Phase Diagram of Ferroelastic Systems in the Presence of Disorder: Analytical Model and Experimental Verification

There is little consensus on the nature of the glass state and its relationship to other strain states in ferroelastic materials which show the shape memory effect and superelasticity. We provide a thermodynamic interpretation of the known strain states, including precursory tweed and strain glass, by mapping the problem onto a spin model and analytically obtaining the phase diagram using real-space renormalization group methods. We further predict a spontaneous transition from the glass state to the ordered martensite phase. We verify this prediction by mapping out the experimental phase diagram for the ternary ferroelastic alloy Ti$_{50}$(Pd$_{50-x}$Cr$_x$) and demonstrate the emergence of the spontaneous transition. Our work thus provides a consistent framework to understand the various experimental and theoretical studies on the glassy behavior associated with ferroelastic materials.