Numerical study of the liquid-solid interface properties for binary alloys using phase-field crystal approach
- PDF / 691,561 Bytes
- 7 Pages / 612 x 792 pts (letter) Page_size
- 19 Downloads / 246 Views
Numerical study of the liquid-solid interface properties for binary alloys using phase-field crystal approach Muhammad Ajmal Choudhary, Julia Kundin and Heike Emmerich Lehrstuhl für Material- und Prozesssimulation, Universität Bayreuth, D-95440 Bayreuth, Germany. ABSTRACT The phase-field crystal (PFC) method has emerged as a promising technique to simulate the evolution of crystalline patterns with atomistic resolution on mesoscopic time scales. We use a 2D PFC model based on Elder et al. [Phy. Rev. B 75, 064107 (2007)] to perform a systematic analysis of a liquid-solid interface for a binary alloy system. We propose the method of determining interfacial energies for a curved liquid-solid interface by stabilizing the circular solid seed in the surrounding liquid phase and the liquid droplet in the solid phase for various seed sizes in a finite system. We also investigate the impact of model parameters on the resulting interface energies. The interface energies are computed with various system sizes in order to study the system size effects. In particular, we compare the simulation results in the form of the interface energy as a function of radius with the existing theories. INTRODUCTION In 1990's, the non-classical theories of crystal nucleation were developed which resolved the dependency of the surface energy on the undercooling. This dependency is caused by the dependency of the surface energy on the nucleus size that contradicts to the classical nucleation theory. In the field of non-classical theories the modified self-consistent classical theory [1, 2], the field theoretic approaches based on the density functional theory [3 - 5] and the diffusion interface theory [6, 7] were introduced (see also a recent review of non-classical theories in [8]). The various phenomenological dependencies of the surface energy on the nucleus size were also proposed [2, 9]. Gránásy et al. [6] formulated his diffusion interface theory (DIT), in which the dependence of the interfacial energy on the curvature can be derived in the following way: (
*+ )
(1)
where is the interface thickness. Further, the phase-field model was applied to study the predictions made on the basis of the DIT. The phase-field approach is a powerful technique to address such issues due to its ability to describe a diffuse interface based on the Landau-Ginzburg free energy functional [10, 11]. In the field of crystal nucleation in highly undercooled melts, the predictions of the DIT were demonstrated for a hypothetical system [12], using both the continuum phase-field approach and the results of the atomistic simulations of a Lennard-Jones system. It was shown that the nucleation barrier vanishes as a result of vanishing surface energy for a smaller nucleus at a critical undercooling.
The non-classical theory of the liquid-vapour phase separation was developed by Tolman. It proposed that the surface energy of small liquid droplets existing in equilibrium with the vapour phase depends on its radius as (2) where is the Tolman length. A number of investig
Data Loading...
