English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

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 energyincludes (seemingly innocuous) harmonic terms, in the $n = 6 -N_{OP}$ {\itnon}-order-parameter strains. Four 3D transitions are considered,tetragonal/orthorhombic, cubic/tetragonal, cubic/trigonal andcubic/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, assimpler examples. Following Barsch and Krumhansl, we scale the free energy toabsorb most material-dependent elastic coefficients into an overall prefactor,by scaling in an overall elastic energy density; a dimensionless temperaturevariable; and the spontaneous-strain magnitude at transition $\lambda <<1$.  To leading order in $\lambda$ the scaled Landau minima becomematerial-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, whoseradius is unity at transition. The `polyhedra' for the four 3D transitions arerespectively, a line, a triangle, a tetrahedron, and a hexagon. We minimize the$n$ terms harmonic in the non-order-parameter strains, by substitutingsolutions of the 'no dislocation' St Venant compatibility constraints, andexplicitly obtain powerlaw anisotropic, order-parameter interactions, for alltransitions. In a reduced discrete-variable description, the competing minimaof the Landau free energies induce unit-magnitude pseudospin vectors, with $N_V+1$ values, pointing to the polyhedra corners and the (zero-value) center.

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