Conclusion and future elaboration.

by Dr. Leonid Sakharov

Numerical experiment for simulation of crystal growth was done. The Monte-Carlo algorithm to mimic molecule processes at the surface of the growing crystals was developed and semi-theoretical formulas are developed for growth rate, surface roughness, concentration of hole-like defects.


The algorithm for mimicking molecule transitions at the surface of the growing crystal is developed and implemented into the software application LeoMonteCrystal.

Large Series > 10000 of numerical experiments for simulating crystal growth for wide range of initial thermodynamic and crystallographic parameters was performed with the help of LeoMonteCrystal.

Semi-analytical fitting formulas, with coefficients contains only mathematical constants, for growth rate, surface roughness and concentration hole like defects were found to replace lengthy numerical experiment were constructed and incorporated into LeoMonteCrystal software application.

Temperature curves of crystal growth rate, roughness of surface and hole like defects produced by semi-theoretical formulas shows wide variety of patterns making possible to compare these curve with obtained in physical experiment to obtain information about mechanism of phase transition for specifically important cases and helping in optimization of technology of production industrial materials.

Directions of future elaboration.

There are limited number of experimentally measured temperature curves for crystal growth rate. Using developed semi-theoretical formulas and knowledge about thermodynamic of this specific phase transition, crystallographic data and making educated assumptions about surface energy it is possible to compare output of semi-theoretical formulas to find best fit with actually happened. It could be especially beneficial because physical experiment is in most cases so expensive that saving project from performing even several less experiment could produce great saving of time and money. Interesting point is that variation of the size and shape of the molecule in finding parameters of semi-theoretical formulas due to knowledge of crystal structure cells should be limited due to tried size of molecule is reasonable to be aliquot to crystal lattice cell.

The range of the applicability of found semi-theoretical formulas can be tested on more and more power computers. This part of the project has open end proposition. Enlarger simulation field, making smaller time steps and longer time of simulation researcher can do continuously improving accuracy of single numerical simulation experiment. The present level of accuracy of numerical experiment is satisfactory for revealing fundamental dependencies and structure of formulas describing growth rate in the intermediate between pure two-dimensional nuclei mechanism and continues growth. It could be very interesting to see where pure theoretical formulas for two-dimensional nuclei is mated with semi-theoretical formulas and where areas of their area applicability lies. 

Dr. Leonid Sakharov who have been moving this project practically on his own two decades is practically exhausted his own recourses. Without outside support the project will be virtually frozen out. Donate, please.

or Contact us with proposition that ought to include monetary compensation:

Nov. 6, 2017; 13:09 EST


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