INTERACTIVE SCIENTIFIC VISUALIZATION
Lectures for the
in honour of Prof. J.M. Araujo, Oporto, Portugal, 23rd-29th August 1998.
SUPPLEMENT TO LECTURE no 2: THREE DIMENSIONAL VISUALIZATION for
INTRODUCTION TO MOLECULAR DYNAMICS FOR SOLIDS
is simply solving Newton's
equations of motion for atoms
and molecules. This requires:
CALCULATIONS OF FORCES (POTENTIALS)
- - -
from first principles
and/or from experimental data.
(For our carbon modelling we used the
potentials of Tersoff [Phys.Rev.Lett. 61 (1988) 2879]
and Brenner [Phys.Rev.B 42 (1990) 9458])
METHODS FOR INTEGRATING EQUATIONS OF MOTION
- - -
fast, converging algorithms
and enough computer time and memory.
(We usually use either the
leap-frog or the
Gear predictor-corrector algorithms.)
TECHNIQUES FOR VISUALIZATION OF RESULTS
- - -
3D visualization and animation.
(We do our interactive visualization in OpenGL and C.)
EXPERIMENTAL DATA FOR COMPARISON
- - - for example, our carbon modelling
motivated by the desire to explain certain
ion implantation results of Rafi Kalish
and data on CVD diamond films of Alon Hoffman. We also relate to
heat capacity, thermal conductivity,
and phonon spectra of diamond.
POTENTIALS: The question of potentials is a delicate and controversial
one. The same issue arises in the context of molecular statics or in the
use of simulated annealing to find optimum configurations at a particular
temperature. Obviously, the best ``potential'' is found from a quantum
mechanical study. This can only be done for a system of very limited size,
and extremely limited time development.
Next best is something in the spirit of ``tight-binding'' molecular dynamics,
followed by manybody potentials assembled from first principle results and
Excellent agreement between manybody potentials
and first principle results can be found
for the case of carbom, which is not an easy system to model because of the
different bonding configurations. Saada, Adler and Kalish (in preparation)
found such agreement in a series of calculations concerning the surface
graphitization of diamond with
judicious use of Tersoff/Brenner
manybody potentials. The weakest potentials for general use are the
simple potentials, such as Lennard-Jones. These are great for argon, but do not
give a good approximation to semiconductors or ceramics. However they do
enable study of large samples for long times, development of new molecular
dynamics techniques and validation of temperature maintenance algorithms.
VISUALIZATION OF POTENTIAL COMPARISON:
The above graph gives
some insight into the time and size scales at which
different types of potentials can be utilized.
(This graph has been prepared to
correspond to the computational resources of the Computational Physics
Group at the Technion in 1998 for obvious reasons.)
The graph gives a symbolic representation within a space whose axes are
the three most important variable scales
for this type of modelling.
The vertical (y) axis represents system size,
the horizontal (x) one decreasing accuracy
of description, and the axis going into the page (z) represents
time development. Ideally we would like to study samples at large values of
x and z and small values of x, but in reality low x values (high accuracy of
description) correspond also to small y and z values.
The smallest box in the lefthand corner represents the
limited range of quantum
mechanical models within this space.
The larger box symbolises the relatively larger size and
timescale range of the
manybody potentials. The region outside the boxes
is accesible only with simplistic
Lennard Jones type potentials.
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