Scaled free energies, power-law potentials, strain pseudospins and quasi-universality for first-order structural transitions

Abstract

We consider ferroelastic first-order phase transitions with $N_{OP}$ order-parameter strains entering Landau free energies as invariant polynomials, that have $N_V$ structural-variant Landau minima. The total free energy includes (seemingly innocuous) harmonic terms, in the $n=6-N_{OP}$ {\it non}-order-parameter strains. Four 3D transitions are considered, tetragonal/orthorhombic, cubic/tetragonal, cubic/trigonal and cubic/orthorhombic unit-cell distortions, with respectively, $N_{OP}=1,2,3$ and 2; and $N_V=2,3,4$ and 6. Five 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 'quasi-universality'. The scaled minima in $N_{OP}$-dimensional order-parameter space, fall at the centre and at the $N_V$ 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 non-order-parameter strains, by substituting solutions of the 'no dislocation' St Venant compatibility constraints, and explicitly obtain powerlaw 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 $N_V+1$ values, pointing to the polyhedra corners and the (zero-value) center.

submitted to PRB

References in corpus (7)

• Ferroelastic Dynamics and Strain Compatibility
• Simulations of cubic-tetragonal ferroelastics
• Time evolution of tetragonal-orthorhombic ferroelastics
• A Simple Spin Glass Perspective on Martensitic Shape-memory Alloys
• Statics and dynamics of domain patterns in hexagonal-orthorhombic ferroelastics
• Microstructure from ferroelastic transitions using strain pseudospin clock models in two and three dimensions: a local mean-field analysis
• Random Field Potts model with dipolar-like interactions: hysteresis, avalanches and microstructure

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