Thermodynamics and kinetics of metallic amorphous phases in the framework of the CALPHAD approach

Amorphous alloys are metastable phases which have generated considerable interest in recent years because of their promising properties. This review considers thermodynamic and kinetic aspects in the modelling of metallic amorphous phases.     

Description of the thermodynamic properties of pure gold in the solid and liquid states from 0 K

Thermodynamic data for pure gold were critically assessed using an extended Einstein model from 0 K for the crystalline FCC_A1 phase and a two state model for the liquid phase. During the assessment, careful critical evaluation of the experimental data on thermodynamic properties of solid (FCC_A1) and liquid phases was carried out. Due to the fact that there is a large scatter in the experimental data for crystalline gold in the temperature range between 200 K and the melting point, we carried out additional ab initio calculations of the thermodynamic properties. In order to fulfil the need for a precise evaluation of S^o_298.15 we needed to use an additional technique using multiple Einstein functions, which allows the experimental heat capacity and enthalpy data for the solid phase to be approximated accurately from 0 K up to the melting point. It was found during the data analysis that there is a large scatter in experimental data for the enthalpy of fusion and the liquid phase.     

Thermodynamic modelling of the spontaneous vitrification process using transformation diagrams

Spontaneous vitrification is a phenomenon where a crystalline phase transforms to the amorphous phase on annealing at low temperatures. It has been reported to occur in several binary alloy systems. This phenomenon has been widely investigated in the Ti–Cr system through experiments as well as thermodynamic modeling. The models reported in literature suffer from several drawbacks. They are not consistent with experimental observations. These models treat this non-equilibrium process as an essentially equilibrium process albeit involving two meta-stable phases. The thermodynamics of the “spontaneous vitrification” process has been modeled using the concept of Transformation Diagrams. This method considers the thermodynamics of non-equilibrium phase transformation and does not involve assumptions of equilibrium at any stage. A significant conclusion derived from the present model is that it is the close-packed hcp structure that transforms to the amorphous phase whereas the transformation of the relatively open bcc structure to the amorphous phase is forbidden thermodynamically. These conclusions are in contrast with the predictions of the earlier models.     

Thermodynamic description of the Ti–O system using the associate model for the liquid phase

The thermodynamic assessment of the Ti–O system was carried out by the CALPHAD method using the associate model for the liquid phase and the compound energy formalism for the solid phases. The derived set of parameters gives reasonable representation of the phase equilibria and thermodynamic properties of phases in the Ti–O system, while providing good extrapolation capability.     

The use of free energy vs composition curves in the prediction of phase formation in codeposited alloy thin films

An hypothesis is put forward and tested in a number of alloy systems, which accurately predicts the phases found in codeposited alloys deposited at low substrate temperatures. The hypothesis was developed for the prediction of crystalline phases but is clearly also applicable to the prediction of amorphous phases. It is hoped that codeposited alloy thin films may provide valuable information in the further characterisation of phase diagrams and in the understanding of low temperature phase stability.     

Thermodynamic evaluation and optimization of the As–Co,As–Fe and As–Fe–S systems

A critical evaluation of all available phase diagram and thermodynamic data for the As–Co and As–Fe binary systems as well as the As–Fe–S ternary system has been performed and thermodynamic assessments over the whole composition ranges are presented using the CALPHAD method. To predict thermodynamic properties and phase equilibria for these systems, the Modified Quasichemical Model (MQM) for short range ordering was used for the liquid phases. The Compound Energy Formalism (CEF) was used for the solid solutions. Since Co and Fe are ferromagnetic, magnetic contributions were added to describe the Gibbs energy of cobalt and iron rich solid solutions. Important uncertainties remain for the liquidus of As-rich regions in the binary subsystems.     

Thermodynamic assessment of the Ga–Se–Te system

In this study, the Ga–Te binary system was reassessed by means of the CALPHAD method using a modified lattice stability parameter for Te as well as experimental data for this binary system. The two-sublattice ionic solution model was applied for the liquid phase, and the intermediate phases were described by the sublattice model. A set of self-consistent thermodynamic parameters was optimized for all the phases in the Ga–Te binary system, which reproduced the phase diagram and the thermodynamic properties well. Using the reevaluated Ga–Te system, previously assessed Ga–Se system, and modified Se–Te system, a critical evaluation of the Ga–Se–Te ternary system was performed. The calculated vertical sections, isothermal sections, and liquidus projection agreed reasonably well with the experimental data. Immiscibility in the liquid phase was observed, and the origin of this behavior is discussed from a thermodynamic perspective.     

Estimation of thermodynamic properties of oxide compounds from polyhedron method

This paper describes a method to calculate the thermodynamic properties like enthalpy, entropy and molar volume of oxide mineral phases from their constituent polyhedra. Based on thermodynamic properties of 48 silicate and 19 titanate compounds collected from the critically evaluated and optimized FactSage database, thermodynamic properties of 18 polyhedra were optimized by weighted multiple linear regression analysis. The optimized properties of constituent polyhedra accurately reproduced the entropy, enthalpy and molar volume of all compounds, and were used for the prediction of thermodynamic properties of ternary oxide compounds in titanate systems.     

Thermodynamic assessment of the cesium–oxygen system by coupling density functional theory and CALPHAD approaches

The thermodynamic properties of cesium oxides were calculated by combining ab initio calculations at 0 K and a quasi-harmonic statistical thermodynamic model to determine the temperature dependency of the thermodynamic properties. In a second approach, the CALPHAD method was used to derive a model describing the Gibbs energy for all the cesium oxide compounds and the liquid phase of the cesium–oxygen system. For this approach, available experimental data in the literature was reviewed and it was concluded that only experimental thermodynamic data for Cs₂O are reliable. All these data together with the thermodynamic data calculated by combining ab initio and the statistical model were used to assess the Gibbs energy of all the phases of the cesium–oxygen system. A consistent thermodynamic model was obtained. The variation of the relative stability of the different oxides is discussed using structural and bond data for the oxides investigated by ab initio calculations. This work suggests that the melting point for Cs₂O₂ reported in the literature (863 K) is probably overestimated and should be re-measured.