Abstract
In directional solidification of binary eutectics, it is often observed that two-phase lamellar growth patterns grow tilted with respect to the direction z of the imposed temperature gradient. This crystallographic effect depends on the orientation of the two crystal phases α and β with respect to z. Recently, an approximate theory was formulated that predicts the lamellar tilt angle as a function of the anisotropy of the free energy of the solid(α)-solid(β) interphase boundary. We use two different numerical methods-phase field (PF) and dynamic boundary integral (BI)-to simulate the growth of steady periodic patterns in two dimensions as a function of the angle θ(R) between z and a reference crystallographic axis for a fixed relative orientation of α and β crystals, that is, for a given anisotropy function (Wulff plot) of the interphase boundary. For Wulff plots without unstable interphase-boundary orientations, the two simulation methods are in excellent agreement with each other and confirm the general validity of the previously proposed theory. In addition, a crystallographic "locking" of the lamellae onto a facet plane is well reproduced in the simulations. When unstable orientations are present in the Wulff plot, it is ex...Continue Reading
References
Nov 15, 1991·Physical Review. a·K Kassner, C Misbah
Oct 9, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·S AkamatsuA Karma
Dec 20, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jean-Marc DebierreRahma Guérin
Nov 5, 2004·Physical Review Letters·Silvère AkamatsuGabriel Faivre
Feb 9, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Blas EchebarriaMathis Plapp
Aug 11, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R Folch, M Plapp
Nov 9, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Mathis Plapp
Apr 3, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Abhik Choudhury, Britta Nestler
Citations
Aug 31, 2016·Physical Review. E·Jean-Marc DebierreKlaus Kassner
Mar 18, 2016·Physical Review. E·Zhi-Feng Huang
Aug 18, 2018·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Kamal ChoudharyFrancesca Tavazza
Jul 15, 2018·Scientific Reports·Zhenyuan LuXi Li
Jan 24, 2020·Small·Saman MoniriAshwin J Shahani