Luminescence study of the 4f5d configuration of Nd in LiYF4, LiLuF4 and BaY2F8 crystals

Ultraviolet fluorescence of Nd³⁺ ions induced by triphotonic excitation process was studied in Nd-doped LiYF₄, LiLuF₄ and BaY₂F₈ crystals using a technique of time-resolved spectroscopy. The observed ultraviolet luminescence was due to transitions between the bottom of 4f²5d configuration and 4f³ states of Nd³⁺ ions. Narrow emission lines superposed to the broadband emissions were observed. A detailed analysis of luminescence spectrum revealed that the narrow emissions are due to parity and spin allowed radiative transitions from the Stark levels of ⁴K_11/2(5d) state created by the electrostatic interaction between the 5d electron and the two electrons of the 4f² configuration. The narrow emissions are related to the high spin state (S=3/2) which gives f-f characteristics to the f-d broadband emissions. The narrow emissions superposed to the wide emission correspond to 18%, 34% and 43% of the integrated broadband emission at 262 nm observed in LiYF₄, LiLuF₄ and BaY₂F₈ crystals, respectively. Although the 5d-4f² interaction is observed to be weaker than 5d-crystal field interaction, it is stronger enough to select only the radiative transitions from 4f²5d configuration to 4f³ states that preserves the total spin S=3/2.     

Classical stability of direct products of spheres in gravitational systems

Classical stability of Einstein spaces S^d₁ ×?×S^d_n(d_j ? 2) against all fluctuations is investigated in euclidean gravity with a cosmological constant. It is shown that S^d is classically stable, while S^d₁ ×?× S^d_n(n ? 2) is classically unstable. As a generalization of this analysis it is proved that a compact Einstein space B₁ ×?× B_n(n ? 2) which is a direct product of each Einstein space is classically unstable. Non-Einstein spaces M² × S⁴ (M² × S² × S²) are also considered in six- dimensional Einstein-Maxwell theory and are shown to be classically stable (unstable).     

Pressure dependence of phase transitions in K2SnCl6 from NQR frequency measurements

The influence of hydrostatic pressure 0 ? p ? 4 kbar on the ³⁵Cl NQR in K₂SnCl₆ was studied in the temperature range 238 K ? T ? 300 K. The phase transition temperatures T_C1 and T_C2 were determined from changes in the NQR line pattern.The phase boundaries in the p-T diagram are straight lines in the region studied. The pressure coefficients are given by dT_C1/dP = 1.35 (10) K kbar^?1 and dT_C2/dP=?1.25 (20) K kbar^?1.     

Calculation of the hyperfine structure of the 42 S 1/2, 42 P 1/2, 42 P 3/2 states in the 3d 10 nl configuration of Cu

The hyperfine structure of the 4² S _1/2, 4² P _1/2, 4² P _3/2 states in the 3d ¹⁰ nl configuration of Cu has been evaluated using many-body perturbation theory. Polarisation effects were included in all orders and correlation to third-order. By the use of iteration methods, a large number of higher order diagrams were also included. The correlation effects between the valence electron and the 3d shell were found to be very important. The results forA(² S _1/2) andA(² P _1/2) 5827MHz and 440 MHz, respectively, are in good agreement with the experimental results, whereas the result forA(² P _3/2)=83 MHz is far from the experimental value. No explanation was found for the discrepancy. The quadrupole values were found to be ?206 mb for⁶³Cu and ?185 mb for⁶⁵Cu.     

Vibrational and electronic spectra of alkali halides doped with CrO42− ions

The i.r. spectra of alkali halides doped with FrO₄^2? ions are very sensitive to the concentration of background divalent impurities. Highly pure crystals containing CrO₄^2? ions show a 5 line i.r. spectrum in the v₃ stretch frequency region. One of these lines is attributed to CrO₄^2? ions in perfect crystal surroundings having T_d symmetry and the other 4 lines are attributed to C_s symmetry produced by a charge compensating anion vacancy in the nearest neighbour position. If the crystal contains a concentration of divalent cation impurity which is equal to or more than that of CrO₄^2? ions, a different spectrum characteristic of C_2x symmetry as well as the line corresponding to T_d symmetry are obtained. The crystals of ordinary purity contain all the three (C_s, C_2x and T_d symmetry) species and show eight line spectra. The changes in force constants calculated from the observed splitting of the energy levels agree with those evaluated from the known polarizability of the chromate ions.At 600°C, the vibration spectra of the highly pure crystals doped with CrO₄^2? ions show an increase in intensity of the line characteristic of T_d symmetry and the other lines practically disappear, because the anion vacancies move away from the neighbourhood of the CrO₄^2? ions at high temperatures. The energy of association of the vacancy with CrO₄^2? ions and the energy of migration of the vacancy are derived from the spectra obtained at different temperatures and with different heat treatments.The electronic spectra of the crystals show 3 bands (at 345, 270 and 240 nm for KCI). The lowest energy band has a fine structure with a spacing of about 800 cm^?1 at LAT. Since the transition involved is from a non-bonding to an antibonding state, the Condon parabola is shifted in the excited state and therefore the fine structure is attributed to a vibrational progression involving a totally symmetric frequency 800 cm^?1 in the excited state.     

Observation of resonance recombination lines in electron excited auger spectra of Gd

Combined measurements of electron excited N_4,5 Auger spectra and photoelectron emission on clean and oxidized Gd lead to a distinction between Auger lines originating from 4d → continuum and 4d → 4? resonance excitations. Several Auger structures are identified as due to the direct recombination of 4d⁹4?⁸ states with the 4f and valence electrons. The shape of the most prominent Auger line for oxidized Gd agrees perfectly with the Fano profile of the 4? photoemission intensity.     

Analysis of the spectra of In XII–XIV and Sn XIII–XV in the far-VUV region

The 4p ⁶4d?(4p ⁶5p + 4p ⁶4f + 4p ⁵4d ²) transitions in the spectra of In XIII-Sn XIV and the 4p ⁶4d ²?(4p ⁶4d5p + 4p ⁶4d4f + 4p ⁵4d ³) transitions in the spectra of In XII-Sn XIII are investigated. About 150 spectral lines in the wavelength range 120–160 Å, which is important for projection vacuum UV lithography, have been classified for the first time. The fine structure intervals of the ground state 4p ⁶4d ² D and the energies of eight levels of the 4p ⁶5p, 4p ⁶4f, and 4p ⁵4d ² configurations are measured in each spectrum of In XIII and Sn XIV. The energies of all levels of the ground configuration 4p ⁶4d ² and the energies of 35 levels of the interacting configurations (4p ⁶5p + 4p ⁶4f + 4p ⁵4d ³) are determined in the spectra of In XII and Sn XIII. The resonant transitions 4p ^{6 1} S ₀?4p ⁵4d ¹ P ₁ in the spectra of In XIV and Sn XV are also identified. The semiempirical parameters of the configurations under study determined by mean-square fitting of measured level energies are in agreement along both isoelectronic and isonuclear sequences of the spectra.     

Nonradiative decay from 5d states of rare earths in crystals

Nonradiative decay from 4f^n?1 5d states was investigated for trivalent rare earths in Y₃Al₅O₁₂. The rates of both 5d→4f and 5d→5d transitions were determined from measurements of the lifetimes and intensities of 5d fluorescence from Ce³⁺ and Pr³⁺. Because of the stronger ion-lattice coupling, nonradiative decay rates for transitions involving 5d states are much faster than those between 4f states. Decay rates are dependent upon the temperature and the energy gap to the next-lower level. The temperature dependences of the 5d fluorescence lifetimes from 77 to 700°K are reported.     

Estimates of critical lengths and critical temperatures for classical and quantum lattice systems

Local Ward identities are derived which lead to the mean-field upper bound for the critical temperature for certain multicomponent classical lattice systems (improving by a factor of two an estimate of Brascamp-Lieb). We develop a method for accurately estimating lattice Green's functionsI _d yielding 0.3069<I ₄<0.3111 and the global bounds (d?1/2)^?<I _d <(d?1)^? for alld?4. The estimate forI _d implies the existence of a critical length for classical lattice systems with fixed length spins. Forv-component spins with fixed lengthb on the lattice ? ^d ,v=1, 2, 3, 4, the critical temperature for spontaneous magnetization satisfies $$\frac{{2Jb^2 }}{k}\frac{{d - 1}}{v}< T{}_c \leqslant \frac{{2Jb^2 }}{k}\frac{d}{v} for d \geqslant 4$$ ford4 Using GHS or generalized Griffiths' inequalities, we find that the upper bounds on the critical temperature extend to certain classical and quantum systems with unbounded spins. Absence of symmetry breakdown at high temperature for quantum lattice fields follows from bounding the energy density by a multiple ofkT. Path space techniques for finite degrees of freedom show that the high-temperature limit is classical.     

Perturbation of the Laplacian supported by null sets,with applications to polymer measures and quantum fields

We discuss hamiltonians in L²(R^d, dx) of the form H = ?Δ + V, with V a potential supported by a zero measure set C. In particular if C is a path of a brownian motion b such that V(x) = ∫₀¹λ(x, ω)δ(x-b(s, ω)) ds, we show that H exists as a nontrivial, self-adjoint, lower bounded perturbation of ?Δ when d ?5. We must choose λ to be an infinitesimal, negative function for d = 4,5, but for d ? 3 any bounded real-valued function λ will do. The connection with Edward's model of polymers as well as with quantum fields of the ?_d⁴-type is also discussed. The proofs use methods of nonstandard analysis.     

Renormalisation group calculation of the critical exponents of the special transition in semi-infinite systems

Renormalisation group calculations of the correlation function exponents η^sp_⊥ and η^sp_∥ of the special transition in semi-infinite φ⁴ systems to second order in ?=4?d are presented.     

High pressure tuning of optical transitions in Mg[Pt(CN)4]·7H2O

Mg[Pt(CN)₄]·7H₂O belongs to the class of tetracyanoplatinates(II) which crystallize in columnar structures. In different M_x[Pt(CN)₄]·yH₂O (MCP) single crystals the in-chain Pt-Pt-distance R varies between 3.67 Å (NaCP) and 3.15 Å (MgCP). Two optical transitions can be observed in polarized emission with the electric field vector E either parallel or perpendicular to the columnar (c)-axis. Polarized emission spectra of MgCP are recorded under hydrostatic pressure up to p ≈ 18 kbar (at 295 K). The transition energy v?₆ can be tuned from 17,600 cm^-1 to about 12,000 cm^-1 (2.18-1.48 eV). The pressure induced red shift for the two transitions is: E 6 c: dv?₆/dp = -320±20 cm^-1/kbar, E ⊥ c: dv?_⊥/dp = -270±20 cm^-1/kbar. These values are discussed in the context of the known functional relationship (for ambient conditions) between v? and R.     

The random-walk representation of classical spin systems and correlation inequalities

We use the random-walk representation to prove the first few of a new family of correlation inequalities for ferromagnetic ?⁴ lattice models. These inequalities state that the finite partial sums of the propagator-resummed perturbation expansion for the 4-point function form an alternating set of rigorous upper and lower bounds for the exact 4-point function. Generalizations to 2n-point functions are also given. A simple construction of the continuum ? _d ⁴ quantum field theory (d<4), based on these inequalities, is described in a companion paper.     

Complete breakdown of the one-electron picture of auger spectra of solids

The very broad M₄₅?N₂₃N₄₅ (3d^-1 → 4p^-14d^-1) Auger spectra for metals in the range Pd to Te arise from complete breakdown of the one-electron picture of the final state double vacancy due to 4p^-14d^-1 ? 4d^-3?f giant Coster-Kronig fluctuation and decay processes. This is an example of atomic-like effects giving rise to level shifts and broadening which are large in comparison with typical widths of d-bands in solids. The 4p^-14d^-1 two-hole spectral function can be approximated by a 4p^-1 single-hole spectral function perturbed by a static, sharp 4d^-1 hole. The resulting Auger line-shapes are different from single-hole 4p^-1 line-shapes from XPS and XES. Analogous effects also occur for double vacancies involving one or two 4s-holes.     

Fourier space analysis of the Yvon-Born-Green equation in the critical region

The pair correlation function implied by the Yvon-Born-Green (YBG) integral equation is analyzed in Fourier space in the critical region. For potentials of infinite range decaying like r^-d-σ the upper borderline dimensionality above which the solutions can be Ornstein-Zernike-like is d_> = 4 for σ ? 2 but d_> = 2σ for σ < 2, while for finite range potentials d_> = 4, confirming results found by real-space analysis. Although the borderline dimensionality is in agreement with expectations from lattice models and field theory, the analysis indicates that below d_> the solutions of the YBG equation cannot exhibit a physically acceptable critical regime. Moreover, it is shown that corrections to the YBG equation arising from further terms in the BBGKY hierarchy diverge at criticality even for d>d_>.     

Electronic structure of dichalcogenide and dipnictide anions

The Self-Consistent-Field Xα Scattered Wave Cluster MO method is used to calculate molecular orbital energy level diagrams for O₂, O₂^?, O₂^2?, S₂, S₂^2?, Se₂^2?, P₂^4?, As₂^4? and AsS^3?. Calculated energies are in good agreement with those measured by photoemission spectroscopy for O₂, S₂, S₂^2? in ZrS₃, Se₂^2? in ZrSe₃ and P₂^4? in TiP₂. For O₂^? the calculated energy of the π_u → π_g transition agrees fairly well with that of the UV absorption observed in LiO₂. The predicted photoemission spectrum of O₂^2? is consistent with a preliminary study on BaO₂. Calculated valence region widths in peroxides are found to be significantly greater than the calculated oxygen atomic valence _s-p separation while valence widths for the other anions closely match atomic valence s-p splittings. This effect arises from the instability of the peroxide antibonding orbitals which correlates with the absence of dsun peroxides and Superoxides. Calculations on a Cin2v geometry FeO₆su9? cluster show that the difference in energy of O2p nonbonding and Fe3d crystal field type orbitals drops sharply as an O-O edge is contracted, providing a mechanism for Fe³⁺ → Fe²⁺ reduction at high pressure.     

EPR study of the impurity paramagnetic centres in (CaO−Ga2O3−GeO2) glasses

The X-band EPR spectra of Cr³⁺, Mn²⁺, and Fe³⁺ impurity ions in glasses of (CaO?Ga₂O₃?GeO₂) system are investigated in the 77÷300 K temperature range. The experimental data analysis yields the following results: (i) Impurity chromium ions are incorporated into the (CaO?Ga₂O₃?GeO₂) glasses network in Cr³⁺ (3d³,⁴F_3/2) paramagnetic valence state only and occupy the strong distorted oxygen coordinated octahedral sites. (ii) For all activated and non-activated (CaO?Ga₂O₃?GeO₂) glasses the iron impurity is present at concentration roughly 0.01 wt.%. Isotropic EPR signals atg _eff=4.29 andg _eff=2.00 are assigned to Fe³⁺ (3d⁵,⁶S_5/2) ions in the sites with strong rhombic distortion and in the sites with nearly cubic symmetry respectively. (iii) The manganese EPR spectrum in (CaO?Ga₂O₃?GeO₂) glasses is weakly dependent on temperature, doping procedure as well as manganese concentration. EPR spectra of impurity manganese ions in glasses with Ca₃Ga₂Ge₃O₁₂ and Ca₃Ga₂Ge₄O₁₄ compositions are virtually identical and belong to Mn²⁺ (3d⁵,⁶S_5/2) ions. Impurity manganese ions are incorporated into the (CaO?Ga₂O₃?GeO₂) glass network as isolated Mn²⁺ centres and clusters of Mn²⁺ ions.     

Role of structure imperfection in the formation of the magnetotransport properties of rare-earth manganites with a perovskite structure

The structure, the structure imperfection, and the magnetoresistance, magnetotransport, and microstructure properties of rare-earth perovskite La_0.3Ln_0.3Sr_0.3Mn_1.1O_3–δ manganites are studied by X-ray diffraction, thermogravimetry, electrical resistivity measurement, magnetic, ⁵⁵Mn NMR, magnetoresistance measurement, and scanning electron microscopy. It is found that the structure imperfection increases, and the symmetry of a rhombohedrally distorted R3?c perovskite structure changes into its pseudocubic type during isovalent substitution for Ln = La³⁺, Pr³⁺, Nd³⁺, Sm³⁺, or Eu³⁺ when the ionic radius of an A cation decreases. Defect molar formulas are determined for a real perovskite structure, which contains anion and cation vacancies. The decrease in the temperatures of the metal–semiconductor (T _ms) and ferromagnet–paramagnet (T _C) phase transitions and the increase in electrical resistivity ρ and activation energy E _a with increasing serial number of Ln are caused by an increase in the concentration of vacancy point defects, which weaken the double exchange 3d ⁴(Mn³⁺)–2p ⁶(O^2–)–3d ³(Mn⁴⁺)–V ^(a)–3d ⁴(Mn³⁺). The crystal structure of the compositions with Ln = La contains nanostructured planar clusters, which induce an anomalous magnetic hysteresis at T = 77 K. Broad and asymmetric ⁵⁵Mn NMR spectra support the high-frequency electronic double exchange Mn³⁺(3d ⁴) ? O^2–(2p ⁶) ? Mn⁴⁺(3d ³) and indicate a heterogeneous surrounding of manganese by other ions and vacancies. A correlation is revealed between the tunneling magnetoresistance effect and the crystallite size. A composition–structure imperfection–property experimental phase diagram is plotted. This diagram supports the conclusion about a strong influence of structure imperfection on the formation of the magnetic, magnetotransport, and magnetoresistance properties of rare-earth perovskite manganites.