Modulated dilatometry as a tool for simultaneous study of vacancy formation and migration

A model is presented to derive both vacancy formation and migration characteristics from length change measurements upon modulated time-linear heating. The length variation with linear heating yields access to the equilibrium concentration of thermal vacancies. The modulation amplitude and the phase shift between modulated temperature and length change is determined by the ratio of equilibration rate and modulation frequency which yields access to the vacancy migration characteristics. The contribution from thermal lattice expansion is obtained from a reference measurement at high modulation frequencies. Compared to static isothermal equilibration measurements after temperature jumps, the processes are monitored under quasi-equilibrium conditions avoiding obstacles associated with fast temperature changes. Furthermore, in contrast to the static isothermal case where the equilibration rate is obtained from the time-exponential decay, its determination from the amplitude and phase shift of modulation offers higher precision. The method is suitable for materials with high thermal vacancy concentrations and low vacancy diffusivities, among which is the important class of intermetallic compounds with B2-structure.