Simulated Martensitic Transformations
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SIMULATED MARTENSITIC TRANSFORMATIONS
P.C. Clapp and J. Rifkin University of Connecticut,
Storrs, Connecticut 06268
ABSTRACT Molecular dynamic computer simulations have recently provided some very graphic portrayals of how model lattices can surmount nucleation barriers of various types and accomplish certain kinds of first order displacive transitions. A survey of the different two-and three-dimensional transformations observed to date, along with relevant details about interatomic potential, potencies of nucleating defects and preferred transformation paths will be presented. The simulation of other types of first order transformation in solids, such as melting and allotropic transformations will be touched upon. Methods by which a close representation of martensitic transformations in real systems should be obtainable will be discussed.
METHOD The motions of the atoms are calculated by integrating the Newtonian equations of motion, with the atom positions and velocities specified at time = 0. The starting positions are chosen to simulate a particular lattice and defect. The velocities are chosen at random but distributed to conform to a Maxwellian distribution at a chosen temperature, and constrained to have zero linear momentum. Integration of the equations of motion was done with a predictor-corrector type algorithm [1]. Algorithms of this type perform the integration in discrete time steps, updating the particle velocities and positions at each step. The motion of the atoms are also bound by two constraints. The first constraint is the periodic boundary condition. Atoms bordering on one face of their container are considered neighbors of those atoms on the opposite face, and any atom passing through one face reappears through its opposite. The second constraint is the temperature clamp. Because these simulations liberate latent heat with phase change it was necessary to remove excess kinetic energy. This was done by scaling the velocities over some time interval so as to bring the temperature to a predetermined limit. In our first attempts we scaled the velocities at each step to keep the instantaneous temperature constant. However we discovered that this created an unwanted high frequency component in the particle velocities. Consequently we have changed our temperature constraint to ease the temperature toward its limit. For example, if a factor (call it EFAC) brings the velocities in agreement with the imposed temperature limit, we instead multiply the velocities by EFAC**(I/33). This has the effect of bringing the instantaneous temperature to our set limit in 33 computational time steps, which is the approximate time of the fastest atomic vibrations. Physically, this cooling can be considered as an extremely rapid radiative heat loss.
INTERATOMIC POTENTIAL It effects Mat.
Res.
is through the interatomic potential that quantum mechanical In our can be included in the otherwise classical hamiltonian.
Soc. Symp. Proc.
Vol.
21
(1984)
Published by Elsevier
Science Publishing Co.,
Inc.
644
simu
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