O6 O7 O8 a
xort
yort
zort
Ueqa,ort
xmon
ymon
zmon
Ueq,amon
0.7570(2) 0.2640(2) 0.1669(3) 0.8223(3) 0.3727(2) 0.6355(2) 0.6535(2) 0.3391(3) 0.248(2) 0.744(2) 0.237(2) 0.245(2) 0.740(2) 0.375(2) 0.620(2) 0.757(2)
0.0532(1) 0.0577(1) 0.88561(6) 0.38438(7) 0.75360(5) 0.74753(5) 0.91648(5) 0.41524(5) 0.924(1) 0.415(1) 0.366(1) 0.7846(9) 0.284(1) 0.6908(5) 0.1898(5) 0.128(1)
0.1693 0.3308(1) 0.1603(1) 0.3391(1) 0.1985(1) 0.3008(1) 0.2416(1) 0.2579(1) 0.2151(5) 0.2804(8) 0.3139(7) 0.1837(4) 0.3242(9) 0.2441(3) 0.2541(3) 0.1801(6)
0.0169(8) 0.0169(6) 0.0131(3) 0.0138(3) 0.0113(3) 0.0115(3) 0.0115(3) 0.0118(3) 0.0115(4) 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115
0.7456(2) 0.2659(2) 0.1807(3) 0.8109(4) 0.8671(3) 0.3571(3) 0.8350(4) 0.3266(4) 0.248(2) 0.741(2) 0.738(2) 0.238(2) 0.248(2) 0.750(2) 0.385(2) 0.638(2)
0.0541(2) 0.6970(2) 0.88495(8) 0.13434(9) 0.25347(6) 0.00266(5) 0.41594(6) 0.16545(6) 0.420(1) 0.174(1) 0.368(1) 0.118(1) 0.286(1) 0.036(1) 0.6916(5) 0.0591(5)
0.16955(9) 0.08069(9) 0.33909(4) 0.58953(5) 0.30128(4) 0.55100(4) 0.25811(4) 0.50811(4) 0.2792(6) 0.5282(6) 0.3177(6) 0.5647(6) 0.1773(7) 0.5754(7) 0.2547(3) 0.5058(3)
0.025(2) 0.024(1) 0.0162(6) 0.0178(6) 0.0220(6) 0.0242(6) 0.0173(6) 0.0184(6) 0.0115(4) 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115 0.0115
U(eq) is defined as one-third of the trace of the orthogonalized U tensor.
that the structural parameters are given in the setting of the combined refinement, which is in concordance with Table 1 and while the setting used in the Supplementary material is that of the conventional settings for the two space groups. The refinement converges to an R value of 3.6 for a model with 99 refinable parameters and 4757 unique reflections. Refinement was carried out on F, treating negative intensities as zero. While this is a principally questionable procedure, the
negative values were generally below 0.1 s(F2) and always below 0.2 s(F2). The volume ratio of orthorhombic to monoclinic is close to 50% indicating that the twinning may well be balanced. This in turn indicates that the domains are quite small, yielding a statistical distribution of the two phases. 2.2. Structural description The two structures are very similar, both being built from infinite rods of Sb3O4, with Sb in the 3 or 3 þ 1 coordination typical for Sb3þ (Fig. 3). The loci of the Sb3O4 rods form a triangular 36 net [5] in projection along the short axis. The hexagonal symmetry is broken by the elliptic cross-section of the rods, and rods with the same ellipse orientation form lines in the plane creating a herringbone pattern. Within such a line of equal orientation, the rods are out-of-step in height. Neighbouring herringbone line can only be arranged in one unique way, but for next nearest neighbours there are two possibilities where the loci of in-step rods form either straight lines or zigzag lines. Straight line arrangements lead to monoclinic symmetry and zigzag line arrangements lead to orthorhombic symmetry. The energy difference between the two arrangements is expected to be small, explaining the two-phase behaviour of the crystals. Between the Sb3O4 rods, the iodine ions form a graphene type 63 net, each I being loosely associated to six Sb atoms. The local arrangement of Sb around I depends only on nearest neighbours, and is hence the same for the monoclinic and the orthorhombic phases. The SbeI distances are all longer ˚. than 3.3 A 3. Conclusions
Fig. 3. Relative arrangement of two columns of Sb3O4. Note how the blue and orange spheres marking difference in position along a (vertical) are positioned. The image is created from the monoclinic polymorph, but the corresponding image from the orthorhombic polymorph is indistinguishable.
The two phases of Sb3O4I behave rather as expected structurally. The Sb3O4 substructure consists of infinite, one dimensional, rods that couple only weakly via the I ions. A complication in the elucidation of the structure is the biphasic
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Z. Hugonin et al. / Solid State Sciences 11 (2009) 24e28
nature of the crystals. This behaviour is not wholly unprecedented, but still unusual for a single crystal material. The similarities between the structures of the compound do, however, afford a hint at the underlying reasons for this effect. The energy difference between the two polymorphs must be minute, and since the molecular units are large, one would expect that restructuring is kinetically difficult. Thus, the multiphase behaviour is not unexpected, and the surprise is really that the compound orders at all. The possibility to simultaneously refine two structures from one set of single crystal data is very appealing. The main problem involved is solving the structures when both are unknown. This requires that the structures involved are not too different so that the intensity distribution of the overlapping reflections is relatively similar for the two structures. The present study deals with such a case and then the discrepancy between intensities of overlapping and nonoverlapping reflections can be handled relatively easily. Further, the phasing of the overlapping reflections is expected to be quite similar for similar structures, and this again facilitates structural solution. Finally, it should be emphasized that two structures that intergrow seamlessly as those in this study are expected to be quite similar, or else the intergrowth would be difficult to understand. This means that the restriction that only similar structures can be treated by the procedure is a mild one. 4. Experimental Single crystals of Sb3O4I were obtained from Sb2O3 and SbI3 mixed in the stoichiometric molar ratio 4:1. The starting mixture was sealed in an evacuated silica tube and heat treated in a muffle furnace at 320 C for 192 h. As starting materials Sb2O3 (Acros Organics, 99.999%) and SbI3 (Acros Organics, 98%) were used. The synthesis product was a mixture of an orange powder of undetermined composition and colorless needle-like Sb3O4I single crystals. The crystals subject to analyses were selected manually based on color and morphology. Analysis of the powder X-ray pattern revealed the presence of the target Sb3O4I phase in the orange powder. Some of the remaining peaks were identified as belonging to starting materials. However, the powder pattern is complex and some peaks remain unidentified. The chemical composition of the Sb3O4I was characterized with a scanning electron microscope (SEM, JEOL 820) equipped with an energy-dispersive spectrometer (EDS, LINK AN10000). EDS based on five different
crystals confirmed the presence and the stoichiometry of the heavy elements to be 75.7 1.7 at% Sb, and 24.2 1.6 at% I. The silicon content is below the detection limit of the instrument indicating that there was no substantial reaction with the silica tubes. The values are in good agreement with the structural refinement that gives 75 at% Sb, and 25 at% I. Single crystal X-ray diffraction data were collected by use of an Oxford Xcalibur 3 system, mounted with a Mo Ka source. Integration of the reflection intensities and absorption correction were made using the software provided by the diffractometer manufacturer [6]. Initial phasing of the structures was achieved using Charge Flipping [7] as implemented in the program Superflip [8] and refined using full matrix least squares on jFj using the program JANA2000 [9]. All illustrations were made with the program DIAMOND [10]. Acknowledgement This work has been carried out through the financial support from the European Union (HPHN-CT-2002-00193) and the Swedish Research Council. Supplementary material has been sent to Fachinformationszentrum Karlsruhe, Abt. PROKA, 76344 Eggenstein-Leopoldshafen, Germany (fax: þ49 7247 808 666; e-mail: [email protected]), and can be obtained on quoting the deposit numbers 418722 and 418723, respectively. References [1] V. Kra¨mer, M. Schumacher, R. Nitsche, Mater. Res. Bull. 8 (1973) 65e74. [2] H. Katzke, Y. Oka, Y. Kanke, K. Kato, T. Yao, Z. Kristallogr. 214 (1999) 284e289. [3] V. Kra¨mer, Acta Crystallogr. B31 (1975) 234e237. [4] W. Altenburger, W. Hiller, I.R. Jahn, Z. Kristallogr. 181 (1987) 227e234. [5] B. Gru¨nbaum, G.C. Shephard, Tilings and Patterns, W.H. Freeman and company, New York, 1987. [6] CrysalisRED, software for the integration of the reflection intensities and absorption correction, Oxford diffraction, Poland, 2007. [7] G. Oszla´nyi, A. Su¨to, Acta Crystallogr. A60 (2) (2004) 134e141. [8] L. Palatinus, G. Chapuis, Superflip, a computer program for the solution of crystal structures by charge flipping in arbitrary dimensions, J. Appl. Crystallogr. 40 (2007) 786e790. [9] V. Petricek, M. Dusek, L. Palatinus, Jana2000, the Crystallographic Computing System, Institute of Physics, Praha, Czech Republic, 2000. [10] G. Bergerhoff, DIAMOND, visual crystal information system, Bonn, 1999.