Diffusion limited crystal growth processes have been studied both experimentally and numerically for better understanding of the instabilities on a moving solidification front.
In the experiments quasi-two-dimensional samples of various organic crystals and liquid crystals (the nematic - smectic B first order phase transition) have been investigated. The peculiarity of liquid crystals for this field of research is that both the low-temperature phase (‘crystal’) and the high-temperature phase (‘melt’) may be anisotropic.
The numerical calculations were carried out using the phase-field model based on the Ginzburg-Landau formalism which takes into account the anisotropies of the surface tension and that of the phase transformation kinetics in the same time.
Crystallization of impure biphenyl was
studied in thin-sample directional solidification (T-DS) experiments. The
platelike growth shape of the monoclinic biphenyl crystals includes two
low-mobility (001) facets and four high-mobility (110) facets. Upon T-DS,
biphenyl plates oriented with (001) facets parallel to the sample plane can exhibit either a strong growth-induced
plastic deformation (
The growth of polycrystals and grain boundary dynamics
was studied in directional solidification for the
In directional solidification
the nematic-smectic B interface of
The effect of oscillatory pressure and periodic heating on the dendritic morphology in solidification was analized in details. The sensitivity of this phenomenon to the relevant parameters, the frequency and amplitude of the modulation, the initial undercooling and the anisotropies of the interfacial free energy and molecule attachment kinetics, has been explored. It has been shown, that in addition the side-branching mode synchronous with the external perturbation, modes that oscillate with higher harmonic frequencies are also present with perceptible amplitudes.
Two review articles summarize experimental and numerical (phase-field simulation) results about solidification in systems with large anisotropy (faceted growth), dendritic growth, solidification from anisotropic melt and crystal growth in the presence of time-periodic external modulations.
The dendritic morphology is often observed in solidification. The noisy character of the sidearm formation (Fig.a.) was intensively studied by various groups. We have shown that spatially homogeneous time-periodic external modulations (pressure oscillation, heat pulses) regulate the dendritic growth (Fig.b.).
An aging behaviour was observed in alkyl-bicyclohexyl-carbonitrile compounds which strongly influences the growth of smectic B germs in the undercooled nematic phase. The aging also results in a broadening of the phase coexistence temperature ranges and in a saturating shift of phase transition temperatures with a temperature dependent dynamics. An experimental evidence has been given that the air atmosphere is responsible for the thermally induced ageing.
The growth of a homeotropic smectic domain is associated with small surface tension anisotropy and kinetic anisotropy. This allows one to concentrate on the effects coming from the anisotropy of the liquid (nematic) phase. One interesting result is that anisotropic diffusion in the liquid phase causes an elongation of the growing crystals in the direction of the slow diffusion. The experimental observations have been reproduced by phase-field simulations.
The shape of quickly growing dendrites is also influenced by the diffusion anisotropy of the surrounding nematic phase. The analysis of four armed dendrites reveal, that the arms which propagate in the direction of slower diffusion are faster.
Dendritic and faceted growth in strongly anisotropic systems has been characterized experimentally and the observed growth forms have been reproduced numerically using phase-field simulations.
The growth of a planar smectic domain (smectic layers perpendicular to the plane of the sample) is associated with large surface tension anisotropy and kinetic anisotropy, often resulting in faceted growth.
Three types of smectic-B germs with respect to the director orientation inside and outside the germ have been found. The planar germs undergo a dramatic change of morphology as a function of undercooling, starting from an elongated, rectangle-like shape to dendritic growth of fourfold symmetry. Near equilibrium the homeotropic germs have a circular form with a small hexagonal modulation, and show a dense branching morphology for larger undercoolings.
An interesting “inverse process” has been detected in melting of the rapidly grown smectic B phase. The stable nematic phase nucleated substancially below the phase transition temperature. Most of these nematic germs had uniform oval shape, totally different from that of the equilibrium smectic seed.
Equilibrium shapes of the nematic–smectic-B liquid-crystal interface have been investigated. From the shape of the germs the angle dependence of the surface tension was determined.
The interface of a growing smectic phase in a supercooled nematic liquid crystal was studied. A change in the morphology and the side-branching activity was observed with the undercooling. Nonparabolic dendrites with faceted dissymmetric tips were found for small undercooling.