The lattice vibrations (phonon modes) of crystals underpin a large number of material properties. The harmonic phonon spectrum of a solid is the simplest description of its structural dynamics and can be straightforwardly derived from the Hellman-Feynman forces obtained in a ground-state electronic structure calculation. The presence of imaginary harmonic modes in the spectrum indicates that a structure is not a local minimum on the structural potential-energy surface and is instead a saddle point or a hilltop, for example. This can in turn yield important insight into the fundamental nature and physical properties of a material. In this review article, we discuss the physical significance of imaginary harmonic modes and distinguish between cases where imaginary modes are indicative of such phenomena, and those where they reflect technical problems in the calculations. We outline basic approaches for exploring and renormalising imaginary modes, and demonstrate their utility through a set of three case studies in the materials sciences.

The tin monochalcogenides SnS and SnSe adopt four different crystal structures, viz. orthorhombic Pnma and Cmcm and cubic rocksalt and π-cubic (P2_13) phases, each of which has optimal properties for...

Thermoelectric materials convert waste heat to electricity and are part of the package of technologies needed to limit global warming. The tin chalcogenides SnS and SnSe are promising candidate thermoelectrics, with orthorhombic SnSe showing some of the highest figures of merit ZT reported to date. As for other Group IV chalcogenides, SnS and SnSe can form rocksalt phases under certain conditions, but the thermoelectric properties of these phases are largely unexplored. We have applied a fully ab initio modelling protocol to compare the ZT of the orthorhombic and rocksalt phases of SnS and SnSe. Electronic structures from hybrid density-functional theory were used to calculate the three electrical transport properties, including approximate models for the electron relaxation times, and lattice dynamics calculations were performed to model the phonon spectra and lattice thermal conductivities. We obtained good estimates of the ZT of the well-studied orthorhombic phases. The rocksalt phases were predicted to show larger electrical conductivities and similar Seebeck coefficients to the orthorhombic phases, resulting in higher thermoelectric power factors, but these were offset by larger thermal conductivities. These results therefore motivate further investigation of the recently discovered “π-cubic” phases of SnS and SnSe, which are based on distorted rocksalt supercells, to establish their thermoelectric performance.

We present a detailed study of the structural dynamics, energetic and dynamical stability, and thermal transport of the bismuth chalcogenides Bi 2 S 3 , Bi 2 Se 3 , and Bi 2 Te 3 and their alloys. The active Bi lone pairs lead to competition between orthorhombic Pnma and rhombohedral R3̅ m phases, with the latter favored by the heavier chalcogens, while the reported nonambient Bi 2 Se 3 and Bi 2 Te 3 phases show phonon instabilities under ambient conditions. The Pnma structure has intrinsically weaker chemical bonding and stronger phonon anharmonicity than the R3̅ m phase, resulting in lower lattice thermal conductivity. A thermodynamic model of Bi 2 (Se 1−x S x ) 3 indicates that the R3̅ m structure is energetically favored only at low S content, but the stability window may be extended with lower formation temperatures. R3̅ m Bi 2 (Se 1−x Te x ) 3 is a nonideal solid solution due to a strong preference for the Se and Te atoms to occupy the interior and exterior sites, respectively, in the constituent quintuple layers. Strain-field fluctuations from chemical bonding inhomogeneities are shown to play an important role in the heat transport in the alloys, and chalcogen disorder is found to be an important factor in the lower thermal conductivity of Bi 2 SeTe 2 compared to Bi 2 Te 3 . The microscopic insight from this study provides a new theoretical perspective on bismuth chalcogenides and their alloys to inform ongoing research on the thermoelectric performance of these and related systems.

Controlling aspects of the μ2‐X− bridging anion in the metal–organic framework Ga‐MIL‐53 [GaX(bdc)] (X−=(OH)− or F−, bdc=1, 4‐benzenedicarboxylate) is shown to direct the temperature at which thermally induced breathing transitions of this framework occur. In situ single crystal X‐ray diffraction studies reveal that substituting 20 % of (OH)− in [Ga(OH)(bdc)] (1) for F− to produce [Ga(OH)0.8F0.2(bdc)] (2) stabilises the large pore (lp) form relative to the narrow pore (np) form, causing a well‐defined decrease in the onset of the lp to np transition at higher temperatures, and the adsorption/desorption of nitrogen at lower temperatures through np to lp to intermediate (int) pore transitions. These in situ diffraction studies have also yielded a more plausible crystal structure of the int‐[GaX(bdc)] ⋅ H2O phases and shown that increasing the heating rate to a flash heating regime can enable the int‐[GaX(bdc)] ⋅ H2O to lp‐[GaX(bdc)] transition to occur at a lower temperature than np‐[GaX(bdc)] via an unreported pathway.