A numerical simulation is based on Monte Carlo implementation
of modified cellular automaton model. Simulated crystal surface
is represented by two dimensional matrix where value and position
of the elements define 3D location of the molecule on the surface
of the crystal.
At every next time step each position on the surface of the crystal
can accept new molecule and move forward, stay on place or emit
molecule and move backward.
Relative probabilities to accept or emit molecule are calculated
on the base of model of thermally activated reaction depending
on near surrounding of each molecule on the surface that allows
direct introducing of the surface energy into the model of the crystal growth.
A model also permit calculation of concentration hole type defects
formed as result of plugging bottle neck like structures on the rough surface.
Setting experimental parameters:
Parameters of single experiment can be typed in to data panel
with flexible choice of to use favorite measurement units.
LeoMonteCrystal provides unit converter capabilities, permitting
to use initial parameters defined in various unit systems as
fit a user customary.
Data input panel instantly displays theoretical values for velocity
crystal growth calculated for competitive theoretical models
and plus most valuable - with formulas found as result of our
research for given set of initial parameters. The temperature
dependence of growth rate, surface roughness and defects concentration
calculated by our formulas are displayed at separate chart.
After modification of any one parameters all dependable variables
are automatically updated accordingly providing functionality
of thermodynamic and crystallography calculator.
Frequently used set of parameters, corresponded to compound of
interest, can be saved or imported to or from coma delimited
file (MS Excel compatible).
There are helpful key shortcuts incorporated in for managing special
cases to try for researcher: varying effective size of presumed
molecule by multiplying or dividing its dimensions by integer
value; estimating value of surface energy; calculating temperature
dependence of theoretical values given set of other parameters.
Setting parameters of run for numerical simulation:
LeoMonteCrystal permits to set size of simulation field and time step for one
turn in convenient for user form. One can play from choosing
the probability of one molecule to jump into crystalline phase
during turn time (or number of such molecules for given size
of the field); user also can set conditions to stop a simulation
by limiting a time of computer simulation or number of layers
filled by molecules.
On the panel for setting technical parameters for experiment run there is graph
presenting probabilities that in time step given position depend
on neighbor surrounding on simulation field of crystal surface
a molecule will incorporated into crystalline phase or emitted
outside or stay unmoved.
User can run single experiment for thermodynamic and kinetic
variables set on Data panel as well to program experimental plan,
series experiments flexible varying temperature, surface energy
and other parameters.
Experiment plan can be saved in or open from a file.
View panel offers three options to observe surface of the growing crystal
during numerical simulation: grey iso-altitude map; bird like
view in perspective projection and stereo pair red and blue images
to be observed via glasses with corresponding colors.
User can to move by arrow keys on keyboard position of virtual
observer above surface selecting best vantage point.
At the "Results" panel during simulation there are charts displaying
timeline of: distance of crystal surface growth progress, its
roughness, instant growth rate and concentration of the hole like defects.
Current characteristics of the numerical simulation: number of
time steps, rate of crystal growth, roughness of surface, induction
period of critical two dimensional nuclei on smooth surface,
concentration of holes and some derivatives from these are displayed
in numerical form.
Depended on simulation conditions type of current mechanism of
growth is defined.
Upon end of experiment conditions of simulation and results of
experiment automatically recorded into log file.
We provide white pages with description of algorithm for numerical
simulation, results of our numerical experiments and discovered
To protect our intellectual property we reserve the right distinct
between level of specificity in available for different users
supporting papers depend on their verified identity and support
of our research.
View panel permits to observe in real time growing crystal surface during numerical simulation. There are options to see crystal surface as grey iso-altitude map;bird like view in perspective projection and stereo pair red and blue images to be observed via glasses with corresponding colors.
Run panel is for setting parameters of experiment and run it in software for numerical simulation of the crystal growth. User can choose dimensions of simulation field, setting time of one step and design a series of experiment to run automatically varying specific parameters of the process.
Results panel of LeoMonteCryslal presents of results of numerical simulation of crystal growth in chart form showing advance of surface,growth rate, roughness of surface and concentration of defects in real time during simulation.