Landau’s Theory with a One-Component Order Parameter
摘要
Landau’s theory employs an order parameter to describe phase transitions. Generally, it is an n-component entity characterized by specific symmetry properties. However, this book focuses on cases involving a one-component order parameter for several reasons. First and foremost, this represents the most technically simple scenario. Given the complexities surrounding the problem of process zones, it is pragmatic to start with a technically less demanding case. Moreover, many characteristics of process zones are observed to be invariant, irrespective of the number of order parameter components. Thus, investigating these fundamental properties through simple examples becomes important. Additionally, in the case of a multicomponent order parameter, there are often low-symmetry phases where its different nonzero components are equal to one another. One adequately describes such phases by a single order parameter component. With certain caveats, one can model the corresponding process zones using a one-component order parameter framework. Last, we want to get the reader to the point as soon as possible rather than engage in a voluminous discussion of the classical Landau’s theory for transitions with multicomponent order parameters. Consequently, our analysis centers on the characteristics of zones governed by a one-component order parameter. Landau’s theory of phase transitions is fundamentally based on two key concepts: (i) the relationship between phase transformation and changes in crystal symmetry, and (ii) the bifurcation phenomenon. The former is expressed using the language of group theory, while the latter is described by the time-dependent Ginzburg-Landau equation or a system of such equations. These equations can be interpreted as equations of motion or state for the atoms involved in the phase transformation, averaged over their ensemble. Together, they provide a universal framework for understanding the internal mechanisms governing phase transformations.