Effect of Thermal Vacancy on Thermodynamic Behaviors in BCC W Close to Melting Point: A Thermodynamic Study

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.

On Gibbs Energy for the Metastable bcc_A2 Phase with a Thermal Vacancy in Metals and Alloys

“…For instance, the Gibbs energy for the stable reference state and the liquid phase are known from the Scientific Group Thermodata Europe (SGTE) compilation by Dinsdale [14]. To analyze the metastable bcc_A2 pure metals with thermal vacancy, the model (k ,Va) is employed; the molar Gibbs energy of the bcc_A2 phase (Gmbcc_A2) can be expressed as [8,9,15]: Gmbcc_A2=Gkpure−bcc+yvaykGva+RTfalse(lnyk+yvayklnyvafalse)+yvaL Here, Gkpure-bcc is the molar Gibbs energy of pure bcc k without a thermal vacancy, and Gva is the vacancy energy. The site fractions of k and Va are yk and yva.…”

“…The value of Gva is fixed as 0.2 RT , a value slightly larger than the critical value, which ensures a unique equilibrium state as proposed by Frank [8]. A similar treatment was adopted in our previous work to describe a stable bcc W [9]. The points in Figure 3a,b are calculated critical values of the interaction parameter by using Equation (4) in both solid and liquid phase regions of metastable bcc_A2 Ni and Zn at each temperature.…”

“…In recent studies, positive values like +30 T [4], +(ln10) RT [5,6,7], or +0.2 RT [8], have been assigned as the Gibbs energy for thermal vacancy in the bcc_A2 phase. Previously, we [9] proposed an effective strategy to determine reasonable thermodynamic descriptions for pure bcc_A2 metals by considering the contribution of thermal vacancy, and successfully applied this approach to bcc W. However, this approach [9] requires further experimental data, such as the concentration of thermal vacancy and heat capacity, especially at temperatures close to melting. Therefore, this strategy is valid only for the stable bcc_A2 phase since it is difficult to experimentally obtain Gibbs values for the metastable bcc_A2 phase of pure metals and alloys.…”

Third-Generation Thermodynamic Descriptions for Ta-Cr and Ta-V Binary Systems

“…To develop an accurate thermodynamic database over the whole temperature region with physical sense, the concept of a third-generation thermodynamic database has been proposed since 1995 [ 14 ]. Under this framework, several research groups [ 14 , 15 , 16 , 17 , 18 , 19 ] have made efforts to establish new thermodynamic models for pure elements by using the Debye or Einstein models. Recently, a kind of third-generation thermodynamic model [ 13 ], which enables one to describe the thermodynamic properties of pure elements down to 0 K as well as thermal vacancy concentration near the melting point, has been proposed by combining the Segmented Regression (SR) model [ 15 ], two-state model [ 20 ] and thermal vacancy description [ 18 ].…”

“…Under this framework, several research groups [ 14 , 15 , 16 , 17 , 18 , 19 ] have made efforts to establish new thermodynamic models for pure elements by using the Debye or Einstein models. Recently, a kind of third-generation thermodynamic model [ 13 ], which enables one to describe the thermodynamic properties of pure elements down to 0 K as well as thermal vacancy concentration near the melting point, has been proposed by combining the Segmented Regression (SR) model [ 15 ], two-state model [ 20 ] and thermal vacancy description [ 18 ]. By applying such a model, a third-generation thermodynamic database for MoNbTaW RHEAs was developed [ 13 ].…”