Simulations of the nucleation of AgBr from solution

Journal of Chemical Physics

Volumn 113, Issue 15, 2000, Pages 6276-6284

  Shore, Joel D ^a   Perchak, Dennis ^a   Shnidman, Yitzhak ^b  

^a EASTMAN KODAK COMPANY   (United States)

^b POLYTECHNIC UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; CRYSTALS; FREE ENERGY; MOLECULAR DYNAMICS; NEGATIVE IONS; NUCLEATION; NUMERICAL METHODS; PHASE DIAGRAMS; POSITIVE IONS; WATER;

BORN-MAYER-HUGGINS POTENTIALS; CLUSTER SIZE; CLUSTERS; IN VACUO;

SILVER COMPOUNDS;

EID: 0034297748     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1308517     Document Type: Article

References (53)

1. Recent books and review articles on precipitation include J. A Dirksen and T. A. Ring, Chem. Eng. Sci. 46, 2289 (1991); in Advances in Industrial Crystallization, edited by J. Garside, R. J. Davey, and A. G. Jones (Butterworth-Heinemann, Oxford, 1991); O. Soehnel and J. Garside, Precipitation-Basic Principles and Industrial Applications (Butterworth-Heinemann, New York, 1992); in Crystallization Processes, edited by H. Ohtaki (Wiley, Chicester, 1998).
2. Recent books and review articles on precipitation include J. A Dirksen and T. A. Ring, Chem. Eng. Sci. 46, 2289 (1991); in Advances in Industrial Crystallization, edited by J. Garside, R. J. Davey, and A. G. Jones (Butterworth-Heinemann, Oxford, 1991); O. Soehnel and J. Garside, Precipitation-Basic Principles and Industrial Applications (Butterworth-Heinemann, New York, 1992); in Crystallization Processes, edited by H. Ohtaki (Wiley, Chicester, 1998).
3. Recent books and review articles on precipitation include J. A Dirksen and T. A. Ring, Chem. Eng. Sci. 46, 2289 (1991); in Advances in Industrial Crystallization, edited by J. Garside, R. J. Davey, and A. G. Jones (Butterworth-Heinemann, Oxford, 1991); O. Soehnel and J. Garside, Precipitation-Basic Principles and Industrial Applications (Butterworth-Heinemann, New York, 1992); in Crystallization Processes, edited by H. Ohtaki (Wiley, Chicester, 1998).
4. Recent books and review articles on precipitation include J. A Dirksen and T. A. Ring, Chem. Eng. Sci. 46, 2289 (1991); in Advances in Industrial Crystallization, edited by J. Garside, R. J. Davey, and A. G. Jones (Butterworth-Heinemann, Oxford, 1991); O. Soehnel and J. Garside, Precipitation-Basic Principles and Industrial Applications (Butterworth-Heinemann, New York, 1992); in Crystallization Processes, edited by H. Ohtaki (Wiley, Chicester, 1998).
5. A review of silver halide precipitation in particular is given by J. S. Wey, in Lead Tin Telluride, Silver Halide, and Czochralski Growth, Preparation and Properties of Solid State Materials, Vol. 6, edited by W. R. Wilcox (Dekker, New York, 1981), pp. 67-117.
6. Reviews of nucleation phenomena in general, some of which include discussions of simulations, can be found in G. S. Springer, Adv. Heat Transfer 14, 281 (1978); K. F. Kelton, in Solid State Physics, edited by H. Ehrenreich and D. Turnbull (Academic, New York, 1991), Vol. 45, pp. 75-177; R. D. Mountain, in Nucleation and Crystallization in Liquids and Glasses, Ceramic Transactions, edited by M. C. Weinberg (The American Ceramic Society, Westerville, OH, 1993), Vol. 30, pp. 55-64; A. Laaksonen, V. Talanquer, and D. W. Oxtoby, Annu. Rev. Phys. Chem. 46, 489 (1995); D. W. Oxtoby, Acc. Chem. Res. 31, 91 (1998).
7. Reviews of nucleation phenomena in general, some of which include discussions of simulations, can be found in G. S. Springer, Adv. Heat Transfer 14, 281 (1978); K. F. Kelton, in Solid State Physics, edited by H. Ehrenreich and D. Turnbull (Academic, New York, 1991), Vol. 45, pp. 75-177; R. D. Mountain, in Nucleation and Crystallization in Liquids and Glasses, Ceramic Transactions, edited by M. C. Weinberg (The American Ceramic Society, Westerville, OH, 1993), Vol. 30, pp. 55-64; A. Laaksonen, V. Talanquer, and D. W. Oxtoby, Annu. Rev. Phys. Chem. 46, 489 (1995); D. W. Oxtoby, Acc. Chem. Res. 31, 91 (1998).
8. Reviews of nucleation phenomena in general, some of which include discussions of simulations, can be found in G. S. Springer, Adv. Heat Transfer 14, 281 (1978); K. F. Kelton, in Solid State Physics, edited by H. Ehrenreich and D. Turnbull (Academic, New York, 1991), Vol. 45, pp. 75-177; R. D. Mountain, in Nucleation and Crystallization in Liquids and Glasses, Ceramic Transactions, edited by M. C. Weinberg (The American Ceramic Society, Westerville, OH, 1993), Vol. 30, pp. 55-64; A. Laaksonen, V. Talanquer, and D. W. Oxtoby, Annu. Rev. Phys. Chem. 46, 489 (1995); D. W. Oxtoby, Acc. Chem. Res. 31, 91 (1998).
9. Reviews of nucleation phenomena in general, some of which include discussions of simulations, can be found in G. S. Springer, Adv. Heat Transfer 14, 281 (1978); K. F. Kelton, in Solid State Physics, edited by H. Ehrenreich and D. Turnbull (Academic, New York, 1991), Vol. 45, pp. 75-177; R. D. Mountain, in Nucleation and Crystallization in Liquids and Glasses, Ceramic Transactions, edited by M. C. Weinberg (The American Ceramic Society, Westerville, OH, 1993), Vol. 30, pp. 55-64; A. Laaksonen, V. Talanquer, and D. W. Oxtoby, Annu. Rev. Phys. Chem. 46, 489 (1995); D. W. Oxtoby, Acc. Chem. Res. 31, 91 (1998).
10. Reviews of nucleation phenomena in general, some of which include discussions of simulations, can be found in G. S. Springer, Adv. Heat Transfer 14, 281 (1978); K. F. Kelton, in Solid State Physics, edited by H. Ehrenreich and D. Turnbull (Academic, New York, 1991), Vol. 45, pp. 75-177; R. D. Mountain, in Nucleation and Crystallization in Liquids and Glasses, Ceramic Transactions, edited by M. C. Weinberg (The American Ceramic Society, Westerville, OH, 1993), Vol. 30, pp. 55-64; A. Laaksonen, V. Talanquer, and D. W. Oxtoby, Annu. Rev. Phys. Chem. 46, 489 (1995); D. W. Oxtoby, Acc. Chem. Res. 31, 91 (1998).
11. J. Anwar and P. K. Boateng, J. Am. Chem. Soc. 120, 9600 (1998).
12. P. R. ten Wolde and D. Frenkel, Science 277, 1975 (1997); D. Frenkel in an invited talk at the American Physical Society Centennial Meeting in Atlanta, GA (March 24, 1999); see also, V. Talanquer and D. W. Oxtoby, J. Chem. Phys. 109, 223 (1998).
13. P. R. ten Wolde and D. Frenkel, Science 277, 1975 (1997); D. Frenkel in an invited talk at the American Physical Society Centennial Meeting in Atlanta, GA (March 24, 1999); see also, V. Talanquer and D. W. Oxtoby, J. Chem. Phys. 109, 223 (1998).
14. P. R. ten Wolde and D. Frenkel, Science 277, 1975 (1997); D. Frenkel in an invited talk at the American Physical Society Centennial Meeting in Atlanta, GA (March 24, 1999); see also, V. Talanquer and D. W. Oxtoby, J. Chem. Phys. 109, 223 (1998).
15. H. Ohtaki, Adv. Inorg. Chem. 39, 401 (1992); I. Okada and H. Ohtaki in Crystallization Processes (Ref. 1), pp. 159-202.
16. H. Ohtaki, Adv. Inorg. Chem. 39, 401 (1992); I. Okada and H. Ohtaki in Crystallization Processes (Ref. 1), pp. 159-202.
17. M. A. Larson in Advances in Industrial Crystallization (Ref. 1), pp. 20-30; N. P. Balsara, C. Lin, and B. Hammouda, Phys. Rev. Lett. 77, 3847 (1996) ; B. A. Garetz, J. E. Aber, N. L. Goddard, R. G. Young, and A. S. Myerson, ibid. 77, 3475 (1996); A. S. Myerson (private communication).
18. M. A. Larson in Advances in Industrial Crystallization (Ref. 1), pp. 20-30; N. P. Balsara, C. Lin, and B. Hammouda, Phys. Rev. Lett. 77, 3847 (1996) ; B. A. Garetz, J. E. Aber, N. L. Goddard, R. G. Young, and A. S. Myerson, ibid. 77, 3475 (1996); A. S. Myerson (private communication).
19. M. A. Larson in Advances in Industrial Crystallization (Ref. 1), pp. 20-30; N. P. Balsara, C. Lin, and B. Hammouda, Phys. Rev. Lett. 77, 3847 (1996) ; B. A. Garetz, J. E. Aber, N. L. Goddard, R. G. Young, and A. S. Myerson, ibid. 77, 3475 (1996); A. S. Myerson (private communication).
20. M. A. Larson in Advances in Industrial Crystallization (Ref. 1), pp. 20-30; N. P. Balsara, C. Lin, and B. Hammouda, Phys. Rev. Lett. 77, 3847 (1996) ; B. A. Garetz, J. E. Aber, N. L. Goddard, R. G. Young, and A. S. Myerson, ibid. 77, 3475 (1996); A. S. Myerson (private communication).
21. In this article, we discuss only homogeneous nucleation. Homogeneous nucleation occurs due to fluctuations in the bulk material while heterogeneous nucleation is nucleation which occurs preferentially at defects, contaminants, container surfaces, etc. In the real world, heterogeneous nucleation tends to dominate and thus homogeneous nucleation is the exception rather than the rule. Indeed, one of the greatest challenges in performing experiments on homogeneous nucleation is to avoid heterogeneous nucleation. Nonetheless, for the large degree of supersaturation present in the precipitation of photographic emulsions (and some other industrial precipitation processes), it is believed that homogeneous nucleation is the dominant mechanism.
22. D. R. Perchak and J. M. O'Reilly, J. Non-Cryst. Solids 167, 211 (1994).
23. MOLDY, Version 2.13, written by Keith Refson, Oxford University [http:// www.earth.ox.ac.uk/%7Ekeith/moldy.html]; K. Refson, Comput. Phys. Commun. 126, 309 (2000).
24. MOLDY, Version 2.13, written by Keith Refson, Oxford University [http:// www.earth.ox.ac.uk/%7Ekeith/moldy.html]; K. Refson, Comput. Phys. Commun. 126, 309 (2000).
25. Detailed discussions of molecular dynamics simulation techniques can be found in M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford University Press, Oxford 1989); D. C. Rapaport, The Art of Molecular Dynamics Simulation (Cambridge University Press, Cambridge 1995); D. Frenkel and B. Smit, Understanding Molecular Simulations: From Algorithms to Applications (Academic, New York, 1996).
26. Detailed discussions of molecular dynamics simulation techniques can be found in M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford University Press, Oxford 1989); D. C. Rapaport, The Art of Molecular Dynamics Simulation (Cambridge University Press, Cambridge 1995); D. Frenkel and B. Smit, Understanding Molecular Simulations: From Algorithms to Applications (Academic, New York, 1996).
27. Detailed discussions of molecular dynamics simulation techniques can be found in M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford University Press, Oxford 1989); D. C. Rapaport, The Art of Molecular Dynamics Simulation (Cambridge University Press, Cambridge 1995); D. Frenkel and B. Smit, Understanding Molecular Simulations: From Algorithms to Applications (Academic, New York, 1996).
28. Frenkel and Smit (Ref. 11), Appendix B; Allen and Tildesley (Ref. 11), Sec. 5.5.
29. When we used our homegrown code that does not perform the Ewald sums, we introduced a "screening factor" in the final term in Eq. (3.1) to make this potential short-ranged in a way that is supposed to account, in an approximate way, for the Ewald sums [see Eq. (1) in Ref. 9 and the associated discussion therein]. The adjustable parameter β in that screening factor was chosen to be 2.9 Å, which gives approximately the correct lattice constant for bulk AgBr.
30. D. Beeman, J. Comput. Phys. 20, 130 (1976).
31. K. Refson, Physica B 131, 256 (1985).
32. B. Quentrec and C. Brot, J. Comput. Phys. 13, 430 (1975); see also Allen and Tildesley (Ref. 11).
33. M. Parrinello and A. Rahman, J. Appl. Phys. 52, 7182 (1981).
34. S. Nosé and M. L. Klein, Mol. Phys. 50, 1055 (1983).
35. In principle, we should enforce the pressure to be atmospheric pressure. However, we simply enforce the stress to be zero because for the liquid and solid systems that we study the distinction between zero pressure and atmospheric pressure is inconsequential; in particular, in the simulations the fluctuations in pressure about zero are a few orders-of-magnitude greater than one atmosphere.
36. C. R. A. Catlow, J. Corish, J. H. Harding, and P. W. M. Jacobs, Philos. Mag. A 55, 481 (1987).
37. For properties of bulk silver halides, see The Theory of the Photographic Process, 4th ed., edited by T. H. James (Macmillan, New York, 1977).
38. All the fits to experimental data shown for the energy are taken from J. Carré, H. Pham, and M. Rolin, Bull. Soc. Chim. Fr. 36, 2322 (1969). Those labeled "Carre" in the legend are their own results while those labeled "Kelley" are those reported by Carré, Pham, and Rolin to be from K. K. Kelley, U.S. Bureau of Mines Bulletin No. 584 (1960). The experimental data shown for the lattice constant is taken from Fig. 2 of Ref. 20.
39. All the fits to experimental data shown for the energy are taken from J. Carré, H. Pham, and M. Rolin, Bull. Soc. Chim. Fr. 36, 2322 (1969). Those labeled "Carre" in the legend are their own results while those labeled "Kelley" are those reported by Carré, Pham, and Rolin to be from K. K. Kelley, U.S. Bureau of Mines Bulletin No. 584 (1960). The experimental data shown for the lattice constant is taken from Fig. 2 of Ref. 20.
40. R. C. Baetzold. C. R. A. Callow, J. Corish, F. M. Healy, P. W. M. Jacobs, M. Leslie, and Y. T. Tan, J. Phys. Chem. Solids 50, 791 (1989).
41. T. P. Martin, Phys. Rep. 95, 167 (1983); N. G. Phillips, C. W. S. Conover, and L. A. Bloomfield, J. Chem. Phys. 94, 4980 (1991); J. P. Rose and R. S. Berry, ibid. 96, 517 (1992); C. Ochsenfield and R. Ahlrichs, ibid. 97, 3487 (1992); Ber. Bunsenges. Phys. Chem. 98, 34 (1994); R. Ahlrichs and C. Ochsenfield, ibid. 96, 1287 (1992).
42. T. P. Martin, Phys. Rep. 95, 167 (1983); N. G. Phillips, C. W. S. Conover, and L. A. Bloomfield, J. Chem. Phys. 94, 4980 (1991); J. P. Rose and R. S. Berry, ibid. 96, 517 (1992); C. Ochsenfield and R. Ahlrichs, ibid. 97, 3487 (1992); Ber. Bunsenges. Phys. Chem. 98, 34 (1994); R. Ahlrichs and C. Ochsenfield, ibid. 96, 1287 (1992).
43. T. P. Martin, Phys. Rep. 95, 167 (1983); N. G. Phillips, C. W. S. Conover, and L. A. Bloomfield, J. Chem. Phys. 94, 4980 (1991); J. P. Rose and R. S. Berry, ibid. 96, 517 (1992); C. Ochsenfield and R. Ahlrichs, ibid. 97, 3487 (1992); Ber. Bunsenges. Phys. Chem. 98, 34 (1994); R. Ahlrichs and C. Ochsenfield, ibid. 96, 1287 (1992).
44. T. P. Martin, Phys. Rep. 95, 167 (1983); N. G. Phillips, C. W. S. Conover, and L. A. Bloomfield, J. Chem. Phys. 94, 4980 (1991); J. P. Rose and R. S. Berry, ibid. 96, 517 (1992); C. Ochsenfield and R. Ahlrichs, ibid. 97, 3487 (1992); Ber. Bunsenges. Phys. Chem. 98, 34 (1994); R. Ahlrichs and C. Ochsenfield, ibid. 96, 1287 (1992).
45. T. P. Martin, Phys. Rep. 95, 167 (1983); N. G. Phillips, C. W. S. Conover, and L. A. Bloomfield, J. Chem. Phys. 94, 4980 (1991); J. P. Rose and R. S. Berry, ibid. 96, 517 (1992); C. Ochsenfield and R. Ahlrichs, ibid. 97, 3487 (1992); Ber. Bunsenges. Phys. Chem. 98, 34 (1994); R. Ahlrichs and C. Ochsenfield, ibid. 96, 1287 (1992).
46. T. P. Martin, Phys. Rep. 95, 167 (1983); N. G. Phillips, C. W. S. Conover, and L. A. Bloomfield, J. Chem. Phys. 94, 4980 (1991); J. P. Rose and R. S. Berry, ibid. 96, 517 (1992); C. Ochsenfield and R. Ahlrichs, ibid. 97, 3487 (1992); Ber. Bunsenges. Phys. Chem. 98, 34 (1994); R. Ahlrichs and C. Ochsenfield, ibid. 96, 1287 (1992).
47. CRC Handbook of Chemistry and Physics, 79th ed. (CRC, Boca Raton, 1998), p. 5-93.
48. W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. L. Klein, J. Chem. Phys. 79, 926 (1983).
49. S. J. Stuart and B. J. Berne, J. Phys. Chem. 100, 11934 (1996).
50. K. Heinzinger, Physica B 131, 196 (1985).
51. 3. The waters are initially positioned without regard to the cluster; overlap with the cluster is prevented by subsequently eliminating those waters that are too close to any of the ions (or to each other). By adjusting the size of the box and the cutoff distances for considering the waters to be too close to the ions or other waters, a configuration can be created having exactly the desired number of water molecules.
52. J. N. Glosli (private communication).
53. R. M. Shroll and D. E. Smith, J. Chem. Phys. 111, 9025 (1999).