Calculation of binodals and spinodals in multicomponent alloys by different statistical methods with application to iron-copper-manganese alloys

Statistical derivation of basic equations of diffusional kinetics in alloys with application to the description of diffusion of carbon in austenite

“…Here parameters λ ρ i (which are both time-and space-dependent, in general) can be called "site chemical potentials" for ρ-species atoms; they are related to local chemical potentials µ ρ i and µ h i of ρ-species and host atoms as λ ρ i = (µ ρ i − µ h i ) [21]. H int in (12) is the same as in (4); the parameters h ρ...σ i...j in (13) (also depending on both time and space) describe possible renormalizations of interactions; and Ω is determined by normalization.…”

“…33), we should use some approximate method of statistical physics, such as the MFA or cluster methods [12]. As discussed in detail in [15,21,29], employing the MFA for calculations of chemical potentials λ ρ i in real alloys often leads to great errors, while the pair cluster approximation (PCA) usually combines simplicity of calculations with a high accuracy, particularly for dilute alloys. As an illustration (used also below for interstitial alloys), we present the PCA expressions for λ ρ i in a binary A-B-v alloy with host atoms h=A and minority atoms α=B (skipping index B at λ B i = λ i and c B i = c i for brevity):…”

“…For a multicomponent alloy A-B 1 -...B m -v, the PCA methods of calculations of site chemical potentials λ ρ i are described in [21]. In calculations of correlators b p ij (33), we first consider for simplicity the case of configuration-independent saddle-point energies when differences ∆p α and ∆ p α in Eqs.…”

“…( 21)-( 24) and ( 40)-(43) of Ref. [21] to the case of interstitial alloys Me-X. The quasi-equilibrium Gibbs distribution (15) and the generalized grand canonical potential Ω g for the effective Hamiltonian (55) have the form…”

Experimental and theoretical study of the formation and growth of pearlite colonies in eutectoid steels

“…If we take into account possible phase separation, that is, if we minimize the total free energy (2) also with respect to the number of Me and X atoms in each phase, we can write total equilibrium equations for any two phases, 1 and 2, in the well-known form: (11) where µ is the chemical potential of carbon with respect to iron [21]. Simulations of phase transformations described below were made mainly for three thermodynamic models: for the symmetric model 1 from [12] with the following values of parameters in Eqs.…”