Theoretical Evaluation of Thermal Properties of TiO₂ Anatase and Rutile by using Einstein-Debye Approximation

Abstract

In this work, we propose a new approach to accurate calculation of heat capacities at constant volume and pressure of TiO2 anatase and rutile. The evaluation model is based on the Einstein-Debye approximation which has been extensively used in solid state physics. The application of proposed approach to anatase and rutile titanium dioxide computations results is shown to be well numerically satisfactory. This approach is valid in wide temperature ranges and can be suggested for accurate evaluation of thermal properties of solids. The calculation results are in well agreement with the literature values reported by other studies.

Hot electron dynamics in ultrafast multilayer epsilon-near-zero metamaterials

“…where A is the absorption, F is the fluence, L is the penetration depth, τ p is the pump pulse duration, and t 0 is the response delay. We use the electron specific heat capacity of Au, C e (T e )= 62.9T e J/(mK 2 ) [41], since by pumping at 470 nm, the generation of hot electrons occur only due to the existence of the Au layers in the composition of the designed multilayer metamaterial.The lattice specific heat capacity of Au is 2.51×10 6 J/(m 3 K), whereas that of TiO 2 is 2.77×10 6 J/(m 3 K) [42], which are both independent of the lattice temperature up to very high temperatures (>5000 K). We take the average of the lattice specific heat capacities of the two materials with respect to their composition in the metamaterial and employ an effective specific heat capacity, C l = 2.68× 10 6 J/(m 3 K).…”

AN ANALYTICAL TECHNIQUE FOR EVALUATING HEAT CAPACITY OF GeS, GeSe, GeTe AND SnS SEMICONDUCTORS USING EINSTEIN-DEBYE APPROXIMATION

“…To obtain the specific heat capacity at constant pressure and volume, we use the formulas presented in Refs. [31,32], respectively: 0 ( ) ( ) 1 ( )…”

“…Thus, taking into account the analytical Einstein-Debye suggested method [25,26], this paper aims to propose an accurate formulation for the evaluation of the heat capacities of semiconductors in the arbitrary temperature range. In recent studies [27][28][29][30][31], successful results were obtained for the calculation of the heat capacities of materials using the Einstein-Debye approach. The new approximation obtained here provides an effective way to calculate high and low temperature behavior of the heat capacities of semiconductors.…”