【作者】 谭晓明；

【导师】 邝小渝；

【作者基本信息】 四川大学 ， 原子与分子物理， 2007， 博士

【摘要】 掺杂过渡金属离子的晶体常具有特殊的光学、磁学和电学等性质，因而这些晶体常被作为良好的光电材料和非线性光学材料等而得到广泛地应用。由于掺杂离子与被取代离子的半径或电荷间存在着差异，所以掺杂晶体的局域结构往往要发生畸变。掺杂晶体的光学、磁学、电学及电子顺磁共振（EPR）谱等性质与这种局域结构畸变有很大的关系，特别是EPR零场分裂（ZFS）参量对掺杂晶体的微观局域结构非常敏感，因此可通过分析实验零场分裂参量来确定畸变后的局域结构。这对理解杂质离子与基质晶体的相互作用及认识晶体掺杂的微观机理是很有意义的，并可进一步为材料设计人员提供有利的理论依据。对d⁴离子，它们具有较多的未成对电子，在晶体场中容易发生Jahn-Teller畸变，从而使其产生很大的零场分裂，这就使它们在通常的EPR实验中由于频率太小而得不到信号，故长期以来，这方面的实验研究非常少见。近年来，随着科学技术的发展，实验物理学家能够通过高频电子顺磁共振（HF—EPR）实验观测到此类金属离子的信号，从而得到相应的零场分裂参量，这才使这方面的实验研究成为可能。理论方面，关于d⁴配合物的晶体场研究，已由早期的自旋五重态近似发展到五重态加三重态近似，但还未见把自旋单态也考虑在内的完全计算。如果一种理论方法不考虑自旋单态，它就不能用于研究单态能级，也不能用于研究旋轨耦合导致的单态对三重态的直接影响及单态通过三重态对五重态的间接影响，更不能用于研究十分重要的高、低自旋转换现象，即使对高、中自旋转换也不适用。因此作为完全计算，必须考虑由全部自旋态构成的d⁴电子组态的210维空间。这样，构造体系特别是低对称体系完全能量矩阵的工作将变得十分复杂，甚至使人望而止步。本文在这种背景下，进行了如下的研究：（1）采用一种对自旋与对称性均匹配的标准基概念。这种概念强调整个d^N组态空间基矢的标准化。按照这种标准化，基矢的各个分量有确定的形式，诸分量按照特别的规则排序并分组，每一组属于一定的自旋和一定的不可约表示子空间并按照一定的变换规则构成该子空间的标准基。而且与一个点群链的各级相匹配的那些标准基中的每一个都是由前一个经过特殊的线性变换得出的，它们形成一个基链。采用这种标准基，不仅可使能量矩阵很好地方块对角化，而且，通过把构造矩阵的波函数方法同算符方法相结合，还可以大大地简化构造完全矩阵的手续。（2）运用一种完全计算的统一晶场耦合（Unified Crystal Field Coupling）图象的晶体场理论方法，我们成功构造了四角场中d⁴体系的完全能量矩阵。所谓UCFC方法就是采用上述的对自旋与对称性均匹配的标准基以建造完全能量矩阵。此方法中，只要造出了哈密顿在立方对称标准基中的矩阵，就可以把它的各个方块作为元素，象拼凑方块图案那样构造出较低对称条件下的矩阵，无需重算矩阵元。这实质上就是与标准基之间的线性变换相对应的一种相似变换。由于基矢的特殊构造，哈密顿中的静电项在立方对称标准基中的矩阵是由一些很小的矩阵构成的方块对角阵，而且每个小矩阵可直接从Griffith附表中照搬。立方晶场算符的矩阵则是完全对角化的，其矩阵元的计算极其简单。这样就大大简化了构造完全能量矩阵的过程。此方法可实现将哈密顿各项一视同仁地予以对角化，而不必区分晶体场的强弱，是一种对所有过渡金属离子适用的统一的方法。本文中标准基和能量矩阵的特点，十分有利于标识能级、分析各种d-d跃迁的可能性、研究不同自旋多重性和不同对称性的态对谱学计算结果的影响、借助群链追溯能态的隶属关系等。（3）用上述的完全能量矩阵，系统地研究了前人通常忽略的自旋单态对零场分裂参量的影响。我们的结果显示，自旋单态对基态零场分裂参量a和F的贡献很大，以致忽略自旋单态我们将不可能得到准确的零场分裂参量值。这种贡献来源于旋轨耦合导致的自旋单态通过自旋三重态对自旋五重态的间接影响。（4）用对角化完全能量矩阵方法，研究了ZnS：Cr²⁺Jahn-Teller系统的局域晶格结构。通过分析实验零场分裂参量，获得了上述Cr²⁺杂质中心的局域结构参量。结果显示，当Cr²⁺杂质进入ZnS晶体时，其将引起局域结构发生一膨胀畸变。这可能是由于Cr²⁺的半径比Zn²⁺的半径大，所以当其掺入到ZnS晶体中时，其将推动S配体向外移动，从而引起局域结构的膨胀畸变。由于此系统为一Jahn-Teller系统，我们也得到了相应的Jahn-Teller畸变能，这一结果与实验值符合得很好。（5）研究了CdGa₂S₄：Cr²⁺体系的占位与局域晶格结构。CdGa₂S₄晶体中有两个阳离子晶位，这两个晶位均为四配位的四面体结构，对称性均为D_2d。因此，确定Cr²⁺杂质在CdGa₂S₄晶体中的占位是一个很有意义的问题。由于Cr²⁺离子的零场分裂参量值对其所处的局域结构非常敏感，因此我们通过比较不同占位时计算的零场分裂值与实验零场分裂值来确定其占位。结果显示，当Cr²⁺离子掺入CdGa₂S₄晶体中时，其将占据Cd²⁺位置，与此同时，该体系的局域结构畸变参量也被确定了。计算表明，此局域结构为一压缩畸变。这可能是由于Cr²⁺的半径小于Cd²⁺的半径，所以当其占据Cd²⁺晶位时，四周的配体将向中心方向移动，从而引起压缩效应。更多还原

【Abstract】 The crystals doped with transition metal ions are extensively applied as optoelectronic and nonlinear optical materials, because they have special optical, magnetic and electric properties. As is known, the local structure of the doped crystal will have a distortion, because there are differences in the radii or charges between the impurity ions and the host ions. The optical, magnetic, electric and electron paramagnetic resonance （EPR） spectrum are very closely related to the local structure. Especially, the EPR zero field splitting （ZFS） parameters are very sensitive to the local structure distortion, so the local structure can be studied by analyzing the experimental zero field splitting parameters. These studies are very significant for understanding the interaction between impurity ions and host crystals and realizing the doped microscopic mechanism. Furthermore, it may be helpful to material designers.The systems of the d⁴ ions have larger ZFS values, so there are no EPR signals in the conventional EPR experiments. In recent years, the EPR studies of d⁴ ions become feasible because of the advances in the HF-EPR technology. In the previous theoretical works, the calculations are not complete because the contributions of the spin singlets are not considered. If the spin singlets are neglected, the important spin transitions can not be studied. So, for the complete calculation, all spin states should be considered. Thus, it will be very difficult to construct the complete energy matrix, because the Hamiltonian matrix has a dimension of 210 if including all the spin states. Considering this, we do the following works:（1） The concept of the standard basis adapted to the double group chain presented by Zhou Kang-Wei is adopted. This concept emphasizes the standardization of the basis of the whole d^N configuration space. From this, the basis functions can be constructed for each irreducible representation of the double group and each basis function has certain expression. Each standard basis adapted to the double group chain can be got from the former by a linear transformation, which forms a basis chain. Thus, it will be convenient to construct the complete energy matrix by the wave-function and operator methods in this standard basis chain.（2） We successfully constructed the complete energy matrix of d⁴ ions in tetragonal field by the UCFC （Unified Crystal Field Coupling） scheme crystal field method suggested by Zhou Kang-Wei. The Hamiltonian matrix with respect of the corresponding basis functions will become a block diagonal form. Especially, as for the lower symmetry field, its energy matrix can be easily constructed from the cubic field matrix. Each matrix block of the cubic matrix can be directly added into the matrix of the lower symmetry field, thus the cubic component needs not to be calculated. The electrostatic component forms a block diagonal matrix in the cubic standard basis. In each block, the matrix elements are just the same as the electrostatic matrix in the tables of Griffith’s book. The matrix of the cubic crystal field will be fully diagonal and the diagonal elements can be easily obtained. UCFC method is not only a complete calculation method considering all multiplets, but also a unified, standardization and terse theoretical method system. It overcomes the limitations of the traditional strong field method, weak field method, and needs not to distinguish the crystal field strength, thus can be applied to arbitrary transition metal complexes in principle. With this standard basis and matrix, it is very convenient to assign energy levels, analyze d-d transition probability, elucidate the influence of the spin multiplets and symmetry on spectrum data and track down the subjection relationship of the energy states by the group chain.（3） The contributions of the spin singlets to zero field splitting are investigated for the first time with the above matrix. Our calculations show that the contributions of spin singlets to the zero field splitting parameters a and P are so large that neglecting this contribution one cannot obtain more accurate values of zero field splitting parameters. The contributions arise from the interaction of the spin quintuplets with both spin triplets and spin singlets via spin-orbit coupling. However, the selection rule of spin-orbit coupling shows that the spin singlets do not affect the quintuplets directly but indirectly via the spin triplets.（4） The local structure of ZnS:Cr²⁺ Jahn-Teller system is studied by diagonalizing the complete matrix. By analyzing the experimental zero field splitting parameters, the local structure parameters are obtained. The results show that the local structure of ZnS:Cr²⁺ system has an expansion distortion. The expansion distortion may be ascribed to the fact that the radius of Cr²⁺ is bigger than that of Zn²⁺. Thus, the Cr²⁺ will push the ligands outward when it is doped into the crystal. ZnS:Cr²⁺ system undergoes a static Jahn-Teller distortion, then we obtain the Jahn-Teller energy which is in good agreement with the experiments.（5） The substitution position and the local lattice structure of CdGa₂S₄:Cr²⁺ system are investigated on the basis of the complete energy matrix. There are two tetrahedrally coordinated cation positions in the crystal and they both show D_2d symmetry. Therefore, the problem of determining the position of Cr²⁺ becomes quite important. By computing the zero field splitting parameters at different positions, we can determine the substitution position. Our results show that the Cd²⁺ site is the only subgtitutional position for Cr²⁺. From our calculations, the lattice structure parameters of this system are also determined. It has a compression distortion, which may be ascribed to the fact that the radius of Cr²⁺ is smaller than that of Cd²⁺ and the Cr²⁺ ion will pull the ligands inward.更多还原