Order-disorder theory

Nix and Shockley [6] gave a detailed review of the status of order-disorder theory and experiment up to 1938, with emphasis on analytic improvements to the original Bragg-Williams theory, some of which will be... 

B( n) is the contribution to Bn of all the configurations in which n defects are assigned to m sites. The summation over m in Eq. (205) is essentially similar in character to that employed in 0. Retention of only m = 1, 2 corresponds to the familiar quasichemical approximation of order-disorder theory.33... 

Principles and types of modular series have been summarized in a book by Ferraris et al. (2004). A hierarchical classification of structure has been introduced as well as the application of modularity to structure description and modelling. The order/disorder theory has been presented as fundamental to developing a systematic theory of polytypism, dealing with structures based on both ordered and disordered stacking of one or more layers. The structures of a great number of compounds (minerals, complex oxides, salts, etc.) have been described and discussed. 

ORDER-DISORDER THEORY AND APPLICATIONS. Phase transitions in binary liquid solutions, gas condensations, order-disorder transitions in alloys, ferromagnetism, antiferromagnetism, ferroelectncity, anti-ferroelectricity, localized absorptions, helix-coil transitions in biological polymers and the one-dimensional growth of linear colloidal aggregates are all examples of transitions between an ordered and a disordered state. 

Marx and Dole and Miyake have presented descriptive models for the 19° C transition in terms of order-disorder theories. Studies of transitions at high pressure in polytetrafluoroethylene have been reported by Bridgman, Weir (1953), and Beecroft and Swenson. The phase diagram in Fig. 7 shows that in addition to the two crystalline phases which are separated by the 19° transition at atmospheric pressure there is a third modification at high pressures. The triple point has been... 

These observations can be represented as a special case of the general rate equation derived by the application of order-disorder theory to diffusionless transitions in solids.3 According to this equation, the shape of the rate curve is determined by the relative numerical values of zkp/kn and of c. The larger the factor is relative to c, the more sigmoidal the curves become. This is understandable since the propagation effect which is responsible for the autocatalytic character of the transformation becomes more noticeable when kPlkn is large and c small. Under these conditions some time elapses before a sufficient number of nucleation sites are formed then the... 

Utilization of Order-Disorder Theory in Physical Adsorption... 

Several approaches were used to quantify inhibition effects of metal adlayers. These involved calculations of currents of H2 evolution based on the order-disorder theory of alloys (141, 144, 145], and simulations based on geometric [150, 151, 153] and long-range electronic effects [150, 151], Verification of the models used in some simulations seems... 

Beyond this point, one must proceed by standard theory here, we have simply indicated how order-disorder theory may be applied to situations that seem far removed from the original concepts. 

We note that order-disorder theory provides a unified description for a variety of phenomena that come under the umbrella of organizational problems. It is in principle a simple matter to extend the... 

Lastly, a reminder an alternative approach treatment, based on order-disorder theory, was provided in Section 3.10. 

P2 > between 0 and 1 describe degrees of ordering intermediate between completely isotropic and completely ordered. It is the task of order-disorder theory to (a) determine the temperature dependence of < P2 >, (b) calculate the thermodynamic and other properties in terms of < P >, and (c) demonstrate the precise way in which the transformation from finite < P2 > to zero order occurs. We will now examine these questions. 

---