Exact linear response of reacting thermal defects driven by creation processes

The exact, linear response at steady state is calculated for reacting, but otherwise noninteracting, thermal defects driven by defect creation processes. The theory applies to vacancies and interstitials in the bulk, or to adatoms and advacancies on surface terraces. A wide variety of possible driving forces includes nuclear reaction, particle irradiation, epitaxial growth, surface erosion, and sublimation. When the defect life cycle typically starts and ends with spontaneous pair creation and annihilation, both species respond to the difference of their separate driving terms (the “Poisson” regime), and the law of mass action holds everywhere with a position dependent chemical potential μ^*(r). The value of μ^*(r) in linear response is employed here to discuss the conditions under which thermal defects precipitate, particularly as islands on terraces and dislocation loops in the bulk. It is shown, for the Poisson regime, that an approximate symmetry exists between processes for the two antidefects. Specifically, if μ_c^* suffices to nucleate a precipitate of one antidefect, then −μ_c^* is required to nucleate the other.