Scaled free energies, power-law potentials, strain pseudospins, and quasiuniversality for first-order structural transitions
- School of Physics, University of Hyderabad, Hyderabad 500046 (India)
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
We consider ferroelastic first-order phase transitions with N{sub OP} order-parameter strains entering Landau free energies as invariant polynomials that have N{sub V} structural-variant Landau minima. The total free energy includes (seemingly innocuous) harmonic terms, in the n=6-N{sub OP} nonorder-parameter strains. Four three-dimensional (3D) transitions are considered, tetragonal/orthorhombic, cubic/tetragonal, cubic/trigonal, and cubic/orthorhombic unit-cell distortions, with, respectively, N{sub OP}=1, 2, 3, and 2; and N{sub V}=2, 3, 4, and 6. Five two-dimensional (2D) transitions are also considered, as simpler examples. Following Barsch and Krumhansl, we scale the free energy to absorb most material-dependent elastic coefficients into an overall prefactor, by scaling in an overall elastic energy density; a dimensionless temperature variable; and the spontaneous-strain magnitude at transition {lambda}<<1. To leading order in {lambda} the scaled Landau minima become material independent, in a kind of ''quasiuniversality.'' The scaled minima in N{sub OP}-dimensional order-parameter space, fall at the center and at the N{sub V} corners, of a transition-specific polyhedron inscribed in a sphere, whose radius is unity at transition. The ''polyhedra'' for the four 3D transitions are, respectively, a line, a triangle, a tetrahedron, and a hexagon. We minimize the n terms harmonic in the nonorder-parameter strains, by substituting solutions of the ''no dislocation'' St Venant compatibility constraints, and explicitly obtain power-law anisotropic, order-parameter interactions, for all transitions. In a reduced discrete-variable description, the competing minima of the Landau free energies induce unit-magnitude pseudospin vectors, with N{sub V}+1 values, pointing to the polyhedra corners and the (zero-value) center. The total scaled free energies then become Z{sub N{sub V+1}} clocklike pseudospin Hamiltonians, with temperature-dependent local Landau terms, nearest-neighbor Ginzburg couplings, and power-law St Venant interactions that drive the elastic domain-wall texturing. The scaled free energies can be used in relaxational or underdamped dynamic simulations to study ferroelastic strain textures and their dynamical evolution pathways. The pseudospin models can similarly be studied via local meanfield treatments and Monte Carlo simulations.
- OSTI ID:
- 21421451
- Journal Information:
- Physical Review. B, Condensed Matter and Materials Physics, Vol. 82, Issue 14; Other Information: DOI: 10.1103/PhysRevB.82.144103; (c) 2010 The American Physical Society; ISSN 1098-0121
- Country of Publication:
- United States
- Language:
- English
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SUPERCONDUCTIVITY AND SUPERFLUIDITY
ANISOTROPY
COMPUTERIZED SIMULATION
CRYSTAL-PHASE TRANSFORMATIONS
DISLOCATIONS
ENERGY DENSITY
FREE ENERGY
HAMILTONIANS
INTERACTIONS
MONTE CARLO METHOD
ORDER PARAMETERS
ORTHORHOMBIC LATTICES
SCALING
STRAINS
TEMPERATURE DEPENDENCE
TEXTURE
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS
CALCULATION METHODS
CRYSTAL DEFECTS
CRYSTAL LATTICES
CRYSTAL STRUCTURE
DIMENSIONLESS NUMBERS
ENERGY
LINE DEFECTS
MATHEMATICAL OPERATORS
PHASE TRANSFORMATIONS
PHYSICAL PROPERTIES
QUANTUM OPERATORS
SIMULATION
THERMODYNAMIC PROPERTIES