We have investigated the transmission of the 5 keV proton beam through a graphene sheet containing monovacancy, adatom, and Stone–Wales defects. The proton–graphene interaction potential was constructed using the Doyle–Turner's proton–carbon interaction potential. The closed form of the scattering law was obtained using the momentum approximation. Angular distributions of the transmitted protons were analyzed using the morphological method based on the inspection of the rainbow patterns in the impact parameter and scattering angle planes generated by the rainbow scattering. We have demonstrated that rainbows in the impact parameter plane are attracted and repelled by the nearest saddles and maxima of the reduced proton–graphene interaction potential. This explains why the rainbow pattern is so sensitive to the redistribution of the potential extrema caused by defects. Each defect type produces its distinctive rainbow pattern that dominantly determines the shape of the angular distribution. The ridge maxima of the angular distributions were investigated and related to the spectrum of the Jacobian matrix of the map generated by the scattering law. In the end, it has been shown how observed rainbow patterns could be used to determine the unknown defect densities of the complicated sample containing a combination of the different defect types.

中文翻译：

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石墨烯点缺陷形成的彩虹图案的形态分析

我们研究了 5 keV 质子束通过含有单空位、吸附原子和斯通-威尔士缺陷的石墨烯片的传输。质子-石墨烯相互作用势是使用 Doyle-Turner 的质子-碳相互作用势构建的。散射定律的封闭形式是使用动量近似获得的。基于对撞击参数中的彩虹图案和彩虹散射产生的散射角平面的检查，使用形态学方法分析了透射质子的角分布。我们已经证明，撞击参数平面中的彩虹被最近的鞍点和降低的质子 - 石墨烯相互作用势的最大值吸引和排斥。这就解释了为什么彩虹图案对由缺陷引起的潜在极值的重新分布如此敏感。每种缺陷类型都会产生其独特的彩虹图案，主要决定角分布的形状。研究了角分布的脊最大值并与由散射定律生成的地图的雅可比矩阵的频谱相关。最后，展示了如何使用观察到的彩虹图案来确定包含不同缺陷类型组合的复杂样品的未知缺陷密度。研究了角分布的脊最大值并与由散射定律生成的地图的雅可比矩阵的频谱相关。最后，展示了如何使用观察到的彩虹图案来确定包含不同缺陷类型组合的复杂样品的未知缺陷密度。研究了角分布的脊最大值并与由散射定律生成的地图的雅可比矩阵的频谱相关。最后，展示了如何使用观察到的彩虹图案来确定包含不同缺陷类型组合的复杂样品的未知缺陷密度。