Shear,dilation, and swap: Mixing in the limit of fast diffusion

Molecules of different species mix by local rearrangement and long-range migration. Under certain conditions, the molecules are partially jammed: they rearrange slowly, but migrate fast. Here we formulate a theory of mixing when the long-range migration of molecules is fast, and the local rearrangement of molecules sets the time needed for mixing. In this limit, the time needed for mixing is independent of the length scale of inhomogeneity. We identify three modes of local rearrangement: shear, dilation, and swap. All three modes break and form intermolecular bonds. We place the three modes on equal footing, as distinct, concurrent, nonequilibrium processes. Our theory thus removes the bias that assumes local chemical equilibrium but allows the nonequilibrium process of shear. We propose a kinetic model of four independent viscosity-like coefficients, and a thermodynamic model of ideal mixing of molecules of unequal sizes and nonzero volume of mixing. We illustrate the theory with several examples, including the development of growth stress, the homogenization of a bilayer, and the disappearance of an inclusion in a matrix.     

Electronegativity difference, atomic size parameter and widths of supercooled liquid regions of Sb2S3-As2S3-Sb2Te3 glasses

Electronegativity difference Δ_x, atomic size parameter δ and width of supercooled liquid region (ΔT_x = T_x − T_g, where T_x is the onset crystallization temperature and T_g the glass transition temperature) are analysed for glasses of the ternary system Sb₂S₃-As₂S₃-Sb₂Te₃ as a function of arsenic atomic percentage.Correlation is investigated between the two bonds parameters (Δ_x and δ) and the width of supercooled liquid region ΔT_x (which is generally reliable in estimating the stability against the crystallization of the glasses). It is found that this width of supercooled liquid region of the glasses in Sb₂S₃-As₂S₃-Sb₂Te₃ system depends on electronegativity difference and atomic size parameter.     

High pressure x-ray diffraction measurements on Mg2SiO4 glass

The structure factors of Mg₂SiO₄ glass have been measured using high energy x-ray diffraction up to pressures of 30.2 GPa, and the equation of state measured up to 12.8 GPa. The average Mg-O coordination numbers were extracted from the experimental pair distribution functions assuming two cases (i) there is no change in Si-O coordination number with pressure and (ii) the average Si-O coordination number increases the same as for pure SiO₂ glass. Both analyses give similar results and show a gradual increase in the average Mg-O coordination number from 5.0 at ambient pressure to ~ 6.6(6) at 30.2 GPa. There is good qualitative agreement between the experimental structure and equation of state data for the glass compared to several recent molecular dynamics simulations carried out on liquid Mg₂SiO₄.     

Absorption and photoluminescence of PbS QDs in glasses

Optical properties of PbS quantum dots (QDs) precipitated inside the oxide glass matrix were investigated. Photoluminescence (PL) from the PbS QDs showed peak wavelengths located at 1170–1680 nm with widths of 150–550 nm. Radii of QDs in glasses were 2.3–4.7 nm depending upon the thermal treatment. Peak wavelengths of PL bands shifted as much as 70 nm as the temperatures and excitation irradiances increased. Calculated effective local temperatures indicated that these shifts of PL spectra were associated with local heating induced by the temperatures and laser beam.     

Thermal,IR, Raman characteristics,Raman gain coefficient and bandwidths in quaternary glasses

Tellurite glasses with composition 75TeO₂–5WO₃–15Nb₂O₅–5M_xO_y in mol%, where M_xO_y = (Na₂O, Ag₂O, ZnO, MgO, CuO, NiO, TiO₂, MnO₂) have been prepared by using the conventional melt-quenching method. Thermal characteristic of prepared glasses were investigated by using DTA techniques. It was found that the glass with the composition 751TeO₂–5WO₃–15Nb₂O₅–5TiO₂ had high thermal stability (ΔT = 122 °C at heating rate 15 K/min). Raman gain coefficients and bandwidths of prepared glasses for Raman gain media were evaluated. The glass with composition 75TeO₂–5WO₃–15Nb₂O₅–5Na₂O had the maximum value of Raman gain coefficient (g = 4.43 × 10⁻¹² m/W) and it was 24 times as large as silica glass. The highest value of full width half maximum (FWHM ≈ 185 cm⁻¹) was observed in glass system 75TeO₂–5WO₃–15Nb₂O₅–5NiO. Finally, the structure of the glasses was investigated through deconvolution Raman and IR spectra.     

Intense orange emission in Pr3+ doped lead phosphate glass

Spectroscopic properties of one mol% Pr₂O₃ embedded in 40%PbO–60%P₂O₅ glass have been investigated at room temperature. From the absorption spectra energy levels of the observed bands are assigned. Using free ion Hamiltonian theoretical values of energy of 13 multiplets of Pr³⁺ are calculated. Judd–Ofelt intensity parameters have been estimated by including and excluding the hypersensitive transition (³H₄→³P₂). The best set of Judd–Ofelt parameters are obtained by omitting ³H₄→³P₂ transition from the calculation. These parameters are used to evaluate the important laser parameters for various emission lines. Our investigation reveals that the present glass may be utilized as a laser active medium corresponding to ³P₀→³H₄ and ¹D₂→³H₄ transitions respectively, for 484.6 nm (blue) and 599.5 nm (strong orange) emissions. Indirect and direct optical band gap energies of Pr³⁺ doped lead phosphate glass matrix have also been reported.     

Exact results and open questions in first principle functional RG

Some aspects of the functional RG (FRG) approach to pinned elastic manifolds (of internal dimension d) at finite temperature T > 0 are reviewed and reexamined in this much expanded version of Le Doussal (2006) [67]. The particle limit d = 0 provides a test for the theory: there the FRG is equivalent to the decaying Burgers equation, with viscosity ν ∼ T-both being formally irrelevant. An outstanding question in FRG, i.e. how temperature regularizes the otherwise singular flow of T = 0 FRG, maps to the viscous layer regularization of inertial range Burgers turbulence (i.e. to the construction of the inviscid limit). Analogy between Kolmogorov scaling and FRG cumulant scaling is discussed. First, multi-loop FRG corrections are examined and the direct loop expansion at T > 0 is shown to fail already in d = 0, a hierarchy of ERG equations being then required (introduced in Balents and Le Doussal (2005) [36]). Next we prove that the FRG function R(u) and higher cumulants defined from the field theory can be obtained for any d from moments of a renormalized potential defined in an sliding harmonic well. This allows to measure the fixed point function R(u) in numerics and experiments. In d = 0 the beta function (of the inviscid limit) is obtained from first principles to four loop. For Sinai model (uncorrelated Burgers initial velocities) the ERG hierarchy can be solved and the exact function R(u) is obtained. Connections to exact solutions for the statistics of shocks in Burgers and to ballistic aggregation are detailed. A relation is established between the size distribution of shocks and the one for droplets. A droplet solution to the ERG functional hierarchy is found for any d, and the form of R(u) in the thermal boundary layer is related to droplet probabilities. These being known for the d = 0 Sinai model the function R(u) is obtained there at any T. Consistency of the ?=4-d expansion in one and two loop FRG is studied from first principles, and connected to shock and droplet relations which could be tested in numerics.     

Eu-Mn energy transfer in white-light-emitting T-phase (Ba,Ca)2SiO4:Eu, Mn phosphor

White-light-emitting T-phase Eu²⁺/Mn²⁺-codoped (Ba, Ca)₂SiO₄ phosphors are achieved in terms of the energy transfer between Eu²⁺ and Mn²⁺ ions. All spectra consist of the relatively broad green and the red emission bands, which thus result in a warm-white color with a color temperature of ∼4000 K. With increasing Eu²⁺ ions at fixed Mn²⁺ concentrations, a strong correlation between the luminescence and the electron paramagnetic resonance spectra is observed. This demonstrates that Eu²⁺ doping causes a perturbation of Mn²⁺ sites and the violation of their selection rules that enhances Mn²⁺-related emissions.