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Multiphase binary diffusion in infinite and semi-infinite media: Part II. On the numerical calculation of the rate constants for formation of product phases

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Abstract

The equations describing multiphase binary diffusion derived in the preceding article are arranged in an order such that the unknowns in the equations are expressed as two series of sequential functions of the corresponding two independent variables. The conditions to be satisfied between one series of functions and the other are given, and a numerical method for solving this type of equations of two unknowns is developed. For the numerical calculation of the parabolic rate constants for formation of product phases, data of average interdiffusion coefficients, partial molal volumes, and phase boundary compositions are required for an infinite medium. For a semi-infinite medium, in addition to these data, information on the equilibrium surface composition and the ratio of mole transfers of the two components at the surface is required.

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Abbreviations

n :

number of possible phases present in a diffusion specimen

N + A :

atomic fraction of componentA on the right-hand side of the original diffusion specimen

N j,j± 1 A :

atomic fraction of componentA of phasej coexisting with phasesj - 1 orj + 1

−V j i :

partial molal volume of componenti for phasej

−D j :

interdiffusion coefficient for phasej

Ω + :

initial value of Ωn, n−1

N - A :

atomic fraction of componentA on the lefthand side of the original diffusion couple

Ω - :

initial value of Ω1,2

t :

diffusion annealing time

N s A :

atomic fraction of componentA at the surface of a specimen

γ :

ratio of the number of moles of componentA from the gas into the substrate to that of componentB in the opposite direction

R i :

relative atomic mass of speciesi

Ω s :

initial value of Ωs

λ j,j± 1 :

rate constant for moving the interface(j/ j+1) relative to theX j = 0 plane (=Ω j,j± 1⋅≈D1/2 j)

K j :

rate constant for layer growth of product phasej (=λj,j+1 - λj,j-1)

δ j/j+1 :

rate constant for longitudinal change resulting from mutual transfers of componentsA andB between phasesj andj + 1 ( = λj,j+1.- λj+1.j)

X j,j± 1 :

displacement of the interfaces(j/j-l) and(j/j+1) relative to theX j = 0 plane(=2t 1/2 . λj ,j± 1)

W j :

layer width of phase j (=2t1/2 ⋅kj)

δT :

change in the thickness of a diffusion specimen on mixing of componentsA andB (=2t 1/2⋅Σn- 1 j=1δj/j+1)

λ s :

rate constant for moving the surface relative to theX 1 = 0 plane(=Ω s⋅≈D1/2 1)

Km :

rate constant for mass change per unit area of the surface

δM :

change in the mass of a specimen per unit area of the surface before and after reaction(=2t 1/2⋅km)

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  1. Department of Mechanical and Precision Systems, School of Science and Engineering, TeikyoUniversity, 320, Utsunomiya, Japan

    S. Tsuji (Professor)

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Tsuji, S. Multiphase binary diffusion in infinite and semi-infinite media: Part II. On the numerical calculation of the rate constants for formation of product phases. Metall Mater Trans A 25, 753–761 (1994). https://doi.org/10.1007/BF02665452

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