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Title:  Topics in D1 Dimensional Statistical Mechanics: 1. Statistical Mechanics of Equilibrium Crystal Shapes: Interfacial Phase Diagrams and Phase Transitions. 2. Symmetry Classifications of TwoDimensional Phase Transitions 
Author(s):  Rottman, Craig Alan 
Department / Program:  Physics 
Discipline:  Physics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Physics, Condensed Matter 
Abstract:  This thesis consists of two parts. The first part, contained in Chapter 1, concerns interfacial phase diagrams and phase transitions associated with equilibrium crystal shapes. The second portion, contained in Chapter 2, deals with symmetry classifications of phase transitions in two dimensions. In Chapter 1 we review the present status of the statistical mechanical theory of equilibrium crystal shapes. Special emphasis is placed on the relation between singularities occurring in the shapes of threedimensional (d = 3) crystals and the phase transitions of certain d = 2 models. We exploit the thermodynamic conjugacy of the Wulff plot and the equilibrium crystal shape to give interfacial phase diagrams in both density and field variables. From this perspective, sharp edges or points on the crystal shape correspond to firstorder phase transitions, while smooth joining of curved and planar ("faceted") regions corresponds to secondorder phase transitions. Equilibrium crystal shapes of a simplecubic (Ising) lattice gas with nearestneighbor (attractive) and nextnearestneighbor (nnn) interactions are considered in detail. Typical equilibrium crystal shapes at nonzero temperature consist of facets and smoothly curved surfaces. When nnn interactions are attractive, only secondorder transitions occur. Both KosterlitzThouless ("roughening") and PokrovskyTalapov (GruberMullins) universality classes are represented. When nnn interactions are repulsive, firstorder transitions and tricritical behavior also occur. The present experimental situation is summarized. Chapter 2 begins with statistical mechanical background. It then discusses properties of the phases which form the focus of attention in the remainder of the chapter. A statistical mechanical model of the transitions between these phases and the solution within the approximation known as Landau theory are discussed. The reasons why Landau theory, despite its shortcomings, may be useful in describing these phase transitions are presented. The grouptheoretical calculations of this study predict which phase transitions may be second order and also identify the universality classes to which these belong. Other phase transitions are predicted to be first order. These calculations extend the work of others to include all symmetries within certain classes of twodimensional space groups, namely, usual space groups and magnetic space groups. 
Issue Date:  1983 
Type:  Text 
Language:  English 
Description:  170 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 1983. 
URI:  http://hdl.handle.net/2142/77365 
Other Identifier(s):  (UMI)AAI8410038 
Date Available in IDEALS:  20150513 
Date Deposited:  1983 
This item appears in the following Collection(s)

Dissertations and Theses  Physics
Dissertations in Physics 
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois