On the equivalence of the quasi-chemical method and the limiting case of the method of Kramers and Wannier for the treatment of cooperative phenomena
β Scribed by E. Dempsey
- Publisher
- Elsevier Science
- Year
- 1964
- Weight
- 420 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0001-6160
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β¦ Synopsis
Darken(l) has pointed out that, for the o&se of constant molal volume and no porosity, the origin established by the Matano analysis is identioal with the initial interface. This fact may also be demonstrated by equating the right&and sides of (13a) and (13b) and substituting (16) into this equation.
With the assumptions of constant molal volume and the absence of porosity, Darken's equations, (1) and (2), are readily transformed into Heumann's equations, ( 13) and ( 14), for the intrinsic diffusion coefficients. This transformation is outlined by the following development. The integral in (1) can be seen by reference to Fig. 1 to be equal to marker from each end of the couple before and after diffusion. As pointed out above, the measurement of these distances is not necessary if the couple is made up of pure components. In addition, if porosity occurs in the diffusion zone, it is not proper to apply the Matano analysis but the intrinsic diffusion coefficients may nevertheless be obtained from the appropriate equations of Heumann.
One of the authors, V. Ruth, wishes to acknowledge the Fulbright travel grant whioh he received.
π SIMILAR VOLUMES
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The Laplace transform is applied to remove the time-dependent variable in the di usion equation. For nonharmonic initial conditions this gives rise to a non-homogeneous modiΓΏed Helmholtz equation which we solve by the method of fundamental solutions. To do this a particular solution must be obtained