Models of Matter Transport: Their Verification and Use for Dilute Systems with the Aid of Statistical Theories

Statistical expressions for the Onsager phenomenological coefficients are now available for several models of matter transport in systems which are dilute in solutes, vacancies and interstitials. They describe transport by unpaired and paired defects, as in the familiar five-frequency model. The role of atomistic calculations of the parameters of such models in validating, simplifying or improving them is illustrated. In general it may be difficult to convincingly determine from experiment all the parameters of a given model or to distinguish between closely related models, such as between those retaining first or first and second neighbour binding between a solute and a vacancy. Nevertheless, there is particular utility in knowledge of all the Onsager coefficients for models suggested by atomistic calculations and other information, when one interprets phenomena involving coupled fluxes. This is illustrated by the example of coupled fluxes of a solute, vacancies and interstitials in a dilute alloy under steady irradiation by high energy particles. Here, essential contributions to modelling solute segregation to grain boundaries can be made; striking qualitative differences between closely related models can occur in this case. Finally, the limitations of the current statistical results are examined for systems where the solutes and defects carry effective charges. Limitations are suggested at low temperatures by the existence of a phase transition in the restricted primitive model of dilute aqueous electrolytes. The range of concentration and temperature within which the current procedures, stemming from the early work of Teltow and Lidiard, have been properly validated is limited. In the absence of recent theoretical advances Monte Carlo simulation is becoming the method of choice in investigating such limitations and in studying the transition to higher concentrations where there are larger clusters of defects.