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Setting parameters and run an experiment in software for numerical simulation of the crystal growth.

The "Run" panel of LeoMonteCrystal is to set technical parameters of numerical simulation experiment.

The Fig. 1 shows screenshot of the “Run” panel.


Fig. 1. Run panel contains groups of controls combined by functional attributes for editing or displaying technical parameters of numerical experiment.

"Area of simulation"

controls group permits defining dimensions of a matrix that represented area of surface numerical simulation is performed in.

 

 
  Fig. 2. Group of controls for setting size of matrix to perform simulation experiment.  


Selection of the size of simulation field is a matter of compromise as it is almost always true when discussing numerical simulation. The larger field the closer to reality (not always if we talking about nano size objects) the smaller the faster simulation.
Usually one can presume that for most cases 100×100 and large field is quite sufficient and 10×10 is too small. Normally filed size should be large enough to accommodate at least one critical nucleus. It means that at very smaller supercooling when theoretical value of critical nuclei is approaching infinity simulation field size should be as large as possible for stable outcomes that putting hardware performance limitations on the method.


Time step and probability chart

 

 
  Fig. 3. Group of controls for setting time step at numerical simulation experiment and displaying probabilities for one molecule to be incorporated into crystal or jump out from it. Red line represents probability for molecule at surface to be emitting - locally stepping one layer back, green line gives probability to incorporate one molecule in crystal at the position making step ahead.  
 

The group of controls for defining time steps value during numerical simulation contains three hard interconnected parameters each of them defined two others. User can edit any of them hit enter key and other two will be update automatically.

The N value gives average number of molecules that will be randomly jump into crystalline phase from outside to be incorporated at next time step randomly at positions of whole simulation field.

Probability P for any specific molecule position to accept molecule and move one layer ahead will be N divided on number positions in the simulation field.

The value of the time step in seconds is probability
for a molecule to jump scaled by frequency coefficient calculated from model of thermally activated reaction:

Δtstep = P / (γo * exp(-Ea/kT))

where γo - frequency of thermal vibrations of molecules in crystal and surrounded liquid phase, Ea - activation energy for jump incorporating into crystalline phase, k - Boltzmann's constant,  T - temperature.

Pushing a button: "Set default" user asking a program to set parameters described above to the recommended values.

Most useful parameter to set experiment is to the probability P. Usually the value of probability 0.001 is the best fitting compromise between reliability of calculation and computation time necessary to reach stable results.

Depend on neighborhood surrounding of the molecule on crystal surface specifically value of part of molecule that is in direct contact with others near neighbors in crystal there are different probabilities to incorporate next molecule into crystal at this position or emitting one molecule into surrounding phase.

We use state of art proprietary algorithm for calculation of these probabilities of stepping ahead or back or staying unmoved as third alternative these are functions of on part of molecule surface in direct contact with other molecules of the crystal.

It's worth to note that probability to jump in - P from time step group is equal to probability to jump in in actual simulation only for the case when probability jump back is approaching zero - that is the situation of the "valley" like position on the crystal surface when part of molecule in direct contact with crystal approaching 1.

Depend on curve behavior of Pin(ΔSm) and Pout(ΔSm) curves on the Fig. 3 user can make education suggestion about adequacy of selecting value of P. Specifically if to chose value P too large like >0.1 one can see that at even at areas of values of ΔSm around 0.5 probability jump out could approach to 1 that could be clear sign of results distortion. Other way around the setting too small value of P<1e-5 could produce artifact effects connected with size of increment step in random number generator used in the program.

The chart of probabilities is the most powerful tool for user to exam correctness of setting parameters of numerical simulation.

Condition to stop simulation

controls group allow to set time oor distance limits for one numerical experiment:

 

 
  Fig. 4. Group of controls to set stop conditions for one experiment.  
 

User have options to let simulation run indefinitely long until computer permits or limit one experiment by distance of advance of crystal surface or by physical time of experiment or both whatever comes first. The option is mostly valuable when series of experiments are running automatically that could be essential for situations: a) large supercooling when experiment can be accomplished in very short physical computer time and there is no need to continue longer then let say 100 layers of growth; b) at small supercooling filling even several layers can take days so limiting time for one of experiment in whole series looks like reasonable.

User also have an option to include in the algorithm possibility of creation hole like defects when well like molecule structure is clogged at neck by other molecule creating empty space inside crystal. 

Experimental plan control

displayed at Fig. 5:

 

 
  Fig. 5. Experimental plan control.  
 

Group of controls are combined together permit: to run single numerical experiment or series of experiments follow users instructions.

A button "Run" starts a single experiment with currently set parameters. The experiment will start from smooth surface.

Pressing button "Pause/Resume" permits to pause a simulation at any point and then resume it with or without changing of conditions for simulation experiment. User can use it by variety reasons like for instance to learn how changing temperature affect crystal growth and estimating time for accommodation from one regime to another.

A menu and list of tasks at "Experiment plan" control can be use for setting series of numerical experiments to be run automatically. There is description of  menu commands contained in the control:

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