Crystal growth as an excitable medium

Crystal growth has been widely studied for many years, and, since the pioneering work of Burton, Cabrera and Frank, spirals and target patterns on the crystal surface have been understood as forms of tangential crystal growth mediated by defects and by two-dimensional nucleation. Similar spirals and target patterns are ubiquitous in physical systems describable as excitable media. Here, we demonstrate that this is not merely a superficial resemblance, that the physics of crystal growth can be set within the framework of an excitable medium, and that appreciating this correspondence may prove useful to both fields. Apart from solid crystals, we discuss how our model applies to the biomaterial nacre, formed by layer growth of a biological liquid crystal.

Diagnostic of Pre-Nucleation and Nucleation By Spectroscopic Methods and Background on the Physics of Crystal Growth

Unlike the crystallization of small inorganic molecules, the problem of protein crystallization was first approached by trial and error methods without any theoretical background. A physico-chemical approach was chosen because crystallographers and biochemists needed criteria to rationally select crystallization conditions. In fact, the problem of the production of homogeneous and structurally perfect protein crystals is set the same as the production of high-quality crystals for opto-electronic applications, because, in both cases, the crystal growth mechanisms are the same. Biological macromolecules and small organic molecules follow the same rules concerning crystallization even if each material exhibits specific characteristics. This chapter introduces the fundamentals of crystallization: supersaturation, nucleation, and crystal growth mechanisms. Phase diagrams are presented in Chapter 10. Special attention will be paid to the behaviour of the macromolecules in solution and to the techniques used for their analysis: light scattering (LS), small angle X-ray scattering (SAXS), small angle neutron scattering (SANS), and osmotic pressure (OP). Before obtaining any nucleation or growth, it is necessary to dissolve the biological macromolecules under consideration in some good solvent. However, it may immediately be asked whether a good solvent is a solvent in which the material is highly soluble, or in which nucleation is easily controlled, or in which growth is fast, or solvent in which the crystals exhibit the appropriate morphology. In practice, the choice of the solvent often depends on the nature of the material to be dissolved, taking into account the well known rule which says that ‘like dissolves like’. This means that, for dissolution to occur, it is necessary that the solute and the solvent exchange bonds: between an ion and a dipole, a dipole and another dipole, hydrogen bonds, and/or Van der Waals bonds. Therefore, the nature of the bonds depends on both the nature of the solute and the solvent which can be dipolar protic, dipolar aprotic, or completely apolar. Once the material has dissolved, the solution must be supersaturated in order to observe nucleation or growth. The solution is supersaturated when the solute concentration exceeds its solubility. There are several ways to achieve supersaturation.