Separate determination of reaction-diffusion constants

It is obvious that from any experimental dependence of the total layer thickness upon time it is only possible to determine the sum of the chemical constants as well as the sum of physical (diffusional) constants. The former sum is to be found from an initial portion of this dependence plotted in the coordinates x - t, while the latter from its long-time portion plotted in the coordinates x2- t or x - /l/2. For their separate determination, it is necessary to measure the increases in thickness of the ApBq layer at its both interfaces with initial substances A and B. 

The specimen, most suitable for such measurements, is shown schematically in Fig. 1.8. The upper part of the specimen is used for comparison. To prevent the interaction of components A and B in this part, a thin barrier layer of some substance which does not react with both A and B under chosen experimental conditions is deposited. The position of the layer interfaces is measured at certain moments of time relative to the inert markers located at the initial interface between substances A and B and/or inside the ApBq layer. Microhardness indentations onto the specimen cross-section surface, thin wires and strips of chemically inert materials, bubbles of inert gases, etc., can serve as the markers (for more detail, see for example Refs 35, 124). 

Separate determination of the chemical constants kim and k()A2 can be carried out in practice using the following procedure. First, it is necessary 

To determine the physical (diffusional) constants k]m and k]A2, it is necessary to establish the conditions under which the total thickness of the ApBq layer increases with time parabolically. Then, like the previous case, the increases, Axm and AxA2, in thickness of the layer at its interfaces 1 and 2 are to be measured. The values of the physical (diffusional) constants k m and k A2 are computed from the equations 

It should be noted that the value of each of the chemical constants kom and k0A2 depends on the physical-chemical properties of two reacting phases. The value of kom depends on the nature of substance A and the compound ApBq, while the value of k0A2 depends on the nature of substance B and the compound ApBq. Both physical (diffusional) constants depend only on the nature of the chemical compound ApBq and are therefore characteristic of this compound layer wherever it grows. However, as will be demostrated in the next chapters, the stoichiometry of adjacent phases must also be taken into account when estimating the growth rate of the ApBq layer in various reaction couples of the A-B binary system. 

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