We propose a simple new way to evaluate the effect of anharmonicity on a system's thermodynamic functions, such as heat capacity. In this approach, the contribution of all the potentially complicated anharmonic effects to the constant-volume heat capacity is evaluated using one parameter only: the coefficient of thermal expansion. Importantly, this approach is applicable not only to crystals, but also to glasses and viscous liquids. To support this proposal, we perform molecular dynamics simulations of several crystalline and amorphous solids as well as liquids, and find a good agreement between the results from theory and simulations. We observe an interesting non-monotonic behavior of the liquid heat capacity with a maximum, and explain this effect as being a result of competition between anharmonicity at low temperature and decreasing number of transverse modes at high temperature.

By considering the lattice dynamics between bond strain and transverse vibration, we establish a common model for ceramic and hybrid materials that exhibit negative thermal expansion (NTE). We show that pressure-induced softening, increase in NTE with pressure, and variation of NTE with temperature all arise naturally from the same mechanical model that gives rise to the NTE itself.

We use a combination of neutron and x-ray total scattering measurements together with pair distribution function (PDF) analysis to characterize the variation in local structure across the orbital order/disorder transition in ${\mathrm{LaMnO}}_3$. Our experimental data are inconsistent with a conventional order/disorder description of the transition, and reflect instead the existence of a discontinuous change in local structure between ordered and disordered states. Within the orbital ordered regime, the neutron and x-ray PDFs are best described by a local structure model with the same local orbital arrangements as those observed in the average (long-range) crystal structure. We show that a variety of meaningfully different local orbital arrangement models can give fits of comparable quality to the experimental PDFs collected within the disordered regime; nevertheless, our data show a subtle but consistent preference for the anisotropic Potts model proposed previously [M. R. Ahmed and G. A. Gehring, Phys. Rev. B 79, 174106 (2009)]. The key implications of this model are electronic and magnetic isotropy together with the loss of local inversion symmetry at the Mn site. We conclude with a critical assessment of the interpretation of PDF measurements when characterizing local symmetry breaking in functional materials.

The vibrational properties of crystalline bulk materials are well described by Debye theory, which successfully predicts the quadratic ω² low-frequency scaling of the vibrational density of states. However, the analogous framework for nanoconfined materials with fewer degrees of freedom has been far less well explored. Using inelastic neutron scattering, we characterize the vibrational density of states of amorphous ice confined inside graphene oxide membranes and we observe a crossover from the Debye ω² scaling to an anomalous ω³ behaviour upon reducing the confinement size L. Additionally, using molecular dynamics simulations, we confirm the experimental findings and prove that such a scaling appears in both crystalline and amorphous solids under slab-confinement. We theoretically demonstrate that this low-frequency ω³ law results from the geometric constraints on the momentum phase space induced by confinement along one spatial direction. Finally, we predict that the Debye scaling reappears at a characteristic frequency ω_× = vL/2π, with v the speed of sound of the material, and we confirm this quantitative estimate with simulations.