Vacancy point defects chemical potential

Let us now discuss some details of practical relevance. From the Gibbs phase rule, it is evident that crystals consisting of only one component (A) become nonvariant by the predetermination of two thermodynamic variables, which for practical reasons are chosen to be Pand T. In these one-component systems, it is easy to recognize the (isobanc) concentration dependence of the point defects on temperature. From the definition of the vacancy chemical potential for sufficiently small vacancy mole fractions Nv, namely //v = /A (P, T) + RT- In Vv, together with the condition of equilibrium with the crystal s inerL surroundings (gas, vacuum), one directly finds... 

The doped semiconductor materials can often be considered as well-characterized, diluted solid solutions. Here, the solutes are referred to as point defects, for instance, oxygen vacancies in TiC - phase, denoted as Vq, or boron atoms in silicon, substituting Si at Si sites, Bj etc. See also -> defects in solids, -+ Kroger-Vink notation of defects. The atoms present at interstitial positions are also point defects. Under stable (or metastable) thermodynamic equilibrium in a diluted state, - chemical potentials of point defects can be defined as follows ... 

If the pressure P and temperature T are fixed, then the total concentrations of point defects at thermodynamic equilibrium in a compound with n components can only be dependent upon the n — 1) independent chemical potentials fXi of the components (i.e. upon the (n — 1) component activities <2.). For example, the concentration of electronic defects in silicon that has been doped with aluminum (or phosphorus) is uniquely determined by the activity of the dopant element, since this is a binary system. In a completely analogous way, the concentrations of electron holes and cation vacancies in NiO are uniquely dependent upon the oxygen partial pressure as long as overall equilibrium can be assumed. 

Finally, it should be mentioned that the calculation of correlation effects for crystals in which fluxes occur as the result of chemical potential gradients yields extra terms not yet pointed out because of the spatial inhomogeneity of defects. This higher approximation has been calculated for the case of a vacancy diffusion coefficient, and is known as a result of the vacancy wind . It can be neglected in first order calculations [5]. 

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