Lattice disordering-ordering transition

Consider, as an example, a disorder-order transition in Cu-Au (8 1) alloy. In this case, we can choose the simplest (scalar) order parameter t], which is a normalized difference between probabilities to find either gold or copper atoms in the center of the cubic cell, see Fig. 6.3. in the higher temperature (and higher symmetry) phase an atom of gold has equal probability to be at any lattice site included the central one (but not between the sites), and order parameter t] = 0. in the ideally ordered, zero-temperature phase, an Au atom is always in the central position and t] = 1. Generally, in the low-temperature phase, the central position is more often populated by a gold atom than by a particular copper atom and 0 < t] < 1. 

As mentioned above the disorder-order transition in aqueous dispersions of charged latex particles, in particular well characterized polystyrene latices, has been investigated extensively. These particles interact through screened Coulombic interactions, the range of which depends on the electrolyte concentration in the suspension medium. At very low electrolyte concentration (10 M or lower) the transition from the milky white (disordered) state to the iridescent (ordered) state may occur at volume fractions below 1%. This means that colloidal spheres in suspension can maintain themselves in a regular lattice structure even when the interparticle spacing is several diameters. 

The Ag (100) surface is of special scientific interest, since it reveals an order-disorder phase transition which is predicted to be second order, similar to tire two dimensional Ising model in magnetism [37]. In fact, tire steep intensity increase observed for potentials positive to - 0.76 V against Ag/AgCl for tire (1,0) reflection, which is forbidden by symmetry for tire clean Ag(lOO) surface, can be associated witli tire development of an ordered (V2 x V2)R45°-Br lattice, where tire bromine is located in tire fourfold hollow sites of tire underlying fee (100) surface tills stmcture is depicted in tlie lower right inset in figure C2.10.1 [15]. 

The features in —dxjdE, particularly peaks due to first-order transitions, are broadened by disorder. Disorder can be incorporated in lattice-gas... 

Studies on crystalline CggO [39] using calorimetry and high-resolution X-ray powder diffraction show a face centered cubic lattice (a = 14.185 A) with an orientational disorder at room temperature. An orientational ordering transition occurs at 278 K, upon which a simple cubic phase develops. At 19 K this phase, which is similar to the orientational ordered phase of Cgg itself, shows additional randomness due to a distribution of orientation of the oxygens in CggO. 

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