基于第一性原理和参数化模型的稀土发光材料研究
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摘要
本论文系统地研究了镧系离子的f电子与d电子晶场参数和自旋轨道耦合参数的计算方法。绪论部分介绍了稀土发光材料的研究背景,并介绍当前研究稀土离子能级和分析稀土发光光谱的主要方法,包括唯象模型、Dorenbos等的研究f-d跃迁光谱的经验模型和段昌奎教授的简化模型。这些模型在解释稀土离子能级和光谱时存在诸多局限性,如唯象模型使用时需要实验数据进行拟合,且因f-d跃迁光谱包含较多的声子边带和涉及到参数个数较多而难以精确拟合,Dorenbos等的经验模型对于预言镧系离子在晶体中的f-d跃迁及电荷迁移态跃迁比较有效,但此经验公式成立的条件及其可靠性等方面都存在不确定因素。简化模型通常对单一晶场能级执行自由离子部分计算,因5d电子的晶场分裂属于主要的相互作用而不能够预言f-d跃迁光谱的主要能级结构。
第一章介绍了当前研究稀土离子的最重要的理论方法唯象模型,唯象模型在解释稀土离子的光谱和预测稀土离子发光方面有广泛的应用,我们从中心场近似出发,通过介绍f~N组态和f~(N-1)d组态中电子之间的相互作用(包括库伦作用、自旋轨道耦合作用、晶场作用、组态间相互作用等)来介绍稀土离子的能级结构。
第二章中介绍了我们结合密度泛函理论来计算唯象模型中的参数的方法。这种方法结合唯象模型的精确度高的优点,以及密度泛函理论可以几乎不需要实验数据而对于任何体系进行直接计算的优点。我们首次将这种方法应用于稀土离子的计算。
本论文的第三章和第四章都是基于模空间方法计算镧系离子的晶场参数和自旋轨道耦合参数。其中第三章主要是计算Ce~(3+)在各种基质(包括格位对称群为S_4的LiYF_4、O_h群的CaF_2和Cs_2NaYCl_6、C_(4v)对称的KY_3F_(10)、D_2对称的YAG)环境下的晶场参数和自旋轨道耦合参数,我们系统地分析了不同的对称群下计算的晶场参数结果,由于稀土离子在晶体中的晶场参数与其所处的对称性有关,在不同的对称性下晶场参数的符号和个数一般不同,我们的计算结果中参数的个数和符号与群论知识预测的一致。此外,我们还将我们计算的参数与各种文献报道的拟合参数进行对比,我们的参数在合理精度范围内与其他人拟合的参数一致。
第四章以D_(2d)对称的YPO_4晶体和C_2对称的BaBPO_5晶体为例,分别计算Ce~(3+)、Pr~(3+)、Nd~(3+)、Eu~(3+)在YPO_4晶体中和Ce~(3+)、Tb~(3+)在BaBPO_5晶体中的晶场参数和自旋轨道耦合参数。我们的计算表明通过模空间方法计算的参数在镧系元素中的变化趋势与理论预计的一致,即晶场参数随核电荷数的增加而减小,自旋轨道耦合参数随核电荷数的增加而增大。更进一步,我们使用文献已报道的镧系离子原子实部分的参数和模空间方法计算的晶场参数来重构镧系离子的哈密顿量,并计算其本征能级和本征态。通过计算跃迁矩阵元来模拟镧系离子的吸收光谱,并与实验测量的激发光谱进行对比。通过此方法我们计算出的Ce~(3+)的5个激发峰与实验测量的一致,Pr~(3+),Nd~(3+),Eu~(3+)的峰与实验的峰也大致接近,计算出了Tb~(3+)的自旋禁戒跃迁与自旋允许跃迁的强度与实验测量的激发峰也比较接近。
本论文的第五章以SrCl_2: Yb~(2+)为例计算稀土离子的激发态吸收光谱,通过与实验测量的光谱的比较,可以推测稀土离子处于4f~(N-1)5d组态的键长与4f~N组态键长的变化情况。
第六章计算了Er~(3+)在不同晶体(CaF_2, LiYF_4和Cs_2NaYF_6)中的f-d跃迁光谱,并细致研究Er~(3+)的f-d跃迁光谱对于晶体场模型中f-d之间的库伦相互作用参数和d电子的自旋轨道耦合参数的依赖关系。
The calculation of crystal-field parameters and spin-orbit coupling parameters of f electron and d electron of lanthanide ions was systematically studied in this paper. In the introduction section we described the background of rare earth ions as luminescent materials, the research and analysis methods of energy levels and spectra of rare earth ions including phenomenological model, empirical formula on f-d transition spectra proposed by Dorenbos and simplified model by Duan Chang-kui. There were many limitations when the models were applied to analysis the energy levels and spectra of rare earths ions. Such as, exact experimental data were needed when using the phenomenological model and a large number of parameters were too difficult to fit in case of the f-d spectra containing a lot of phonon spectra. Dorenbos’model was widely used by experimental physicists on predicting f-d transition and transitions of charge transfer state of lanthanide ions in crystals rare earths, but it was still uncertain of its reliability. Simplified model was usually used for the single 5d crystal-field level of ions. Since the 5d crystal-field splitting usually formed the main parts of the f-d transition spectra, the simplified model was not able to predict the main f-d transition spectra of lanthanide ions in crystals.
As the most important method in the study of rare earth ions at present, phenomenological model was introduced in Chapter 1. It was widely used in explaining and predicting spectra of rare earth ion as luminescence materials. We started from the center-field approximation, explained the energy levels of lanthanide ions in crystals by introducing the interactions in f~N configuration and f~(N-1)d configuration, such as Coulomb interaction, spin-orbit interaction, crystal field and configuration interaction.
In Chapter 2, we described the method of calculating the parameters of the phenomenological model in combination of density functional theory. The approach combined the advantages of high accuracy of phenomenological model and no experimental data needed in the density functional theory. We applied this approach to the calculation of rare earth ions as the first time.
In Chapters 3 and 4, crystal-field parameters and spin-orbit coupling parameter were calculated for various lanthanides ions in different crystals by the method basing the module space model. In chapter 3, the crystal-field parameters and spin-orbit coupling parameters of Ce~(3+) in various groups, including S_4 in LiYF_4, O_h group in CaF_2 and Cs_2NaYCl_6, C_(4v) in KY_3F_(10) and D_2 in YAG. We systematically analyzed the results on crystal-field parameters in various symmetry groups. The numbers of crystal-field parameters were related to the groups and symmetry. Our results were consistent with the prediction by group theory in the number of parameters and symbols of crystal-field parameters. In addition, we also compared our calculated parameters with those reported in the literature. The accuracy of our parameters was in a reasonable range and our parameters were close to those by fitting.
In Chapter 4, we calculated crystal-field parameters and spin-orbit coupling parameter of Ce~(3+), Pr~(3+), Nd~(3+), Eu~(3+) in YPO_4 crystal and Ce~(3+), Tb~(3+) in BaBPO_5 crystal. Our calculations showed that the parameters calculated by module space method of lanthanides were consistent with the expected trend, that was, the crystal-field parameters decreased while spin-orbit coupling parameters increased with the nuclear charge. Furthermore, we used atomic parameters in literatures and the calculated parameters to reconstruct the Hamiltonian of lanthanide ions and calculated the eigen value energy levels and eigen states. By calculating the transition matrix elements, we simulated the absorption spectra of lanthanide ions, and compared with the excitation spectra. Using this method, we found that our calculation was quite consistent with the experimental spectra. We also found that the strengths of spin allowed and spin forbidden transitions were close to those in experiment.
In Chapter 5, we calculated excited state absorption spectrum of Yb~(2+) in SrCl_2. By comparing the calculated spectrum with the experimental spectrum, we might speculate the changes of bond lengths of rare earth ions when they transitioned from 4f~N configuration to 4f~(N-1)5d configuration.
In Chapter 6, we calculated f-d transition spectra of Er~(3+) in different crystals such as CaF_2, LiYF_4 and Cs_2NaYCl_6. We studied dependency of f-d transition spectra of Er~(3+) on the parameters of the f-d Coulomb interaction and spin-orbit parameters of 5d electron.
第一章介绍了当前研究稀土离子的最重要的理论方法唯象模型,唯象模型在解释稀土离子的光谱和预测稀土离子发光方面有广泛的应用,我们从中心场近似出发,通过介绍f~N组态和f~(N-1)d组态中电子之间的相互作用(包括库伦作用、自旋轨道耦合作用、晶场作用、组态间相互作用等)来介绍稀土离子的能级结构。
第二章中介绍了我们结合密度泛函理论来计算唯象模型中的参数的方法。这种方法结合唯象模型的精确度高的优点,以及密度泛函理论可以几乎不需要实验数据而对于任何体系进行直接计算的优点。我们首次将这种方法应用于稀土离子的计算。
本论文的第三章和第四章都是基于模空间方法计算镧系离子的晶场参数和自旋轨道耦合参数。其中第三章主要是计算Ce~(3+)在各种基质(包括格位对称群为S_4的LiYF_4、O_h群的CaF_2和Cs_2NaYCl_6、C_(4v)对称的KY_3F_(10)、D_2对称的YAG)环境下的晶场参数和自旋轨道耦合参数,我们系统地分析了不同的对称群下计算的晶场参数结果,由于稀土离子在晶体中的晶场参数与其所处的对称性有关,在不同的对称性下晶场参数的符号和个数一般不同,我们的计算结果中参数的个数和符号与群论知识预测的一致。此外,我们还将我们计算的参数与各种文献报道的拟合参数进行对比,我们的参数在合理精度范围内与其他人拟合的参数一致。
第四章以D_(2d)对称的YPO_4晶体和C_2对称的BaBPO_5晶体为例,分别计算Ce~(3+)、Pr~(3+)、Nd~(3+)、Eu~(3+)在YPO_4晶体中和Ce~(3+)、Tb~(3+)在BaBPO_5晶体中的晶场参数和自旋轨道耦合参数。我们的计算表明通过模空间方法计算的参数在镧系元素中的变化趋势与理论预计的一致,即晶场参数随核电荷数的增加而减小,自旋轨道耦合参数随核电荷数的增加而增大。更进一步,我们使用文献已报道的镧系离子原子实部分的参数和模空间方法计算的晶场参数来重构镧系离子的哈密顿量,并计算其本征能级和本征态。通过计算跃迁矩阵元来模拟镧系离子的吸收光谱,并与实验测量的激发光谱进行对比。通过此方法我们计算出的Ce~(3+)的5个激发峰与实验测量的一致,Pr~(3+),Nd~(3+),Eu~(3+)的峰与实验的峰也大致接近,计算出了Tb~(3+)的自旋禁戒跃迁与自旋允许跃迁的强度与实验测量的激发峰也比较接近。
本论文的第五章以SrCl_2: Yb~(2+)为例计算稀土离子的激发态吸收光谱,通过与实验测量的光谱的比较,可以推测稀土离子处于4f~(N-1)5d组态的键长与4f~N组态键长的变化情况。
第六章计算了Er~(3+)在不同晶体(CaF_2, LiYF_4和Cs_2NaYF_6)中的f-d跃迁光谱,并细致研究Er~(3+)的f-d跃迁光谱对于晶体场模型中f-d之间的库伦相互作用参数和d电子的自旋轨道耦合参数的依赖关系。
The calculation of crystal-field parameters and spin-orbit coupling parameters of f electron and d electron of lanthanide ions was systematically studied in this paper. In the introduction section we described the background of rare earth ions as luminescent materials, the research and analysis methods of energy levels and spectra of rare earth ions including phenomenological model, empirical formula on f-d transition spectra proposed by Dorenbos and simplified model by Duan Chang-kui. There were many limitations when the models were applied to analysis the energy levels and spectra of rare earths ions. Such as, exact experimental data were needed when using the phenomenological model and a large number of parameters were too difficult to fit in case of the f-d spectra containing a lot of phonon spectra. Dorenbos’model was widely used by experimental physicists on predicting f-d transition and transitions of charge transfer state of lanthanide ions in crystals rare earths, but it was still uncertain of its reliability. Simplified model was usually used for the single 5d crystal-field level of ions. Since the 5d crystal-field splitting usually formed the main parts of the f-d transition spectra, the simplified model was not able to predict the main f-d transition spectra of lanthanide ions in crystals.
As the most important method in the study of rare earth ions at present, phenomenological model was introduced in Chapter 1. It was widely used in explaining and predicting spectra of rare earth ion as luminescence materials. We started from the center-field approximation, explained the energy levels of lanthanide ions in crystals by introducing the interactions in f~N configuration and f~(N-1)d configuration, such as Coulomb interaction, spin-orbit interaction, crystal field and configuration interaction.
In Chapter 2, we described the method of calculating the parameters of the phenomenological model in combination of density functional theory. The approach combined the advantages of high accuracy of phenomenological model and no experimental data needed in the density functional theory. We applied this approach to the calculation of rare earth ions as the first time.
In Chapters 3 and 4, crystal-field parameters and spin-orbit coupling parameter were calculated for various lanthanides ions in different crystals by the method basing the module space model. In chapter 3, the crystal-field parameters and spin-orbit coupling parameters of Ce~(3+) in various groups, including S_4 in LiYF_4, O_h group in CaF_2 and Cs_2NaYCl_6, C_(4v) in KY_3F_(10) and D_2 in YAG. We systematically analyzed the results on crystal-field parameters in various symmetry groups. The numbers of crystal-field parameters were related to the groups and symmetry. Our results were consistent with the prediction by group theory in the number of parameters and symbols of crystal-field parameters. In addition, we also compared our calculated parameters with those reported in the literature. The accuracy of our parameters was in a reasonable range and our parameters were close to those by fitting.
In Chapter 4, we calculated crystal-field parameters and spin-orbit coupling parameter of Ce~(3+), Pr~(3+), Nd~(3+), Eu~(3+) in YPO_4 crystal and Ce~(3+), Tb~(3+) in BaBPO_5 crystal. Our calculations showed that the parameters calculated by module space method of lanthanides were consistent with the expected trend, that was, the crystal-field parameters decreased while spin-orbit coupling parameters increased with the nuclear charge. Furthermore, we used atomic parameters in literatures and the calculated parameters to reconstruct the Hamiltonian of lanthanide ions and calculated the eigen value energy levels and eigen states. By calculating the transition matrix elements, we simulated the absorption spectra of lanthanide ions, and compared with the excitation spectra. Using this method, we found that our calculation was quite consistent with the experimental spectra. We also found that the strengths of spin allowed and spin forbidden transitions were close to those in experiment.
In Chapter 5, we calculated excited state absorption spectrum of Yb~(2+) in SrCl_2. By comparing the calculated spectrum with the experimental spectrum, we might speculate the changes of bond lengths of rare earth ions when they transitioned from 4f~N configuration to 4f~(N-1)5d configuration.
In Chapter 6, we calculated f-d transition spectra of Er~(3+) in different crystals such as CaF_2, LiYF_4 and Cs_2NaYCl_6. We studied dependency of f-d transition spectra of Er~(3+) on the parameters of the f-d Coulomb interaction and spin-orbit parameters of 5d electron.
引文
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