Phase Transitions and Crystal Symmetry - Softcover

Inhaltsangabe

1. Introduction to Phenomenological Phase Transition Theory.- 1. Fundamentals of Landau's Thermodynamic Theory.- Elementary thermodynamic analysis.- Spontaneous symmetry breaking at a continuous phase transition.- The Landau condition for a second-order phase transition.- Further development of Landau's theory.- 2. Prerequisites on Space-group Representations.- Space-group irreducible representations.- Irreducible representations and their decomposition.- References.- 2. Physical Realization of the Order Parameters at a Microscopic Level of Description.- 3. Tensor Representation of the Space Group on a Basis of Localized Atomic Functions.- Constructing crystal space group reducible representations.- The stabilizer method.- Constructing basis functions for star arms.- 4. Permutational Representation and its Basis.- A summary of formulas.- The OP for ordering in AB type alloys.- The OP for ordering in Nb-H and Ta-H hydrides.- 5. Vector Representation and its Basis.- A summary of formulas.- The OP at a structural phase transition in A-15 compounds.- The OP at a structural phase transition in C-15 compounds.- 6. Pseudovector Representation and its Basis.- A description of the magnetically ordered state.- The OP at a magnetic phase transition in a garnet.- References.- 3. Symmetry Change at Phase Transitions.- 7. Change in Translational Symmetry.- The Brillouin zone and the symmetric points in it.- Arm mixing and the transition channel.- Magnetic lattices.- 8. The Total Symmetry Change.- Principles for finding the symmetry group of a new phase.- An example of a group-theoretic method of searching for dissymmetric phases.- 9. Domains.- Domains as a consequence of the Curie principle.- A symmetry classification of domains.- Arm, orientational and antiphase domains.- Examples of an analysis of the domain structure.- 10. The Paraphase.- The initial phase and the paraphase.- Major criteria for paraphase search.- An example of choosing the paraphase.- References.- 4. Analysis of the Thermodynamic Potential.- Invariant Expressions of the Thermodynamic Potential.- A straightforward (direct) method of constructing polynomial invariants.- Constructing the ? for the structural phase transition in C-15 compounds.- Constructing the ? for the structural phase transition in A-15 compounds.- 12. Integral Rational Basis of Invariants.- General remarks.- The IRBI construction algorithm.- Solvability of the group and the minimal IRBI.- 13. Examples of the Construction of an IRBI.- Constructing the IRBI for the structural transition in C-15 compounds.- Construction of the IRBI for the structural transition in A-15 compounds.- Constructing the IRBI for the structural transition in MnAs.- 14. Irreducible Representation Images and Thermodynamic Potential Types.- General information on the I groups.- Two- and three-component order parameters.- A multicomponent order parameter.- I groups and rotation groups in multidimensional space.- Universal classes.- 14. Irreducible Representation Images and Thermodynamic Potential Types.- 5. Phase Diagrams in the Space of Thermodynamic Potential Parameters.- 15. Theoretical Fundamentals of the Phase Diagram Construction Method.- Major physical principles.- Requisite theorems from the algebra of polynomials.- 16. The One-Component Order Parameter.- The form ofthe thermodynamic potential.- The ?6 model.- The ?8 model.- Succession of solutions to equations of state.- 17. The Two-Component Order Parameter.- The ?4 model.- The ?6 model.- Cubic invariants in the ?4 model.- Cubic invariants in the ?6 model.- 19. The Role of the IRBI in the Construction of Phase Diagrams.- The two-component order parameter.- The three-component order parameter.- 20. Coupling Order Parameters.- The interplay of two one-component order parameters.- Phase transitions in MnAs.- Phase transitions in KMnF3.- Orientation transitions.- References.- 6. Macroscopic Order Parameters.- 21. Transformation Properties of the Order Parameters.- Physical re

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