Correlation between the dimensionality and the constants of elasticity of rare-earth doped borate glasses

This work was devoted to explore the correlation between the dimensionality and the computed theoretically constants of elasticity of borate based glasses doped with rare-earth oxides. The dimensionality of the glassy network has been calculated in terms of the d ratio which is equal to 4 C ₄₄/K _e and discussed in terms of the cross-link density and number of network bonds per unit volume of these glasses. Constants of elasticity were calculated in terms of the bond compression model and the Makishima-Mackenzie model. The average cross-link density, the number of network bonds per unit volume, the average stretching-force constant, and the ratio of the estimated bulk modulus (K _bc) to the experimentally determined (K _e) have been calculated and discussed in terms of the bond-compression model. Young??s modulus, the packing density, and the dissociation energy have been calculated and analyzed in terms of the Makishima-Mackenzie model. The results showed that the computed elastic moduli and the dimensionality of the borate glasses containing La₂O₃ or Gd₂O₃ are strongly dependent on the concentration of the structural units of the constituent oxides and types of bonds between these units.     

Infrared spectral studies of nanostructured Co2+-substituted Li-Ni-Zn ferrites

Polycrystalline Li_0.5Ni_0.25–0.5x Co_0.5x Zn_0.5Fe₂O₄ ferrites (x = 0.0, 0.1, 0.2, 0.3, 0.4, and 0.5) were prepared by standard auto-combustion method and characterized by XRD and IR spectra. The XRD results suggest that all samples were single-phase with a cubic spinel-type structure. The lattice constant, particle size, metal-oxygen bond length (R _A and R _B), cation radii (r _A and r _B) on A and B-sub lattices were found to increase while the X-ray density and porosity, decrease with increasing x. The IR spectra show two absorption bands, at ν₁ about 600 cm^?1 and ν₂ at about 425 cm^?1, which were attributed to tetrahedral (A) and octahedral (B) sites of the spinel structure, respectively. The band positions were found to depend on x. The force constants, K _t and K _o, were calculated and plotted against cobalt concentration x. Compositional dependence of the force constants is explained in terms of cation-oxygen bond distances and redistribution of cations.     

Synthesis and characterization of clinopyroxene based glasses and glass-ceramics along diopside (CaMgSi2O6)-jadeite (NaAlSi2O6) join

The crystallization behavior and mechanical characterization of glasses based upon the compositions along diopside (CaMgSi₂O₆)-jadeite (NaAlSi₂O₆) join has been investigated. Six glasses were obtained by the melt-quenching technique. Structural and thermal behaviors of these glasses were investigated by density and molar volume, infrared spectroscopy (FTIR) and dilatometry. The crystallization behavior of glasses was investigated by using differential scanning calorimetry (DSC). Sintering and crystallization behavior of the glass-ceramics were investigated under non-isothermal heating conditions up to temperatures of 850 °C. Mechanical characterization of glasses was investigated by using the measurement of Vickers indentation hardness and elastic constants such as Young's modulus (E), shear modulus (G), bulk modulus (K) and Poisson's ratio (ν). These data of the glasses were correlated with the structure of glasses, nature and role played by glass forming cations.     

Equilibrium ring concentrations and the statistical conformations of polymer chains: 14. Calculation of the concentrations of medium sized cyclics in poly(dimethyl siloxane) equilibrates

Theoretical molar cyclization equilibrium constants K_x for dimethyl siloxane cyclics [(CH₃)₂SiO]_x in undiluted poly(dimethyl siloxane) equilibrates are calculated for values of x in the range 7 < x < 13. The Jacobson and Stockmayer theory is used for the calculations and K_x values are computed by finding the statistically weighted fraction of the 3^2x?3 conformations [defined by the Flory, Crescenzi and Mark (FCM) rotational isomeric state model of poly(dimethyl siloxane)] that have terminal atoms in close proximity for ring formation. The FCM model gives theoretical K_x values in good agreement with experiment for x = 8, 9, 10 but yields a K₁₁ value that is nine times greater than that found experimentally. This result is discussed in terms of the molecular structure of dimethyl siloxane chains. The effect on the calculated K_x values of modifying the FCM model by assigning a smaller value to the SiOSi bond angle is explored.     

Elastic constants and thermal expansivity of gel-spun polyethylene fiber and its composites

The five independent stiffness constants, C₁₁, C₃₃, C₄₄, C₆₆, and C₁₃, and the axial and transverse thermal expansivity of unidirectional gel-spun polyethylene fiber reinforced composites have been measured as functions of fiber volume fraction V_f. The axial extensional modulus C₃₃ and axial Poisson's ratio v₁₃ follow the rule of mixtures, while the axial shear modulus C₄₄, transverse shear modulus C₆₆, and transverse plane-strain bulk modulus C_t ( = C₁₁ − C₆₆) obey the Halpin-Tsai equation. Extrapolation to V_f = 1 gives the five stiffness constants of gel-spun polyethylene fiber. The tensile property of the fiber is highly anisotropic, with the axial Young's modulus about 40 times higher than the transverse Young's modulus. In contrast, the axial shear modulus exceeds the transverse shear modulus by only 5%. A similar treatment of the thermal expansivity data in terms of the Schapery equations gives an axial thermal expansivity of −1.25 × 10⁻⁵ K⁻¹ and a transverse thermal expansivity of 11.7 × 10⁻⁵ K⁻¹ for the fiber.     

Titanium coordination in TiO2-Na2O-SiO2 glasses of xTiO2 · (100 ? x) [2Na2O · 3SiO2] (0 ≤ x ≤ 30) composition based on Raman spectroscopy

The structural position of Ti⁴⁺ ions in TiO₂-Na₂O-SiO₂ glasses of xTiO₂ · (100 ? x) [2Na₂O · 3SiO₂] (0 ?? x ?? 30) composition has been studied with Raman spectroscopy. The analysis of spectra recorded has demonstrated that Ti⁴⁺ ions in the studied glasses can be in two structural groups??TiO₅ and TiO₆. Titanium ions with a coordination number of 5 are present in the structure of all Ti-containing glasses, whereas the highly coordinated state exists at x > 10 mol % TiO₂.     

Equilibrium ring concentrations and the statistical conformations of polymer chains: Part 11. Cyclics in poly(ethylene terephthalate)

Methods have been developed for extracting cyclic oligomers from poly(ethylene terephthalate) samples and for analysing the extracts by gel permeation chromatography. These methods have been used to measure the molar cyclization equilibrium constants K_x for cyclics (CO.C₆H₄.CO.O.CH₂.CH₂.O)_t with x=3–9 in the undiluted polymer at 543K and in solution in 1-methyl naphthalene at 523K. The close agreement between the measured K_x values over the range x=3–9 shows that oligomeric ethylene terephthalate chains adopt similar conformations in the two environments (which contain 95% w/w and 6% w/w linear polymer respectively). K_x values were calculated by the Jacobson and Stockmayer theory by assuming that the corresponding open chain molecules obey Gaussian statistics and describing their statistical conformations by Williams and Flory's rotational isomeric state model. These theoretical values were found to be lower than the experimental values by factors of at least two over the whole range of cyclics x=3–9. Poor agreement between experiment and theory was also obtained when K₃ and K₄ values were calculated by computing the end-to-end distances of acyclic trimeric and tetrameric ethylene terephthalate chains in all discrete conformations defined by the Williams and Flory model. It is suggested that these discrepancies might result, at least in part, from substantial correlations between the positions and directions of the termini of oligomeric ethylene terephthalate chains. Observed decreases in the concentrations of cyclics in commercial poly(ethylene terephthalate) samples resulting from heating the samples in the solid state are discussed briefly.     

Microstructural characterization and crystallization kinetics of (1 − x)TeO2–xK2O (x = 0.05, 0.10, 0.15, 0.20 mol) glasses

Microstructural characterization and crystallization kinetics of (1 − x)TeO₂–xK₂O (x = 0.05, 0.10, 0.15, and 0.20 in molar ratio) glasses were investigated using DTA, XRD, Raman spectroscopy, optical microscopy and SEM techniques. Whereas only one exothermic peak was observed for the 0.95TeO₂–0.05K₂O and 0.90TeO₂–0.10K₂O glasses, two crystallization peaks were present on the DTA plots of the 0.85TeO₂–0.15K₂O and 0.80TeO₂–0.20K₂O glasses. On the basis of the XRD and Raman spectrophometry investigations, α-TeO₂, γ-TeO₂ and K₂Te₄O₉ crystal phases were present in the (1 − x)TeO₂–xK₂O (x = 0.05, 0.10, 0.15, and 0.20 in molar ratio) glass samples heated above the peak crystallization temperatures, T_p. SEM/EDS investigations of (1 − x)TeO₂–xK₂O (x = 0.05, 0.10, 0.15, and 0.20 in molar ratio) glasses heated above T_p revealed the presence of distinct TeO₂-rich and K₂Te₄O₉ in the 0.95TeO₂–0.05K₂O and triangular wedge-shaped crystalline regions in the 0.90TeO₂–0.10K₂O, 0.85TeO₂–0.15K₂O and 0.80TeO₂–0.20K₂O glasses. DTA analyses were carried out at different heating rates and the Avrami constant for the 0.95TeO₂–0.05K₂O glass was calculated as 0.94, an indication of surface crystallization also confirming SEM results. On the other hand, the n values were between 1.7 and 1.87 for the exothermic peaks of the 0.80TeO₂–0.10K₂O, 0.85TeO₂–0.15K₂O and 0.80TeO₂–0.20K₂O glasses, indicating one-dimensional crystalline growth mechanisms for these glasses. Activation energies for one-dimensional crystal growth mechanisms in these crystals determined from the modified Kissinger plots were found to vary between 550 and 650 kJ/mol.     

Impact of the cation field strength on physical properties and structures of alkali and alkaline-earth borosilicate glasses

The impact of the cation field strength (CFS) of the glass network-modifier cations on the structure and properties of borosilicate glasses (BS) were examined for a large ensemble of mixed-cation (R/2)M₍₂₎O–(R/2)Na₂O–B₂O₃–KSiO₂ glasses with M⁺ ={Li⁺, Na⁺, K⁺, Rb⁺} and M²⁺ ={Mg²⁺, Ca²⁺, Sr²⁺, Ba²⁺} from four series of {K, R} combinations of K = n(SiO₂)/n(B₂O₃) = {2.0, 4.0} and R =[n(M₍₂₎O) ?+ ?n(Na₂O)]/n(B₂O₃) = {0.75, 2.1}. Combined with results from La³⁺ bearing glasses enabled the probing of physical-property variations across a wide CFS range, encompassing the glass transition temperature (T_g), density, molar volume and compactness, as well as the hardness (H) and Young's modulus (E). We discuss the inferred composition–structure/CFS–property relationships. Each of T_g, H, and E revealed a non-linear dependence against the CFS and a strong T_g/H correlation, where each property is maximized for the largest alkaline-earth metal cations, i.e., Sr²⁺ and Ba²⁺, along with the high-CFS La³⁺ species. The ¹¹B MAS NMR-derived fractional BO₄ populations decreased linearly with the average M^z+/Na⁺ CFS within both K–0.75 glass branches, whereas the NBO-rich K–2.1 glasses manifested more complex trends. Comparisons with results from RM₂O–B₂O₃–KSiO₂ glasses suggested no significant “mixed alkali effect”.     

Systematics of elastic and thermodynamic properties of super-hardness cubic boron nitride under high pressure

The elastic constants of cubic boron nitride (c–BN) are calculated by the first-principles method at ambient condition. The dependence of the elastic constants, the bulk modulus B, and the shear modulus G on the applied pressure are presented. The calculated results are in good agreement with the comparable experimental and theoretical values. The deviation from the Cauchy relation and the elastic anisotropy are investigated. The normalized elastic constants c_ij ′ are introduced to investigate elasticity of c–BN in more detail. Moreover, the thermodynamic properties (Debye temperature, melting temperature) and sound velocity have been investigated under high pressure for the first time.     

Equilibrium ring concentrations and the statistical conformations of polymer chains: Part 7. Cyclics in poly(1,3-dioxolane)

Cyclic oligomers [CH₂OCH₂CH₂O]_x with x = 2–9 were found to be present in poly(1,3-dioxolane) samples prepared by monomer-polymer equilibrations using boron trifluoride diethyl etherate as catalyst. The molar cyclization equilibrium constants K_x for cyclics [CH₂OCH₂CH₂O]_x with x = 1–8 were measured for an undiluted and a solution equilibrate at 333K. The K_x values for the cyclics with x ?5 were in agreement with those calculated by the Jacobson-Stockmayer theory, using a rotational isomeric state model to describe the statistical conformations of the corresponding chains and assuming that the chains obey Gaussian statistics.     

Microstructural and mechanical characterization of sol gel-derived Si–O–C glasses

The mechanical properties of three silicon oxycarbide glasses pyrolysed under inert (Ar) atmosphere were studied as a function of the pyrolysis temperature. The silicon oxycarbide glasses were prepared from various alkyl substituted alkoxysilanes such as HSi(OEt)₃ and HMeSi(OEt)₂ in different ratios by using the sol-gel method. The Si–O–C-glasses obtained were respectively: (i) silicon oxycarbide network with excess carbon, (ii) stoichometric SiC_xO_2(1−x) where x=0.30 and (iii) silicon oxycarbide matrix with an excess of Si. Si–C bonds introduced in the starting silica gel network can be partially retained in the final glass after pyrolysis under inert atmosphere. After pyrolysis at temperatures between 600–1500 °C, the presence of tetracoordinated C atoms in the silica network results in an improvement of mechanical properties and thermal stability compared with silica glass. By using elemental analysis, density, SEM, BET and XRD (combined with Rietveld-analysis), the glass characterization was performed. Flexural strength (MOR), elastic modulus (E) and Vickers hardness (H_V) were measured and will be discussed in terms of glass composition and microstructure.     

Sound velocities and elastic properties of PbTiO3 and PbZrO3 under pressure: First principles study

The elastic constants and sound velocities as a function of pressure for perovskite materials PbTiO₃ (PTO) and PbZrO₃ (PZO) were investigated by first principles calculations. Under ambient pressure, the calculated structural parameters were calculated and found to be in good agreement with known values. To study properties under pressure, PTO and PZO were calculated at several reduced volumes, each of which corresponds to the system under pressure. The C₁₁, C₁₂ and C₄₄ elastic constants are all found to increase with pressure for the pressure range studied. Because the sound velocities are directly derived from the elastic constants, the relationships between the sound velocities and pressure also follow similar trends. The longitudinal modes are all larger than those of the transverse modes.     

Property analysis of triglyceride-based thermosets

Triglycerides with acrylate functionality were prepared from various oils and model triglycerides. The triglyceride-acrylates were homopolymerized and copolymerized with styrene. The cross-link densities of the resulting polymer networks were predicted utilizing the Flory-Stockmayer theory. Although the model predictions overestimated the cross-link density, the trends in the cross-link density predictions matched the experimental results. In both cases, the cross-link density was found to increase gradually at low levels of acrylation and then linearly at higher levels of acrylation. The deviation in the experimental results and model predictions were the result of intramolecular cross-linking. Approximately 0.5 and 0.8 acrylates per triglyceride were lost to intramolecular cyclization for homopolymerized triglyceride-acrylates and triglycerides copolymerized with styrene, respectively. The glass transition temperature (T_g) increased approximately linearly with the cross-link density from as low as −50 °C to as high as 92 °C. Simple models accurately predicted the effect of cross-link density on T_g. The tensile strength and modulus of triglyceride-based polymers increased exponentially at low levels of acrylate functionality, but increased linearly at higher levels of acrylate functionality, as predicted by vector percolation theory.     

Ionic association and mobility in propylene carbonate

Molar conductivities were measured at 298.15 K for symmetric quaternary ammonium picrates, R₄NPic, with R equal to C₁ to C₅ as well as for potassium picrate in propylene carbonate. The molar conductivities at infinite dilution, association constants of ion pairs, ionic conductivities at infinite dilution, and Stokes radii were calculated for the ions employed. The salts, Me₄NPic and Et₄NPic, were found to be dissociated, the others are associated. For the associated salts the data conform to the Fuoss model for the association process.     

The optical band gap and the tailing states determination in glasses of TeO2-V2O5-K2O system

Ternary amorphous samples of 50TeO₂-(50 ? x)V₂O₅-xK₂O compositions with 0 ≤ x ≤ 20 (in mol %) have been prepared using the press-melt quenching method. The optical absorption spectra of glass have been recorded in the wavelength range 300–900 nm by UV-visible spectrophotometer. According to The Tauc and Urbach theories, the optical band gap and width of the tail of localized states have been evaluated. In addition the temperature glass transition (T _g ) of glasses have been determined by differential scanning calorimetry, confirming the amorphous nature of samples. The density and molar volume have been studied, indicating act of K₂O as network modifier.     

Equilibrium ring concentrations and the statistical conformations of polymer chains: Part 13. Cyclics in two aliphatic polyesters

Methods have been developed for measuring the molar cyclization equilibrium constants K_x for cyclics [O(CH₂)₁₀OCO(CH₂)₄CO]_x with x=1–5 in an undiluted ring-chain equilibrate of poly(decamethylene adipate) (PDA) at 423K, and for cyclics [O(CH₂)₃OCO(CH₂)₂CO]_x with x=1–7 in an undiluted equilibrate of poly(trimethylene succinate) (PTS) at the same temperature. The experimental K_x values are compared with theoretical values calculated by the Jacobson and Stockmayer theory. The latter were obtained by assuming that chains in the undiluted melts adopt random-coil conformations obeying Gaussian statistics and have average dimensions predicted by the rotational isomeric state model of Flory and Williams. The agreement between experiment and theory is excellent for the cyclic oligomers containing 54, 72 and 90 skeletal bonds in the PDA equilibrate. By contrast, the experimental K_x values for cyclic oligomers of comparable size in the PTS equilibrate are approximately half the calculated values. These differences suggest that the statistical conformations of oligomeric aliphatic polyester chains depend on the relative numbers of methylene groups and ester linkages that they contain.     

Fluorophosphate glasses activated by rare-earth ions and AgBr

Analysis of the absorption band position for colloidal silver in fluorophosphate glasses of the composition (0.95 ? x ? y)(MgCaBaSrAl₂F₁₄)-0.05Ba(PO₃)₂-xPbF₂-yLnF₃ (where Ln = Eu, Ce, Sm, Tb; 0 ?? x ?? 0.2; y = 0.01, 0.02) with small additives of AgBr (0.04 wt % above 100%) has been performed. It has been shown that joint introduction of AgBr and EuF₃ with additional heat treatment of the glasses below the temperature of the onset of crystallization leads to a rise of the plasmon absorption band of silver nanoparticles. It has been assumed that the reason for the observed shift of the plasmon absorption band is the formation of a ??0.5-nm-thick shell of AgBr on the surface of a metallic Ag _n ⁰ -cluster.     

Physical Properties,Optical band gaps and Radiation Shielding Parameters Exploration for Dy<Superscript>3+</Superscript>-doped Alkali/Mixed Alkali Multicomponent Borate Glasses

Six compositions of 1 mol % Dy³⁺-doped multicomponent borate glasses containing single Li₂O, Na₂O, K₂O and mixed Li₂O–Na₂O, Li₂O–K₂O, and Na₂O–K₂O oxides have been synthesized by well-known melt-quenching technique. Following the measured density and refractive index values, various physical parameters were estimated for all the glass samples and differences in them are correlated with structural changes. To explore optical properties like absorption edge (λ_cut-off), optical band gap energy (E_opt), and Urbach energy (ΔE), optical absorption spectra were recorded for all the glasses. The E_g has been calculated using Davis and Mott theory for direct allowed, and indirect allowed transitions and the results were reported. The E_g values are also estimated using absorption spectrum fitting (ASF) method. The optical parameters variations have also been associated with the structural changes occurring in the glasses with different alkali/mixed alkali oxides content presence. The shielding properties of the prepared glasses were studied in terms of effective atomic numbers (Z_eff), mean free path (MFP), half value layer (HVL) and macroscopic effective removal cross-section (Σ_R). From these results, it was found that Potassium (K) glass shows superior gamma ray shielding properties due to a higher value of Z_eff and lower values of both MFP and HVL. These results indicate that the prepared glasses might be utilized in place of some common shielding materials to shield γ-rays and neutrons.     

First-principles study of structural,mechanical, and thermodynamic properties of cubic Y2O3 under high pressure

The structural, mechanical, and thermodynamic properties of cubic Y₂O₃ crystals at different hydrostatic pressures and temperatures are systematically investigated based on density functional theory within the generalized gradient approximation. The calculated ground state properties, such as equilibrium lattice parameter a₀, the bulk modulus B₀, and its pressure derivative B₀′ are in favorable agreement with the experimental and available theoretical values. The pressure dependence of a/a₀ and V/V₀ are also investigated. Furthermore, the elastic constants C_ij, bulk modulus B, shear modulus G, Young's modulus E, the ductile or brittle (B/G), Vickers hardness H_v, isotropic wave velocities and sound velocities are calculated in detail in a pressure range from 0 to 14 GPa. It was found that the Debye temperature decreases monotonically with an increase in pressure, the calculated elastic anisotropic factors indicate that Y₂O₃ has low anisotropy at zero pressure, and that its elastic anisotropy increases as the pressure increases. Finally, the thermodynamic properties of Y₂O₃, such as the dependence of the heat capacities C_V and C_P, the thermal expansion coefficient α, the isothermal bulk modulus, and the Grüneisen parameter γ on temperature and pressure, are discussed from 0 to 2000 K and from 0 to 14 GPa, respectively, applying the non-empirical Debye model in the quasi-harmonic approximation.