Cryst. Res. Technol. 42, No. 9, 914 – 919 (2007) / DOI 10.1002/crat.200710927 © 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Incorporation of surface tension to interface energy balance in crystal growth M. Yildiz and S. Dost* Crystal Growth Laboratory, Department of Mechanical Engineering, University of Victoria, Victoria, BC, V8W 3P6, Canada Received 27 February 2007, revised 25 March 2007, accepted 6 April 2007 Published online 12 June 2007 Key words crystal growth from solution, jump conditions, Gibbs-Thomson effect. PACS 81.10.Dn, 47.10.ab, 47.55.dm Effect of surface tension across a growth interface is known as the Gibbs-Thomson effect, and the associated energy balance is widely referred to as the Stefan condition in the literature, which is derived from thermodynamics. In this article, the interface energy balance that accounts for the effect of surface tension is derived by writing the jump condition for the energy balance on a surface of discontinuity which represents in crystal growth the evolving growth interface (solidification front) between the liquid and solid phases. To the best of our knowledge, the derivation of energy balance by writing jump conditions on a surface of discontinuity (interface) is new. © 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1 Introduction In crystal growth when the growth interface has a large curvature, the surface tension may play a significant role in the evolution of growth interface shape, affecting the concentration distribution in the melt/solution near the interface. In such a case, the inclusion of the effect of interface curvature (known as the Gibbs-Thomson effect) in a model may become necessary for accurate predictions. In addition, if a free surface exists in the system, the thermal and solutal gradients along the growth interface give rise to an additional convective flow in the melt/solution near the interface, which is known as the Marangoni convection. In crystal growth modeling involving an interface, either a free surface or an interface between the liquid and solids phases, writing accurate expressions for interface conditions is a challenge. In thermomechanics of a continuum, the associated boundary and interface conditions are obtained by writing the jump conditions for mass, momentum, and energy balances on a moving surface of discontinuity on which certain quantities may suffer jumps. This approach provides confidence in obtaining accurate boundary and interface conditions for a selected model. The derivation of the jump conditions related to mass, momentum, and energy balances through this approach is well-known (see for instance [1]). Surface tension appears in the momentum balance since it contributes to the force balance along the boundary of the domain. However, when the effect of surface tension needs to be included in the energy balance on a solidifying interface, referred to as the Stefan condition in the literature, the derivation is done through thermodynamics considerations, by introducing the effect of surface tension in temperature [2,3]. Similarly, the effect of surface tension on growth rate in crystal growth is included through its incorporation into concentration [4]. The contribution of surface tension may also be incorporated into growth rate by modifying the mass transport equation writing the jump condition for the species mass balance on a surface of discontinuity (interface) [5,6]. In this article, we present the derivation of the interface energy balance that accounts for the effect of surface tension, by writing the jump condition for the energy balance on a surface of discontinuity [7]. Here, a ____________________ * Corresponding author: e-mail: sdost@me.uvic.ca