| 三维稳态晶体生长的物理本质 |
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| 引用本文： | 王凤英,陈明文,孙仁济,王自东. 三维稳态晶体生长的物理本质[J]. 北京科技大学学报, 2003, 25(3): 230-233 |
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| 作者姓名： | 王凤英 陈明文 孙仁济 王自东 |
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| 作者单位： | 1. 北京科技大学应用科学学院数力系,北京,100083
2. 北京科技大学材料科学与工程学院,北京,100083 |
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| 基金项目： | 国家重大基础研究项目(No.G2000067206_1)，北京市科技新星计划(No.954811800) |
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| 摘 要： | 考虑在均匀流场的作用下，分析了金属熔液凝固过程中晶体生长的三维稳态数学模型。应用傅里叶级数展开法，在周期性条件下得到了相应的八阶常微分方程的精确解析解，并确定了解中各系数之间的关系。该解揭示了在均匀流场的作用下，晶体生长呈现了一种周期性振荡式的模式，从理论上证实了固液界面前沿浓度呈现指数振荡衰减性是晶体生长的一个本质特性。
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| 关 键 词： | 金属凝固过程 晶体生长 三维稳态数学模型 傅里叶级数展开法 常微分方程 解析解 生长机制 |
| 修稿时间： | 2002-07-24 |
Physical Essence of Crystal Growth in the Three-Dimension Stable State Problem |
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| WANG Fengying,CHEN Mingwen,Sun Renji,WANG Zidong. Physical Essence of Crystal Growth in the Three-Dimension Stable State Problem[J]. Journal of University of Science and Technology Beijing, 2003, 25(3): 230-233 |
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| Authors: | WANG Fengying CHEN Mingwen Sun Renji WANG Zidong |
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| Affiliation: | WANG Fengying,CHEN Mingwen,Sun Renji,WANG ZidongDepartment of Mathematics and Mechanics,University of Science and Technology Beijing,Beijing 100083,ChinaMaterial Science and Engineering School,University of Science and Technology Beijing,Beijing 100083,China |
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| Abstract: | A corresponding three-dimension steady state model concerned with dendrite growth is analyzed considering the influence of a uniform convection field. By using Fourier series, an eight-order ordinary differential equation is finally solved and an accurate analytic solution is obtained in a very neat form. At the same time the correlations among the coefficients in the analytic solution are determined. The obtained solution shows that the crystal growth in the steady state presents cyclic oscillation attenuation along the dendrite growth direction under the influence of a uniform fluid field, and theoretically confirms that this feature is an intrinsic character. |
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| Keywords: | metal solidification crystal growth partial differential equation fourier series |
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