Abstract—Non-point vacancy-gas defects (VGD) (pores, blisters) in the crystal lattice arise as a result of its irradiation with an inert gas Xe⁺⁺, the process is considered as the formation of first-order phase transition nuclei by means of computational mathematics, kinetic theory, and the theory of stochastic dynamic variables and Wiener random processes. The characteristics of disordered porosity in samples consisting of layers (“dielectric/metal”) at various layer thicknesses are calculated. The formation of spherical shape defects in materials at times of the order of 10^–4 s, when the porosity of the material nucleates, is preceded or accompanied by the appearance of microcracks. Irradiation of surfaces with an inert gas with ion energies of 5–10 keV refers to low-temperature blistering; in the model, the constancy of the influence of radiation fluxes stimulating a phase transition creates the condition of an “open” physical system in which it is possible to combine lattice defects into structures that cause local stresses, and the constancy of the temperature of the sample, the pressure of the implantable “monomers” of the gas, and supersaturation (similar to the parameters of vapor condensation) are characteristic of the fluctuation unstable stage of the phase transition move. Partial kinetic equations with nonlinear coefficients (Kolmogorov–Feller and Einstein–Smoluchowski) are solved by the method of stochastic molecular dynamics, which establishes a connection between the solution of Ito stochastic equations in the sense of Stratonovich and kinetic equations; stable numerical methods are used. The conditions for the formation of VGD are determined taking into account the influence of the elastic properties of the lattice, and the porosity and local stresses in thin layers of irradiated materials are calculated.

中文翻译：

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惰性气体离子辐照样品时孔隙成核的随机模型

摘要—惰性气体Xe ⁺⁺辐射导致晶格中出现非点空位缺陷（VGD）（孔，气泡），该过程被认为是一阶相变核的形成借助计算数学，动力学理论以及随机动态变量和维纳随机过程的理论。计算了由不同厚度的层（“电介质/金属”）组成的样品中无序孔隙率的特征。材料中球形缺陷的形成时间约为10 ^–4当材料的孔隙度成核时，则在出现或出现微裂纹之前。用离子能量为5–10 keV的惰性气体辐照表面是指低温起泡。在模型中，辐射通量刺激相变的恒定性创造了一个“开放”物理系统的条件，在该条件下，有可能将晶格缺陷结合到引起局部应力的结构中，并且温度的恒定性也得以实现。样品中，气体的可植入“单体”的压力和过饱和度（类似于蒸汽冷凝的参数）是相变运动不稳定波动阶段的特征。用随机分子动力学方法求解具有非线性系数的局部动力学方程（Kolmogorov–Feller和Einstein–Smoluchowski），该方法在Stratonovich的意义上建立了Ito随机方程解与动力学方程之间的联系。使用稳定的数值方法。确定VGD的形成条件时要考虑晶格的弹性，并计算出被辐照材料薄层中的孔隙率和局部应力。