Cleavage fracture of a crystal: Density functional theory calculations based on a model which includes structural relaxations

Physical Review B - Condensed Matter and Materials Physics

Volumn 78, Issue 10, 2008, Pages

  Lazar, P ^a   Podloucky, R ^b  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^b UNIVERSITY OF VIENNA   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 52949089341     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.104114     Document Type: Article

References (37)

1. A. A. Griffith, Philos. Trans. R. Soc. London, Ser. A PTRMAD 0962-8428 10.1098/rsta.1921.0006 221, 163 (1921).
2. P. Lazar, R. Podloucky, and W. Wolf, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.2149988 87, 261910 (2005).
3. J. H. Rose, J. R. Smith, and J. Ferrante, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.28.1835 28, 1835 (1983).
4. A. Banerjea and J. R. Smith, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.37.6632 37, 6632 (1988).
5. UBER fails for breaking strongly directed bonds, e.g., when cleaving diamond in the [111] direction between planes with the shortest layer-to-layer distance, because of maximum in the Eb curve at large x. This effect is due to reordering of strong covalent bonds. However, compared to other cleavage directions this particular [111] cleavage is highly unfavorable because of its very large stress and energy.
6. P. E. Blöchl, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.50. 17953 50, 17953 (1994).
7. G. Kresse and D. Joubert, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.59.1758 59, 1758 (1999).
8. J. P. Perdew and Y. Wang, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.45.13244 45, 13244 (1992).
9. Y. Le Page and P. Saxe, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.63.174103 63, 174103 (2001).
10. Y. Le Page and P. Saxe, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65.104104 65, 104104 (2002).
11. R. L. Hayes, M. Ortiz, and E. A. Carter, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.69.172104 69, 172104 (2004).
12. O. Nguyen and M. Ortiz, J. Mech. Phys. Solids JMPSA8 0022-5096 10.1016/S0022-5096(01)00133-8 50, 1727 (2002).
13. E. A. A. Jarvis, R. L. Hayes, and E. A. Carter, ChemPhysChem CPCHFT 1439-4235 10.1002/1439-7641(20010119)2:1<55::AID-CPHC55>3.0.CO;2-S 2, 55 (2001).
14. B. Lawn, Fracture of Brittle Solids (Cambridge University Press, New York, 1993).
15. T. Hoshi, Y. Iguchi, and T. Fujiwara, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.075323 72, 075323 (2005).
16. D. Hull, P. Beardmore, and A. P. Valentine, Philos. Mag. PHMAA4 0031-8086 10.1080/14786436508228132 12, 1021 (1965).
17. J. Riedle, P. Gumbsch, H. F. Fischmeister, V. G. Glebovski, and V. N. Semenov, Mater. Lett. MLETDJ 0167-577X 10.1016/0167-577X(94)90036-1 20, 311 (1994).
18. M. Ludwig and P. Gumbsch, Acta Mater. ACMAFD 1359-6454 10.1016/S1359-6454(98)00013-5 46, 3135 (1998).
19. J. H. Schneibel, J. A. Horton, and W. D. Porter, Mater. Sci. Eng., A 152, 126 (1992). 0921-5093
20. P. Lazar and R. Podloucky, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.024112 75, 024112 (2007).
21. K. M. Chang, R. Darolia, and H. A. Lipsitt, Acta Metall. Mater. AMATEB 0956-7151 10.1016/0956-7151(92)90343-D 40, 2727 (1992).
22. R. Darolia, K. M. Chang, and J. E. Hack, Intermetallics IERME5 0966-9795 10.1016/0966-9795(93)90023-O 1, 65 (1993).
23. J. M. Brzeski, J. E. H. R. Darolia, and R. Field, Mater. Sci. Eng., A MSAPE3 0921-5093 10.1016/0921-5093(93)90364-K 170, 11 (1993).
24. S. N. Sun, N. Kioussis, and M. Ciftan, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.54.3074 54, 3074 (1996).
25. J. R. Rice, J. Mech. Phys. Solids JMPSA8 0022-5096 10.1016/S0022-5096(05) 80012-2 40, 239 (1992).
26. P. Lazar and R. Podloucky, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.73.104114 73, 104114 (2006).
27. J. A. Hauch, D. Holland, M. P. Marder, and H. L. Swinney, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.3823 82, 3823 (1999).
28. A. M. Lomonosov and P. Hess, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.095501 89, 095501 (2002).
29. N. Bernstein and D. W. Hess, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.025501 91, 025501 (2003).
30. T. Cramer, A. Wanner, and P. Gumbsch, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.788 85, 788 (2000).
31. A. Mattoni, L. Colombo, and F. Cleri, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.115501 95, 115501 (2005).
32. E. Orowan, Rep. Prog. Phys. RPPHAG 0034-4885 10.1088/0034-4885/12/1/309 12, 185 (1949).
33. J. J. Gilman, in The Strength of Ceramic Crystals, edited by, C. Klingsberg, (Gordon and Breach, New York, 1963), p. 240.
34. S. Sidhu and C. S. Menon, J. Phys. D 34, 465 (2001). 0022-3727
35. In Griffith's paper (Ref.) the surface energy γ= 1 2 G being half of the cleavage energy was utilized. This relation is only valid only for high-symmetry cases for which both cleavage surfaces are equivalent.
36. J. F. Nye, Physical Properties of Crystals (Oxford University Press, Oxford, 1993), e.g., for a cubic crystal the uniaxial rigid modulus C is defined in terms of the three cubic elastic constants c11, c12, c44 and the direction cosines h,k,l by C= c11 -2 (c11 - c12 -2 c44) (h2 k2 + h2 l2 + k2 l2).
37. In Ref. the prefactor was erroneously given as 0.24, because units of Å were used instead of nm. The correct factor is now 0.24 10 =0.75.