Solidification microstructures and solid-state parallels: Recent developments, future directions

-- Part C: 1. The continuum approach to crystal interfaces: basics. I: Theoretical framework. 2. Operators for orientation-dependent parameters. 3. Mechanics and thermodynamics of interfaces. 4. Equilibrium structures of junctions, edges and vertices. 5. Growth: kinematic wave theory revisited. 6. Kinetic behaviour of junctions, edges and vertices. 7. Structural phase transitions of a crystal surface as a branch of soliton physics. 8. Miscellaneous topics. II: Growth rate functions. 9. Analytic representations of R(n,A) functions. 10. Nonlinear networks and the 'assembled function' notation. 11. Physical aspects of assembling operations. 12. The systematic construction of R(n,A) functions by a sequence of assembling steps. 13. Notes on sphere-growth experiments. 14. Summary: Conclusions and outstanding questions. References. List of symbols, abbreviations and notations.

Morphology of crystals

Confined crystallization of polymeric materials

Polymer spherulites: A critical review

In general, when a crystal is molten, all molecules forget about their mutual correlations and long-range order is lost. Thus, a regrown crystal does not inherit any features from an initially present crystal. Such is true for materials exhibiting a well-defined melting point. However, polymer crystallites have a wide range of melting temperatures, enabling paradoxical phenomena such as the coexistence of melting and crystallization. Here, we report a self-seeding technique that enables the generation of arrays of orientation-correlated polymer crystals of uniform size and shape ('clones') with their orientation inherited from an initial single crystal. Moreover, the number density and locations of these cloned crystals can to some extent be predetermined through the thermal history of the starting crystal. We attribute this unique behaviour of polymers to the coexistence of variable fold lengths in metastable crystalline lamellae, typical for ordering of complex chain-like molecules.

https://www.chemie.tu-darmstadt.de/media/chemie/pdfs/polymer-kristalle.pdf

Cloning polymer single crystals through self-seeding.

The morphology diagram of possible structures in two-dimensional diffusional growth is given in the parameter space of undercooling \ensuremath{\Delta} versus anisotropy of surface tension \ensuremath{\epsilon}. The building block of the dendritic structure is a dendrite with parabolic tip, and the basic element of the seaweed structure is a doublon. The transition between these structures shows a jump in the growth velocity. We also describe the structures and velocities of fractal dendrites and doublons destroyed by noise. We introduce a renormalized capillary length and density of the solid phase and use scaling arguments to describe the fractal dendrites and doublons. The resulting scaling exponents for the growth velocity and the different length scales are expressed in terms of the fractal dimensions for surface and bulk of these fractal structures. All the considered structures are compact on length scales larger than the diffusion length and they show fractal behavior on intermediate length scales between the diffusion length and a small size cutoff which depends on the strength of noise. \textcopyright{} 1996 The American Physical Society.

Structure formation and the morphology diagram of possible structures in two-dimensional diffusional growth.

We propose a phase diagram for the selection of growth patterns in systems with a conserved quantity which evolve at asymptotically constant growth rate The occurrence of different growth forms like fractal, compact or dendritic, and the various transitions between them are characterized by scaling relations

http://iopscience.iop.org/article/10.1209/0295-5075/17/6/010/pdf

Kinetic Phase Diagram and Scaling Relations for Stationary Diffusional Growth

A theory for the morphology diagram of possible structures in two-dimensional diffusional growth is presented. The main control parameters are undercooling Δ, anisotropy of surface tension e and the strength of noise. Basic patterns are dendrites and seaweed. The building block of the dendritic structure is a dendrite with parabolic tip, and the basic element of the seaweed structure is a doublon. The transition between these structures shows a jump in the growth velocity. The possible extension of these results to three-dimensional growth is shortly discussed.

Morphology diagram of possible structures in diffusional growth

The growth of two-dimensional crystals with and without anisotropy in a channel is analyzed by a Green's-function method. A one-sided diffusional model is treated in quasistationary approximation. Our numerical results on the steady-state growth of symmetrical fingers are in agreement with approximate analytical predictions (E. Brener, M. Geilikman, and D. Temkin, Zh. Eksp. Teor. Fiz. 94, 241 (1988) [Sov. Phys. JETP 67, 1002 (1988)]). For fixed supercooling the dependence of growth velocity versus channel width is nonmonotonic, passing a maximum. We did not find stationary solutions for supercooling less than 0.5. When the width of the channel exceeds some critical value we observed that the symmetrical finger becomes unstable against tip splitting. In this case we found stable steady-state growth of nonsymmetrical fingers. We have also found an expected instability of two fingers in the common diffusion field caused by competition.

/pdf/crystal-growth-in-a-channel-numerical-study-of-the-one-sided-1zioh6z9sc.pdf

D. E. Temkin

Papers

Structure formation and the morphology diagram of possible structures in two-dimensional diffusional growth.

Kinetic Phase Diagram and Scaling Relations for Stationary Diffusional Growth

Morphology diagram of possible structures in diffusional growth

Crystal growth in a channel: Numerical study of the one-sided model.

Kinetics of isothermal phase transformations above and below the peritectic temperature: Phase-field simulations