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Manuscript Title: Computer simulation of extended defects in metals.
Authors: R.E. Dahl Jr., J.R. Beeler Jr., R.D. Bourquin
Program title: GRAINS
Catalogue identifier: ACQY_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 2(1971)301
Programming language: Fortran.
Computer: UNIVAC 1108.
RAM: 48K words
Word size: 36
Peripherals: magnetic tape, graph plotter.
Keywords: Solid state physics, Discrete lattice theory, Computer simulation, Grain boundaries, Quasi-dynamic and fully dynamic methods of solution, Classical mechanics, Interatomic potential functions, Defects.
Classification: 7.1.

Nature of problem:
The program is designed to determine the atomistic structure of extended defects in crystals with cubic structure, and their interactions with point defects. The extended defects which can be studied are grain boundaries, twin boundaries, free surfaces, cracks and dislocations. In addition, elementary aspects of grain boundary sliding can be studied.

Solution method:
The lowest potential energy configuration for a given extended defect is computed using the quasi-dynamical method of Gibson et al. This method develops a many-body description of the equilibrium configuration on the basis of newtonian mechanics. The central difference approximation is used to numerically integrate the equations of motion for every atom in the crystallite simultaneously. The interatomic forces used in solving the equations of motion are obtained from a short-range, semi-empirical atomic interaction function.

The capability of the program for studying defect interactions as a function of relative positions is limited by the size of the computational cell. This, in turn, is limited by computer storage capacity. The largest number of atoms which can be considered in a crystallite is 3500. About half of these are contained in an enveloping mantle of immovable atoms which induces the proper crystal structure and volume cohesive forces. The remainder can be moved arbitrarily and comprise the central portion of the crystallite. This set of movable atoms is called the computational cell.

Unusual features:
A variety of orientations for the defected crystallite are available. Either the axis (linear defect) or the habit plane normal (planar defect) for the extended defect under consideration can be oriented along any one of the directions <100>, <100>, <111> and <112>. The dynamical stability of an equilibrium configuration obtained via the quasi-dynamical method, effectively at absolute zero temperature, can be tested at an arbitrary non-zero temperature by assigning a randomly directed velocity vector to each atom in the computational cell. These randomly directed velocity vectors have a common magnitude determined by the test temperature.

Running time:
The time required on 1108 UNIVAC computer for the construction of a grain boundary and convergence to a structure in which the total internal energy of the system did not vary by more than 0.001 eV was about 10 minutes for a cell containing approximately 2000 atoms. The time for solution is dependent upon the convergence criterion, and is approximately linearly dependent upon the number of movable atoms.