In this paper 1D crystal lattice is analyzed within harmonic approximation, with one atom per elementary cell and nearest neighbor interaction included. For this type of crystal lattice dispersion relations are well known. Thermodynamic functions (specific heat and phonon thermal conductivity) are calculated via phonon density of states given in exact form. Thermodynamic variables are calculated for a whole temperature range. In limiting cases of low and high temperatures these thermodynamic variables can be found in analytic forms. For thermal conductivity the results of Callaway model for exact phonon density of states are compared with the results of Callaway model for Debye approximation of phonon density of states.
In the nanocylinder, a cut-off from the molecular crystal, dielectric permeability tensor is investigated. Excitons in the nanocylinder arise due to the exciting of the electron subsystem of the molecule. In evaluation of dielectric permeability Dzhyaloshinskii-Pitaevskii approach is used, connected with retarded and advanced exciton Green's functions and correct use of Paulion Green's function. It turned out that refraction and absorption indices depend on configuration coordinates, having maximal values at boundary cross-sections and minimal value at central cross-section of the nanocylinder broken symmetry structure. Although it was expected that boundary conditions make higher refractive and absorptive characteristics of the nanocylinder, this appeared not to be possible because Paulion Green's function is not proportional to the exciton concentration.
In this paper, we investigated the influence of size effect on thermodynamic properties of ultra-narrow wires with a simple cubic lattice, by means of two-time dependent Green functions method, adjusted to confined crystalline structures. Poles of Green functions, which defining phonon spectra, are found by solving the secular equation. For different boundary parameters, this problem is presented graphically. The temperature behavior of ultra-narrow wire thermal capacitance is compared to that of bulk structures. It turned out that in low-temperature region thermal capacitance of the ultra-narrow wire is notably lower than in the corresponding bulk sample. How this fact reflects the thermal, conducting and superconducting properties of materials, is discussed in the conclusion.
The dispersion law, density states of phonons, thermodynamics properties and thermal conductivity was analyzed in this paper. It has been shown that at low temperatures, thermal conductivity of thin film is considerably lower that of bulk-structure. It turned out that phonons in thin film require activation energy for exciting. This leads to extremely low specific heat and specific conductivity at low temperatures. Consequences of quoted facts were discussed in detail and their influence on kinetic and thermodynamic properties of thin films is estimated.
Spectra of possible phonon states, as well as thermodynamic characteristics of nanocrystals (ultrathin film and quantum wire) of simple cubic crystalline structure are analyzed in this paper, using the method of two-time dependent Green functions. From energy spectra and internal energy of the system the thermal capacitance of these structures in low temperature region is found. The temperature behavior of specific heat is compared to that of corresponding bulk structure. It is shown that at extremely low temperatures thermal capacitance of quantum wire is considerably lower than the thermal capacitance of film as well as the bulk sample. Consequences of this fact are discussed in detail and its influence to thermodynamic properties of materials is estimated.
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