Interpretation of europium(III) spectra

The rich set of interactions between individuals in society results in complex community structure, capturing highly connected circles of friends, families or professional cliques in a social network. Thanks to frequent changes in the activity and communication patterns of individuals, the associated social and communication network is subject to constant evolution. Our knowledge of the mechanisms governing the underlying community dynamics is limited, but is essential for a deeper understanding of the development and self-optimization of society as a whole. We have developed an algorithm based on clique percolation that allows us to investigate the time dependence of overlapping communities on a large scale, and thus uncover basic relationships characterizing community evolution. Our focus is on networks capturing the collaboration between scientists and the calls between mobile phone users. We find that large groups persist for longer if they are capable of dynamically altering their membership, suggesting that an ability to change the group composition results in better adaptability. The behaviour of small groups displays the opposite tendency-the condition for stability is that their composition remains unchanged. We also show that knowledge of the time commitment of members to a given community can be used for estimating the community's lifetime. These findings offer insight into the fundamental differences between the dynamics of small groups and large institutions.

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Quantifying social group evolution

The superposition model was originally developed to separate the geometrical and physical information in crystal field parameters. Its success in the analysis of lanthanide spectra has been paralleled by the success of the related angular overlap model in the analysis of d-electron spectra. The basic ideas, method of application and reliability of the superposition model are discussed and its relationship with the angular overlap model is clarified. Developments described are the application of the superposition model to the ground (L=0) multiplet splittings of d5 and f7 ions, orbit-lattice interactions, transition intensities and correlation crystal fields. Special attention is paid to work which has been claimed to support or disprove the postulates of the model.

https://iopscience.iop.org/article/10.1088/0034-4885/52/6/002/pdf

The superposition model of crystal fields

１ Ｂａｓｉｃ ｎｅｐｈｒｏｌｏｇｙ（生理；免疫・病理；分子生物学；検査・診断） ２ Ｃｌｉｎｉｃａｌ ｎｅｐｈｒｏｌｏｇｙ（糸球体障害；尿細管・間質障害；全身性疾患と腎障害；水電解質異常；腎不全）

Annual review 腎臓

The polarized optical spectra of the ions Ti3+, V3+, Cr3+, Mn3+, Co3+, and Ni3+ in corundum single crystals have been studied at temperatures from 4.2° to 1200°K. A theory of the band strength based on the point‐charge model and p‐d mixing has been developed and applied to the data with results in fair agreement with experiment. The effects of temperature show that the vibrational‐electronic contribution to band strength is quite small at low temperature but may be appreciable at high temperatures. The crystal‐field parameters have been calculated as convergent lattice sums. The observed trigonal‐field parameter has the opposite sign from that calculated by the point‐charge model if the impurity ion is assumed to occupy an Al3+ ion position in the lattice, but has the same sign as calculated for an ion 0.1 A displaced along the c3 axis toward the empty octahedral site. Details of the spectra have been interpreted as showing that the surroundings of an ion are distorted in some electronic states.

Optical spectra of transition-metal ions in corundum

Crystal field and microscopic spin Hamiltonians approach including spin–spin and spin–other-orbit interactions for d2 and d8 ions at low symmetry C3 symmetry sites: V3+ in Al2O3

Ligand field analysis of the 3dN ions at orthorhombic or higher symmetry sites

In this paper, we critically review the existing microscopic spin Hamiltonian (MSH) approaches, namely the complete diagonalization method (CDM) and the perturbation theory method (PTM), for 3d8(3d2) ions in a trigonal (C3v, D3, D3d) symmetry crystal field (CF). A new CDM is presented and a CFA/MSH computer package based on our crystal-field analysis (CFA) package for 3dN ions is developed for numerical calculations. Our method takes into account the contribution to the SH parameters (D, g∥ and g⊥) from all 45 CF states for 3d8(3d2) ions and is based on the complete diagonalization of the Hamiltonian including the electrostatic interactions, the CF terms (in the intermediate CF scheme) and the spin-orbit coupling. The CFA/MSH package enables us to study not only the CF energy levels and wavefunctions but also the SH parameters as functions of the CF parameters (B20, B40 and B43 or alternatively Dq, v and v') for 3d8(3d2) ions in trigonal symmetry. Extensive comparative studies of other MSH approaches are carried out using the CFA/MSH package. First, we check the accuracy of the approximate PTM based on the `quasi-fourth-order' perturbation formulae developed by Petrosyan and Mirzakhanyan (PM). The present investigations indicate that the PM formulae for the g-factors (g∥ and g⊥) indeed work well, especially for the cases of small v and v' and large Dq, whereas the PM formula for the zero-field splitting (ZFS) exhibits serious shortcomings. Earlier criticism of the PM approach by Zhou et al (Zhou K W, Zhao S B, Wu P F and Xie J K 1990 Phys. Status Solidi b 162 193) is then revisited. Second, we carry out an extensive comparison of the results of the present CFA/MSH package and those of other CDMs based on the strong- and weak-CF schemes. The CF energy levels and the SH parameters for 3d2 and 3d8 ions at C3v symmetry sites in several crystals are calculated and analysed. Our investigations reveal serious inconsistencies in the CDM results of Zhou et al and Li (Li Y 1995 J. Phys.: Condens. Matter 7 4075) based on the strong-CF scheme for Ni2+ ions in LiNbO3 crystals. The correctness of our CFA/MSH package is verified by comparing our results with the predictions of Ma et al (Ma D P, Ma N, Ma X D and Zhang H M 1998 J. Phys. Chem. Solids 59 1211, Ma D P, Ma X D, Chen J R and Liu Y Y 1997 Phys. Rev. B 56 1780) and Macfarlane (Macfarlane R M 1964 J. Chem. Phys. 40 373) for α-Al2O3 : V3+(3d2) and MgO : Ni2+(3d8). It appears that the two independent approaches show perfect agreement with our approach, unlike those of Zhou et al and Li, which turn out to be unreliable. Our results reveal that the contributions to the ZFS parameter from the higher excited states cannot be neglected; also, the ZFS parameter is very sensitive to slight changes of the crystal structure. Hence our CFA/MSH package, which takes into account the contributions to the ZFS parameter from the higher excited states, can provide reliable results and proves to be a useful tool for the studies of the effect of the lattice distortions, defects and structural disorder on the spectroscopic properties of 3d2 and 3d8 ions at trigonal symmetry sites in crystals.

https://iopscience.iop.org/article/10.1088/0953-8984/14/22/314/pdf

Microscopic spin Hamiltonian approaches for 3d8 and 3d2 ions in a trigonal crystal field - perturbation theory methods versus complete diagonalization methods

Superposition-model analyses for the Cr3+ 4A2 ground state.

The microscopic spin-Hamiltonian (MSH) parameters and the crystal field (CF) energy levels for Ni2+ ions in LiNbO3 crystals have been investigated using the crystal field analysis/microscopic spin-Hamiltonian package recently developed. The investigations considered for the first time the spin–spin (SS) and spin-other-orbit (SOO) interactions. The low-symmetry effects (LSE) arising from the additional terms (Im(B43)≠0) induced at the C3 symmetry sites by the distortion angle ϕ, which have been omitted in earlier works, have also been dealt with. This study shows that for LiNbO 3 : Ni 2+ the contributions arising from SS and SOO interactions to the zero-field splitting parameter D are appreciable, whereas those to g|| and g⊥ are quite small. Since the distortion angle ϕ (≅0.68°) for LiNbO 3 : Ni 2+ is rather small, the contributions to the spin-Hamiltonian (SH) parameters arising from LSE are also small. Feasibility of application of the superposition model is also discussed. A good overall agreement between the theoretical and experimental results for the SH parameters and the CF energy levels has been obtained.

Yau Yuen Yeung

Papers

Crystal field and microscopic spin Hamiltonians approach including spin–spin and spin–other-orbit interactions for d2 and d8 ions at low symmetry C3 symmetry sites: V3+ in Al2O3

Ligand field analysis of the 3dN ions at orthorhombic or higher symmetry sites

Microscopic spin Hamiltonian approaches for 3d8 and 3d2 ions in a trigonal crystal field - perturbation theory methods versus complete diagonalization methods

Superposition-model analyses for the Cr3+ 4A2 ground state.

Microscopic spin-Hamiltonian parameters and crystal field energy levels for the low C3 symmetry Ni2+ centre in LiNbO3 crystals