Related papers: How good is the Debye model for nanocrystals ?
We study the simplest possible model of nanocrystal consisting in a simple cubic lattice with a small number of atoms (NA ~ 10-10^3), where each atom is linked to its nearest neighbor by a quantum harmonic potential. Some properties…
When analyzing thermodynamic and kinetic properties of crystals whose anisotropy is not large and the considered effects do not relate to the existence of singled-out directions in crystals, one may use a more simple model of an isotropic…
Recent progress in the synthesis and processing of nano-structured materials and systems calls for an improved understanding of thermal properties on small length scales. In this context, the question whether thermodynamics and, in…
Self-consistent approach for interacting phonons description in lattice, which generalized Debye model, is proposed. Notion of "self-consistent" phonons is introduced, speed of which depends on temperature and is determined from non-linear…
We discuss, from a geometric standpoint, the specific heat of a solid. This is a classical subject in solid state physics which dates back to a pioneering work by Einstein (1907) and its refinement by Debye (1912). Using a special…
Below 1 K, the specific heat Cp of glasses depends approximately linearly on temperature T, in contrast with the cubic dependence observed in crystals, and which is well understood in terms of the Debye theory. That linear contribution has…
The phonon number fluctuations in the Debye model of solid are calculated and are demonstrated to be proportional to the temperature cubed at low temperature, similar to the celebrated Debye's law of the heat capacity. For a fixed number of…
We construct a quantum mechanical model of perfectly isotropic amorphous solids as fuzzy crystals and establish an analytical theory of vibrations for glasses at low temperature. Our theoretical framework relies on the basic principle that…
The low-temperature thermal properties of dielectric crystals are governed by acoustic excitations with large wavelengths that are well described by plane waves. This is the Debye model, which rests on the assumption that the medium is an…
Realistic phenomena can be described more appropriately using generalized canonical ensemble, with proper parameter sets involved. We have generalized the Einstein's theory for specific heat of solid in Tsallis statistics, where the…
The low-temperature properties of glasses present important differences with respect to crystalline matter. In particular, models such as the Debye model of solids, which assume the existence of an underlying regular lattice, predict that…
Crystal defect statistics is developed by minimizing the Gibbs free energy of defect formation, which is commonly converted to a crystallite size-independent equation by applying Stirling's approximation. Solutions of this equation forecast…
Disordered systems show deviations from the standard Debye theory of specific heat at low temperatures. These deviations are often attributed to two-level systems of uncertain origin. We find that a source of excess specific heat comes from…
The evaluation of the specific heat of an open, damped quantum system is a subtle issue. One possible route is based on the thermodynamic partition function which is the ratio of the partition functions of system plus bath and of the bath…
A commercially available calorimeter has been used to investigate the specific heat of a high-quality \kn\ single crystal. The addenda heat capacity of the calorimeter is determined in the temperature range $0.02 \, \mathrm{K} \leq T \leq…
We consider a regular chain of quantum particles with nearest neighbour interactions in a canonical state with temperature $T$. We analyse the conditions under which the state factors into a product of canonical density matrices with…
Analytic expressions for the $N$-dimensional Debye function are obtained by the method of brackets. The new expressions are suitable for the analysis of the asymptotic behavior of this function, both in the high and low temperature limits.
Much scientific and practical interest is currently focused on the atomic-scale mechanical behaviors of metallic nanocrystals with different crystal structures at room temperature, while the high-temperature plastic deformation in tungsten…
We consider a quantum system consisting of a regular chain of elementary subsystems with nearest neighbor interactions and assume that the total system is in a canonical state with temperature $T$. We analyze under what condition the state…
It is shown that the isobaric heat capacity of chalcogenides , , , and can be described by the Debye and Einstein models for the phonon frequency spectrum within their uncertainties; the models give the results for the isochoric heat…