Local Lattice Structure Research Articles

Local molecular structure and thermal expansion coefficient for octahedral Fe 3+ center in AlF 3:Fe 3+system

A theoretical method for studying the inter-relation between electronic and molecular structure has been proposed by diagonalizing the complete energy matrices for d 5 configuration ion in a trigonal ligand-field. Based on this method, the local lattice distortion of Fe 3+ in AlF 3:Fe 3+ system (AlF 3 is the component of fluoride glasses or is the single crystal) has been studied by considering the second-order and fourth-order EPR parameters D and ( a − F), simultaneously. The results indicate that the local lattice structure around octahedral Fe 3+ center has an expansion distortion whether AlF 3:Fe 3+ is the component of fluoride glasses or Fe 3+ is doped in the AlF 3 single crystal. The expansion distortion may be ascribed to the fact that the radius of Fe 3+ ion is larger than that of Al 3+ ion, and the Fe 3+ ion will push the fluoride ligand outwards, respectively. Furthermore, the thermal expansion coefficient of Fe 3+ in the single crystal AlF 3:Fe 3+ depending on the temperature are reported and some characteristics of it are also analyzed.

EPR Theoretical Study of the Local Lattice Structure of Fe3+ Doped in MgTiO3 and LiTaO3

The EPR zero-field splittings of Fe3+ doped in MgTiO3 and LiTaO3 are studied by diagonalizing the complete energy matrices of the electron-electron repulsion, ligand-field and spin-orbit coupling interactions for a d5 configuration ion in a trigonal ligand-field. It is shown that, when Fe3+ is doped in aMgTiO3 or LiTaO3 crystal, the local lattice structure around the octahedral Fe3+ center has an obvious distortion along the C3 axis. By simulating the second- and fourth-order EPR parameters D and (a−F) simultaneously, the local structure parameters of Fe3+ doped inMgTiO3 and LiTaO3 crystals are determined, which reveal that Fe3+ occupies both the Mg2+ and Ti4+ sites in the MgTiO3:Fe3+ system and occupies the Li+ site rather than the Ta5+ site in the LiTaO3:Fe3+ system. The results accord with the ENDOR and EPR experiments. - PACS numbers: 71.70.Gm; 75.30.Et; 71.70.Ch.

Effect on the EPR and site symmetry of Cr 3+ ions doping spinel crystals: A complete energy matrices study

The EPR parameters ( D, g ∥, g ⊥) for chromium doped in spinels (MgAl 2O 4, ZnAl 2O 4 and ZnGa 2O 4) have been calculated by diagonalizing the 120 × 120 complete energy matrices for d 3 configuration ion in trigonal ligand field. The Zeeman effect of Cr 3+ ion in the trigonally distorted octahedral site of spinels has been studied, suggesting that there is a nonlinear relation between the Δ g (Δ g = g ∥ − g ⊥) and orbital reduction factor k. Both the site symmetries D 3 d and C 3 v of this impurity have been discussed for the three host lattices, and the local lattice structure around the impurity has also been determined.

Theoretical study of local lattice structure of Fe 3+–V M system in iron-doped AMF 3 crystals

A theoretical method for investigating the inter-relation between the electronic and the molecular structures of a d 5 ion in a tetragonal ligand-field has been established on the basis of a 252 × 252 complete energy matrix. Using this method, the local structure parameters of the Fe 3+–V M system in AMF 3:Fe 3+ crystals are determined by the experimental EPR spectra at T = 300 K. It is shown that, the local lattice structure around an octahedral Fe 3+ center has a compression distortion along the crystalline axis in AMF 3:Fe 3+ crystal. From our analysis, we also conclude that Δ R vs. 10 4 b 2 0 is approximately linear for the Fe 3+–V M system in AMF 3:Fe 3+ crystals.

Optical spectrum and local lattice structure for ruby

By diagonalizing the 120 x 120 complete energy matrices for d(3) ion in trigonal crystal field, which contains the electrostatic interaction, the trigonal field as well as the spin-orbit interaction, the unified calculation of the whole optical and EPR spectra for ruby are made. And matrix elements of the Zeeman energy with the magnetic field parallel or perpendicular to the trigonal axis are introduced into the complete energy matrices for obtaining the g factors of the energy levels. It is concluded that zero-field splitting and optical spectra as well as g factors are in good agreement with the experimental data and the distorted local lattice structure is determined firstly results from a stretching of the O2- ions along the C-3 axis. The pressure-induced shifts of energy levels, g factors and local lattice structure are also discussed. In particular, all the calculations are carried out successfully within the framework of the crystal-field model which is consistent with the opinion of Macfarlane and Sturge that if all terms within the d(3) configuration are included, one need not go outside conventional crystal-field theory.

Theoretical study of local lattice structure of Mn 2+ in perovskite fluorides A 2MF 4 (A=K, Rb; M=Mg, Zn, Cd) series

A theoretical method for investigating the inter-relation between the molecular structure and electronic structure has been established on the basis of the 252×252 complete energy matrices for a 3d 5 configuration ion in a tetragonal ligand field. By means of this method, which is independent of the X-ray diffraction, the local structure of the paramagnetic Mn 2+ ion in perovskite fluorides A 2MF 4 (A=K, Rb; M=Zn, Mg, Cd) are determined directly by analyzing the EPR spectrum of octahedral Mn 2+ center in A 2MF 4 crystals and the optical absorption spectrum of the (MnF 6) 4− cluster. It is shown that, comparing with the octahedral cubic structure, the local micro-structure in the vicinity of Mn 2+ displays an elongated distortion when b 2 0 > 0 and a compressed distortion when b 2 0 < 0 , and Δ R vs. 1 0 4 b 2 0 as well as Δ R vs. 1 0 4 b 4 0 in the distortion region is, respectively, approximately linear. Simultaneously, the theoretical zero-field-splitting parameters b 2 0 , b 4 0 and b 4 4 are in good agreement with the experimental values.

Study of optical absorption and EPR spectra of Mn2+ ion in cadmium maleate dihydrate

The optical absorption and EPR spectra of Mn2+ ion doped in cadmium maleate dihydrate have been theoretically investigated by diagonalizing the complete energy matrices for a d5 configuration ion in a trigonal ligand-field. According to the suggestion of the optical absorption studies, we assume that the Mn2+ ion enters the host lattice interstitially and the distorted octahedral symmetry for the impurity ion is trigonal. Moreover, the local lattice structure parameters of the system are determined. The results show that the six oxygen ions around the Mn2+ ion are at the same distance R=2.115 A, and there are three Mn-O bonds forming an angle θ1 of 66.26° with the C3-axis and three others forming an angle θ2 of 43.40°.

Theoretical study of EPR spectra for Mn 2+ ion in [Mg(H 2O) 6]SnCl 6 single crystal

The relationship between the impurity structures and the electron paramagnetic resonance (EPR) parameters D, ( a– F) have been studied by diagonalizing the complete energy matrices for Mn 2+ ion in [Mg(H 2O) 6]SnCl 6 single crystal in a trigonal ligand field within a weak-field-representation. It is shown that the local lattice structure around Mn 2+ ion in [Mg(H 2O) 6]SnCl 6 exhibits an elongation distortion which is different at 290 K and 77 K. The local structure parameters R = 2.223 ± 0.027 Å, θ = 52.966 ± 0.004° and R = 2.205 ± 0.030 Å, θ = 53.155 ± 0.047° for Mn 2+ ion in [Mg(H 2O) 6]SnCl 6 are determined at different temperatures 290 K and 77 K, respectively, and EPR parameters D and ( a– F) can also get a satisfactory explanation simultaneously.

Local structure and EPR g factors for KAl(MoO 4) 2:Cr 3+ and RbIn(MoO 4) 2:Cr 3+ systems

For a d 3 configuration ion, the 120 × 120 complete energy matrix which contains the electron–electron repulsion interaction, the ligand field interaction, the spin–orbit coupling interaction as well as the Zeeman interaction, has been established. By diagonalizing the complete energy matrix, local structure and EPR g factors for Cr 3+ ions doped in KAl(MoO 4) 2 and RbIn(MoO 4) 2 have been investigated, respectively. It is found that the orbit reduction effect is very important to understand the EPR g factors for Cr 3+ ions doped in KAl(MoO 4) 2 and RbIn(MoO 4) 2, and some characteristics of orbit reduction on the EPR g factors are discussed firstly. Simultaneously, by simulating the calculated optical spectra and the EPR spectra data to the experimental results, we obtain the local structure parameters R = 2.043 Å, θ = 53.5940° and R = 2.065 Å, θ = 56.0434° for Cr 3+ ions doped in KAl(MoO 4) 2 and RbIn(MoO 4) 2, respectively. The calculated results show the local lattice structure of the octahedral Cr 3+ centers in KAl(MoO 4) 2 and RbIn(MoO 4) 2 exhibit an elongation and a compression distortions, respectively.

Theoretical study of local lattice structure of Fe 3+–V cd and Fe 3+–Li + systems in RbCdF 3 and CsCdF 3 crystals

A theoretical method for investigating the inter-relation between the electronic and the molecular structures of a 3d 5 ion in a tetragonal ligand-field has been established on the basis of a 252×252 complete energy matrix. By means of this method, the local structure of the Fe 3+–V cd and Fe 3+–Li + systems in RbCdF 3:Fe 3+ and CsCdF 3:Fe 3+ crystals are determined by the experimental EPR spectrum. Our calculation show that the local lattice structure around an octahedral Fe 3+ center has a compression distortion along the crystalline axis in RbCdF 3 as well as in CsCdF 3 crystals, and that the compression magnitude of a tetragonal Fe 3+–Li + system is larger than that of the Fe 3+–V cd system. This may be ascribed to the fact that a Fe 3+ ion replaces a Cd 2+ ion and a Li + ion substitutes for another Cd 2+ ion next to the Fe 3+ ion in the Fe 3+–Li + system, and the Li + ion will shift to the Fe 3+ ion, which pushes the F 1 ion toward the Fe 3+ ion. Using this method, the experimental EPR parameters b 2 0 , b 4 0 and b 4 4 are also interpreted simultaneously.

EPR theoretical study of local lattice structure in YAG:Mn2+ system

EPR theoretical study of local lattice structure in YAG:Mn2+ system

EPR theoretical investigation of substitution site and local lattice structure of tetragonal Cr 2+ in cadmium thiogallate

By analyzing the experimental EPR zero-field-splitting (ZFS) parameters a, D and F, the substitution position and the local lattice structure of tetragonal Cr 2+ center in cadmium thiogallate (CdGa 2S 4) crystal have been studied on the basis of the complete energy matrix for a d 4 configuration in a tetragonal ligand-field within a strong-field-representation. Our results show that the Cd 2+ site is the only substitutional position for Cr 2+ in CdGa 2S 4 and the local structure around the Cr 2+ is a compression distortion. From EPR calculations, the local lattice structure parameters R = 2.44 A and θ = 57.74° are determined.

Theoretical investigation of the local lattice structure of Mn 2+ ion doped in tetragonal K 2ZnF 4 crystal

The complete energy matrices(252 x 252) for a d(5) configuration ion in a tetragonal ligand-field has been constructed on the basis of the complete set of basis vertical bar L, S, M-L, M-S > of d(5) configuration (252 dimension), and the relationship between the low-symmetry EPR parameters b(2)(0), b(4)(0) and the local distortion parameters has been established based on the complete energy matrices. As an application, we have studied the EPR parameters and the local lattice structure of Mn2+ ion doped in tetragonal K2ZnF4 system. The calculation indicated that the local lattice structure around a tetragonal Mn2+ ion center has an expansion distortion. Simultaneously, the local lattice structure parameters R-1 = 2.0727 angstrom, R-2 = 2.0801 angstrom at room temperature (295 K) and R-1' = 2.0439 angstrom, R-2' = 2.05478 angstrom at low temperature (4.2 K) are determined.

Characterization of Electronic Transition Energies and Trigonal Distortion of the (FeO6)9- Coordination Complex in the Al2O3:Fe3+ System: A Simple Method for Transition-Metal Ions in a Trigonal Ligand Field

A theoretical method for studying the inter-relationships between electronic and molecular structure has been proposed on the basis of the complete energy matrices of electron-electron repulsion, the ligand field, and the spin-orbit coupling for the d5 configuration ion in a trigonal ligand field. As an application, the local distortion structure and temperature dependence of zero-field splitting for Fe3+ ions in the Al2O3:Fe3+ system have been investigated. Our results indicate that the local lattice structure of the (FeO6)(9-) octahedron in the Al2O3:Fe3+ system has an elongated distortion and the value of distortion is associated with the temperature. The elongated distortion may be attributed to the facts that the Fe3+ ion has an obviously larger ionic radius than the Al3+ ion and the Fe3+ ion will push the two oxygen triangles upward and downward, respectively, along the 3-fold axis. By diagonalizing the complete energy matrices, we found that the theoretical results of electronic transition energies and EPR spectra for Fe3+ ions in the Al2O3:Fe3+ system are in good agreement with the experimental findings. Moreover, to understand the detailed physical and chemical properties of the Al2O3, the theoretical values of the zero-field splitting parameters and the corresponding distortion parameters in the range 50 K <or= T <or= 250 K are reported first.

EPR spectra and local lattice structure of Fe 3+ impurity ions in ferroelectric LiNbO 3

The optical absorption and EPR spectra of Fe 3+ impurity ions doped in near stoichiometric LiNbO 3 crystal are studied by diagonalizing the complete energy matrices for a d 5 configuration ion in a trigonal ligand-field. By analyzing the optical absorption and EPR spectra simultaneously, the distortion parameters Δ θ 1 = 3.42°, Δ θ 2 = −7.22° are determined for Li + substitutional position supported by ENDOR experiments. The theoretical results indicate that there exists a compressed distortion in LiNbO 3:Fe 3+ system, which may be ascribed to the fact that the radius of Fe 3+ ion is slightly smaller than that of the host ion. Meanwhile, the local structure parameters R 1 = 2.08 A, R 2 = 1.91 A, θ 1 = 47.99° and θ 2 = 62.52° for the octahedral Fe 3+ center in LiNbO 3 crystal are also determined, which are close to that of the αFe 2O 3. The calculated transition energies of octahedral Fe 3+ center in LiNbO 3 are in good agreement with those of Fe 3+ cations in other oxides due to the similar octahedral (FeO 6) 9− cluster.

EPR investigation of local lattice structure of Mn 2+ in diamagnetic garnets

An analysis of the relationship between the EPR trigonal-field parameters and the local crystal structure of octahedral Mn 2+ centre in diamagnetic garnets is presented by diagonalizing the complete energy matrices for a d 5 configuration ion in a trigonal ligand-field. Both the second-order and fourth-order EPR parameters D and ( a − F) are taken simultaneously into the structural investigation. It is shown that the local lattice structure around an octahedrally coordinated Mn 2+ centre in diamagnetic garnets have expansion distortions, which may be attributed to the fact that the radius of Mn 2+ ion is larger than that of Al 3+ or Ga 3+ ion, and the Mn 2+ ion will push the oxygen ligands outwards. The local lattice structure parameters R and θ for octahedral Mn 2+ ion centre in the crystals are determined, respectively. Meanwhile, it is also demonstrated that the empirical impurity-ligand distance R ≈ R H + 1 2 ( r i - r h ) is not suitable for Mn 2+ in diamagnetic garnets, which has been approximately taken in previous works.

EPR theoretical study of local molecular structure for tetrahedral Fe 3+ centers in zinc oxide

A theoretical method for studying the inter-relation between electronic and molecular structure has been proposed by diagonalizing the complete energy matrices for a d 5 configuration ion in a trigonal ligand field. As for ZnO:Fe 3+system, the local lattice distortion for the tetrahedral Fe 3+ centers in zinc oxide has been investigated by considering the second-order and fourth-order EPR parameters D and ( a − F) simultaneously. The results indicate that the local lattice structure around tetrahedral Fe 3+ centers exhibits a compression distortion, i.e., the (FeO 4) 5− entity in ZnO:Fe 3+ system is smaller than the (ZnO) 6− entity in ZnO crystal. The local lattice structure distortion parameters Δ R = −0.119 A and Δ θ = 0.339° for Fe 3+ ion in ZnO:Fe 3+ system are determined. Furthermore, the displacements Δ Z 1 = −0.050 A for transition-metal ion along the C 3 axis, and Δ Z 2 = −0.169 A for the distance variation between the O 2− along the C 3 axis and the lower oxygen plane are obtained.

EPR zero-field splitting parameters and structural distortion study of Mn 2+-doped (CH 3) 4NCdCl 3 crystal in high-temperature phases

The EPR zero-field splitting parameters and structural distortion of Mn 2+-doped (CH 3) 4NCdCl 3 crystal in high-temperature phases have been studied by diagonalizing the complete energy matrices. The zero-field splitting parameters D and ( a − F) are demonstrated to be negative and positive, respectively, and obtain a reasonable explanation together. Simultaneously, the distortion magnitude of local lattice structure around the Mn 2+ ion in this crystal is determined, namely, Δ R = −0.13 Å and Δ θ = 2.975° for T = 124 K; Δ R = −0.12 Å and Δ θ = 2.610° for T = 297 K; Δ R = −0.26 Å and Δ θ = 2.870° for T = 573 K. From the structural distortion, we deduce that a new structural phase transition should occur to the (CH 3) 4NCdCl 3 crystal at temperatures ranging from 297 to 573 K. This is also in agreement with recent differential scanning calorimetric measurements.

EPR theoretical study of local lattice structure on Mn 2+ ion doped in calcite and differences between single crystal and fresh water snail, Pila globosa

By diagonalizing the complete energy matrices for a d 5 configuration ion in a trigonal ligand-field and considering the second-order, fourth-order EPR parameters D and ( a − F) simultaneously, the substitution position of Mn 2+ ion in the CaCO 3:Mn 2+ system has been studied by analyzing the optical absorption and EPR spectra of single crystal and the ostracum layer of operculum of fresh water snail Pila globosa. The results show that in the single crystal there is an obvious compressed distortion Δ R = −0.158 Å and Δ θ = 0.70°, and the distortion in P. globosa is Δ R = −0.107 Å and Δ θ = −0.34° ∼ −0.23°. Meanwhile the EPR parameters 10 4( a − F) = 7.02–7.29 cm −1 and 10 4 a = 6.35 cm −1 are predicted in P. globosa.

Theoretical study of electron paramagnetic resonance spectrum and local lattice distortion for Mn 2+ in Al 2O 3:Mn 2+ system

Electron paramagnetic resonance spectrum and local lattice distortion for Mn 2+ ion in Al 2O 3:Mn 2+ system have been studied by means of the complete energy matrices for electron–electron repulsion, spin–orbit coupling and ligand–field interactions. It is shown that the local lattice structure around Mn 2+ ion in Al 2O 3:Mn 2+ system exhibits an elongation distortion in the local lattice structure. The elongation distortion may be ascribed to the facts that the radius of Mn 2+ is larger than that of the host ion Al 3+, and the Mn 2+ ion will push the oxygen ligands outwards. By simulating the second- and fourth-order EPR parameters D and ( a− F) simultaneously, the bond length of the upper and lower oxygen triangle R 1 = 2.112 – 2.137 A , R 2 = 2.003 – 2.028 A , and the angles between the chemical bond length and C 3 axis θ 1 = 52.944 – 52.950 ° , θ 2 = 57.910 – 57.960 ° are determined. Furthermore, the displacements Δ Z 1 = 0.2225 – 0.2345 A for transition-metal ion and Δ Z 2 = 0.171 – 0.198 A for the distance variation between the two oxygen planes are derived.