Avrami Exponent Values Research Articles

Nanocrystallization kinetics understood as multiple microprocesses following the classical theory of crystallization

In this work, we propose a model for using the classical Johnson-Mehl-Avrami-Kolmogorov (JMAK) crystallization theory to analyze nanocrystallization processes as a set of multiple microprocesses. This model is based on the well-known microstructure observations of nanocrystalline systems for which, although the number of crystallites increases along the process, the growth of each crystallite is limited to a much shorter time than the needed one for completing the process. The very low values of the Avrami exponent, n∼1, are well reproduced assuming a set of multiple classical JMAK processes with constant nucleation rate and diffusion controlled growth, ni = 2.5 for each i individual microprocess. It is shown that the values of Avrami exponent experimentally observed and lying out of the theoretical range can be assumed as effective values derived from a complex process consisting of multiple microprocesses, which can be individually treated as classical ones.

Effect of Sn additive on the structure and crystallization kinetics in Ge–Se alloy

The structure of Ge20Se80−xSnx glassy alloys and crystallization phases are identified using the X-ray diffraction (XRD) and Scanning Electron Microscope (SEM). The glass transition kinetics and the crystallization mechanism of the system are studied using Differential Scanning Calorimeter (DSC) under non-isothermal condition. The results reveal that glass transition temperature (Tg) increases with increasing Sn content which is attributed to the increase in the coordination number. The increase of the glass transition activation energy (Eg) with increasing Sn content is attributed to the decrease in the internal energy of the system as Sn increases. The compositional dependence of both glass forming ability and thermal stability are studied. From the experimental data, the thermal stability parameter (S) is found to be maximum for Ge20Se78Sn2 alloy, which indicates that this alloy is thermally more stable in the composition range under investigation. The effect of composition on the crystallization mechanism is discussed using different kinetic models. The crystallization activation energy (Ec) decreases with increasing Sn. This is attributed to the addition of Sn increases the tendency of crystallization. The calculated values of Avrami exponent (n) indicates the crystallization process occurs in one-and two dimensions for Sn is less than or equals 12 at%, respectively.

A comparative study on the isochronal and isothermal crystallization kinetics of Co46.45Fe25.55Ta8B20 soft magnetic metallic glass with high thermal stability

The crystallization kinetics of Co46.45Fe25.55Ta8B20 soft magnetic metallic glass with high thermal stability has been systematically investigated during isochronal and isothermal annealing treatments. The kinetics parameters have been calculated using different approaches, such as Kissinger, Ozawa, Augis–Bennett, Gao and Johnson-Mehl-Avrami (JMA) for isochronal crystallization and JMA for the isothermal regime. According to the isoconversional approach, it has been shown that the nucleation of the (Co,Fe)21Ta2B6 phase during continuous heating needs a higher energy barrier compared to its growth, where the average activation energy value is smaller than the apparent one. The Avrami exponent values for isochronal crystallization at all heating rates, calculated according to the Gao model, shows a good agreement with those determined by the JMA model at the beginning of crystallization. The JMA model demonstrates that the average Avrami exponent is around 2 for isochronal crystallization, revealing a three-dimensional diffusion-controlled crystal growth with a decreasing nucleation rate. It has been shown that based on the JMA model, the site saturation occurs for crystallized fraction (α) beyond 0.3 in the isochronal condition, so that the normal grain growth (NGG) model with an exponent of 0.32 can be applied for α ≥ 0.5. The results manifest that the average Avrami exponent and the overall nucleation rate of (Co,Fe)21Ta2B6 crystals in the isothermal and isochronal conditions are comparable and the nucleation process occurs over a notably larger crystallized fraction in the isothermal condition.

A kinetic analysis of the melting HA/Y-PSZ/HDPE nano bio composite for hard tissue materials

Melting characteristics of high-density polyethylene (HDPE) mixed with nano-size ceramic fillers (hydroxyl apatite and yttria stabilised zirconia) was analysed using the isochronal heating rate between 10°Cmin−1 and 80°Cmin−1. In this investigation, the kinetics of melting of HDPE-ceramic composites was analysed using the Avrami equation and the Kissinger model, applied to the Avrami formalism. The magnitude of the apparent energy barrier for the melting of HDPE falls within a range of 12kJmol−1 and 22kJmol−1, with a tendency for heterogeneous melting which was determined by characterising the value of Avrami exponent, n found to vary between 1 and 2. The heterogeneous nature of melting was also confirmed using the scanning electron microscopy, from which the evidences for both nano- and micro-scale interactions of HDPE with ceramic fillers (HA and yttria stabilised zirconia) were confirmed on a microscopic scale.

Nonisothermal crystallization kinetics, fragility and thermodynamics of Ti20Zr20Cu20Ni20Be20 high entropy bulk metallic glass

Abstract

Phase Transition of Sb-rich Alloy Films under Isothermal and Constant Heating Rate Annealings

The phase changed alloy films have great potential applications in the thermal sensor materials beside in the optical and electrical memory materials due to their stable phase transitions. The academic investigation methods on the phase transformation of the phase changed films are annealings either at constant heating rate or isothermal annealing. Both methods are applied and compared for the Sb-rich alloy films. The transitions from amorphous to crystalline of Sb-rich chalcogenide alloys with composition ratio of element group 14 to Sb ranged from 0.46 to 0.17 were investigated. The crystallization temperature at both annealing methods increases with the decrease of the ratio of element group 14 to Sb. The activation energies decided from both annealing methods are comparable, which implies the same crystallization mechanism. The Avrami exponents, ranged between 1.7 and 2.4, are extra values obtained from the isothermal measurements. The 2-D growth mechanism is implicitly dominated by the Avrami exponent values. Sb rhombohedral and Sb 7 Te are the major crystallized phases observed and SnTe and InTe phases are mixed among the major phase matrix when the samples are annealed at 250 o C for 30 min.

Crystallization and properties of B2O3 doped LZAS vitrified bond for diamond grinding tools

The effects of B2O3 on the crystallization and properties of Li2O–ZnO–Al2O3–SiO2 (LZAS) vitrified bonds were investigated for diamond grinding tool application. The results show that the [BO3] in the glass structure increased with increasing B2O3 content. The glass transition temperature and the first crystallization peak temperature decreased, while the second crystallization peak temperature increased with increasing B2O3 content. The increase in B2O3 content has a little influence on the value of Avrami exponent (n), keeping two-dimensional crystal growth mechanism. Realized composite with 8mol% B2O3 of LZAS vitrified bond has a higher crystal volume fraction and a uniform sphere-shaped microstructure. Moreover, vitrified bond B8 exhibits a high bending strength (198MPa), a good chemical durability (20days, DR=3.1×10−9g/cm2min), an appropriate TEC (4.63×10−6/°C) and a good wettability to diamond abrasives, suggesting that it would be a promising material for diamond grinding tool.

Thermally induced crystallization of amorphous Fe40Ni40P14B6 alloy

The crystallization mechanism and kinetics of Fe40Ni40P14B6 amorphous alloy were studied under non-isothermal conditions. Thermal stabilization of this alloy manifests in DSC through two complex peaks, corresponding to crystallization and recrystallization, respectively. The complex crystallization DSC peak was deconvoluted into individual steps corresponding to crystallization of individual phases, where the results using both Gaussian–Lorentzian cross-product and Fraser–Suzuki function were compared. It was determined that the values of kinetic triplets of the individual steps did not exhibit any significant difference, depending on the deconvolution function. Anisotropic growth was indicated to be the prevailing type of impingement for all crystallization steps. Using the calculated values of the respective kinetic triplets and the mechanisms determined from the value of Avrami exponent, distinct values of activation energies for nucleation and crystal growth for crystallization of each individual phase were calculated, showing significantly higher values for nucleation than those for crystal growth. Alloy samples treated non-isothermally in the DSC cell exhibit inhomogeneous surface morphology with highly granulated structure dependent on heating rate.

Thermal properties and crystallization kinetics of poly(butylene suberate)

In this work, we synthesized poly(butylene suberate) (PBSub) with a weight average molecular weight of 3.64 × 104 g/mol from the monomers of butanediol and suberic acid via a two-step melt polycondensation method. The basic thermal behaviors, overall isothermal melt crystallization kinetics, crystal structure, spherulitic morphology and growth, thermal stability, and hydrolytic degradation of PBSub were systematically investigated for the first time. PBSub has a low glass transition temperature of about −61 °C, a melting point of 55.2 °C, and an equilibrium melting point of 61.4 °C. The overall isothermal melt crystallization kinetics of PBSub was investigated at different crystallization temperature values and analyzed by the Avrami equation. PBSub has an average Avrami exponent value of about 3, suggesting that the crystallization mechanism of PBSub may correspond to three-dimensional truncated sphere growth with athermal nucleation. An obvious spherulitic morphology was observed for PBSub, and the spherulitic growth rates decrease with increasing crystallization temperature. PBSub exhibits a crystallization regime II to regime III transition on the basis of the secondary nucleation theory. The crystal structure study reveals that PBSub is highly crystalline, presenting strong diffraction peaks and a great crystallinity of about 55%. The thermogravimetric analysis study demonstrates that PBSub has both a high decomposition temperature at 5 wt% weight loss of about 377 °C and a high temperature at the maximum degradation rate of about 421 °C, suggesting its good thermal stability. PBSub may undergo a hydrolytic degradation, which may be of interest for its end use as a degradable material in some special application fields.

Homocrystal and stereocomplex formation behavior of polylactides with different branched structures

Effect of chain architecture on homocrystallization and stereocomplex formation behavior of polylactide (PLA) in quiescent conditions was investigated by means of differential scanning calorimetry (DSC) and optical microscopy. Non-isothermal and isothermal crystallization of star shaped, comb like and hyper branched poly(L-lactides) (PLLAs) with similar molecular weights were studied and compared to a linear one. In dynamic mode, branched PLAs reached higher crystallinity and revealed much higher spherulite density as compared to linear PLA. Also blends of linear and branched PLA with different blending ratios revealed faster crystallization than neat linear PLA. Based on kinetics data obtained in isothermal crystallization experiments, much faster crystallization was achieved with a 4–14 fold decrease in crystallization half-time as a consequence of non-linear chain architecture. Crystallization upon cooling, reduced cold crystallization temperature, increased spherulite density and lower Avrami exponent values for branched PLAs in comparison to linear one suggest enhanced nucleation process as a result of a branched chain architecture. On the other hand, total crystallinity and growth rate were decreased by branching. Stereocomplex formation between linear PLLA and branched poly(D-lactides) (PDLAs) showed dependency of stereocomplex formation to branched architecture. Also, stereocomplex crystals nucleated PLA homocrystallization process while different internal morphology between stereocomplex and homocrystal spherulites was observed. These results confirm that chain architecture has a profound effect on the crystallization behavior of PLA.

The effects of ultra-high pressure on the structural, rheological and retrogradation properties of lotus seed starch

Lotus seed starch in water (15%, w/w) was subjected to ultra-high pressure (UHP, 100–600 MPa) for 30 min. The effects of UHP on the structural, rheological and retrogradation properties of starch were investigated using polarized light microscopy, solid-state 13C CP/MAS NMR, rheometry, and differential scanning calorimetry. At 600 MPa, there was loss of the polarization cross, but some birefringence remained, indicating gelatinization. The 13C CP/MAS NMR results revealed a reduction in crystallinity and peak intensity in the crystalline state with increasing pressure. Native and UHP-treated starch pastes exhibited shear-thinning pseudoplastic behavior. Both G′ and G″ increased significantly at 100–500 MPa and decreased at 600 MPa, indicating that excessive pressurization weakens gel structures. UHP-treated starch pastes recovered more slowly their original structures under low-high-low shear conditions than native starch. During storage, UHP-treated starch gels had higher Avrami exponent values and lower recrystallization rates compared with native starch, which suggested a lower retrogradation tendency.

Kinetics of Geopolymer Solidification Study Using Texture Analyzer

The aim of this work was to study on the solidification kinetics of geopolymer using the Avrami Kinetics Theory by varying types of alkali solution and alkali concentration at different temperatures. Tests were carried out using Leatherhead Food Research Association (LFRA) Texture Analyzer to analyze the solidification profile. The results indicated that potassium hydroxide at low concentration had better performance in achieving faster time for geopolymerization process. Higher temperatures of 35°C used in the solidifying process of the geopolymer reduced the setting time. Based on the kinetic study, the growth rate (K) increased with the concentration of alkali activator and temperature. The Avrami exponent (n) trend was increased as growth rate increased. From the values of Avrami exponent obtained it could be suggested that the geopolymer had one, two or three dimension growth forms depending on the parameters selected.

Synthesis and characterization of machinable glass-ceramics added with B2O3

Glasses based on the SiO2–Al2O3–MgO–BaO–MgF2 system added with B2O3 were synthesized and characterized by differential thermal analysis (DTA), X-ray powder Diffraction (XRD), Fourier transform infrared spectroscopy (FTIR) and scanning electron microscopy (SEM) techniques. The glass transition temperature (Tg) and first crystallization peak temperature (Tp1) decreased, whilst the second crystallization peak temperature (Tp2) increased with increasing B2O3 content. The crystallization kinetics of amorphous glass specimens have been studied through DTA. The increase in B2O3 content has little influence on the value of Avrami exponent (n), keeping three-dimensional crystals growth mechanism. An interlocking blocky microstructure with a house-of-cards crystals structure was observed with high B2O3 content and at heat treated temperature from 800°C to 1050°C for 5h. As the B2O3 content and heat treated temperature increased the Vickers hardness decreased slightly on formation of the interconnected barium fluorophlogopite phase, which contributes to the improvement of machinability of glass-ceramics.

Study of non-isothermal crystallization of Eu3+ doped Zn2SiO4 powders through the application of various macrokinetic models

Abstract Various macrokinetic models (Avrami, Evans, Tobin, Malkin, Dietz, Nakamura, and modified first-order models) were applied to describe non-isothermal crystallization kinetics of Eu 3+ doped zinc silicate powders prepared via the sol–gel method. Analysis of the experimental data was carried out using a direct-fitting method such that the experimental data were fitted directly to each macrokinetic model using a non-linear multivariable regression computation procedure. Comparison of kinetic parameters obtained from the non-linear computation approach to those obtained from the traditional analytical procedure suggested that applicability and reliability of the direct-fitting method were satisfactory. Judging from the quality of the fit, only Nakamura’s model properly describe the temperature dependence of the relative crystallinity, which resulted in the total rejection of the Tobin model in describing the crystallization. With detailed kinetic examination it was concluded that crystallization mechanism of α-willemite doped samples combusted in a microwave oven (MW) follows interface controlled growth with an increasing nucleation rate, attached with geometric process-rate function obeying the improved ( corrected ) Nakamura’s model. It was found that the presence of non integer Avrami exponent values may indicate that crystallization occurs by more than one reaction mechanism, including the occurrence of autocatalytic behavior of a given system.

Blends of polylactide/thermoplactic elastomer: Miscibility, physical aging and crystallization behaviors

The PLA/PAE blends with four different weight ratios were prepared by melt mixing. PLA and PAE in PLA/PAE blends were almost immiscible while the weak interaction between PLA and PAE existed. The sub-micrometer PAE domains were dispersed in PLA matrix uniformly. The physical aging of PLA could be inhibited by introducing PAE. For PLA/PAE, the structure formed by physical aging at room temperature induced the accelerated crystallization of PLA during heating. However, for neat PLA, the structure formed by physical aging had a negligible effect on the crystallization of PLA during heating. The isothermal crystallization kinetics of neat PLA and PLA/PAE were analyzed by Avrami theory. The values of Avrami exponent were within the range 2.1–3.0. The crystallization rate of PLA was enhanced significantly by addition of PAE.

Mechanism and kinetics of crystallization of amorphous Fe81B13Si4C2 alloy

Crystallization process of amorphous Fe81B13Si4C2 alloy manifested as a slightly asymmetrical exothermic peak in temperature range 770–820K of differential scanning calorimetry (DSC) curves. Complex crystallization DSC peak was deconvoluted into three steps corresponding to formation of α-Fe(Si), Fe3B and Fe2B crystalline phases. Fe2B phase is formed from the amorphous matrix, while metastable Fe3B decomposes, providing constituents for subsequent formation of Fe2B phase. Examination of mechanism and kinetics of each individual step of crystallization yielded similar values of kinetic triplets, indicating similar crystallization mechanism for all individual phases, which was subsequently discussed using the values of Avrami exponents of individual crystallization steps. Both the range of and changes in values of the local Avrami exponent suggested the appearance of impingement, which precluded full applicability of JMA equation, and mixed nucleation type with accelerating nucleation for crystallization of all phases. Position of the transformation-rate maxima of individual crystallization steps indicates that anisotropic growth is the prevailing type of impingement. Estimation of lifetime showed very high stability of the alloy against crystallization at room temperature, with exponential decline in lifetime with temperature increase.

The equilibrium melting temperature and isothermal crystallisation kinetics of cyclic poly(butylene terephthalate) and styrene maleimide (c-PBT/SMI) blends

The equilibrium melting point (\( T_{\text{m}}^{0} \)) and isothermal crystallisation kinetics of cyclic poly(butylene terephthalate) (c-PBT) and styrene maleimide (SMI) blends prepared by solid dispersion and in situ polymerisation of cyclic butylene terephthalate oligomers (CBT) within SMI were investigated. This c-PBT/SMI blend is a miscible semicrystalline–amorphous blend system. The \( T_{\text{m}}^{0} \) of c-PBT/SMI blends was determined using the Hoffman and Weeks method, while Avrami crystallisation kinetic model have been applied to study their isothermal crystallisation kinetics. It was found that \( T_{\text{m}}^{0} \) decreased with increasing SMI content in the blend compositions. All the crystallisation exotherms were obtained from differential scanning calorimetry under isothermal experimental conditions. The average value of Avrami exponent, n, is in the range of 2.4–2.8 for the primary crystallisation process for c-PBT and its blends, which suggest that heterogeneous nucleation of spherulites occurred and growth of spherulites was between two-dimensional and three-dimensional.

Phase transformation and crystallization kinetics of Te67.5Ga2.5As30 amorphous alloy

The amorphous to crystalline transformation in Te67.5Ga2.5As30 occurs under non-isothermal conditions. The crystallization parameters of this amorphous material are estimated using differential scanning calorimetery (DSC). The activation energy of crystallization (Ec) and the frequency factor (K0) are calculated to be 113.16±1.5kJ/mol and 1.04×1010±31.70s−1, respectively. The crystallization mechanism is found to be one-dimensional growth mechanism as indicated from the estimated Avrami exponent value. X-ray investigations confirm the amorphous phase and crystalline state for the as-prepared and annealed samples, respectively. The crystallized grain sizes of nanoscale are calculated from the XRD peaks.

Thermal Stability and Crystallization Kinetics of Ti<sub>40</sub>Zr<sub>10</sub>Cu<sub>34</sub>Pd<sub>14</sub>Sn<sub>2</sub> Bulk Metallic Glass

In this work, the isochronal and isothermal activation energies for the primary crystallization process of Ti40Zr10Cu34Pd14Sn2 bulk metallic glass have been studied by differential scanning calorimetry and determined using the Kissinger approach and the Johnson-Mehl-Avrami analysis, respectively. The activation energy for crystallization evaluated by the Kissinger method is 253 kJ/mol. Similar activation energy for crystallization was obtained from the viscosity measurements. The values of the differential Avrami exponent are also determined from the isothermal data. Assuming diffusion-controlled growth, it is shown that thermal treatment of the samples in the supercooled liquid region considerably influences the behavior of the nucleation rate during the crystallization process.

TDNMR characterization of a model crystallizing surfactant system

Complex fluids with high concentrations of crystallizing fatty acids are important for consumer skin care products. These fluids exhibit solid-like elastic behavior at rest, but yield and flow under an applied strain. Such behavior is characteristic of isotropic, space-filling networks. The processing determines the microstructure of these systems, which in turn influences their macroscopic rheological properties. The kinetics of crystal growth in model system compositions, comprising (by weight) 9% sodium dodecyl sulfate, 3% cocamidopropyl betaine, and different specified amounts of palmitic acid in H2O or D2O, were studied by time domain nuclear magnetic resonance (TDNMR) and differential scanning calorimetry (DSC). The data were analyzed using the Avrami equation; both DSC and TDNMR gave consistent Avrami exponent values of approximately 1.5 for formulations with 11wt% and greater amounts palmitic acid content. The Avrami exponent is consistent with two-dimensional crystal growth limited both by diffusion and surface incorporation. The solids content at 25°C was found to be proportional to the concentration of palmitic acid level above its solubility limit of ca. 2wt%. TDNMR, combined with DSC, microscopy, and rheology provide valuable insights into the molecular structure and mechanism of crystallization in surfactant/fatty acid systems.