A mesoscopic model of a two-dimensional solid state structural transformation: Statics and dynamics

Journal of Physics Condensed Matter

Volumn 16, Issue 43, 2004, Pages 7733-7752

  Rao, Madan ^a,b   Sengupta, Surajit ^c  

^a RAMAN RESEARCH INSTITUTE   (India)

^b TATA INSTITUTE OF FUNDAMENTAL RESEARCH   (India)

^c S N BOSE NATIONAL CENTRE FOR BASIC SCIENCES   (India)

Author keywords

[No Author keywords available]

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); HAMILTONIANS; MATHEMATICAL MODELS; MICROSTRUCTURE; QUANTUM THEORY; QUENCHING; TENSORS; THERMODYNAMICS;

LATTICE SPACING; SOLID STATE TRANSFORMATION; STRUCTURAL TRANSITION;

SOLID STATE DEVICE STRUCTURES;

EID: 9144240140     PISSN: 09538984     EISSN: None     Source Type: Journal    
DOI: 10.1088/0953-8984/16/43/013     Document Type: Article

References (53)

1. Khachaturyan A G 1983 The Theory of Structural Transformations in Solids (New York: Wiley) Olson G B and Owen W S (ed) 1992 Martensite (Metals Park, OH: American Society of Metals)
2. Khachaturyan A G 1983 The Theory of Structural Transformations in Solids (New York: Wiley) Olson G B and Owen W S (ed) 1992 Martensite (Metals Park, OH: American Society of Metals)
3. Metals Handbook 1973 (Metals Park, OH: American Society of Metals)
4. Rao M and Sengupta S 2003 Phys. Rev. Lett. 91 045502
5. Jacobs A E 1985 Phys. Rev. B 31 5984 Kartha S, Castán T, Krumhansl J A and Sethna J P 1991 Phys. Rev. Lett. 67 3630 Kartha S, Krumhansl J A, Sethna J P and Wickham L K 1995 Phys. Rev. B 52 803 Onuki A 1999 J. Phys. Soc. Japan 68 5 Shenoy S R, Lookman T, Saxena A and Bishop A R 1999 Phys. Rev. B 60 12537
6. Jacobs A E 1985 Phys. Rev. B 31 5984 Kartha S, Castán T, Krumhansl J A and Sethna J P 1991 Phys. Rev. Lett. 67 3630 Kartha S, Krumhansl J A, Sethna J P and Wickham L K 1995 Phys. Rev. B 52 803 Onuki A 1999 J. Phys. Soc. Japan 68 5 Shenoy S R, Lookman T, Saxena A and Bishop A R 1999 Phys. Rev. B 60 12537
7. Jacobs A E 1985 Phys. Rev. B 31 5984 Kartha S, Castán T, Krumhansl J A and Sethna J P 1991 Phys. Rev. Lett. 67 3630 Kartha S, Krumhansl J A, Sethna J P and Wickham L K 1995 Phys. Rev. B 52 803 Onuki A 1999 J. Phys. Soc. Japan 68 5 Shenoy S R, Lookman T, Saxena A and Bishop A R 1999 Phys. Rev. B 60 12537
8. Jacobs A E 1985 Phys. Rev. B 31 5984 Kartha S, Castán T, Krumhansl J A and Sethna J P 1991 Phys. Rev. Lett. 67 3630 Kartha S, Krumhansl J A, Sethna J P and Wickham L K 1995 Phys. Rev. B 52 803 Onuki A 1999 J. Phys. Soc. Japan 68 5 Shenoy S R, Lookman T, Saxena A and Bishop A R 1999 Phys. Rev. B 60 12537
9. Jacobs A E 1985 Phys. Rev. B 31 5984 Kartha S, Castán T, Krumhansl J A and Sethna J P 1991 Phys. Rev. Lett. 67 3630 Kartha S, Krumhansl J A, Sethna J P and Wickham L K 1995 Phys. Rev. B 52 803 Onuki A 1999 J. Phys. Soc. Japan 68 5 Shenoy S R, Lookman T, Saxena A and Bishop A R 1999 Phys. Rev. B 60 12537
10. King A H and Zhu Y 1993 Phil. Mag. A 67 1037 Zhu Y, Suenaga M and Tafto J 1993 Phil. Mag. A 67 1057 Chu C 1993 PhD Thesis Univ. Minnesota
11. King A H and Zhu Y 1993 Phil. Mag. A 67 1037 Zhu Y, Suenaga M and Tafto J 1993 Phil. Mag. A 67 1057 Chu C 1993 PhD Thesis Univ. Minnesota
12. King A H and Zhu Y 1993 Phil. Mag. A 67 1037 Zhu Y, Suenaga M and Tafto J 1993 Phil. Mag. A 67 1057 Chu C 1993 PhD Thesis Univ. Minnesota
13. Sankararaman S and Shankar R 2003 Phys. Rev. B 67 245102 Rao M, Sengupta S and Shankar R 1997 Phys. Rev. Lett. 79 3998
14. Sankararaman S and Shankar R 2003 Phys. Rev. B 67 245102 Rao M, Sengupta S and Shankar R 1997 Phys. Rev. Lett. 79 3998
15. Falk F 1983 Z. Phys. B 51 177 Barsch G R and Krumhansl J A 1984 Phys. Rev. Lett. 53 1069
16. Falk F 1983 Z. Phys. B 51 177 Barsch G R and Krumhansl J A 1984 Phys. Rev. Lett. 53 1069
17. Semenovskaya S and Khachaturyan A G 1991 Phys. Rev. Lett. 67 2223 Semenovskaya S and Khachaturyan A G 1992 Phys. Rev. B 46 6511 Semenovskaya S, Zhu Y, Suenaga M and Khachaturyan A G 1993 Phys. Rev. B 47 12182
18. Semenovskaya S and Khachaturyan A G 1991 Phys. Rev. Lett. 67 2223 Semenovskaya S and Khachaturyan A G 1992 Phys. Rev. B 46 6511 Semenovskaya S, Zhu Y, Suenaga M and Khachaturyan A G 1993 Phys. Rev. B 47 12182
19. Semenovskaya S and Khachaturyan A G 1991 Phys. Rev. Lett. 67 2223 Semenovskaya S and Khachaturyan A G 1992 Phys. Rev. B 46 6511 Semenovskaya S, Zhu Y, Suenaga M and Khachaturyan A G 1993 Phys. Rev. B 47 12182
20. Rao M and Sengupta S 1997 Phys. Rev. Lett. 78 2168 Rao M and Sengupta S 1999 Curr. Sci. 77 382
21. Rao M and Sengupta S 1997 Phys. Rev. Lett. 78 2168 Rao M and Sengupta S 1999 Curr. Sci. 77 382
22. Sengupta S, Nielaba P, Rao M and Binder K 2000 Phys. Rev. E 61 1072 Sengupta S, Nielaba P and Binder K 2000 Phys. Rev. E 61 6294
23. Sengupta S, Nielaba P, Rao M and Binder K 2000 Phys. Rev. E 61 1072 Sengupta S, Nielaba P and Binder K 2000 Phys. Rev. E 61 6294
24. Becquart C S, Clapp P C and Rifkin J A 1993 Phys. Rev. B 48 6 Meyer R and Entel P 1997 LANL Preprint cond-mat/9706248 Daw M S and Baskes M I 1983 Phys. Rev. Lett. 50 1285 Daw M S and Baskes M I 1984 Phys. Rev. B 29 6443
25. Becquart C S, Clapp P C and Rifkin J A 1993 Phys. Rev. B 48 6 Meyer R and Entel P 1997 LANL Preprint cond-mat/9706248 Daw M S and Baskes M I 1983 Phys. Rev. Lett. 50 1285 Daw M S and Baskes M I 1984 Phys. Rev. B 29 6443
26. Becquart C S, Clapp P C and Rifkin J A 1993 Phys. Rev. B 48 6 Meyer R and Entel P 1997 LANL Preprint cond-mat/9706248 Daw M S and Baskes M I 1983 Phys. Rev. Lett. 50 1285 Daw M S and Baskes M I 1984 Phys. Rev. B 29 6443
27. Becquart C S, Clapp P C and Rifkin J A 1993 Phys. Rev. B 48 6 Meyer R and Entel P 1997 LANL Preprint cond-mat/9706248 Daw M S and Baskes M I 1983 Phys. Rev. Lett. 50 1285 Daw M S and Baskes M I 1984 Phys. Rev. B 29 6443
28. Weber T A and Stillinger F H 1993 Phys. Rev. E 48 4351
29. Squire D R, Holt A C and Hoover W G 1969 Physica 42 388
30. Hoover W G, Ashurst W T and Graver R 1972 J. Chem. Phys. 57 1259 Hoover W G, Hoover N E and Hanson K 1979 J. Chem. Phys. 70 1837 Hoover W G and Ree F H 1968 J. Chem. Phys. 49 3609
31. Hoover W G, Ashurst W T and Graver R 1972 J. Chem. Phys. 57 1259 Hoover W G, Hoover N E and Hanson K 1979 J. Chem. Phys. 70 1837 Hoover W G and Ree F H 1968 J. Chem. Phys. 49 3609
32. Hoover W G, Ashurst W T and Graver R 1972 J. Chem. Phys. 57 1259 Hoover W G, Hoover N E and Hanson K 1979 J. Chem. Phys. 70 1837 Hoover W G and Ree F H 1968 J. Chem. Phys. 49 3609
33. Frenkel D and Smit B 1996 Understanding Molecular Simulations (San Diego, CA: Academic)
34. Chaikin P M and Lubensky T C 1995 Principles of Condensed Matter Physics (Cambridge: Cambridge University Press)
35. Born M and Huang K 1998 Dynamical Theory of Crystal Lattices (Oxford: Oxford University Press)
36. Ramakrishnan T V and Yussouff M 1979 Phys. Rev. B 19 2775
37. Hansen J-P and McDonald I R 1986 Theory of Simple Liquids (London: Academic)
38. See for e.g. Denton A R and Ashcroft N W 1989 Phys. Rev. A 39 426
39. For reviews of density wave theory see e.g. Tareyeva E and Ryzhov V 1997 LANL Preprint cond-mat/9712265 Löwen H 1994 Phys. Rep. 237 249 Hansen J-P, Levesque D and Zinn-Justin J (ed) 1991 Liquids, Freezing and Glass Transition (Les Hauches) (Amsterdam: North-Holland)
40. For reviews of density wave theory see e.g. Tareyeva E and Ryzhov V 1997 LANL Preprint cond-mat/9712265 Löwen H 1994 Phys. Rep. 237 249 Hansen J-P, Levesque D and Zinn-Justin J (ed) 1991 Liquids, Freezing and Glass Transition (Les Hauches) (Amsterdam: North-Holland)
41. For reviews of density wave theory see e.g. Tareyeva E and Ryzhov V 1997 LANL Preprint cond-mat/9712265 Löwen H 1994 Phys. Rep. 237 249 Hansen J-P, Levesque D and Zinn-Justin J (ed) 1991 Liquids, Freezing and Glass Transition (Les Hauches) (Amsterdam: North-Holland)
42. Denton A R, Kahl G and Hafner J 1999 J. Non-Cryst. Solids 15 250
43. Rosenfeld Y 1990 Phys. Rev. A 42 5978
44. A similar situation exists for the body centered cubic lattice in three dimensions. Second-order contributions always prefer a close-packed face centered cubic structure and in order to discuss the relative stability of these two lattices three body correlations have to be invoked; Sengupta S 1991 PhD Thesis Indian Institute of Science, Bangalore For an application to the system of charge stabilized colloids, see Sengupta S and Sood A K 1991 Phys. Rev. A 44 1233 Choudhury N and Ghosh S K 1995 Phys. Rev. E 51 4503
45. A similar situation exists for the body centered cubic lattice in three dimensions. Second-order contributions always prefer a close-packed face centered cubic structure and in order to discuss the relative stability of these two lattices three body correlations have to be invoked; Sengupta S 1991 PhD Thesis Indian Institute of Science, Bangalore For an application to the system of charge stabilized colloids, see Sengupta S and Sood A K 1991 Phys. Rev. A 44 1233 Choudhury N and Ghosh S K 1995 Phys. Rev. E 51 4503
46. A similar situation exists for the body centered cubic lattice in three dimensions. Second-order contributions always prefer a close-packed face centered cubic structure and in order to discuss the relative stability of these two lattices three body correlations have to be invoked; Sengupta S 1991 PhD Thesis Indian Institute of Science, Bangalore For an application to the system of charge stabilized colloids, see Sengupta S and Sood A K 1991 Phys. Rev. A 44 1233 Choudhury N and Ghosh S K 1995 Phys. Rev. E 51 4503
47. Landau L D and Lifshitz E M 1986 Theory of Elasticity 3rd edn (Oxford: Pergamon)
48. Scott J F 1974 Rev. Mod. Phys. 4683
49. Such a treatment has been commonly used in the study of phase transitions in liquid crystals using density wave theory, see for e.g. Singh Y 1984 Phys. Rev. A 30 583 Mahato M C, Lakshmi M R, Pandit R and Krishnamurthy H R 1988 Phys. Rev. A 38 1049
50. Such a treatment has been commonly used in the study of phase transitions in liquid crystals using density wave theory, see for e.g. Singh Y 1984 Phys. Rev. A 30 583 Mahato M C, Lakshmi M R, Pandit R and Krishnamurthy H R 1988 Phys. Rev. A 38 1049
51. Yethiraj A, Wouterse A, Groh B and van Blaaderen A 2004 Phys. Rev. Lett. 92 058301
52. See also articles in Arora A K and Tata B V R (ed) 1996 Ordering and Phase Transitions in Charged Colloids (New York: VCH)
53. Biswas R and Hamann D R 1987 Phys. Rev. B 36 6434