Title: The density and pressure of helium nano-bubbles encapsulated in silicon Show Chinese title

Title: 氦纳米气泡在硅中的密度和压力

Abstract: The $1s^2->1s2p(^1P)$ excitation in confined and compressed helium atoms in either the bulk material or encapsulated in a bubble is shifted to energies higher than that in the free atom. For bulk helium, the energy shifts predicted from non-empirical electronic structure computations are in excellent agreement with the experimentally determined values. However, there are significant discrepancies both between the results of experiments on different bubbles and between these and the well established descriptions of the bulk. A critique is presented of previous attempts to determine the densities in bubbles by measuring the intensities of the electrons inelastically scattered in STEM experiments. The reported densities are untrustworthy because it was assumed that the cross section for inelastic electron scattering was the same as that of a free atom whilst it is now known that this property is greatly enhanced for atoms confined at significant pressures. It is shown how experimental measurements of bubbles can be combined with data on the bulk using a graphical method to determine whether the behavior of an encapsulated guest differs from that in the bulk material. Experimental electron energy loss data from an earlier study of helium encapsulated in silicon is reanalyzed using this new method to show that the properties of the helium in these bubbles do not differ significantly from those in the bulk thereby enabling the densities in the bubbles to be determined. These enable the bubble pressures to be deduced from a well established experimentally derived equation of state. It is shown that the errors of up to 80% in the incorrectly determined densities are greatly magnified in the predicted pressures which can be too large by factors of over seven. This has major practical implications for the study of radiation damage of materials exposed to $\alpha$ particle bombardment. Show Chinese abstract

Abstract: 在受限和压缩的氦原子中的$1s^2->1s2p(^1P)$激发，无论是处于块体材料中还是被包裹在气泡中，其能量都高于自由原子中的能量。 对于块体氦，从非经验性电子结构计算中预测的能量位移与实验确定的值非常吻合。 然而，不同气泡实验的结果之间存在显著差异，并且这些结果与已确立的块体描述之间也存在显著差异。 对之前通过测量STEM实验中非弹性散射电子的强度来确定气泡中密度的尝试进行了批判性分析。 报告的密度不可靠，因为假设非弹性电子散射的截面与自由原子相同，而现在已经知道，在高压下受限的原子的这一特性大大增强。 展示了一种图形方法，如何将气泡的实验测量与块体数据结合起来，以确定封装的客体行为是否与块体材料中的行为不同。 利用这种方法重新分析了早期研究硅中封装氦的实验电子能量损失数据，以表明这些气泡中氦的性质与块体中的性质没有显著差异，从而能够确定气泡中的密度。 这些数据使可以通过一个已建立的实验得出的状态方程推导出气泡压力。 显示了在错误确定的密度中高达80%的误差在预测的压力中被大大放大，可能导致压力过大超过七倍。 这对于研究受到$\alpha$粒子轰击的材料的辐射损伤具有重要的实际意义。