A Microscopic Theory for Domain Wall Motion and Its Experimental Verification in Fe‐Al Alloy Domain Growth Kinetics
A Microscopic Theory for Domain Wall Motion and Its Experimental Verification in Fe‐Al Alloy Domain Growth Kinetics
复制标题
DOI：
10.1051/jphyscol:1977709
复制
发表时间：
1977-12
期刊：
影响因子：
--
通讯作者：
J. Cahn;S. Allen
中科院分区：
文献类型：
--
作者：
J. Cahn;S. Allen
- 有序结构中弯曲反相畴壁运动的微观理论导致了速度与平均曲率成正比的预测。与以前的模型不同，速度与畴壁自由能不成比例。在一定温度、时间和成分范围内，有序FeAl合金中畴生长的实验结果与理论一致。在畴壁自由能趋于零的临界温度附近，畴生长没有减慢。导论. - 反相畴界是真实的有序合金的非平衡特征。由于存在与这些边界相关联的正的过量表面自由能，它们通过扩散以这样的方式移动，使得边界的总面积减小。界面运动的一个长期存在的唯象理论[1-3]指出，界面速度与热力学驱动力成比例，比例常数是称为迁移率的正量。该理论中的热力学驱动力是边界的局部平均曲率和单位面积边界的超额表面自由能的乘积。有序合金中高阶转变的一个特征是，当接近临界温度时，反相边界能接近零[4，5]。因此，界面运动的唯象理论似乎表明，当接近有序化的临界温度时，反相畴的生长应该变得非常缓慢。在本文中，一个新的界面速度的表达式将推导出使用的微观模型。在这个新的公式中没有出现单位面积的过量表面自由能，因此，系统在临界点附近的行为更清楚地表示。应用新的结果的宏观反相畴生长的问题导致一个简单的实验测试的理论。微观理论- 连续有序化的动力学方程反映了有序参数r1不是守恒量的事实。如果自由能不是在最小值相对于局部变化r\有一个即时的变化r\由dr\ SF 5？其中dFjStj是系统的自由能相对于r1的局部变化的变分导数，并且α是正的动力学系数。在非均匀系统中[5] bF\br\ = dF/dri 2 K VTJ（2）其中dF/drj是均匀有序系统的自由能变化率，2 K Vr 1是r1在空间上变化的系统中的梯度能量贡献。对于时间依赖问题，我们得到
— A microscopic theory for curved antiphase domain wall motion in ordered structures leads to a prediction that velocity is proportional to mean curvature. Unlike previous models, the velocity is not proportional to domain wall free energy. Experimental results on domain growth in ordered FeAl alloys over a range of temperatures, times and compositions, are consistent with the theory. In the vicinity of the critical temperature where domain wall free energy tends to zero, domain growth is not slowed. Introduction. — Antiphase domain boundaries are a non-equilibrium feature of real ordered alloys. Since there is a positive excess surface free energy associated with these boundaries, they move by diffusion in such a way that the total area of the boundaries is reduced. A long-standing phenomenological theory of interface motion [1-3] states that interfacial velocity is proportional to the thermodynamic driving force, the proportionality constant being a positive quantity called a mobility. The thermodynamic driving force in this theory is the product of the local mean curvature of the boundary and the excess surface free energy per unit area of boundary. A feature of higher-order transitions in ordering alloys is that the antiphase boundary energy approaches zero as the critical temperature is approached [4, 5]. Thus, the phenomenological theory of interface motion would seem to indicate that as the critical temperature for ordering is approached, antiphase domain growth should become very sluggish. In this paper, a new expression for interfacial velocity will be derived using a microscopic model. The excess surface free energy per unit area does not appear in this new formulation, and hence, the behavior of systems near critical points is more clearly represented. Application of the new result to the problem of macroscopic antiphase domain growth leads to a simple experimental test of the theory. Microscopic theory. — The kinetic equations of continuous ordering reflect the fact that the order parameter r\ is not a conserved quantity. If the free energy is not at a minimum with respect to a local variation in r\ there is an immediate change in r\ given by dr\ SF 5 ? = K ^ (1) where dFjStj is the variational derivative of the free energy of the system with respect to a local change in r\, and a is a positive kinetic coefficient. In a non-uniform system [5] bF\br\ = dFjdri 2 K VTJ (2) where dF/drj is the rate of change in free energy for uniformly ordered systems and 2 K Vr\ is the gradient energy contribution in a system in which r\ is varying spatially. We obtain for the time dependent problem