A method to compute the migration rate of planar solid–liquid interfaces in binary alloys.pdf

Journal of Crystal Growth 253 (2003) 549–556 A method to compute the migration rate of planar solid–liquid interfaces in binary alloys R.S. Qin, E.R. Wallach* Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK Received 10 December 2002; accepted 20 February 2003 Communicated by M. Uwaha Abstract A method for computing the migration rate of planar solid–liquid interfaces in binary alloys has been developed, and is based on the generalised kinetic equation and phase-field technique for crystal growth. The migration rate of the solid–liquid interface is expressed as a function of diffusivity, interfacial energy, temperature, solute concentration, molar volume, free energy and chemical potentials. Each quantity in the expression is either available from handbooks or can be computed using a thermodynamic database. Numerical calculations based on the present theory for the solidification of Al–Si, Al–Cu and Al–Mg binary alloys have been performed. Data fitting by the KGT model, v ? ADTn; reveals that 0:7ono1: The results agree well with prior metallurgical knowledge. r 2003 Elsevier Science B.V. All rights reserved. PACS: 81.10.Aj; 68.45.v; 64.70.Dv Keywords: A1. Growth models; A2. Growth from melt; B1. Alloys 1. Introduction Phase-field models based on the time-dependent Ginzburg–Landau theory are used to reproduce many solidification microstructures that can be observed experimentally [1,2]. Hence such models have the potential to predict accurately solidifica- tion in real alloy systems. Many of the necessary relationships between the various parameters in the governing equations of the phase-field model and classical thermodynamic quantities have been established [3–5]. Among these parameters is phase-field mobility which is concerned with the propagation rates of planar interfaces [3]. How- ever, relatively little is known about the propaga- tion rates of planar interfaces in alloys even though more comple