Phase diagram of ferroelastic systems in the presence of disorder: Analytical model and experimental verification

Abstract

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 Ti50(Pd50−xCrx) 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. PhaseOP characterization RG fixed point Austenite m = q = 0, p small ∆ * = +∞, J * = 0, σ * J = 0 Martensite m = 0, p = 0, q = 0 ∆ * = −∞, J * = ∞, σ * J J * = 0 Tweed m = q = 0, p large ∆ * = −∞, J * = 0, σ * J = 0 Strain glass m = 0, p = 0, q = 0 ∆ * = −∞, J * = 0, σ * J = ∞

A new mechanism for low and temperature-independent elastic modulus

“…Without considering the LFE, the above phase field model has shown that self-accommodation among different martensitic variants during nucleation and growth dominated by the long-range elastic interactions leads to normal sharp martensitic transformations producing long-range ordered (LRO) polytwin domain structures162832394041 via autocatalysis and collective nucleation. As will be shown below that the presence of the LFE will screen the long-range interactions, suppress autocatalysis and limit the extent of growth, and convert a sharp MT into a smooth STGT, to which the Elinvar anomaly could be attributed.…”

Multiferroic (ferroelastic/ferromagnetic/ferrimagnetic) aspects of phase transitions in RCo2Laves phases

“…In metals the development of tweed microstructure is a characteristic pretransition effect ahead of martensitic transitions (e.g. as modelled recently in [53] and [54]), and can also be associated with magnetic ordering (see e.g. [55]).…”

The transitions from glassy state to long‐range‐ordered state in ferroic glasses

“…The spontaneous strain glass to normal martensite transition has been found in three kinds of strain‐glass alloys, Ti 50 (Ni 44.5 Fe 5.5 ), Ti 50 (Pd 40 Cr 10 ), and Ni 45 Co 10 Mn 20 Ga 25 . Such a spontaneous transition in strain‐glass alloys is accompanied by several unique experimental characterizations as well, including dynamical mechanical properties, average structures, and microstructures.…”

“…(a) Dielectric permittivity as a function of temperature shows two features of spontaneous transition in a relaxor: sudden drop of dielectric permittivity and large thermal hysteresis (after Dai et al , Copyright (1993) AIP Publishing LLC). (b) Dynamic mechanical properties (tan δ and storage modulus) as a function of temperature show two features of spontaneous transition in a strain glass: internal friction peak and large thermal hysteresis (after Vasseur et al , Copyright (2012) by the American Physical Society).…”