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Phenomenology of crystal growth.

Crystals are state of the matter with long-range order of atoms in it. It means that in some direction the pattern of atoms locations will periodically repeat themselves. Conventionally this statement will be true in any direction in three dimensional space but for some special cases such as liquid-crystals (yes, it may be the key material in your computer monitor you staring now at) in some directions atoms will be randomly located but in others could have a long-range order.


Thermodynamic potential of crystal growth.
A process of phase transition of first-order such as crystallization is accompanied with heat release that reflected a difference between energy levels of crystal phase and surrounding it matter that is the 'soil' for the growing crystal. The amount of heat is equivalent to difference of enthalpies between characterized crystalline phase and in initial phase :

Qcryst =-ΔH = Hcryst - Hraw  (1),

where ΔH - change of enthalpy during crystal growth,  Hcryst and Hr...

Models of growth of crystal surface.
The model of thermally activated crystal growth as described in the article leaves aside the very important feature of crystal growth phenomena namely the influence of surface energy.

A difference in levels of free energy between molecule situated at the surface of the crystal incorporated in it and if belonged to amorphous phase is designated by addition of component that reflect on change surface of crystal in case of molecule transformation:

† ΔG = ΔμVm ...

A model of thermally activated crystal growth.

A model of thermally activated crystal growth is a foundation for theory of crystallization.

In the model of thermally activated crystal growth addresses to the elemental act of incorporation of molecule on the surface into crystal. In the spite (or because) simple mathematical formulation and universality of the model itself meanings of elements in it are sometimes paradoxical and demands separate discussions and definition in any specific situation.

In the model of thermally act...

Dislocation induced crystal growth.
An observation of the crystals growing with flat surfaces and in the same time difficulty of quantitative application of the two dimensional nuclei model for quantitative explanation of experimental data for temperature dependence of rate of crystal growth as well an occasional the observation spiral like formations on the crystal surfaces leads to some specific theory of crystallization named spiral dislocation model.

The model bypasses the necessity of random formation of two dimensional nuc...

Mechanism of two-dimensional nuclei growth.
One of the models of layer by layer growth of crystal is based on the random process of forming two dimensional nucleus that schematically displayed on the following picture:

Fig. 1. Schematic view of two dimensional nucleus on the flat crystal surface. 

A change of free Gibbs energy as a result of formation such disc-like island represents a formula:

ΔG = dπr2×ΔGv + 2πrd×σ       ...

Nucleation from own melt.

A phenomena of spontaneous appearance of crystal phase inside of liquid and then self sustained growth up to the point of complete transformation of liquid into crystal is the very commonly observed for producing ice in refrigerator and most paradoxical from point of clear demonstration of limitations of direct application of thermodynamic laws in case when macro effects are seed out from micro scale incident when statistical fluctuations play major role.

The paradox of nucleation...

Formulas for numbers of molecules on the surface of a large nucleus.

Numerical simulation of nucleation phenomena during crystallization demands a definition several parameters of the clusters of crystalline molecules in initial amorphous phase. Among of such key parameters are a numbers of molecules on the surface of cluster these can be transformed from one phase to other changing number of molecules in the cluster.

Letís cluster has i molecules with volume vm each.

Effective size of d is defined by equation vm = d3

The volume of the cl...

Estimation of surface energy.

A phenomenon of surface energy plays a central role in analyses of most aspects of phase transitions in general and crystallization specifically. If for liquid surface energy (tension) can be measured directly for crystals such measurements practically impossible to carry out with any level of reliability. Most pronounce phenomena where surface energy of crystalline phase could be estimated on the base of experimental data are kinetic of crystal nucleation and growth. There two major complica...