The evolution of point defect concentrations under irradiation is controlled by their diffusion properties, and by their formation and elimination mechanisms. The latter includes the mutual recombination of vacancies and interstitials, and the elimination of point defects at sinks. Two models are traditionally used to predict the defect concentration evolution, the standard rate theory (SRT) and the atomistic kinetic Monte Carlo (AKMC). We show in this work a large discrepancy in the defect concentrations between both methods when the average number of defects in the AKMC simulation box is close or lower than one. The reason is that AKMC naturally captures strong space and time correlations between vacancies and interstitials generated by the finite size of the periodic simulation box. These correlations strongly affect the recombination rate and the point defect concentrations. SRT fails to predict such correlations, and the corresponding solution deviates from the more accurate solution given by the AKMC simulation under similar conditions. These finite size correlation effects are strong when the elimination of point defects occurs by recombination only, but can still be significant in the presence of sinks. In order to account for the spacio-temporal correlation in a continuum framework, we introduce a Correlated Pair Theory (CPT). This theory fully takes into account the correlations between vacancy and interstitial pairs and predicts point defect concentrations in good agreement with AKMC simulations. Inversely, if the goal is for the AKMC to reproduce defect concentrations in bulk using small simulation boxes, the naturally occurring correlations need to be corrected. We show here that the CPT can be used to modify the elimination rates in the AKMC simulations, so as to yield point defect concentrations in agreement with SRT.

辐照下点缺陷浓度的变化受其扩散特性及其形成和消除机理的控制。后者包括空位和填隙的相互复合，以及消除汇点缺陷。传统上使用两种模型来预测缺陷浓度的变化，即标准速率理论（SRT）和原子动力学蒙特卡罗（AKMC）。我们在这项工作中显示出，当AKMC仿真框中的平均缺陷数接近或小于1时，两种方法之间的缺陷浓度存在很大差异。原因是AKMC自然地捕获了由周期性模拟框的有限大小生成的空位和间隙之间的强时空相关性。这些相关性强烈影响重组率和点缺陷浓度。SRT无法预测这种相关性，并且相应的解决方案偏离了在相似条件下AKMC仿真给出的更准确的解决方案。当仅通过重组消除点缺陷时，这些有限的大小相关效果就很强，但是在存在凹陷的情况下仍然很重要。为了考虑连续性框架中的时空相关性，我们引入了相关对理论（CPT）。该理论充分考虑了空位和填隙对之间的相关性，并预测了与AKMC模拟完全吻合的点缺陷浓度。相反，如果目标是AKMC使用小型仿真箱批量复制缺陷浓度，自然发生的相关性需要校正。我们在这里表明，CPT可用于修改AKMC模拟中的消除率，从而产生与SRT一致的点缺陷浓度。