Comparison of experiments and modern theories of crystal nucleation

Journal of Chemical Physics

Volumn 107, Issue 9, 1997, Pages 3634-3644

  Gránásy, László ^a   Iglói, Ferenc ^a,b  

^a WIGNER RESEARCH CENTRE FOR PHYSICS   (Hungary)

^b UNIVERSITY OF SZEGED   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; CRYSTAL STRUCTURE; CRYSTALS; GLASS; HYDROCARBONS; LIQUID METALS; MATHEMATICAL MODELS; MOLECULES; MONTE CARLO METHODS; OXIDES; PROBABILITY DENSITY FUNCTION;

CLASSICAL NUCLEATION THEORY; DIFFUSE INTERFACE THEORY; INTERFACIAL FREE ENERGY; OXIDE GLASS; PERTURBATIVE DENSITY FUNCTIONAL APPROXIMATION;

NUCLEATION;

EID: 0031237024     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.474721     Document Type: Review

References (139)

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42. For example, J. L. Schmitt, A. Zalabsky, and G. W. Adams, J. Chem. Phys. 79, 4496 (1983); P. E. Wagner and R. Strey, ibid. 80, 5266 (1984); G. W. Adams, J. L. Schmitt, and R. A. Zalabsky, ibid. 81, 5074 (1984); R. Strey, P. E. Wagner, and T. Schmeling, ibid. 84, 2325 (1986); C.-H. Hung, M. J. Krasnopoler, and J. L. Katz, ibid. 90, 1856 (1989); 92, 7722 (1990).
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47. 6 [H. Reiss, J. L. Katz, and E. R. Cohen, J. Chem. Phys. 48, 5553 (1968)]. A later work implies that the correction is negligible [H. Reiss, J. Stat. Phys. 2, 83 (1970)]. A recent full dynamical treatment of density functional theory gives results almost indistinguishable from the classical choice of the pre-exponential factor [V. Talanquer and D. W. Oxtoby, J. Chem. Phys. 100, 5190 (1994)]. In the case of crystal nucleation in liquid or glass the rotational and translational contributions to the cluster free energy are expected to be negligible [see, e.g., Y. Miyazawa and G. M. Pound, J. Cryst. Growth 23, 45 (1974); J. W. Christian, The Theory of Transformations in Metals and Alloys, 2nd ed. (Pergamon, Oxford, 1975), Chap. 10, Sec. 49; Ref. 6(a)].
48. 6 [H. Reiss, J. L. Katz, and E. R. Cohen, J. Chem. Phys. 48, 5553 (1968)]. A later work implies that the correction is negligible [H. Reiss, J. Stat. Phys. 2, 83 (1970)]. A recent full dynamical treatment of density functional theory gives results almost indistinguishable from the classical choice of the pre-exponential factor [V. Talanquer and D. W. Oxtoby, J. Chem. Phys. 100, 5190 (1994)]. In the case of crystal nucleation in liquid or glass the rotational and translational contributions to the cluster free energy are expected to be negligible [see, e.g., Y. Miyazawa and G. M. Pound, J. Cryst. Growth 23, 45 (1974); J. W. Christian, The Theory of Transformations in Metals and Alloys, 2nd ed. (Pergamon, Oxford, 1975), Chap. 10, Sec. 49; Ref. 6(a)].
49. 6 [H. Reiss, J. L. Katz, and E. R. Cohen, J. Chem. Phys. 48, 5553 (1968)]. A later work implies that the correction is negligible [H. Reiss, J. Stat. Phys. 2, 83 (1970)]. A recent full dynamical treatment of density functional theory gives results almost indistinguishable from the classical choice of the pre-exponential factor [V. Talanquer and D. W. Oxtoby, J. Chem. Phys. 100, 5190 (1994)]. In the case of crystal nucleation in liquid or glass the rotational and translational contributions to the cluster free energy are expected to be negligible [see, e.g., Y. Miyazawa and G. M. Pound, J. Cryst. Growth 23, 45 (1974); J. W. Christian, The Theory of Transformations in Metals and Alloys, 2nd ed. (Pergamon, Oxford, 1975), Chap. 10, Sec. 49; Ref. 6(a)].
50. 6 [H. Reiss, J. L. Katz, and E. R. Cohen, J. Chem. Phys. 48, 5553 (1968)]. A later work implies that the correction is negligible [H. Reiss, J. Stat. Phys. 2, 83 (1970)]. A recent full dynamical treatment of density functional theory gives results almost indistinguishable from the classical choice of the pre-exponential factor [V. Talanquer and D. W. Oxtoby, J. Chem. Phys. 100, 5190 (1994)]. In the case of crystal nucleation in liquid or glass the rotational and translational contributions to the cluster free energy are expected to be negligible [see, e.g., Y. Miyazawa and G. M. Pound, J. Cryst. Growth 23, 45 (1974); J. W. Christian, The Theory of Transformations in Metals and Alloys, 2nd ed. (Pergamon, Oxford, 1975), Chap. 10, Sec. 49; Ref. 6(a)].
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67. A uniquely defined spinodal point and the related anomalies (divergence of correlation length, W*→0, etc.) are direct consequences of the meanfield approximation which is only exact for infinite range interactions. For finite range interactions the shape of the (coarse-grained) free energy-order parameter curve, and the position of the spinodal points depend strongly on the coarse-graining length. These are supported by the findings that neither the Monte Carlo simulations on the Ising-model, nor the experiments on phase separating alloys show discontinuity at the meanfield spinodal. [See, e.g., J. D. Gunton, M. San Miguel, and P. S. Sahni, Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic, New York, 1983), Vol. 8, p. 267; K. Binder, Rep. Prog. Phys. 50, 783 (1987).] The square-gradient approximation (SGA) is only valid for smooth order parameter changes across the interface. This condition is not necessarily fulfilled at the crystal/liquid interface. For example, if the SGA is avoided a sharper interface and a reduced interfacial free energy can be obtained [Ref. 8(a)]. [See also Refs. 8(b)-8(d).]
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78. Note, that the γ defined this way is rather an effective interfacial free energy, since during the derivation of Eq. (2) the size-independence of the interfacial free energy is utilized. However, lacking a well proven theory, the experimentalists usually derive this quantity from their data. Therefore, it seems reasonable to evaluate the same quantity from theory. This effective γ is the quantity compatible with the interfacial free energy definition used in the CNT.
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80. -9.
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87. Data communicated to the author by D. W. Oxtoby.
88. 2 where a = 0.9655 and b=-0.4158, and c=-0.4470.
89. D. Turnbull, J. Chem. Phys. 20, 411 (1952).
90. f, etc. The procedure converges fast.
91. -1.
92. c (probably by a few orders of magnitude), since a number of molecules may be adsorbed on the surface of a single heterogeneity.
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100. D. Kashcbiev, Surf. Sci. 18, 209 (1969).
101. The origin of this deviation from linearity is yet unknown. Possible explanations are that (a) the nucleation transient was not treated properly in the experiments; (b) the size dependence of the interfacial free energy is reversed for small sizes (Ref. 31). For further discussion, see, M. C. Weinberg and E. D. Zanotto, J. Non-Cryst. Solids 108, 99 (1989).
102. tot apply for the SDFA and DIT fits, while the highest values to the MWDA.)
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107. For example, (a) H. M. Huffman, M. E. Gross, D. W. Scott, and J. P. McCullough, J. Phys. Chem. 65, 495 (1961); (b) A. Defrain, J. Chim. Phys. 74 851 (1977); J. H. Perepezko and J. S. Paik, J. Non-Cryst. Solids 61/62, 113 (1984); (c) H. S. Chen and D. Turnbull, J. Chem. Phys. 48, 2560 (1968); H. W. Kui and D. Turnbull, J. Non-Cryst. Solids 94, 62 (1987).
108. For example, (a) H. M. Huffman, M. E. Gross, D. W. Scott, and J. P. McCullough, J. Phys. Chem. 65, 495 (1961); (b) A. Defrain, J. Chim. Phys. 74 851 (1977); J. H. Perepezko and J. S. Paik, J. Non-Cryst. Solids 61/62, 113 (1984); (c) H. S. Chen and D. Turnbull, J. Chem. Phys. 48, 2560 (1968); H. W. Kui and D. Turnbull, J. Non-Cryst. Solids 94, 62 (1987).
109. For example, (a) H. M. Huffman, M. E. Gross, D. W. Scott, and J. P. McCullough, J. Phys. Chem. 65, 495 (1961); (b) A. Defrain, J. Chim. Phys. 74 851 (1977); J. H. Perepezko and J. S. Paik, J. Non-Cryst. Solids 61/62, 113 (1984); (c) H. S. Chen and D. Turnbull, J. Chem. Phys. 48, 2560 (1968); H. W. Kui and D. Turnbull, J. Non-Cryst. Solids 94, 62 (1987).
110. For example, (a) H. M. Huffman, M. E. Gross, D. W. Scott, and J. P. McCullough, J. Phys. Chem. 65, 495 (1961); (b) A. Defrain, J. Chim. Phys. 74 851 (1977); J. H. Perepezko and J. S. Paik, J. Non-Cryst. Solids 61/62, 113 (1984); (c) H. S. Chen and D. Turnbull, J. Chem. Phys. 48, 2560 (1968); H. W. Kui and D. Turnbull, J. Non-Cryst. Solids 94, 62 (1987).
111. For example, (a) H. M. Huffman, M. E. Gross, D. W. Scott, and J. P. McCullough, J. Phys. Chem. 65, 495 (1961); (b) A. Defrain, J. Chim. Phys. 74 851 (1977); J. H. Perepezko and J. S. Paik, J. Non-Cryst. Solids 61/62, 113 (1984); (c) H. S. Chen and D. Turnbull, J. Chem. Phys. 48, 2560 (1968); H. W. Kui and D. Turnbull, J. Non-Cryst. Solids 94, 62 (1987).
112. J. H. Perepezko and D. H. Rasmussen, Metall. Trans. 9A, 1490 (1978).
113. K. Takahashi and T. Yoshio J. Ceram. Soc. Jpn. 81, 534 (1973).
114. V. I. Babushkin, G. M. Matveyev, and O. P. Mchedlov-Petrossyan, Thermodynamics of Silicates (Springer, Berlin, 1985) p. 202.
115. For example, F. Iglói, J. Phys. C. 19, 6907 (1986).
116. A. D. J. Haymet, J. Phys. Chem. 89, 887 (1985).
117. L. Gránásy, J. Non-Cryst. Solids (in press).
118. V. Talanquer and D. W. Oxtoby, J. Phys. Chem. 99, 2865 (1995).
119. J. G. Harris, J. Phys. Chem. 96, 5077 (1992).
120. K. W. Sarkies and N. E. Frenkel, Phys. Rev. A 11, 1724 (1975).
121. Landolt-Börnstein, Zahlenwerte und Funktionen, Mechanische-Termische Zustandgrössen (Springer, Berlin, 1960), Vol. 2, Part 1.
122. 3 groups by Y. Jin and B. Wunderlich, J. Phys. Chem. 95, 9000 (1991). The polynomial for the crystal was fitted to data shown in Fig. 3 of the same paper. The respective Kauzmann temperatures are fully compatible with those given by K. Kishore, S. Bharat, and S. Kannan, J. Chem. Phys. 105, 11 364 (1996).
123. 3 groups by Y. Jin and B. Wunderlich, J. Phys. Chem. 95, 9000 (1991). The polynomial for the crystal was fitted to data shown in Fig. 3 of the same paper. The respective Kauzmann temperatures are fully compatible with those given by K. Kishore, S. Bharat, and S. Kannan, J. Chem. Phys. 105, 11 364 (1996).
124. Polynomials were fitted to log μ data of Landolt-Börnstein, Zahlenwerte und Funktionen (Springer, Berlin, 1969) Vol. 5, and of A. K. Doolittle, J. Appl. Phys. 22, 1031 (1951).
125. Polynomials were fitted to log μ data of Landolt-Börnstein, Zahlenwerte und Funktionen (Springer, Berlin, 1969) Vol. 5, and of A. K. Doolittle, J. Appl. Phys. 22, 1031 (1951).
126. CRC Handbook of Chemistry and Physics, edited by D. R. Lide (Chemical Rubber, Boca Raton, 1990).
127. R. Hultgren et al., Selected Values of Thermodynamic Properties of the Elements (American Society for Metals, Metals Park, Ohio, 1973).
128. Polynomial fitted to the data from Ref. 54.
129. R. P. Chhabra and D. K. Sheth, Z. Metallkde. 81, 264 (1990).
130. E. D. Zanotto and E. Müller, J. Non-Cryst. Solids 130, 220 (1991).
131. E. G. Rowlands and P. F. James, The Structure of Non-Crystalline Solids, edited by P. H. Gaskell (Taylor and Francis, London, 1977), p. 215.
132. x are the enthalpy and temperature of crystallization of the glass.
133. The thermodynamic functions were evaluated using the experimental data of Ref. 55. The details are given in Ref. 28(e). These data yield 52.7 kJ/mol for the room temperature heat of crystallization, which is in an excellent agreement with a recent value (53.5±4 kJ/mol) by S. Sen et al., J. Non-Cryst. Solids 168, 64 (1994). Therefore, they are preferred to those selected by the JANAF, JANAF Thermochemical Tables, 2nd ed. (U.S. Department of Commerce, National Bureau of Standards, Washington, D. C., 1971), which correspond to less than 45.1 kJ/mol at the same temperature.
134. The thermodynamic functions were evaluated using the experimental data of Ref. 55. The details are given in Ref. 28(e). These data yield 52.7 kJ/mol for the room temperature heat of crystallization, which is in an excellent agreement with a recent value (53.5±4 kJ/mol) by S. Sen et al., J. Non-Cryst. Solids 168, 64 (1994). Therefore, they are preferred to those selected by the JANAF, JANAF Thermochemical Tables, 2nd ed. (U.S. Department of Commerce, National Bureau of Standards, Washington, D. C., 1971), which correspond to less than 45.1 kJ/mol at the same temperature.
135. This viscosity function is consistent with the transient time data of Ref. 43(b).
136. Evaluated from the data of C. J. R. Gonzalez-Oliver et al., J. Mater. Sci. 14, 1159 (1979), for a glass containing extra amount of water.
137. K. Matusita and M. Tashiro, J. Ceram. Soc. Jpn. 81, 500 (1973).
138. O. V. Mazurin, M. V. Streltsina, and T. P. Shvaiko-Shvaikovskaya, Handbook of Glass Data, Physical Science Data 15, Part C (Elsevier, Amsterdam, 1987), p. 99.
139. V. M. Fokin, Ph.D. thesis, Insitut of Silicate Chemistry of Russian Academy of Sciences, 1980.