Relaxation of glasses: The Kohlrausch exponent

Relaxation of glasses is analyzed in the framework of the generalized Vogel-Fulcher-Tamann law. In this model the relaxation times of the cooperative and individual motions (α and β) verify the relation log τ_α(T,T′) = 1/n(T,T′) log τ_β(Τ) . In the glass state the equivalent temperature T′ is the temperature of the liquid (at equilibrium) which has the volume of the glass, T′ is then the function of the aging time and of the experiment time. In the liquid state (T = T′), n(T) ~ T − T₀ is the Kohlrausch exponent (T₀ is the Vogel temperature). In the glass state the parameter, n(T,T′), is a function of the aging time and temperature, of the rheological parameters of the liquid (WLF constants C₁ and C₂) and of the expansion coefficients of the liquid and glass states. The Kohlrausch exponents deduced from the properties below Tg (volume, creep, stress relaxation) are deduced from the generalized VFT model.     

Positron annihilation and broadband dielectric spectroscopy: A series of propylene glycols

We report a thorough joint analysis of the behavior of the ortho-positronium lifetime as obtained from positron annihilation lifetime spectroscopy and of the dipolar relaxation spectra investigated by broadband dielectric relaxation spectroscopy in a series of glass-forming propylene glycols including propylene glycol, dipropylene glycol and tripropylene glycol. A number of empirical correlations between the temperature dependence of the ortho-positronium annihilation lifetime, τ₃(T), and the various spectral and relaxational quantities have been found. The phenomenological evaluation of the quasi-sigmoidal τ₃(T) dependence reveals three characteristic temperatures: T_g^PALS, T_b1 = (1.23 − 1.27)T_g^PALS and T_b2 = (1.46 − 1.53)T_g^PALS, which are found to decrease with increasing fragility. The slighter change of slope in the PALS response at T_b1 in this series of propylene glycols appears to be related to the crossover from the α-process to the excess wing or secondary relaxation, found in the dielectric spectra. The onset of the high-temperature plateau in the τ₃(T) plot at T_b2 occurs when τ₃ matches the average relaxation time of the primary α process. Moreover, the plateau region lies in the vicinity of the crossover in the dielectric parameters of the structural relaxation in all the samples, i.e. spectral width and relaxation strength. In addition it is approximately related to a crossover of the α relaxation time τ_α(T) from non-Arrhenius to Arrhenius regime. In summary, all the empirical correlations support further very close connections between the PALS response and the dielectric relaxation behavior in the series of propylene glycols.     

A derivation of the Vogel-Fulcher-Tammann relation for supercooled liquids

The non-Arrhenius Vogel-Fulcher-Tamman relation for the viscosity, η, known for about 8 decades, describes simply one of the most characteristic features of supercooled liquids. It may be written η=η₀exp[U/k(T−T₀)]. Using the Dyre et al. result demonstrating that U is proportional to the shear modulus, G, and the Interstitialcy Theory of Condensed Matter (ITCM) we derive this relation and obtain T₀/Tg=γ/(γ+1) and U=U₀/(1+γ), where U₀ is the interstitialcy diffusion energy at the glass temperature. Here, γ is a fragility softening parameter given by γ = βT_g(dc /dT)|_Tg. β is the shear susceptibility − d ln G /dc, and c is the interstitialcy concentration. γ is also a fragility parameter ranging from 0 for strong materials to 3 or above for fragile ones.     

Fragility in mixed alkali tellurites

Linear viscoelastic stress relaxation and calorimetric measurements were performed on a series of mixed alkali tellurite glasses of composition 0.3([xNa₂O+(1−x)Li₂O])+0.7TeO₂ at temperatures near and above the glass transition temperature, T_g. The stress relaxation data were well described by the stretched exponential function, G(t)=G₀exp[−(t/τ)^β], where τ is the relaxation time, β is the distribution of relaxation times and G₀ is the high frequency modulus. The fragility, determined from the temperature dependence of τ, exhibited a minimum in the middle of the mixed alkali composition. A possible connection between the kinetic and the thermodynamic dimensions of this system was established, wherein the heat capacity change at the T_g, ΔC_p(T_g), and the fragility are correlated.     

Insulator-like electrical transport in structurally ordered Al65Cu20+xRu15−x (x = 1.5, 1.0, 0.5, 0.0 and −0.5) icosahedral quasicrystals

Low-temperature resistivities, in zero-field and 8 T field, and magnetoresistance have been measured down to 1.4-300 K for stable icosahedral quasicrystals Al₆₅Cu_20+xRu_15−x (x = 1.5, 1.0, 0.5, 0.0 and −0.5). The analysis of the magnetoresistance data shows an overwhelming presence of anti weak-localization effect (τ_so ∼ 10⁻¹² s). But the sample with x = −0.5 shows anomalous magnetoresistance and the anti weak-localization effect breaks down (τ_so to be 10⁻¹⁵ s). The in-field σ-T between 5 K and 20 K, for x = 1.0, 0.5, 0.0 and −0.5 samples, and between 1.4 K and 40 K for x = 1.5 sample, follow a power-law behavior with an exponent of 0.5 and above ∼30 K the exponent ranges from 1.17 to 1.58. The observed power-laws basically characterize the presence of critical regime of the metal-insulator (MI) transition, dominated by electron-electron and electron-phonon inelastic scattering events respectively. In samples with x = 1.0, 0.5, 0.0 and −0.5 the in field σ-T has been found to follow ln σ-vs-T^1/4 below 5 K, which indicates the presence of variable range hopping. The observed transport features indicate the occurrence of proximity of metal-insulator transition in these Al-Cu-Ru quasicrystal samples.     

Role of the poly-dispersity and the dipolar interaction in magnetic nanoparticle systems: Monte Carlo study

In this paper, roles of the poly-dispersity and the dipolar interaction in frozen ferrofluid are studied by Monte Carlo method. A sample containing the uniaxial anisotropy and the random orientation is used to investigate. The temperature dependence of the coercivity is calculated to consider the magnetic phase transition under the influence of the dipolar interaction. We show that in the poly-dispersity and interacting sample, the temperature dependence of coercive field does not follow the classical expression, H_C/H_A = 0.48[1 − (T/T_B)^½]. We find that the transition temperature, which separates the anti-ferromagnetic and ferromagnetic states of strongly interacting sample, is not unique and it strongly depends on the variation of concentration. We also discuss about the concentration dependence of the coercivity at the different size distributions. At the finite temperature, the curve expresses a cusp which is due to the competition between the blocking and super-paramagnetic state at the low concentration. Therefore, we can see that the poly-dispersity also contributes to the complexity of magnetic phase of frozen ferrofluids.     

Arrhenius model for high-temperature glass-viscosity with a constant pre-exponential factor

A simplified form of the Arrhenius equation, ln η = A + B(x)/T, where η is the viscosity, T the temperature, x the composition vector, and A and B the Arrhenius coefficients, was fitted to glass-viscosity data for the processing temperature range (the range at which the viscosity is within 1-10³ Pa s) while setting A = constant and treating B(x) as a linear function of mass fractions of major components. Fitting the Arrhenius equation to over 550 viscosity data of commercial silicate glasses and approximately 1000 viscosity data of glasses for nuclear-waste glasses resulted in the A values of −11.35 and −11.48, respectively. The fraction of the variability (R²) value ranged from 0.92 to 0.99 for commercial glasses and was 0.98 for waste glasses. The Arrhenius models estimate viscosities for melts of commercial glasses containing 42-84 mass% SiO₂ within the temperature range of 1100-1550 °C and viscosity range of 5-400 Pa s and for waste glasses containing 32-60 mass% SiO₂ within the temperature range of 850-1450 °C and viscosity range of 0.4-250 Pa s.     

Structural investigations of magnesium silicate glasses by Si 2D Magic-Angle Flipping NMR

The two-dimensional Magic Angle Flipping Nuclear Magnetic Resonance (2D MAF NMR) experiment on ²⁹Si nuclei is used to determine the distribution of Q⁽ⁿ⁾ sites in two ²⁹Si-enriched magnesium silicate glasses with compositions 2MgO·SiO₂ and MgO·SiO₂. A significant degree of polymerization is observed in the 2MgO·SiO₂ glass, supporting previous studies using Raman and ²⁹Si NMR spectroscopy. Relative abundances of 0.629 ± 0.001 for Q⁽⁰⁾ and 0.371 ± 0.001 for Q⁽¹⁾ were obtained from spectral fits of the 2D MAF spectrum of the 2MgO·SiO₂ glass. Mole fractions for the free oxygen anion and each Q⁽ⁿ⁾-species were calculated and used in a thermodynamic model of Q⁽ⁿ⁾ disproportionation to calculate an equilibrium constant of k₀ = 0.04 ± 0.02 in 2MgO·SiO₂. In the MgO·SiO₂ glass relative abundance of 0.014 ± 0.001 for Q⁽⁰⁾, 0.191 ± 0.003 for Q⁽¹⁾, 0.530 ± 0.004 for Q⁽²⁾, 0.252 ± 0.003 for Q⁽³⁾, and 0.014 ± 0.001 for Q⁽⁴⁾ were measured. The mole fractions for the free oxygen anion and each Q⁽ⁿ⁾-species in MgO·SiO₂ were used to calculate corresponding disproportionation equilibrium constants of k₁ = 0.19 ± 0.02, k₂ = 0.174 ± 0.009, and k₃ = 0.11 ± 0.01. A comparison of k₃ values from previous MAF studies of various alkali and alkaline earth silicate glasses indicate an exponential increase in k₃ with the increasing modifying cation potential. Using the van't Hoff relation, we show that differences in both thermal history and modifier cation potential contribute to this spread in k₃ values. Nuclear shielding tensor anisotropy, ζ, and asymmetry, η, values of ζ = 0.0 ppm and η = 0.0 for Q⁽⁰⁾ and ζ = 33.0 ± 0.1 ppm, and η = 0.4 ± 0.1 for Q⁽¹⁾ in 2MgO·SiO₂ glass were determined from its 2D MAF spectrum. These values were used in obtaining the remaining values of ζ = − 36.0 ± 0.5 ppm and η = 0.99 ± 0.01 for Q⁽²⁾, and ζ = − 27.5 ± 0.5 ppm and η = 0.45 ± 0.11 for Q⁽³⁾, ζ = 0.0 ppm and η = 0.0 for Q⁽⁴⁾ in the MgO·SiO₂ glass from its 2D MAF spectrum. The magnitude of ζ values observed are lower than those reported in previous MAF studies of alkali and alkaline earth silicate glasses containing different modifier cations, consistent with previously reported trends in ζ versus modifying cation potential.     

Physical ageing and the Johari-Goldstein relaxation in molecular glasses

Based on some of our earlier dielectric relaxation studies during structural relaxation of molecular glasses, we describe certain features specific to the change in the Johari-Goldstein (JG) relaxation and examine their consequences for understanding of the molecular mechanism of the JG process. The parameter for the distribution of relaxation times increases slightly (loss curve becomes narrower) and the relaxation rate either remains constant or increases on ageing. In all cases, contribution to permittivity from the JG relaxation, Δε_JG decreases with time, with a rate constant k according to a relation, Δε_JG (t) = Δε_JG (t → ∞) − [Δε_JG (t = 0) − Δε_JG ( t → ∞)][1− exp[−(kt)]. This reduces to an equation of the type Δε_JG(t) = a + b exp(− kt) where a and b are constants of the glass as well are dependent on the thermal history of quenching of the glassy system. On decreasing the temperature, the relaxation rate for a rigid molecular glass follows the Arrhenius equation in a range that extends from liquid to glass, but deviates from it as a result of structural relaxation of the two alcohols, while the distribution of relaxation times decreases. The variation of Δε_JG with temperature shows an increase in slope on heating through T_g or else a deep and broad minimum before T_g is reached and the slope increases are remarkably similar to the changes observed for volume and thermodynamic properties on heating a glass. These findings need to be considered for a molecular mechanism in the potential energy view of JG relaxation, in analyzing the physical ageing of the α-relaxation process. It is argued that a recent suggestion for considering the JG relaxation within the picture of potential energy landscape may not be inconsistent with its molecular origin and dynamics in localized regions of structurally inhomogeneous glass. But there is still need to determine how the apparent dynamic heterogeneity evident from the broad distribution of the JG relaxation times can be reconciled with the dynamic heterogeneity used to explain less-broad spectra of the α − relaxation process.     

A low silica, barium borate glass-ceramic for use as seals in planar SOFCs

A low silica, barium borate glass-ceramic for use as seals in planar SOFCs containing 64 mol%BaO, 3 mol%Al₂O₃ and 3 mol%SiO₂ was studied. Coefficient of thermal expansion (CTE) between 275-550 °C, glass transition temperature (T_g), and dilatometric softening point (T_s) of the parent glass were 11.9 × 10⁻⁶ °C⁻¹, 552 °C, and 558 °C, respectively. Glass-ceramic was produced by devitrification heat treatment at 800 °C for 100 h. It was found that nucleation heat treatment, seeding by 3 wt%ZrO₂ as glass-composite and pulverization affected the amount, size and distribution of crystalline phases. SEM-EDS and XRD results revealed that crystalline phases presented in the devitrified glass-ceramic were barium aluminate (BaAl₂O₄), barium aluminosilicate (BaAl₂Si₂O₈) possibly with boron associated in its crystal structure, and barium zirconate (BaZrO₃). CTE of the devitrified glass-ceramic was in the range of (10.1-13.0) × 10⁻⁶ °C⁻¹. Good adhesion was obtained both in the cases of glass and devitrified glass-ceramic with YSZ and AISI430 stainless steel. Interfacial phenomena between these components were discussed.     

The effect of composition on UV-vis-NIR spectra of iron doped glasses in the systems Na2O/MgO/SiO2 and Na2O/MgO/Al2O3/SiO2

Glasses with the compositions xNa₂O · 10MgO · (90 − x)SiO₂, 10Na₂O · xMgO · (90 − x)SiO₂, 5Na₂O · 15MgO · xAl₂O₃ · (80 − x)SiO₂, xNa₂O · 10MgO · 10Al₂O₃ · (80 − x)SiO₂, 10Na₂O · 10MgO · xAl₂O₃ · (80 − x)SiO₂, 10Na₂O · 5MgO · 10Al₂O₃ · (80 − x)SiO₂ were melted and studied using UV-vis-NIR spectroscopy in the wavenumber range from 5000 to 30 000 cm⁻¹. At [Al₂O₃] > [Na₂O], the UV-cut off is strongly shifted to smaller wavenumbers and the NIR peak at around 10 000 cm⁻¹ attributed to Fe²⁺ in sixfold coordination gets narrower. Furthermore, the intensity of the NIR peak at 5500 cm⁻¹ increases. This is explained by the incorporation of iron in the respective glass structures.     

Occurrence of Kondo-like behavior in electrical-conductivity of Al70Pd20+xMn10−x (x = 0, 1 and 2) icosahedral quasicrystals

Zero-field and in-field (at 8 T) conductivity vs temperature (σ-T), magneto-resistance (Δρ/ρ), magnetization vs temperature (M-T) and magnetization vs field (M-H) of unannealed Al₇₀Pd₂₀Mn₁₀ and annealed Al₇₀Pd₂₀Mn₁₀, Al₇₀Pd₂₁Mn₉ and Al₇₀Pd₂₂Mn₈ quasicrystalline alloys have been studied in the temperature range of 1.4-300 K. Room temperature resistivity and the low-temperature magneto-resistance show a correlation with the corresponding magnetization. The σ-T for all the studied samples shows a pair of minima and maxima. The σ-T maxima show a correlation with the total magnetization. The analysis shows that σ-T is dominated by weak-localization effects. The minima are arising due to competing inelastic scattering times τ_i (e-ph scattering in the dirty metallic limit, τ_i ∝ T⁻²) and the Kondo-type spin-flip scattering time τ_sf whereas the maxima has been attributed to ‘Kondo-maxima’, occurring due to maxima in the spin-flip rate . The magneto-resistance of these samples shows a changeover from negative to positive where the negative component shows a correlation with the magnetization of the sample. The values of parameters derived from refinement give spin-flip scattering fields, which are found to be correlated with the total sample magnetization.     

Rotational probe relaxation and scaling in fragile glass formers

The rotational dynamics of a stiff paramagnetic tracer dissolved in supercooled SALOL is investigated via electron spin resonance spectroscopy. The study shows that the molecular rotation follows different dynamical regimes as the temperature is lowered. In particular, on cooling through the critical temperature T_C of the SALOL, the coupling between rotational relaxation and viscosity weakens and enhanced rotational diffusion is observed. In this temperature interval, the relationship between rotational correlation times and viscosity is fairly well described by a power law τ∝η^ξ (Fractional Debye-Stokes-Einstein law). Activated reorientation is observed in the temperature region around the glass transition of the SALOL. The rotational dynamics of the tracer dissolved in SALOL are compared with its rotation in ortotherphenyl (OTP) investigated in previous studies, and a scaling procedure is proposed.     

Structure and properties of Ni60(Nb100−xTax)34Sn6 bulk metallic glass alloys

Refractory bulk metallic glasses and bulk metallic glass composites are formed in quaternary Ni-Nb-Ta-Sn alloy system. Alloys of composition Ni₆₀(Nb_100−xTa_x)₃₄Sn₆ (x = 20, 40, 60, 80) alloys were prepared by injection-casting the molten alloys into copper molds. Glassy alloys are formed in the thickness of half mm strips. With thicker strips (e.g., 1 mm), Nb₂O₅ and Ni₃Sn phases and the amorphous phase form an in situ composite. Glass transition temperatures, crystallization temperatures, and ΔT_x, defined as T_x1 − T_g (T_x1: first crystallization temperature, T_g: glass transition temperature) of the alloys increase dramatically with increasing Ta contents. These refractory bulk amorphous alloys exhibit high Young’s modulus (155-170 GPa), shear modulus (56-63 GPa), and estimated yield strength (3-3.6 GPa).     

Observing the twinkling fractal nature of the glass transition

A fundamental understanding of the nature and structure of the glass transition in amorphous materials is currently seen as a major unsolved problem in solid-state physics. A new conceptual approach to understanding the glass transition temperature (T_g) of glass-forming liquids called the twinkling fractal theory (TFT) has been proposed in order to solve this problem. The main idea underlying the TFT is the development of dynamic rigid percolating solid fractal structures near T_g, which are said to be in dynamic equilibrium with the surrounding liquid. This idea is coupled with the concept of the Boltzmann population of excited vibrational states in the anharmonic intermolecular potential between atoms in the energy landscape. Solid and liquid clusters interchange or “twinkle” at a cluster size dependent frequency ω_TF, which is controlled by the population of intermolecular oscillators in excited energy levels. The solid-to-liquid cluster transitions are in accord with the Orbach vibrational density of states for a particular fractal cluster g(ω) ~ ω^df − 1, where the fracton dimension d_f = 4/3. To an observer, these clusters would appear to be “twinkling.” In this paper, experimental evidence supporting the TFT is presented. The twinkling fractal characteristics of amorphous, atactic polystyrene have been captured via atomic force microscopy (AFM). Successive two-dimensional height AFM images reveal that the percolated solid fractal clusters exist for longer time scales at lower temperatures and have lifetimes that are cluster size dependent. The computed fractal dimensions, ≈ 1.88, are shown to be in excellent agreement with the theory of the fractal nature of percolating clusters in accord with the TFT. The twinkling dynamics of polystyrene within its glass transition region are captured with time-lapse one-dimensional AFM phase images. The autocorrelation cluster relaxation function was found to behave as C(t) ~ t^− 4/3 and the cluster lifetimes τ versus width R were found to be in excellent agreement with the TFT via τ ~ R^1.42. This paper provides compelling new experimental evidence for the twinkling fractal nature of the glass transition.     

Dielectric study and ac conductivity of iron sodium silicate glasses

A series of glasses with formula (SiO₂)_0.7−x(Na₂O)_0.3(Fe₂O₃)_x with ( 0.0 ≤ x ≤ 0.20) were prepared and studied by means of AC measurements in the frequency range 20 kHz to 13 MHz at room temperature. The study of frequency dependence of both dielectric constant ε' and dielectric loss ε" showed a decrease of both quantities with increasing frequency. The results have been explained on the basis of frequency assistance of electron hopping besides electron polarization. From the Cole-Cole diagram the values of the static dielectric constant ε_s, infinity dielectric constant ε_∞, macroscopic time constant τ, and molecular time constant τ_m are calculated for the studied amorphous samples. The frequency dependence of the ac conductivity obeys a power relation, that is σ_ac (ω) = Α ω^s. The obtained values of the constant s lie in the range of 0.7 ≤ s ≤ 1 in agreement with the theoretical value which confirms the simple quantum mechanical tunneling (QMT) model. The increase in ac conductivity with iron concentration is likely to arise due to structural changes occurring in the glass network. The structure of a glass with similar composition was published and showed clustering of Fe²⁺ and Fe³⁺ ions which favor electron hopping and provide pathways for charge transport.     

Non-isothermal crystallization kinetics study on new amorphous Ga20Sb5S75 and Ga20Sb40S40 chalcogenide glasses

Bulk glasses of the system Ga₂₀Sb_xS_80−x (x = 5 and 40) were prepared for the first time by the known melt quenching technique. Non-isothermal differential scanning calorimetric (DSC) measurements of as-quenched Ga₂₀Sb_xS_80−x (x = 5 and 40) chalcogenide glasses reveal that the characteristic temperatures e.g. the glass transition temperature (T_g), the temperature corresponding to the maximum crystallization rate (T_p) recorded in the temperature range 400-650 K for x = 5 and 480-660 K for x = 40 are strongly dependent on heating rate and Sb content. Upon heating, these glasses show a single glass transition temperature (T_g) and double crystallization temperatures (T_p1 and T_p2) for x = 5 which overlapped and appear as a single crystallization peak (T_p) for x = 40. The activation energies of crystallization E_c were evaluated by three different methods. The crystallization data were examined in terms of recent analysis developed for non-isothermal conditions. The crystalline phases resulting from (DSC) have been identified using X-ray diffraction.     

Optical band gap and refractive index dispersion parameters of In-Se-Te amorphous films

Different compositions of In_x(Se_0.75Te_0.25)_100 − x (where 0 ≤ x ≤ 10 at.%) chalcogenide glasses were prepared by the usual melt quench technique. Chalcogenide thin films of these glasses were prepared by using thermal evaporation method. The film transmittance (T(λ)) at normal incidence for these films was measured in the wavelength range 400-2500 nm using a double beam spectrophotometer. Successfully applying Swanepoel's method helps us to determine the film thickness and the real (n) and imaginary (k) parts of the complex index of refraction with high accuracy. Optical absorption measurements show that, the fundamental absorption is due to the allowed non-direct transitions. It was found that, the addition of In content leads to the increase of the refractive index increases while the optical band gap decreases. The obtained results are well discussed in terms of the chemical bond approach and the cohesive energy.     

Crystallization behavior of (GeS2)0.1(Sb2S3)0.9 glass

The crystal growth kinetics of antimony trisulfide in (GeS₂)_0.1(Sb₂S₃)_0.9 glass has been studied by microscopy and DSC. The linear crystal growth kinetics has been confirmed in the temperature range 492 ? T ? 515 K (E_G = 405 ± 7 kJ mol⁻¹). The applicability of standard growth models has been assessed. From the crystal growth rate corrected for viscosity plotted as a function of undercooling it has been found that the most probable mechanism is interface controlled 2D nucleated growth. The non-isothermal DSC data, corresponding to the bulk sample, can be described by the Johnson-Mehl-Avrami equation.     

Simulation of metastable zone width and induction time for a seeded aqueous solution of potassium sulfate

The metastable zone width (MSZW, ΔT_m) and induction time (t_ind) were determined with computer simulation for seeded batch crystallization of potassium sulfate from aqueous solution. The MSZW and induction time determined with simulation showed the same behavior as experimental values reported in the literature; log (ΔT_m) increased linearly with an increase in log R (R: cooling rate) and t_ind decreases in proportion to (ΔT)⁻ⁿ (ΔT: supercooling, n: nucleation order in the secondary rate expression of B=k_n(ΔT)ⁿ). The secondary nucleation parameters (k_n and n) were deduced both from the simulated MSZW and induction times by using the previously proposed model [J. Cryst. Growth, 2010, 312, 548–554]. The secondary nucleation rate calculated with the deduced parameters was in agreement with that calculated with the parameters input for simulation.