八面体中3d～1离子的自旋哈密顿参量的理论研究
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摘要
3d~1离子(如V~(4+)、Ti~(3+)等)是非常重要的过渡金属离子，人们对掺杂3d~1离子物质的电子顺磁共振谱(EPR)进行了大量研究，积累了丰富的实验数据。但是，对这些EPR实验结果的理论解释则不太令人满意。例如，大多数工作都采用粗糙的g因子和超精细结构常数二阶微扰公式，其中只考虑了中心离子旋轨耦合作用对自旋哈密顿参量的贡献，而忽略了配体轨道及配体旋轨耦合作用的贡献，因而对一些实验结果难以给出合理的解释。此外，尚有部分实验数据至今未有理论上的分析。为了克服前人工作中的不足，本文基于离子簇模型，采用Marcfarlane强场微扰法得到四角和斜方畸变的压缩八面体中3d~1离子的g因子和超精细结构常数的三阶微扰公式，并将这些公式应用于(NH_4)_2SbCl_5中的四角VO~(2+)中心、锐钛矿填隙位置的四角、V~(4+)中心、金红石系列晶体中的斜方、V~(4+)中心等体系，满意地解释了EPR实验结果，并获得了掺杂离子的局部结构信息。
(1)对于(NH_4)_2SbCl_5中四角VO~(2+)中心，考虑了配体轨道及旋轨耦合作用的贡献。同时确定了前人实验未给出的超精细结构常数A因子的符号。
(2)对于锐钛矿中填隙、V~(4+)中心，克服了前人采用较多的调节参量，忽略配体轨道及旋轨耦合作用对自旋哈密顿参量贡献的不足，同时给出了超精细结构常数A的定量解释。
(3)对于金红石中填隙、V~(4+)中心，发现当V~(4+)离子占据填隙位后，原来的压缩八面体环境会略微伸长即平行方向键长伸长0.28(?)(R_∥(?)1.95(?))，垂直方向键长缩收0.14(?)(R_x(?)2.09(?))，显然此时的局部环境仍是压缩八面体。
(4)对于金红石型MO_2(M=Ti、Ge、Sn)晶体替位、V~(4+)中心，研究发现，由于Jahn-Teller效应，配体多面体由母体时的伸长八面体变成杂质中心的压缩八面体。另外，由于体系具有较强的共价性，配体轨道和旋轨耦合作用的贡献不能忽略。
As important model systems, 3d~1 ions (Ti~(3+), V~(4+), Cr~(5+)) have been extensivelyinvestigated by means of electron paramagnetic resonance (EPR), and manyexperimental data for spin Hamiltonian parameters g factors and the hyperfine structureconstants were also measured. As for the theoretical analyses, some experimental resultsfor 3d~1 ions in tetragonally and rhombically compressed octahedra were not been treated,and some others were not satisfasctorily interpreted. The weakness of the previousstudies lies in (ⅰ) adoption of the simple second-order perturbation formulas of the gfactors and (ⅱ) neglecting of the contributions from the ligand orbits and spin-orbitcoupling coefficients. In order to make further investigations on the spin Hamiltonianparameters for the above 3d~1 centers, they are quantitatively analyzed from theirhigh-order perturbation formulas for a 3d~1 ion in tetragonally and rhombicallycompressed octahedra. In these formulas, the contributions to the spin Hamiltonianparameters from the s- and p-orbital as well as the spin-orbit coupling of ligands aretaken into account based on the cluster approach. In addition, the information about thedefect structures of the 3d~1 impurity centers can be connected with the low symmetricaldistortions and thus the spin Hamiltonian parameters.
(1) For the tetragonal VO~(2+) in (NH_4)_2SbCl_5, the contributions to the spin Hamiltonianparameters from the s- and p-orbital as well as the spin-orbit coupling of ligands arefound to be significant and cannot be neglected, and the signs of the experimentalhyperfine structure constants are also theoretically determined.
(2) For the interstitial V~(4+) in anatase (TiO_2), the above contributions to the spinHamiltonian parameters are also taken into account and the quantitative interpretation tothe hyperfine structures A_i factors are carried out.
(3) For the interstitial V~(4+) in rutile (TiO_2), stretching and contraction of the parallel andperpendicular bonding lengthes by about 0.28(?) and 0.14(?) compare to those in thehost is obtained for the impurity.
(4) For the substitutional V~(4+) centers in rutile type MO_2(M=Ti,Ge,Sn), the (VO_6)~(8-)clusters change from elongation in the hosts to compression in the impurity centers due to the Jahn-Teller effect. In additon, the contributions from the ligand orbital andspin-orbit coupling contributions are not negligible because of the significant covalencyof the systems.and the liand ions become significant, because of the high valence stateof the impurity V~(4+). So contributions from the s- and p-orbital as well as the spin-orbitcoupling of ligands must be consider in theoretical studies on Spin Hamiltonianparameters of 3d~1 impurity centers. The second, local distortion octahedron consisted ofV~(4+) and ligands usually are compressed because of the Jahn-Teller effect and the groundstate is orbital singlet ~2B_(2g).
(1)对于(NH_4)_2SbCl_5中四角VO~(2+)中心，考虑了配体轨道及旋轨耦合作用的贡献。同时确定了前人实验未给出的超精细结构常数A因子的符号。
(2)对于锐钛矿中填隙、V~(4+)中心，克服了前人采用较多的调节参量，忽略配体轨道及旋轨耦合作用对自旋哈密顿参量贡献的不足，同时给出了超精细结构常数A的定量解释。
(3)对于金红石中填隙、V~(4+)中心，发现当V~(4+)离子占据填隙位后，原来的压缩八面体环境会略微伸长即平行方向键长伸长0.28(?)(R_∥(?)1.95(?))，垂直方向键长缩收0.14(?)(R_x(?)2.09(?))，显然此时的局部环境仍是压缩八面体。
(4)对于金红石型MO_2(M=Ti、Ge、Sn)晶体替位、V~(4+)中心，研究发现，由于Jahn-Teller效应，配体多面体由母体时的伸长八面体变成杂质中心的压缩八面体。另外，由于体系具有较强的共价性，配体轨道和旋轨耦合作用的贡献不能忽略。
As important model systems, 3d~1 ions (Ti~(3+), V~(4+), Cr~(5+)) have been extensivelyinvestigated by means of electron paramagnetic resonance (EPR), and manyexperimental data for spin Hamiltonian parameters g factors and the hyperfine structureconstants were also measured. As for the theoretical analyses, some experimental resultsfor 3d~1 ions in tetragonally and rhombically compressed octahedra were not been treated,and some others were not satisfasctorily interpreted. The weakness of the previousstudies lies in (ⅰ) adoption of the simple second-order perturbation formulas of the gfactors and (ⅱ) neglecting of the contributions from the ligand orbits and spin-orbitcoupling coefficients. In order to make further investigations on the spin Hamiltonianparameters for the above 3d~1 centers, they are quantitatively analyzed from theirhigh-order perturbation formulas for a 3d~1 ion in tetragonally and rhombicallycompressed octahedra. In these formulas, the contributions to the spin Hamiltonianparameters from the s- and p-orbital as well as the spin-orbit coupling of ligands aretaken into account based on the cluster approach. In addition, the information about thedefect structures of the 3d~1 impurity centers can be connected with the low symmetricaldistortions and thus the spin Hamiltonian parameters.
(1) For the tetragonal VO~(2+) in (NH_4)_2SbCl_5, the contributions to the spin Hamiltonianparameters from the s- and p-orbital as well as the spin-orbit coupling of ligands arefound to be significant and cannot be neglected, and the signs of the experimentalhyperfine structure constants are also theoretically determined.
(2) For the interstitial V~(4+) in anatase (TiO_2), the above contributions to the spinHamiltonian parameters are also taken into account and the quantitative interpretation tothe hyperfine structures A_i factors are carried out.
(3) For the interstitial V~(4+) in rutile (TiO_2), stretching and contraction of the parallel andperpendicular bonding lengthes by about 0.28(?) and 0.14(?) compare to those in thehost is obtained for the impurity.
(4) For the substitutional V~(4+) centers in rutile type MO_2(M=Ti,Ge,Sn), the (VO_6)~(8-)clusters change from elongation in the hosts to compression in the impurity centers due to the Jahn-Teller effect. In additon, the contributions from the ligand orbital andspin-orbit coupling contributions are not negligible because of the significant covalencyof the systems.and the liand ions become significant, because of the high valence stateof the impurity V~(4+). So contributions from the s- and p-orbital as well as the spin-orbitcoupling of ligands must be consider in theoretical studies on Spin Hamiltonianparameters of 3d~1 impurity centers. The second, local distortion octahedron consisted ofV~(4+) and ligands usually are compressed because of the Jahn-Teller effect and the groundstate is orbital singlet ~2B_(2g).
引文
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