Structure elements of a unary solid

The first two types of stmcture elements are normal elements of the solid, while the others are native point defects. In general, a given solid contains several types of defects, which will be as many components in the thermodynamic sense of the term, and will form a solution with the normal elements. In practice, the problem boils down to the superposition of the equilibria of a base of the vector space. Usually, the defects are very dilute in comparison to the normal elements, so that they can be considered to be solvents with constant activity and the activities of the defects can be considered equal to their site fractions. 

To construct the basis of the vector space of the balance equations, besides the electronic equilibrium between electrons and holes, we will use the equilibria of the formation of defects the vacancies, the interstitials and the equilibria of ionization and association. 

Neutral vacancies are formed by displacement of atoms initially in the normal position within the lattice toward normal positions on the surface of the crystal or other extended defects such as dislocations. We say that the source (and, conversely, the well) of the vacancies is an extended defect. When the surface comes into play, this results in an increase in the crystal s dimensions. If we take account of all the structure elements which are involved, the equilibrium of formation of the neutral vacancies is written as  

The ionization of the vacancies can be written in two different ways, depending on whether the electrons or electron holes are involved. For example, to form a vacancy once ionized negatively, we would have  

- if there are no neutral vacancies, we can directly write the formation of the ionized vacancies by superposing the equilibria [3R.8] and [3R.9], in the form  

---