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按照零场分裂（ＺＦＳ）的三阶微扰理论和叠加晶场模型，建立了ＺＦＳ参量Ｄ与ＣｓＣｄＦ_３：Ｃｒ~（３＋）晶格结构之间的定量关系；同时考虑了晶格畸变和Ｃｄ~（２＋）空位对零场分裂参量Ｄ的贡献，计算了ＣｓＣｄＦ_３：Ｃｒ~（３＋）晶体的零场分裂参量Ｄ，计算结果与实验符合甚好．证明了晶格畸变和Ｃｄ~（２＋）空位的存在；同时得到包围 Ｃｒ~（３＋）离子的 Ｆ~－离子向中心 Ｃｒ~（３＋）离子分别移动Ｘ_１＝０．００２９１ｎｍ，Ｘ_２＝０．００１ｎｍ，Ｘ_３＝０．００２６ｎｍ．ＣｓＣｄＦ_３：Ｃｒ~（３＋）晶体基态的ＺＦＳ主要来自Ｃｄ~（２＋）空位，但晶格畸变的贡献是不能忽略的．
According to the third order perturbation theory and the superposition crystal field model of zero field splitting (ZFS), the quantitative relationship between the ZFS parameter D and the lattice structure of CsCdF_3: Cr ~ (3+) crystal was established. The lattice distortion and Cd ~ (2 +) vacancies to the zero field splitting parameter D, the zero field splitting parameter D of CsCdF_3: Cr ~ (3 +) crystal was calculated. The calculated results are in good agreement with the experiment. The lattice distortion and the vacancy of Cd 2+ have been proved. At the same time, the F 3 ions surrounded by Cr 3+ ions move to the central Cr 3+ ions by X 1 = 0.00291 nm and X 2 = 0.001 nm, respectively , X_3 = 0.0026 nm. The ground state of CsCdF_3: Cr ~ (3 +) crystal mainly comes from the Cd2 + vacancy, but the contribution of lattice distortion can not be neglected.