Abstract
As temperature increases, the thermal vacancy concentration in pure metals dramatically increases and causes some strongly non-linear thermodynamic behaviors in pure metals when close to their melting points. In this paper, we chose body-centered cubic (bcc) W as the target and presented a thermodynamic model to account for its Gibbs energy of pure bcc W from 0 K to melting point by including the contribution of thermal vacancy. A new formula for interaction part was proposed for describing the quadratic temperature behavior of vacancy formation energy. Based on the experimental/first-principles computed thermodynamic properties, all the parameters in the Gibbs energy function were assessed by following the proposed two-step optimization strategy. The thermodynamic behaviors, i.e., the strong nonlinear increase for temperature dependence of heat capacities at high temperatures and a nonlinear Arrhenius plot of vacancy concentration, in bcc W can be well reproduced by the obtained Gibbs energy. The successful description of thermal vacancy on such strongly non-linear thermodynamic behaviors in bcc W indicates that the presently proposed thermodynamic model and optimization strategy should be universal ones and are applicable to all other metals.
Highlights
Thermal vacancy is the simplest but extremely important structural defect in pure metals.As temperature increases, the thermal vacancy concentration in pure metals dramatically increases, and makes an apparent contribution to different physical quantities of materials, such as heat capacity, melting point, diffusivity, thermal conductivity, and so on [1,2,3]
When submitting Equation (7) into Equation (8), it can be found that the effects of thermal vacancy on heat capacity will become obvious with the increase of the temperature, which is excepted to describe the strongly non-linear behavior of thermodynamic properties near the melting point
The heat capacity shows a rapid increase at high temperatures especially close to the melting point
Summary
Thermal vacancy is the simplest but extremely important structural defect in pure metals. Taking body cubic centered (bcc) W that has been proposed for use in the divertor of future fusion devices [4,5], for example, its thermal vacancy concentration can be larger than 0.02 at its melting point [6,7] With such a large thermal vacancy concentration, the heat capacity of bcc W over the high-temperature region shows a strong non-linear increase, as demonstrated by most of the experimental data available in the literature [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23].
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