Lanczos and recursion techniques for multiscale kinetic Monte Carlo simulations

Progress in Materials Science

Volumn 52, Issue 2-3, 2007, Pages 319-332

  Rudd, Robert E ^a   Mason, D R ^b   Sutton, A P ^b  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; ELASTIC MODULI; ELASTICITY; MICROSTRUCTURE; MONTE CARLO METHODS; RECURSIVE FUNCTIONS;

ANHARMONIC ELASTIC ENERGY; KINETIC MONTE CARLO SIMULATION; VACANCY HOPPING;

MATERIALS SCIENCE;

EID: 33846178215     PISSN: 00796425     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.pmatsci.2006.10.005     Document Type: Review

References (42)

1. Haydock R., Heine V., and Kelly M.J. Electronic structure based on the local atomic environment for tight-binding bands. J Phys C 5 (1972) 2845-2858
2. Haydock R. The recursive solution of the Schrödinger equation. Solid State Phys 35 (1980) 215-294
3. Pettifor D.G. New many-body potential for the bond order. Phys Rev Lett 63 (1989) 2480-2483
4. Pettifor D.G., and Oleinik I.I. Analytic bond-order potentials beyond Tersoff-Brenner I. Theory. Phys Rev B 59 (1999) 8487-8499
5. Mason D.R., Rudd R.E., and Sutton A.P. Atomistic modelling of diffusional phase transformations with elastic strain. J Phys: Condens Matter 16 (2004) S2679-S2697
6. Mason D.R., Rudd R.E., and Sutton A.P. Stochastic kinetic Monte Carlo algorithms for long-range Hamiltonians. Comput Phys Commun 160 (2004) 140-157
7. In: Cahn R.W. (Ed). Physical metallurgy (1970), North-Holland, Amsterdam
8. Rudd R.E., Briggs G.A.D., Sutton A.P., Medieros-Ribiero G., and Williams R.S. Equilibrium model of bimodal distributions of epitaxial island growth. Phys Rev Lett 90 (2003) 146101
9. Rudd R.E., and Broughton J.Q. Concurrent coupling of length scales in solid state systems. Phys Stat Sol (b) 217 (2000) 251-291
10. Mehl RF. The historical development of physical metallurgy. In: Cahn [7], Chapter 1, p. 1-31.
11. Guinier A. Structure of age-hardened Al-Cu alloys. Nature (London) 142 (1938) 569-570
12. Preston G.D. The diffraction of X-rays by age-hardening aluminium copper alloys. Proc Roy Soc A 167 (1938) 526-538
13. Nabarro F.R.N. The strains produced by precipitation in alloys. Proc Roy Soc London A 175 (1940) 519-538
14. Cohen J.B. The internal structure of Guinier-Preston zones in alloys. Solid State Phys 39 (1986) 131-206
15. Wang S.C., and Starink M.J. Precipitates and intermetallic phases in precipitation hardening Al-Cu-Mg-(Li) based alloys. Int Mater Rev 50 (2005) 193-215
16. Gerold V. On the structure of GP zones in Al-Cu alloys. Scr Met 22 (1988) 927-932
17. Silcock J.M., Heal T.J., and Hardy H.K. Structural aging characteristics of binary aluminium-copper alloys. J Inst Met 82 (1954) 239-248
18. Hardy H.K. The ageing characteristics of some ternary Al-Cu-Mg alloys with Cu:Mg weight ratios of 7:1 and 2.2:1. J Inst Met 84 (1954) 17-34
19. Yoshida H., Cockayne D.J.H., and Whelan M.J. Study of Guinier-Preston zones in aluminum-copper alloys using weak-beam technique of electron-microscopy. Philos Mag 34 (1976) 89-100
20. Konno J., Kawasaki M., and Hiraga K. Direct imaging of Guinier-Preston zones by high-angle annular detector dark-field scanning transmission electron microscopy. J Electron Microsc 50 (2001) 105-111
21. Hono K. Nanoscale microstructural analysis of metallic materials by atom probe field ion microscopy. Prog Mater Sci 47 (2002) 621-729
22. Ringer S.P., Hono K., and Sakurai T. The effect of trace additions of sn on precipitation in Al-Cu alloys: an atom probe field ion microscopy study. Metall Mater Trans A 26 (1995) 2207-2217
23. Gao N., Davin L., Wang S., Cerezo A., and Starink M.J. Precipitation in stretched Al-Cu-Mg alloys with reduced alloying content studied by DSC, TEM and atom probe. Mater Sci Forum 396-402 (2002) 923-928
24. Khachaturyan A.G. Theory of structural transformations in solids (1983), Wiley, New York
25. Khachaturyan A.G., Semenovskaya S., and Tsakalakos T. Elastic strain energy of inhomogeneous solids. Phys Rev B 52 (1995) 15909-15919
26. Rautiainen T.T., and Sutton A.P. Influence of the atomic diffusion mechanism on morphologies, kinetics, and the mechanisms of coarsening during phase separation. Phys Rev B 59 (1999) 13681-13692
27. Flynn C.P. Point defects and diffusion (1972), Clarendon Press, Oxford
28. Wolverton C. First-principles theory of 250,000-atom coherent alloy micro-structure. Modell Simul Mater Sci Eng 8 (2000) 323-333
29. Wang J., Wolverton C., Müller S., Liu Z.-K., and Chen L.-Q. First-principles growth kinetics and morphological evolution of Cu nanoscale particles in Al. Acta Mater 53 (2005) 2759-2764
30. Ravi C., and Wolverton C. First-principles study of crystal structure and stability of Al-Mg-Si-(Cu) precipitates. Acta Mater 52 (2004) 4213-4227
31. Finnis M.W., and Sinclair J.E. A simple empirical n-body potential for transition metals. Philos Mag A 50 (1984) 45-55
32. Sutton A.P., and Chen J. Long-range Finnis-Sinclair potentials. Philos Mag Lett 63 (1991) 217-224
33. Allen M.P., and Tildesley D.J. Computer simulation of liquids (1987), Clarendon Press, Oxford
34. Lanczos C. An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J Res Natl Bur Stand 45 (1950) 255-282
35. Saad Y. Iterative methods for sparse linear systems (1996), PWS, Boston
36. Press W.H., Teukolsky S.A., Vetterling W.T., and Flannery B.P. Numerical recipes in Fortran. 2nd ed. (1992), Cambridge University Press, Cambridge
37. Bortz A.B., Kalos M.H., and Lebowitz J.L. A new algorithm for Monte Carlo simulation of Ising spin systems. J Comput Phys 17 (1975) 10-18
38. Fichthorn K.A., and Weinberg W.H. Theoretical foundations of dynamical Monte Carlo simulations. J Chem Phys 95 (1991) 1090-1096
39. Athènes M., Bellon P., and Martin G. Identification of novel diffusion cycles in B ordered phases by Monte Carlo simulation. Philos Mag A 76 (1997) 565-585
40. Mason D.R., Hudson T.S., and Sutton A.P. Fast recall of state history in kinetic Monte Carlo simulations utilizing the Zobrist key. Comput Phys Commun 165 (2005) 37-48
41. Eshelby J.D. The elastic field outside an ellipsoidal inclusion. Proc Roy Soc A 252 (1959) 561-569
42. Misner C.W., Thorne K.S., and Wheeler J.A. Gravitation (1973), W.H. Freeman, San Francisco Section 32.7