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

用Ginzburg-Landau展开式建立了动力学方程，用来分析Cu3AU-型(LL2)合金的有序化过程及其微观结构的变化。L1_2晶胞有四个晶格点，分为α-和β-亚格点。由于α和β亚格点的数目不同(1个和3个)，因此根据哪个晶格点是β格点，L1_2有四个相。单个序参数不能描述包括相位在内的序的状态，只要它有实数。在本研究中，我们引入了一个矢量化序参数S=S(eta1，eta2，eta3，eta4)，遵循Potts模型。每个参数eta1、eta2、eta3、eta4具有非负值。首先确定了动力学方程中的能量系数，从而再现了铜-铂的平衡相图。通过使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。得到以下结果：(1)在反相界附近，相变平稳，相变的方式是eta1减小，eta2补偿增大。(Ii)在反相界面上，形成了一个零有序度、铂浓度较高的狭窄区域，对应于一种“润湿现象”。(3)由本模拟得到的序参数分布与用团簇变分方法计算的序参数分布符合得很好。(4)通过模拟成功地再现了周期性反相界湮没过程中的发夹机制。(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.