When molar fluxes (unit: mol/m
2·s) are employed for binary interdiffusion, there are supposedly three types of fluxes. The first and second are the fluxes measured relative to the volume and the number of moles fixed frame of reference, respectively. The last are the fluxes which pass through the plane fixed relative to Kirkendall marker.
On the assumption that the total molar volume of alloy is a linear function of mole fraction, reference planes of the first fluxes are fixed relative to
x axis. Reference planes of the second fluxes are not fixed relative to the
x, but to ξ axis. Although intrinsic fluxes relative to the marker plane are independent of the frame of reference, moving velocity of the marker which is observed from the
x differs from that observed from the ξ. Intrinsic diffusivities calculated by use of marker velocity, therefore, depend on the frame of reference.
The intrinsic diffusivities,
Di, obtained on the volume fixed frame of reference are represented by the following equation
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\
oindentwhere \ ilde
D is the ordinary interdiffusion coefficient and
CiVi (
i=1, 2) is volume fraction. When
D1 is assumed to be equal to
D2, the sum of intrinsic flux of component 1 and that of component 2 is not equal to zero. The intrinsic diffusivities obtained on the number of moles fixed frame of reference have the same characteristics as the diffusivities represented by the well-known Darken’s relation which has been derived on the assumption of constant molar volume.
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