为了研究金属杂质粒子周围基质温度场的分布, 基于Mie理论和强吸收体热传导理论模型提出了以金属杂质粒子为球心的复合球体热传导模型, 利用有限元分析思想方法和拉普拉斯变换方法, 得到嵌入熔石英的金属杂质粒子周围基质的温度场分布模型。该模型适用于模拟不同半径的金属杂质粒子周围基质的温度场分布。通过研究在波长为1 053 nm, 持续时间为10 ns的激光辐照下, 半径为100 nm的铜杂质粒子周围熔石英基质温度场的分布结果, 表明基质温度较高的区域主要集中在100~200 nm之间; 在激光脉冲末端, 复合球体半径约为100 nm处, 基质温度达到最高; 基质吸收率的大小受温度影响且与温度成正比关系, 在温度场的模拟过程中基质吸收率的变化所产生的影响不容忽视。通过对基质温度场的研究分析, 进一步明晰了激光诱导材料发生损伤的机理, 该模型对激光诱导材料发生损伤的形态以及材料周围应力场的分布研究具有重要的意义。

In order to study the distribution of the matrix temperature field around the metal impurity particles, a composite sphere heat conduction model with metal impurity particles as the center of sphere is proposed based on the Mie theory and the model of heat transfer of strong absorber theory. By adopting the method of finite element analysis and the Laplace transform method, the temperature field distribution model of the matrix surrounding the metal impurity particles embedded in fused silica is obtained. The model is suitable for simulating the temperature field distribution of the matrix around metal impurity particles with different radii. The distribution of the fused silica matrix temperature field around a 100 nm radius of copper impurity particle irradiated by a laser with a wavelength of 1 053 nm and a duration of 10 ns is studied. The results show that the areas with high matrix temperature are mainly concentrated between 100 nm and 200 nm. At the end of the laser pulse, the radius of the composite sphere is about 100 nm, and the matrix temperature reaches the highest. The absorption rate of the matrix is affected by temperature and is proportional to the temperature. The influence of the change of the matrix absorption rate during the temperature field simulation cannot be ignored. By studying and analyzing the matrix temperature field, the mechanism of the laser-induced material damage is further clarified. This model has important significance for the morphology of laser-induced material damage and the distribution of stress field around the material.