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
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
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...
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
Effective size of d is defined by equation vm =
The volume of the cl...
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
A change of free Gibbs energy as a result of formation such disc-like island
represents a formula:
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 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...
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.
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
where ΔH - change of enthalpy during crystal
growth, Hcryst and Hr...