A two-sublattice model for molten solutions with different tendency for ionization
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I.
INTRODUCTION
g great majority of the solid, crystalline phases have an ordered arrangement of the different atoms. Each element prefers to go into a particular type of lattice site. It is convenient to describe this situation by dividing the lattice into sublattices. As an example, crystalline NaC1 has a simple cubic lattice which can be divided into two interwoven face-centered cubic sublattices, one occupied by Na and the other one by C1, In a few cases, this well-ordered arrangement breaks down at high temperatures, first by some atoms going into wrong lattice sites and then by a complete disappearance of the difference in occupancy between the sublattices. Some short-range order still exists but it decreases as the temperature is increased further. The short-range order may be described as a tendency for unlike atoms to be nearest neighbors. When a substance, that does not disorder at high temperatures, is finally melted, the possibility of having real long-range order vanishes because it is impossible to tell whether two atoms, that are sufficiently far apart, belong to the same or different sublattices. This is due to the topological disorder introduced by melting. It is still possible that the tendency for chemical order is so large that each atom is practically surrounded by unlike atoms. This may be the case for ionic substances and it is common to describe that situation by postulating the existence of two sublattices, one for the cations and one for the anions. This concept was used by Temkin ~when he suggested that the configurational entropy of a salt mixture could be estimated by assuming that all the cations mix at random with each other and all the anions do the same. According to this model for a pure salt there will be no contribution to the entropy of melting from chemical disorder, and the situation in the melt is described with the formalism used for crystalline phases with complete long-range order. For molten substances with a lower tendency for ordering it may be necessary to apply a model that can describe the MATS HILLERT, ProfessorofPhysical Metallurgy, and BO JANSSON, BO SUNDMAN, and JOHN AGREN, Research Associates, are with the Division of Physical Metallurgy, Royal Institute of Technology. S-100 4;4 Stockholm. Sweden. Manuscript submitted March 8, 1984. METALLURGICALTRANSACTIONS A
variation of ordering with temperature and composition. It may then seem appropriate to borrow a formalism from ordering in the solid state. However, all such theories seem to predict a transition from long-range to short-range order which does not seem to have any correspondence in the molten state. An alternative approach for describing the ordering in a melt is based on the assumption of molecularlike associates between unlike atoms, the so-called associate solution model. It is sometimes applied under the argument that such molecular-like associates actually exist; 2 sometimes the model is regarded as a convenient way of formally representing the thermodynamic effects of ordinary shortrange order. 3
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