INTERACTIVE SCIENTIFIC VISUALIZATION

SUPPLEMENT TO LECTURE no 2: THREE DIMENSIONAL VISUALIZATION for MOLECULAR DYNAMICS

INTRODUCTION TO MOLECULAR DYNAMICS FOR SOLIDS

Molecular Dynamics 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 experimental measurements of 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 experimental measurements. Excellent agreement between manybody potentials and first principle results can be found even 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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