Analysis of Ordering Dynamics in Ll_2-Alloys with a Vectorized Order-Parameter

为了分析Cu_3Au型（Ll_2）合金的有序化过程及相应的微观结构变化，采用Ginzburg-Landau展开法建立了动力学方程。Ll_2晶胞有四个格点，分为α亚格点和β亚格点。由于α-和β-亚晶格位置的数目彼此不同（1和3），Ll_2具有四个相，这取决于哪个晶格点是β-位置。一个单一的序参量不能描述包括相位在内的有序状态，只要它是一个真实的数。在本研究中，引入了一个矢量化的序参数S=S（eta 1，eta 2，eta 3，eta 4），以下Potts模型。每个参数eta 1、eta 2、eta 3、eta 4具有非负值。首先，确定了动力学方程中的能量系数，从而重现了Cu-Pt的平衡相图。利用动力学方程进行计算机模拟，分析了与有序化相关的微观结构的变化。结果表明：（1）在反相边界附近，相位以补偿性地减小eta 1而增大eta 2的方式平滑变化; (ii)在反相界面处，形成了一个有序度为零且Pt浓度高的狭窄区域，这对应于“润湿现象”。“（iii）由本模拟得到的序参量分布与用团簇变分法计算的结果吻合得很好。(iv)模拟结果再现了周期性反相界湮灭过程中的发夹机制。(v)用该动力学方程分析了反相界的其他重要行为和显微组织的变化。

A kinetic equation has been formulated with the Ginzburg-Landau expansion in order to analyze the ordering processes and the associated changes of microstructures in Cu_3Au-type (Ll_2)alloys. The Ll_2 unit-cell has four lattice points which are divided into alpha-and beta-sublattice sites. Since the numbers of alpha-and beta-sublattice sites are different from each other (1 and 3), Ll_2 has four phases depending on which lattice point is beta-site. A single order-parameter cannot describe the state of order including the phase, as far as it has a real number. In the present study, a vectorized order-parameter S=S (eta1, eta2, eta3, eta4) is introduced, following a Potts model. Each parameter, eta1, eta2, eta3, eta4, has a non-negative value. First, the energy coefficients in the kinetic equation were determined so that the equilibrium phase diagram for Cu-Pt was reproduced. The changes in microstructures associated with ordering were analyzed by performing compuersimulation using the kinetic equation. Following results were obtained : (i) Around an antiphase boundary, the phase changes smoothly in the way that eta1 decreases and eta2 increases compensationally. (ii) At an antiphase boundary, there forms a narrow region of a zero-degree of order and of high concentration of Pt, which corresponds to a "wetting phenomenon." (iii) The profiles of order-parameters obatined by the present simulation agree well with those calculated by a cluster-variation method. (iv) The hairpin mechanism in the annihilation process of periodic antiphase boundaries was successfully reproduced by the simulation. (v) Other important behaviors of antiphase boundaries and changes in microstructure were analyzed with the present kinetic equation.