A Numerical Model Describing Multiphase Binary Diffusion in Liquid Metal/Solid Metal Couples

Abstract

A numerical model for multiphase binary diffusion in liquid metal/solid metal infinite couples is developed by introducing a bisection method which determines a location of the Matano interface. The model makes use of phase diagram sources and kinetic data without any adjustable parameters. The model gives displacements of the interphase interfaces including the liquid/solid interface relative to the x = 0 plane, a change in the mass of a solid metal and a distance-composition profile at diffusion time given. The calculated rates of phase layer growth agreed reasonably well with the measured rates by other researchers in liquid Sn saturated with Cu/solid Cu couples and liquid Zn/solid Fe couples in the diffusion-controlled stage.

Appendix: Nomenclature

1.1 Subscripts

A:

Principal component of a liquid metal

B:

Principal component of a solid metal

i :

Any component in a binary system

n :

Terminal phase of a solid metal

j / j + 1:

Phase interface between phase j and j + 1

j, j  − 1:

Phase boundary in phase j coexisting with phase j − 1

j, j + 1:

Phase boundary in phase j coexisting with phase j + 1

1.2 Prefix

k :

Rate constant expressed by amount per square root of time

1.3 Common Symbols

N _i :

Atomic fraction of component i

V _i :

Partial molal volume of component i

c _i :

Number of moles for component i per unit volume

D(L):

Diffusion coefficient in a liquid metal

D(j):

Diffusion coefficient in a solid phase j

AM _i :

Atomic mass of component i

N _i (S):

Atomic fraction of component i in a solid metal at t = 0

N _i (L):

Atomic fraction of component i in a liquid metal at t = 0

θ(L/S):

Ratio of molar transfer of component B to that of component A through the interface (L/S)

W(j) :

Layer thickness of an intermediate phase j

kW(j):

$= W\left( j \right)/t^{1/2}$

X(j/j + 1):

Displacement of an interface (j/j + 1) relative to the x = 0 plane

kW(j, j + 1):

$= X\left( {j/j + 1} \right)/{t^{1/2}}$

ω (j, j + 1):

$= kX\left( {j/j + {\text{ }}1} \right)/\left[ {2 \cdot D{{\left( j \right)}^{1/2}}} \right]$

ω (j+ 1, j):

$= kX\left( {j/j + {\text{ }}1} \right)/\left[ {2 \cdot D{{\left( {j + {\text{ }}1} \right)}^{1/2}}} \right]$