Thermodynamic modeling of the Ge-La binary system

Abstract

The Ge-La binary system was critically assessed by means of the calculation of phase diagram (CALPHAD) technique. The associate model was used for the liquid phase containing the constituent species Ge, La, Ge 3 La 5 , and Ge 1.7 La. The terminal solid solution diamond-(Ge) with a small solubility of La was described using the substitutional model, in which the excess Gibbs energy was formulated with the Redlich-Kister equation. The compounds with homogeneity ranges, α(Ge 1.7 La), β(Ge 1.7 La), and (GeLa), were modeled using two sublattices as α(Ge,La) 1.7 La, β(Ge,La) 1.7 La, and (Ge,La)(Ge,La), respectively. The intermediate phases with no solubility ranges, Ge 4 La 5 , Ge 3 La 4 , Ge 3 La 5 , and GeLa 3 , were treated as stoichiometric compounds. The three allotropic modifications of La, dhcp-La, fcc-La, and bcc-La, were kept as pure element phases since no solubility of Ge in La was reported. A set of self-consistent thermodynamic parameters of the Ge-La binary system was obtained. The calculation results agree well with the available experimental data from literatures.

Modeling of Precipitation Behavior of Complex Precipitates in Ferrite and Validation with Experiment

“…Assuming that the precipitates are spherical and nucleate at dislocation, the overall energy change can be expressed as: where , and are the chemical free energy, the interfacial energy between precipitate and matrix and the dislocation core energy, respectively, and they are given by: where R is the average radius of precipitates, is the driving force for precipitation per unit volume, is the surface energy of the precipitate, is the shear modulus of matrix, and b is the Burgers vector. is given by: …”

“…where R is the average radius of precipitates, ΔG v is the driving force for precipitation per unit volume, γ is the surface energy of the precipitate, μ is the shear modulus of matrix, and b is the Burgers vector. ΔG v is given by [15] :…”

“…Based on the assumption that the precipitation process is limited by alloying elements rather than interstitial elements, many kinetic models [2,[9][10][11][12][13][14][15] were proposed for simple precipitates, such as NbC, [9,13] V(CN), [11] Ti(CN). [15] In these models, the concentration and the diffusivity of only one kind of substitutional element was used to calculate the nucleation rate, growth rate and coarsening rate of precipitation. But for complex precipitate that has more than one kind substitutional element, such asTi and Nb or Ti and V or Ti, Nb, and V, the entire precipitation process was controlled by concentration and diffusivity of the substitutional elements, so all existing models should be improved in the equations for nucleation, growth and coarsening to predict the precipitation behavior of complex precipitate.…”

“…However, the approach to deriving equations in their model is very complex. Based on the assumption that the precipitation process is limited by alloying elements rather than interstitial elements, many kinetic models were proposed for simple precipitates, such as NbC, V(CN), Ti(CN) . In these models, the concentration and the diffusivity of only one kind of substitutional element was used to calculate the nucleation rate, growth rate and coarsening rate of precipitation.…”