Diffuse scattering in metallic tin polymorphs

Abstract

The lattice dynamics of the metallic tin β and γ polymorphs has been studied by a combination of diffuse scattering, inelastic x-ray scattering and density functional perturbation theory. The non-symmorphic space group of the β-tin structure results in unusual asymmetry of thermal diffuse scattering. Strong resemblance of the diffuse scattering intensity distribution in β and γ-tin were observed, reflecting the structural relationship between the two phases and revealing the qualitative similarity of the underlying electronic potential. The strong influence of the electron subsystem on inter-ionic interactions creates anomalies in the phonon dispersion relations. All observed features are described in great detail by the density functional perturbation theory for both β- and γ-tin at arbitrary momentum transfers. The combined approach delivers thus a complete picture of the lattice dynamics in harmonic description.

Stabilization of the γ-Sn phase in tin nanoparticles and nanowires

“…This phase is only slightly different from a simple hexagonal structure. We find that this polymorph is structurally very similar and energetically quasi-degenerate to bulk b-Sn for a wide range of exchange-correlation functionals (Table S1 in the supplementary material 26 ), which is also in correspondence to its experimental occurrence at temperatures higher than 170 C. [19][20][21] Here, we show that indeed lower surface energies are obtained for c-phase compared to b-phase. The temperature-size phase diagram is determined, revealing that c-Sn is the most stable phase at room temperatures for nanoparticles smaller than 10 nm.…”

Soft phonon modes in rutileTiO2

“…The formalism can be found elsewhere [10,20,21]. Debye-Waller factors were calculated from a fine phonon grid with a spacing of 0.005Å −1 .…”

In-between Bragg reflections: thermal diffuse scattering and vibrational spectroscopy with x-rays

“…The lattice dynamics of γ-tin (stabilized by indium addition) was also studied by INS [47]. In [48] we investigate the lattice dynamics of the metallic tin polymorphs employing a combination of TDS, IXS and DFPT in order to obtain the full description of the lattice dynamics at arbitrary momentum transfer.…”

“…First principles lattice dynamics calculations were performed with the CASTEP package [27,28] at 0 K. The acoustic sum rule correction was applied to the calculated dynamical matrix in order to account for translational invariance with maximal correction of 2 meV at Γ point. More details are given in [48].…”