Crystallization Activation Energy Research Articles

Composites made of Ginkgo biloba fibers and polylactic acid exhibit non-isothermal crystallization kinetics

Polymer crystallization affects material microstructure and the final product quality, and the crystallization kinetics that govern this process are critical. In this study, alkali-treated Ginkgo biloba fibers (GFs) were melt blended with polylactic acid (PLA) to obtain GF/PLA blends. The non-isothermal crystallization kinetics of the GF/PLA composites were subsequently investigated using the Avrami, Jeziorny, Ozawa, and Liu-Mo methods, and the crystallization activation energies of the systems were calculated by Kissinger and Friedman models. The results showed that the GFs significantly promoted PLA crystallization, accelerated the crystallization rate, and shortened the crystallization time. The Avrami method showed some deviation from the linear relationship due to the effect of secondary crystallization, while the numeric value obtained by the Jeziorny method increased with the cooling rate. The Ozawa method could only be used in a very narrow range of temperatures, while the Liu-Mo method showed a more desirable fit. Crystallization activation energy calculations showed that the GFs promoted an increase in the crystallization capacity of the blend and a decrease in the effective potential barrier. This resulted in more selective biocomposites than pure PLA, offering greater applicability in domains including tissue engineering and 3D printing.

Crystallization kinetics of Sb70Se30 thin films for phase change memories under the non-isothermal conditions

We investigate the non-isothermal crystallization kinetics of Sb70Se30 thin films using differential scanning calorimetry and determine the kinetic triplet of Sb70Se30 thin films at various heating rates by combining model-free and model-fitting approaches. The results indicate that the crystallization activation energy decreases with increasing crystallization fraction α, confirming the presence of multi-step crystallization mechanism. In accordance with the local Avrami index n(α), the crystallization mechanism shifts from three-dimensional growth with an increased nucleation rate at 0.05 ≤ α ≤ 0.8 to three- and two-dimensional growth with a reduced nucleation rate at α＞0.8. Afterwards, we deduce that the Sb70Se30 thin films follow a second-order reaction model within the heating rate range of 20 to 40 K/min. Moreover, the Sb70Se30 thin film shows excellent data retention capability when predicting data processing and data storage time based on phase change memory units. These findings provide valuable insights into the crystallization kinetics of Sb70Se30 thin films, contributing to the advancement of phase change materials.

Effect of the SiO2/Na2O ratios on the structure and crystallization properties of photo-thermo-refractive glass

Photo-thermo-refractive (PTR) glass is a type of functional optical glass material with multi-component and multivalent particles, which is a substrate material for volume Bragg gratings (VBGs) and widely used in high power laser, holography and other applications. Recording VBGs in PTR glass involves photo-thermo-induced crystallization (UV exposure and subsequent heat treatment), while spontaneous crystallization in the unexposed area is one of the important reasons for the light scattering loss of PTR glass, which can also lead to a decrease in the refractive index modulation and absolute diffraction efficiency of the prepared VBGs. In order to optimize spontaneous crystallization of PTR glass, we analyzed the effects of variations in the SiO2/Na2O ratio on the structure and crystallization behaviors of SiO2–Na2O–Al2O3–ZnO–NaF PTR glass using Raman spectroscopy, FTIR spectroscopy, DSC, XRD, and SEM. As the molar ratio (Rm) of SiO2/Na2O increases from 3.37 to 5.38, the polymerization of the silica network structure is significantly enhanced, the crystallization activation energy of original PTR glass increases from 93.52 kJ/mol to 285.23 kJ/mol, and the crystal growth index decreases from 3.57 to 1.49. In the isothermal crystallization process, we observed that increasing the SiO2/Na2O ratio significantly decreases the grain density and homogenizes the grain distribution of sodium fluoride (NaF) crystals under long-time crystallization conditions, which contributes to maintaining the high transmittance of the crystallized PTR glass in both visible and near-infrared regions.

Study on the structure and optical properties of the Tb3+-doped SrO–MgO–SiO2–TiO2–B2O3 glasses

In this investigation, Tb3+-doped SrO–MgO–SiO2–TiO2–B2O3 glasses were prepared using the melting-cooling technique. The amorphous nature of the glass was confirmed through XRD analysis. The thermodynamic parameters of the glass were determined by DSC testing, and the crystallization activation energy was calculated. Using infrared spectroscopy, the network structure of the glass was investigated. At 376 nm excitation, the emission spectrum was obtained, which contained six emission bands: 415 nm (5D3→7F5), 437 nm (5D3→7F4), 489 nm (5D4→7F6), 545 nm (5D4→7F5), 586 nm (5D4→7F4) and 623 nm (5D4→7F3). With the increase of Tb2O3 ion-doping concentration, the emission intensity of the 5D3 excited state decreases gradually, while that of the 5D4 excited state increases gradually. Also measured were the lifetimes of Tb3+: 5D3 and 5D4 fluorescence decay. The luminescence of the glass falls within the green region of the CIE chromaticity coordinates, and the correlated color temperature index indicates that the luminescence is pale green. The results show that the Tb3+ doped SrO–MgO–SiO2–TiO2–B2O3 glasses system has a potential application prospect in the field of green light display.

Crystallization kinetics from Ge-rich Ge–Sb–Te thin films: Influence of thickness

The phase transition temperature and crystallization kinetics of phase-change materials (PCMs) are crucial characteristics for their performance, data retention, and reliability in memory devices. Herein, the crystallization behavior and kinetics of a compositionally optimized, N-doped Ge-rich Ge–Sb–Te alloy (GGST) in the slow crystallization regime are systematically investigated using synchrotron x-ray diffraction (XRD) in situ during heat treatment. Uniform thin films (50, 25, 10, and 5 nm) of initially amorphous N-doped GGST are investigated. The specimens were heated up to 450 °C at a rate of 2 °C/min to estimate crystallization onsets by quantifiying the crystallized quantity during material transformation from the XRD patterns. Subsequent isothermal anneals have been performed to assess crystallization behavior and activation energies. Nucleation-controlled crystallization that progresses in two steps is observed, together with the emergence of Ge preceding cubic Ge2Sb2Te5, with a mild dependence of crystallization temperature on film thickness that is inverse to what has been observed in other systems. Ge and GST crystallization may be described occurring in three-time stages: (i) an incubation period; (ii) a fast growth period; and (iii) a very slow-growth period. Very high activation energies (between 3.5 and 4.3 eV) for each phase are found for the incubation time t0. The activation energy for Ge in the fast growth regime is close to the one reported for the crystallization of pure Ge films. In the case of Ge, the incubation time is strongly thickness-dependent, which may have important consequences for the scaling of memories fabricated with this class of materials.

Designing mould fluxes to prevent longitudinal cracking for peritectic steel slab casting

ABSTRACT During continuous casting of hypo-peritectic steel slabs, control of horizontal heat transfer rate in mould is important to avoid longitudinal cracks. This rate can be manipulated by mould slag crystallization. From an industrial situation where the longitudinal cracking index was too high, a new mould flux was designed with appropriate crystallization kinetics. The mould flux crystallization process was analysed in laboratory through differential scanning calorimetry. The Friedman isoconversional method was applied to determine the activation energy of crystallization from melt. Besides, a new quick test was developed to evaluate crystallization kinetics. The industrial tests have shown that the new mould flux decreases the longitudinal cracking index, and this is related to the decrease of horizontal heat transfer rate during the continuous casting process, which in turn is related to crystallization from mould slag.

A method locating Cu-Ti-based glass formers using Ni-Zr binary clusters

Formation abilities and mechanical properties are essential for the application of amorphous alloys. In this work, the concept of similar elements has been expanded to similar clusters. Firstly, taking the topologically dense packed clusters Ni-Ni6Zr6 from the Ni-Zr system as the basic structural unit, a series of Cu-Ti-based alloy compositions with high formation ability are parsed and designed. The best composition is Cu46.15Ni7.69Ti32.70Zr13.46 with the cluster expression of Ni-Cu6Zr1.75Ti4.25. Then, the amorphous formation abilities are analyzed from the perspective of the packing degree of clusters and the mixing entropies. Secondly, the crystallization activation energies for characteristic temperatures deduced by Kissinger's approach are analyzed. Finally, the plasticity of Cu-Ti-based amorphous alloys is investigated and Cu46.15Ni7.69Ti32.70Zr13.46 exhibits outstanding fracture strength of 2168 MPa. The results in this paper lay the foundation for further exploration of amorphous alloys with high formation ability, good thermal stability, and high compressive plasticity.

Melting and Crystallization Behaviors of Mold Flux with the Addition of Waste Electrolyte

The influence of waste fluoride electrolyte addition on key properties of mold flux is investigated, with the aim to convert the hazardous waste in electrolytic aluminum industry into treasure in steel industry. The results show that the initial melting temperature of mold fluxes decreases from 1614.40 K (1341.40 °C) to 1564.67 K (1291.67 °C), and the complete melting temperature decreases from 1704.45 K (1431.45 °C) to 1674.34 K (1401.34 °C) with the addition of waste electrolyte from 10.08 to 24.89 wt%. The crystallization of mold flux is enhanced, and its crystallization mechanism transforms from “constant nucleation rate and 2D growth” into “constant nucleation number and 3D growth” with the addition of waste electrolyte. The main precipitated crystals in mold fluxes are grossular (Ca3Al2(SiO4)3) and CaF2, but the phase transforms into gehlenite (Ca2(Al(AlSi)O7) at higher temperature. In addition, the crystallization activation energy is 13.80, 12.40, 12.01, 11.03, and 10.27 kJ mol−1, respectively, which further confirms that the addition of waste electrolyte can reduce the energy barrier of crystallization and promote the crystallization ability of mold flux.

Dynamic heterogeneity and mechanical relaxation of Ti20Zr20Cu20Ni20Be20 high-entropy metallic glass probed by quasi-elastic neutron scattering and stress relaxation

Heterogeneity is an intrinsic property of metallic glasses (MGs) and is closely related to their physical properties. Relaxation dynamics provides a powerful approach to understanding the heterogeneity of MGs. State-of-the-art quasi-elastic neutron scattering (QENS) and stress relaxation are used to study the atomic relaxation dynamics, dynamic heterogeneity, diffusion coefficients and mechanical relaxation of Ti20Zr20Cu20Ni20Be20 high-entropy metallic glass (HE-MG). The dynamic susceptibility derived from the QENS self-intermediate scattering function was used to evaluate the presence of dynamic heterogeneity, which increases gradually with decreasing temperature. The average self-diffusion coefficient of Ni and Ti atoms in the Ti20Zr20Cu20Ni20Be20 HE-MG melt is much higher than that in the Ti13.8Zr41.2Cu12.5Ni10Be22.5 Vit1 MG melt. The Ti20Zr20Cu20Ni20Be20 HE-MG melt has higher atomic mobility with respect to the Vit1 MG melt. In addition, the activation energy for crystallization of the Ti20Zr20Cu20Ni20Be20 HE-MG is considerably larger than that of the Vit1 MG. In the stress relaxation test, both Ti20Zr20Cu20Ni20Be20 HE-MG and Vit1 MG exhibit a relaxation decoupling phenomenon, indicating a two-step relaxation process. The slow and fast relaxation processes of the two alloy ribbons have a stretched exponential decay. At the measured temperatures, the relaxation times for both of the relaxation processes for the Ti20Zr20Cu20Ni20Be20 HE-MG are larger than those for the Vit1 MG, meaning that the Ti20Zr20Cu20Ni20Be20 ribbon has a slower stress decay. This in-depth investigation will improve our understanding of the intrinsic heterogeneity and mechanical relaxation mechanism in HE-MG.

Nanocrystallization of Cu46Zr33.5Hf13.5Al7 Metallic Glass

The recently discovered Cu46Zr33.5Hf13.5Al7 (at.%) bulk metallic glass (BMG) presents the highest glass-forming ability (GFA) among all known copper-based alloys, with a record-breaking critical casting thickness (or diameter) of 28.5 mm. At present, much remains to be explored about this new BMG that holds exceptional promise for engineering applications. Here, we report our study on the crystallization behavior of this new BMG, using isochronal and isothermal differential scanning calorimetry (DSC), X-ray diffraction (XRD), and transmission electron microscopy (TEM). With the calorimetric data, we determine the apparent activation energy of crystallization, the Avrami exponent, and the lower branch of the isothermal time–temperature–transformation (TTT) diagram. With XRD and TEM, we identify primary and secondary crystal phases utilizing samples crystallized to different degrees within the calorimeter. We also estimate the number density, nucleation rate, and growth rate of the primary crystals through TEM image analysis. Our results reveal that the crystallization in this BMG has a high activation energy of ≈360 kJ/mole and that the primary crystallization of this BMG produces a high number density (≈1021 m−3 at 475 °C) of slowly growing (growth rate < 0.5 nm/s at 475 °C) Cu10(Zr,Hf)7 nanocrystals dispersed in the glassy matrix, while the second crystallization event further produces a new phase, Cu(Zr,Hf)2. The results help us to understand the GFA and thermal stability of this new BMG and provide important guidance for its future engineering applications, including its usage as a precursor to glass–crystal composite or bulk nanocrystalline structures.

Glass transition temperatures and crystallization kinetics of a synthetic, anhydrous, amorphous calcium-magnesium carbonate.

We report the first calorimetric observations of glass transition temperatures and crystallization rates of anhydrous, amorphous calcium-magnesium carbonate using fast scanning differential scanning calorimetry. Hydrous amorphous Ca0.95Mg0.05CO3 · 0.5H2O (ACMC) solid was precipitated from a MgCl2-NaHCO3 buffered solution, separated from the supernatant, and freeze-dried. An aliquot of the freeze-dried samples was additionally dried at 250°C for up to 6 h in a furnace and in a high-purity N2 atmosphere to produce anhydrous ACMC. The glass transition temperature of the anhydrous Ca0.95Mg0.05CO3 was determined by applying different heating rates (1000-6000 K s-1) and correcting for thermal lag to be 376°C and the relaxational heat capacity was determined to be Cp = 0.16 J/(g K). Additionally, the heating rate dependence of the temperature that is associated with the corrected crystallization peaks is used to determine the activation energy of crystallization to be 275 kJ mol-1. A high-resolution transmission electron microscopy study on the hydrous and anhydrous samples provided further constraints on their compositional and structural states. This article is part of the theme issue 'Exploring the length scales, timescales and chemistry of challenging materials (Part 1)'.

Production of glass-ceramics from MSW-fly ash and Dexing copper mine-tailing: Crystallization kinetics, structure, properties and immobilization of heavy metals

To reduce the environmental pollution from MSW-fly ash and Dexing copper mine-tailing and realize their maximum utilization, this research used them to synthesize novel eco-friendly glass-ceramics. Effects of different nucleation-crystallization temperatures on the crystal evolution, microstructure, properties, leaching behavior of heavy metals were discussed. The findings indicate that the crystallization activation energy E is 381 kJ/mol, and the crystallization mechanism is two-dimensional crystallization controlled by diffusion with an increasing nucleation rate. The difference in the nucleation-crystallization temperature will affect the precipitation and growth of crystal (CaAl2Si2O8) in this glassy system, and further affect the microstructure and properties of the prepared glass-ceramics. Furthermore, because the glass-ceramics is the combination of glass and crystal, an obvious immobilization effect for heavy metals Fe, Mn and Cr can be obtained in our glass-ceramics. Apart from the high immobilization efficiencies for heavy metals, our glass-ceramics also show low density (2.715–2.761 g/cm3) and water absorption (0.026–0.045%), high Vickers hardness (5.72–6.39 GPa), good chemical stability (kH2SO4: 3.68–28.72%, kNaOH: 0.01–0.96%), which confirms the potential and feasibility of the MSW-fly ash-Dexing copper mine-tailing-derived glass-ceramics as building decoration material.

Preparation and Properties of MgO-Al2O3-SiO2 Glass–Ceramics with Controllable Crystalline Phases

MgO–Al2O3–SiO2 (MAS) glass–ceramics with controllable crystalline phases were successfully prepared using the melting method followed by heat treatment. The effects of the main components of glass on the crystallisation kinetics, nucleation, crystallisation and properties of glass–ceramics were investigated in detail. As the Al2O3 and MgO contents increase and SiO2 content decreases, the crystallisation peak temperature and activation energy of MAS glass decrease, while the crystal growth tends to follow a homogeneous nucleation crystallisation. The MAS glass nucleation temperature and time increase with higher concentrations of Al2O3 and MgO and with a lower SiO2 concentration. Mg2(Al4Si5O18) indialite and MgAl2O4 spinel precipitate simultaneously in the MAS glass after crystallisation; the relative proportion of crystalline phases is related to the composition and crystallisation temperature. A higher SiO2 content allows the formation of a dominant indialite phase, while higher MgO and Al2O3 contents promote the formation of a dominant spinel phase. The MAS glass ceramic with a greater indialite phase has good dielectric properties with a dielectric constant of 6.499 and dielectric loss of 0.0064, while that of a higher spinel phase possesses improved mechanical properties, with a Vickers hardness of 715 Hv and a bending strength of 244.9 MPa.

2,5-Tetrahydrofurandimethanol as a sustainable comonomer for modification of polyethylene terephthalate: Liter-level pilot test and non-isothermal crystallization kinetics

2,5-tetrahydrofurandimethanol (THFDM), which is an alicyclic diol in products of 5-hydroxymethylfurfural (HMF), is a sustainable monomer to protect environment for replacing the role of isophthalic acid (IPA) and 1,4-cyclohexanedimethanol (CHDM) which were optimized polyethylene terephthalate (PET) performance. By direct esterification method, poly (ethylene-co-tetrahydrofurandimethanol terephthalate) (PETT) was synthesized in 2.5 L reactor. The results showed that the contents of THFDM in copolyester were less than that feeding ratio attributed to its lower reaction reactivity. The color of PETT slightly turned yellow. PETT performed broader processing temperature window, while Tg maintained in good range because of the cyclic structure of THFDM. Especially, the cold crystallization occured in PETT but not in PET after finishing melt crystallization. Otherwise, the thermal stability and crystal structure of PETT remained the same as PET. The crystallization activity of PETT became significantly lower than PET. What proved THFDM was effective in reducing PET crystallinity was that crystallization kinetics using Jeziorny theory and the trend of activation energy of melt crystallization which was calculated by Friedman method. And PETT-2 fibre had comparable mechanical property to PET fibre. In the advancement of green chemistry, THFDM has added a choice of cyclic bio-based comonomers.

Synthesis and Electrical Behavior of Sodium Doped Monoclinic SrSiO3

The operating temperature of solid oxide fuel cells, oxygen division membranes, and oxygen sensors is determined by oxide-ion electrolytes. There is a strong incentive to reduce the operating temperature in solid oxide fuel cells, from 800°C to 500°C. The use of low-cost Na+ instead of K+ as dopant in monoclinic SrSiO3 offers a wider solid solution range (0.1<x< 0.5) in Sr1-xNaxSiO3-δ and obtains an oxide ion conductivity of 10-2 Scm-1 at 600°C, reducing the temperature of a smooth transition to full impairment of mobile oxide ions. For electrochemical characterization, the flat surfaces of the pellets were pasted with silver (Ag) paste and then sintered at 1200°C for 24 hours. The production of the Na2Si2O5 phase was observed for most compositions due to thermal treatment. Crystallization of Na2Si2O5 from glass was obtained in single-step calcination at 850°C after synthesis in an acetone medium, resulting in the highest conductivity. Although double calcination reduced conductivity, it improved thermal stability. Due to its low activation energy and lack of crystallization of other silicates, this material showed maximum conductivity after long-standing maturity at 600°C. Ethanol was used in place of acetone for powder assimilation and double calcination was also performed.

A comparative study on nanocrystalline soft magnetic Fe-Si-B-Nb-Cu alloys made of pure elements and ferro-alloys

In the present study, we report a cost-effective method of flux-shielded air induction melting using commercial grade master alloys to produce nanocrystalline soft magnetic Fe73.5Si13.5B9Nb3Cu1 alloy. For comparison, the alloy was made from highly pure raw materials as well. The structure and soft magnetic properties of the commercial grade alloy is similar to the pure one. Air induction melting process with flux not only removed impurities through chemical reactions, it also provided protection from oxidation. Studies of glass formation through experimental findings and Glass Forming Ability (GFA) calculations through ΔT value, α-parameter and PHSS parameter and studies using Calphad (Calculation of Phase Diagram) method have shown that the impurities present in the commercial grade alloy did not affect the glass formation compared to the pure grade alloy. Impurities present in the commercial grade alloy increase the activation energy of crystallization of Fe3Si phase, which in turn influences the volume fraction and grain size of Fe3Si phase during annealing treatment. Amorphous phase TC was found to decrease due to the impurities present in the amorphous phase and this decreased exchange interaction between Fe-Fe atoms. Saturation magnetization and coercivity of commercial grade alloy are almost equivalent to the alloys prepared with pure elements and they are independent of type and concentration of impurities. Lowest coercivity in commercial grade alloy can be achieved in less annealing time which can lead to increase the productivity and reduce the cost further.

Crystallization and microwave dielectric properties of novel CaO-Al2O3-B2O3 glass-ceramics with different Al2O3 content

CaO-Al2O3-B2O3 (CAB) glass-ceramics with varying Al2O3 content were fabricated using the melting method including melting and quenching of mixture of raw materials. The obtained glass powder was pressed into the desired shape and sintered for measurement. At 900 °C, the crystallinity initially increased and then decreased with increasing Al2O3 content. The highest crystallinity of 62.29 % was obtained when the Al2O3 content was 0.5 mol%, and exhibited excellent dielectric properties: εr = 4.35, Q × f = 53,085 GHz, and τf = –33.95 ppm/°C. The variation of dielectric properties with increasing Al2O3 content is attributed to the crystallinity process. The crystallization process of CAB system was determined by crystallization activation energy, the lowest value of 302.085 kJ/mol corresponds to the highest crystallinity. The crystallization, dielectric properties and sintering behavior of CAB system indicate that CAB system prepared by melting method have promising prospect as new LTCC glass-ceramics.

Tuning energy storage and light transmittance properties in ZrO2-modified Na2O–K2O–Nb2O5–SiO2 glass-ceramics

Crystallization kinetics in ZrO2-modified glass-ceramics, (35-x)Na2O–5K2O–40Nb2O5–20SiO2-xZrO2 (x = 0, 1, 3, 5, 10 mol%), is analyzed by crystallization activation energy Ec and kinetic parameter k. A large kinetic parameter k of 1.657 × 1025 is found for the sample with x = 1, which indicates a high tendency toward crystallization. NaNbO3 is formed as the major phase, and its crystallinity changes significantly by the addition of ZrO2. It is found that the dielectric permittivity and maximum polarization are affected by crystallinity. Large domains are formed, and a relaxation process appears at high frequencies. In addition, the breakdown strength (BDS) is affected by the strong electric field distortion rather than the resistance in this system. Complex impedance analysis shows that resistance decreases with the addition of ZrO2. The electric field distortion of the glass-ceramics is simulated by COMSOL. A low interfacial polarization activation energy Ea of 0.821 eV is achieved by the addition of ZrO2. The maximum pulse power density reaches 90 MW/cc at 350 kV/cm for the sample with x = 10, and the pulse energy density attains 0.91 J/cm3 at 300 kV/cm for the sample with x = 1. Light transmittance is achieved because of the low crystallinity and the disappearance of cristobalite SiO2 in the Na2O–K2O–Nb2O5–SiO2 glass-ceramics.

Preparation of glass-ceramic by low-pressure hot-pressing sintering of CaO-MgO-Al2O3-SiO2(-CaCl2) glass powder

CaCl2 can dissolve in the silicate glasses, and thus, using the CaCl2-bearing glass for the preparation of glass-ceramic could be a potential method for treating CaCl2-bearing wastes. In this work, two kinds of glass powders, CaO-MgO-Al2O3-SiO2 and CaO-MgO-Al2O3-SiO2-CaCl2, were sintered at 825–850 ℃ to prepare the glass-ceramic. Besides, a low-pressure (19.1kPa) hot-pressing sintering technology was applied to reduce the porosity and pore size of the glass-ceramic. The addition of CaCl2 (5 wt%) reduced the polymerization degree, glass transition temperature, crystallization peak temperature, and crystallization activation energy of the glass. Augite was the main crystalline phase of the glass-ceramic, and the addition of CaCl2 promoted the precipitation of anorthite. The glass-ceramic prepared from the Cl-containing glass always exhibited a higher bending strength than that obtained from the Cl-free glass. When sintered at 825 ℃ for 8 h, the glass-ceramic showed the highest bending strength of 171 MPa.

Crystallization kinetics in a lithium disilicate glass revisited: Model-free and model-fitting approaches

The present work estimated the crystallization activation energy, Eα, the pre-exponential term, A, and the reaction model, g(α), of a lithium disilicate glass using model-free and model-fitting approaches. Samples with distinct granulometry (PD1: < 105 μm; and PD5: 600–850 μm) were heated at several rates (0.5 to 30 K/min). Our results show that Eα, A, and g(α) are susceptible to particle size. PD1 crystallizes in a single step, and the surface mainly governs it all β values. On the other hand, the overall crystallization of PD5 is more complex and can be described by different Avrami reaction models, with n = 1, 1.5, 2, and 3. In addition, we found that the crystallized fraction at the crystallization peak (αTp) varies significantly with the particle size and heating rate, which confirms that all the methods that assume that the αTp is constant are inadequate to describe the crystallization of glasses over a wide range of heating rates.