Analysis of the lattice,strong coupling series for g0φ4 field theory in d dimensions

We analyze the renormalized strong coupling series for lattice g₀φ⁴ field theory which is a double series in x = M⁴a⁴/g₀a_4?dandy = 1/M²a², where M is the renormalized mass, a the lattice spacing, g₀ the bare coupling constant and d the dimension of space-time. We extrapolate to large y for fixed x by using a Padé-like extrapolation technique. We study the dimensionless renormalized coupling constant G/M^4?d and find that as we approach the continuum(x → 0, y → ∞) the entire spectrum of g₀ from zero to infinity can be studied. Our results for d = 1,2,3,4 based on a series in y up to y⁵ and in x up to x³ show that for fixed lattice spacing a, G/M^4?d is a monotonic function of g₀ ranging from zero at g₀ = 0 to a maximum at g₀ = ∞. Using the high temperature expansion results, we have also derived 9 terms in y on 8 lattices of dimension 1,2,3 and 4 for the linear term in x, and studied this series to see if one can see a breakdown in this monotonic behavior of G for large y. The analysis of this latter series is inconclusive.     

Bonding in the Doubly Disordered Ba1−x Sn x Cl1+y F1−y Solid Solution

New materials were prepared in the SnF₂/BaCl₂ system by precipitation, and in the SnF₂/BaCl₂/BaF₂ system by direct reactions at high temperature in dry conditions. Stoichiometric BaSn₂Cl₂F₄ and BaSnClF₃?0.8H₂O, and a wide Ba_1?x Sn _x Cl_1+y F_1?y solid solution were prepared for the first time. Elemental analysis, X-ray diffraction and ¹¹⁹Sn Mössbauer spectroscopy were used for the characterization and study of bonding in the new materials. Mössbauer spectroscopy was shown to be an excellent method for probing both the type of bonding at tin(II) (ionic or covalent) and the bond strength at the tin sublattice. Tin(II) is covalently bonded in the stoichiometric phases and ionic (Sn²⁺ stannous ion) in the precipitated Ba_1?x Sn _x Cl_1+y F_1?y solid solution. The case of Ba_1?x Sn _x Cl_1+y F_1?y prepared in dry conditions is more complex. At negative y values (Cl: F <1) and more particularly at high x (solid solution rich in tin), a mixture of Sn²⁺ and covalent Sn(II) is observed, with a normal sublattice strength for Sn(II). At positive y values (Cl:F >1) and more particularly at low x (poor in tin), all the tin(II) is in the ionic form. Furthermore, at high x and high y, the tin(II) sublattice strength decreases so drastically that the tin recoil free fraction at ambient temperature is nearly zero. The bonding type and tin sublattice strength can be explained in terms of preference of covalent bonding with F and when tin clustering occurs, whereas an excess Cl around Sn(II) forms ionic bonding and tin rattling due to ionic size mismatch.     

Electron paramagnetic resonance in mixed crystals (BaF<Subscript>2</Subscript>)<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>(LaF<Subscript>3</Subscript>)<Subscript>x</Subscript> activated by Ce<Superscript>3+</Superscript> ions

The electron paramagnetic resonance (EPR) spectra of mixed crystals (BaF₂)_{1?x? y}(LaF₃)_x(CeF₃)_y (y = 0.001 = 0.1%, x = 0–0.02) are investigated in a magnetic field H‖C₄ at a frequency of 9.5 GHz. The angular dependence of the EPR spectrum is measured for the sample with x = 0.02. The lines attributed to Ce³⁺ impurity centers with tetragonal symmetry and g factors (g_‖ = 0.75, g_⊥ = 2.4) close to those measured for the KY₃F₁₀: Ce³⁺ compound are separated in the complex EPR spectrum. The assumption is made that the aforementioned impurity centers are cubooctahedral clusters of the La₆F₃₇ type in which one of the La³⁺ ions is replaced by the Ce³⁺ ion.     

A study by E.S.R. of Mn2+ in potassium chromate

Divalent manganese ions are found in potassium chromate single crystals after heating at 600°C in the presence of iodine. These ions occupy three differently oriented sites with the same spin Hamiltonian parameters: g_z = 2·000, g_x = 2·008, g_y = 2·015; A_z = ?88·4 G, A_x = A_y = ?91 G; D = 190 and E = ?30 G.The authors suggest that Mn²⁺ occupies a substitutional (K⁺) position rather than an interstitial one. The influence of iodine is discussed.     

ESR of Cu doped cadmium (II) formate dihydrate

Electron spin resonance (ESR) of Cu²⁺ doped cadmium formate dihydrate single crystal was studied at room temperature. Copper enters the lattice substitutionally and is trapped at two magnetically inequivalent sites. The observed spectra are fitted to a spin-Hamiltonian of rhombic symmetry with the following values of the spin-Hamiltonian parameters, Cu²⁺(I): g_x=2.097±0.002, g_y=2.1166±0.002, g_z=2.2887±0.002 and A_x=(140±2)×10⁻⁴ cm⁻¹, A_y=(151±2)×10⁻⁴ cm⁻¹, A_z=(239±2)×10⁻⁴ cm⁻¹, Cu²⁺(II): g_x=2.0843±0.002, g_y=2.1045±0.002, g_z=2.2742±0.002 and A_x=(141±2)×10⁻⁴ cm⁻¹, A_y=(158±2)×10⁻⁴ cm⁻¹, A_z=(267±2)×10⁻⁴ cm⁻¹. The ground state wave function of the Cu²⁺ ion in this lattice is evaluated. It is found that the ground state is predominantly |x²−y²〉. The g-factor anisotropy is also calculated and compared with the experimental value. With the help of the optical absorption study, the nature of bonding in the complex has been discussed.     

ESR study of vanadyl ion in tripotassium citrate

ESR spectra of VO²⁺ doped tripotassium citrate are recorded at room temperature. The observed spectra are fitted to a spin Hamiltonian of orthorhombic symmetry with g_x = 2.001 ± 0.001, g_y = 1.997 ± 0.001, g_z = 1.945 ± 0.001, A_x = (49.0 ± 1) × 10⁻⁴ cm⁻¹, A_y = (66.8 ± 1) × 10⁻⁴ cm⁻¹ and A_z = (168.4 ± 1) × 10⁻⁴ cm⁻¹. The covalency and Fermi contact terms are evaluated and compared with those of other lattices.     

Spin-spin interaction and the EPR spectrum of KDy(WO<Subscript>4</Subscript>)<Subscript>2</Subscript>

The EPR spectrum of a KDy(WO₄)₂ monoclinic crystal is investigated. It is found that the EPR spectrum of magnetically concentrated materials at a low frequency (9.2 GHz) undergoes a substantial transformation in addition to the well-known broadening of the EPR lines. At low Dy³⁺ concentrations (x<10^?2), the EPR spectrum of an isomorphic crystal, namely, KY_(1?x)Dy_x(WO₄)₂, is characterized by the parameters g_x=0, g_y=1.54, and g_z=14.6. For a magnetically concentrated crystal KDy(WO₄)₂, the g values are as follows: g_x=0, g_y=0.82, and g_z=2.52. It is demonstrated that the difference in the parameters is associated with the specific spin-spin interaction between Dy³⁺ ions, including the Dzyaloshinski interaction, which is not observed at high frequencies.     

ESR study of vanadyl ion in trisodium citrate pentahydrate

ESR study of VO²⁺ doped trisodium citrate pentahydrate is undertaken at room temperature. The observed spectra are correlated with the available crystal structure data and are fitted to a spin Hamiltonian of orthorhombic symmetry with g_x = 1.998 ± 0.001, g_y = 1.992 ± 0.001, g_z = 1.934 ± 0.001, A_x = (70.0 ± 1) × 10^-4cm^-1, A_y = (66.6 ± 1) × 10^-4cm^-1 and A_z = (175.4 ± 1) × 10^-4cm^-1. The covalency and Fermi contact parameters are evaluated and compared with those of VO²⁺ in other lattices.     

ESR identification of a new N2− defect in X-ray irradiated NaN3

A relatively weak ESR spectrum is observed in single crystals of NaN₃ after X-ray irradiation at 77 K. This spectrum, which has an anisotropic g value and exhibits a resolved 5-line hyperfine structure with components in the ratio 1:2:3:2:1, corresponds to a single unpaired electron interacting symmetrically with two spin-one nuclei, in three inequivalent sites. The spin-Hamiltonian parameters are: g_x = 2.0054 ± 0.0005, g_y = 2.0045 ± 0.0005, g_z = 1.9688 ± 0.0005, |A_x| = 4.0 ± 0.2 G, |A_y| = 20.0 ± 0.2 G, and |A_z| = 4.9 ± 0.2 G, c-axis, and y is perpendicular to the c-axis. This spectrum, which is clearly different from that of substitutional N₂^?reported by Gelerinter and Silsbee, is attributed to interstitial N₂^?.     

EPR and optical absorption studies on VO ions in zinc lactate trihydrate

EPR and optical absorption studies of VO²⁺-doped zinc lactate trihydrate single crystals are done at room temperature. The EPR spectra of VO²⁺ are characteristic of tetragonally compressed octahedral site. The angular variation of the EPR spectra shows single site occupying interstitial position in the lattice. The spin Hamiltonian parameters are evaluated as g_x=1.9771, g_y=2.0229, g_z=1.9236 and A_x=76, A_y=104, A_z=197 (×10⁻⁴) cm⁻¹. Using these parameters and optical absorption data various bonding parameters are determined and the nature of bonding in the complex is discussed.     

The anomalous quasi isotropic [g] tensor found for CdBr2:Ag2+ and AgBr0.15Cl0.85:Ag2+: An explanation through strong covalency

The “anomalous” quasi-isotropic [g] tensor observed in systems containing the elongated AgBr⁴⁻₆ unit (g_∥ = 2.078 ± 0.003; g⊥ = 2.065 ± 0.003) is reasonably explained, within a rigorous Molecular Orbital framework, in terms of a very high covalency, consistent with the optical electronegativity of Ag²⁺ and previous results on other Cu²⁺ and Ag²⁺ complexes. For the antibonding level 3b_1g(x² − y²) about 90% of the electronic charges should be on bromine ions. The present analysis reveals that g_∥ − g₀ is dominated by charge-transfer excitations while g_⊥− g₀ is dominated by crystal-field excitations.     

EPR and optical absorption studies of V O ions in L-asparagine monohydrate

Electron paramagnetic resonance (EPR) studies of V O²⁺ ions in L-asparagine monohydrate single crystals are reported at room temperature. It is found that the V O²⁺ ion takes up an interstitial site. The angular variations of the EPR spectra in three mutually perpendicular planes are used to determine the principal g and A values and their direction cosines. The values of g and A parameters are: g_x=1.9011, g_y=2.1008, g_z=1.9891 and A_x=100, A_y=78, A_z=126 (×10⁻⁴) cm⁻¹. The optical absorption spectrum of V O²⁺ ions in L-asparagine monohydrate is also studied at room temperature. The band positions are calculated using the energy expressions and compared with the observed band positions to confirm the transitions. The best-fit values of the crystal field (Dq) and tetragonal (Ds and Dt) parameters are evaluated from the observed band positions.     

Single crystal EPR and optical absorption study of Cr doped l-histidine hydrochloride monohydrate

EPR study of the Cr³⁺ ion doped l-histidine hydrochloride monohydrate single crystal is done at room temperature. Two magnetically inequivalent interstitial sites are observed. The hyperfine structure for Cr⁵³ isotope is also obtained. The zero field and spin Hamiltonian parameters are evaluated from the resonance lines obtained at different angular rotations and the parameters are: D=(300±2)×10⁻⁴ cm⁻¹, E=(96±2)×10⁻⁴ cm⁻¹, g_x=1.9108±0.0002, g_y=1.9791±0.0002, g_z=2.0389±0.0002, A_x=(252±2)×10⁻⁴ cm⁻¹, A_y=(254±2)×10⁻⁴ cm⁻¹, A_z=(304±2)×10⁻⁴ cm⁻¹ for site I and D=(300±2)×10⁻⁴ cm⁻¹, E=(96±2)×10⁻⁴ cm⁻¹, g_x=1.8543±0.0002, g_y=1.9897±0.0002, g_z=2.0793±0.0002, A_x=(251±2)×10⁻⁴ cm⁻¹, A_y=(257±2)×10⁻⁴ cm⁻¹, A_z=(309±2)×10⁻⁴ cm⁻¹ for site II, respectively. The optical absorption studies of single crystals are also carried out at room temperature in the wavelength range 195-925 nm. Using EPR and optical data, different bonding parameters are calculated and the nature of bonding in the crystal is discussed. The values of Racah parameters (B and C), crystal field parameter (Dq) and nephelauxetic parameters (h and k) are: B=636, C=3123, Dq=2039 cm⁻¹, h=1.46 and k=0.21, respectively.     

Search for the stannous ion in a chloride/fluoride matrix: cases of Ba1−x Sn x Cl1+y F1−y and of Ba2SnCl6

With the exception of anhydrous SnCl₂, in divalent tin fluorides and chlorides, tin(II) is always covalent bonded, i.e. its valence orbitals are hybridized and the tin lone pair is located in one of the hybrid orbitals. This lone pair is highly stereoactive and generates a large efg, resulting in a large quadrupole splitting. A doubly disordered Ba_1?x Sn _x Cl_1+y F_1?y solid solution has been prepared and found to contain either ionic tin(II) (Sn²⁺ ions) or a mixture of ionic and covalent tin(II), depending on x, y and the method of preparation. The ionic tin(II) spectrum in Ba_1?x Sn _x Cl_1+y F_1?y gives a Mössbauer single line that is broadened by the lattice efg, like in SnCl₂. Now, Sn²⁺ has been found to be present in an undistorted octahedral coordination in a newly isolated compound, Ba₂SnCl₆. It should be the first example of Sn²⁺ that is fully ionic and has a perfectly spherical lone pair.     

Firing of Clays Studied by X-ray Diffraction and Mössbauer Spectroscopy

Covalently bonded BaSnF₄, BaSn₂F₆ and new barium tin(II) chloride fluorides BaSn₂Cl₂F₄, BaSnClF₃?0.8H₂O, and non-stoichiometric Ba_1?x Sn _x Cl_1+y F_1?y were prepared and their stability upon long time storage in air was studied, with respect to tin(II) oxidation to tin(IV). The materials containing covalently bonded tin(II), i.e., all the stoichiometric phases, were found to passivate well due to particle coverage by a thin layer of SnO₂ and/or kinetic stabilization of hybridized tin(II), and they show a very minimal increase of tin(IV) signal with increasing storage time. At high temperature, passivation breaks down, then self restores. In contrast, the Ba_1?x Sn _x Cl_1+y F_1?y solid solution is not as well passivated. The rate of increase of tin(IV) Mössbauer signal is significantly higher for the precipitated solid solution, and was found to be inversely related to the amount of tin(IV) already present in the young sample. For the solid solution prepared in dry conditions, the ratio of tin oxidation was found to be higher at positive y values (Cl:F>1) and to decrease with increasing x (tin rich solid solution). In the solid solution, the bond type and strength vary widely with x and y, and so does the rate of oxidation. “Unprotected” Sn²⁺, weakly bound to the lattice, oxidizes much faster than covalently bonded tin(II).     

Hole concentration dependence of Mn eg orbital state in bilayer manganites studied by magnetic Compton profile measurement

Magnetic Compton profiles (MCP) have been measured in the [100], [110] and [001] directions on the single crystals of La_2−2xSr_1+2xMn₂O₇ (x=0.30, 0.35 and 0.42) at 10 K. The occupation numbers in t_2g and two e_g type orbitals (x²−y² and 3z²−r²) of Mn-3d state are evaluated from the line-shape analysis of MCP's in the [001] direction by using theoretical profiles derived from the ab initio calculations for (MnO₆)⁸⁻cluster. It has been found that the e_g state is dominated by the x²−y² type orbital at every hole concentration, x, and the 3z²−r² type orbital population decreases with increasing x. From the result, the connections of e_g orbital state with the electron correlation effect, exchange interactions, lattice distortion and electronic inhomogeneity are discussed.     

ESR and optical study of Cu-doped Bis(l-asparaginato)zinc(II)

The Electron spin resonance (ESR) study of Cu²⁺-doped Bis(l-asparaginato)zinc(II) has been done at room temperature. Two magnetically equivalent sites for Cu²⁺ have been observed. The spin-Hamiltonian parameters evaluated with the fitting of spectra to rhombic symmetry crystalline field are g_x=2.0341±0.0002, g_y=2.0649±0.0002, g_z=2.2390±0.0002, A_x=(51±2)×10⁻⁴ cm⁻¹, A_y=(75±2)×10⁻⁴ cm⁻¹and A_z=(169±2)×10⁻⁴ cm⁻¹. The ground state wave function of Cu²⁺ has also been determined. The g-anisotropy has been estimated and compared with the experimental value. Further with the help of optical study, the nature of bonding of metal ion with different ligands in the complex has been discussed.     

EPR of Co+2 in Mg(CH3COO)2·4H2O

EPR spectra of the ⁵⁹Co⁺² ion in oriented crystals of Mg(CH₃COO)₂·4H₂O have been measured at 9.4 GHz and a temperature of 4.2 K. The data for each of the two metal ion sites per unit cell are well-described by a spin Hamiltonian for $\text{S =}\text{1}\text{2}\text{, I =}\text{7}\text{2}$ with g_x = 6.13, g_y = 389, g_z = 2.49 and A_x = 0.0193, A_y' = 0.075, A_z' = 0.0032 cm^?1. Only the x-axes of the g- and A-tensors coincide. Orientation of the principal directions relative to the crystal axes has been established for the g- and A-tensors at both sites. They are consistent with the weakly ferromagnetic canted antiferromagnetism found in Co(CH₃COO)₂·4H₂O below T_N ?85mK.     

Anisotropic magnetic susceptibility of erbium and ytterbium in zircon,ZrSiO4

Magnetic susceptibility measurements have been made for both Er- and Yb-doped (1&#x0303;0³ppm) zircon single crystals with the magnetic field perpendicular and parallel to the [001] axis. Large susceptibility anisotropies were found in both cases. Our observed anisotropies of ZrSiO₄: Yb indicate small populations (1&#x0303;9%) of Yb ions at the axial (tetragonal) sites, as the susceptibility of ZrSiO₄: Yb would be nearly isotropic if the Yb ions only occupied the orthorhombic sites. For Er³⁺ in orthorhombic sites of zircon, our data indicate that the first excited state is paramagnetic with g_x = 9 and g_y 5&#x0303; at 20 cm^?1 above the ground state (g_x 0&#x0303;, g_y 1&#x0303;5). The first excited state is quite similar to the ground states observed for Er³⁺ in many host lattices     

Luminescent properties of HTP AgGd1−xW2O8:Eux and AgGd1−x(W1−yMoy)2O8:Eux phosphor for white LED

Intense red phosphors, AgGd_1−xEu_x(W_1−yMo_y)₂O₈ (x=0.0-1.0, y=0.0-1.0), have been synthesized through traditional solid-state reaction and characterized by X-ray diffraction (XRD) and photoluminescence (PL). XRD results reveal that AgGd_1−xEu_xW₂O₈ synthesized at 1000 °C has a tetragonal crystal structure, which is named as high temperature phase (HTP) AgGdW₂O₈. All phosphors compositions with Eu³⁺ show red and green emission on excitation either in the charge-transfer or Eu³⁺ levels. Analysis of the emission spectra with different Eu³⁺ concentrations reveal that the optimum dopant concentration for Eu³⁺ is x=0.6 in the HTP AgGd_1−xEu_xW₂O₈ (x=0.0-1.0). Studies on the AgGd_0.4Eu_0.6(W_1−yMo_y)₂O₈ (y=0.0-1.0) and AgGd_1−xEu_x(W_0.7Mo_0.3)₂O₈ (x=0.0-1.0) show that the emission intensity is maximum for compositions with y=0.3 and x=0.5, respectively, and a decrease in emission intensity is observed for higher y or x values. The Mo⁶⁺ and Eu³⁺ co-doped AgGd(WO₄)₂ phosphors show higher emission intensity in comparison with the singly Eu³⁺-doped AgGd(WO₄)₂ in UV region. The intense emission of the tungstate/molybdate phosphors under 394 and 465 nm excitations, respectively, suggests that these materials are promising candidates as red-emitting phosphors for near-UV/blue GaN-based white LED for white light generation.