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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 l...

The microscopic origin of the spin Hamiltonian (SH) parameters for Ni 2+ (3d 8 ) ions in a trigonal type I symmetry (C 3v , D 3d , D 3 ) crystal field (CF) is studied. In addition to the spin-orbit (SO) interaction, we consider also the spin-spin (SS) and spin-other-orbit (SOO) interactions. The relative importance of the four (SO, SS, SOO, and combined SO-SS-SOO) contributions to the SH parameters is investigated using the CFA/MSH package and the complete diagonalization method (CDM). The SO mechanism is dominant for all CF parameter (CFP) ranges studied, except where the contributions D SO to the zero-field splitting (ZFS) parameter D change sign. For the trigonal CFP, v c ≈ 1200 cm −1 D due to the other three mechanisms exceeds D SO . Although |D SOO | is quite small, the combined |D SO−SOO | is appreciable. The SO-based perturbation theory (PT) works generally well for the g-factors: g and g ⊥ , while it fails for D in the vicinity of v c and for large |v | and v > 0. The high percentage discrepancy ratio δ D = 2020% for v c indicates unreliability of D SO (in PT). Applications to Ni 2+ ions at trigonal symmetry sites in LiNbO 3 , α-LiIO 3 , and Al 2 O 3 , are provided. The theoretical SH parameters are in good agreement with the experimental data. The low symmetry (C 3 ) effects induced by the angle ϕ are tentatively studied, but appear to be quite small.

The porous carbons (PCs) with tunable morphologies and pore sizes were prepared by the sol–gel process via a freeze-drying technique for microwave absorption applications. The results of Raman spectroscopy and nitrogen sorption analysis showed that the graphitization degree was barely influenced as the ratio of tert-butanol (T) to resorcinol (R) decreased, while the pore morphologies changed from the disordered slit-shaped pores to the uniform cage-like pores. Dielectric properties of the as-prepared carbon samples were determined by a vector network analyzer in the frequency range of 8.2–12.4 GHz. Results showed that the effect of pore morphology on the dielectric loss of PCs was dominant in the case of similar graphitization. When the T/R ratio was 7.5, the sample with cage-like pores revealed the maximum values in the real part ε′ and the imaginary part ε″ of complex permittivity, which were 13.2–6.5 and 15.6–10.1, respectively, suggesting a better capacity of dielectric loss in the 8.2–12.4 GHz range. The proposed mechanism for the effect of the pore morphologies on microwave absorption performance was discussed.

Biodiesel produced by the transesterification of vegetable oils or animal fats with short-chain alcohols (typically methanol) is a promising alternative fuel for diesel engines, because of the limited resources of fossil fuels and environmental concerns. In this work, Li/ZnO catalysts were prepared using an impregnation method followed by calcinations, and then they were tested for soybean oil transesterification. It was determined that Li/ZnO catalysts exhibited good catalytic activities, and the catalytic performance was greatly dependent on (i) the loading amount of lithium and (ii) the calcination temperature. This Li/ZnO catalyst, at an amount of 5 wt %, resulted in a soybean oil conversion of 96.3% in 3 h using a reflux of methanol and a 12:1 molar ratio of methanol to oil. Moreover, the catalyst was characterized using X-ray diffractometry (XRD), X-ray photoelectron spectroscopy (XPS), infrared (IR) spectroscopy, thermogravimetry−differental thermal analysis (TG-DTA), and the Hammett titration method. It was shown that the activity of the catalysts for the transesterification reaction is closely related to their basic properties.