Point defects of elements

As mentioned above, the non-stoichiometric compounds originate from the existence of point defects in crystals. Let us consider a crystal consisting of mono-atoms. In ideal crystals of elements, atoms occupy the lattice points regularly. In real crystals, on the other hand, various kinds of point defects can exist in thermodynamic equilibrium. First, we shall consider vacancies , which are empty regular lattice points. Consider a crystal composed of one element which has N atoms sited on regular lattice points and vacancies, 

Another type of lattice defect for elements is interstitial atoms, in which an atom is transferred from a regular lattice point to an interstitial position, normally unoccupied by an atom. Consider a crystal which has N atoms sited on regular lattice points and N, atoms sited on interstitial lattice points (the number of interstitial lattice points is A, which is fixed by the crystal structure under consideration), by a similar calculation, the free energy increment from the ideal crystal is expressed as 

For the usual metals, interstitial atoms are very rare, because the energy is very large for example, Sj is estimated to be 3 eV for Cu, i.e. NJN = 10 at 1000 K. 

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From consideration of the point defects of elements mentioned in Section 1.3.1, the nature of the point defects of compounds MX, where M is metal and X is O, S, N, H (volatile elements) etc., can be easily understood. Possible point defects of the compounds MX are as follows ... 

The number of interstitial atoms Np in the Frenkel type and the number of vacancies TYj in the Schottky type at thermal equilibrium can be obtained, following a similar calculation to that for the concentration of point defects of elements mentioned in Section 1.3.1, as... 

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