Self-oscillatory instability of the driven phase front propagation induced by liberation of latent heat.

We theoretically address crystals exhibiting first-order phase transformations subjected to a steadily propagating temperature gradient. The latter drives a nonisothermal propagation of a phase front. We theoretically demonstrate that for the phase transformations of the displacive type, the phase front always steadily follows the isotherm.

Transformation toughness induced by surface tension of the crack-tip process zone interface: A field-theoretical approach.

We study a crystal with a motionless crack exhibiting the transformational process zone at its tip within the field-theoretical approach. The latter enables us to describe the transformation toughness phenomenon and relate it to the solid's location on its phase diagram. We demonstrate that the zone extends backward beyond the crack tip due to the zone boundary surface tension.

Morphological transformation of the process zone at the tip of a propagating crack. I. Simulation.

Stress concentration at a crack tip engenders a process zone, a small domain containing a phase, different from that in the bulk of the solid. We demonstrate that this zone at the tip of a propagating crack exhibits a morphological transformation with an increase of the crack velocity. The concave zone shape with an invagination in its back that is characteristic of a slow crack transforms into a droplet-shaped convex zone upon exceeding a critical velocity value, v_{G}.

Morphological transformation of the process zone at the tip of a propagating crack. II. Geometrical parameters of the process zone.

The morphological transformation of the process zone at the tip of a propagating crack occurs with the increase of the crack velocity. The zone configuration changes its shape from concave to convex, dropletlike form. The latter exhibits a metastable wake.

Crack-tip process zone as a bifurcation problem.

Stress concentration at a crack tip generates a solid structural transformation in its vicinity, the process zone. We argue that its formation represents a local phase transition described by a multicomponent order parameter. We derive a system of equations describing the dynamics of the order parameter driven by an inhomogeneous, time-dependent stress field in the solid and show that it exhibits a bifurcation.

Relation between bulk and interface descriptions of alloy solidification.

From a simple bulk model for the one-dimensional steady-state solidification of a dilute binary alloy we derive the corresponding interface description. Our derivation leads to exact expressions for the fluxes and forces at the interface and for the set of Onsager coefficients. The constitutive equations, connecting the crystallization and diffusion fluxes and forces, decouple in the low-velocity limit and there generate an occasionally negative, but nevertheless thermodynamically consistent friction coefficient.

Domain of oscillatory growth in directional solidification of dilute binary alloys.

The oscillatory growth of a dilute binary alloy has recently been described by a nonlinear oscillator equation that applies to small temperature gradients and large growth velocities in the setup of directional solidification. Based on a one-dimensional stability analysis of stationary solutions of this equation, we explore in the present paper the complete region where the solidification front propagates in an oscillatory way. The boundary of this region is calculated exactly, and the nature of the oscillations is evaluated numerically in several segments of the region.

Capillary-wave description of rapid directional solidification.

A recently introduced capillary-wave description of binary-alloy solidification is generalized to include the procedure of directional solidification. For a class of model systems a universal dispersion relation of the unstable eigenmodes of a planar steady-state solidification front is derived, which readjusts previously known stability considerations. We moreover establish a differential equation for oscillatory motions of a planar interface that offers a limit-cycle scenario for the formation of solute bands and, taking into account the Mullins-Sekerka instability, of banded structures.

Diffusion-induced oscillations of extended defects.

From a simple model for the driven motion of a planar interface under the influence of a diffusion field we derive a damped nonlinear oscillator equation for the interface position. Inside an unstable regime, where the damping term is negative, we find limit-cycle solutions, describing an oscillatory propagation of the interface. In the case of a growing solidification front this offers a transparent scenario for the formation of solute bands in binary alloys and, taking into account the Mullins-Sekerka instability, of banded structures.

Self-oscillating regime of crack propagation induced by a local phase transition at its tip.

We report an analytical study of propagation of a straight crack with a stress-induced local phase transition at the tip. We obtain its contribution to the dynamic fracture energy in explicit form and demonstrate that it nonmonotonically depends upon the crack tip velocity. We show that its descending part gives rise to the instability of the steady propagation regime.

Capillary-wave model for the solidification of dilute binary alloys.

Starting from a phase-field description of the isothermal solidification of a dilute binary alloy, we establish a model where capillary waves of the solidification front interact with the diffusive concentration field of the solute. The model does not rely on the sharp-interface assumption and includes nonequilibrium effects, relevant in the rapid-growth regime. In many applications it can be evaluated analytically, culminating in the appearance of an instability that, interfering with the Mullins-Sekerka instability, is similar to that found by Cahn in grain-boundary motion.

Segregation instabilities of moving interfaces.

The segregation of solute particles on a moving interface leads to the appearance of two types of instabilities near competing velocity thresholds. This behavior is shown to occur in a variety of exactly solvable models where the interface motion is coupled to a diffusion process of the solute particles. These models directly apply to the propagation of internal domain walls, but can also be generalized to surfaces of growing crystals in the kinetics-limited regime.

Kinetic complete wetting of a planar defect close to a bulk tricritical point.

The nucleation of a new phase at a moving planar defect is considered in the high-symmetry phase of a bulk tricritical point. In the first-order regime a kinetic complete-wetting transition is found where the thickness of the nucleation layer diverges, inducing a change of the drag coefficient of the defect. When the tricritical point is approached, the complete-wetting transition disappears, and, in the adjacent second-order regime, the layer thickness is finite in the full nucleation region.

Kinetic wetting of a moving planar defect by a new phase.

Close to a bulk phase transition, a moving planar defect can be covered by a layer of the ordered phase. This, in fact, happens above the transition point in some finite region of the temperature-velocity diagram. In the case of a first-order transition this region is furnished with a net of nonequilibrium phase-transition lines.