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Journal articles on the topic 'Avrami exponent'

Author: Grafiati
Published: 4 June 2025
Last updated: 6 July 2025

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1

Luo, Hai Wen, Lian Zi An, and Hong Wei Ni. "A New Approach to Model Heterogonous Recrystallization Kinetics Based on the Natural Inhomogeneity of Deformation." Materials Science Forum 558-559 (October 2007): 1139–44. http://dx.doi.org/10.4028/www.scientific.net/msf.558-559.1139.

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The classical JMAK equation was modified by combination with distribution density of the rate parameter k, which was deduced from a normal distribution of local strain. The modified equation is able to calculate the JMAK plots and the average Avrami exponent to characterize the entire heterogeneous recrystallization process. This new extension can successfully describe the relevant experimental observations, such as a smaller exponent than the basic JMAK theory predicts, and a decreasing slope of JMAK plots with the proceeding recrystallization. Moreover, it reveals that the Avrami exponent observed experimentally should significantly decrease with the increasing standard deviation of local strain distribution. In addition, it has a great potential to explain why most of experimentally observed values of Avrami exponents are less than 2 and why the Avrami exponent is insensitive to temperature and deformation conditions when the real standard deviation of local strain distribution in deformed metals is known.
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2

Fjeldberg, E., and Knut Marthinsen. "On the Recrystallization Kinetics of 3D Potts Monte Carlo Simulations." Materials Science Forum 715-716 (April 2012): 959–64. http://dx.doi.org/10.4028/www.scientific.net/msf.715-716.959.

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The present simulations have clearly demonstrated that the kinetics, as derived directly from the 3D Potts Monte Carlo simulations, deviate strongly from the classical JMAK theory. The Avrami plots exhibit a strong initial transient and the Avrami exponents are far from constant and generally much lower than predicted by the classical JMAK theory. However, by introducing a suitable time delay,t0, due to a non-zero volume fraction of recrystallized grains at the start-up of the simulations, this initial transient can be removed and the Avrami plots are made close to linear at the same time as the Avrami exponent is in better agreement with theory.
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3

Rezaei-Shahreza, Parisa, Amir Seifoddini, Saeed Hasani, Zahra Jaafari, Agata Śliwa, and Marcin Nabiałek. "Isokinetic Analysis of Fe41Co7Cr15Mo14Y2C15B6 Bulk Metallic Glass: Effect of Minor Copper Addition." Materials 13, no. 17 (2020): 3704. http://dx.doi.org/10.3390/ma13173704.

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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.
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4

Wang, Yan. "A fractal model for the crystallization kinetics." Thermal Science 25, no. 2 Part B (2021): 1313–15. http://dx.doi.org/10.2298/tsci191212027w.

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The Kolmogorov-Johnson-Mehl-Avrami equation is wildly applied in the crystallization kinetics, and Avrami exponent involved in the equation plays an important role in crystallization process. Here we show that the Kolmogorov-Johnson-Mehl-Avrami equation can be obtained by a fractal crystallization model, and the exponent is explained as the fractal dimension in time, which depends upon the chain length and molecule weight.
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5

Luo, Haiwen, Jilt Sietsma, and Sybrand van der Zwaag. "Characteristics of the Static Recrystallization Kinetics of an Intercritically Deformed C-Mn Steel." Materials Science Forum 467-470 (October 2004): 293–98. http://dx.doi.org/10.4028/www.scientific.net/msf.467-470.293.

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The austenite recrystallization kinetics in the intercritical region of a C-Mn steel is investigated by means of stress relaxation tests. It is found that the Avrami exponent, n, decreases significantly with decreasing temperature, i.e. with increasing ferrite fraction. This behaviour deviates from that of austenite recrystallization in the purely austenitic state, in which case the Avrami exponent is constant and independent of temperature and deformation. To interpret this, the influence of spatial variation of the plastic strain in the intercritical austenite grains on recrystallization kinetics is modelled quantitatively. The modelling results seem to indicate that the strain heterogeneity is responsible for the decreasing Avrami exponent with decreasing intercritical temperature.
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6

Gu, Xiao Hua, Peng Zeng, Xi Wei Zhang, and Xue Song. "Nonisothermal Crystallization Kinetics of Poly(m-xylylene adipamide)." Advanced Materials Research 971-973 (June 2014): 103–6. http://dx.doi.org/10.4028/www.scientific.net/amr.971-973.103.

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Abstract.In this paper, the nonisothermal crystallization kinetics was investigated by differential scanning calorimetry for the poly(m-xylylene adipamide) (MXD6) which were prepared by polymerization in reactor. The Avrami theory modified by Jeziorny and Z.S. Mo equation were used to describe the nonisothermal crystallization kinetics. The analysis based on the Avrami theory modified by Jeziorny shows that the Avrami exponent n of MXD6 ranges from 2.3 to 3.3, Moreover, both Avrami exponent (n) were around 3.0, which probably suggests a thermal nucleation and a three-dimensional crystal growth. The good linearity of the plots indicates the successful application of Z.S. Mo method in this case.
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7

Lelito, Janusz. "Crystallization Kinetics Analysis of the Amorphouse Mg72Zn24Ca4 Alloy at the Isothermal Annealing Temperature of 507 K." Materials 13, no. 12 (2020): 2815. http://dx.doi.org/10.3390/ma13122815.

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This paper presents tests of metallic glass based on Mg72Zn24Ca4 alloy. Metallic glass was made using induction melting and further injection on a rotating copper wheel. A differential scanning calorimeter (DSC) was used to investigate the phase transformation of an amorphous ribbon. The tests were carried out at an isothermal annealing temperature of 507 K. The Kolmogorov-Johnson-Mahl-Avrami-Evans model was used to analyze the crystallization kinetics of the amorphous Mg72Zn24Ca4 alloy. In this model, both Avrami’s exponent n and transformation rate constant K were analyzed. Both of these kinetic parameters were examined as a function of time and the solid fraction. The Avrami exponent n value at the beginning of the crystallization process has value n = 1.9 and at the end of the crystallization process has value n = 3.6. The kinetic constant K values change in the opposite way as the exponent n. At the beginning of the crystallization process the constant K has value K = 9.19 × 10−7 s−n (ln(K) = −13.9) and at the end of the crystallization process has the value K = 6.19 × 10−9 s−n (ln(K) = −18.9). These parameters behave similarly, analyzing them as a function of the duration of the isothermal transformation. The exponent n increases and the constant K decreases with the duration of the crystallization process. With such a change of the Avrami exponent n and the transformation rate constant K, the crystallization process is controlled by the 3D growth on predetermined nuclei. Because each metallic glass has a place for heterogeneous nucleation, so called pre-existing nuclei, in which nucleation is strengthened and the energy barrier is lowered. These nuclei along with possible surface-induced crystallization, lead to rapid nucleation at the beginning of the process, and therefore a larger transformed fraction than expected for purely uniform nucleation. These sites are used and saturated with time, followed mainly by homogeneous nucleation. In addition, such a high value of the Avrami exponent n at the end of the crystallization process can cause the impingement effect, heterogeneous distribution of nuclei and the diffusion-controlled grain growth in the Mg72Zn24Ca4 metallic glassy alloy.
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8

Ji, Mo, Martin Strangwood, and Claire Davis. "Effect of Strain-Induced Precipitation on the Recrystallization Kinetics in a Model Alloy." Metallurgical and Materials Transactions A 52, no. 5 (2021): 1963–75. http://dx.doi.org/10.1007/s11661-021-06206-8.

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AbstractThe effects of Nb addition on the recrystallization kinetics and the recrystallized grain size distribution after cold deformation were investigated by using Fe-30Ni and Fe-30Ni-0.044 wt pct Nb steel with comparable starting grain size distributions. The samples were deformed to 0.3 strain at room temperature followed by annealing at 950 °C to 850 °C for various times; the microstructural evolution and the grain size distribution of non- and fully recrystallized samples were characterized, along with the strain-induced precipitates (SIPs) and their size and volume fraction evolution. It was found that Nb addition has little effect on recrystallized grain size distribution, whereas Nb precipitation kinetics (SIP size and number density) affects the recrystallization Avrami exponent depending on the annealing temperature. Faster precipitation coarsening rates at high temperature (950 °C to 900 °C) led to slower recrystallization kinetics but no change on Avrami exponent, despite precipitation occurring before recrystallization. Whereas a slower precipitation coarsening rate at 850 °C gave fine-sized strain-induced precipitates that were effective in reducing the recrystallization Avrami exponent after 50 pct of recrystallization. Both solute drag and precipitation pinning effects have been added onto the JMAK model to account the effect of Nb content on recrystallization Avrami exponent for samples with large grain size distributions.
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9

Sidel, S. M., F. A. Santos, V. O. Gordo, et al. "Avrami exponent of crystallization in tellurite glasses." Journal of Thermal Analysis and Calorimetry 106, no. 2 (2011): 613–18. http://dx.doi.org/10.1007/s10973-011-1312-4.

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10

Sun, N. X., X. D. Liu, and K. Lu. "An explanation to the anomalous avrami exponent." Scripta Materialia 34, no. 8 (1996): 1201–7. http://dx.doi.org/10.1016/1359-6462(95)00657-5.

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11

Chen, Xiaohua, Weijie Fan, Wenwen Jiang, Deye Lin, Zidong Wang, and Simeng Jiang. "Effects of Pressure on Homogeneous Nucleation and Growth during Isothermal Solidification in Pure Al: A Molecular Dynamics Simulation Study." Metals 12, no. 12 (2022): 2101. http://dx.doi.org/10.3390/met12122101.

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Effects of different pressures on the isothermal-solidification process of pure Al were studied by molecular dynamics (MD) simulation using the embedded-atom method (EAM). Al was first subjected to a rapid-cooling process, and then it was annealed under different pressures conditions. Mean first-passage times (MFPT) method, Johnson-Mehl-Avrami (JMA) law, and X-ray diffraction (XRD) simulation analysis method were used to qualify the solidification- kinetic processing. Nucleation rate, critical-nucleus size, Avrami exponent, growth exponent, and crystallite size were calculated. Results show that the nucleation rate increases as the pressure increases. The change of critical-nucleation size is not obvious as the pressure increases. With the pressure increasing, growth exponent decreases, indicative of decreased grain-growth rate. It was also found that with the pressure increasing, the Avrami exponent decreases, indicating that the increased pressure has an effect on growth modes during solidification, which changes from three-dimensional growth to one-dimensional growth. Results of XRD simulation shows that with pressure increasing, crystallite size decreases.
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12

Ji, Mo, Claire Davis, and Martin Strangwood. "Effect of Grain Size Distribution on Recrystallisation Kinetics in an Fe-30Ni Model Alloy." Metals 9, no. 3 (2019): 369. http://dx.doi.org/10.3390/met9030369.

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This paper discusses the role of grain size distribution on the recrystallisation rates and Avrami values for a Fe-30 wt. % Ni steel, which was used as a model alloy retaining an austenitic structure to room temperature. Cold deformation was used to provide uniform macroscopic strain distributions (strains of 0.2 and 0.3), followed by recrystallisation during annealing at 850–950 °C. It was shown that the Avrami parameter was directly related to the grain size distribution, with a lower Avrami exponent being seen for a larger average and wider grain size distribution. A method to predict the Avrami exponent from the grain size distribution was proposed. In situ heating in an SEM with EBSD showed the recrystallisation kinetics to be affected by differences in stored energy and nucleation in the different grain sizes supporting the proposed relationship.
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13

Zhaosheng, Tan, Zhang Bangwei, and Zhang Hen. "Avrami exponent of crystallization in metallic glass Cu73.8P13.8Ni8.3Sn4.1." Journal of Materials Science 27, no. 15 (1992): 4021–23. http://dx.doi.org/10.1007/bf01105099.

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14

Zamri, N. H., Lukman Ismail, Rosniza Hanim Abdul Rahim, Ahmer Ali Siyal, Zakaria Man, and Khairun Azizi Azizli. "Kinetics of Geopolymer Solidification Study Using Texture Analyzer." Materials Science Forum 803 (August 2014): 75–80. http://dx.doi.org/10.4028/www.scientific.net/msf.803.75.

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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.
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15

Zhang, Rong Hua, Biao Wu та Xiao Ping Zheng. "Study on the β1→α+β2 Transformation Kinetics of Ti-6Al-4V Alloy by DSC". Applied Mechanics and Materials 508 (січень 2014): 110–13. http://dx.doi.org/10.4028/www.scientific.net/amm.508.110.

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The temperature and duration of β1→α+β2 transformation of Ti-6Al-4V alloy in cooling process were measured by differential scanning calorimetry, and transformation activation energy and Avrami exponent of β1→α+β2 were also calculated. The results show that the cooling rate is in the range of 在5～20°C/min, the transformation temperature and the transformation duration β1→α+β2 transformation of Ti-6Al-4V alloy decreased with the increasing cooling rate, its transformation activation energy decreased with the increasing phase transformation volume fraction, and Avrami exponent was between 1 and 2 at 660°C.
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16

Hukari, Kyle, Rand Dannenberg, and E. A. Stach. "Nitrogen Effects on Crystallization Kinetics of Amorphous TiOxNy Thin Films." Journal of Materials Research 17, no. 3 (2002): 550–55. http://dx.doi.org/10.1557/jmr.2002.0077.

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The crystallization behavior of amorphous TiOxNy (x ≫ y) thin films was investigated by in situ transmission electron microscopy. The Johnson–Mehl–Avrami–Kozolog (JMAK) theory was used to determine the Avrami exponent, activation energy, and the phase velocity pre-exponent. Addition of nitrogen inhibited diffusion, increasing the nucleation temperature, while decreasing the growth activation energy. Kinetic variables extracted from individual crystallites were compared to JMAK analysis of the fraction transformed, and a change of 6% in the activation energy led to agreement between the methods. From diffraction patterns and index of refraction the crystallized phase was found to be predominantly anatase.
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17

Sadi, Salaheddine, Abdelkader Hanna, Thierr Baudin, et al. "Evaluation of static recrystallization and grain growth kinetics of hot-rolled AZ31 alloy." Journal of Metals, Materials and Minerals 32, no. 1 (2022): 12–26. http://dx.doi.org/10.55713/jmmm.v32i1.1241.

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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.
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18

Zhou, Ping, Mi Zhou, Jing Ying Hu, and Xin Qian. "Isothermal Crystallization Behavior of PLA/PIL Composites." Advanced Materials Research 1096 (April 2015): 465–69. http://dx.doi.org/10.4028/www.scientific.net/amr.1096.465.

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The effect of Poly (ionic liquid) (PIL) on the crystallization of polylactide (PLA) has been investigated by means of differential scanning calorimetry. The nonisothermal crystallization result showed that PIL enhanced the crystallization of PLA. The Avrami method was used to describe the isothermal crystallization behavior of PLA/PIL composites. The Avrami exponent (n) revealed that the PIL accelerated PLA crystallization through heterogeneous nucleation.
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19

Hu, Chun Xia, Gai Lian Li, and Yang Shi. "Crystallization Kinetics of the Cu47.5Zr47.5Al5 Bulk Metallic Glass under Continuous and Iso-Thermal Heating." Applied Mechanics and Materials 99-100 (September 2011): 1052–58. http://dx.doi.org/10.4028/www.scientific.net/amm.99-100.1052.

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The crystallization kinetics of Cu47.5Zr47.5Al5 BMG was studied by differential scanning calorimetry (DSC) using the mode of continuous heating and isothermal annealing. It is found that Tg, Tx, and Tp, display a dependence on the heating rate in the case of continuous heating. The activation energies, Eg, Ex and Tp determined by the Kissinger method, yield 445, 264 and 285 kJ/mol, respectively. The local activation energy, E(x), was determined by the Doyle-Ozawa method, which gives the average activation energy 204 kJ/mol. On the other hand, the isothermal kinetics was modeled by the Johnson-Mehl-Avrami (JMA) equation, the Avrami exponent versus crystallization fraction was calculated at different temperatures. Details of nucleation and growth behaviors are discussed in terms of the local Avrami exponent and local activation energy during the isothermal crystallization. X-ray shows that the quenched BMG only includes the glass single phase. The BMG heated to 873 K has the precipitation of the body-center cubic (BCC) CuZr.
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20

Maruoka, Hirokazu. "The New Method Using Shannon Entropy to Decide the Power Exponents on JMAK Equation †." Proceedings 46, no. 1 (2019): 28. http://dx.doi.org/10.3390/ecea-5-06660.

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The JMAK (Johnson–Mehl–Avrami–Kolmogorov) equation is exponential equation inserted power-law behavior on the parameter, and is widely utilized to describe the relaxation process, the nucleation process, the deformation of materials and so on. Theoretically the power exponent is occasionally associated with the geometrical factor of the nucleus, which gives the integral power exponent. However, non-integral power exponents occasionally appear and they are sometimes considered as phenomenological in the experiment. On the other hand, the power exponent decides the distribution of step time when the equation is considered as the superposition of the step function. This work intends to extend the interpretation of the power exponent by the new method associating Shannon entropy of distribution of step time with the method of Lagrange multiplier in which cumulants or moments obtained from the distribution function are preserved. This method intends to decide the distribution of step time through the power exponent, in which certain statistical values are fixed. The Shannon entropy to which the second cumulant is introduced gives fractional power exponents that reveal the symmetrical distribution function that can be compared with the experimental results. Various power exponents in which another statistical value is fixed are discussed with physical interpretation. This work gives new insight into the JMAK function and the method of Shannon entropy in general.
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21

Eltahir, Yassir A., Haroon A. M. Saeed, Chen Yuejun, Yumin Xia, and Wang Yimin. "Parameters characterizing the kinetics of the non-isothermal crystallization of polyamide 5,6 determined by differential scanning calorimetry." Journal of Polymer Engineering 34, no. 4 (2014): 353–58. http://dx.doi.org/10.1515/polyeng-2013-0250.

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Abstract The non-isothermal crystallization behavior of polyamide 5,6 (PA56) was investigated by differential scanning calorimeter (DSC), and the non-isothermal crystallization kinetics were analyzed using the modified Avrami equation, the Ozawa model, and the method combining the Avrami and Ozawa equations. It was found that the Avrami method modified by Jeziorny could only describe the primary stage of non-isothermal crystallization kinetics of PA56, the Ozawa model failed to describe the non-isothermal crystallization of PA56, while the combined approach could successfully describe the non-isothermal crystallization process much more effectively. Kinetic parameters, such as the Avrami exponent, kinetic crystallization rate constant, relative degree of crystallinity, the crystallization enthalpy, and activation energy, were also determined for PA56.
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22

Lu, K., and J. T. Wang. "On Avrami exponent for crystallization of NiP glass." Scripta Metallurgica 21, no. 9 (1987): 1185–88. http://dx.doi.org/10.1016/0036-9748(87)90346-2.

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23

Mao, Ming, and Z. Altounian. "Accurate determination of the Avrami exponent in phase transformations." Materials Science and Engineering: A 149, no. 1 (1991): L5—L8. http://dx.doi.org/10.1016/0921-5093(91)90797-q.

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24

Sinha, I., and R. K. Mandal. "Avrami exponent under transient and heterogeneous nucleation transformation conditions." Journal of Non-Crystalline Solids 357, no. 3 (2011): 919–25. http://dx.doi.org/10.1016/j.jnoncrysol.2010.11.005.

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25

Chen, Xiaohua, Weijie Fan, Wenwen Jiang, et al. "Effects of Cooling Rate on the Solidification Process of Pure Metal Al: Molecular Dynamics Simulations Based on the MFPT Method." Metals 12, no. 9 (2022): 1504. http://dx.doi.org/10.3390/met12091504.

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Isothermal solidification process of pure metal Al was studied by molecular dynamics (MD) simulation using EAM potential. The effects of different cooling rates on the isothermal solidification process of metallic Al were studied. Al was first subjected to a rapid cooling process, and then it was annealing under isothermal conditions. The mean first-passage times (MFPT) method and Johnson-Mehl-Avrami (JMA) law were used to qualify the solidification kinetic processing, and the nucleation rate, critical nucleus size, Avrami exponent and growth exponent of grains were calculated. Results show that the nucleation rate and critical size decrease as the cooling rate increases. Also, an increase in the cooling rate leads to the increase of grain growth rate. At all investigated cooling rates, nucleation and growth processes are in the typical three-dimensional growth mode.
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26

Kwak, Woo-Chul, and Yun-Mo Sung. "Crystallization Kinetics of Sol-gel-derived (1x)SrBi2Ta2O9–xBi3TiTaO9 Ferroelectric Thin Films." Journal of Materials Research 17, no. 6 (2002): 1463–68. http://dx.doi.org/10.1557/jmr.2002.0217.

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The crystallization kinetics of Sr0.7Bi2.3Ta2O9 (SBT) and 0.7SrBi2Ta2O9–0.3Bi3TiTaO9 (SBT-BTT) thin films formed by the sol-gel and spin coating techniques were studied. Phase formation and crystal growth are greatly affected by the film composition and crystallization temperature. Isothermal kinetic analysis was performed on the x-ray diffraction results of the thin films heated in the range of 730 to 760 °C at 10 °C intervals. Activation energy and Avrami exponent values were determined for the fluorite-to-Aurivillus phase transformation. A reduction of approximately 51 kJ/mol in activation energy was observed for the SBT-BTT thin films, and an Avrami exponent value of approximately 1.0 was obtained for both the SBT and SBT-BTT. A comparison is made, and the possible crystallization mechanism is discussed.
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27

Kumar, P. A., Pisupati Swathi, and V. G. K. M. Pisipati. "Orthogonal Smectic Layers Favour Nucleation through Diffusioncontrolled Transformations: A Systematic Crystallization Kinetics Study." Zeitschrift für Naturforschung A 57, no. 5 (2002): 226–32. http://dx.doi.org/10.1515/zna-2002-0504.

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Systematic investigations of the crystallization kinetics of two representative compounds of p-phenylbenzylidene-p´ -alkylanilines are performed, using differential scanning calorimetry, to study the influence of the kinetophase (occurs prior to the crystal phase) on the nucleation process. The dimensionality of the crystal growth and the related crystallization process are discussed in terms of the Avrami parameters n and b. The trend in the magnitude of the Avrami exponent n supports the occurrence of temperature-dependent transformations in the orthorhombic molecular array.
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28

Wahid, Mohd Fitri Mohamad, Kevin J. Laws, and Michael Ferry. "Crystallization Kinetics and Fragility of Al-Based Amorphous Alloy." Materials Science Forum 1010 (September 2020): 3–8. http://dx.doi.org/10.4028/www.scientific.net/msf.1010.3.

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Crystallization among amorphous alloy is a crucial study since it generally affects it properties, which may detrimental or beneficial, depending in the intended application of the materials. Controlling crystallization is crucial for obtaining the desired properties. The crystallization study was performed using differential scanning calorimeter (DSC). Samples were heated at heating rate between 20 and 40 K·min-1. Structural evolution during crystallization was studied under X-ray diffraction (XRD). Apparent activation energy for each temperature characteristics was determined using Kissinger’s equation. Local Avrami exponent was investigated using modified Johnson-Mehl-Avrami-Kolgomorov equation. Liquid fragility, which indicates the strength of the glass formation, was predicted using temperature characteristics instead of its viscosity. It was found that upon crystallization both as-cast samples crystallize to cubic-Al, Al2CuMg and Al2Cu and Al3Ni. Alloy with composition of (Al75Cu17Mg8)95Ni5 shows superior activation energy at every temperature characteristics than alloy with composition of Al75Cu10Mg8Ni7. Local Avrami exponent and local activation energy for (Al75Cu17Mg8)95Ni5 show high values at the beginning and at the end of crystallization process. From liquid fragility, it was predicted that the samples are stronger glass former than previous studied Al-amorphous alloys.
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29

CHOI, YONGSOO. "KINETICS OF GRAIN NUCLEATION IN SUPERCOOLED QUASI-TWO-DIMENSIONAL Cu." Modern Physics Letters B 27, no. 12 (2013): 1350082. http://dx.doi.org/10.1142/s0217984913500826.

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Grain nucleation kinetics of nanocrystalline Cu in a quasi-two-dimensional system was investigated using molecular dynamics. Nanoscale grains nucleate rapidly from supercooled Cu under isothermal annealing conditions. An Avrami exponent from the JMAK equation implies that the kinetics follows the continuous nucleation model. Observation of grain growth during the nucleation stage shows that the kinetics follows the classical grain growth model with a low growth exponent. The lower value of the exponent illustrates the rapid growth of grains during this stage. Using the growth exponent, the activation energy for nucleation in Cu was obtained and compared with the values obtained in earlier studies.
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30

Hua, Neng Bin, Wen Zhe Chen, and Zhen Long Liao. "Effects of Zr Content on the Bending Property and Crystallization Behavior of Ductile Zr-Based Bulk Metallic Glasses." Materials Science Forum 913 (February 2018): 765–75. http://dx.doi.org/10.4028/www.scientific.net/msf.913.765.

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In this study, the effects of Zr content on the bending property, non–isothermal and isothermal crystallization kinetics of high–Zr–based BMGs were investigated. The BMGs exhibit high bending strength and their bending plasticity enhances with increasing Zr content, which is due to more free volume with high–Zr–content. During continuous heating, the crystallization phases for Zr66 and Zr70 BMGs are Zr2Cu and Zr2Ni phases. Zr70 alloy exhibits the highest activation energies for glass transition and crystallization because of the sluggish diffusion of large Zr atoms. Under isothermal condition, the average Avrami exponent of Zr66 alloy modeled by the JMA equation is about 2.6, implying a diffusion–controlled three dimensional crystallization growth with an increasing nucleation rate. The average Avrami exponent of 2.0 for Zr70 alloy indicates a diffusion–controlled three dimensional crystallization growth with a decreasing nucleation rate, which can be attributed to its higher activation energy for crystallization.
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31

ABOLHASANI, MOHAMMAD MAHDI, MINOO NAEBE, AZAM JALALI-ARANI та QIPENG GUO. "CRYSTALLINE STRUCTURES AND α → β AND γ POLYMORPHS TRANSFORMATION INDUCED BY NANOCLAY IN PVDF-BASED NANOCOMPOSITE". Nano 09, № 06 (2014): 1450065. http://dx.doi.org/10.1142/s1793292014500659.

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Poly(vinylidene fluoride) (PVDF) nanocomposites were prepared by melt-mixing. The dispersion of clay platelets and rheology of nanocomposites were analyzed using X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM) and rheometric mechanical spectrometer (RMS). The transformation of α to β and γ phase in PVDF was induced by the addition of nanoclay and subsequently the isothermal crystallization kinetics of neat PVDF and its nanocomposite have been investigated. The interaction between clay nanofillers and PVDF macromolecular chains induced the change of conformation from trans-gauche to all-trans crystal structure in PVDF segment. The isothermal crystallization of PVDF/clay nanocomposites was carried out by Differential Scanning Calorimetry (DSC) technique. The influence of clay platelets on nucleation crystallization rate and Avrami exponent were studied. PVDF/clay nanocomposite showed higher crystallization rate indicating that nanoclay has acted as an effective nucleation agent. This nucleation effect of nanoclay increased the Avrami exponent and decreased the degree of crystallinity.
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32

Fukami, Takeshi, I. Noda, M. Asada, D. Okai, and T. Yamasaki. "Crystal Growth in Amorphous Binary Alloys of Zr-Ni System." Advanced Materials Research 26-28 (October 2007): 675–78. http://dx.doi.org/10.4028/www.scientific.net/amr.26-28.675.

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A crystallization process in an amorphous state under isothermal condition is examined for binary alloys ZrNi and ZrNi2 by differential thermal analysis (DTA). Time dependence of DTA curves is measured at several constant temperatures just below crystallization temperature. The fraction of crystallized volume in amorphous state and its time evolution during isothermal annealing are measured. These data are analyzed by the Johnson-Mehl–Avrami formula. The Avrami exponent is 2.4±0.1 for ZrNi and 3~4 depending on the set temperature for ZrNi2. The activation energy for crystallization of amorphous ZrNi and ZrNi2 was estimated by plots of lnt1/2 vs. 1/T.
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33

Lee, Sergey, Ayako Yamamoto, and Setsuko Tajima. "Kinetic study of (Bi,Pb)2Sr2Ca2Cu3O10+x phase formation in KCl flux." Journal of Materials Research 17, no. 9 (2002): 2281–85. http://dx.doi.org/10.1557/jmr.2002.0335.

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The kinetics of (Bi,Pb)2Sr2Ca2Cu3O10+x phase formation in KCl flux was studied, and kinetic analysis using the Avrami relation for isothermal phase transformation gave the Avrami exponent n = 2.5 at 855 °C for the whole process of (Bi,Pb)-2223 phase formation. The estimated value of the activation energy Ea = 150 kJ/mol for the formation of (Bi,Pb)-2223 phase at 845–855 °C is the lowest among the previously reported values. The low value of activation energy explains the fast formation of single-phase (Bi,Pb)-2223 powder in the KCl flux.
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34

Aman, Aman, Amir Awaluddin, Adrianto Ahmad, and Monita Olivia. "Pengaruh Variasi Temperatur Terhadap Kinetika Reaksi Solidifikasi Fly Ash Paving Blok Geopolimer." Dinamika Lingkungan Indonesia 5, no. 2 (2018): 126. http://dx.doi.org/10.31258/dli.5.2.p.126-130.

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This paper reported about the investigated of fly ash solidification with geopolymer process that studied temperature variation on the rate of solidification using Vicat Nidle apparatus and leaching tests on the content of heavy metals Cu, Pb, Cr and Cd in paving blocks after solidification. The transformation process of geopolymer crystalline formation was analyzed by Avrami’s kinetics theory (Avrami’s kinetica theory). From the results of the study obtained the optimum temperature of 80 oC, the highest rate of crystal growth solidification (K) value of 0.0475 and the Avrami exponent value (n) of 2.310 in this geopolymerization process shows a two-dimensional structure. From the results of leaching levels of heavy metals Cu, Pb, Cr and Cd in fly ash paving blocks are very small degraded in water and still below the environmental threshold.
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35

Lu, K., and J. T. Wang. "Variation of Avrami exponent for crystallization of melt-spun amorphous ribbons." Journal of Non-Crystalline Solids 117-118 (February 1990): 716–20. http://dx.doi.org/10.1016/0022-3093(90)90629-z.

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36

Calin, Mariana, Mihai Stoica, Na Zheng, et al. "Thermal Stability and Crystallization Kinetics of Ti40Zr10Cu34Pd14Sn2 Bulk Metallic Glass." Solid State Phenomena 188 (May 2012): 3–10. http://dx.doi.org/10.4028/www.scientific.net/ssp.188.3.

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In this work, the isochronal and isothermal activation energies for the primary crystallization process of Ti40Zr10Cu34Pd14Sn2bulk 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.
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37

Gokhman, Aleksandr, Petr Motyčka, Pavel Salvetr, et al. "Kinetics of Austenite Decomposition in 54SiCr6 Steel during Continuous Slow Cooling Conditions." Materials 16, no. 13 (2023): 4619. http://dx.doi.org/10.3390/ma16134619.

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In this study, dilatometry and metallography were used to investigate the effect of silicon and copper alloying on the decomposition kinetics of 54SiCr6 steel during continuous slow cooling. It is different from the published literature for using the approach of the local activation energy of the austenite decomposition Ef and the local Avrami exponent n of the volume fraction of the transformed phase f to study the kinetics of austenite-pearlitic transformation in cooled 54SiCr steel at slow cooling rates. The Johnson–Mehl–Avrami equation was used to determine the dependence of the local activation energy for austenite decomposition Ef and the local Avrami exponent n on the volume fraction of the transformed phase f. The mechanism of the austenite decomposition was analysed based on the calculated values of n. Both the local and average activation energies were used to evaluate the alloying effect, and the results were compared with those obtained from other methods. The type of microstructure formed as a result of cooling at rates of 0.5 K/s, 0.3 K/s, 0.1 K/s and 0.05 K/s was determined. The effects of changes in the cooling rate and the content of silicon (1.5–2.5 wt.%) and copper (0.12–1.47 wt.%) on the dimension of nucleation and growth kinetics of the transformed phase were studied. It was revealed that the pearlite microstructure was formed predominantly in 54SiCr6 steel as a result of continuous cooling at slow cooling rates. It was also found that alloying this steel with copper led to a significant decrease in the value of Ef, as well as to a change in the mechanism of the kinetics of the austenite-pearlite transformation, which was realised in predominantly two- and three-dimensional nucleation and growth at a constant nucleation rate. At the same time, alloying this steel with silicon led only to a slight change in Ef. The results of the study of 54SiCr steel presented the dependence of the activation energy of transformation and the local Avrami exponent on the volume fraction of the transformed phase at a given cooling rate at different copper and silicon contents. In addition, the study provides insight into the mechanism of kinetics in cooled 54SiCr steel as a function of the cooling rate.
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38

Zemenová, Petra, Robert Král, Miroslava Rodová, Karel Nitsch, and Martin Nikl. "Calculations of Avrami exponent and applicability of Johnson–Mehl–Avrami model on crystallization in Er:LiY(PO3)4 phosphate glass." Journal of Thermal Analysis and Calorimetry 141, no. 3 (2019): 1091–99. http://dx.doi.org/10.1007/s10973-019-09068-w.

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39

Zhang, Yan, Qichao Fan, Xiaofeng Zhang, Zhaohui Zhou, Zhihui Xia, and Zhiqiang Qian. "Avrami Kinetic-Based Constitutive Relationship for Armco-Type Pure Iron in Hot Deformation." Metals 9, no. 3 (2019): 365. http://dx.doi.org/10.3390/met9030365.

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The work presents a full mathematical description of the stress-strain compression curves in a wide range of strain rates and deformation temperatures for Armco-type pure iron. The constructed models are based on a dislocation structure evolution equation (in the case of dynamic recovery (DRV)) and Avrami kinetic-based model (in the case of dynamic recrystallization (DRX)). The fractional softening model is modified as: X = ( σ 2 − σ r 2 ) / ( σ d s 2 − σ r 2 ) considering the strain hardening of un-recrystallized regions. The Avrami kinetic equation is modified and used to describe the DRX process considering the strain rate and temperature. The relations between the Avrami constant k ∗ , time exponent n ∗ , strain rate ε ˙ , temperature T and Z parameter are discussed. The yield stress σ y , saturation stress σ r s , steady stress σ d s and critical strain ε c are expressed as the functions of the Z parameter. A constitutive model is constructed based on the strain-hardening model, fractional softening model and modified Avrami kinetic equation. The DRV and DRX characters of Armco-type pure iron are clearly presented in these flow stress curves determined by the model.
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40

Pangestu, Ferdinandus Archie, Nurheni Sri Palupi, Nur Wulandari, and Dimas Supriyadi. "Kinetika Kristalisasi Campuran Minyak Sawit Bebas Asam Lemak Trans untuk Produksi Margarin." Jurnal Teknologi dan Industri Pangan 34, no. 1 (2023): 37–47. http://dx.doi.org/10.6066/jtip.2023.34.1.37.

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Non-trans-fat (NTF) margarine was produced by substituting partially-hydrogenated palm oil in margarine oil blend with fully-hydrogenated palm oil. Three types of NTF oil blends were used in this study. To obtain an NTF oil blend with similar physical properties to the reference oil blend, which contain partially-hydrogenated oil, the melting properties and crystallization kinetics were evaluated. The iodine value of raw material oil was measured, and the oil was mixed to form the margarine oil blends. Fatty acid composition (FAC) and solid fat content (SFC) of the oil blends were examined. Melting properties of the oil blends were determined based on SFC analysis, while crystallization kinetics were determined using Avrami model. The results showed that there was no trans fatty acids detected in the NTF oil blends. The rate of crystallization constant (k) of the Avrami index of reference oil and NTF-1 oil blend were 0.1413 ± 0.0047 and 0.1369 ± 0.0016 min-n, respectively, whilst their Avrami exponent (n) were 0.93 ± 0.02 and 0.94 ± 0.01, respectively. There was no significant difference on these Avrami indexes, and therefore NTF-1 oil blend could be selected as an alternative oil blend for margarine production.
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41

Wang, Jun, Chen Wei, Haoxue Yang, Tong Guo, Tingting Xu, and Jinshan Li. "Phase Transformation Kinetics of a FCC Al0.25CoCrFeNi High-Entropy Alloy during Isochronal Heating." Metals 8, no. 12 (2018): 1015. http://dx.doi.org/10.3390/met8121015.

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The phase transformation kinetics of a face-centered-cubic (FCC) Al0.25CoCrFeNi high-entropy alloy during isochronal heating is investigated by thermal dilation experiment. The phase transformed volume fraction is determined from the thermal expansion curve, and results show that the phase transition is controlled by diffusion controlled nucleation-growth mechanism. The kinetic parameters, activation energy and kinetic exponent are determined based on Kissinger–Akahira–Sunose (KAS) and Johnson–Mehl–Avrami (JMA) method, respectively. The activation energy and kinetic exponent determined are almost constant, indicating a stable and slow speed of phase transition in the FCC Al0.25CoCrFeNi high-entropy alloy. During the main transformation process, the kinetic exponent shows that the phase transition is diffusion controlled process without nucleation during the transformation.
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42

Horiuchi, Kengo, Toshio Ogawa, Zhilei Wang, and Yoshitaka Adachi. "Three-Dimensional Analysis of Ferrite Grains Recrystallized in Low-Carbon Steel during Annealing." Materials 14, no. 15 (2021): 4154. http://dx.doi.org/10.3390/ma14154154.

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We performed a three-dimensional (3D) analysis of ferrite grains recrystallized in low-carbon steel during annealing. Cold-rolled specimens were heated to 723 K and held for various periods. The 3D morphology of ferrite grains recrystallized during the annealing process was investigated. The progress of recovery in low-carbon steel was more inhibited than that in pure iron. However, ferrite recrystallization in low-carbon steel was more rapid than that in pure iron. The Avrami exponent was inconsistent with the 3D morphology of the recrystallized ferrite grains in pure iron but consistent with that of the grains in low-carbon steel. Thus, the Avrami exponent depends on the recovery and recrystallization behaviors. Furthermore, the recrystallized ferrite grain growth was virtually 2D. Three types of recrystallized ferrite grains were observed: recrystallized ferrite grains elongated along the transverse or rolling direction; plate-shaped recrystallized ferrite grains grown in the transverse and rolling directions; fine and equiaxed recrystallized ferrite grains. These results suggest that the recrystallized ferrite grains did not grow in the normal direction. Thus, we concluded that the 3D morphology of recrystallized ferrite grains depends on the kinetics of recrystallization and the initial microstructure before recrystallization.
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43

Brand, Helen E. A., Nicola V. Y. Scarlett, and Ian E. Grey. "In situstudies into the formation kinetics of potassium jarosite." Journal of Applied Crystallography 45, no. 3 (2012): 535–45. http://dx.doi.org/10.1107/s002188981201607x.

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This paper reports the results of time-resolved synchrotron powder diffraction and small-angle scattering experiments designed to investigate the kinetics of formation of potassium jarosite by co-precipitation at 353, 368 and 393 K. Only jarosite was produced in these syntheses, and the particles that formed nucleated on the walls of the capillary reaction vessels with a disc-like shape. Relative Rietveld scale factors indicating jarosite abundance have been used as the basis for kinetic modelling of the nucleation and growth stages using a modified form of the Avrami kinetic equation. The results show that jarosite forms by a single nucleation event followed by two distinct stages of growth, each characterized by a different Avrami exponent. The value of this exponent is initially between 1 and 2, and then reduces to around 1. This suggests that jarosite growth after nucleation is controlled by effects at the solution–boundary interface, with the first stage best described by two-dimensional growth which transitions to one-dimensional growth later in the reaction. An activation energy of 89 kJ mol−1was estimated for the first stage of growth, in good agreement with previous work.
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44

Wang, J., H. C. Kou, X. F. Gu, et al. "On discussion of the applicability of local Avrami exponent: Errors and solutions." Materials Letters 63, no. 13-14 (2009): 1153–55. http://dx.doi.org/10.1016/j.matlet.2009.01.027.

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45

Hu, Wangyu, Lingling Wang, Lijun Wu, Bangwei Zhang, and Hengrong Guan. "The activation energy and the Avrami exponent for crystallization in amorphous Fe70.45W1.55Si3B25." Physica B: Condensed Matter 203, no. 1-2 (1994): 147–50. http://dx.doi.org/10.1016/0921-4526(94)90288-7.

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46

Wang, X. D., Q. Wang, and J. Z. Jiang. "Avrami exponent and isothermal crystallization of Zr/Ti-based bulk metallic glasses." Journal of Alloys and Compounds 440, no. 1-2 (2007): 189–92. http://dx.doi.org/10.1016/j.jallcom.2006.09.047.

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47

Pierwoła, Aleksandra, Janusz Lelito, Halina Krawiec, et al. "Non-Isothermal Analysis of the Crystallization Kinetics of Amorphous Mg72Zn27Pt1 and Mg72Zn27Ag1 Alloys." Materials 17, no. 2 (2024): 408. http://dx.doi.org/10.3390/ma17020408.

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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
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48

Vyazovkin, Sergey. "Jeziorny Method Should Be Avoided in Avrami Analysis of Nonisothermal Crystallization." Polymers 15, no. 1 (2022): 197. http://dx.doi.org/10.3390/polym15010197.

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The Jeziorny method treats nonisothermal crystallization data by replacing the variable temperature (T) values with the corresponding values of time and substituting them into the isothermal Avrami plot, ln[−ln(1 − α)] vs. lnt. For isothermal data, the slope of this plot is the Avrami exponent, n and the intercept is the rate constant, kA. This does not hold for nonisothermal data. Theoretical analysis suggests that in the case of nonisothermal data the intercept cannot be interpreted as kA, and its “correction” by dividing over the temperature change rate β is devoid of any meaning. In turn, the slope cannot be interpreted as n. It is demonstrated that the slope changes with time and its value depends not only on n but also on the temperature, temperature range, and activation energy of crystallization. Generally, the value of the slope is likely to markedly exceed the n value. The theoretical results are confirmed by analysis of simulated data. Overall, the Jeziorny method as well as other techniques that substitute nonisothermal data into the isothermal Avrami plot should be avoided as invalid and useless for any reasonable Avrami analysis. It is noted that n can be estimated from the nonlinear plot of ln[−ln(1 − α)] vs. T.
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49

Ong, MY, and WS Chow. "Kinetics of crystallization for polypropylene/polyethylene/halloysite nanotube nanocomposites." Journal of Thermoplastic Composite Materials 33, no. 4 (2018): 451–63. http://dx.doi.org/10.1177/0892705718807953.

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The aim of this study is to investigate the kinetics of non-isothermal crystallization of polypropylene/high-density polyethylene/halloysite nanotube (PP/HDPE/HNT) nanocomposites using three methods, that is, Avrami equation, combined Ozawa–Avrami method (hereafter called Mo model), and Kissinger equation. The Avrami exponent ( n) is in the range of 1–2 for all the PP/HDPE/HNT nanocomposites indicating instantaneous nucleation while the crystallization rate constant ( Zt) values of PP/HDPE increased with the addition of HNT. This proved that addition of HNT increases the crystallization rate. The reduction of half crystallization time ( t 1/2) for PP/HDPE as the increasing HNT loading indicates faster crystallization rate. In the Mo model, the cooling rate chosen at unit crystallization time F( T) values for PP/HDPE decreases with the addition of HNT. Kissinger equation showed that the activation energy ( E a) of crystallization for the PP/HDPE decreases with the addition of HNT. All the results demonstrated that HNT can accelerate the crystallization rate for the PP/polyethylene blends.
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50

Yang, Ming, Yong Shun Yang, and Dong Dong Yang. "A Study on Dynamic Recrystallization Behaviours of AZ80 Magnesium Alloy." Advanced Materials Research 189-193 (February 2011): 2847–50. http://dx.doi.org/10.4028/www.scientific.net/amr.189-193.2847.

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Using the compression tests on a Gleeble-1500 thermo-mechanical simulator to study the dynamic recrystallization behaviours of AZ80 magnesium alloy in the temperature range of 593-683K and strain rate range of 0.01-10s-1. By the analysis of the dynamic recrystallization kinetics, the Avrami exponent (m) and the constant (k) have been determined, and they aren’t constant and depend on the dimensionless parameter(Z/A).
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