Thermal conductivity of solids and liquids under pressure is covered in this review. Experimental techniques are critically considered and compared, and an introduction to theory is provided. Results are presented and discussed for ionic crystals, normal molecular crystals, plastic crystal phases, clathrate hydrates, polymers and glass-formers, liquids, covalent and semiconducting crystals, rocks and metals. Special attention is given to isochoric conditions, change of crystal structure and molecular orientational disorder. Available reliable measurements at pressures up to a few GPa indicate the need for theoretical development, especially in connection with molecular crystals and ferromagnetic metals.

http://iopscience.iop.org/article/10.1088/0034-4885/47/10/002/pdf

Thermal conductivity of solids and liquids under pressure

Advances in terahertz (THz) spectroscopy and solid‐state density functional theory (DFT) have enabled a better understanding of low‐frequency molecular phonon modes in the region that includes intermolecular interactions. Normal modes in this region, in particular, may have contributions under the harmonic approximation from both intermolecular and intramolecular nuclear motions. A newly developed mode analysis allows us to characterize molecular optical phonon modes in terms of intermolecular and intramolecular vibrational mixing for the C60 , anthracene, adenine, α‐glycine, and l‐alanine crystals. Through systematic investigation, two forms of the vibrational mixing have been identified. One is strong mixing within similar characteristic frequency regions, while the other is weak mixing of distinct characteristic frequency regions separated by a large gap. The former is predictable from classical mechanics and appears in molecular systems having structural flexibility. The latter is nonclassical and has been illustrated in amino acids. This finding provides new insights into the nature of molecular optical phonon modes and related physical and/or chemical processes such as energy transfer between internal and external modes with large energy separation. WIREs Comput Mol Sci 2016, 6:386–409. doi: 10.1002/wcms.1256

Mixing of intermolecular and intramolecular vibrations in optical phonon modes: terahertz spectroscopy and solid-state density functional theory

Dynamic processes in crystalline solids are reflected in the atomic displacement amplitudes determined, together with the atomic coordinates, by crystal structure analysis. The interpretation of such amplitudes poses two severe problems: (a) The relative phases of the atomic displacements are lost; and (b) the amplitudes may reflect disorder in the structure and systematic error in the diffraction experiment in addition to motion, but the three contributions cannot be separated on the basis of measurements at a single temperature. Several approximate ways to solve these problems, e.g. rigid-body and segmented-rigid-body analysis, are reviewed together with their limitations. A more recent approach that represents a significant advance with respect to both difficulties is also described: Crystal structures are determined over a range of temperatures; the mean square amplitude quantities are interpreted by taking explicit account of their temperature dependence, i.e. by exploiting the difference in behavior...

Motion and disorder in crystal structure analysis: measuring and distinguishing them.

A theory is given of the incoherent scattering cross section from high frequency intramolecular vibrational modes (ωλ) in a molecular crystal. It is assumed that ωλ≫ωD, where ωD is the maxium frequency of the low frequency lattice phonon continuum. It is shown that the scattering from a ωλ mode is proportional to a Debye–Waller factor arising only only from the internal molecular modes, multiplied by Ss(K,ω−ωλ), where Ss(K, ω) is the self‐correlation function of the molecular lattice. In the case when the Debye–Waller factor due to the lattice phonons is negligibly small, we show that Ss(K, ω−ωλ) is a Gaussian in ω−ωλ with Doppler broadening due to translational and rotational motion. Our theory is a development of the short‐time approximation and explains the unexpectedly strong intensity of the C–H stretching and bending modes recently observed by Jobic, Ghosh, and Renouprez in hexamethylenetetramine (HMT). The present paper gives the theoretical basis for the quantitative interpretation of the high energy intramolecular vibrational spectrum measured by inelastic neutron scattering.

Theory of the effective Debye–Waller factor in neutron scattering from high frequency molecular modes

Lattice vibrational dispersion curves for the ``intermolecular'' modes in the triclinic, one molecule per unit cell β phase of p‐C6D4Cl2 and p‐C6H4Cl2 have been obtained by inelastic neutron scattering. The deuterated sample was investigated at 295 and at 90°K and a linear extrapolation to 0°K was applied in order to correct for anharmonic effects. Calculations based on the atom‐atom model for van der Waals' interaction and on general potential parameters for the aromatic compounds agree reasonably well with the experimental observations. There is no substantial improvement in fit obtained either by consideration of electrostatic forces or by further anisotropy in the dispersion forces not described in the atom‐atom model. Anharmonic effects are shown to be large, but the dominant features in the temperature variation of frequencies are describable by a quasiharmonic model.

Lattice vibrations in chlorobenzenes: Experimental dispersion curves for β‐paradichlorobenzene by neutron scattering

The technique of coherent inelastic neutron scattering has been used to measure the dis-persion curves of intermolecular modes propagating along various high symmetry directions in the organic molecular crystal deuterated hexamethylenetetramine, at 100 and 298 K. The results are analysed in terms of phenomenological models involving interactions between supposedly rigid molecules. Interactions with both first and second nearest-neighbour molecules are found to be necessary for an adequate description. A simplified five-parameter model, which assumes centrosymmetric molecules, provides almost as good a fit to the results as that given by a generalized twelve-parameter model. Group theory shows that the effects of assuming centrosymmetry may be significant in the [££0] or E direction. Assuming that the replacement of deuterium by hydrogen does not change the intermolecular forces, the frequency distribution of function and the heat capacity of hydrogenous hexamethylenetetramine are calculated. The agreement between the computed and measured heat capacities is good. The frequency distribution function shows many obvious critical points and other singular features. The existence of logarithmically infinite singularities in this function is investigated. The elastic constants computed from the force models show discrepancies from those measured ultrasonically, and these discrepancies are thought to be significant. The long wavelength optical librational frequency measured in the present work differs considerably from that deduced from optical measurements, and an explanation of this apparent discrepancy is suggested. The 2 % hydrogen content in the specimen results in the presence of hydrogenous 9defect’ molecules, and the effects of these on the normal vibrations of the host lattice are shown to be very small.

B. M. Powell

Papers

Intermolecular dynamics of hexamethylenetetramine