A theory for polymorphic melting in binary solid solutions
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Mo Lia) 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 (Received 23 July 2010; accepted 17 February 2011)
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.
I. INTRODUCTION
Melting of crystalline solids is a topological order-todisorder transition in which a solid phase with long-range translational symmetry becomes a liquid with topological disorder. Melting is a first-order phase transition that involves discontinuous change in latent heat and volume at melting point.1 Born,2 on the one hand, described melting as a mechanical instability of solid phase associated with the loss of shear rigidity, which implies that melting is a continuous transition without nucleation and growth of the melt.3,4 Lindemann,5,6 on the other hand, related melting to thermal vibrations of atoms: melting occurs when the atomic mean square displacement (MSD) reaches a critical value. Both models are one-phase theory without consideration of the liquid phase and do not take into account the discontinuous character of first-order phase transition. Experimentally, elastic shear moduli of solids decrease with increasing temperature but do not reach zero at melting point. The MSD, on the other hand, does show increase in magnitude as melting point is approached. Tallon7–9 modified Born’s criterion by stating that the shear modulus of a cubic crystal could reach zero at a higher melting temperature if the volume of the crystal is extrapolated smoothly across the gap at melting to that of the liquid phase. To induce the Born–Tallon instability, large volume expansion is needed by introducing a large number of point defects, such as vacancies10,11 and a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2011.55 J. Mater. Res., Vol. 26, No. 8, Apr 28, 2011
interstitials,12,13 and sometimes line defects.14 For thermal melting, these scenarios may seem farfetched as it is impossible to achieve such high defect densities (a few percent) in either experiment o
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