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

An approach was proposed to obtain a reasonable thermodynamic description of a thermal vacancy in the metastable disordered body centered cubic (bcc_A2) phase, which had been consistently ignored in previous thermodynamic assessments. The present approach was first applied to obtain the thermodynamic descriptions for pure metastable bcc Ni and Zn, and then in the binary Ni-Zn system. The thermodynamic descriptions for both the metastable disordered bcc_A2 phase and the stable ordered bcc_B2  phases in the Ni-Zn binary system were updated based on the corresponding experimental equilibria. With these updated thermodynamic descriptions, several drawbacks, including the multiple solutions for thermal vacancy concentrations and the artificial phase boundaries in previous assessments, can be avoided. Moreover, the calculated phase boundaries and invariant reactions related to the  phase agree well with the experimental data.

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

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.

Role of Thermal Vacancies on Temperature Dependence of Lattice Parameter and Elastic Moduli in B2-type FeAl

ABSTRACTTemperature dependence of the lattice parameter and elastic moduli in Fe-40 and -43Al (at.%) was investigated by high temperature X-ray diffractometry (XRD) and the Electro-Magnetic Acoustic Resonance (EMAR) method. The thermal vacancy concentration was estimated from the activation enthalpy and entropy data of vacancy formation previously reported for FeAl. It was found that both the lattice parameter and the elastic moduli of FeAl have a linear relationship with temperature even in the temperature range where thermal vacancy concentration rapidly increases (above 400 °C), thus suggesting that newly generated thermal vacancies at elevated temperature do not make significant influence on the lattice parameter and the elastic properties of B2-type FeAl.