Modified Kissinger Equation Research Articles

Crystallization behavior of Li1+xAlxGe2-x(PO4)3 glass-ceramics: Effect of composition and thermal treatment

Lithium aluminum germanium phosphate (LAGP) glass-ceramics are promising solid electrolytes for all solid-state lithium ion batteries and other electrochemical applications. LAGP glass-ceramics (Li1+xAlxGe2-x(PO4)3, x = 0.5–0.8) were synthesized using a two-step heat treatment based on characteristic temperatures from Differential scanning calorimeter (DSC) analysis. X-ray diffraction (XRD) and scanning electron microscope (SEM) were used to characterize the crystal phases and their morphologies. Our results show that high purity ion conductive phase can be obtained for the compositions with P/Ge = 2.3 and 2.4 by a two-step heat treatment, instead of the commonly adopted single step heat treatment for composition with P/Ge = 2.0. Electrochemical impedance spectroscopy (EIS) measurements show that Tg + 60%∆T (∆T = Tc-Tg) is the optimal nucleation temperature to obtain high ionic conductivity. Crystallization energies were calculated from the modified Kissinger equation based on DSC measurements and it was concluded that the crystal phase form mainly through internal nucleation. We have found in this paper that, by using a two-step heat treatment, high phase purity LAGP glass-ceramics with lower GeO2 concentration can be obtained to achieve high ionic conductivity.

Enhanced microstructural, thermal and tensile characteristics of heat treated Sn-5.0Sb-0.3Cu (SSC-503) Pb-free solder alloy under high pressure

The Sn-5.0Sb-0.3Cu (SSC-503) solder alloy was pressurized by 1.0 GPa during heat treatment at 130 °C for 2 h (SSC-PHT) in order to refine its β-Sn grains and enhance the thermal and tensile properties. Microstructure of SSC-503 solder has irregular wavy coarsened grains. Refined grains with random irregular texture were observed after pressuring. This can be attributed to work hardening and shortened diffusion paths which promoted the crystal defects. XRD calculations revealed that the crystallite size of β-Sn phase of SSC-PHT sample was decreased by ~23% with respect to SSC-503 sample while the average lattice strain (η) was higher than heat treated sample (SSC-HT) by ~ 51%. Hence, pressuring during heat treatment causes an increase in dislocation density which strains the lattice and stores more strain energy. Differential scanning calorimeter (DSC) measurements indicated that the applied pressure inhibited the degree of undercooling from 3.04° to 1.47°C. This could endorse the solidification and restrain the growth rate of β-Sn dendrites due to the creation of new nucleation paths through preferential heterogeneous starting sites. The solidification activation energy of SSC-HT and SSC-PHT samples was evaluated as 60.52 and 52.31 kJ/mol respectively by utilizing modified Kissinger equation. After Appling pressure, a detectable enhancement was recorded in ultimate tensile strength (σUTS) by 63% and in yield stress (σYS) by 61% without deterioration of the ductility. These improvements related to the change in microstructure of SSC-PHT solder since high-pressure generated plenty of mixed dislocations as well as more defects. Moreover, the solid solution and dispersion hardening strengthening restricted the motion of the dislocations.

Mathematical-physical imperfections in frequently used models for analyzing glass crystallization and glass transition processes

In this paper, the modified Kissinger equation and the Ozava type equation were obtained by using a process of homogenization from dimensional analysis, thus making them correct in relation to the application of a logarithmic function. An equation that holds at maximum reaction rate is applied for the chosen reference heating rate βr and also for a heating rate βi that was used. In that way the modified Kissinger equation lnTmr2Tmi2βiβr=−ER1Tmi+ER1Tmr was obtained. The modified Ozava type equation was obtained in the form.lnβiβr=−mEnR1Tmi+mEnR1Tmrwhere Tmr and Tmi are the temperatures of the maximum obtained with βr and βi respectively. In these equations, free terms are explicitly defined and from their values it is possible to calculate the value of activation energy E, as from the slope of straight lines. The main advantage of the modified equations compared to the original Kissinger equation and the Ozava type equation is not the more accurate value of the activation energy, but the more precise form of the equation.With the goal to overcome all imperfections of the Lasocka equation, we propose the modified relationship Tg = Ag + Bg log(β/βr + 1) between the glass transition temperature Tg and the heating rate β. In this equation, the logarithm is calculated from dimensionless values, where βr is the chosen reference heating rate. In contrast to the original Lasocka equation, the modified Lasocka equation parameters Ag and Bg have the same units. The temperature Tg0 = Ag can be obtained by extrapolation of experimental results to β = 0. This is impossible to get from the original Lasocka equation, but it can be obtained from the modified one.

Crystallization kinetics of Li2O–Al2O3–GeO2–P2O5 glass–ceramics system

Lithium aluminum germanium phosphate glass–ceramics with NASICON structure find potential application in the field of energy storage device/solid-state battery. Two different glasses with nominal compositions (a) Li1.5Al0.5Ge1.5P2.9Si0.1O12 (LAGP1) and (b) Li1.5Al0.5Ge1.5P2.5Si0.5O12 (LAGP2) were prepared by standard melt-quench technique, and crystallization kinetics phenomenon in these systems was studied using differential thermal analysis technique (DTA). In addition to different conventional methods for crystallization kinetics analysis, model-free kinetics was also applied. The values obtained for activation energy of crystallization (E a) are compared and used for determination of crystallization index, n and m. The E a value obtained for LAGP1 is 375 ± 17 kJ mol−1 which is higher as compared to the E a value of LAGP2, 199 ± 22 kJ mol−1. LAGP2 with higher amount of Si(0.5) causes significant structural modification in the phosphate network and an early phase separation in the silico-phosphate glass. Thus, LAGP2 shows lower activation energy value as compared to LAGP1. The kinetic parameter, n, related to crystal nucleation, was evaluated from crystallized volume fraction (x) at a fixed temperature using predetermined E a value, and other parameter ‘m’ related to the crystal growth was determined using the modified Kissinger equation. The model-free kinetics was used to evaluate the variation of E a, m and n with temperature and suggests a dynamic nucleation and crystallization process with progressive change in kinetic parameters. In LAGP1 sample, an unusual increase in E a value was observed at x value > 0.2 and can be correlated with the existing ‘self-feeding’ process, which is observed in DTA plots. In both of these systems, the values of n and m are found to be equal and more than 3 which suggests three-dimensional growths of Li1.5Ge1.5Al0.5(PO4) crystals on a constant number of already grown nuclei. XRD and micro-Raman spectroscopy were used to identify the crystalline phase formed and various structural units present in the glass and glass–ceramics samples. Minor amount of LiAlPO4 was confirmed from XRD and Raman spectroscopy along with major Li1.5Ge1.5Al0.5(PO4) phase. In addition, using advanced kinetics and technology solution software non-isothermal data were simulated and the isothermal conversion data were extracted for various temperatures which are found to be very close to experimental isothermal data.

Crystallization behavior of WO3-MoO3-TeO2 glasses

In the present study, crystallization behavior of tungsten molybdenum tellurite glasses was investigated by non-isothermal methods using differential scanning calorimetry (DSC), X-ray diffraction (XRD), energy dispersive X-ray spectroscopy (EDS) and scanning electron microscopy (SEM) techniques. Thermal properties of glasses were investigated to calculate the values of glass transition temperature (Tg), crystallization temperature (Tc/Tp), temperature difference (ΔT), thermal stability (S), glass transition activation energy (Eg) and fragility parameter (m). Average cross-link density (nc¯) values were calculated for the physical investigation of the glasses. The crystallization kinetics was studied at different heating rates and the values of Avrami constant (n) and morphology index (m) were calculated from the Ozawa equation and the activation energy of crystallization (Ec) was determined using the modified Kissinger equation. The crystallized and/or transformed phases and their morphologies were determined by XRD and SEM analysis. Studied glass compositions were found to be thermally stable, resistant to crystallization and therefore suitable for opto-electronic applications.

Structure and crystallization kinetics of lithium tellurite glasses

In this work, structure and crystallization kinetics of lithium tellurite glasses were investigated. Thermal stability and glass formation ability was monitored using differential scanning calorimetry through the calculation of temperature difference, ΔT, thermal stability, S, Hrubÿ parameter, Hr and reduced glass transition temperature, Trg. Physical features of lithium tellurite glasses were investigated in terms of density, ρ, molar volume, VM, oxygen molar volume, VO, oxygen packing density, number of bonds per unit volume, nb, and Poisson's ratio, μcal and the structural transformations on the glass network were studied using Fourier transform infrared spectroscopy. The crystallization kinetics was studied under non-isothermal conditions. The values of Avrami constant, n, and morphology index, m were calculated from the Ozawa equation and the activation energy of crystallization, EC, was determined by modified Kissinger equation. The crystallization behavior of crystallized and/or transformed phases was confirmed by X-ray diffraction and scanning electron microscopy analysis.

Austenite Formation from Martensite in a 13Cr6Ni2Mo Supermartensitic Stainless Steel

Abstract The influence of austenitization treatment of a 13Cr6Ni2Mo supermartensitic stainless steel (X2CrNiMoV13-5-2) on austenite formation during reheating and on the fraction of austenite retained after tempering treatment is measured and analyzed. The results show the formation of austenite in two stages. This is probably due to inhomogeneous distribution of the austenite-stabilizing elements Ni and Mn, resulting from their slow diffusion from martensite into austenite and carbide and nitride dissolution during the second, higher temperature, stage. A better homogenization of the material causes an increase in the transformation temperatures for the martensite-to-austenite transformation and a lower retained austenite fraction with less variability after tempering. Furthermore, the martensite-to-austenite transformation was found to be incomplete at the target temperature of 1223 K (950 °C), which is influenced by the previous austenitization treatment and the heating rate. The activation energy for martensite-to-austenite transformation was determined by a modified Kissinger equation to be approximately 400 and 500 kJ/mol for the first and the second stages of transformation, respectively. Both values are much higher than the activation energy found during isothermal treatment in a previous study and are believed to be effective activation energies comprising the activation energies of both mechanisms involved, i.e., nucleation and growth.

Preparation and Characterization of Nd3+:ZnO-B2O3-Al2O3-SiO2 Transparent Glass-Ceramics

Nd3+:ZnO-B2O3-Al2O3-SiO2 transparent glass-ceramic was prepared by melting and crystallization technology.The nucleating agent content on Nd3+:ZnO-B2O3-Al2O3-SiO2 transparent glass ceramic nucleation and crystallization performance were investigated by DTA,XRD,SEM,UV-Vis-NIR spectrophotometer,fluorescence spectrum measurement.The modified Kissinger equation of nucleating agent on the crystallization kinetics parameters,the crystallization activation energy E and crystallization kinetics of criterion,using Augis-Bennett equation to calculate Avrami parameter.the relations of microstructure and optical transmittance was analyzed,and the optical properties were studied.

Kinetics of Crystallization of Co-Based Multi-Component Amorphous Alloy

Abstract Crystallization is a thermally activated process in non-crystalline and amorphous solids. The kinetics of the solid state phase transformations can be studied using thermal analysis techniques such as differential scanning calorimetry (DSC). For the kinetic analysis of the crystallization process under non-isothermal conditions, the choice of a reliable method is very important. The methods for the analysis of non-isothermal data are, in general, derived by extending the formalism developed for isothermal conditions. Most methods for the kinetic analysis of crystallization processes rely on the isokinetic hypothesis to separate the kinetics of the transformation from its dependence on temperature. It is assumed that the transformation rate can be described by a differential equation separable in α (transformed fraction) and T (temperature), i.e., for continuous heating regime, (dα/dT)=(1/β)k(T)f(α), where β is the heating rate, k(T) is the rate constant, and f(α) is the kinetic function (reaction model). The crystallization kinetics of glassy Co66Si16B12Fe4Mo2 have been studied with DSC and analyzed using non-isothermal theoretical expressions. The Avrami exponent, (n), frequency factor, (A), and activation energy, (E), of crystallization are evaluated using Matusita and Sakka (MS) and modified Kissinger equations. Besides, isoconversional kinetic analysis has been applied to DSC data for the determination of these different kinetic parameters. The isoconversional methods calculate Eα values at progressive degrees of conversion, α, without modelistic assumptions, and hence, this approach takes care of the variation of kinetic parameters with the fraction crystallized. The activation energy has been determined using both linear integral and differential isoconversional methods and also by the non-linear isoconversional method suggested by Vyazovkin and Wight. These methods are found to give consistent results for E. Furthermore, a comparison has been made among various kinetic parameters obtained using different approaches to investigate the relative applicability and usefulness of the proposed methods.

Crystallization kinetics of the tungsten–tellurite glasses

The crystallization kinetics of the (1 − x)TeO 2– xWO 3 (where x = 0.10, 0.15, and 0.20, in molar ratio) glass system was studied by non-isothermal methods using differential scanning calorimetry (DSC), X-ray diffraction (XRD) and scanning electron microscopy (SEM) techniques. DSC measurements were performed at different heating rates to study crystallization kinetics of the first crystallization reactions of the glasses. XRD analysis of tungsten–tellurite glasses heat-treated above the first crystallization temperatures revealed that the first crystallization peaks attributed to the α-TeO 2 and γ-TeO 2 crystalline phases for 0.90TeO 2–0.10WO 3 and 0.85TeO 2–0.15WO 3 samples and α-TeO 2 and WO 3 crystalline phases for the 0.80TeO 2–0.20WO 3 sample. Avrami constants, n, calculated from Ozawa equation, were found between 1.14 and 1.44. The activation energies, E A , for the first crystallization reactions were determined by using the modified Kissinger equation as 379 kJ/mol, 288.1 kJ/mol and 228.8 kJ/mol, for 0.90TeO 2–0.10WO 3, 0.85TeO 2–0.15WO 3 and 0.80TeO 2–0.20WO 3 glasses, respectively.

Effect of Nucleating Agents on Crystallization Glass Ceramics Produced from Nickel Slag

A laboratory preparation process of glass ceramics from nickel slag was introduced. The controlled heat treatment processes were carried out on the basis of differential scanning calorimetric (DSC) measurements. Mineral phase and microstructure of crystallized glass were analyzed by X-ray diffraction (XRD) and scanning electron microscopy (SEM). The modified Kissinger equation was employed to investigate the crystallization kinetic parameters, activation energy E and the k(Tp). The Avrami exponent, n, was calculated by Augis-Bennett equation. Analysis indicated that the glass with 10%TiO2 added was peril to crystallize, of a large value of k(Tp), its k(Tp) is 0.244, E is 522.76kJ/mol and n is 3.42. The crystal phase is diopside.

Microstructural characterization and crystallization behaviour of (1 − x)TeO 2– xWO 3 ( x = 0.15, 0.25, 0.3 mol) glasses

DTA, XRD and SEM investigations were conducted on the (1 − x)TeO 2– xWO 3 glasses (where x = 0.15, 0.25 and 0.3). Whereas the 0.75TeO 2–0.25WO 3 and 0.7TeO 2–0.3WO 3 glasses show no exothermic peaks, an indication of no crystallization in their glassy matrices, two crystallization peaks were observed on the DTA plot of the 0.85TeO 2–0.15WO 3 glass. On the basis of the XRD measurements of the 0.85TeO 2–0.15WO 3 glass samples heated to 510 °C and 550 °C (above the peak crystallization temperatures), α-TeO 2 (paratellurite), γ-TeO 2 and WO 3 phases were detected in the sample heated to 510 °C and the α-TeO 2 and WO 3 phases were present in the sample heated to 550 °C. SEM micrographs taken from the 0.85TeO 2–0.15WO 3 glass heated to 510 °C showed that centrosymmetrical crystals were formed as a result of surface crystallization and were between 3 μm and 15 μm in width and 12 μm and 30 μm in length. On the other hand, SEM investigations of the 0.85TeO 2–0.15WO 3 glass heated to 550 °C revealed the evidence of bulk massive crystallization resulting in lamellar crystals between 1 μm and 3 μm in width and 5 μm and 30 μm in length. DTA analyses were carried out at different heating rates and the Avrami constants for the 0.85TeO 2–0.15WO 3 glass heated to 510 °C and 550 °C were calculated as 1.2 and 3.9, respectively. Using the modified Kissinger equation, activation energies for crystallization were determined as 265.5 kJ/mol and 258.6 kJ/mol for the 0.85TeO 2–0.15WO 3 glass heated to 510 °C and 550 °C, respectively.

Study of non-isothermal crystallization of amorphous Cu50Ti50 alloy

The crystallization kinetics of amorphous Cu 50 Ti 50 has been studied using differential scanning calorimetry (DSC) under non-isothermal conditions. The curves at different linear heating rates (2, 4, 8 and 16 K min -1 ) show sharp crystallization peaks. The crystallization peak shifts to higher temperatures with increasing heating rate. The Kissinger's method of analysis of the shift in the transformation peak is applied to evaluate the activation energy (E c ). The KJMA formalism, which is basically developed for isothermal experiments, is also used to obtain E c and the Avrami parameter (n). The DSC data have been analysed in terms of kinetic parameters, viz. activation energy (E c ), Avrami exponent (n) and frequency factor K 0 using three different theoretical models. It is observed that the activation energy values derived from KJMA approach and modified Kissinger equation agree fairly well with each other. The activation energy values obtained from normal Kissinger method, and Gao and Wang expression underestimate the activation energy.

Kinetics of crystallization of amorphous Cu50Ti50 alloy

The kinetics of crystallization of amorphous Cu50Ti50 alloy has been studied with the help of non-isothermal scanning experiments in a differential scanning calorimeter. The thermograms at different scanning rates show a sharp crystallization peak followed by a broad, diffuse exothermic event. The method suggested [K. Matusita, S. Sakka, Phys. Chem. Glasses 20 (1979) 77] and the peak shift method given by Kissinger have been utilized to derive important kinetics parameters namely activation energy of crystallization Ec, Avrami exponent, n; and dimensionality of growth m. The derived value of Ec=303±83kJ/mol, obtained via the modified Kissinger equation, is in fair agreement with the reported value 280kJ/mol for Cu50Ti50 [K.H.J. Buschow, Acta Metall. 31 (1983) 155; Scripta Metall. 17 (1983) 1135] and 261.2kJ/mol for Cu40Ti60 glass reported by Miao et al. The results indicate bulk crystallization in the present amorphous alloy. The dimensionality of growth has been found to decrease with an increase in the heating rate.

Crystallization kinetics of a multicomponent Fe-based amorphous alloy using modulated differential scanning calorimetry

The kinetics of crystallization of a Fe-based multicomponent metallic glass Fe 67Co 18B 14Si 1, commercially known as 2605CO, is studied using modulated differential scanning calorimetry (MDSC) which still remains much less explored for the study of crystallization kinetics. The modified Kissinger equation and the one given by Matusita and Sakka for the non-isothermal crystallization have been employed to analyze the crystallization data at various heating rates. The effect of non-linear heating on the kinetics of crystallization has been discussed. It has been found that the dimensionality of crystallization is heating rate independent in case of DSC while in case of MDSC it is heating rate dependent.

Crystallization kinetics of tape cast bioactive glass 45S5

The crystallization kinetics of tape cast bioactive glass 45S5 was studied using non-isothermal methods. XRD confirmed that Na 2Ca 2Si 3O 9 was formed during heating up to 1000 °C. The modified Kissinger equation was used to determine that the activation energy for crystallization was 350 kJ/mol. The Avrami exponent, n, was determined to be 0.96 (Ozawa method) and 0.94 (Augis–Bennett method). Such results indicated that the particulate jet milled bioactive glass 45S5 (3 μm average particle size) undergoes surface crystallization during heat treatment. Previous results showed that the porosity of tape cast sintered bioactive glass 45S5 strongly influenced the in vitro bioactivity. Ease of crystallization of tape cast bioactive glass 45S5 suggested that it is fully crystalline prior to undergoing significant densification above 800 °C.

Crystallization Kinetics and Mechanism of Low‐Expansion Lithium Aluminosilicate Glass‐Ceramics by Dilatometry

The crystallization kinetics and mechanism of a precursor glass of lithium aluminosilicate (LAS)‐based commercial low‐expansion glass‐ceramics were investigated using a dilatometer. The isothermal crystallization behavior of β‐quartz solid solution (ss) was found to obey the Avrami equation. Nonisothermal crystallization data were analyzed by the Ozawa method and modified Kissinger equation. The value of the Avrami exponent (n) was ∼1.5, and the apparent activation energy (Ea) was ∼500 kJ/mol, which was close to that of the diffusion of silicon and aluminum ions as well as metal–oxygen bond strengths, suggesting a three‐dimensional (3D) diffusion‐controlled reaction mechanism.

Fractal growth kinetics during crystallization of amorphous Cu 50Zr 50

Cu-Zr is among the family of the binary metallic glasses which are well-known for their superior mechanical and magnetic properties. From the structure point of view, the amorphous metallic glasses are in non-equilibrium solid state. Therefore, it becomes important to study the factors, which may have crucial bearings on its end applications, related to the amorphous metallic structures. Stability is an important factor related to crystallization, which is generally a thermally activated process of transition from a disordered amorphous structure to an ordered crystal structure. Study of kinetics of crystallization provides E c, the activation energy of crystallization and parameters like Avrami exponent n, responsible for the mechanism of crystallization. This helps to determine the thermal stability of the metallic glasses. Cu 50Zr 50 metallic glass had been prepared by single roller melt-spinning technique. The DSC thermogram recorded at four different heating rates exhibits a two stage crystallization of this glassy system. Kinetics of crystallization of this glass has been studied in terms of activation energy using the Matusita and Sakka equation. It is found that the crystallization process is diffusion-controlled. The dimensionality of the fractal crystal growth is interpreted in terms Avrami exponent n, which has been found to be 2.6, 2.4 and 2.2 for the temperatures 539 K, 545 K and 549 K respectively. Besides, the activation energy of crystallization has also been independently derived through modified Kissinger equation.

Crystallization behaviour of glasses produced from fly ash

Abstract The crystallization behaviour of fly ash based glass samples annealed at 600°C for 2 and 10 h was investigated by DTA, XRD and SEM. On the basis of DTA, nucleation experiments of two glass samples were carried out at 680 and 687°C for 5 h and crystallization experiments were performed at 924 and 892°C for 20 min. The Avrami constant for both glass samples was calculated as 4, which indicates bulk crystallization, predicted by the Ozawa equation. Using the modified Kissinger equation, activation energies of crystal growth were determined as 318 and 312 kJ/mol for samples annealed at 2 and 10 h, respectively. Single peak analysis technique proved that the activation energy is independent of DTA heating rate. SEM observations indicated that the produced glass–ceramic samples have fine grained microstructure. The crystallized phase was identified as diopside [Ca(Mg,Al)(Si,Al)2O6] by X-ray diffraction analysis. The results of Vickers microhardness tests showed that the hardness values of the produced glass–ceramic samples decreased with the increase in holding time at the annealing temperature.

Kinetics of crystallization of a ternary titanium based amorphous alloy

Temperature-modulated differential scanning calorimetry (DSC) has been used to study the crystallization kinetics of Ti 50Cu 20Ni 30 metallic glass. The method of Matusita and Sakka for the kinetic study of crystallization seems to be still applicable despite the temperature modulation on four various linear heating rates (5, 10, 15 and 20°C/min) as it utilizes fractional crystallization at various temperatures of the crystallization curve in a continuous temperature domain. The modified Kissinger equation, on the other hand, underestimates the activation energy of crystallization as it incorporates particular discrete temperature points, i.e. peak crystallization temperatures at different heating rates.