Pathologies of the large-N limit for RPN−1, CPN−1, QPN−1 and mixed isovector/isotensor σ-models

We compute the phase diagram in the N→∞ limit for lattice RP^N−1, CP^N−1 and QP^N−1 σ-models with the quartic action, and more generally for mixed isovector/isotensor models. We show that the N=∞ limit exhibits phase transitions that are forbidden for any finite N. We clarify the origin of these pathologies by examining the exact solution of the one-dimensional model: we find that there are complex zeros of the partition function that tend to the real axis as N→∞. We conjecture the correct phase diagram for finite N as a function of the spatial dimension d. Along the way, we prove some new correlation inequalities for a class of N-component σ-models, and we obtain some new results concerning the complex zeros of confluent hypergeometric functions.     

Synthesis,microstructure and dielectric properties of (1−x)PSN−xPLuN

Ceramic lead niobates and their solid solutions PSN–PLuN (pure lutecium niobate) were synthesized by solid state reactions. The sequence of phases formed at PSN–PLuN synthesis has been studied by X-ray analysis. Their symmetry changed from rhombohedral for PSN to pseudo-monoclinic for the 0.75PSN–0.25PLuN compositions. The performed EDS investigations revealed that the samples PSN–PLuN are perfectly sintered. They contain a little glassy phase and their grains are well shaped. The increase of lutecium content in the examined solid solution caused downward shift of the temperature of the phase transition. The decrease of the achieved permittivity values ? was observed as well.     

Magnetic susceptibility studies of Zn1−xFexSe and Zn1−xFexS

The magnetic susceptibility of diluted magnetic semiconductors Zn_1−xFe_xSe and Zn_1−xFe_xS has been calculated within a crystal field model and by applying the extended nearest-neighbour pair approximation. The results are compared with available experimental data. It appears that a good agreement between theory and experiment is obtained for Zn_1−xFe_xSe taking the long-range exchange comprising several nearer interionic distances, whereas in Zn_1−xFe_xS the exchange interaction with nearest-neighbours alone gives a better solution.     

Oxygen non-stoichiometry, redox thermodynamics, and structure of LaFe1 − x Co x O3 − δ

The oxygen non-stoichiometry and redox thermodynamic properties of the LaFe_{1 ? x} Co _x O_{3 ? δ} system (x?=?0.25 and 0.75) are studied. At low temperatures, the LaCoO₃ and LaFeO₃ systems show partial solid solubility. At 1,273 K (in air), both compounds are single phases and are orthorhombic and rhombohedral for x?=?0.25 and 0.75, respectively. Thermogravimetry has been used to measure the oxygen non-stoichiometry versus oxygen partial pressure at three temperatures, 1,223, 1,273, and 1,323 K. Redox thermodynamic quantities are extracted directly from the oxygen non-stoichiometry curves. The extracted enthalpies of oxidation do not vary significantly with stoichiometry, and for x?=?0.25 and 0.75, they are ?640?±?60 and ?440?±?60 kJ (mol O₂)^?1, respectively. Ideal solid solution thermodynamic models are used to analyze the redox mechanisms.     

Local configurations and atomic intermixing in as-quenched and annealed Fe1−xCrx and Fe1−xMox ribbons

Local atomic configuration, phase composition and atomic intermixing in Fe-rich Fe_1?xCr_x and Fe_1?xMo_x ribbons (x = 0.05, 0.10, 0.15), of potential interest for high-temperature applications and nuclear devices, are investigated in this study in relation to specific processing and annealing routes. The Fe-based thin ribbons have been prepared by induction melting, followed by melt spinning and further annealed in He at temperatures up to 1250 °C. The complex structural, compositional and atomic configuration characterisation has been performed by means of X-ray diffraction (XRD), transmission Mössbauer spectroscopy and differential scanning calorimetry (TG-DSC). The XRD analysis indicates the formation of the desired solid solutions with body-centred cubic (bcc) structure in the as-quenched state. The Mössbauer spectroscopy results have been analysed in terms of the two-shell model. The distribution of Cr/Mo atoms in the first two coordination spheres is not homogeneous, especially after annealing, as supported by the short-range order parameters. In addition, high-temperature annealing treatments give rise to oxidation of Fe (to haematite, maghemite and magnetite) at the surface of the ribbons. Fe_1?xCr_x alloys are structurally more stable than the Mo counterpart under annealing at 700 °C. Annealing at 1250 °C in He enhances drastically the Cr clustering around Fe nuclei.     

Defects and transport in SrFe1−xCoxO3−δ

The non-stoichiometry and chemical diffusion coefficient of SrFe_1−xCo_xO_3-δ have been measured by steady state and transient thermogravimetry in the temperature range 750–1200 °C at different oxygen partial pressures. At high oxygen partial pressures, the chemical diffusion coefficient was in the range 1·10⁻⁴ – 7·10⁻⁴ cm²/s. This, combined with high concentration of disordered vacancies make these materials perhaps the fastest solid oxygen ion diffusers known at high temperatures and high oxygen partial pressures. However, due to the high concentration of defects in SrFe_1−xCo_xO_3-δ the compound transforms from a cubic (disordered) perovskite to a brownmillerite type of structure under reduced oxygen partial pressures below approx. 900 °C. Due to this phase transition, the mobility of oxygen vacancies in SrFe_1−xCo_xO_3-δ decreases up to about an order of magnitude at 850 °C. We also observe an ordering effect at 1000 °C, although smaller in size, and this is suggested to be due to short range ordering of four-coordinated polyhedra of Fe. For possible use as oxygen separation membranes, phase stability against sulphur and carbon containing atmospheres is also discussed with respect to the formation of carbonates and sulphates. Paper presented at the 6th Euroconference on Solid State Ionics, Cetraro, Calabria, Italy, Sept. 12–19, 1999.     

Stability,metastability and spectroscopic constants of electronic states of NH− and CH−

Highly correlated ab initio methods were used in order to calculate potential energy curves (PECs) of the bound electronic states of CH^? and NH^? anions and the long-range parts of their excited states. The spin–orbit interaction between electronic states has been calculated for the cases in which the couplings were assumed to be responsible for perturbations. The spectroscopic constants of bound states were calculated from the PECs and compared with previous theoretical and/or available experimental values. Also, from the ground states of CH/CH^? and NH/NH^?, the adiabatic electron affinities were given and discussed.     

Substrate effect on the electronic structure in GaxIn1−xAsySb1−y/GaSb and GaxIn1−xAsySb1−y/InAs

We present a theoretical study of the substrate effect on electronic structure in cubic Ga_xIn_1−xAs_ySb_1−y lattice-matched to GaSb and InAs. Our calculations are based on the empirical pseudopotential formalism within the virtual crystal approximation where the effect of disorder is taken into account. We show that the electronic band structure of the quaternary alloy Ga_xIn_1−xAs_ySb_1−y is altered by the change of substrate for the entire range of alloy compositions x. Moreover, we find that at Ga concentrations (x≤0.8), the ionicity is less important when Ga_xIn_1−xAs_ySb_1−y is lattice-matched to GaSb instead of InAs. The information will be useful for the choice of substrate in the composition range 0–1 and hence for the determination of the lattice-matching conditions for Ga_xIn_1−xAs_ySb_1−y quaternary materials.     

Dielectric properties of NaCl1−xBr and KCl1−xBrx mixed ionic solution

In the present paper a three-body potential model (TBPM) has been employed for the analysis of dielectric behaviour of NaCl-NaBr and and KCl-KBr mixed crystals with varying compositions. The physical properties like dielectric constants ( ₀ and ), optic mode frequencies ( _OLO and _TO), effective charge parameter (e _s ^* ), optic mode Grüneisen parameters and strain derivatives of ₀ and dielectric constants have been calculated. The results achieved in the present study are found in fairly good agreement with the available experimental data. The results obtained by previous investigators are also shown for the sake of comparison.     

Electrical properties and electronic structure of Cu1−xZnxInSe2 and Cu1−xZnxInS2 single crystals

Temperature dependence of the electrical conductivity of CuInS₂–ZnIn₂S₄ and CuInSe₂–ZnIn₂Se₄ solid solutions possessing n-type conductivity has been studied. It has been established that when the temperature decreases down to ~100 to 27 K, the hopping mechanism of electrical conductivity with a variable jumping length between localized states positioned in a narrow energy band near the Fermi level becomes dominant. The main parameters of the hopping conductivity have been determined. At higher temperatures (150–300 K), in the CuInSe₂–ZnIn₂Se₄ single crystals containing 15 and 20 mol% ZnIn₂Se₄ the thermally activated conductivity with activation energy of 0.018 and 0.04 eV, respectively, is detected. Among the CuInSe₂–ZnIn₂Se₄ single crystals, samples with 5 and 10 mol% ZnIn₂Se₄ were found to be close to degenerate semiconductors. Temperature dependences of the electrical conductivity of CuInS₂–ZnIn₂S₄ single crystals are described by a more complicated function that may indicate a competition of several conduction mechanisms in these compounds. For the CuInS₂–ZnIn₂S₄ solid solutions, X-ray photoelectron core-level and valence-band spectra have been measured for both pristine and Ar⁺ ion-bombarded surfaces. Our results indicate that the Cu_1−xZn_xInS₂ single-crystal surfaces are sensitive to Ar⁺ ion-bombardment. Additionally, for the Cu_1−xZn_xInS₂ crystal with the highest ZnIn₂S₄ content, namely 12 mol% ZnIn₂S₄, the X-ray emission bands representing the energy distribution of the Cu 3d, Zn 3d and S 3p states have been measured and compared on a common energy scale with the X-ray photoelectron valence-band spectrum.     

Inhomogeneous Lattice Paths, Generalized Kostka Polynomials and A n −1 Supernomials

Inhomogeneous lattice paths are introduced as ordered sequences of rectangular Young tableaux thereby generalizing recent work on the Kostka polynomials by Nakayashiki and Yamada and by Lascoux, Leclerc and Thibon. Motivated by these works and by Kashiwara's theory of crystal bases we define a statistic on paths yielding two novel classes of polynomials. One of these provides a generalization of the Kostka polynomials, while the other, which we name the A_nу supernomial, is a q-deformation of the expansion coefficients of products of Schur polynomials. Many well-known results for Kostka polynomials are extended leading to representations of our polynomials in terms of a charge statistic on Littlewood-Richardson tableaux and in terms of fermionic configuration sums. Several identities for the generalized Kostka polynomials and the A_nу supernomials are proven or conjectured. Finally, a connection between the supernomials and Bailey's lemma is made.     

Structure,optical, and magnetic properties of rutile Sn1−xMnxO2 thin films

Sn_1?xMn_xO₂ (x ≤ 0.11) thin films were fabricated by sol–gel and spin-coated method on Si (1 1 1) substrate. X-ray diffraction revealed that single-phase rutile polycrystalline structure was obtained for x up to about 0.078. Evolution of the lattice parameters and X-ray photoelectron spectroscopy studies confirmed the incorporation of Mn³⁺ cations into rutile SnO₂ lattice. Optical transmission studies show that the band gap energy (E_g) broadens with the increasing of Mn content. Magnetic measurements revealed that all samples exhibit room temperature ferromagnetism (RTFM), which is identified as an intrinsic characteristic. Interestingly, the magnetic moment per Mn atom decreases with the increasing Mn content. The origin of RTFM can be interpreted in terms of the bound magnetic polaron model.     

Dielectric and piezoelectric properties of (Bi1−x−yNdxNa1−y)0.5BayTiO3 lead-free ceramics

New lead-free (Bi_1−x−yNd_xNa_1−y)_0.5Ba_yTiO₃ ceramics were prepared by a conventional ceramic technique and their dielectric and piezoelectric properties were studied. X-ray diffraction studies reveal that Nd³⁺ and Ba²⁺ diffuse into the Bi_0.5Na_0.5TiO₃ lattices to form a new solid solution with a pure perovskite structure, and a morphotropic phase boundary (MPB) of rhombohedral and tetragonal phases is formed at 0.04 < y < 0.10. The partial substitutions of Nd³⁺ and Ba²⁺ decrease effectively the coercive field E_c and increase significantly the remanent polarization P_r. Because of lower E_c, larger P_r and the formation of the MPB, the piezoelectric properties of the ceramics are significantly enhanced at x/y = 0.02/0.06: d₃₃ = 150 pC/N and k_p = 30.5%. The ceramics exhibit relaxor characteristic, which is probably resulted from the cation disordering in the 12-fold coordination sites. The depolarization temperature T_d shows a strong compositional dependence and reaches a minimum value at the MPB. The temperature dependences of the ferroelectric and dielectric properties suggest that the ceramics may contain both the polar and non-polar regions near the depolarization temperature T_d, which cause the polarization hysteresis loop become deformed near/above T_d.     

Single crystals of LnFeAsO1−xFx (Ln = La,Pr, Nd,Sm, Gd) and Ba1−xRbxFe2As2: Growth,structure and superconducting properties

A review of our investigations on single crystals of LnFeAsO_1?xF_x (Ln = La, Pr, Nd, Sm, Gd) and Ba_1?xRb_xFe₂As₂ is presented. A high-pressure technique has been applied for the growth of LnFeAsO_1?xF_x crystals, while Ba_1?xRb_xFe₂As₂ crystals were grown using a quartz ampoule method. Single crystals were used for electrical transport, structure, magnetic torque and spectroscopic studies. Investigations of the crystal structure confirmed high structural perfection and show incomplete occupation of the (O, F) position in superconducting LnFeAsO_1?xF_x crystals. Resistivity measurements on LnFeAsO_1?xF_x crystals show a significant broadening of the transition in high magnetic fields, whereas the resistive transition in Ba_1?xRb_xFe₂As₂ simply shifts to lower temperature. The critical current density for both compounds is relatively high and exceeds 2 × 10⁹ A/m² at 15 K in 7 T. The anisotropy of magnetic penetration depth, measured on LnFeAsO_1?xF_x crystals by torque magnetometry is temperature dependent and apparently larger than the anisotropy of the upper critical field. Ba_1?xRb_xFe₂As₂ crystals are electronically significantly less anisotropic. Point-Contact Andreev-Reflection spectroscopy indicates the existence of two energy gaps in LnFeAsO_1?xF_x. Scanning Tunneling Spectroscopy reveals in addition to a superconducting gap, also some feature at high energy (～20 meV).