Thermodynamic Characteristics of 1D Structures

Abstract

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 this paper 1D crystal lattice with one atom per elementary cell is analyzed. The nearest neighbor interaction within harmonic approximation is included. For such a model the dispersion relations are well known. Thermodynamic functions, such as specific heat of lattice and phonon thermal conductivity, are expressed via phonon density of states. In most simple cases, Einstein and Debye approximations are used for phonon density of states. In Einstein approximation the phonon density of states is expressed via Dirac ‐ function, while in Debye approximation the phonon density of states is of the ! di1 type, where d is a dimension of the system. For the assumed 1D structure, it is useful to find thermodynamic characteristics by applying exact relation for phonon density of states and compare them with the results obtained by using Debye approximation. Such analysis of 1D structures can have both theoretical and practical implications for Q1D structures.