Elastic Effects on the Kinetics of a Phase Transition
Elastic Effects on the Kinetics of a Phase Transition
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相变动力学的弹性效应
DOI：
10.1103/physrevlett.82.1506
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发表时间：
1999
影响因子：
8.6
通讯作者：
V. I. Marchenko
中科院分区：
文献类型：
--
作者：
E. Brener;S. V. Iordanskii;V. I. Marchenko
描述了固体一级相变过程中新相的成核和生长动力学。新相的生长中心非常扁平，因为这种形状降低了由两相密度差异引起的变形的弹性能。强调了与裂缝问题的类比。核的生长受弹性效应和潜热扩散的共同作用。弹性裂纹效应导致其生长方式的选择与普通枝晶有本质的不同。[S0031-9007(99)08492-6] PACS编号：81.10。Aj, 62.20。可,81.40。Np成核和生长现象与一阶相变同时发生。在那里，热力学波动形成了临界核。这个细胞核随后以一种确定的方式生长。从熔体或溶液中生长晶体就是这种过程的典型例子。由于众所周知的Mullins-Sekerka不稳定性[1]，树枝状图案经常形成。如果初始亚稳相是晶体，相变动力学的新方面就会出现。由于两相的密度不同，新相成核中心周围的部分晶体会变形，与无应力情况相比，这改变了系统的行为。临界核呈扁圆形，这比球形更有利，因为它降低了弹性能[2,3]。在与裂纹问题类比的基础上，导出了[3]中该成核中心形成的能量和其他一些热力学性质。与无应力情况相比，弹性变形导致原子核形成能量的大幅增加。而在通常的生长现象中，由于Mullins-Sekerka不稳定性，会出现偏离球形的现象；在我们的例子中，它的形状是很扁的，即使对于平衡临界核来说也是如此。这封信的主要目的是描述在弹性效应存在下超临界核的生长。生长界面的运动是由潜热的不可逆扩散（扩散生长）和弹性变形所做的可逆功以及新表面积的形成之间的相互作用决定的。在这种类型的扩散生长过程中，这一过程和图案形成的动力学由于弹性效应而大大改变。我们将发现原子核演化的一种新的生长规律，它与习惯的树突生长规律b[4]有很大的不同。为了确定起见，我们暂时用融化的术语来说。晶体的熔化过程通常是从晶界或自由表面等非均质部位开始的。[5]。然而，通过实验技术可以避免非均相成核；晶体可以过热到超过平衡熔点[6,7]。因此，我们假设新相包含N个粒子，体积为W，它是化学势为m，压力为P的均匀熔体（我们假设外部压力为零）。根据质量守恒定律，熔体体积的表达式如下：
The kinetics of the nucleation and growth of a new phase in the course of a first-order phase transition in a solid is described. The growing center of a new phase is very oblate, because this shape lowers the elastic energy of the deformations which arise due to the difference in the densities of the two phases. An analogy with the crack problem is emphasized. The growth of the nucleus is governed by the combination of the elastic effects and the diffusion of the latent heat. The elastic cracklike effects lead to the selection of the growth mode which is substantially different from the ordinary dendrite. [S0031-9007(99)08492-6] PACS numbers: 81.10.Aj, 62.20.Mk, 81.40.Np Nucleation and growth phenomena occur in conjunction with a first-order phase transition. There a critical nucleus is formed by thermodynamical fluctuations. This nucleus afterward grows in a deterministic way. The growth of a crystal from the melt or from a solution is a typical example of such a process. Due to the well-known Mullins-Sekerka instability [1] the dendritic patterns often form. Novel aspects of the kinetics of phase transitions appear if the initial metastable phase is a crystal. Because of a difference in the densities of the two cooperating phases, a part of the crystal around a nucleation center of the new phase becomes deformed, which modifies the system’s behavior, in comparison with an unstressed situation. The critical nucleus has an oblate shape, which is more favorable compared to a spherical shape because it lowers the elastic energy [2,3]. The energy of the formation of this nucleation center and some other thermodynamic properties have been derived in [3] on the basis of the analogy with the crack problem. The elastic deformation leads to a substantial increase in the energy of the formation of the nucleus in comparison with the unstressed situation. While in the usual growth phenomena the deviation from the spherical shape appears due to the Mullins-Sekerka instability; in our case the shape is very oblate even for the equilibrium critical nucleus. The main purpose of this Letter is to describe the growth of a supercritical nucleus in the presence of the elastic effects. The motion of a growing interface is governed by the interplay between the irreversible diffusion of the latent heat (diffusional growth) and the reversible work done for elastic deformation and the formation of a new surface area. The kinetics of this process and pattern formation during this type of diffusional growth is substantially modified due to the elastic effect. We will find a new growth law for the evolution of the nucleus which is quite different from the customary dendritic growth law [4]. For definiteness, we will speak in terms of melting for the time being. The melting process of crystals is usually initiated at heterogeneous sites such as grain boundaries or free surfaces. [5]. However, providing the heterogeneous nucleation can be avoided by means of experimental techniques; crystals can be superheated above the equilibrium melting point [6,7]. Thus we assume that the new phase, which contains N particles and occupies a volume W ,i s a homogeneous melt with a chemical potential m and a pressure P (we assume that the external pressure is zero). Because of the conservation of mass, we have the following expression for the volume of the melt: