Nanoscale Heterogeneity in Functional Materials
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Heterogeneity in Functional Materials
Turab Lookman and Peter Littlewood Abstract The physical properties that make “functional” materials worthy of their moniker frequently arise because of a phase transition that establishes a new kind of order as the material is cooled from a parent state. Such ordered states include ferroelectrics, ferromagnets, and structurally ordered martensites; because these states all break an orientational symmetry, and it is rare that one can produce the conditions for single domain crystallinity, the observed configuration is generally heterogeneous. However, the conditions under which domain structures form are highly constrained, especially by elastic interactions within a solid; consequently, the observed structures are far from fully random, even if disorder is present. Often the structure of the heterogeneity is important to the function, as in shape-memory alloys. Increasingly, we are surprised to discover new phases inside solids that are themselves a heterogeneous modulation of their parents.
and modeling interfaces and microstructure, which influence constitutive behavior in applications.3,4 Martensites are typically first-order phase transitions accompanied by a nonzero latent heat that are driven by shear strains from one parent crystal symmetry to lower symmetry deformation states or variants of the product phase. As strain, rather than displacement, serves as the appropriate tensor order parameter for lattice degrees of freedom, we examine factors that influence how a given microstructure is obtained as a function of the size of the transformable region. In particular, the elastic interactions at the interfaces between different symmetries (e.g., parent-product interface or habit plane), which lead to decaying fringing fields, compete with the bulk or domain wall energy between different distortions to affect the scale of the patterns observed. As a result, the ferroelastic transition and morphology change as a function of size. We specifically discuss how in a narrow range of the size of the transformed region, the twinned microstructure decays to a checkerboard structure, which we term lattice martensite, containing both the parent and product phases.5 Such checkerboard patterns, with underlying distortions containing thermodynamically inequivalent phases, have been observed experimentally in the perovskite Nd2/3−xLi3x, where there is preferential phase separation of the Li ions on the checkerboard. The scaling ξ ∼ `÷ L
Introduction Heterogeneity and disorder play a fundamental role in influencing and determining the properties of high-Tc superconductors, perovskites such as the colossal magnetoresistive materials, relaxor ferroelectrics, and the more recently studied nickelates and pnictides. If one adds to this list ferroic materials, which contain one or more lower-symmetry deformation or “orientation states” and the ability to switch between them by an external field, we have a large class of functionally adaptive materials where the order parameters (OPs) are cou
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