In Situ Synthesis and Single Crystal Synchrotron X-ray Diffraction Study of ht-Sn₃Sb₂: An Example of How Complex...

Recent developments in X-ray sources and detectors and the parallel development of software for nonstandard crystallography has made analysis of very complex structural problems accessible to nonexperts. Here, we report the successful solution of the structure of ht-Sn₃Sb₂, an analysis that presents several challenges but that is still manageable in a relatively straightforward way. This compound exists only in a narrow temperature regime and undergoes an unquenchable phase transformation on cooling to room temperature; it contains two elements with close to identical scattering factors, and the structure is incommensurately modulated with four symmetry dependent modulation wave vectors. In this study, an attempt was first made to synthesize the title compound by in-house crystal growth in the stability region of ht-Sn₃Sb₂, followed by cooling to room temperature. This is known to produce mutiply twinned stistaite and elemental tin, and this sample, freshly prepared, was then reheated in situ at the single crystal materials beamline Crystal at the synchrotron Soleil. This method was unsuccessful as reheating the sample led to loss of Sn from stistaite as revealed by a change in the measured modulation wave vector. The compound was instead successfully synthesized in situ at the beamline by the topochemical reaction of single crystalline stistaite and liquid tin. A well-formed crystal of stistaite was enclosed in a quartz capillary together with a large excess of tin and heated above the melting point of tin but below the melting point of ht-Sn₃Sb₂. The structure was probed by sychrotron X-ray diffraction using a wavelength close to the absorption edge of Sn to maximize elemental contrast. In the diffraction patterns, first order satellites were observed, making the structure of ht-Sn₃Sb₂ incommensurately modulated. Further analysis exposes four q-vectors running along the body diagonals of the cubic unit cell (q₁' = α α α, q₂' = -α α -α, q₃' = -α -α α, q₄' = α -α -α). To facilitate the analysis, the q vectors were instead treated as axial (q₁ = α 0 0, q₂ = 0 α 0, q₃ = 0 0 α) and an F-type extinction condition for satellites was introduced so that only reflections with hklmnp, mnp all odd or all even, were considered. Further, the modulation functions F(q_i) were set to zero, and only modulation functions of the type F(q_i') were refined. The final model uses the four modulation functions, F(q₁'), F(q₂'), F(q₃'), and F(q₄'), to model occupancy Sn/Sb and positional modulation. The model shows a structure that comprises small NaCl type clusters, typically 7 × 7 × 7 atoms in extension, interspersed between single layers of elemental tin. The terminating layers of tin are slightly puckered, emulating an incipient deformation toward the structure of the layers perpendicular to the [001] direction in elemental tin. It is notable that this model is complementary to that of stistaite. In stistaite, two-dimensionally infinite slabs of rock salt are interspersed between layers of antimony along the trigonal [001] direction, so that the terminating Sb layers are the puckered bilayers typical for elemental Sb. Since all modulation functions are simple first-order harmonics, the structural model describes a locally disordered and most probably dynamic ordering.