Related papers: Elastic constants and thermodynamical quantities f…
Elastic constants are among the most fundamental and important properties of solid materials, which is why they are routinely characterized in both experiments and simulations. While conceptually simple, the treatment of elastic constants…
Simple application of the Einstein model combined with the elastic description of solid state is developed. The frequency of quantum oscillators has been assumed as volume dependent and, furthermore, elastic energy terms of static character…
Using the density functional formalism we derive expression for the distortion free energy for systems with continuous broken symmetry and use it to derive expression for the elastic constants of smectic phases in which director is tilted…
Experiments show that all the derivatives of the thermo-physical variables are nearly constant. The constant value of the derivatives indicates linear relationship between the variables. Neither the volume coefficient of thermal expansion…
We derive expressions for classical isothermal and adiabatic elastic constants for periodic systems with the boundary contributions included explicitly. The potential-dependent part of these expressions is written in terms of potential…
We describe a theoretical and computational approach to calculate the vibrational, elastic, and thermal properties of materials from the low-temperature quantum regime to the high-temperature anharmonic regime. This approach is based on…
Starting from a general classical model of many interacting particles we present a well defined step by step procedure to derive the continuum-mechanics equations of nonlinear elasticity theory with fluctuations which describe the…
The properties of crystals consisting of several components can be widely tuned. Often solid solutions are produced, where substitutional or interstitional disorder determines the crystal thermodynamic and mechanical properties. The…
When describing elastic deformations of a body sometimes it is worth to take in account elastic spatial dispersion. If spatial dispersion is weak, as usually happens, then it can be reduced to dependence of thermodynamic potential on strain…
Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a…
A simple and effective approach to thermodynamics is suggested, which solves the major difficulties in the traditional presentation of the subject. The internal energy is introduced from the behavior of deformable bodies, whereas the…
Using the contemporary thermodynamic equations of elastic solids leads to contradictions with the fundamental statements of thermodynamics. Two examples are presented to expose the inconsistencies. In example one the internal energy between…
Understanding the realization of thermal equilibrium through the thermalization process in a many-body system is a fundamental and complex scientific question, bridging thermodynamics and classical dynamics and connecting to a host of…
We introduce a lattice dynamics package which calculates elastic, thermodynamic and thermal transport properties of crystalline materials from data on their force and potential energy as a function of atomic positions. The data can come…
We give a variational formulation of classical statistical mechanics where the one-body density and the local entropy distribution constitute the trial fields. Using Levy's constrained search method it is shown that the grand potential is a…
We derive expressions for determination of the stress and the elastic constants in systems composed of particles interacting via non-central two-body potentials as thermal averages of products of first and second partial derivatives of the…
A one-dimensional quantum harmonic oscillator perturbed by a smooth compactly supported potential is considered. For the corresponding eigenvalues $\lambda_n$, a complete asymptotic expansion for large $n$ is obtained, and the coefficients…
We use both a perturbative Green's function analysis and standard perturbative quantum mechanics to calculate the decrease in energy and the effective mass for an electron interacting with acoustic phonons. The interaction is between the…
A hydroelastic problem of flexural--gravity waves scattering by a demarcation between two floating elastic plates is investigated within the frame of linear potential-flow theory, where the method of matched eigenfunction expansions is…
The elastic energy of mixing for multi-component solid solutions is derived by generalizing Eshelby's sphere-in-hole model for binary alloys. By surveying the dependence of the elastic energy on chemical composition and lattice misfit, we…