An extended theory of vacancy formation and its application to ionic conduction in the intrinsic and extrinsic regions

ABSTRACT

The theory of the vacancy formation in crystals has been extended by generalising the vacancy formation energy that depends on the number of vacancies resulting from thermal activation. This extension enables to describe the freezing of defect concentrations at lower temperature, while the derived vacancy concentration reduces to the Boltzmann–Arrhenius law at higher temperature. The implications of the low-temperature patterns and its relevance to non-equilibrium process in the defect concentrations have been also touched upon. In addition, based on the approach explored, we further construct a model for the ionic conductivity in the intrinsic and extrinsic regions, which is formulated by focusing on the relation between the number concentration and the mobility of ionic charge carriers. A theoretical background to the continuity (knee) across which the both ionic conductivity patterns are smoothly connected is corroborated by the present work.

KEYWORDS:

• Vacancy formation
• Frenkel type defects
• Freezing defect concentrations
• Intrinsic and extrinsic conductivity

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by JSPS KAKENHI [grant numbers JP20H02430, JP20K05080, JP21K04660].