Avrami Exponent Values Research Articles

Crystallization Kinetics and Melting Behavior of Novel Biobased Poly(butylene 2,5‐thiophenedicarboxylate)

AbstractPoly(butylene 2,5‐thiophenedicarboxylate) (PBTh) is a novel biobased semicrystalline polyester with superior thermal, mechanical, and gas barrier properties; however, the crystallization kinetics and melting behavior of PBTh have not been studied in detail so far. The crystallization kinetics of PBTh was first studied in this research. The Ozawa equation failed to describe the nonisothermal melt crystallization kinetics of PBTh due to the secondary crystallization. The crystallization activation energy value was calculated by the Friedman method, which was negative and exhibited the conversion dependence. The isothermal melt crystallization kinetics of PBTh was well described by the Avrami equation in a wide range of crystallization temperature from 84 to 120 °C. PBTh showed the fastest crystallization rate at 104 °C; moreover, the Avrami exponent value slightly varied between 2.2 and 2.7, suggesting the same crystallization mechanism within the investigated temperature range. PBTh displayed one or two melting endotherms depending on crystallization temperature, which was well explained by the melting, recrystallization, and remelting mechanism. In addition, the equilibrium melting point of PBTh was estimated to be 163.1 °C with the Hoffmann−Weeks equation.

Static recrystallization behavior and strengthening mechanism of a single-phase Cu–18Ni–17Zn alloy

The microstructural evolution and recrystallization behavior of a single-phase Cu–18Ni–17Zn alloy during annealing has been investigated. The strengthening effects of the solute atom concentration, grain size, and recrystallized volume fraction have also been studied. The results have shown that the difference in yield strengths for the fully recrystallized samples mainly depended on the grain boundary strengthening effect. This is attributed to a constant (∼41 MPa) solid-solution strengthening contribution in the completely recrystallized Cu–18Ni–17Zn alloy. When compared with pure copper, this alloy exhibited a high Hall-Petch constant (∼0.36 MPa m1/2), which is due to the higher grain boundary interface energy. A discontinuous recrystallization occurred in the alloy in the temperature range 400 °C–500 °C. Furthermore, the yield strength was linearly correlated to the recrystallized volume fraction in the partial recrystallized samples. Moreover, the addition of Ni and Zn increased the recrystallization temperature and slowed the recrystallization kinetics. The activation energy for the recrystallization was estimated as 92.6 ± 5.1 kJ/mol in the cold-rolled Cu–Ni–Zn alloy, which indicates that the grain boundary migration during recrystallization was mainly controlled by diffusion along the grain boundaries. In addition, the recrystallized grains preferentially nucleated at shear bands with high strain energies in the Cu–Ni–Zn alloy during annealing. As the regions of shear banding were completely consumed, new recrystallized nuclei formed at the grain corners. The limited number of nucleation sites resulted in a low Avrami exponent value that ranged from 0.41 to 0.61.

Crystallization kinetics and structural development of Bi2GeO5 glass-ceramics fabricated by the modified incorporation technique

This study focuses on the fabrication and crystallization kinetics of bismuth germanate (Bi2GeO5) crystals in glass ceramics. Bismuth germanate glass-ceramics were produced from a base glass containing 58.4 mol% Bi2O3, 23.4 mol% GeO2, and 18.2 mol% B2O3 using a modified incorporation technique. Differential thermal analysis was used to determine the crystallization temperature. The X-ray diffraction results showed a dominant peak corresponding to the pure Bi2GeO5 phase, which has an orthorhombic crystal structure. The local Avrami exponent (n(x)) and local crystallization activation energy (Ec(x)) were determined using a non-isothermal method with heating rates ranging from 5 to 20 °C/min. The results indicated that the crystal growth process of the glass-ceramics occurred in all three dimensions, with Avrami exponent values ranging from 1.79 to 2.5. The microstructure also revealed uniform crystallization across the surface and bulk diffusion of crystallites. The modified incorporation method successfully enhanced the crystallization of Bi2GeO5 glass-ceramics, resulting in the transition from one-dimensional needle-like crystals to the desired crystal dimensions.

Non-Isothermal Analysis of the Crystallization Kinetics of Amorphous Mg72Zn27Pt1 and Mg72Zn27Ag1 Alloys.

In this study, thin ribbons of amorphous Mg72Zn27Pt1 and Mg72Zn27Ag1 alloys with potential use in biomedicine were analyzed in terms of the crystallization mechanism. Non-isothermal annealing in differential scanning calorimetry (DSC) with five heating rates and X-ray diffraction (XRD) during heating were performed. Characteristic temperatures were determined, and the relative crystalline volume fraction was estimated. The activation energies were calculated using the Kissinger method and the Avrami exponent using the Jeziorny-Avrami model. The addition of platinum and silver shifts the onset of crystallization towards higher temperatures, but Pt has a greater impact. In each case, Eg > Ex > Ep (activation energy of the glass transition, the onset of crystallization, and the peak, respectively), which indicates a greater energy barrier during glass transition than crystallization. The highest activation energy was observed for Mg72Zn27Pt1 due to the difference in the size of the atoms of all alloy components. The crystallization in Mg72Zn27Ag1 occurs faster than in Mg72Zn27Pt1, and the alloy with Pt has higher (temporary) thermal stability. The Avrami exponent (n) values oscillate in the range of 1.7-2.6, which can be interpreted as one- and two-dimensional crystal growth with a constant/decreasing nucleation rate during the process. Moreover, the lower the heating rate, the higher the nucleation rate. The values of n for Mg72Zn27Pt1 indicate a greater number of nuclei and grains than for Mg72Zn27Ag1. The XRD tests indicate the presence of α-Mg and Mg12Zn13 for both Mg72Zn27Pt1 and Mg72Zn27Ag1, but the contribution of the Mg12Zn13 phase is greater for Mg72Zn27Ag1.

Kinetics of solid-state oxidation of iron, copper and zinc sulfide mixture

The kinetics of solid-state oxidation by air of iron, copper and zinc sulfide natural mixture, which is typical of the pyritic copper ores, is investigated. Using the high-temperature X-ray powder diffraction, thermogravimetry and differential scanning calorimetry, it was found that the process can be represented by five exothermic elementary reactions, corresponding to intensive burning of iron, copper and zinc sulfides, and two endothermic ones, associated with decomposition of copper and iron sulfates. Kinetic analysis is performed by Kissinger and Augis–Bennett methods, the model-free function mechanism was determined from y(α) master plots and iterative optimization of the kinetic parameters. The limiting steps of these reactions are nucleation and crystal growth, and the values of activation energy, pre-exponential factor and Avrami exponent are in the ranges of 140–459 kJ·mol–1, 1.41·104–3.49·1031 s–1, and 1.0–1.7, respectively. Crystallization is followed by an increase in the number of nuclei, which may be formed both at the interface and in the bulk of the ore particles, and crystal growth is one-dimensional and controlled by a chemical reaction at the phase boundary or diffusion. The results of the work can contribute to the development of theoretical ideas about the physicochemical transformations of pyritic ores and concentrates during pyrometallurgical operations.

Evaluation of novel composition (SiO2–CaO–Na2O–P2O5, SrO–CuO) degradable amorphous silicate glasses properties and comprehensive characterization of the thermal features

The current work presents and discusses the findings of a comprehensive study on the structural, chemical and thermal properties of SrO and CuO incorporated SiO2–CaO–Na2O–P2O5 amorphous silicate glass with a novel composition. Here, fundamental features (experimental density, oxygen density, and hardness) of all glasses were determined and chemical as well as phase composition of the glasses was verified with XRF and XRD, respectively. Moreover, the thermal behavior (viscos flow and crystallization kinetics) of amorphous silicate glass was investigated by non-isothermal methods using DTA analysis. The activation energies of glass transition (Eg) were calculated in the range of 546–1115 kJ/mol by Kissinger method, whereas the activation energies of crystallization (Ec) were calculated in the range of 164–270 kJ/mol by three different methods (Kissinger, Ozawa, Yinnon and Uhlmann). Avrami exponent (n) values ranged from 1.17 to 3.28 demonstrated that amorphous silicate glasses have different crystallization mechanism. Working temperature, which is one of the parameters indicating glass stability, increased with the incorporation of Sr and Cu from 187 °C to 245 °C. The initial dissolution measurement has been applied to study the degradability behavior of Sr and Cu incorporated amorphous glasses in vitro. Quantitative evaluation of Si4+ (0.156–0.373 kV), Ca2+ (0.043–0.332 kV), Na+ (0.044–0.329 kV), P5+ (0.057–0.289 kV), Sr2+ (0.134–0.385 kV), and Cu2+ (0.090–0.203 kV) depending on the ion activation energy (Ea-ion) and ion concentration at different temperature values (24, 37 and 55 °C) was performed in contact with Tris-HCl solution by ICP-OES analysis. The results revealed that investigated glasses were degradable and incorporation of Sr and Cu affected the glass initial dissolution. Overall, investigated glasses are suitable for various application such as hot-working production, glass-ceramic manufacturing, and glass or glass-ceramic scaffolds fabrication, due to wide working temperature ranges and high crystallization tendencies of the developed glasses.

An In Situ Decarbonation Kinetic Study of Calcite Using Synchrotron Radiation XRD

ABSTRACT In situ decarbonation kinetics of calcite were investigated at high temperatures, up to 900 °C, using synchrotron radiation powder X-ray diffraction. The sequence of X-ray diffraction spectra reveals that calcite begins to thermally decompose into lime (CaO) and CO2 at 800 °C and ambient pressure. The decarbonation degree gradually increases with temperature, and calcite completely transforms into lime at 900 °C. The kinetic analysis of the isothermal data using an Avrami model involving nucleation and growth yields the values for the decarbonation rate and reaction order. Our results indicate that the decarbonation rate increases from 2.89 × 10–4s–1 to 3.48 × 10–3s–1 with elevated temperature from 840 to 880 °C, showing a positive temperature dependence on the reaction rate. The calculated Avrami exponent (n) values between 1.35 and 2.38 suggest that the thermal decomposition of calcite should be mainly dominated by homogeneous nucleation and CO2 diffusion-controlled growth. In natural carbonate fault rocks, the decarbonation of CaCO3 caused by frictional heating may be strengthened by the action of high shear velocity. In addition, the resulting ultrafine powder and CO2 pressurization can remarkably reduce the friction coefficient between two fault planes, which further leads to carbonate fault weakening. The yielding result will be conductive to better understanding the role of decarbonation of calcite in some active fault zones.

Crystallization and thermal stability of Ni-based metallic glass with high tungsten and boron

Non-isothermal crystallization behavior of the amorphous (Ni51W31.6B17.4)75Co25 alloy with high tungsten and boron content was investigated. Continuous heating DSC analyses of the amorphous samples revealed that the alloy undergoes crystallization with three-step. The thermal stability and crystallization kinetics of the samples were evaluated by Lasocka, Kissinger and Ozawa approaches. Activation energy calculated for the first crystallization step showed that the thermal stability of the NiCoWB alloy is higher than other Ni-based alloys. Avrami exponent value calculated for the early stage of the Niss-phase crystallization indicated a three-dimensional diffusion-controlled mechanism with increasing nucleation. The continuous heating transformation diagram plotted according to non-isothermal analyzes is consistent with the phases detected in isothermal heat treatments. The usability of the continuous heating transformation diagram of the alloy in isothermal heat treatment applications has been demonstrated.

Evaluation of static recrystallization and grain growth kinetics of hot-rolled AZ31 alloy

The static recrystallization/grain growth kinetics of the AZ31 (Mg-3Al-1Zn, wt%) alloy were investigated employing Vickers microhardness and electron backscatter diffraction (EBSD) measurements. The AZ31 alloy was subject to a hot-rolling for 70% of thickness reduction and then annealed at various temperatures (150°C, 250°C, and 350°C) from 5 min to 24 h. First, the static recrystallization kinetics were analysed by means of the Johnson-Mehl-Avrami-Kolmogorov (JMAK) model. The results showed that the recrystallization occurred under two regimes both involving their own Avrami exponent/ activation energy. In regime I, the Avrami exponent was found in the range of 1.5-0.35 depending on the annealing temperature and activation energy of 74.1±5.7 kJ×mol-1. In regime II, an identical value of Avrami exponent was found (0.1-0.2) and a very low activation energy of 14.8±0.7 kJ×mol-1 was found for all annealing conditions. Non-random nucleation sites such as shear bands were considered as the main factor responsible for the deviation from the JMAK model. Moreover, the grain growth kinetics was well fitted by the general equation where . Accordingly, Qg = 109± 0.2 kJ×mol-1 which is median between grain boundary diffusion and bulk diffusion values for Mg and its alloys. The derived activation energies were discussed in terms of influencing factors such as solute drag, formation of basal texture, and microstructural heterogeneities like shear bands and twinning.

Phase transformation and crystallization study of Se100-xBix glassy alloys

Bulk Se100-xBix(x = 0, 5 and 10) glassy compositions were synthesized by the quenching method. The ingot materials were studied by X-ray diffraction, which was used to investigate the structure of the prepared compositions. Differential thermal analysis (DTA) under non-isothermal conditions was used to determine the transition temperatures, activation energies and responses of stability using various models such as Kissinger, Matusita, and Goa-Wang at four different heating rates. For a better understanding of the growth mechanism, the Avrami exponent (n) and the dimensionality of growth (m) have been studied. For the studied system, the obtained Avrami exponent values suggest surface nucleation with one-dimensional growth. The obtained results indicate that the thermal stability of the glassy samples decreases with increasing Bi content.

Effect of plastic deformation on the precipitation reaction in 2024 alloys

The plastic deformation effect on activation energy, transformed volume fraction, and Avrami exponent for the phase precipitation in a 2024 aluminum alloy was evaluated in this study. Differential scanning calorimetry characterization was carried out in deformed and non-deformed samples, focusing on the study of S phase precipitation (Al2CuMg precipitates with orthorhombic structure, space group Cmcm, and lattice parameters a = 4.03 Å, b = 9.3 Å, c = 7.08 Å). The results show that the solid-state reactions were activated, kinetically controlled, and modified by the plastic deformation. The enthalpy changes, activation energy, and peak temperature shifting confirm that the applied deformation alters the reaction sequence. Two different Avrami exponent values were found, one close to 1.7, which indicates that nucleation occurs in preexisting nucleation sites, and the other near 1.3, which corresponds to phase transformation driven by diffusion mechanisms.

Effect of Nb minor addition on the crystallization kinetics of Zr-Cu-Al-Ni metallic glass

The crystallization kinetics of Zr55Cu30Al10Ni5 and (Zr55Cu30Al10Ni5)98Nb2 melt-spun metallic glasses in non-isothermal and isothermal conditions were studied by differential scanning calorimetry. According to the non-isothermal and isothermal conditions, the crystallization activation energy for the Nb-containing sample is lower than the Nb-free sample, suggesting that crystallization transformation becomes easier by Nb microalloying. The time-temperature-transformation (TTT) diagrams demonstrate that the Nb minor addition delays the onset of crystallization by shifting the incubation time to longer times, but then accelerates the crystallization progress by shortening the endset time of crystallization, yielding a narrower crystallization transformation region. The Avrami exponents for both non-isothermal and isothermal conditions have larger values in Nb-containing sample, revealing increased nucleation rates in this glassy alloy. In the isothermal condition, the Avrami exponent values in both alloys are either above or below 2.5, indicating that the governing crystallization mechanism is diffusion-controlled three-dimensional growth with either decreasing or increasing nucleation rate.

Studies of crystallization kinetics and optical properties of ZnO films prepared by sol–gel technique

The crystallization of ZnO prepared by sol–gel technique was investigated under nonisothermal conditions by differential scanning calorimetry (DSC) and prediction isothermal method. The transformation from the amorphous to crystalline state was investigated by X-ray diffraction (XRD). The influence of the annealing temperature on the structure of the ZnO was studied by Filed Emission Scanning Electron Microscopy (FESEM) and Atomic Force Microscopy (AFM). Two exothermic changes were reported between the temperature ranges 590–710 K and 645–750 K for first and second transition, respectively. The isoconversional methods of Friedman, Ozawa and Flynn and Wall (FWO), Kissinger–Akahira–Sunose and the Vyazovkin (minimizing) were used to determine the variation of the effective activation energy with the extent of crystallization, Eα (α) and hence, with temperature Eα (T). In addition, the activation energy was calculated from predicted isothermal results. Analysis of the obtained data shows that the activation energy of crystallization is not constant but varies with the degree of conversion and, hence, with temperature. The value of the local Avrami exponent, n (α), varies within 1.88–1.97 for isothermal study and within 2.35–2.4 for nonisothermal process. By using the Johnson–Mehl–Avrami (JMA) model, a good fit was achieved between experimental and theoretical calculation of the reaction (crystallization) rate. The optical energy gap decreased with increasing annealing temperature.

Kinetics and phase formation during crystallization of Hf64Cu18Ni18 amorphous alloy

ABSTRACT In this work, crystallization kinetics and phase formation of the Hf64Cu18Ni18 glassy ribbon were studied. It was observed that the ribbon crystallizes via two exothermic peaks. Further, the activation energy (E a) corresponding to each peak was calculated by Kissinger and Augis–Bennett methods. These methods showed nearly similar values of E a. The crystallization product of ribbon was identified by X-ray diffraction and discussed in view of prediction using the CALculation of PHAse Diagram (CALPHAD) approach. The identified phases indicate that the HfNi and Hf2Cu, Hf2Ni are formed after the first and second exothermic crystallization peaks, respectively. Further, the Avrami exponent (n) was calculated as 1.2 and 1.4 for the first and second crystallization peaks, respectively. Avrami exponent values show that crystallization takes place at non-random nucleation sites with either one or two-dimensional growth.

Non-isothermal crystallization kinetics of paraffin wax as a phase changing energy storage material

Paraffin waxes are becoming increasingly attractive especially on thermal energy storage field. The crystallization process, considered as a major thermal discharging approach, has a significant impact on the thermal performances of paraffin wax. This study aims to comprehend the mechanism of paraffin wax crystallization under non-isothermal conditions by means of Differential Scanning Calorimetry (DSC). Jeziorny and Mo models were applied to reveal the morphology of paraffin wax crystals. Moreover, the non-isothermal crystallization activation energy was calculated through Kissinger and Friedman methods, respectively. Investigations show that the used kinetics models gratifyingly fitted the experimental data, providing crystallization kinetic parameters such as crystallization rate, half-life time (t1/2) as well as the required cooling rate for a designated relative crystallinity. Furthermore, it was found that the average Avrami exponent value is close to 2 which indicates that the crystals are one-dimensional with needle-like morphologies.

Isokinetic Analysis of Fe41Co7Cr15Mo14Y2C15B6 Bulk Metallic Glass: Effect of Minor Copper Addition.

In the present study, (Fe41Co7Cr15Mo14Y2C15B6)100−xCux (x = 0, 0.25 and 0.5 at.%) amorphous alloys were prepared by copper-mold casting. To clarify the effect of the minor addition of copper on the mechanism of nucleation and growth during the crystallization process, an isokinetic analysis was performed. The activation energies (E) of the various crystallization stages were calculated by using theoretical models including Kissinger–Akahira–Sunose (KAS), Flynn–Wall–Ozawa (FWO), Augis–Bennett and Gao–Wang methods. In addition, Augis–Bennett, Gao–Wang and Matusita methods were used to investigate the nucleation and growth mechanisms and to determine other kinetic parameters including Avrami exponent (n), the rate constant (Kp) and dimensionality of growth (m). The obtained results revealed that the activation energy—as well as thermal stability—was changed with minor addition of copper. In addition, the obtained Avrami exponent values were confirmed by Johnson–Mehl–Avrami–Kolmogorov (JMAK) method. The research findings demonstrated that the value of Avrami exponent is changed with minor addition of copper, so that the Avrami exponents of all crystallization stages, except the second peak for copper-free amorphous alloy, were equal to integer values ranging from two to four, indicating that the growth mechanisms were controlled by interface. Moreover, the kinetic parameters of n and b for all peaks were increased by an increase in crystallization temperature, which can be attributed to the increase in the nucleation rate.

Precipitation kinetics of Ti3Ni4 and multistage martensitic transformation in an aged Ni–rich Ni–Ti shape memory alloy

The precipitation kinetics of Ti3Ni4 in a Ti–51.0 at.% Ni alloy was studied through the martensitic transformations temperatures and the JMAKE model. The influences of different aging temperatures and aging time on martensitic transformations temperatures were investigated using differencial scanning calorimetry and X–ray diffraction. The Ti3Ni4 precipitation is more preferred at aging temperatures between 350 and 450 °C for 1 h. At these aging temperatures, the martensitic transformation occurred in 4 stages due to Ti3Ni4 heterogeneous nucleation. The obtained Avrami exponents suggests that Ti3Ni4 precipitation has unidimensional growth, is diffusion controlled, and presents nucleation site saturation before complete precipitation. Also, heterogeneous nucleation explains why Avrami exponent values were lower than theoretically expected for JMAKE model. The apparent activation energy estimated for Ti3Ni4 precipitation was 108 (± 8) kJ/mol, and the frequency factor 5.1 (± 4.2) 104 s−1. MET and EDS techniques confirmed the presence of Ti3Ni4 precipitates through morphological and chemical characterization. The estimated Ti3Ni4 volumetric fractions at metastable equilibrium were 12.5, 11.4, and 9.2% for 350, 400, and 450 °C, respectively.

Influence of substitution of Cu by Ni on the crystallization kinetics of TiZrHfBeCu high entropy bulk metallic glass

The crystallization kinetics of TiZrHfBe(Cu, Ni) high entropy bulk metallic glasses have been studied using differential scanning calorimetry. Each alloy possesses a complex multi-step crystallization process due to the high entropy effect. It was found that substitution of Cu by Ni significantly improves the glass-forming ability but deteriorates the thermal stability of the TiZrHfBeCu alloy. The activation energies of glass transition and crystallization together with the fragility parameter for the Ni-free and Ni-containing alloys have been calculated. According to the calculated values of local Avrami exponent, the first crystallization event for the studied TiZrHfBe(Cu, Ni) alloys is dominated by a direct growth of crystal nuclei. Substitution of Cu by Ni favors the precipitation of Ni-containing intermetallic compounds and inhibits the formation of CuHf2 phase, resulting in the improvement of glass-forming ability.

Effect of Bis (2-Aminoethyl) Adipamide/Adipic Acid Segment on Polyamide 6: Crystallization Kinetics Study.

The crystallization behavior of novel polyamide 6 (PA6) copolyamides with different amounts of bis (2-aminoethyl) adipamide/adipic acid (BAEA/AA) segment was investigated. The wide-angle X-ray diffraction (WAXD) results showed that as the amount of BAEA/AA segment increased to 10 mole%, the crystalline forms of all PA6 copolyamide were transferred from the stable α-form to the unstable γ-form because of the complex polymer structure. According to studies of crystallization kinetics, the Avrami exponent (n) values for all copolyamide samples ranged from 1.43 to 3.67 under isothermal conditions, implying that the crystallization is involved in the two- to three-dimensional growth at a high temperature of isothermal condition. The copolyamides provided a slower crystallization rate and higher crystallization activation energy (ΔEa) than neat PA6. Polyamide containing 10 mole% of BEAE/AA content exhibited a unique crystallization behavior in the coexistence of the α and γ forms. These results deepen our understanding of the relationship between BAEA/AA content, crystal structure, and its crystallization behavior in low-melting PA6, and they make these types of copolyamides useful for their practical application.

Crystallization kinetics and growth mechanism of 0.5 (Ba0.85 Ca0.15) TiO3−0.5 Ba (Zr0.1 Ti0.9) O3 powders prepared via solid-state reaction

ABSTRACTThe crystallization kinetics of 0.5 (Ba0.85 Ca0.15) TiO3−0.5 Ba (Zr0.1 Ti0.9) O3 (BCZT) powders, synthesized using conventional solid-state reaction, was investigated by differential scanning calorimetry (DSC) in both non-isothermal and isothermal conditions. In non-isothermal mode, the samples were heated from room temperature to ∼1200°C at various heating rates (2.5, 5, 10 and 15°C/min). In isothermal mode, the powders were firstly heated to 823,833 and 838°C and maintained at those temperatures until complete crystallization. The X-ray diffraction analysis (XRD) confirmed the formation of single perovskite phase. The kinetic parameters of the crystallization of BCZT powders were determined using model-free methods. The application of Johnson–Mehl–Avrami model yields a growth index of 0.5 and an average value of avrami exponent of 2.5, indicating a growth of BCZT particles by diffusion-controlled mechanism with a constant nucleation rate.