Assessment And Calculation Of Thermal Expansion Coefficient For Metallic Elements

Thermal expansion is the basic physical property. Study on the law of thermalexpansion coefficients has great theoretical and practical value and indicates the thermalproperty of new material. Over the past century, large amounts of experimentalinformation on thermal expansion have been accumulated and sometimes reviewed.Evaluation methods for thermal expansion:(1) Empirical model,(2) Semiempiricalmodels,(3) Theoretical methods. This paper firstly, thermal expansion coefficients of42pure metallic elements were evaluated on the basis of Semiempirical methods and theimproved Debye–Grüneisen model (in Debye–Grüneisen model, Debye temperature wasregarded as an undetermined constant). Parameters in the model were determined via thenonlinear least squarefit method through MATLAB program. The fitted curve matches theexperimental value well. Assessment by a set of parameters describe the thermal expansioncoefficient have been obtained, which contains a set of average Debye temperatures basedon thermal expansion coefficients. Meanwhile, reliable forecast for high-temperature orlow-temperature thermal expansion can be provided.Secondly thermal expansion coefficients of5kinds of refractory metals (V, Nb, Ta,Mo and W) were evaluated by taking the influence of thermal defects into account on thebasis of Debye–Grüneisen model that describes thermal expansion coefficients. Thecalculation results match the experimental values well, and the average Debye temperaturebased on thermal expansion coefficients under the influence of high temperature thermaldefects has been gained. The influence of thermal defects on refractory metals under hightemperature must not be overlooked. It can better describe thermal expansion coefficientsof high temperature refractory metals to consider thermal defects.Finally by using density functional perturbation theory, thermal expansion coefficientsof Al, Pd elements of fcc structure and Mo, V elements of bcc structure are calculated. Theprinciple is to calculate the total energy and phonon spectra under different latticeconstants, and obtain the relationship between lattice constant and the free energy atdifferent temperatures, by the minimum energy principle, calculate the equilibrium latticeconstant in different temperatures, and then calculate the coefficient of thermal expansion.After calculating, the coefficient of thermal expansion is basically consistent withexperimental data in certain temperature ranges, which verifies the feasibility ofcalculation of thermal expansion coefficient by first-principles. Based on the assessment and calculation of thermal expansion coefficient, satisfactoryresults are obtained, which make the evaluation of thermal expansion and calculationconnect well, and supplement each other. Besides, it has a very good reference value forthe study of the thermodynamic properties of metal elements, and lays a theoretical basisfor establishing database of thermal expansion.