The hodograph equation for slow and fast anisotropic interface propagation

Using the model of fast phase transitions and previously reported equation of the Gibbs–Thomson-type, we develop an equation for the anisotropic interface motion of the Herring–Gibbs–Thomson-type. The derived equation takes the form of a hodograph equation and in its particular case describes motion by mean interface curvature, the relationship ‘velocity—Gibbs free energy’, Klein–Gordon and Born–Infeld equations related to the anisotropic propagation of various interfaces. Comparison of the present model predictions with the molecular-dynamics simulation data on nickel crystal growth (obtained by Jeffrey J. Hoyt et al. and published in Acta Mater. 47 (1999) 3181) confirms the validity of the derived hodograph equation as applicable to the slow and fast modes of interface propagation. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

An Exact Solution of the Reaction-Diffusion Equation for the Speed of the Interface Propagation in Superconductors

The speed of interface propagation in superconductors for the scalar reaction-diffusion equation ut = ∇2u+ F(u) is studied in detail. Here the non linear reaction term F (u) is the time-dependent Ginzburg-Landau or TDGL equation F(u)=u-u3 which describes the dynamics of the order-disorder transition. In contrast to what has been done in previous work [1] here an improved exact solution has derived by using TDGL equation to determine the speed of the front propagation. The analytical treatment of this study has been found in good agreement with the numerical simulation of V. Mendez et al. [2] and Di Bartolo and Dorsey [3]. The Chittagong Univ. J. Sci. 40(1) : 85-95, 2019

The effect of a pre-existing nanovoid on martensite formation and interface propagation: a phase field study

In the present work, the effect of a pre-existing nanovoid on martensitic phase transformation (PT) is investigated using the phase field approach. The nanovoid is created as a solution of the coupled Cahn–Hilliard and elasticity equations. The coupled Ginzburg–Landau and elasticity equations are solved to capture the martensitic nanostructure. The above systems of equations are solved using the finite element method and COMSOL code. The austenite ( A)–martensite ( M) interface propagation is investigated without the nanovoid and with it for different nanovoid misfit strains and different temperatures. With the nanovoid, the evolution of the moving interface is changed even before it reaches the nanovoid surface due to the nanovoid stress concentration. It is also found that for small misfit strains, pre-transformation occurs near the nanovoid. For larger misfit strains, martensite nucleates and grows near the nanovoid surface and coalesces with the moving interface. The nanovoid shows a promotive effect on the PT with an increase in the rate of transformation, which is discussed based on the transformation work distribution. The effect of the nanovoid is more pronounced on a curved interface. The nanovoid-induced martensitic growth is mainly dependent on the transformation strain tensor. Examples for different transformation strains are presented where a stable non-complete transformed sample with no void becomes unstable in the presence of the nanovoid. The presented model and results will help to develop an interaction model between nanovoids and multiphase structures at the nanoscale.

Dissipative structures induced by photoisomerization in a dye-doped nematic liquid crystal layer

Order–disorder phase transitions driven by temperature or light in soft matter materials exhibit complex dissipative structures. Here, we investigate the spatio-temporal phenomena induced by light in a dye-doped nematic liquid crystal layer. Experimentally, for planar anchoring of the nematic layer and high enough input power, photoisomerization processes induce a nematic–isotropic phase transition mediated by interface propagation between the two phases. In the case of a twisted nematic layer and for intermediate input power, the light induces a spatially modulated phase, which exhibits stripe patterns. The pattern originates as an instability mediated by interface propagation between the modulated and the homogeneous nematic states. Theoretically, the phase transition, emergence of stripe patterns and front dynamics are described on the basis of a proposed model for the dopant concentration coupled with the nematic order parameter. Numerical simulations show quite a fair agreement with the experimental observations. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)’.

Interplay between a crystal's shape and spatiotemporal dynamics in a spin transition material

Experimental (top) and theoretical (bottom) snapshots of the interface propagation along the spin transition in the spin-crossover single crystal [Fe(2-pytrz)2{Pd(CN)4}]·3H2O, showing its interplay with the crystal shape.