The distribution of solute atoms around defects is a hot research topic in the solid theory with long-term importance. In the present work, the interaction of solute atmosphere with a spherical void in a spherical elastic solid is studied based on the elastic and statistical mechanics description of solute atmosphere. The rationality of further modeling a solute atom as a point dilatation to obtain the image stress fields is demonstrated. Based on this point dilatation model, a three-dimensional boundary value problem in the framework of elasticity is formulated and solved. The displacement, strain and stress fields due to a point dilatation in a spherical elastic solid containing a spherical void are derived. The statistical mechanics framework is extended to the three-dimensional case of solute atmosphere. Configurational forces on both the solute atoms and spherical void are defined through the gradient of enthalpy and the well-established surface-independent integrals, respectively. Based on the elastic and statistical description of solute atmosphere, Monte Carlo (MC) method is employed to investigate the effects of initial solute distribution and temperature on the solute atom distribution. Carrying out a great number of MC simulations in a wide range of temperature with different total numbers of solute atoms, a metastable equilibrium state is found, which results from the synergistic effects of low temperature and initial solute distribution. It is shown that there are three stages of variations of the enthalpy with the temperature, from which two transition temperatures have been identified.

溶质原子在缺陷周围的分布是固体理论中的一个研究热点，具有长期的重要性。在目前的工作中，基于溶质大气的弹性和统计力学描述，研究了溶质大气与球形弹性固体中球形空隙的相互作用。证明了进一步将溶质原子建模为点膨胀以获得图像应力场的合理性。基于该点膨胀模型，提出并求解了弹性框架下的三维边值问题。推导出包含球形空隙的球形弹性固体中点膨胀引起的位移、应变和应力场。统计力学框架扩展到溶质大气的三维情况。溶质原子和球形空隙上的构型力分别通过焓梯度和公认的表面无关积分定义。基于溶质大气的弹性和统计描述，采用蒙特卡罗(MC)方法研究初始溶质分布和温度对溶质原子分布的影响。在较宽的温度范围内对不同的溶质原子总数进行大量的 MC 模拟，发现了亚稳态平衡状态，这是低温和初始溶质分布的协同作用的结果。结果表明，焓随温度的变化分为三个阶段，从中确定了两个转变温度。