Computer simulation of interstitial diffusion in tungsten Page: 3 of 8
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MODEL
The code employs a block of 2 x 93 atons, corresponding co 10 x 10x 10
cubic cells with periodic boundary conditions. Atoms interact through a
pair potential2 which accurately reproduces experimentally measured
phonon dispersion data and reasonably matches thermal expansion, elastic
constant temperature dependence and shock compression data. The shape
of the fundamental unit was varied in test calculations to in-are the
absence of nonphysical boundary effects. Operating the code in a
relaxation mode, the split <110> configuration was found to corresioni
to equilibrium. Statically, an enthalpy of 0.38 el is required for dii-
fusion of the self-interstitial.
A centered first order finite difference scheme is used to solve the
equations of motion in successive time steps. The time step, Lt, is taket.
equal to 1/15 the value of the reciprocal of the maximums lattice vi'zra-
tional frequency v . This time interval is sufficiently larul to
complete the problem in a reasonable period of time, yet small enough to
give accurate results, e.g., one obtains the same 5ump rate by reducing
the time step by a factor of ten.
The system is initialized by giving each atom random velocity compo-
nents and then allowing sufficient time for the entire system to attain
equilibrium. Tne volume is adjusted to maintain constant pressure at
the desired temperature. Calculation of the diffusion coefficient then.
proceeds by recording all changes in position of the split interstitial.
CALCULATION 02 THE DIFFUSION COEFFICIENT
It is difficult to establish the discreteness of a liffu-::: j:p,
since large center of mass motions s occur which do not nccessar~iy giv
rise to diffusion. TBP divided their lattice into "Iigner-Seitz" cells
and defined the cell which contained two atoms longer than one free
period of oscillation as the position of the interstitial. This method
is unsatisfactory, yielding spuriously low values for All, the enthal_:
m
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Guinan, M.W.; Stuart, R.N. & Borg, R.J. Computer simulation of interstitial diffusion in tungsten, report, October 1, 1975; Livermore, California. (https://digital.library.unt.edu/ark:/67531/metadc863247/m1/3/: accessed April 26, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.