Kinetics of non-isothermal crystallization and glass transition phenomena in Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses by DSC

The crystallization process affects solid properties through the crystal structure and morphology established during the transition process. An important aspect of the crystallization process is its kinetics, both from the fundamental point of view of amorphous material as well as the modeling and phase transition. In the present research work, non-isothermal crystallization data in the form of heat flow vs. temperature curves has been studied by using some well known models for amorphous Ga₁₀Se₈₇Pb₃ and Ga₁₀Se₈₄Pb₆ chalcogenide glasses, prepared by the melt quenching technique. The glass transition phenomena and crystallization of these glasses have been studied by using non-isothermal differential scanning calorimetery (DSC) measurements at constant heating rates of 5, 10, 15, 20, 25 and 30 K/min. The glass transition temperature (T_g), crystallization temperature (T_c), and melting temperature (T_m) were determined from DSC thermograms. The dependence of T_g and T_c on the heating rate was used to determine different crystallization parameters such as the order parameter (n), the glass transition energy (ΔE_g) and the crystallization activation energy (ΔE_c). The results of crystallization were discussed on the basis of different models such as Kissinger's approach and the modification for non-isothermal crystallization in addition to Johnson, Mehl, Ozawa and Avrami.     

Kinetic theory of crystallization of amorphous materials

Careful analysis of the Avrami equation [x = 1 ?exp(?Atⁿ)] shows that an activation energy for crystallization (E_c) for amorphous materials can be defined over a selected range of temperatures. This activation energy can be determined experimentally using non-isothermal differential scanning calorimetry (DSC) by determining the crystallization temperature (T_c) as a function of heating rate (φ). A plot of (ln(φ/T_c) has a slope equal to E_c/n. The activation energy for the crystallization of amorphous arsenic obtained by this non-isothermal method is found to be in fair agreement with that obtained from an isothermal DSC experiment.     

Kinetics of crystallization of titanium based binary and ternary amorphous alloys

Metallic glasses are kinetically metastable materials. These amorphous materials can be transformed into a crystalline state by both isothermal and isochronal methods. The study of this transformation, and hence the thermal stability of metallic glasses, are important from an application view-point. In the present work, the non-isothermal crystallization kinetics of two titanium-based amorphous alloys namely, Cu₅₀Ti₅₀ and Ti₅₀Ni₃₀Cu₂₀, are reported. The activation energies for crystallization, E_c for both the systems have been evaluated using different non-isothermal methods viz. derived through Kissinger, Augis and Bennet and Ozawa. The values of E_c obtained using these methods are consistent for both the metallic glasses and it is found that E_c for the ternary metallic glass is considerably higher than the binary metallic glass. The increase in the activation energy on the substitution of Ni in the Cu–Ti metallic glass suggests the increase in the thermal stability.     

Model-free method for analysis of non-isothermal kinetics of a bulk sample of selenium

In this work, the activation energies of crystallization of amorphous Se were studied under non-isothermal conditions using a differential scanning calorimetric (DSC) technique. The Johnson-Mehl-Avrami and isoconversional models were used to describe the DSC crystallization data. The isoconversional methods of Friedman, Kissinger-Akahira-Sunose (KAS) and Vyazovkin were used to determine the variation of the activation energy for crystallization with temperature, E_α (T). The KAS and Vyazovkin methods gave identical values, and the range of E_α (T) was found to vary in the range 110.4-44.2 kJ mol⁻¹, while the Friedman method gave lower values with E_α (T) in the range 100.5-28.3 kJ mol⁻¹. The effects of annealing were revealed by studying the morphology of the samples with a scanning electron microscope.     

Phase transformation and crystallization kinetics of melt-spun Ni60Nb20Zr20 amorphous alloy

The glass transition and crystallization kinetics of melt-spun Ni₆₀Nb₂₀Zr₂₀ amorphous alloy ribbons have been studied under non-isothermal and isothermal conditions using differential scanning calorimetry (DSC). The dependence of glass transition and crystallization temperatures on heating rates was analyzed by Lasocka's relationship. The activation energies of crystallization, E_x, were determined to be 499.5 kJ/mol and 488.6 kJ/mol using the Kissinger and Ozawa equations, respectively. The Johnson–Mehl–Avrami equation has also been applied to the isothermal kinetics and the Avrami exponents are in the range of 1.92–2.47 indicating a diffusion-controlled three-dimensional growth mechanism. The activation energy obtained from the Arrhenius equation in the isothermal process was calculated to be E_x = 419.5 kJ/mol. The corresponding three dimensional (3D) time–temperature–transformation (TTT) diagram of crystallization for the alloy has been drawn which provides the information about transformation at a particular temperature. In addition, the intermetallic phases and morphology after thermal treatment have been identified by X-ray diffraction (XRD) and scanning electron microscope (SEM).     

Kinetics of relaxation and crystallization of sodium metaphosphate glass

Kinetics of structural relaxation and crystallization of NaPO₃ glassforming melt is studied by means of thermal analyses. It is demonstrated that activation energy depends strongly on fictive temperature T_f. The dependence of the onset temperature T_o of the glass transition interval on the heating rate q⁺ is investigated for samples that were previously cooled down at a rate q⁻ of about 850 K/min. The dimensionless fragility F is a measure of the dependence of the activation energy for spatial rearrangement on the changes of structure. According to the present results F is large for NaPO₃ (i.e. phosphates are ‘fragile’ substances).     

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.     

Effect of laser irradiation on thermal and optical properties of selenium–tellurium alloy

The crystallization parameters such as glass transition temperature (T_g), onset crystallization temperature (T_c), peak crystallization temperature (T_p) and enthalpy released (ΔH_C) of the bulk Se–Te chalcogenide glass has been studied by using Differential Scanning Calorimeter (DSC), under non-isothermal condition at a heating rate of 20 K/min. The values of T_g, T_c, T_p and ΔH_C with and without laser irradiation for different exposure time have been studied. The optical absorption of pristine and laser irradiated thermally evaporated Se–Te films has been measured. The films shows indirect allowed interband transition that is influenced by the laser irradiation. The optical energy gap has been found to decrease from 1.61 to 1.38 eV with increasing irradiation time from 5 to 20 min. The results have been analyzed on the basis of laser irradiation-induced defects in the film.     

Stabilization of metallic glass studied by internal friction measurement

The internal friction Q^?1 and the oscillation frequency f of Zr–Ti–Cu–Ni–Be metallic glass specimens were measured using an inverted torsion pendulum with the free decay method. A single-roller melt-spinning apparatus was used for preparing the specimens. Isothermal annealing near the glass transition temperature T_g was performed to investigate the stabilization of the specimens. Q^?1 decreased with annealing time t due to the stabilization. Q^?1-vs-t was measured at various annealing temperatures T_a, and the values of relaxation time τ for the stabilization process were determined. The dependence of τ on T_a showed that the hydrodynamic behavior represented by the Vogel–Tammann–Fulcher form and the hopping behavior represented by the Arrhenius form were observed in high- and low-temperature regions, respectively. The crossover of the two behaviors was seen at a temperature near and somewhat higher than T_g. The result was discussed on the basis of the viscoelastic relaxation in glassy materials.     

Molecular dynamics in glass-forming poly(phenyl methyl siloxane) as investigated by broadband thermal,dielectric and neutron spectroscopy

The molecular dynamics of glass-forming poly(methyl phenyl siloxane) (PMPS) is studied by thermal (10⁻³–5 × 10² Hz), dielectric (10⁻³–10⁹ Hz) and neutron (5 × 10⁸–10¹² Hz) spectroscopy. Because of the broad frequency range of 15 orders of magnitude the study provides a precise determination of glassy dynamics in a wide temperature range using different probes. The relaxation rates extracted from the different methods agree quantitatively in both their absolute values and in their temperature dependencies. A detailed analysis of the temperature dependence of the relaxation rate f_p by a derivative technique shows that the α-relaxation of PMPS has to be characterized by a high and a low temperature branch separated by a crossover temperature T_B = 250 K. In both temperature ranges the temperature dependence of f_p has to be described by Vogel/Fulcher/Tammann laws with different Vogel temperatures. Also the analysis of the dielectric strength in its temperature dependence gives a crossover behavior from a low to a high temperature region with a similar value of T_B. T_B can be interpreted as onset of cooperative fluctuations and the formation of dynamical heterogeneities. The dependence of the relaxation rate on the scattering vector Q extracted from neutron scattering obeys a power law τ ∼ Q^−Slope, where the power Slope varies between Slope = 2 and Slope = 3.5 with increasing temperature. This anomalous dependence of the relaxation time on the momentum transfer is discussed in terms of dynamic heterogeneities in the underlying motional processes even at temperatures above T_B. Besides the segmental dynamics the fast Methyl group rotation is considered as well. The relaxation rates of this process have an activated temperature dependence with an activation energy of 8.3 kJ/mol. The data were discussed in the framework of the threefold jump model were the incoherent elastic scattering from ‘fixed’ atoms which are frozen on the time scale of the Methyl group rotation was taken into account.     

Variation of Avrami parameter during non-isothermal surface crystallization of glass powders with different sizes

The influence of grain size on the surface crystallization kinetics is investigated by non-isothermal Differential Thermal Analysis and Scanning Electron Microscopy. For this purpose, different powder fractions of a model glass forming diopside via surface crystallization and crystallization induced porosity, are used. The activation energy of crystallization, E_C, is determined from Kissinger plot, and the Avrami parameter, m, is estimated by both Ozawa and of Augis–Bennett methods. The values of E_C decrease from 530 to 300 kJ/mol when grain size increases. Simultaneously, the m value drops from 2.5 to 1.3. This result contradicts to the widespread fallacy that the reaction order should be equal to one in the case of surface crystallization. During the initial stage of surface crystallization three dimensional growth takes place, a fact confirmed by the SEM investigations. Later on, one dimensional growth inwards the grain is observed, leading to the reaction order changes from 3 to 1.     

Kinetics of non-isothermal crystallization of chalcogenide glasses from the Sb32As5S48I15 system

The work considers the kinetics of non-isothermal crystallization, especially from the point of view of the possibility of applying the Augis–Bennett method for the determination of activation energy. The necessity of introducing the usual approximation T ≫ T₀ was analyzed. It was shown that the method can be applied not only in the cases when T ≫ T₀, but also when T > T₀ that is, when the two temperatures differ only by about 10%. We show also that the application of the Augis–Bennett formula in such cases is more accurate the higher the value of the Avrami index n is. The method was applied to study the crystallization kinetics of the glass Sb₃₂As₅S₄₈I₁₅. The results obtained by differential scanning calorimetry (DSC) under non-isothermal conditions were also analyzed using the Kissinger and Matusita method. In the process of glass heating, a single peak is observed for glass transformation and a double peak for glass crystallization. The activation energies of glass transition (E_g) and crystallization (E_c) were determined, as well as the value of the Avrami index n for the second crystallization process. The obtained values for n and m indicate that the crystallization phase involves three-dimensional nucleation and growth. On the other hand, in agreement with the obtained results of the theoretical analysis, such n value justifies the application of the Augis–Bennett method for the investigated glass for which T and T₀ do not differ significantly.     

Molecular dynamics simulation of viscosity in supercooled liquid and glassy AgCu alloy

The viscosity of the model AgCu alloy is simulated by several methods using (i) correlation functions through the Green–Kubo formalism, (ii) a non-equilibrium molecular dynamics approach and (iii) creep tests under constant stress. Temperature dependences of the shear viscosity and the diffusion coefficient show the breakdown of the Stokes–Einstein relation well above the glass-transition temperature T_g. This observation is interpreted as a manifestation of the development of heterogeneities in the supercooled liquid approaching T_g. Based on a generalized Einstein formula for the viscosity of liquid, a temperature dependence of heterogeneity degree of supercooled liquid is estimated. Using the dependence of the deformation rate on external stress, the activation volume is evaluated to be four atomic volumes in liquid state. However, below the mode-coupling temperature T_c the activation volume increases by several times.     

Crystallization kinetics and optical band gap studies of Se96In4 glass before and after slow neutron irradiation

Results of differential scanning calorimetry (DSC) under non-isothermal condition on Se₉₆In₄ semiconducting chalcogenide glass before and after slow neutron irradiation, for different exposure times, have been reported and discussed. Some of Sn atoms have been injected into the glass by nuclear transmutation processes and the binary glass is converted into a ternary. This is accompanied by an increase in the activation energy of crystallization, E_c, and in the glass transition temperature, T_g and a decrease in the glass transition activation energy, E_t, in the onset crystallization temperature, T_c and in the peak temperature of crystallization T_p. Optical band gap measurements have also been carried out, before and after irradiation, on identical thin pellets of Se₉₆In₄ glass. The energy band gap, E_g, is found to decrease upon irradiation. These effects have been attributed to a structural change upon doping and to irradiation induced defects.     

Thermal analysis of bulk amorphous arsenic triselenide

Through the use of differential scanning calorimetry, the heat capacity and crystallization parameters of amorphous As₂Se₃ have been studied. It is found that the heat capacity above the glass transition temperature (T_g) exceeds, by a factor of 1.6, the Dulong-Petit limiting value found below T_g. The crystallization process is found to obey first-order kinetics with an activation enthalpy of 1.24 eV and an enthalpy of crystallization of 0.36 eV · molecule^?1. The effect of sample age on the rate constant is also reported.     

Hall resistivity of a magnetic amorphous alloy — Effects of thermal cycling and annealing

We have studied the effects of thermal cycling and annealing on the Hall resistivity ?_H and electrical resistivity ? of an amorphous magnetic material, Metglas 2826A. Thermal cycling up to 600 K has no significant effect on ? but changes ?_H, especially at T > 300 K. Annealing at higher temperatures T_a affects ?_H more strongly that it influences ?. For T_a = 650 K the Curie temperature jumps by ～300 K and this, combined with X-ray data, is regarded as being symptomatic of the onset of crystallization. It is demonstrated that, for a fixed T, the variation of the extraordinary Hall coefficient R₁ is simply correlated with that of ? for both the amorphous material and the annealed (crystallized) specimens. Furthermore, for a given T_a, the variations of R₁ and ? as functions of temperature exhibit the same formal relationship. The temperature dependence of ? in the annealed specimens is rendered plausible in terms of recent theories of disordered materials. Room-temperature studies of electron spin resonance and the field dependence of the magnetization are also reported.     

Non-isothermal crystallization kinetics of La2CaB10O19 from glass

The non-isothermal crystallization kinetics of La₂CaB₁₀O₁₉ (LCB) from a La₂O₃-CaO-B₂O₃ glass was studied. Differential thermal analysis methods were performed on three glass powders to obtain the kinetic parameters of LCB crystallization mechanism. The activation energies for overall crystallization (E), obtained by the methods of Kissinger and Ozawa, were in the range of 479-569 kJ/mol. Multiple (five) analysis methods were used to estimate the Avrami exponent (n), which could consequently be reduced into the single value of n = 3.1 ± 0.3. The growth morphology index (m) of LCB was corroborated by microscopy (optical and electron) images, which revealed a three dimensional growth. Energy dispersive spectroscopy confirmed that LCB is the crystallizing phase from the glass by an interface controlled mechanism. The parameters of the Johnson-Mehl-Avrami kinetic model for the analysis of LCB crystallization from glass were found to be n = m = 3.     

Crystallization kinetics in Cu46Zr45Al7Y2 bulk metallic glass by differential scanning calorimetry (DSC)

Crystallization transformation kinetics in isothermal and non-isothermal (continuous heating) modes were investigated in Cu₄₆Zr₄₅Al₇Y₂ bulk metallic glass by differential scanning calorimetry (DSC). In isochronal heating process, activation energy for crystallization at different crystallized volume fraction is analyzed by Kissinger method. Average value for crystallization in Cu₄₆Zr₄₅Al₇Y₂ bulk metallic glass is 361 kJ/mol in isochronal process. Isothermal transformation kinetics was described by the Johnson-Mehl-Avrami (JMA) model. Avrami exponent n ranges from 2.4 to 2.8. The average value, around 2.5, indicates that crystallization mechanism is mainly three-dimensional diffusion-controlled. Activation energy is 484 kJ/mol in isothermal transformation for Cu₄₆Zr₄₅Al₇Y₂ bulk metallic glass. These different results were discussed using kinetic models. In addition, average activation energy of Cu₄₆Zr₄₅Al₇Y₂ bulk metallic glass calculated using Arrhenius equation is larger than the value calculated by the Kissinger method in non-isothermal conditions. The reason lies in the nucleation determinant in the non-isothermal mode, since crystallization begins at low temperature. Moreover, both nucleation and growth are involved with the same significance during isothermal crystallization. Therefore, the energy barrier in isothermal annealing mode is higher than that of isochronal conditions.     

Isothermal and non-isothermal crystallization kinetics in amorphous Ni45.6Ti49.3Al5.1 thin films

The crystallization kinetics in Ni_45.6Ti_49.3Al_5.1 film were studied by differential scanning calorimetry through isothermal and non-isothermal approaches. The activation energy for crystallization was determined to be 374 and 280 kJ/mol by the Kissinger and the Augis & Bennett method, respectively, in non-isothermal methods. In the isothermal annealing study, the Avrami exponents were in the range of 2.78-3.80 between 793 and 823 K, suggesting that the isothermal annealing was governed by three dimensional diffusion-controlled growth for Ni_45.6Ti_49.3Al_5.1 thin films, in which the activation energy of nucleation is higher than that of growth. In addition, the transformation rate curves of Ni_45.6Ti_49.3Al_5.1 film were also constructed by isothermal methods. The crystallization kinetics of amorphous Ni_45.6Ti_49.3Al_5.1 film can thus be appreciated and the transformation rate also can be employed to control the degree of crystallization.     

An investigation of the kinetic transformation mechanism of Ge12.5Te87.5 chalcogenide glass under non-isothermal regime

Differential scanning calorimetry (DSC) technique was used to study the kinetics of amorphous to crystalline transformation in Ge_12.5Te_87.5 chalcogenide glass. The kinetic parameters of glassy Ge_12.5Te_87.5 under non-isothermal conditions are analyzed by the model-free and model-fitting approaches from a series of experiments at different constant heating rates (5-50 K/min). The effective activation energy of crystallization was determined by analyzing the data using the isoconversional methods of Kissinger-Akahira-Sunose (KAS), Tang, Starink, Flynn-Wall-Ozawa (FWO) and Vyazovkin. The analysis of the present data shows that the effective activation energy of crystallization is constant throughout the entire interval of conversions and hence with temperature. The transformation mechanism examined using the local Avrami exponents indicates that one mechanism (three-dimensional growth) is responsible for the transformation process for all heating rates used. The reaction model that may describe the transformation process of the Ge_12.5Te_87.5 chalcogenide glass is the Avrami-Erofeev model (g(α) = [− ln(1 − α)]^1/n) with n = 3 for all heating range at the whole range of crystallized fraction (α = 0.05-0.95). A good agreement between the experimental and the reconstructed (α-T) curves has been achieved. The transformation from amorphous to crystalline phase in Ge_12.5Te_87.5 chalcogenide glass demonstrates a single-step mechanism.