On Defects in Solids

The thermodynamical potential for dilute solutions is rederived, generalized and applied to defects in solids. It is shown that there are always defects in solids, i.e. there is no perfect solid at any finite temperature. Apart from the temperature-dependent concentration of defects, another case is presented, where the defect concentration does not depend on temperature. With standard notations we may write dE = −pdV + T dS + µdN (1) at equilibrium, whence d(E + pV − T S − µN) = V dp − SdT − Ndµ. (2) We may introduce the thermodynamical potential Θ = E + pV − T S − µN , (3) and, noticing that E, V, S, N are extensive, while p, T and µ are intensive quantities, we have Θ = ∂Θ/∂N · N. On the other hand, we have from 1