对于岛屿大小分布的双指数缩放函数.
1St. Petersburg State University, Faculty of Physics, Universitetskaya Embankment 13B, 199034 St. Petersburg, Russia.
Physical review. E
|November 18, 2025
概括
这项研究分析了子单一层沉积中的岛屿大小分布,揭示了某些捕获数依赖性的缩放函数奇点. 为了解决这些问题,提出了一个新的分析缩放函数.
科学领域:
- 表面科学是一门科学.
- 材料科学 是一种材料科学.
- 物理化学 物理化学
背景情况:
- 同质核和生长是薄膜形成的基本过程.
- 岛屿大小分布对于理解表面形态和特性至关重要.
- 速率方程和捕获数是建模这些现象的关键理论工具.
研究的目的:
- 为了研究捕获数 (σ(s)) 功能形式在亚单一层沉积过程中对岛屿大小分布的影响.
- 在不同的生长条件下分析现有的缩放函数 (Family-Vicsek) 的有效性和局限性.
- 开发一种新的,无奇点的分析缩放函数,用于改进理论建模.
主要方法:
- 解决岛屿核和生长的连续速率方程.
- 分析捕获数字 (σ(s) ∼s^{α}) 的权力定律大小依赖关系.
- 重新审视巴特尔特-埃文斯理论,并提出了一个新的分析形式,用于缩放的捕获数字C(x).
主要成果:
- 现有的Family-Vicsek缩放函数表现出0≤α<1/2的奇点,随着α的增加而恶化.
- 对于1/2<α<1.1,没有可规范化的缩放解决方案.
- 导出了一个具有双指数形状的分析缩放函数,解决奇点并满足总和规则.
结论:
- 缩放函数的奇点来自最大岛屿大小的零增长率.
- 拟议的分析缩放函数为岛屿大小分布提供了更强大的理论描述.
- 新的函数与动力蒙特卡洛模拟的结果密切匹配,验证了它的准确性.
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