Finite Maxwell field and electric displacement Hamiltonians derived from a current dependent Lagrangian

ABSTRACT

In the common Ewald summation technique for the evaluation of electrostatic forces, the average electric field E is strictly zero. Finite uniform E can be accounted for by adding it as a new degree of freedom in an extended Lagrangian. Representing the uniform polarization P as the time integral of the internal current and E as the time derivative of a uniform vector field A, we define such an extended Lagrangian coupling A to the total current j _t (internal plus external) and hence derive a Hamiltonian resembling the minimal coupling Hamiltonian of electrodynamics. Next, applying a procedure borrowed from nonrelativistic molecular electrodynamics the j _t · A coupling is transformed to P · D form where D is the electric displacement acting as an electrostatic boundary condition. The resulting Hamiltonian is identical to the constant-D Hamiltonian obtained by Stengel, Spaldin and Vanderbilt (SSV) using thermodynamic arguments. The corresponding SSV constant-E Hamiltonian is derived from an alternative extended Lagrangian.     

Anomalous magnetic behavior of superconducting thin films in small magnetic fields [4] close to the transition temperature

Using a specially designed SQUID magnetometer we measured the temperature dependence of the critical current density in a ring patterned thin film for magnetic fields parallel to the c-axis. In addition, the temporal relaxation of the remanent state as prepared by field cooling in an external field of 100 Oe at different temperatures is determined. The j c ( T ) data show a field-dependent anomalous kink close to T_c pointing to reduced dissipation with increasing temperature allowing to construct a corresponding H-T borderline. A similar behavior is observed for the normalized relaxation rate S ( T ) as extracted from the temporal behavior of the remanent state, which, at low temperatures, exhibits the expected increase for increasing T-values, while an anomalous decrease of S ( T ) is found for temperatures above 85 K. While the low-T regime is attributed to creep of 2D pinned single vortex lines, the high-T behavior is suggested to be dominated by collective motion with a more sluggish dynamics. This change in dynamics is also reflected by the activation barriers for flux creep U ( j ), which show a corresponding crossover in μ from 0.06 to 0.99. An additional scaling analysis of the E-j characteristics for according to vortex glass theory reveals quasi-2D collective creep behavior with . Received: 8 April 1998 / Revised: 15 July 1998 / Accepted: 2 September 1998     

Properties of doubly excited states of H- and He associated with the manifolds from N = 6 up to N = 25

This paper discusses theory and results on ¹P⁰ doubly excited states (DES) in He and in H^- of very high excitation, up to the N = 25 manifold. Our calculations employed full configuration interaction (CI) with large hydrogenic basis sets and produced correlated wavefunctions for the four lowest roots at each hydrogenic manifold by excluding open channels and the small contribution of series belonging to lower thresholds. The suitability of the hydrogenic basis sets for such calculations is justified, apart from their practicality, by the fact that, by computing from them natural orbitals, the results were shown to be the same with those of earlier multiconfigurational Hartree-Fock (MCHF) calculations on low-lying DES. In total, 160 states were computed, most of them for the first time. Their energy spectrum should be of use to possible future photoabsorption experiments. For certain low-lying DES up to N = 13, for which previous reliable results are available, comparison of the calculated energies shows good agreement. The correlated wavefunctions contain systematically chosen single and double excitations from each hydrogenic manifold of interest. From their analysis, we determined the “goodness" of different quantum numbers and the geometry (average angles and radii) as a function of excitation. For the Sinano lu-Herrick ( K , T ) classification scheme, whose basis is a restricted CI with hydrogenic functions and which has thus far been tested only on low-lying DES, we established that, whereas T remains a good index as energy increases, K does not. Consequently, a more flexible than K quantum number is needed in order to account for most of the additional correlation. This number, represented by F = N - K - 1, where N and K are not good numbers anymore, produces consistently a much higher degree of purity than the ( K , T ) scheme does, especially as N increases and as the relative significance of various virtual excitations due to electron correlation increases. Among the four states of each manifold, in all cases in H^- and in most cases in He, the three are of the intrashell type and one is of the intershell type with ( F , T ) = (0, 0). The lowest intrashell states and the lowest intershell states exhibit a wide angle geometry tending to 180 ^° as N ↦∞. Received 10 September 2001 and Received in final form 12 November 2001     

Some experimental and theoretical studies on the Mn magnetic moment in Y ( Ni 1 - x Mn x ) 2 B 2 C

The magnetic moment of the Mn impurities was obtained from magnetization measurements of Y ( Ni _{1 - x} Mn _x ) ₂ B ₂ C as a function of the concentration x less than 0.15. Using the coherent potential approximation and starting from 3 d density of states, obtained from the first principles calculations, the magnetic moments are obtained within a two sublattice model. For adequately estimated values of the Coulomb interactions U, the position of the energy level of Mn and adopting values for the intersublattice hybridization term, a qualitative agreement with the observed experimental data is obtained. Received 23 April 2001 and Received in final form 29 October 2001     

Predictions of geometrical structures and ionization potentials for small barium clusters Ba

The geometrical structure of ground state Ba_n clusters (n =2-14) has been predicted from various types of calculations including two ab initio approaches used for the smaller sizes namely HF+MP2( n =2-6), DFT (LSDA)( n =2-6, 9) and one model approach HF+pairwise dispersion used for all sizes investigated here. The lowest energy configurations as well as some isomers have been investigated. The sizes n =4, 7 and 13 are predicted to be the relatively more stable ones and they correspond to the three compact structures: the tetrahedron, the pentagonal bipyramid and the icosahedron. The growth behavior from Ba₇ to Ba₁₃ appears to be characterized by the addition of atoms around a pentagonal bipyramid leading to the icosahedral structure of Ba₁₃ which is consistent with the observed size-distribution of barium clusters. Values for vertical ionization potentials calculated for n =2-5 at the CI level are seen to be in quite good agreement with recent measures. Received: 14 May 1997 / Received in final form: 2 February 1998 / Accepted: 27 February 1998     

Single hole dynamics in the one-dimensional - model

We present a new finite-temperature quantum Monte Carlo algorithm to compute imaginary-time Green functions for a single hole in the t-J model on non-frustrated lattices. Spectral functions are obtained with the Maximum Entropy method. Simulations of the one-dimensional case show that a simple charge-spin separation Ansatz is able to describe the overall features of the spectral function such as the bandwidth and the compact support of the spectral function, over the whole energy range for values of J / t from 1/3 to 4. This is contrasted with the two-dimensional case. The quasiparticle weight Z_k is computed on lattices up to L =128 sites in one dimension, and scales as . Received 15 February 2000     

Toward direct determination of conformations of protein building units from multidimensional NMR experiments III

Chemical shielding anisotropy tensors have been determined, within the GIAO-RHF formalism using a smaller [6-31+G(d)] and two medium-size basis sets [6-311++G(d,p) and TZ2P], for all elements of the conformational library (altogether 27 structures) of the hydrophobic model peptide For-L-Phe-NH₂. The individual chemical shifts and their conformational averages have been compared to their experimental counterparts taken from the BioMagnetic Resonance Bank (BMRB). At the highest level of theory applied, for all nuclei but the amide proton, deviations between statistically averaged theoretical and experimental chemical shifts are as low as a few percent. One-dimensional (1D) chemical shift - structure plots do not allow unambiguous identification of backbone conformations. On the other hand, on chemical shift - chemical shift plots of selected nuclei, e.g., ¹H ^N with ¹⁵N or ¹⁵N with ¹³C ^α , regions corresponding to major conformational motifs have been found, providing basis for the identification of peptide conformers solely from NMR shift data. The 2D ¹H ^α -¹³C ^α as well as the 3D ¹H ^α -¹³C ^α -¹³C ^β chemical shift - chemical shift plots appear to be of special importance for direct determination of conformations of protein building units from multidimensional NMR experiments. 48 pairs of ¹H ^α -¹³C ^α data for phenylalanine residues have been extracted from 18 selected proteins and compared to relevant ab initio results, supporting the calculated results. Thus, the appealing idea of establishing backbone folding information of peptides and proteins from chemical shift information alone, obtained from selected multiple-pulse NMR experiments (e.g., 2D-HSQC, 2D-HMQC, and 3D-HNCA), has received further support.     

Widely usable interpolation formulae for hyperfine splittings in the 127I2 spectrum

Based on new systematic high precision measurements of hyperfine splittings in different rovibrational bands of ¹²⁷I₂ in the near infrared spectral range between 778 nm and 816 nm, and the data in the range from 660 nm to 514 nm available from literature, the quantum number dependence of the different hyperfine interaction parameters was reinvestigated. As detailed as possible parameters were re-fitted from the reported hyperfine splittings in literature, considering that the interaction parameters should vary smoothly with the vibrational and rotational quantum numbers, and follow appropriate physical models. This type of consistency has not been sufficiently taken into account by other authors. To our knowledge it is now possible for the first time to separate the hfs contributions of the two electronic states B ³ and X ¹ Σ ⁺ _g for optical transitions in a very large wavelength range. New interpolation formulae could be derived for both states, describing the quantum number dependences of the nuclear electric quadrupole, of the nuclear spin-rotation and also of the nuclear spin-spin interactions. Using these new interpolation formulae the hyperfine splittings for the components with the quantum number condition F - J = 0 can be calculated with an uncertainty of ≤30 kHz for transitions in the wavelength range between 514 nm and 820 nm. Received 17 July 2001 and Received in final form 17 October 2001     

Merged beam study of the associative ionisation ( C + , N + ? and ? O + )+ O -

Total cross-sections have been measured for the associative ionisation of C ⁺ + O ^- , N ⁺ + O ^- and O ⁺ + O ^- by means of a merged-beam set-up operating with keV beams. These original measurements might be relevant to the understanding of some astrophysical objects or laboratory-made plasmas (flames and etching plasmas). The magnitude of these cross-sections is particularly large whatever the associating system, as these are in the range of 1×10 ^-14 cm² at thermal energies. Their behaviour as a function of energy significantly differs from one system to another, and is characterised by the Wigner law at low energy, and a rapid fall-off at higher energy due to competition with non-associative ionisation processes. Received 10 December 2001 and Received in final form 12 March 2002     

Ferromagnetism in lacunar perovskite manganites Pr 0.7 Sr 0.3 - x x MnO 3 and Pr 0.7 - x x Sr 0.3 MnO 3

Deficiency effects in the A site upon the structural, magnetic and electrical properties in the lacunar perovskite manganite oxides Pr_0.7Sr_{0.3-x x}MnO₃ ( 0 ? x ? 0.3) and Pr_{0.7-x x}Sr_0.3MnO₃ ( 0 ? x ? 0.23) have been investigated. This study focuses on the different parameters which govern the magnetic and electrical properties in such samples. The powder X-ray diffraction patterns for all samples could be indexed either with a rhombohedral perovskite structure and R c space group for x ? 0.2 in strontium deficient samples and for x ? 0.1 for praseodymium deficient ones. For other values of x the samples could be indexed in the orthorhombic structure with Pbnm space group. Magnetic and electrical investigations show that praseodymium and strontium vacancies do not have similar effects on the lacunar compounds. Magnetization measurements versus temperature show that all our samples exhibit a magnetic transition when the temperature decreases. All the praseodymium deficient samples exhibit a paramagnetic-ferromagnetic transition when the temperature decreases while the strontium deficient ones exhibit this transition only for low x values. The magnetic transition temperature shifts to lower values as the strontium deficiency increases (from 265 K for x = 0 to 90 K for x = 0.3) and to higher values with the praseodymium deficiency increase (from 265 K for x = 0 to 315 for x = 0.23). Resistivity measurements as a function of temperature show a semiconducting-metallic transition for all x values in the praseodymium lacunar samples and only for low x values ( 0 ? x ? 0.1) in the strontium lacunar ones when the temperature decreases. Received 12 April 2000 and Received in final form 8 January 2001     

Photophysics and Electrochemistry of some Thione Far-Red/Near-IR Triplet Emitters

The photophysics and cyclic voltammetry of two novel phosphorescent thiones, 2,2-dimethyl-indan-1-one-3-thione (DMIKT) and 2,2-dimethyl-indan-1,3-dithione (DMIDT), and three known phosphorescent thiones, 4H-pyran-4-thione (PT), 4H-1-benzopyran-4-thione (BPT) and 2,2-dimethylindan-1-thione (DMIT), have been characterised and compared. The phosphorescence emission of DMIT, DMIKT and DMIDT extends from the red into the near-IR spectral region. The additional carbonyl or thione group of DMIKT and DMIDT causes a significant shift in the emission maxima to 680 nm compared to that of DMIT, at 637 nm, in perfluorinated hydrocarbons. In acetonitrile the emission maxima of DMIKT and DMIDT are at 696 and 706 nm, respectively, and the spectra show vibronic bands which extend out beyond 850 nm. There is a significant reduction in triplet lifetime along this series (from 44 (±2) μs (DMIT) to 10 ((±0.8) μs (DMIKT) in perfluorinated solvents, and 8.6 (±0.5) (DMIT), 1.3 (±0.5) (DMIKT) and 0.35 (±0.07) μs (DMIDT) in acetonitrile), as well as a reduction in the rate constant for ground-state quenching of the triplet, (from 9.8 ((±0.9) to 3.5 ((±0.6) and 1.3 ((±0.2) × 10⁹ mol⁻¹ dm³ s⁻¹ for the same compounds). The addition of the C=O or C=S groups also causes a decrease in phosphorescence quantum yield with the highest emission quantum yield obtained for DMIT (Φ _P = 0.149 (±0.015)). Electrochemical studies show that while PT and BPT exhibit irreversible redox behaviour, DMIT, DMIKT and DMIDT all show at least one reversible reduction wave attributed to a one-electron process centred on the C=S moiety. The suitability of these lumophores for use in OLEDs is discussed.     

Charge ordering-disordering in the Th-doped CaMnO3

The structural transitions that appear in the manganites Ca_1-xTh_xMnO₃ versus temperature are studied in connection with their magnetic and transport properties, and compared to those of the Ca_1-xLn_xMnO₃ manganites. An orthorhombic to monoclinic transition is observed for low x values (;this structural distortion, also observed for Ln-doped oxides, is related to the magnetoresistance properties. For higher x values (), modulated commensurate and incommensurate phases are obtained at low temperature, with , b =2 a p and , which are related to Mn³⁺/Mn⁴⁺ charge ordering (CO) phenomena. T values, determined from electron diffraction, are in agreement with those determined from the M ( T ) curves. The low temperature electron microscopy shows that the CO in those oxides is more complex than in Ln-doped manganites. In particular, the destabilisation of CO and consequently of the antiferromagnetic interactions is evidenced as the thorium content increases which may explain the appearance of a spin-glass like behavior for higher x values not seen for Ca_1-xSm_xMnO₃ phases . Received 2 November 1998     

Neutron diffraction study of the magnetic ordering in the series R 2 BaNiO 5 (R = Rare Earth)

A neutron diffraction study, as a function of temperature, of the title compounds is presented. The whole family (space group Immm, a ≈ 3.8?, b ≈ 5.8?, c ≈ 11.3?) is structurally characterised by the presence of flattened NiO₆ octahedra that form chains along the a-axis, giving rise to a strong Ni-O-Ni antiferromagnetic interaction. Whereas for Y-compound only strong 1D correlations exist above 1.5 K, presenting the Haldane gap characteristic of 1D AF chain with integer spin, 3D AF ordering is established simultaneously for both R and Ni sublattices at temperatures depending on the rare earth size and magnetic moment. The magnetic structures of R₂BaNiO₅ ( R = Nd, Tb, Dy, Ho, Er and Tm) have been determined and refined as a function of temperature. The whole family orders with a magnetic structure characterised by the temperature-independent propagation vector = (1/2, 0, 1/2). At 1.5 K the directions of the magnetic moments differ because of the different anisotropy of the rare earth ions. Except for Tm and Yb (which does not order above 1.5 K), the magnetic moment of the R³⁺ cations are close to the free-ion value. The magnetic moment of Ni²⁺ is around 1.4 , the strong reduction with respect to the free-ion value is probably due to a combination of low-dimensional quantum effects and covalency. The thermal evolution of the magnetic structures from T _N down to 1.5 K is studied in detail. A smooth re-orientation, governed by the magnetic anisotropy of R³⁺, seems to occur below and very close to T _N in some of these compounds: the Ni moment rotates from nearly parallel to the a-axis toward the c-axis following the R moments. We demonstrate that for setting up the 3D magnetic ordering the R-R exchange interactions cannot be neglected. Received 19 July 2001     

Determination of the Stereochemistry of Substituted 5-Methylenehydantoins and Thiohydantoins by 13C NMR and Homonuclear NOE Experiments

Basically the aim of this work is to define the accurate configuration of the exocyclic double bond of substituted 5-methylenehydantoins and thiohydantoins which have been conceived as potential Aldose Reductase inhibitors. A previsional survey based upon the chemical shifts analysis from ¹H and decoupled ¹³C NMR spectra discloses, for a part of the family of compounds, the assignment of the Zconfiguration for unsubstituted (2,3) and N-3 substituted (6,7,9) derivatives, and the E-configuration for the N-1 substituted (8,11) ones. The qualitative study with Homonuclear NOE (8,11) and the coupling constant measuring ^{3 J}C4-C=C-H6 from coupled ¹³C NMR (1–11), lead to the assignment of the accurate configuration of the whole family's compounds in agreement with the previsional study.     

Thermal conductivity and thermal Hall effect in Bi- and Y-based high-T c superconductors

Measurements of the thermal conductivity (k_xx) and the thermal Hall effect (k_xy) in high magnetic fields in Y- and Bi-based high-T _c superconductors are presented. We describe the experimental technique and test measurements on a simple metal (niobium). In the high-T _c superconductors k_xx and k_xy increase below T _c and show a maximum in their temperature dependence. k_xx has contributions from phonons and quasiparticle (QP) excitations, whereas k_xy is purely electronic. The strong increase of k_xy below T _c gives direct evidence for a strong enhancement of the QP contribution to the heat current and thus for a strong increase of the QP mean free path. Using k_xy and the magnetic field dependence of k_xx we separate the electronic thermal conductivity ( k _xx ^el ) of the CuO ₂ -planes from the phononic thermal conductivity ( k _xx ^ph ). In YBa₂Cu₃O _{7 - δ} k _xx ^el shows a pronounced maximum in the superconducting state. This maximum is much weaker in Bi₂Sr₂CaCu₂O _{8 + δ} , due to stronger impurity scattering. The maximum of k _xx ^el is strongly suppressed by a magnetic field, which we attribute to the scattering of QPs on vortices. An additional magnetic field independent contribution to the maximum of k_xx occurs in YBa₂Cu₃O _{7 - δ} , reminiscent of the contribution of the CuO-chains, as determined from the anisotropy in untwined single crystals. Our data analysis reveals that below T _c as in the normal state a transport (τ) and a Hall ( ) relaxation time must be distinguished: The inelastic (i.e. temperature dependent) contribution to τ is strongly enhanced in the superconducting state, whereas displays the same temperature dependence as above T _c . We determine also the electronic thermal conductivity in the normal state from k_xy and the electrical Hall angle. It shows an unusual linear increase with temperature. Received 23 August 2000     

Magnetic phase transitions in Nd1 ? xDyxFe3(BO3)4 ferroborates

The magnetic properties of ferroborate single crystals with substituted compositions Nd_{1 − x} Dy _x Fe₃(BO₃)₄ (x = 0.15, 0.25) with competing exchange Nd-Fe and Dy-Fe interactions are investigated. For each composition, we observed a spontaneous spin-reorientation transition from the easy-axis to the easy-plane state and step anomalies on the magnetization curves for the spin-flop transition induced by a magnetic field B | c. The measured parameters and effects are interpreted using a unified theoretical approach based on the molecular field approximation and on calculations performed in the crystal-field model for the rare-earth ion. The experimental temperature dependences of the initial magnetic susceptibility from T = 2 K to T = 300 K, anomalies on the magnetization curves for B | c in fields up to 1.8 T, and their evolution with temperature, as well as temperature and field dependences of magnetization in fields up to 9 T are described. In the interpretation of experimental data, the crystal-field parameters in trigonal symmetry for the rare-earth subsystem are determined, as well as the parameters of Nd-Fe and Dy-Fe exchange interactions.     

Resonant Ionization Laser Ion Source Project at TRIUMF

Resonant laser excitation and ionisation is one of the most successful tools for the selective production of radioactive ion beams (RIB) at on-line mass separator facilities. TRIUMF plans to augment the current ion sources with a resonant ionisation laser ion source (RILIS), to use the high production yields from the target, as shown by the delivery of 3*10⁴/s ¹¹Li ions from a standard target ion source with surface ionisation. The development and installation of TRIUMF's RILIS (TRILIS) is necessary to provide beams of short lived isotopes that conventional ion sources could not produce in sufficient intensity and purity for nuclear-, and nuclear astrophysics- experiments. A laser system consisting of three tunable titanium–sapphire (TiSa) lasers with frequency doubling and tripling was employed to demonstrate first off-line resonance ionisation of Ga, and is being installed for first on-line test and a run on ⁶²Ga in December 2004.     

A New Fluorescent Squaraine Probe for the Measurement of Membrane Polarity

The present study was undertaken to evaluate the sensitivity of newly synthesized squaraine dye 1 to the changes in lipid bilayer physical properties and compared it with the well-known dye 2. Partitioning of the dye 1 into lipid bilayer was found to be followed by significant increase of its fluorescence intensity and red-shift of emission maximum, while intensity of the dye 2 fluorescence increased only slightly on going from aqueous to lipidic environment. This suggests that dye 1 is more sensitive to the changes in membrane properties as compared to dye 2. Partition coefficients of the dye 1 have been determined for the model membranes composed of zwitterionic phospholipid phosphatidylcholine (PC) and its mixtures with positively charged detergent cetyltrimethylammonium bromide (CTAB), anionic phospholipid cardiolipin (CL), and sterol (Chol). The spectral responses of the dye 1 in different liposome media proved to correlate with the increase of bilayer polarity induced by Chol and CL or its decrease caused by CTAB. It was concluded that dye 1 can be used as fluorescent probe for examining membrane-related processes.     

Study of excitation transfer Li (3 D → 3 P ) occurring in optical collisions with rare gas atoms experimentally

By selective optical excitation of collision pairs and observation of the reemitted fluorescence information is obtained on the role of the molecular channels involved in inelelastic collisions. As an example case we have studied experimentally the Li( 3 D → 3 P) excitation transfer in Li(3D)X systems with X = Ne, Ar by means of the optical collision process Li (2 P ) + X + h ν→ LiX (3 D Λ) → Li (3 P , 3 D ) + X where LiX (3 D Λ) collision molecules dissociate into Li(3P, 3D) atoms following laser excitation h ν of Li (2 P ) + X pairs. For this purpose we measured the Li 3P/3D population ratio by the fluorescence from these levels as function of the laser detuning Δν from the Li(2P-3D) transition and the rare gas pressure, and determined from this the 3P/3D excitation ratio B (Δν) for single collision conditions. The experiments were performed using two step cw laser excitation of gaseous mixtures Li + X at temperatures around 600 K in the detuning range |Δν| ? 100 cm^-1. The B (Δν) profiles obtained display strong blue-red wing asymmetries both for Li ^* Ne and Li ^* Ar. This reflects different dissociation probabilities from the 3 D Σ or 3 D (Π,Δ) states that are initially prepared by blue wing or red wing excitation, respectively. The results are qualitatively discussed in terms of new ab initio potentials for the two systems. Received 23 February 2000 and Received in final form 5 July 2000     

Structural and magnetic studies of CuO-TeO2 and CuO-TeO2-B2O3 glasses

The glass systems xCuO ^. (1- x)TeO₂ and xCuO ^. (1- x)[75TeO₂ ^. 25B₂O₃] with 0 < x ? 50 mol% were investigated by means of X-ray diffraction, electron paramagnetic resonance (EPR) and a.c. magnetic susceptibility ( ) measurements, the principal aim of the investigation being the study of the structural modifications in the tellurite glasses introduced by the addition of boron oxide. In the case of first glass system, i.e. without B₂O₃, EPR spectra of Cu²⁺ ions undergo changes with the increasing concentration of CuO. At very low concentrations, spectra are due to isolated Cu²⁺ ions in axially distorted octahedral sites. The EPR signal for samples with 3 ? x ? 20 mol% can be explained as being the superposition of two EPR absorptions, one showing the hyperfine structure typical for isolated Cu²⁺ ions and the other consisting of a symmetric line typical for clustered ions. The broadening of the absorption band is due to dipolar as well exchange interaction. The susceptibility data show that for x > 20 mol%, the Cu²⁺ ions are predominantly clustered and are coupled through antiferromagnetic exchange interaction. A comparative study of amorphous X-ray diffraction pattern of the glasses indicates a structural modification in the TeO₂ network with increasing CuO concentration; the effect is quite visible in the samples with CuO concentrations higher than 20 mole percent. Measurements of density corroborate the conclusions drawn from the X-ray diffraction. Additionally, we show that our data validates a model in which CuO rich regions are surrounded by a buffer boundary which separates them from the tellurite glassy network; effect of introducing B₂O₃ can be best described as breaking these regions into smaller size regions. Received 23 October 2000 and Received in final form 1st February 2001