1. See articles in “Structure and Properties of Internal Interfaces”, ed. by Ruhle, M., Baluffi, R.W., Fischmeister, H. and Sass, S.L., J. de Physique
46, C–4 (1985).
Majid, I., Bristowe, P.D. and Baluffi, R.W., Phys. Rev. B
40, 2779 (1989).
Bourret, A. and Bacmann, J.J., Revue Phys. Appl.
22, 563 (1987).
Grovenor, C.R.M., J. Phys. C: Solid State Phys.
18, 4079 (1985).
5. See papers in “Interface Science and Engineering '87”, J. de Physique Colloque, 49, C5 (1988).
6. See papers in “Polycrystalline Semiconductors”, Springer Proceedings in Physics, Vol. 35 (1989).
Car, R. and Parrinello, M., Phys. Rev. Lett.
55, 2471 (1985).
Payne, M.C., Joannopoulos, J.D., Allan, D.C., Teter, M.P. and Vanderbilt, D.H., Phys. Rev. Lett.
56, 2656 (1986).
Starkloff, Th. and Joannopoulos, J.D., Phys. Rev. B
16, 5212 (1977).
10. It is important to assert the validity of the size of the force cutoff, since different criteria are used in different types of calculations. Our 0.1 eV/Å is used among those performing ab-initio calculations while 10−5 eV/Å is commonly used in empirical calculations such as the embedded atom scheme. One can estimate the equivalent error in the total energy as follows. The energy gain in the harmonic approximation is 1/2kx2 and the force is kx where x is the (unknown) displacement from the equilibrium position. That means that the energy can be written in terms of the force two ways: E = (1/2)F2/k and E = (1/2)Fx. The smallest force constant that is likely to occur is about 0.5 eV/Å coming from bond bending and the largest x that is even remotely likely to occur once we are close to convergence is 0.5Å. We can now make two different estimates of the energy convergence resulting from a force smaller than 0.1 eV/Å: E < 0.01 eV and E < 0.025 eV. The error is smaller of the two. Using the worst case scenario in which all the atoms in the cell have the maximal force we find that the error arising from the non-zero forces is smaller than 3.8 meV/Å2.
Payne, M.C., Bristowe, P.D. and Joannopoulos, J.D., J. de Physique Colloque
49, C5–151 (1988).
Bourret, A. and Rouviere, J.L., Centre d'Etudes Nucleaire de Grenoble preprint.
Thomson, R.E. and Chadi, D.J., Phys. Rev. B
29, 889 (1984).
DiVincenzo, D.P., Alerhand, O.L., Schluter, M. and Wilkins, J.W., Phys. Rev. Lett.
56, 1925 (1986).
Chou, M.Y., Cohen, M.L., and Louie, S.G., Phys. Rev. B