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A theory for polymorphic melting in binary solid solutions

Published online by Cambridge University Press:  11 April 2011

Huaming Li  and
Mo Li
Huaming Li
Affiliation:
School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332; and School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332
Mo Li*
Affiliation:
School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332; and Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106
*
a)Address all correspondence to this author. e-mail: mo.li@mse.gatech.edu
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Abstract

We propose a phenomenological Landau theory to describe polymorphic melting in binary solid solutions. We use the mean atomic displacement as the primary order parameter to represent the loss of the long-range order and the elastic strain induced by alloy component as the secondary order parameter. Under polymorphic constraint where alloy concentration fluctuation is restricted, the model predicts the melting line, also called T0-curve that is depressed by two factors, the static strain field caused by the solute, and the anharmonicity induced by the thermal vibration. We also obtain other thermodynamic properties at and around the melting point. The results confirm well with available experimental results for dilute solutions. We extrapolate the melting line to high concentration region for which no experimental data are available. From the results, we discuss the relation between polymorphic melting and glass transition, as well as glass formability.

Keywords

Phase transformationAmorphousPhase equilibria
Type
Articles
Information
Journal of Materials Research , Volume 26 , Issue 8 , 28 April 2011 , pp. 997 - 1005
Copyright
Copyright © Materials Research Society 2011

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References

REFERENCES

1.Ubbelhode, A.R.: The Molten State of Matter: Melting and Crystal Structure (Wiley, New York, 1979).Google Scholar
2.Born, M.: Thermodynamics of crystals and melting. J. Chem. Phys. 7, 591 (1939).CrossRefGoogle Scholar
3.Born, M.: On the stability of crystal lattices I. Proc. Cambridge Philos. Soc. 36, 160 (1940).CrossRefGoogle Scholar
4.Born, M.: Dynamical Theory of Crystal Lattices (Oxford University Press, 1998).Google Scholar
5.Lindemann, F.A.: The calculation of molecular vibration frequencies. Phys. Z. 11, 609 (1910)Google Scholar
6.Gilvarry, J.J.: The Lindemann and Grüneisen laws. Phys. Rev. 102, 308 (1956).CrossRefGoogle Scholar
7.Tallon, J.L., Robinson, W.H., and Smedley, S.I.: A melting criterion based on the dilatation dependence of shear modulii. Nature 266, 337 (1977)CrossRefGoogle Scholar
8.Tallon, J.L.: Crystal instability and melting. Nature 299, 188 (1982)CrossRefGoogle Scholar
9.Tallon, J.L.: A hierarchy of catastrophes as a succession of stability limits for the crystalline state. Nature 342, 658 (1989).CrossRefGoogle Scholar
10.Gorecki, T.: Vacancies and changes of physical-properties of metals at melting-point. Z. Metallkde. 65, 426 (1974)Google Scholar
11.Gorecki, T.: Comments on vacancies and melting. Scr. Metall. 11, 1051 (1977).CrossRefGoogle Scholar
12.Lennard, J.E. and Devonshire, A.F.: Critical and co-operative phenomena III. A theory of melting and the structure of liquids. Proc. R. Soc. London, Ser. A 169, 317 (1939)Google Scholar
13.Nordlund, K. and Averback, R.S.: Role of self-interstitial atoms on the high temperature properties of metals. Phys. Rev. Lett. 80, 4201 (1998).CrossRefGoogle Scholar
14.Ninomiya, T.: Theory of melting, dislocation model I. J. Phys. Soc. Jpn. 44, 263 (1978).CrossRefGoogle Scholar
15.Kanigel, A., Adler, J., and Polturak, E.: Influence of point defects on the shear elastic coefficients and on the melting temperature of copper. Int. J. Mod. Phys. 12, 727 (2001)CrossRefGoogle Scholar
16.Bai, X.M. and Li, M.: Ring-diffusion mediated homogeneous melting in the superheating regime. Phys. Rev. B 77, 134109 (2008).CrossRefGoogle Scholar
17.Uhlmann, D.R.: On the internal nucleation of melting. J. Non-Cryst. Solids 41, 347 (1980).CrossRefGoogle Scholar
18.Cahn, R.W.: Melting and the surface. Nature 323, 668 (1986).CrossRefGoogle Scholar
19.Krivogla, M.A.: Theory of X-Ray and Thermal Neutron Scattering by Real Crystals (Plenum Press, New York, 1969)Google Scholar
20.Kuhs, W.F.: Generalized atomic displacements in the crystallographic structure analysis. Acta Cryst. A 48, 80 (1992).CrossRefGoogle Scholar
21.Voronel, A., Rabinovich, S., Kisliuk, A., Steinburg, V., and Sverbilov, T.: Universality of physical properties of disordered alloys. Phys. Rev. Lett. 60, 2402 (1988)CrossRefGoogle ScholarPubMed
22.Lam, N.Q. and Okamoto, P.R.: A unified approach to solid-state amorphization and melting. Mater. Res. Soc. Bull. XIX 7, 41 (1994)CrossRefGoogle Scholar
23.Lam, N.Q., Okamoto, P.R., and Li, M.: Defect-induced crystal-to-glass transition. J. Nucl. Mater. 251, 89 (1997).CrossRefGoogle Scholar
24.Porter, D.A. and Easterling, K.E.: Phase Transformations in Metals and Alloys, 2nd ed. (Chapman & Hall, 1992).CrossRefGoogle Scholar
25.Kamenatskaya, D.S.: in Growth of Crystals, Vol. 8, edited By Shefta, N.N. (Consultants Bureau, New York, 1969), p. 271 .Google Scholar
26.Allen, W.P., Fecht, H.J., and Perepezko, J.H.: Melting behavior of Sn–Bi alloy droplets during continuous heating. Scr. Metall. 23, 643 (1989)CrossRefGoogle Scholar
27.Lee, K.R., West, J.A., Smith, P.M., Aziz, M.J., and Knapp, J.A.: Measurements of T0 temperatures of supersaturated Si–As alloys. Mater. Res. Soc. Symp. Proc. 205, 31 (1992).Google Scholar
28.Johnson, W.L.: Thermodynamic and kinetic aspects of the crystal to glass transformation in metallic materials. Prog. Mater. Sci. 30, 81 (1986).CrossRefGoogle Scholar
29.Li, M., Johnson, W.L., and Goddard, W.A. III: Configurationally frozen defects, random strains and Landau theory of crystal to glass transition. Mater. Forum 43, 246 (1995)Google Scholar
30.Cowley, R.A.: Structural phase transitions. I. Landau theory. Adv. Phys. 29, 1 (1980)CrossRefGoogle Scholar
31.Lipowsky, R.: Critical surface phenomena at first order bulk transitions. Phys. Rev. Lett. 49, 1575 (1982)CrossRefGoogle Scholar
32.Löwen, H. and Lipowsky, R.: Surface melting away from equilibrium. Phys. Rev. B 43, 3507 (1991).CrossRefGoogle ScholarPubMed
33.Krill, C.E. III, Li, J., Garland, C.M., Ettl, C., Samwer, K., Yelon, W.B., and Johnson, W.L.: Precursors of amorphization in supersaturated Nb–Pd solid solutions. J. Mater. Res. 10, 280 (1995).CrossRefGoogle Scholar
34.Massalski, T.B. and Okamoto, H.: Binary Alloy Phase Diagrams (ASM International, OH, 1992).Google Scholar
35.Kittz, J.A., Reitano, R., Aziz, M.J., Brunco, D.P., and Thompson, M.O.: Time-resolved temperature measurements during rapid solidification of Si–As alloys induced by pulsed-laser melting. J. Appl. Phys. 73, 3725 (1993).Google Scholar
36.Peercy, P.S., Thompson, M.O., and Tsao, J.Y.: Effects of As impurities on the solidification velocity of Si during pulsed laser annealing. Appl. Phys. Lett. 47, 244 (1985)CrossRefGoogle Scholar
37.Baeri, P., Reitano, R., Malvezzi, A.M., and Borghesi, A.: Pulsed laser melting of Si–As supersaturated solid solutions. J. Appl. Phys. 67, 1801 (1990).CrossRefGoogle Scholar
38.Gurvich, L.V. and Veyts, I.V.: Thermodynamic Properties of Individual Substances: Elements and Compounds, Vol 2, 4th ed. (Hemisphere Pub. Corp., CRC Press, 1990).Google Scholar
39.Nikanorov, S.P., Burenkov, Yu.A., and Stepanov, A.V.: Elastic properties of silicon. Sov. Phys. Solid State 13, 2516 (1971).Google Scholar
40.Mohr, P.J., Taylor, B.N., and Newell, D.B.: CODATA recommended values of the fundamental physical constants. Rev. Mod. Phys. 80, 633 (2008).CrossRefGoogle Scholar
41.Hull, R.: Properties of Crystalline Silicon (INSPEC, London, 1999).Google Scholar
42.Cahn, R.W. and Haasen, P.: Physical Metallurgy, 4th ed. (North-Holland, Amsterdam, 1996), pp. 686–687.Google Scholar
43.Murray, J.L.: Calculations of stable and metastable equilibrium diagrams of the Ag–Cu and Cd–Zn systems. Metall. Trans. A 15, 261 (1984).CrossRefGoogle Scholar
44.Li, M. and Johnson, W.L.: Instability of metastable solid solutions and crystal to glass transition. Phys. Rev. Lett. 70, 1120 (1993).CrossRefGoogle ScholarPubMed
45.Johnson, W.L., Li, M., and Krill, C.E. III: The crystal to glass transition in relation to melting. J. Non-Cryst. Solids 156–158, 481 (1993).CrossRefGoogle Scholar
46.Li, M., Johnson, W.L., and Goddard, W.A. III: Evidence of hexatic phase formation in 2-dimensional Lennard–Jones binary arrays. Phys. Rev. B 54, 12067 (1996).CrossRefGoogle Scholar
47.Li, M.: Defect-induced topological order-to-disorder transition in two-dimensional binary substitutional alloys: A molecular dynamics study. Phys. Rev. B 62, 13979 (2000).CrossRefGoogle Scholar
48.Jalali, P. and Li, M.: Atomic size effect on critical cooling rate and glass formability. Phys. Rev. B 71, 013450 (2005).CrossRefGoogle Scholar
49.Lee, H.J., Cagain, T., Johnson, W.L., and Goddard, W.A.: Criteria for formation of metallic glasses: The role of atomic size ratio. J. Chem. Phys. 119, 9858 (2003).CrossRefGoogle Scholar
50.Egami, T. and Waseda, Y.: Atomic size effect on the formability of metallic glasses. J. Non-Cryst. Solids 64, 113 (1984).CrossRefGoogle Scholar
51.Egami, T.: Universal criterion for metallic glass formation. Mat. Sci. Eng. A 226, 261 (1993).Google Scholar