Iodine vacancies and their behavior in the MAPbI3 perovskites are determining factors in the stability of the perovskite to light. In this article, we investigate the formation of iodine vacancy in the CH3NH3PbI3 perovskite analytically and calculate its required energy. Iodine vacancy formation needs a certain amount of energy to separate an iodine ion from its lattice position and transfer it to another lattice position at crystal surface, grain boundaries, and/or dislocations. When a lattice position becomes vacant in a crystal, the atoms around this position lose their equilibrium state and will no longer remain in their primary lattice position. The neighbor ions of the vacancy move slightly from their lattice position to reach a new stable state. This transition from unstable to steady state is called relaxation, and the released energy from this process is called relaxation energy. So, first, we calculate the energy needed to separate an iodine ion from its primary lattice position, and then, to estimate the relaxation energy, the new equilibrium positions and energy changes of the neighbor ions are determined. The vacancy formation energy is equal to the difference between these two energies.

中文翻译：

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CH$_{3}$NH$_{3}$PbI$_{3}$钙钛矿中的碘空位形成能量

MAPbI3 钙钛矿中的碘空位及其行为是钙钛矿对光稳定性的决定性因素。在本文中，我们分析研究了 CH3NH3PbI3 钙钛矿中碘空位的形成并计算了其所需的能量。碘空位的形成需要一定量的能量来将碘离子从其晶格位置分离并将其转移到晶体表面、晶界和/或位错处的另一个晶格位置。当晶体中的晶格位置空置时，该位置周围的原子将失去平衡状态，不再保持在其主要晶格位置。空位的相邻离子从它们的晶格位置略微移动以达到新的稳定状态。这种从不稳定状态到稳定状态的转变称为松弛，这个过程释放的能量称为弛豫能量。因此，首先，我们计算将碘离子与其主晶格位置分离所需的能量，然后，为了估计弛豫能量，确定相邻离子的新平衡位置和能量变化。空位形成能量等于这两种能量之差。