掺杂在晶体中的镧系和锕系离子的f-d跃迁光谱的理论模拟
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摘要
本论文系统地分析研究了近年来得到广泛关注的掺杂镧系和锕系离子的远紫外光谱结构。这些光谱结构主要是由于f-d跃迁导致的。首先,总结了计入f电子和d电子及他们之间的各种相互作用(如库仑作用、自旋轨道作用、晶体场作用及组态混合等效过来的作用)的完整唯象哈密顿理论方法,并对一些体系进行了模拟分析(第一部分);接着,回顾了分析晶体中镧系和锕系离子f-d跃迁光谱的简单模型,并把该模型用于实际光谱分析(第二部分);因模型本身未考虑d电子的t_2轨道在旋轨耦合作用下分裂的影响,对此模型进行了(非平庸的)拓展,并用于相应的体系(第三部分):注意到传统的唯象哈密顿理论在应用中的关键缺点是点群理论未得到充分应用(特别是涉及到5d或6d电子的电子构型中),因此在此探讨了点群基在掺杂晶体中镧系和锕系离子的f~N←→f~(N-1)d跃迁中的应用(第四部分)。
在第一部分中,在总结f-d跃迁的唯象哈密顿理论基础上,采用M.F.Reid教授编写的扩展f-shell程序对Cs_2NaYF_6晶体中Tm~(3+)离子的4f~(12)和4f~(11)5d电子构型的能级进行了详细计算,在此基础上对4f-5d跃迁光谱进行了非常细致的分析和解释:计算给出的4f~(11)5d~1构型的能态涵盖从58318 cm~(-1)到86900 cm~(-1)的范围,它们和在激发光谱上观测到的至少5个结构带的位置和强度相当符合。我们注意到:对于光谱中观测到的跃迁,严格的O_h点群选择定则依然是有效的:仅根据f-d激发谱中振动带的强度而指认第一自旋允许跃迁的能量位置是不可靠的,这是由于4f~(11)5d~1组态中较低能态波函的SLJ混合很厉害,仅仅那些具有合适量子数——满足全部选择定则(△S=0;△L=0,±1;△J=0,±1),注意除了S之外还有LJ——的成分才对跃迁有贡献。d-f发射谱也能用计算结果进行很好的解释,并且大部分强度集中在一个带4f~(11)5d~1(高自旋)→4f~(12)~3H_6上。另外,基于类似的计算,也对Cs_2NaYF_6晶体中Er~(3+)离子的4f-5d激发光谱进行了模型模拟和解释,并且给出了相似的分析和结论。
在第二部分中,总结回顾了用以分析晶体中镧系和锕系离子f-d跃迁光谱结构的简单模型及其应用的情况。这个模型可基于2-3个参数值来给出各个f-d跃迁带的零声子线的位置,进而基于跃迁初末态的量子数计算相对跃迁线强。作为对此模型的应用的一个补充,在此对尚未采用该模型探讨的f~(11)d和f~(12)d电子构型离子进行了分析,同时得到了可供今后使用的参数化的能量矩阵元。作为一个范例,在此专门对CaF_2晶体中Tm~(3+)的f-d激发光谱进行了分析计算。
第三部分为对现有简化模型的拓展。现有简单模型不能很好的用于镧系或锕系离子掺杂在正八面体六配位化合物的情况下的f-d光谱,这是因为其中的5d(或6d)轨道中较低能的t_2在旋轨耦合作用下分裂,从而不能忽略其旋轨耦合作用。在此通过对t_2轨道引入有效角动量l=1,用Racah-Wigner代数重新推导了这种情况下f~(N-1)d组态的能级和f~N←→f~(N-1)d跃迁的相对跃迁线强的表达式,对简化模型进行了重要的拓展。此理论结果首先被用于计算分析Cs_2NaYCl_6晶体中Tb~(3+)离子的低温4f-5d吸收光谱。对更为复杂的Cs_2NaYF_6晶体中Er~(3+)和Tm~(3+)离子的4f-5d激发光谱也基于此拓展模型较为详细地进行了分析。结果和第一部分的详细计算具有很好的一致性,并体现出拓展的简化模型的优点。
第四部分为点群基在掺杂晶体中镧系和锕系离子的f~N -f~(N-1)d跃迁中的应用。基于简化模型(含拓展部分)的分析显示,点群理论的充分运用能简化计算并使计算结果更加清晰,因此,在此把P.H.Butler教授给出点群耦合系数充分地用于晶体中镧系和锕系离子的f~N←→f~(N-1)d跃迁的模拟:表述f~(N-1)d组态的基函数,可以采用多种耦合计划,这些耦合计划可以联系到分析f-d跃迁的简单模型的思想;采用Butler的点群不可约张量耦合技术推导出了f~(N-1)d组态的哈密顿矩阵元以及f~N←→f~(N-1)d跃迁的相对跃迁线强公式。作为一个运用的范例,使用由Butler和其合作者发展的RACAH软件产生的耦合系数,对掺杂在SrCl_2晶体中的Yb~(2+)离子的f-d吸收光谱进行了模拟计算和分析。在此过程中,对各种耦合计划的优势和适用性进行了讨论。此外,也基于Butler的点群基和点群不可约张量耦合技术对第三部分给出的f-d跃迁的相对线强公式进行了进一步的简化。
This thesis presents a theoretical simulation of the f-d transitions of lanthanide and actinide ions doped in crystals,which contains four parts:A)Theoretical study of the f-d transition spectra of Er~(3+)and Tm~(3+)ions doped into the cubic elpasolite Cs_2NaYF_6;B)Review of the simple model for the f-d transition spectra of lanthanide and actinide ions in crystals,and its supplementary applications to two spectra;C) The effective Hamiltonian theory for f-d transition spectra of lanthanide and actinide ions in octahedral crystal field based on the correction due to the spin-orbit interaction of 5d(or 6d)electron(recent advances of the simple model);D)Application of the point group bases to the f~N-f~(N-1)d transitions of lanthanide and actinide ions doped in crystals.
In part A,a detailed interpretation and analysis of the 4f-5d transition spectra of Tm~(3+)ions in Cs_2NaYF_6 is presented,where energy-level and intensity calculation and spectral simulation are performed by using the extended f-shell programs of Prof.M.F. Reid.The electronic states of the 4f~(11)5d~1 configuration are calculated to span from 58318 cm~(-1)to 86900 cm~(-1).At least 5 structured bands observed in the excitation spectrum and their intensities are fairly well simulated by this calculation.Strict O_h point group selection rules are operative for the transitions observed in the optical spectra.Measurements from the intensities of vibronic bands in the f-d excitation spectrum are not always suitable for the assignment of the energy of the first spin-allowed transition,since the lower 4f~(11)5d~1 states are of mixed SLJ parentage in which only certain components with the proper quantum numbers(not only S,but also LJ)which satisfy the select rules△S=0;△L=0,±1;△J=0,±lcontribute to the studied f-d transitions.The d-f emission spectrum is well-explained by this calculation and most of the intensity is located in one band:4f~(11)5d~1(high spin)→4f~(12)H_6.In addition, the f-d excitation spectrum of Er~(3+)ions in Cs_2NaYF_6 is also simulated and interpreted by the calculation results using the extended f-shell programs.Some similar analyses and conclusions for the electronic states of the 4f~(10)5d~1 configuration are also given.
In part B,the development and extension of the simple model for the f-d transitions of lanthanide and actinide ions in crystals is reviewed.The model can give the positions of zero-phonon lines for various f-d transition bands based on the values of 2-3 parameters,and calculate relative transition line strengths based on the quantum numbers of the initial and final states of the transitions.Its successful application to f-d transition spectra of rare-earth ions(4f~3-4f~(11))in crystals is sumraarized.As a supplementary study,this model is further applied to the remaining configurations f~(11)d and f~(12)d,where the parameterized energy matrix elements are obtained and tabulated.As an example,the excitation spectrum of Tm~(3+)doped in crystal CaF_2 is well explained.
In part C,the simple model for f-d transitions is extended to the case where the lanthanide(or actinide)ion substitutes the center ion in the octahedral six-fold coordination compounds,where,for the low-energy tE component of the 5d(or 6d) orbitals,the spin-orbit interaction of the d-electron cannot be neglected due to it induces energy splitting.In this so-called "effective Hamiltonian theory",by introducing a effective orbital angular momentum l=1 for the t_2 orbitals,the expressions of the energy levels for the f~(V-1)d configuration and the relative line strengths for the f~N←→f~(N-1)d transition are rederived in detail based on the Racah-Wigner algebra.The result is firstly applied to the interpretation of the low-temperature 4f-5d absorption spectrum of Cs_2NaYCl_6:Tb~(3+).Applications to the more complicated 4f-5d excitation spectra of Er~(3+)and Tm~(3+)ions in Cs_2NaYF_6 are also explicitly presented.The calculation results and interpretations using this extended theory agree well with those using the extended f-shell programs.
In the last part,the Butler's point-group coupling coefficients are applied to modeling of f~N←→f~(N-1)d transitions of lanthanide and actinide ions in crystals.There are several possible coupling schemes for the states of the f~(N-1)d configuration,which are related to the simple model for f-d transitions.Formulae for matrix elements of the Hamiltonian for the f~(N-1)d configuration and the relative line strengths for f~N←→f~(N-1)d transitions are derived by using the Butler's point-group irreducible tensor coupling techniques.As an example,the f-d absorption spectrum of the crystal Yb~(2+):SrCl_2 are calculated using these coupling coefficients based on the "RACAH" software developed by Butler and co-workers.The advantages and disadvantages of various coupling schemes are demonstrated.Moreover,the formula of the relative line strengths for the f-d transition in part C is further simplified by utilizing the Butler's point-group bases and irreducible tensor coupling techniques.With this expression,a lot of sums of magnetic quantum numbers in the original form are avoided and the evaluation of the relative line strengths simply depends on the angular momentum quantum numbers of the initial and final states of the transitions.
在第一部分中,在总结f-d跃迁的唯象哈密顿理论基础上,采用M.F.Reid教授编写的扩展f-shell程序对Cs_2NaYF_6晶体中Tm~(3+)离子的4f~(12)和4f~(11)5d电子构型的能级进行了详细计算,在此基础上对4f-5d跃迁光谱进行了非常细致的分析和解释:计算给出的4f~(11)5d~1构型的能态涵盖从58318 cm~(-1)到86900 cm~(-1)的范围,它们和在激发光谱上观测到的至少5个结构带的位置和强度相当符合。我们注意到:对于光谱中观测到的跃迁,严格的O_h点群选择定则依然是有效的:仅根据f-d激发谱中振动带的强度而指认第一自旋允许跃迁的能量位置是不可靠的,这是由于4f~(11)5d~1组态中较低能态波函的SLJ混合很厉害,仅仅那些具有合适量子数——满足全部选择定则(△S=0;△L=0,±1;△J=0,±1),注意除了S之外还有LJ——的成分才对跃迁有贡献。d-f发射谱也能用计算结果进行很好的解释,并且大部分强度集中在一个带4f~(11)5d~1(高自旋)→4f~(12)~3H_6上。另外,基于类似的计算,也对Cs_2NaYF_6晶体中Er~(3+)离子的4f-5d激发光谱进行了模型模拟和解释,并且给出了相似的分析和结论。
在第二部分中,总结回顾了用以分析晶体中镧系和锕系离子f-d跃迁光谱结构的简单模型及其应用的情况。这个模型可基于2-3个参数值来给出各个f-d跃迁带的零声子线的位置,进而基于跃迁初末态的量子数计算相对跃迁线强。作为对此模型的应用的一个补充,在此对尚未采用该模型探讨的f~(11)d和f~(12)d电子构型离子进行了分析,同时得到了可供今后使用的参数化的能量矩阵元。作为一个范例,在此专门对CaF_2晶体中Tm~(3+)的f-d激发光谱进行了分析计算。
第三部分为对现有简化模型的拓展。现有简单模型不能很好的用于镧系或锕系离子掺杂在正八面体六配位化合物的情况下的f-d光谱,这是因为其中的5d(或6d)轨道中较低能的t_2在旋轨耦合作用下分裂,从而不能忽略其旋轨耦合作用。在此通过对t_2轨道引入有效角动量l=1,用Racah-Wigner代数重新推导了这种情况下f~(N-1)d组态的能级和f~N←→f~(N-1)d跃迁的相对跃迁线强的表达式,对简化模型进行了重要的拓展。此理论结果首先被用于计算分析Cs_2NaYCl_6晶体中Tb~(3+)离子的低温4f-5d吸收光谱。对更为复杂的Cs_2NaYF_6晶体中Er~(3+)和Tm~(3+)离子的4f-5d激发光谱也基于此拓展模型较为详细地进行了分析。结果和第一部分的详细计算具有很好的一致性,并体现出拓展的简化模型的优点。
第四部分为点群基在掺杂晶体中镧系和锕系离子的f~N -f~(N-1)d跃迁中的应用。基于简化模型(含拓展部分)的分析显示,点群理论的充分运用能简化计算并使计算结果更加清晰,因此,在此把P.H.Butler教授给出点群耦合系数充分地用于晶体中镧系和锕系离子的f~N←→f~(N-1)d跃迁的模拟:表述f~(N-1)d组态的基函数,可以采用多种耦合计划,这些耦合计划可以联系到分析f-d跃迁的简单模型的思想;采用Butler的点群不可约张量耦合技术推导出了f~(N-1)d组态的哈密顿矩阵元以及f~N←→f~(N-1)d跃迁的相对跃迁线强公式。作为一个运用的范例,使用由Butler和其合作者发展的RACAH软件产生的耦合系数,对掺杂在SrCl_2晶体中的Yb~(2+)离子的f-d吸收光谱进行了模拟计算和分析。在此过程中,对各种耦合计划的优势和适用性进行了讨论。此外,也基于Butler的点群基和点群不可约张量耦合技术对第三部分给出的f-d跃迁的相对线强公式进行了进一步的简化。
This thesis presents a theoretical simulation of the f-d transitions of lanthanide and actinide ions doped in crystals,which contains four parts:A)Theoretical study of the f-d transition spectra of Er~(3+)and Tm~(3+)ions doped into the cubic elpasolite Cs_2NaYF_6;B)Review of the simple model for the f-d transition spectra of lanthanide and actinide ions in crystals,and its supplementary applications to two spectra;C) The effective Hamiltonian theory for f-d transition spectra of lanthanide and actinide ions in octahedral crystal field based on the correction due to the spin-orbit interaction of 5d(or 6d)electron(recent advances of the simple model);D)Application of the point group bases to the f~N-f~(N-1)d transitions of lanthanide and actinide ions doped in crystals.
In part A,a detailed interpretation and analysis of the 4f-5d transition spectra of Tm~(3+)ions in Cs_2NaYF_6 is presented,where energy-level and intensity calculation and spectral simulation are performed by using the extended f-shell programs of Prof.M.F. Reid.The electronic states of the 4f~(11)5d~1 configuration are calculated to span from 58318 cm~(-1)to 86900 cm~(-1).At least 5 structured bands observed in the excitation spectrum and their intensities are fairly well simulated by this calculation.Strict O_h point group selection rules are operative for the transitions observed in the optical spectra.Measurements from the intensities of vibronic bands in the f-d excitation spectrum are not always suitable for the assignment of the energy of the first spin-allowed transition,since the lower 4f~(11)5d~1 states are of mixed SLJ parentage in which only certain components with the proper quantum numbers(not only S,but also LJ)which satisfy the select rules△S=0;△L=0,±1;△J=0,±lcontribute to the studied f-d transitions.The d-f emission spectrum is well-explained by this calculation and most of the intensity is located in one band:4f~(11)5d~1(high spin)→4f~(12)H_6.In addition, the f-d excitation spectrum of Er~(3+)ions in Cs_2NaYF_6 is also simulated and interpreted by the calculation results using the extended f-shell programs.Some similar analyses and conclusions for the electronic states of the 4f~(10)5d~1 configuration are also given.
In part B,the development and extension of the simple model for the f-d transitions of lanthanide and actinide ions in crystals is reviewed.The model can give the positions of zero-phonon lines for various f-d transition bands based on the values of 2-3 parameters,and calculate relative transition line strengths based on the quantum numbers of the initial and final states of the transitions.Its successful application to f-d transition spectra of rare-earth ions(4f~3-4f~(11))in crystals is sumraarized.As a supplementary study,this model is further applied to the remaining configurations f~(11)d and f~(12)d,where the parameterized energy matrix elements are obtained and tabulated.As an example,the excitation spectrum of Tm~(3+)doped in crystal CaF_2 is well explained.
In part C,the simple model for f-d transitions is extended to the case where the lanthanide(or actinide)ion substitutes the center ion in the octahedral six-fold coordination compounds,where,for the low-energy tE component of the 5d(or 6d) orbitals,the spin-orbit interaction of the d-electron cannot be neglected due to it induces energy splitting.In this so-called "effective Hamiltonian theory",by introducing a effective orbital angular momentum l=1 for the t_2 orbitals,the expressions of the energy levels for the f~(V-1)d configuration and the relative line strengths for the f~N←→f~(N-1)d transition are rederived in detail based on the Racah-Wigner algebra.The result is firstly applied to the interpretation of the low-temperature 4f-5d absorption spectrum of Cs_2NaYCl_6:Tb~(3+).Applications to the more complicated 4f-5d excitation spectra of Er~(3+)and Tm~(3+)ions in Cs_2NaYF_6 are also explicitly presented.The calculation results and interpretations using this extended theory agree well with those using the extended f-shell programs.
In the last part,the Butler's point-group coupling coefficients are applied to modeling of f~N←→f~(N-1)d transitions of lanthanide and actinide ions in crystals.There are several possible coupling schemes for the states of the f~(N-1)d configuration,which are related to the simple model for f-d transitions.Formulae for matrix elements of the Hamiltonian for the f~(N-1)d configuration and the relative line strengths for f~N←→f~(N-1)d transitions are derived by using the Butler's point-group irreducible tensor coupling techniques.As an example,the f-d absorption spectrum of the crystal Yb~(2+):SrCl_2 are calculated using these coupling coefficients based on the "RACAH" software developed by Butler and co-workers.The advantages and disadvantages of various coupling schemes are demonstrated.Moreover,the formula of the relative line strengths for the f-d transition in part C is further simplified by utilizing the Butler's point-group bases and irreducible tensor coupling techniques.With this expression,a lot of sums of magnetic quantum numbers in the original form are avoided and the evaluation of the relative line strengths simply depends on the angular momentum quantum numbers of the initial and final states of the transitions.
引文
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