Part X – October 1969 - Papers - A Phenomenological Description of Isothermal Electrodiffusion in Gold Including the Vacancy Component

In a special type of electrodiffusion experiment the entire specimen is at constant temperature. The vacancies are then created at one end of the specimen and flow to the other end where they are destroyed. The energy required to operate the corresponding sources and sinks results in a super saturation of vacancies at one end of the specimen and an under -saturation at the other end. This gradient in vacancy concentration produces a chemical-diffusion flux, J(D), of vacancies in addition to the flux, J(E), caused by the electric current. Using the experimental data of Ch. Herzig,5 it is shown that a super saturation of 1 pct can cause J(D) to be about 25 pct of J(E), and thus account for the anomalous behavior of short specimens. THERE are advantages in a phenomenological treatment as contrasted to an atomistic one. For example, there are many reactions involving the element copper that are quantitatively and usefully understood from a phenomenological viewpoint, even though electron theory is not yet able to predict whether copper should be fcc or cph.' Similarly, the lack of a complete atomic theory of vacancies need not prevent the development of a treatment based on thermodynamics and chemical kinetics. In the following discussion, models will be used for the vacancies and for the mechanisms by which they move or are created or destroyed, but the phenomenological treatments are not dependent on the details of these models. The important product of a phenomenological analysis is an equation that describes the relation among the measurable quantities determining the behavior of the system. Based on such an equation, experiments can be performed to study these quantities in detail. Eventually atomic theory will supply an adequate theoretical base for the phenomena in question. A chemical species whose chemical potential was invariant during reactions in binary and ternary systems of varying composition would indeed be an anomaly. Yet this is the role that has frequently been assigned to the vacancies in pure metals, in dilute solutions, and even in ordinary alloys. The weight of available evidence supports the view that supersatu-rations of vacancies are on the order of 1 pct in usual diffusion processes.' Although it may seem strange that such a small deviation from equilibrium could significantly affect the thermodynamic properties of the vacancies, it is well known that the driving force for an ordinary chemical reaction is the departure of the components from their equilibrium state. Similarly, the reaction of vacancies that results in the formation of pores in various types of diffusion3 can reasonably be attributed to the supersaturation of vacancies. In the present paper, it will be shown that small degrees of supersaturation can significantly affect the kinetics of the diffusion process itself. ISOTHERMAL ELECTRODIFFUSION Two different experimental techniques are convenient for studying the behavior of vacancies in a pure metal in the presence of an electric field. Gilder and Lazarus4 studied self-electrodiffusion in a gold specimen in which only the central portion was at high temperatures. In this case the significant vacancy sources operate inside the specimen in the presence of a temperature gradient. In the laboratory of Th. Heumann a method has been devised for studying self-electrodiffusion at constant temperature.5 In principle, there is then no effect of thermodiffusion. It will now be shown why in this case the significant ATungsten disks \^^ ^^ ^Gold disks^^ ^^"T>.... "TTZA ? Up Iy'7 markers ///// ////// initial plane p I y/y/y of joining \I 7//// V7//A_________I_________V//// -I 0 +I Distance from center of specimen (a) -— Direction of flow of electrons —Direction of flw of vacancies %yy} Matano I z~irkendall /%W, vy/A inlerfacej "interface ///// -} HfiK- +/ 0 Distance from center of specimen (6) Fig. 1—-Schematic illustration of the essential features of isothermal self-electrodiffusion. (a) Initial condition of specimen. (b) Condition of specimen after electrodiffusion.