Order-disorder transformations sublattices

A sublattice phase can be envisaged as being composed of interlocking sublattices (Fig. 5.3) on which the various components can mix. It is usually crystalline in nature but the model can also be extended to consider ionic liquids where mixing on particular ionic sublattices is considered. The model is phenomenological in nature and does not define any crystal structure within its general mathematical formulation. It is possible to define internal parameter relationships which reflect structure with respect to different crystal types, but such conditions must be externally formulated and imposed on the model. Equally special relationships apply if the model is to be used to simulate order-disorder transformations. 

S.4.3.4 Order-disorder transformations. The previous examples considered strict site preference for the components in sublattice phases. For example, in the (Cr, Fe)2B compound, B is not considered to mix on the metal sublattice, nor are Cr and Fe considered to mix on the B sublattice. This strict limitation on occupancy does not always occur. Some phases, which have preferential site occupation of elements on different sublattices at low temperatures, can disorder at higher temperatures with all elements mixing randomly on all sublattices. 

It was demonstrated by Sundman (1985) and later by Ansara et al. (1988) that an order-disorder transformation could be modelled by setting specific restrictions on the parameters of a two>sublattice phase. One of the first phases to be considered was an A B-ordered compoimd. In such circumstances the sublattice formula A, B)j(A, B) can be applied and the possible relationships between site fiactions and mole fiactions are given in Figure 5.6. The dashed lines denoted xb = 0.25, 0.5 and 0.75 show variations in order of the phase while the composition is maintained constant. When these lines cross the diagonal joining AjA and B3B the phase has disordered completely as Vb Vb As the lines go toward the boundary edge the phase orders and, at the side and comers of the composition square, there is complete ordering of A and B on the sublattices. 

A structure can be defined as possessing long-range order if at least two sets of positions can be distinguished by a different average occupation. These classes are usually called sub-lattices. The simplest example of an order/disorder transformation occurring in a b.c.c. lattice may be described in terms of two interpenetrating simple cubic arrays. If the occupation probability of each species is the same on both sublattices, then this is equivalent to a fully disordered b.c.c. stmcture, A2 (Fig. 7.1). 

Another exciting feature is the possibility of observing a continuous decrease in the carrier density when absorbing hydrogen, which gives rise to a metal-insulator (M-I) transition somewhere in the interval between 2 and 3 atoms H per atom R. Moreover, temperature dependent M-I transitions have been observed in the p-phase between 250 and BOOK both in sub-stoichiometric LaHs and CeHs- as well as in super-stoichiometric YH2+J and in RH2+ (R=Gd, Ho, Er) with xf 0.1-0.3, which are driven by the order-disorder transformation in the H sublattice mentioned above. 

Phases with order-disorder transformation, like A2IB2 and AI/LI2 can also be described with the sublattice method although this disregards any explicit short range order contributions. A single Gibbs energy function may be used to describe the thermodynamic properties of both the ordered and disordered phases as follows ... 

As illustrated in Fig. 6-13, there are several equilibrium phases near Fe3Al - a disordered solid solution (a) an Fe3Al with an imperfectly ordered B2 structure which transforms below approximately 550 °C to an ordered Fe3Al with the DO3 structure and the two-phase regions a-i-D03, and a + B2. The most reliable equilibrium diagram is considered to be that of Okamoto and Beck (1971), whereas that of Oki et al. (1973) represents a metastable condition. The unit cells of the ordered B2 and DO3 structures can be distinguished because the B2 superlattice is a bcc cell with Fe on one sublattice and Al on the other, whereas the DO3 superlattice consists of eight B2 superlattices stacked to maximize the distance... 

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