Abstract—

The experimentally studied surface morphology of films of the Heusler alloy Fe₂CoAl is compared to the theory of the formation of the fractal surface of films. This theory is based on the Cauchy problem for the simplified Kardar–Parisi–Zhang equation. It is shown that for the initial fractal shape of the film it can be solved immediately by applying the Oleinik–Lax principle (a weak solution to the problem). Within the framework of the exhaustive search method, numerical implementation of the Oleinik–Lax principle is proposed. A vector criterion of the quality of surface growth of the studied film is introduced. As the components of this criterion, the following functionals are tested: the norm of the spectral density of the autocorrelation function of the film surface in Hilbert space, Shannon information, and fractal dimension of the film surface. All these functionals are calculated over the shape of the film surface at each moment of time. A procedure for obtaining samples of the Fe₂CoAl Heusler alloy is described.

中文翻译：

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Heusler合金外延膜的生长模型

摘要—

实验研究的Heusler合金Fe ₂薄膜的表面形貌将CoAl与膜的分形表面形成理论进行了比较。该理论基于简化的Kardar–Parisi–Zhang方程的Cauchy问题。结果表明，对于膜的初始分形形状，可以通过应用Oleinik-Lax原理（对该问题的较弱解决方案）立即解决。在穷举搜索方法的框架内，提出了Oleinik-Lax原理的数值实现。介绍了研究薄膜表面生长质量的向量判据。作为此标准的组成部分，测试了以下功能：希尔伯特空间中薄膜表面自相关函数的光谱密度范数，香农信息和薄膜表面的分形维数。所有这些功能都是在每个时间点根据薄膜表面的形状进行计算的。铁样品的获取程序₂ CoAl Heusler合金的描述。