Nonlinear and nonlocal continuum model of transformation precursors in martensites

Percolated Strain Networks and Universal Scaling Properties of Strain Glasses

Strain glass is being established as a conceptually new state of matter in highly doped alloys, yet the understanding of its microscopic formation mechanism remains elusive. Here, we use a combined numerical and experimental approach to establish, for the first time, that the formation of strain glasses actually proceeds via the gradual percolation of strain clusters, namely, localized strain clusters that expand to reach the percolating state. Furthermore, our simulation studies of a wide variety of specific materials systems unambiguously reveal the existence of distinct scaling properties and universal behavior in the physical observables characterizing the glass transition, as obeyed by many existing experimental findings. The present work effectively enriches our understanding of the underlying physical principles governing glassy disordered materials.

Effect of magnetism on kinetics of γ-α transformation and pattern formation in iron

The kinetics of polymorphous γ-α transformation in Fe is studied numerically within a model taking into account both the lattice and the magnetic degrees of freedom, based on first-principle calculations of the total energy for different magnetic states. It is shown that a magnetoelastic phenomenon, namely the strong sensitivity of the potential relief along the Bain deformation path to the magnetic state, is crucial for a picture of the transformation. With increasing temperature, a scenario for the phase transformation evolves from a homogeneous lattice instability at T < M(s) (M(s) is the temperature of the beginning of the martensitic transformation) to the growth and nucleation of embryos of the new phase at T > M(s). In the latter case, the formation of a tweed-like structure occurs, with a strong short-range order and slow interphase fluctuations.

Coarse-graining microscopic strains in a harmonic, two-dimensional solid: elasticity, nonlocal susceptibilities, and nonaffine noise

In soft matter systems the local displacement field can be accessed directly by video microscopy enabling one to compute local strain fields and hence the elastic moduli in these systems using a coarse-graining procedure. We study this process in detail for a simple triangular, harmonic lattice in two dimensions. Coarse-graining local strains obtained from particle configurations in a Monte Carlo simulation generates nontrivial, nonlocal strain correlations (susceptibilities). These may be understood within a generalized, Landau-type elastic Hamiltonian containing up to quartic terms in strain gradients [K. Franzrahe, Phys. Rev. E 78, 026106 (2008)10.1103/PhysRevE.78.026106]. In order to demonstrate the versatility of the analysis of these correlations and to make our calculations directly relevant for experiments on colloidal solids, we systematically study various parameters such as the choice of statistical ensemble, presence of external pressure and boundary conditions. Crucially, we show that special care needs to be taken for an accurate application of our results to actual experiments, where the analyzed area is embedded within a larger system, to which it is mechanically coupled. Apart from the smooth, affine strain fields, the coarse-graining procedure also gives rise to a noise field (χ) made up of nonaffine displacements. Several properties of χ may be rationalized for the harmonic solid using a simple "cell model" calculation. Furthermore the scaling behavior of the probability distribution of the noise field (χ) is studied. We find that for any inverse temperature β, spring constant f, density ρ and coarse-graining length Λ the probability distribution can be obtained from a master curve of the scaling variable X=χβf/ρΛ(2).

Martensitic transformation B2-R in Ni-Ti-Fe: experimental determination of the Landau potential and quantum saturation of the order parameter

The Landau potential of the martensitic phase transformation in Ni(46.8)Ti(50)Fe(3.2) was determined using high resolution x-ray diffraction to measure the spontaneous strain and calorimetric measurements to determine the excess specific heat of the R phase. The spontaneous strain is proportional to the square of the order parameter which is tested by the relation of the excess entropy and the order parameter. The parameters of the Landau free energy were determined by fitting the temperature evolution of the order parameter and using the scaling between the excess entropy and the order parameter. The double well potential at absolute zero temperature was calculated and the interface energy and domain wall thickness were estimated.

Three-dimensional elastic compatibility and varieties of twins in martensites

We model a cubic-to-tetragonal martensitic transition by a Ginzburg-Landau free energy in the symmetric strain tensor. We show in three dimensions (3D) that solving the St. Venant compatibility relations for strain, treated as independent field equations, generates three anisotropic long-range potentials between the two order parameter components. These potentials encode 3D discrete symmetries, express the energetics of lattice integrity, and determine 3D textures. Simulation predictions include twins with temperature-varying orientation, helical twins, competing metastable states, and compatibility-induced elastic frustration. Our approach also applies to improper ferroelastics.