Large deviation from stoichiometry. II. Ordered structure

6 Large deviation from stoichiometry. II. Ordered structure 

Consider a crystal of composition M0.5X, the metal vacancies are regularly arranged among the lattice sites at lower temperatures, shown in Fig. 1.18 as a basic model of a vacancy-ordered structure with a two-dimensional lattice (in this figure, the anion atoms are omitted for clarity). This structure is realized if the composition of the crystal is Mq 5X, and metal atoms M fully occupy the B-sites and metal vacancies fully occupy the A-sites, this only occurs at absolute zero temperature (perfect order). The occupation probabilities, p and Pg, denote the ratio of number of metal atoms on the A-sites (ma) to the number of lattice points of the A-sites ( 1V) and the ratio of number of metal atoms on the B-sites (Ug) to the number of lattice points of the B-sites (ilV), respectively. Thus p and pg can be expressed as 

The crystal having the composition Mg 5X, which is the stoichiometric composition of the vacancy-ordered structure, shows disordering such as Pa and - with increasing temperature. With decreasing number of vacancies in the composition Mj X, increases towards 1 at absolute zero temperature. (In this example 5 ranges from 0 to 0.5 in the expression 

From the definition of p and pg, we obtain the following relationship vacancy-ordered structure pg vacancy-disordered structure p = Pb 

Thus we can observe the order disorder transition by changing temperature at constant 6 and also changing S at constant temperature. 

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