Inherent anharmonicity of harmonic solids

Atomic vibrations, in the form of phonons, are foundational in describing the thermal behavior of materials. The possible frequencies of phonons in materials are governed by the complex bonding between atoms, which is physically represented by a spring-mass model that can account for interactions (spring forces) between the atoms (masses). The lowest order, harmonic, approximation only considers linear forces between atoms and is thought incapable of explaining phenomena like thermal expansion and thermal conductivity, which are attributed to non-linear, anharmonic, interactions. Here we show that the kinetic energy of atoms in a solid produces a pressure much like the kinetic energy of atoms in a gas does. This vibrational or phonon pressure naturally increases with temperature, as it does in a gas, and therefore results in a thermal expansion. Because thermal expansion thermodynamically defines a Grüneisen parameter, which is a typical metric of anharmonicity, we show that even a harmonic solid will necessarily have some anharmonicity. A consequence of this phonon pressure model is a harmonic estimation of the Grüneisen parameter from the ratio of the transverse and longitudinal speeds of sound. We demonstrate the immediate utility of this model by developing a high-throughput harmonic estimate of lattice thermal conductivity that is comparable to other state-of-the-art estimations. By linking harmonic and anharmonic properties explicitly, this study provokes new ideas about the fundamental nature of anharmonicity, while also providing a basis for new materials engineering design metrics.

Упругие свойства и ангармонизм твердых тел

The squares of the velocities of the longitudinal and transverse acoustic waves separately are practically not associated with anharmonicity, and their ratio (vL2 / vS2) turns out to be a linear function of the Grüneisen parameter γ - the measure of anharmonicity. The obtained dependence of (vL2 / vS2) on γ is in satisfactory agreement with the experimental data. The relationship between the quantity (vL2 / vS2) and anharmonicity is explained through its dependence on the ratio of the tangential and normal stiffness of the interatomic bond λ, which is a single-valued function of the Grüneisen parameter λ (γ). The relationship between Poisson's ratio μ and Grüneisen parameter γ, established by Belomestnykh and Tesleva, can be substantiated within the framework of Pineda's theory. Attention is drawn to the nature of the Leont'ev formula, derived directly from the definition of the Grüneisen parameter by averaging the frequency of normal lattice vibration modes. The connection between Grüneisen, Leontiev and Belomestnykh-Tesleva relations is considered. The possibility of a correlation between the harmonic and anharmonic characteristics of solids is discussed.

Pressure dependence of the Grüneisen parameter and melting temperature of some metals

We have used a method for determining volume dependence of the Grüneisen parameter in the Lindemann law to study the pressure dependence of melting temperatures in case of 10 metals viz. Cu, Mg, Pb, Al, In, Cd, Zn, Au, Ag and Mn. The reciprocal gamma relationship has been used to estimate the values of Grüneisen parameters at different volumes. The results for melting temperatures of metals at high pressures obtained in this study using the Lindemann law of melting are compared with the available experimental data and also with the values calculated from the instability model based on a thermal equation of state. The analytical model used in this study is much simpler than the accurate DFT calculations and molecular dynamics.

Ionic Conductors: Effect of Temperature on Conductivity and Mechanical Properties and Their Interrelations

The ionic transport and the mechanical properties in solids are intimately related. However, few studies have been done to elucidate the background of that relation. With the objective to fill this gap and gain further understanding on the fundamental properties of ion conducting materials, we are studying systematically the mechanical properties of different materials. In the present study, after showing briefly our previous results obtained in crystalline materials, results regarding the relation between ionic conduction and mechanical properties in superionic glasses is presented. All these results indicate the intimate relation between the mechanical and ionic conduction. The results also indicate that the Grüneisen parameter and the Anderson–Grüneisen parameter of ionic conductors exhibit large temperature dependence and increase with temperature.