The equilibrium format is the one that minimizes ΔGγ, the free energy of the surface of a crystal – the sum of the individual products of surface areas multiplied by the interface energy 1. It’s possible to modify the crystal shape with the introduction of ions or molecules that alter the format of the twists during growth by way of interaction with the edge of the steps. These growth modifiers can be organic and include both peptides and large proteins, but even small inorganic modifiers may play a role in this process, given their presence in naturally occurring cellular fluids.
Step Immobilization: Some types of impurities prevent adhesion of molecules on the edges of a step. The only way the step can continue to advance is to grow around them. Counting on the distance between the impurities as being greater than the critical radius of the curve of a step, the step can continue to grow. But, if the distance between the impurities were equal or smaller than the critical radius r*, the step growth will be halted. The immobilization of the step is highly dependant on the interaction details between the impurity and the step. As a consequence, the same impurities that block one type of step can allow propagation on adjacent faces of the crystal – or even other types of steps on the same facet.
Incorporation: Impurity incorporation occurs when foreign ions or molecules become captured by advancing steps or otherwise incorporate at kink sites along a step edge to become part of the growing crystal. Typically the impurity molecules distort the crystal structure, thereby increasing the internal energy of the solid through an enthalpic contribution. Incorporation does not have to result in decreasing growth rates and can even increase the growth rate at sufficiently low impurity concentrations. In low concentrations, incorporation of impurities increases crystal stability and reduces solubility in water.
Kink blocking: When impurities adsorb to kink sites for very short residence times, they lead to an effective reduction in kink sites density, with or without incorporation. As with step pinning, because this effect is highly dependent on specific impurity-step interactions, kink blocking can result in a change in crystal shape.
Surfactants: surfactants are compounds characterized by the capacity to alter the surface and interfacial properties of a liquid. Act as surfactants in the formation of crystals certain impurities that, adsorbed to the edges of the steps may modify certain growth parameters by reducing the interfacial energy between the crystal edge and the liquid medium.
1 The authors consider the cube (rhombohedron), because of calcite growth. With a cube the free energy can be found by adding the area of all the sides (total surface area) and multiplying the result by the interface energy between the surface and the center of the cube.
