The Lattice Compatibility Theory: Supports from the Generalized Simha-Somcynsky Chemical Physics-Related Theory

The earliest models used in the study of lattice structures are mean field theories, which do not contain structural dependence. The Lattice Compatibility Theory (LCT) proposes here a novel framework where the measure of the disorder is based on Urbach tailing features and lattice matching features between the host matrix and doping agent intrinsic structures. This study has been implemented on a particular compound (BTO:Co) and refers to the Simha-Somcynsky (SS) theory, a mean field theory where the measure of the disorder is stated as holes. 1. Introduction The knowledge of doping agents behaviors within host lattice matrix is of considerable importance for the optimal design for applications such as semiconductor windows functional glasses, transparent electrodes in flat panel displays, buffer layers, and solar cells [1–9]. Although such behaviors have been studied for many host-doping agent lattice systems, theoretical fundaments and updated principles are still important for predicting or correlating the stability behavior of many systems within a wide range of lattice shapes. The first theories based on mean field theory and independent from the design of lattice structures failed in the statistical thermodynamics of branched macromolecules. Studies on branched structures served as attempts to mathematically correct the mean field theories. One of the most important of these studies is the Lattice-Cluster Theory (LCT), developed by Freed and Bawendi [1]. For complex lattice systems, other theories have been developed. Dee and Walsh [2, 3] proposed the lattice theory as a tool for depicting the thermodynamic properties of heterogeneous structures. This theory was an enhancement of those of Flory [4, 5] and Huggins [6] concerning chain structures. Lennard-Jones and Devonshire [7, 8], and Prigogine et al. [9–11] developed the cell model, according to which molecules can move in neighbors-induced potential holes. Later, Simha et al. [12, 13] noted that free volume theories, especially hole theories, could delineate the thermodynamic properties of solid structures, and they introduced the notion of free volume. The so-called Simha-Somcynsky (SS) model [12] defined accurately the holes in the lattice-like structure and determined the statistical behavior by finding out the combination of the holes formed within lattice intermolecular sites. In the hole theory, a major change in volume is explained by the number of holes, and the change in cell size plays a minor role while in the cell theory [14–16], the changes in volume with changes in temperature and