三维棒状共晶生长稳定性和选择性的解析研究

凝固过程中共晶生长的稳定性和选择性等问题一直是材料科学、凝聚态物理学和非线性科学领域中非常重要的前沿课题。有关揭示共晶生长机理相关理论的突破将推动各大学科领域的相互渗透,将为共晶等自生复合材料的制备与发展开辟广阔的前景。本项目旨在用解析的方法对在定向凝固系统中发生的三维棒状共晶生长的稳定性和选择性进行深入细致的研究，揭示共晶生长现象后的物理本质。将以棒状共晶生长实验系统作为研究对象，结合凝固热力学和动力学，建立棒状共晶非稳态生长的数学模型；应用渐近分析方法寻求椭圆柱型棒状共晶生长系统的全局一致有效的解析解；应用稳定性理论和分岔理论对棒状共晶生长进行稳定性和选择性分析，定量地获得棒状共晶稳定生长区域和各种生长模式的临界转变区域或临界点；定量地获得各种生长模式下共晶形貌特征尺寸与工艺条件的变化规律。

Stability and selection of eutectic growth during solidification remain much attractive research problems in materials science and condensed state physics and nonlinear science. The scientific breakthroughs of revealing essence of the eutectic growth will promote the mutual development of the three disciplines. These scientific breakthroughs will also open up broader prospects for preparing and developing such eutectic composites. This project arms at studying stability and selection of three-dimensional rod eutectic growth in directional solidification using analytical methods and revealing the physical nature after the eutectic growth phenomenon. Based on experiments of the rod eutectic growth, the mathematical model of the unsteady growth will be given by combining with solidification thermodynamics and kinetics. The global uniformly valid analytical solutions of the elliptic cylinder type rod eutectic growth will be obtained by using asymptotic analytical methods. The stability and selection of the eutectic growth will be studied by using stability theory and bifurcation theory. The stable region and the critical transformable region or the critical points will be fixed quantitatively. The relationships of the characteristic scales of the eutectic morphologies with the process conditions will be also given quantitatively.