Beyond Pair Potentials in Elemental Transition Metals and Semiconductors

Solid State Physics - Advances in Research and Applications

Volumn 43, Issue C, 1990, Pages 1-91

  Carlsson, A E ^a  

^a WASHINGTON UNIVERSITY   (United States)

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EID: 0039682810     PISSN: 00811947     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0081-1947(08)60323-9     Document Type: Article

References (217)

1. Ashcroft, N.W., Mermin, N.D., Chapter 32. “Solid State Physics,”, 1976, Holt, Rinehart, and Winston, New York.
2. Kittel, C., Chapter 8. “Quantum Theory of Solids,”, second edition, 1987, Wiley, New York.
3. Fuchs, K., Proc. R. Soc. London, Ser. A, 153, 1936, 622 A very early attempt was made by.
4. Ziman, J.M., Chapter 5. “Electrons and Phonons,”, 1960, Oxford University Press, Oxford.
5. However, in semiconductors and insulators, electrons at isolated defects can sometimes remain in excited-state configurations for times long in comparison with typical time scales for ionic motion, invalidating a ground-state description. This issue will be discussed in Section 12.
6. Heine, V., Weaire, D., Ehrenreich, H., Seitz, F., Turnbuil, D., (eds.) “Solid State Physics, Advances in Research and Applications”, 24, 1970, Academic, New York, 250.
7. Car, R., Parrinello, M., Phys. Rev. Lett., 55, 1985, 2471 “Simulated annealing” is a promising technique for ab initio materials studies. See.
8. A widely ranging collection of articles on interatomic forces in condensed matter is found. Philos. Mag. A, 58(1), 1988.
9. Finnis, M.W., Paxton, A.T., Pettifor, D.G., Sutton, A.P., Ohta, Y., Philos. Mag. A, 58, 1988, 143 Simplified energy functional for transition metals are discussed in.
10. Stoneham, A.M., Torres, V.T.B., Masri, P.M., Schober, H.R., Philos. Mag. A, 58, 1988, 93 “Angular forces in semiconductors are reviewed by.
11. Haliocioglu, T., Pamuk, H.O., Erkoc, S., Phys. Stat. Sol. B, 149, 1988, 81.
12. Pettifor, D.G., Cahn, R.W., Haasen, P., (eds.) “Physical Metallurgy,”, 1983, North-Holland, New York, 73 An extensive treatment of bonding in metals is given by.
13. Heine, V., Ehrenreich, H., Seitz, F., Turnbull, D., (eds.) “Solid State Physics, Advances in Research and Applications”, 35, 1980, Academic, New York, 1 Some closely related aspects of transition metal bonding are discussed by.
14. Taylor, R., Physica, 131B, 1985, 103.
15. Torrens, I.M., “Interatomic Potentials.”, 1972, Academic, New York A broadly based discussion of interatomic potentials is given in.
16. Hafner, J., “From Hamiltonians to Phase Diagrams—The Electronic and Statistical Mechanical Theory of Metals and Alloys,” Solid State Sciences, 70, 1987, Springer, Berlin.
17. Lee, J.K., (eds.) “Interatomic Potentials and Lattice Defects”, 1981, Metallurgical Society of AIME, Warrendale, PA.
18. See, in particular, articles by J. Th. M. de Hosson (p. 3), E. S. Machlin (p. 33), D. M. Esterling (p. 53), and R. Taylor (p. 71).
19. Harrison, W.A., Chap. 13. “Electronic Structure and the Properties of Solids,”, 1980, W. H. Freeman, San Francisco.
20. Catlow, C.R.A., Freeman, C.M., Islam, M.S., Jackson, R.A., Leslie, M., Tomlinson, S.M., Philos. Mag. A, 58, 1988, 123.
21. Gordon, R.G., Kim, Y.S., J. Chem. Phys., 56, 1972, 3122.
22. Dalgarno, A., Davison, W.D., Adv. At. Mol. Phys., 2, 1966, 1.
23. van Schilfgaarde, M., Harrison, W.A., Phys. Rev. B, 33, 1986, 2653.
24. Gehlen, P.C., Beeler, J.R., Jaffee, R.I., (eds.) “Interatomic Potentials and the Simulation of Lattice Defects”, 1972, Plenum, New York.
25. Johnson, R.A., J. Phys. F, 3, 1973, 295.
26. Haydock, R., J. Phys. F, 17, 1987, 87 See articles by (p. 216) and M. J. Kelley (p. 296), in Ref. 12. Simplified versions of these methods are described in D. M. Esterling, D. K. Som, A. K. Chatterjee, and I. M. Boswarva.
27. Kittel, C., “Introduction to Solid State Physics,”, sixth edition, 1986, Wiley, New York, 55.
28. Seeger, A., Mehrer, H., Seeger, A., Schumacher, D., Schilling, W., Diehl, J., (eds.) “Vacancies and Interstitials in Metals”, 1970, North-Holland, Amsterdam, 1.
29. Weast, R.C., Astle, M.J., Beyer, W.H., (eds.) “CRC Handbook of Chemistry and Physics”, 1987, CRC Press, Boca Raton, Florida, F-172.
30. Tersoff, J., Phys. Rev. B, 37, 1988, 6991.
31. Flynn, C.P., “Point Defects and Diffusion,”, 1972, Clarendon, Oxford, 6.
32. Johnson, R.A., Phys. Rev. B, 6, 1972, 2094 “Extended” Cauchy relations can also be derived from radial pair potentials. See.
33. Cousins, C.S.G., Martin, J.W., J. Phys. F, 8, 1978, 2279.
34. Åslund, N., Barrow, R.F., Richards, W.G., Travis, D.N., Ark. Fys., 30, 1965, 171.
35. Carlsson, A.E., Gelatt, C.D., Ehrenreich, H., Philos. Mag., 41, 1980, 241.
36. Johnson, R.A., Radial. Eff., 2, 1969, 1.
37. Esterling, D.M., Swaroop, A., Phys. Status Solidi, 96, 1979, 401.
38. Carlsson, A.E., Ashcroft, N.W., Phys. Rev. B, 27, 1983, 2101.
39. Matthai, C.C., Grout, P.J., March, N.H., J. Phys. Chem. Solids, 42, 1981, 317 Another underlying physical picture that has been used to generate interatomic potentials is the “bond charge” model. It has been applied to both transition metals.
40. Phillips, J.C., Phys. Rev., 166, 1968, 832 and semiconductors [Ref. 17, Chap. 9;.
41. Martin, R.M., Phys. Rev., 186, 1969, 871 We do not treat these methods here because they have not been developed to the point that they can be used in atomistic simulations.
42. Harrison, W.A., “Pseudopotentials in the Theory of Metals,”, 1966, Benjamin, New York.
43. N.W. Ashcroft Ref. 23, p. 91.
44. Finnis, M.W., J. Phys. F, 4, 1974, 1645.
45. Rasolt, M., Taylor, R., Phys. Rev. B, 11, 1975, 2717 Some higher-order contributions can also be included in pair schemes such as these. See.
46. Harrison, R.J., Surf. Sci., 144, 1984, 215.
47. Manninen, M., Jena, P., Nieminen, R.M., Lee, J.K., Phys. Rev. B, 24, 1981, 7507 Even for Al, generally regarded as a very free-electron-like metal, vacancy formation energies are obtained poorly by constant-volume potentials. See.
48. Harrison, W.A., Phys. Rev., 181, 1969, 1036.
49. Moriarty, J.A., Phys. Rev. B, 5, 1972, 2066.
50. Moriarty, J.A., Phys. Rev. B, 16, 1977, 2537.
51. Moriarty, J.A., Phys. Rev. B, 26, 1982, 1754.
52. Dagens, L., J. Phys. F, 6, 1976, 1801.
53. Dagens, L., Phys. Status Solidi, 84, 1977, 311.
54. Dagens, L., J. Phys. F, 7, 1977, 1167.
55. Upadhyaya, J.C., Dagens, L., J. Phys. F, 8, 1978, L21.
56. Upadhyaya, J.C., Dagens, L., J. Phys. F, 9, 1979, 2177.
57. Lam, N.Q., Dagens, L., Doan, N.V., J. Phys. F, 13, 1983, 2503.
58. Wills, M., Harrison, W.A., Phys. Rev. B, 28, 1983, 4363.
59. Phys. Rev. B, 29, 1984, 5486.
60. Hausleitner, C., Hafner, J., J. Phys. F, 18, 1988, 1025.
61. Moriarty, J.A., Phys. Rev. Lett., 55, 1985, 1502.
62. Moriarty, J.A., Phys. Rev. B, 38, 1988, 3199.
63. Cyrot-Lackmann, F., J. Phys. Chem. Solids, 29, 1968, 1235.
64. Cyrot-Lackmann, F., Surf. Sci., 15, 1969, 535.
65. Ducastelle, F., J. Phys. (Paris), 31, 1970, 1055.
66. Friedel, J., Chap. 8. Ziman, J., (eds.) “The Physics of Metals”, 1969, Cambridge University Press.
67. Gelatt, C.D. Jr., Ehrenreich, H., Watson, R.E., Phys. Rev. B, 15, 1977, 1613.
68. Pettifor, D.G., J. Phys. F, 8, 1978, 219.
69. Phillips, J.C., “Bonds and Bonds in Semiconductors.”, 1973, Academic, New York.
70. Ackland, G.J., Finnis, M.W., Vitek, V., J. Phys. F, 18, 1988, L153 To obtain Eq. (5.6) for arbitrary band fillings, it is necessary to assume a fixed electronic charge per atom. See.
71. Pettifor, D.G., Phys. Rev. Lett., 42, 1979, 846.
72. Allan, G., Ann. Phys. (Paris), 5, 1970, 169.
73. Abell, G.C., Phys. Rev. B, 31, 1985, 6184 The weakening of the bond strength with increasing coordination number has also been discussed by.
74. Sutton, A.P., Finnis, M.W., Pettifor, D.G., Ohta, Y., J. Phys. C, 21, 1988, 35.
75. Ohta, Y., Finnis, M.W., Pettifor, D.G., Sutton, A.P., J. Phys. F, 17, 1987, L273.
76. NøSrskov, J.K., Lang, N.D., Phys. Rev. B, 21, 1980, 2131.
77. Stott, M., Zaremba, E., Phys. Rev. B, 22, 1980, 1564.
78. Puska, M.J., Nieminen, R.M., Manninen, M., Phys. Rev. B, 24, 1982, 3037.
79. NøSrskov, J.K., Phys. Rev., 26, 1982, 2875.
80. Manninen, M., Phys. Rev. B, 34, 1986, 8486.
81. Jacobsen, K.W., NøSrskov, J.K., Puska, M.J., Phys. Rev. B, 35, 1987, 7423.
82. Daw, M.S., Baskes, M.I., Phys. Rev. Lett., 50, 1983, 1285.
83. Daw, M.S., Baskes, M.I., Phys. Rev. B, 29, 1984, 6443.
84. Moruzzi, V.L., Janak, J.F., Williams, A.R., Chapter 3. “Calculated Electronic Properties of Metals,”, 1978, Pergamon, New York.
85. Kohn, W., Sham, L.J., Phys. Rev., 140, 1965, A1133.
86. Tersoff, J., Cardillo, M.J., Hamann, D.R., Phys. Rev. B, 32, 1985, 5044 [For example, quantum-mechanical calculations for a variety of metal and semiconductor surfaces have shown that corrugations in the charge density are well reproduced by superposing atomic charge densities, at least if the surface layer atoms are equivalent. However, asymmetric Si reconstructions are treated poorly [A. Sakai, M. J. Cardillo, and D. R. Hamann (unpublished), quoted by Tersoff et al. (above)].
87. Foiles, S.M., Baskes, M.I., Daw, M.S., Phys. Rev. B, 33, 1986, 7983.
88. Phys. Rev. B, 37, 1988, 10378.
89. Finnis, M.W., Sinclair, J.M., Philos. Mag. A, 50, 1984, 45.
90. Philos. Mag. A, 53, 1986, 161.
91. Foiles, S.M., Phys. Rev. B, 32, 1985, 3409.
92. Carlsson, A.E., Phys. Rev. B, 32, 1985, 4866.
93. Carlsson, A.E., Farkas, D., Dyment, F., (eds.) “Alloy Theory and Phase Equilibria,”, 1986, American Society for Metals, Metals Park, Ohio, 103.
94. Hirai, K., Kanamori, J., J. Phys. Soc. Jpn., 50, 1981, 2265.
95. Jaynes, E.T., Phys. Rev., 106, 1957, 620.
96. Phys. Rev., 108, 1957, 171.
97. Mead, L.R., Papanicolaou, N., J. Math. Phys., 25, 1984, 2404.
98. Collins, R., Wragg, A., J. Phys. A, 10, 1977, 1441.
99. Brown, R.H., Carlsson, A.E., Phys. Rev. B, 32, 1985, 6125.
100. Ducastelle, F., Cyrot-Lackmann, F., J. Phys. Chem. Solids, 31, 1970, 1295.
101. Ducastelle, F., Cyrot-Lackmann, F., J. Phys. Chem. Solids, 32, 1971, 285.
102. Turchi, P., Ducastelle, F., Pettifor, D.G., Weaire, D.L., (eds.) “The Recursion Method and Its Applications”, 1985, Springer, New York, 104.
103. A.E. Carlsson (unpublished).
104. Pettifor, D.G., J. Phys. C, 3, 1970, 367.
105. Andersen, O.K., Madsen, J., Poulsen, U.K., Jepsen, O., Kollar, J., Physica, 86–88B, 1977, 249.
106. Heine, V., Samson, J.H., J. Phys. F, 10, 1980, 2609.
107. Heine, V., Samson, J.H., J. Phys. F, 13, 1983, 2155.
108. Ref. 26, p. 284.
109. R.B. Phillips A.E. Carlsson (unpublished).
110. Dagens, L., Phys. Lett., 101A, 1984, 283.
111. Dagens, L., J. Phys. F, 16, 1986, 1705.
112. Carlsson, A.E., Phys. Rev. Lett., 59, 1987, 1108.
113. Macdonald, A.H., Taylor, R., Can. J. Phys., 62, 1984, 796.
114. Lam, N.Q., Dagens, L., J. Phys. F, 16, 1986, 1373.
115. Sanchez, J.M., Ducastelle, F., Gratias, D., Physica, 128A, 1984, 334.
116. Carlsson, A.E., Phys. Rev. B, 35, 1987, 4858.
117. Ducastelle, F., Gautier, F., J. Phys. F, 6, 1976, 2039.
118. Bieber, A., Gautier, F., Acta Metall., 35, 1987, 1839.
119. Stocks, G.M., Nicholson, D.M., Pinski, F.J., Butler, W.H., Sterne, P., Temmerman, W.M., Gyorffy, B.L., Johnson, D.D., Gonis, A., Zhang, X.-G., Turchi, P.E.A., Stoloff, N.S., Koch, C.C., Liu, C.T., Izumi, O., (eds.) “High-Temperature Ordered Alloys”, 1987, Materials Research Society, Pittsburgh, 15.
120. Gonis, A., Stocks, G.M., Butler, W.H., Winter, H., Phys. Rev. B, 29, 1984, 555.
121. Connolly, J.W.D., Williams, A.R., Phys. Rev. B, 27, 1983, 5168.
122. Andersen, O.K., Jepsen, O., Phys. Rev. Lett., 53, 1984, 257.
123. Andersen, O.K., Pawlowska, Z., Jepsen, O., Phys. Rev. B, 34, 1986, 5253.
124. Ackland, G.J., Tichy, G., Vitek, V., Finnis, M.W., Philos. Mag. A, 56, 1987, 735.
125. Matthai, C.C., Bacon, D.J., Philos. Mag. A, 52, 1985, 1.
126. Harder, J.M., Bacon, D.J., Philos. Mag. A, 54, 1986, 651.
127. Oh, D.J., Johnson, R.A., J. Mater. Res., 3, 1988, 471.
128. Johnson, R.A., Phys. Rev. B, 37, 1988, 3924.
129. Phys. Rev. B, 37, 1988, 6121.
130. Masuda, K., J. Phys. (Paris), 43, 1982, 921.
131. Maysenhölder, W., Philos. Mag. A, 53, 1986, 783.
132. Rebonato, R., Welch, D.O., Hatcher, R.D., Bilello, J.C., Philos. Mag. A, 55, 1987, 655.
133. Ackland, G.J., Finnis, M.W., Philos. Mag. A, 54, 1986, 301.
134. Shuttleworth, R., Proc. Phys. Soc. A, 62, 1949, 167.
135. Proc. R. Soc. London, Ser. A, 63, 1950, 444.
136. Bikerman, J.J., Phys. Status Solidi, 10, 1965, 3.
137. Zangwill, A., Chap. 1. “Physics at Surfaces,”, 1988, Cambridge, New York.
138. Chen, S.P., Voter, A.F., Srolovitz, D.J., Phys. Rev. Lett., 57, 1986, 1308.
139. Masuda, K., Phys. Status Solidi B, 105, 1981, K119.
140. Foiles, S.M., Surf. Sci., 191, 1987, L779 and references therein.
141. Daw, M.S., Foiles, S.M., Phys. Rev. Lett., 59, 1987, 2756.
142. Dodson, B.W., Phys. Rev. B, 35, 1987, 880.
143. Dodson, B.W., Phys. Rev. Lett., 60, 1988, 2288.
144. Ercolessi, F., Tosatti, E., Phys. Rev. Lett., 57, 1986, 719.
145. Ercolessi, F., Parrinello, M., Tosatti, E., Philos. Mag. A, 58, 1988, 213.
146. Gollisch, H., Surf. Sci., 166, 1986, 87.
147. J.N. Schmit Ph.D. Thesis, University of Liege (unpublished). (Quoted in Ref. 132.).
148. A.E. Carlsson (unpublished).
149. Benedek, R., J. Phys. F, 8, 1978, 1119.
150. Ref. 132, p. 62.
151. Tomanek, D., Bennemann, K.H., Surf. Sci., 163, 1985, 503.
152. Moritz, W., Wolf, D., Surf. Sci., 163, 1985, L655.
153. Chan, C.M., Van Hove, M.A., Surf. Sci., 171, 1986, 226.
154. Felter, T., Barker, R.A., Estrup, P.J., Phys. Rev. Lett., 38, 1977, 1138.
155. Fu, C.L., Freeman, A.J., Wimmer, E., Weinert, M., Phys. Rev. Lett., 54, 1985, 2261.
156. Daw, M.S., Hatcher, R.L., Solid State Commun., 56, 1985, 697.
157. Garrison, B.J., Winograd, N., Deaven, D.M., Reimann, C.T., Lo, D.Y., Tombrello, T.A., Harrison, D.E. Jr., Shapiro, M.H., Phys. Rev. B, 37, 1988, 7197.
158. Sato, A.K., Masuda, K., Philos. Mag. B, 43, 1981, 1.
159. Oh, Y., Vitek, V., Acta. Metall., 34, 1986, 1941.
160. Harder, J.M., Bacon, D.J., Philos. Mag. A, 58, 1988, 165.
161. Ackland, G.J., Thetford, R., Philos. Mag. A, 56, 1987, 15.
162. Aryasetiawan, F., Silbert, M., Stott, M.J., J. Phys. F, 16, 1986, 1419.
163. A.E. Carlsson (unpublished).
164. Masuda, K., Yamamoto, R., Doyama, M., J. Phys. F, 13, 1983, 1407.
165. Stillinger, F.H., Weber, T.A., LaViolette, R.A., J. Chem. Phys., 85, 1986, 6460.
166. Pearson, E., Takai, T., Halicioglu, T., Tiller, W.A., J. Cryst. Growth, 70, 1984, 33.
167. Choi, D.K., Sakai, T., Erkoc, S., Halicioglu, T., Tiller, W.A., J. Cryst. Growth, 85, 1987, 9.
168. Ding, K., Andersen, H.C., Phys. Rev. B, 34, 1986, 6987.
169. Biswas, R., Hamann, D.R., Phys. Rev. B, 36, 1987, 6434.
170. Lannoo, M., Bourgoin, J., Chap. 4. “Point Defects in Semiconductors I,”, 1981, Springer, New York.
171. Bourgoin, J., Lannoo, M., Chapters 2 and 3. “Point Defects in Semiconductors II,”, 1983, Springer, New York.
172. Zunger, A., Ehrenreich, H., Turnbull, D., (eds.) “Solid State Physics: Advances in Research and Applications”, 1986, Academic, New York, 275.
173. Keating, P.N., Phys. Rev., 145, 1966, 637.
174. Kane, E.O., Phys. Rev. B, 31, 1985, 7865.
175. Jones, R., J. Phys. C, 20, 1987, L271.
176. Stillinger, F.H., Weber, T.A., Phys. Rev. B, 31, 1985, 5262.
177. Biswas, R., Hamann, D.R., Phys. Rev. Lett., 55, 1985, 2001.
178. Brenner, D.W., Garrison, B.J., Phys. Rev. B, 34, 1986, 1304.
179. Axilrod, B.M., Teller, E., J. Chem. Phys., 11, 1943, 299.
180. A.E. Carlsson Atomistic Modeling of Materials: Beyond Pair Potentials, edited by V. Vitek and D. R. Srolovitz (Plenum, New York, in press).
181. Cowley, E.R., Phys. Rev. Lett., 60, 1988, 2379.
182. Batra, I.P., Abraham, F.F., Phys. Rev. B, 35, 1987, 9552.
183. Dodson, B.W., Phys. Rev. B, 33, 1986, 7361.
184. Blaisen-Baroja, E., Levesque, D., Phys. Rev. B, 34, 1986, 3910.
185. Feuston, B.P., Kalia, R.K., Vashishta, P., Phys. Rev. B, 35, 1987, 6222.
186. Abraham, F.F., Batra, I.P., Surf. Sci., 163, 1985, L752.
187. Takai, T., Halicioglu, T., Tiller, W.A., Surf. Sci., 164, 1985, 341.
188. Schneider, M., Schuller, I.K., Rahman, A., Phys. Rev. B, 36, 1987, 1340.
189. Gawlinski, E.T., Gunton, J.D., Phys. Rev. B, 36, 1987, 4774.
190. Khor, K.E., Das Sarma, S., Phys. Rev. B, 36, 1987, 7733.
191. Balamane, H., Halicioglu, T., Tiller, W.A., J. Cryst. Growth, 85, 1987, 16.
192. Pearson, E.M., Halicioglu, T., Tiller, W.A., J. Cryst. Growth, 83, 1987, 502.
193. Abraham, F.F., Broughton, J.O., Phys. Rev. Lett., 56, 1986, 734.
194. Broughton, J.Q., Abraham, F.F., J. Cryst. Growth, 75, 1986, 613.
195. Landman, U., Luedtke, W.D., Cleveland, C.L., Ribarsky, M.W., Arnold, E., Ramesh, S., Baumgart, H., Martinez, A., Khan, B., Phys. Rev. Lett., 56, 1986, 155.
196. Landman, U., Luedtke, W.D., Ribarsky, M.W., Barnett, R.N., Cleveland, C.L., Phys. Rev. B, 37, 1988, 4637.
197. Luedtke, W.D., Landman, U., Ribarsky, M.W., Barnett, R.N., Cleveland, C.L., Phys. Rev. B, 37, 1988, 4647.
198. Dodson, B.W., Taylor, P.A., Appl. Phys. Lett., 49, 1986, 642.
199. Kluge, M.D., Ray, J.R., J. Chem. Phys., 85, 1986, 4028.
200. Broughton, J.Q., Li, X.P., Phys. Rev. B, 35, 1987, 9120.
201. Kluge, M.D., Ray, J.R., Rahman, A., Phys. Rev. B, 36, 1987, 4234.
202. Biswas, R., Grest, G.S., Soukoulis, C.M., Phys. Rev. B, 36, 1987, 7437.
203. Luedtke, W.D., Landman, U., Phys. Rev. B, 37, 1988, 4656.
204. Takai, T., Halicioglu, T., Tiller, W.A., Scr. Metall., 19, 1985, 709.
205. Yin, M.T., Cohen, M.L., Phys. Rev. B, 26, 1982, 5668.
206. Phys. Rev. Lett., 45, 1980, 1004.
207. Pandey, K.C., Phys. Rev. Lett., 49, 1982, 223.
208. Raghavachari, K., Logovinsky, V., Phys. Rev. Lett., 55, 1985, 2853.
209. Tomanek, D., Schlüter, M., Phys. Rev. Lett., 56, 1986, 1055.
210. Zallen, R., Chap. 6. “The Physics of Amorphous Solids,”, 1983, Wiley, New York An estimate of 0.1%, on the basis of electron-spin-resonance experiments, is probably more accurate. See.
211. Car, R., Parrinello, M., Phys. Rev. Lett., 60, 1988, 204.
212. Tersoff, J., Phys. Rev. Lett., 56, 1986, 632.
213. Tersoff, J., Phys. Rev. B, 38, 1988, 9902.
214. Dodson, B.W., Phys. Rev. B, 35, 1987, 2795.
215. Khor, K.E., Das Sarma, S., Phys. Rev. B, 38, 1988, 3318.
216. Baskes, M.I., Phys. Rev. Lett., 59, 1987, 2666.
217. Kelires, P., Tersoff, J., Phys. Rev. Lett., 61, 1988, 562.