Yau Yuen 楊友源 Yeung

Superposition model and crystal-field analysis of the 4A2 and a2E states of Cr3+ ions at C3 sites in LiNbO3

The energy levels and wavefunctions including the two lowest-lying levels, namely 4A2 and a2E, for which reliable experimental data exist for Cr3+ ions at C3 symmetry sites in LiNbO3, are calculated using the complete matrix diagonalization method within the 3d3 configuration. The Hamiltonian considered includes the electrostatic term, the Trees correction, the spin-orbit interaction and the crystal-field interaction. The role of the additional low-symmetry crystal-field term B4-3O4-3 (in the Stevens operator notation), neglected in the C3v approximation used so far in the literature, is studied. The superposition model is developed for 3d3 ions at C3 symmetry sites and applied to study the site occupancy of Cr3+ in LiNbO3. Analysis of the optical data indicates that Cr3+ ions substitute at Nb sites and Li sites simultaneously. The present considerations offer an improvement over the earlier approximations using C3v symmetry only. The zero-field splitting predicted by the crystal-field calculations for Cr3+ at the Nb site matches the experimental value from EPR studies very well. This is contrary to the earlier prediction by the superposition model analysis of the spin-Hamiltonian parameters indicating that the zero-field splitting for Cr3+ ions at Li sites matches the experimental zero-field splitting better than that for Cr3+ at Nb sites. Since the present calculations involve fitting not only the zero-field splitting but also the energies of the a2E state, the present predictions may be more reliable than the previous predictions.

Crystal field invariants and parameters for low‐symmetry sites

Relationships between crystal field invariants and superposition model parameters are established. Various strategies are examined for determining and assessing the reliability of crystal field parameters for lanthanide ions in low‐symmetry sites. In particular, a new method of estimating crystal field parameters is proposed using crystal field invariants in conjunction with the superposition model. The importance of using a fixed reference frame throughout a series of fitting based on approximate symmetries is stressed and this leads us to identify a new simplified parametrization for lanthanide ions in LaF3 which is not related to an approximate symmetry.

Orbitally correlated crystal field parametrization for lanthanide ions

Analogous to the treatment of the spin‐correlated crystal field, a new type of lanthanide correlation crystal field, which depends on the relative orientations of the individual 4f electron orbital angular momenta and the total orbital angular momentum, is postulated. Associated sets of parameters have been obtained for TmCl3⋅6H2O, Er3+:LaCl3, and Pr3+:LaCl3 from the quadratic moments of the J‐multiplet energy levels. The results show that this field is noticeable in the Pr3+:LaCl3 spectrum in which the particularly well known deviance of the 1D2 multiplet found in conventional crystal field fitting is largely eliminated.

An experience of teaching for learning by observation: Remote-controlled experiments on electrical circuits

In order to facilitate senior primary school students in Hong Kong to engage in learning by observation of the phenomena related to electrical circuits, a design of a specific courseware system, of which the interactive human-machine interface was created with the use of an open-source software called the LabVNC, for conducting online remote-controlled experiments was developed in this study. The statistically significant results of a pre-test-post-test evaluation study showed that the LabVNC-based system has potential to promote students to learn the target topic under the approach of learning by observation. The assertion of the teacher on the pedagogical value of the remote-controlled experimentation and the enthusiasm of students in using the LabVNC-based system reveal the potential to integrate the use of the LabVNC-based system with the practice of scientific experiments. Based on the feedback from the teacher and students, the existing LabVNC-based system will be refined under the design-based research approach.

Local distortion and zero-field splittings of 3d5 ions in oxide crystals

A lattice relaxation model is employed to calculate the distorted ligand positions of Mn2+ and Fe3+ doped in cubic sites of some alkaline-earth metal oxides and the non-cubic sites of Fe3+:MgO as well. A superposition model analysis is then carried out for the spin parameters of the 6S5/2 ground-state zero-field splittings of both 3d5 ions. A consistent set of intrinsic parameters is obtained which gives good predictions for the spin parameters of Fe3+ in non-cubic sites of MgO and Mn2+ in the C3i site of some garnets.

High order crystal field invariants and the determination of lanthanide crystal field parameters

The relationship between high order J‐multiplet splitting moments and crystal field invariants is investigated. Expressions for corrections due to crystal field intermultiplet coupling are obtained. The formalism is applied to determine the crystal field parameters of lanthanide ions in cubic sites from ground multiplet energies alone, without fitting energy levels.

Local distortion and spin-Hamiltonian parameters for Eu2+ sites in the alkali halides

A detailed model is developed for calculating the local distortion near Eu2+ impurity sites in the alkali halides. The ionic positions obtained using this model are then used to carry out a superposition model analysis of the spin-Hamiltonian parameters. The results are consistent with results obtained for Eu2+ and Gd3+ in other systems and provide a significant extension of the understanding of the properties of S-state ion spin-Hamiltonian parameters. Although the predictions of the local distortion model do not provide detailed agreement with the experimental spin-Hamiltonian parameters, it is shown that very small corrections in the ionic positions produce excellent agreement, thus demonstrating the viability of the approach.

Macroscopic study of the social networks formed in web-based discussion forums

It is proposed and outlined in this paper on how to investigate the macroscopic features of those large-size social networks formed in web-based discussion forums. Some preliminary results on the pattern of the distribution of replies for individual topics, views for individual topics and co-discussants of individual participants will be presented. The present results will be compared with those found in other areas of large-size social networks and the significances and future work on those macroscopic properties of social networks for better understanding of computer-supported collaborative learning will be discussed.

A new approach to the determination of lanthanide spin-correlated crystal field parameters

A simple technique for determining spin-correlated crystal field parameters from spectroscopic data, which depends on the superposition model, is developed. This avoids the need for detailed simultaneous fits to both free-ion and crystal field parameters and provides a practicable method for low-symmetry systems. New sets of parameters have been obtained for the systems Ho3+:YPO4, Er3+:YAlO3 and Nd3+:PbMoO4. Similar results to those from the detailed fitting procedure were obtained for HO3+:LaCl3. The results conform that the rank-six spin-correlated crystal field contributes significantly to lanthanide crystal field splittings.

Crystal-field and superposition-model analyses of Pr3+-LaF3 in C2 symmetry

Abstract Carnall and coworkers have recently carried out an extensive analysis of the crystal-field levels of trivalent rare-earth ions in LaF3. Unfortunately, because they used an approximate C2v symmetry in their fits, rather than the true C2 symmetry, their crystal-field parameters do not contain the maximum possible information for testing models of the interaction between the rare-earth ions and the F− ligands. Here we report fits to Pr3+-LaF3 using the full C2 symmetry. Superposition-model parameters are determined from both the C2 and the C2v crystal-field parameters.