Relevant bibliographies by topics / Avrami equations / Journal articles

To see the other types of publications on this topic, follow the link: Avrami equations.

Journal articles on the topic 'Avrami equations'

Author: Grafiati

Published: 4 June 2025

Last updated: 15 July 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Avrami equations.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

Villar Goris, N. A., A. R. Selva Castañeda, E. E. Ramirez-Torres, et al. "Correspondence between formulations of Avrami and Gompertz equations for untreated tumor growth kinetics." Revista Mexicana de Física 66, no. 5 Sept-Oct (2020): 632. http://dx.doi.org/10.31349/revmexfis.66.632.

Full text

Abstract:

The classical and modified equations of Kolmogorov-Johnson-Mehl-Avrami are compared with the equations of conventional Gompertz andMontijano-Bergues-Bory-Gompertz, in the frame of growth kinetics of tumors. For this, different analytical and numerical criteria are usedto demonstrate the similarity between them, in particular the distance of Hausdorff. The results show that these equations are similar fromthe mathematical point of view and the parameters of the Gompertz equation are explicitly related to those of the Avrami equation. It isconcluded that Modified Kolmogorov-Johnson-Mehl-Avrami and Montijano-Bergues-Bory-Gompertz equations can be used to describe thegrowth kinetics of unperturbed tumors.

APA, Harvard, Vancouver, ISO, and other styles

Kurkin, A. S. "Mathematical research of the phase transformation kinetics of alloyed steel." Industrial laboratory. Diagnostics of materials 85, no. 12 (2019): 25–32. http://dx.doi.org/10.26896/1028-6861-2019-85-12-25-32.

Full text

Abstract:

Regulation of the process parameters allows obtaining the desired properties of the metal. Computer simulation of technological processes with allowance for structural and phase transformations of the metal forms the basis for the proper choice of those parameters. Methods of mathematical modeling are used to study the main diffusion and diffusion-free processes of transformations in alloyed steels during heating and cooling. A comparative analysis of the kinetic equations of phase transformations including the Kolmogorov – Avrami and Austin – Rickett equations which describe in different ways the time dependence of the diffusion transformation rate and attained degree of transformation has been carried out. It is shown that the Austin – Rickett equation is equivalent to the Kolmogorov – Avrami equation with a smooth decrease of the Avrami exponent during the transformation process. The advantages of the Kolmogorov – Avrami equation in modeling the kinetics of ferrite-pearlite and bainite transformations and validity of this equation for modeling the kinetics of martensite transformations during tempering are shown. The parameters for describing the tempering process of steel 35 at different temperatures are determined. The proposed model is compared with equations based on the Hollomon – Jaffe parameter. The diagrams of martensitic transformation of alloyed steels and disadvantages of the Koistinen – Marburger equation used to describe them are analyzed. The equations of the temperature dependence of the transformation degree, similar to the Kolmogorov – Avrami and Austin – Rickett equations, are derived. The equations contain the minimum set of the parameters that can be found from published data. An iterative algorithm for determining parameters of the equations is developed, providing the minimum standard deviation of the constructed dependence from the initial experimental data. The dependence of the accuracy of approximation on the temperature of the onset of transformation is presented. The complex character of the martensitic transformation development for some steels is revealed. The advantage of using equations of the Austin – Rickett type when constructing models from a limited amount of experimental data is shown. The results obtained make it possible to extend the approaches used in modeling diffusion processes of austenite decomposition to description of the processes of formation and decomposition of martensite in alloyed steels.

APA, Harvard, Vancouver, ISO, and other styles

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.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

Barbadillo, Fernando, A. Fuentes, Salvador Naya, Ricardo Cao, José Luís Mier, and Ramón Artiaga. "Study of the Degradation of a Polyesther-Polyurethane by TGA and the Logistic Mixture Model." Materials Science Forum 587-588 (June 2008): 525–28. http://dx.doi.org/10.4028/www.scientific.net/msf.587-588.525.

Full text

Abstract:

The logistic mixture model was successfully studied previously in the separation of overlapping steps in some polymeric systems by the authors. In the present work, this method is applied to a polyesther-polyurethane degradation under air and inert atmospheres at several heat rates (5, 10, 15, 20 and 25 °C/min) in dynamic TGA. Every logistic component is fitted by reaction order, Johnson-Mehl-Avrami and Sestak-Berggren kinetics equations in order to calculate its kinetic parameters (activation energy, frequency factor and exponents). The reaction order model gives a good fitting and reproduces accurtelly the experimental curves. Johnson-Mehl-Avrami and Sestak- Berggren equations resulted to be not suitables because of the activation energy values obtained.

APA, Harvard, Vancouver, ISO, and other styles

Bianchi, O., R. V. B. Oliveira, R. Fiorio, J. De N. Martins, A. J. Zattera, and L. B. Canto. "Assessment of Avrami, Ozawa and Avrami–Ozawa equations for determination of EVA crosslinking kinetics from DSC measurements." Polymer Testing 27, no. 6 (2008): 722–29. http://dx.doi.org/10.1016/j.polymertesting.2008.05.003.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Levine, L. E., K. Lakshmi Narayan, and K. F. Kelton. "Finite size corrections for the Johnson–Mehl–Avrami–Kolmogorov equation." Journal of Materials Research 12, no. 1 (1997): 124–32. http://dx.doi.org/10.1557/jmr.1997.0020.

Full text

Abstract:

The Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation is frequently used to describe phase transformations involving nucleation and growth. The assumptions used in the derivation of this equation, however, are frequently violated when making experimental measurements; use of the JMAK equation for analyzing such data can often produce invalid results. Finite-size effects are among the most serious of these problems. We present modified analytic JMAK equations that correct for the finite-size effects and are roughly independent of both the sample shape and the shape of the growing nuclei. A comparison with computer simulations shows that these modified JMAK equations accurately reproduce the growth behavior over a wide range of conditions.

APA, Harvard, Vancouver, ISO, and other styles

Martin, David. "Application of Kolmogorov–Johnson–Mehl–Avrami equations to non-isothermal conditions." Computational Materials Science 47, no. 3 (2010): 796–800. http://dx.doi.org/10.1016/j.commatsci.2009.11.005.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Vyazovkin, Sergey, and Nicolas Sbirrazzuoli. "Nonisothermal Crystallization Kinetics by DSC: Practical Overview." Processes 11, no. 5 (2023): 1438. http://dx.doi.org/10.3390/pr11051438.

Full text

Abstract:

Providing a minimum of theory, this review focuses on practical aspects of analyzing the kinetics of nonisothermal crystallization as measured with differential scanning calorimetry (DSC). It is noted that kinetic analysis is dominated by approaches based on the Avrami and Arrhenius equations. Crystallization kinetics should not be considered synonymous with the Avrami model, whose nonisothermal applications are subject to very restrictive assumptions. The Arrhenius equation can serve only as a narrow temperature range approximation of the actual bell-shaped temperature dependence of the crystallization rate. Tests of the applicability of both equations are discussed. Most traditional kinetic methods tend to offer very unsophisticated treatments, limited only to either glass or melt crystallization. Differential or flexible integral isoconversional methods are applicable to both glass and melt crystallization because they can accurately approximate the temperature dependence of the crystallization rate with a series of the Arrhenius equations, each of which corresponds to its own narrow temperature interval. The resulting temperature dependence of the isoconversional activation energy can be parameterized in terms of the Turnbull–Fisher or Hoffman–Lauritzen theories, and the parameters obtained can be meaningfully interpreted and used for kinetic simulations.

APA, Harvard, Vancouver, ISO, and other styles

Gough, Terry, and Reinhard Illner. "Modeling Crystallization Dynamics when the Avrami Model Fails." VLSI Design 9, no. 4 (1999): 377–83. http://dx.doi.org/10.1155/1999/38517.

Full text

Abstract:

Recent experiments on the formation of crystalline CO2 from a newly discovered binary phase consisting of CO2 and C2H2 at 90° K fail to be adequately simulated by Avrami equations. The purpose of this note is to develop an alternative to the Avrami model which can make accurate predictions for these experiments. The new model uses empirical approximations to the distribution densities of the volumes of three-dimensional Voronoi cells defined by Poisson-generated crystallization kernels (nuclei). Inside each Voronoi cell, the growth of the crystal is assumed to be linear in diameter (i.e., cubic in volume) until the cell is filled by the CO2 crystals and the C2H2 (thought of as a waste product). The cumulative growth curve is computed by averaging these individual growth curves with respect to the distribution density of the volumes of the Voronoi cells. Agreement with the experiments is excellent.

APA, Harvard, Vancouver, ISO, and other styles

Ahmadi, R., Madaah Hosseini, and A. Masoudi. "Avrami behavior of magnetite nanoparticles formation in co-precipitation process." Journal of Mining and Metallurgy, Section B: Metallurgy 47, no. 2 (2011): 211–18. http://dx.doi.org/10.2298/jmmb110330010a.

Full text

Abstract:

In this work, magnetite nanoparticles (mean particle size about 20 nm) were synthesized via coprecipitation method. In order to investigate the kinetics of nanoparticle formation, variation in the amount of reactants within the process was measured using pH-meter and atomic absorption spectroscopy (AAS) instruments. Results show that nanoparticle formation behavior can be described by Avrami equations. Transmission electron microscopy (TEM) and X-ray diffraction (XRD) were performed to study the chemical and morphological characterization of nanoparticles. Some simplifying assumptions were employed for estimating the nucleation and growth rate of magnetite nanoparticles.

APA, Harvard, Vancouver, ISO, and other styles

Ruitenberg, G., E. Woldt, and A. K. Petford-Long. "Comparing the Johnson–Mehl–Avrami–Kolmogorov equations for isothermal and linear heating conditions." Thermochimica Acta 378, no. 1-2 (2001): 97–105. http://dx.doi.org/10.1016/s0040-6031(01)00584-6.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Tseng, Chiah-Hsiung, and Ping-Szu Tsai. "The Isothermal and Nonisothermal Crystallization Kinetics and Morphology of Solvent-Precipitated Nylon 66." Polymers 14, no. 3 (2022): 442. http://dx.doi.org/10.3390/polym14030442.

Full text

Abstract:

Solvent-precipitated nylon 66 (SP PA66) is a key material used to fabricate microfiltration membranes. The crystallization kinetics and behavior of SP PA66 were investigated through differential scanning calorimetry (DSC), polarized optical microscopy (POM) and X-ray diffraction (XRD). The Avrami equation was used to describe the isothermal crystallization of SP PA66. Nonisothermal crystallization behaviors were analyzed using Avrami equations modified by Jeziorny, Ozawa and Mo. The Avrami analysis demonstrated that the k values of SP PA66 were higher than those of neat PA66. The n was between 2 and 3 indicating the presence of two- and three-dimensional mode with thermal nucleation. With an increasing cooling rate, the Jeziorny crystallization rate constant increased for SP PA66; however, the Ozawa model was not satisfactory for all SP PA66 samples. The Mo method suggested that SP PA66 had a faster crystallization rate than neat PA66 during the nonisothermal crystallization process. The solvents dissolved nylon 66, rearranged it and formed a regular hydrogen-bonded region. These regions served as nucleation sites and increased the crystallization rate constant in the subsequent melting process. The crystal morphology of the SP PA66 under the POM investigation exhibited Maltese cross spherulites. The sizes of the spherulites of SP PA66 were significantly smaller than those of neat PA66. Wide-angle XRD revealed that SP PA66 had the same crystal structure and a higher crystal perfection than neat PA66.

APA, Harvard, Vancouver, ISO, and other styles

Mrázová, Martina, Alexandra Kloužková, and Martina Kohoutková. "Kinetic studies on leucite precursors." Open Chemistry 7, no. 2 (2009): 205–10. http://dx.doi.org/10.2478/s11532-009-0003-5.

Full text

Abstract:

AbstractKinetic studies were performed on two types of leucite precursors. These precursors were prepared using a hydrothermal method at 150°C; the reaction time was 1.5 hours. In order to obtain precursors having different amounts of seed the molarity of KOH was changed. These intermediate products were subsequently calcinated from 5 minutes to 72 hours at temperatures of 850°C, 900°C, 950°C, 1000°C and 1050°C. The crystallinities of the powders were calculated by X-ray diffraction analysis. The crystallization curves for the synthesis of leucite exhibited a typical sigmoidal characteristic. Using different kinetic equations it was found that the Avrami-Eroféev model is the most appropriate to describe the experimental data. Using the Avrami-Eroféev model n reaches an average value of 2.9 which is connected with the three-dimensional growth of nuclei. The calculated activation energy of crystallization of leucite was 385 kJ mol-1 for non-seeded precursors and 246 kJ mol-1 for seeded precursors, respectively.

APA, Harvard, Vancouver, ISO, and other styles

Lee, Seung-Hwan, and Tsutomu Ohkita. "Bamboo fiber (BF)-filled poly(butylenes succinate) bio-composite – Effect of BF-e-MA on the properties and crystallization kinetics." Holzforschung 58, no. 5 (2004): 537–43. http://dx.doi.org/10.1515/hf.2004.081.

Full text

Abstract:

Abstract Effects of bamboo fiber (BF)-esterified with maleic anhydride (MA) (BF-e-MA) on the properties of BF-filled poly(butylene succinate) (PBS) bio-composites were investigated. Adding 5% BF-e-MA increased the tensile strength of the PBS/BF (70/30) composite from 21 MPa to 28 MPa in the presence of radical initiator (0.5%). Melt viscosity was also increased by adding BF-e-MA. The Avrami and Ozawa equations were used to analyze the isothermal and nonisothermal crystallization kinetics, respectively. At the same crystallization temperature, all composites showed lower values for the Avrami and Ozawa exponents than pure PBS. Furthermore, the values for the PBS/BF-e-MA composite were smaller than those for the PBS/BF composite. Equilibrium water-sorption amount (M ∞) were highest for the composite without BF-e-MA, followed by the composites with BF-e-MA and finally pure PBS. The diffusion coefficient (D) was smaller for the composites with BF-e-MA than without. Scanning electron microscopy revealed that interfacial adhesion between BF and PBS matrix was improved after addition of BF-e-MA.

APA, Harvard, Vancouver, ISO, and other styles

Rios, Paulo R., and Elena Villa. "On the Generalisation of JMAK's Theory." Materials Science Forum 753 (March 2013): 137–42. http://dx.doi.org/10.4028/www.scientific.net/msf.753.137.

Full text

Abstract:

In their pioneer work Johnson-Mehl, Avrami and Kolmogorov (JMAK) developed well-known analytical expressions to describe the transformation kinetics of nucleation and growth transformations. Their work and its subsequent development has been extensively applied by Vandermeer and coworkers to recrystallisation studies. With the help of methods from Stochastic Geometry it has been possible to generalise JMAK's equations to situations well beyond their original assumptions. Although the motivation for this paper was recrystallisation the expressions derived here may be applied to nucleation and growth reactions in general.

APA, Harvard, Vancouver, ISO, and other styles

Çavdar, Sükrü, Emre Deniz, Haluk Koralay, Neslihan Turan, Ahmet Tolga Taşçı та Özgür Öztürk. "THE NUCLEATION EFFECT OF PbSe ADDITIVE ON Bi2Sr2CaCu2Oδ GLASS CERAMICS". Steklo i Keramika, № 2 (2022): 47–48. http://dx.doi.org/10.14489/glc.2022.02.pp.047-048.

Full text

Abstract:

The crystallisation kinetics and effects of doping on Bi2Sr2CaCu2Oδ (BSCCO) glass ceramic system with 0.0, 0.1, 0.3 and 0.5 % PbSe were investigated in this study. Using differential thermal analysis (DTA), the effects of PbSe doping on glass transition, nucleation and crystallisation temperature of glass were investigated. The DTA results were analysed using the Ozawa, Augis–Bennett, Takhor and Kissinger equations for nucleation kinetics to uncover the activation energies and Avrami parameters. Thermogravimetric analysis revealed that the amount of oxidation in the structure increased with increasing PbSe-doping concentration.

APA, Harvard, Vancouver, ISO, and other styles

Marthinsen, Knut, Jesper Friis, and Olaf Engler. "Modelling Time-Dependent Nucleation of Recrystallization in Aluminium Alloys." Materials Science Forum 753 (March 2013): 147–52. http://dx.doi.org/10.4028/www.scientific.net/msf.753.147.

Full text

Abstract:

The basic equations and mathematical framework of a mean-field model for recovery and recrystallization, the latter based on the Johnson-Mehl-Avrami-Kolmogorov (JMAK) approach, capable of handling time-dependent nucleation of recrystallization, is presented. Different approaches to account for time-dependent nucleation are discussed. A physically-based nucleation model where “nucleation” of recrystallization is brought about by “abnormal” subgrain growth seems most appealing, in terms of realism and mathematical convenience. Its implementation and effects on the recrystallization behavior are demonstrated through an example of back-annealing after cold deformation of a generic aluminium alloy case

APA, Harvard, Vancouver, ISO, and other styles

Bobet, J.-L., M. Kandavel, and S. Ramaprabhu. "Effects of ball-milling conditions and additives on the hydrogen sorption properties of Mg + 5 wt% Cr2O3 mixtures." Journal of Materials Research 21, no. 7 (2006): 1747–52. http://dx.doi.org/10.1557/jmr.2006.0206.

Full text

Abstract:

Effects of particle size of Cr2O3 catalyst on the hydrogen absorption/desorption kinetics of Mg + 5 wt% Cr2O3 mixtures have been studied. To explain the effect of particle size of Cr2O3 and also to yield information about the role of Cr2O3 during the sorption process, the kinetics data have been analyzed using Avrami–Erofeev rate equations. The activation energies and diffusion coefficients of these mixtures are in the ranges of 50.6–63.2 kJ/mol and 1.2.10−11 to 8.9.10−10 cm2/s, respectively. The addition of nano-oxides led to an increase of the diffusion coefficient of hydrogen by one order of magnitude.

APA, Harvard, Vancouver, ISO, and other styles

Qu, Zhiwei, Min Lei, Guohua Chen, Chaowen Huang, Dan Liu, and Ai Luo. "Kinetics of Martensite/Austenite Decomposition during Tempering of Ultrafine Nano-Bainitic Steels." Materials 17, no. 11 (2024): 2690. http://dx.doi.org/10.3390/ma17112690.

Full text

Abstract:

In this study, the decomposition of a martensite/austenite (M/A) microconstituent in bainitic steels was analyzed using differential scanning calorimetry (DSC) data in conjunction with Kissinger’s and Johnson–Mehl–Avrami–Kolmogorov (JMAK)’s formulas. In bainitic steel subjected to austempering heat treatment, the presence of an M/A microstructure adversely affects the mechanical properties. According to the kinetic equations derived, it is observed that after tempering the sample at 600 °C for 4000 s, the generation of each phase reaches its maximum. The SEM images taken before and after tempering reveal extensive decomposition of the M/A constituent in the microstructure. The proportion of the M/A microstructure decreased significantly from about 10% before tempering to less than 1% after. Additionally, the content of residual austenite also reduced nearly to zero. These observations are consistent with the predictions of the kinetic equations.

APA, Harvard, Vancouver, ISO, and other styles

Dimitra, Kourtidou, and Chrissafis Konstantinos. "Nonisothermal Crystallization Kinetics: Studying the Validity of Different Johnson–Mehl–Avrami–Erofeev–Kolmogorov (JMAEK) Based Equations." Thermochimica Acta 704 (October 2021): 179030. http://dx.doi.org/10.1016/j.tca.2021.179030.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Serik, Mashekov, Nugman Yerik, Mashekova Aigerim, Sekerbek Aimangul, Sembayev Nurbolat, and Akparova Symbat. "DEVELOPMENT OF TECHNOLOGIES FOR HOT PRESSING OF RODS MADE FROM 7075 ALUMINUM ALLOY ON A RADIALSHEAR MILL OF A NEW DESIGN – NUMERICAL MODELING." Eastern-European Journal of Enterprise Technologies 5, no. 12 (107) (2020): 23–31. https://doi.org/10.15587/1729-4061.2020.214919.

Full text

Abstract:

The paper proposes a radial shear mill (RSM) of a new design, which allows manufacturing metal rods of small diameters or wires with a fine-grained structure. The paper presents the results of modeling the evolution of the structure during hot rolling-pressing of aluminum alloy 7075 on the RSM. Mathematical modeling of the technological process was carried out using the MSC.SuperForge, and the empirical Johnson-Mehl-Avrami-Kolmogorov equation was used to predict the passage of softening processes. Due to the absence of the coefficients of the Avrami equation, a series of experiments on physical modeling of the rolling-pressing technological process were conducted on an STD 812 torsion rheometer. The experiments were conducted at the temperature range of 250–450 ℃ and a strain rate of 1.0–20 s<sup>-1</sup>. By using physical modeling, it was proved that during processing on the RSM, it is necessary to develop a torsional deformation over the entire section of the workpiece, which leads to effective refinement of the structure. The derived formulas and simulation modeling of the obtained values of the stress-strain state (SSS) were used to simulate the technology of the combined process. Moreover, rational temperature-rate conditions were determined to deform the workpiece on the RSM. It was proved by mathematical modeling that shear deformations develop along the entire section of the workpiece during processing on the RSM, which leads to effective refinement of the structure and the formation of a fine-grained structure in the rods, i. e. products of the required quality are manufactured

APA, Harvard, Vancouver, ISO, and other styles

Vo, Phuong, Mohammad Jahazi, and Steve Yue. "FEM Modelling of Recrystallization Behaviour for Near-Alpha Ti Alloy IMI834." Advanced Materials Research 89-91 (January 2010): 592–97. http://dx.doi.org/10.4028/www.scientific.net/amr.89-91.592.

Full text

Abstract:

The recrystallization behaviour of near-alpha titanium alloy IMI834, which is primarily used for high temperature aerospace compressor disc applications, has been investigated at hot working temperatures. The latest results of a finite element model, developed using the commercial code DEFORM-3D with constitutive equations adapted from available literature, will be presented. Model development and validation involved the hot compression of specimens with an initial bimodal alpha+beta microstructure at temperatures of 1000°C-1100°C, strain rates of 0.01s 1-1s 1, and varied post-deformation annealing times. The characterization of microstructure through quantitative metallography revealed beta grain refinement achieved primarily through static/metadynamic recrystallization. The beta recrystallization kinetics were subsequently predicted through an Avrami-type relationship.

APA, Harvard, Vancouver, ISO, and other styles

TOMELLINI, M., and M. FANFONI. "SCALING, VORONOI TESSELLATION, AND KJMA: THE DISTRIBUTION FUNCTION IN THIN SOLID FILMS." International Journal of Nanoscience 09, no. 01n02 (2010): 1–18. http://dx.doi.org/10.1142/s0219581x10006569.

Full text

Abstract:

Among several aspects concerning the growth of thin films on solid surfaces, we focus our discussion on the physical observable known as the island size distribution function (SDF). Since this is a subject large enough to require a full review, even a whole book, we have limited our survey to the scaling properties of the distribution function and to some of its possible shapes. In particular, we discuss the fast and slow nucleation processes in diffusional growth and the KJMA (Kolmogorov–Johnson–Mehl–Avrami) distributions. Space has been given to the mathematical demonstration of the principal equations, in order to render the paper usable also to neophytes of thin film growth. Experimental particle (SDFs) are also reported and discussed.

APA, Harvard, Vancouver, ISO, and other styles

BURGER, MARTIN, and VINCENZO CAPASSO. "MATHEMATICAL MODELLING AND SIMULATION OF NON-ISOTHERMAL CRYSTALLIZATION OF POLYMERS." Mathematical Models and Methods in Applied Sciences 11, no. 06 (2001): 1029–53. http://dx.doi.org/10.1142/s0218202501001227.

Full text

Abstract:

This paper is devoted to the study of mathematical problems arising in the modelling of nonisothermal polymer crystallization under industrial conditions. A review of the hybrid stochastic-deterministic modelling procedure, which yields an averaged model,5,8 is given and supplied by the study of mathematical problems arising from it. Furthermore, multiple scale effects in the crystallization process are studied using different scalings, focussing either on the heat conduction or on the crystallization part. It is shown that in the limit of fast nucleation and slow growth, the model is equivalent to a direct extension of the classical Avrami–Kolmogorov model equations. In addition, numerical simulations are presented to illustrate the behavior during crystallization. Finally, open questions from mathematical and engineering view points are discussed.

APA, Harvard, Vancouver, ISO, and other styles

Gomez, G. R., M. Bühler, and T. Perez. "Austenite Decomposition in Low Carbon Steels with Microalloy Additions." Materials Science Forum 500-501 (November 2005): 395–402. http://dx.doi.org/10.4028/www.scientific.net/msf.500-501.395.

Full text

Abstract:

A metallurgical model to describe the formation of ferrite, perlite and bainite during continuous cooling was developed. The model uses classical nucleation and early growth theories to calculate the beginning of the reaction, and Avrami-type equations to evaluate the transformation progress. The materials studied were plain carbon steels with different Mn contents, and microalloyed steels with Nb, Ti and/or V additions. The model predictions were adjusted and validated with experimental results obtained from dilatometric tests. The range of cooling rates considered was between 5°C/sec and 50°C/sec. From the comparison with the experimental data it was found that the model correctly describes the dependence of the reaction kinetic on the cooling rate, as well as on the steel chemistry.

APA, Harvard, Vancouver, ISO, and other styles

Gusak, A., and A. Titova. "NEW THERMODYNAMIC APPROACHES TO FAILURE ANALYSIS IN MICROELECTRONIC MATERIALS." Cherkasy University Bulletin: Physical and Mathematical Sciences, no. 1 (2022): 33–46. https://doi.org/10.31651/2076-5851-2022-33-46.

Full text

Abstract:

Failure of the microelectronic device may be treated in the frame of non-equilibrium thermodynamics applied to open systems under the condition of incompatibility of steady states for different processes. The criterion of failure can be related to some threshold amount of the structural entropy produced and accumulated in the system by the external forces. This hypothesis provides a simple interpretation of the empirical Black equation for the mean time to failure in the case of electromigration, and helps to predict similar equations for the cases of thermo- and stress migration. The failure itself can be treated as a phase/structure transformation in the open system and described by kinetics similar to Kolmogorov-Avrami kinetics of the first-order phase transformations.

APA, Harvard, Vancouver, ISO, and other styles

Kleber, Siegfried, and Christof Sommitsch. "Stress Relaxation Measurements of Meta-Dynamic and Static Recrystallization of Alloy 80A." Materials Science Forum 467-470 (October 2004): 1237–42. http://dx.doi.org/10.4028/www.scientific.net/msf.467-470.1237.

Full text

Abstract:

The stress relaxation method has been applied to the nickel-based alloy 80A to predict meta-dynamic (MDRX) and static recrystallization (SRX) kinetics. Compression tests were performed on a Gleeble 3800 system atr different temperatures (950-1200°C). The strain rate was varied in the case of MDRX and the pre-strain in the case of SRX. To investigate MDRX, the prestrain was set to twice the peak strain in order to reach steady state before holding. To focus on the interaction of MDRX and SRX, the pre-strain was set to the peak strain, where dynamic recrystallization (DRX) starts but does not yet reach steady state. Avrami type equations for the prediction of both the MDRX and SRX were adapted to feed a semi-empirical grain structure model.

APA, Harvard, Vancouver, ISO, and other styles

GÖTZ, THOMAS, RENE PINNAU, and JENS STRUCKMEIER. "OPTIMAL CONTROL OF CRYSTALLIZATION PROCESSES." Mathematical Models and Methods in Applied Sciences 16, no. 12 (2006): 2029–45. http://dx.doi.org/10.1142/s0218202506001807.

Full text

Abstract:

In this paper an optimal control problem for polymer crystallization is investigated. The crystallization is described by a non-isothermal Avrami–Kolmogorov model and the temperature at the boundary of the domain serves as control variable. The cost functional takes into account the spatial variation of the crystallinity and the final degree of crystallization. This results in a boundary control problem for a parabolic equation coupled with two ordinary differential equations, which is treated by an adjoint variable approach. We prove the existence and uniqueness of solutions to the state system as well as the existence of a minimizer for the cost functional under consideration. The adjoint system is derived and we use a steepest descent algorithm to solve the problem numerically. Numerical simulations illustrate the applicability and performance of the optimization algorithm.

APA, Harvard, Vancouver, ISO, and other styles

Müller, M., C. L. Azanza Ricardo, R. Di Maggio, and P. Scardi. "Growth kinetics of Cu2ZnSnS4 thin films and powders." Powder Diffraction 28, S2 (2013): S228—S241. http://dx.doi.org/10.1017/s0885715613001012.

Full text

Abstract:

The growth kinetics of Cu2ZnSnS4 thin films and powders was studied using in-situ synchrotron data. Isothermal and isochronal measurements were performed at the MCX beamline of the Elettra synchrotron (Trieste, Italy). Diffraction line profile analysis was used to follow the changes in the domain size distribution during isothermal measurements, and the change in the mean volume of the domains was studied using the Johnson-Mehl-Avrami equation. The growth was found to be diffusion controlled from small dimensions while the nucleation rate is temperature dependent. An activation energy of 210 kJ/mol could be estimated. In case of the isochronal data, the evolution of inverse of the integral breadth of the diffraction peaks in dependence on temperature was studied using the Ozawa and Šatava equations. The activation energy determined for the growth process is between 112(2) and 145(5) kJ/mol.

APA, Harvard, Vancouver, ISO, and other styles

Sanz, L., B. Pereda, and B. López. "Analysis of the Static Recrystallization Behavior of Nb-Ti Microalloyed Steels Including Low Strain Levels." Materials Science Forum 879 (November 2016): 1170–75. http://dx.doi.org/10.4028/www.scientific.net/msf.879.1170.

Full text

Abstract:

Semi-empirical models for predicting the austenite static recrystallization behavior are widely used in designing thermomechanical treatments to improve final mechanical properties. However, a problem with these models is that their utility can be limited to the range of deformation conditions and chemical compositions they were developed for. This work focuses on the study of the applicability of current recrystallization models to the range of low strain conditions and/or high Nb microalloying additions (≈0.1%). To do so, the recrystallization behavior of two low carbon Nb-Ti microalloyed steels (0.04 and 0.11% Nb and ≈0.01% Ti) has been investigated by torsion tests. Experimental results for recrystallization time and recrystallized grain size have been compared to previously developed equations. It has been observed that at low strains (ε = 0.1) the predictions fail. A dependence of the n Avrami exponent both on temperature and applied strain was also found.

APA, Harvard, Vancouver, ISO, and other styles

Hasheminezhad, S. A., M. Haddad-Sabzevar, and S. Sahebian. "Non-Isothermal Crystallization Kinetics of Co₆₇Fe₄Cr₇Si₈B₁₄ Amorphous Alloy." Materials Science Forum 706-709 (January 2012): 1311–17. http://dx.doi.org/10.4028/www.scientific.net/msf.706-709.1311.

Full text

Abstract:

Non-isothermal crystallization kinetics of Co67Fe4Cr7Si8B14amorphous ribbons was studied by differential scanning calorimetry (DSC) technique under 10, 20, 30, 40 and 80 °Cmin-1heating rates. It is found that Co67Fe4Cr7Si8B14amorphous alloy exhibits two-stage crystallization on heating. The two crystallization peaks shift to higher temperatures with increasing heating rate. The apparent activation energies (EC) for the first stage of crystallization were determined as 443.44 and 434.47 kJmol-1by using the Kissinger and Ozawa equations, respectively. Frequency factor (A) estimated to be 1.084×1026s-1using Kissinger equation. Kinetics parameters such as Crystallization exponent (n) and dimensionality of growth (Ndim) were determined using JMA (Johnson-Mehl-Avrami) method. Details of the nucleation and growth behaviours during the non-isothermal crystallization were studied in terms of local activation energy EC(x) by the OFW (Ozawa, Flynn and Wall) method. Also the activation energy for nucleation (En) and growth (Eg) separately estimated.

APA, Harvard, Vancouver, ISO, and other styles

Wang, Qiang Song, Guo Liang Xie, Xu Jun Mi, Bai Qing Xiong, and Xiang Peng Xiao. "The Ageing Characteristics and Strengthening Mechanism of a Cu-2.1Ni-0.5Si-0.2Zr-0.05Cr Alloy." Advanced Materials Research 680 (April 2013): 25–30. http://dx.doi.org/10.4028/www.scientific.net/amr.680.25.

Full text

Abstract:

The ageing process of a Cu-2.1Ni-0.5Si-0.2Zr-0.05Cr alloy in the temperature range from 673 K to 773 K is investigated in this research. The phase transformation process, electric conductivities and mechanical properties during the ageing process are also studied by experimental methods. The precipitation sequence during the aging process of Cu-Ni-Si alloy is GP zone→ (Cu,Ni)3Si→ δNi2Si phase. The conductivity of the aged specimen increases from 20% IACS to 40-45% with prolonging time during aging process in the temperature range from 673 K to 773 K. The dynamic curve of precipitation is obtained by Avrami-equations, based on which the increase of yield strength can be estimated according to Orowan mechanism. Experimental data have been compared with the calculated results in this paper, indicating this method is reasonable, suggesting that strengthening is mainly attributed to Orowan by passing mechanism.

APA, Harvard, Vancouver, ISO, and other styles

Fiume, Elisa, Enrica Verné, and Francesco Baino. "Crystallization behavior of SiO2–P2O5–CaO–MgO–Na2O–K2O bioactive glass powder." Biomedical Glasses 5, no. 1 (2019): 46–52. http://dx.doi.org/10.1515/bglass-2019-0004.

Full text

Abstract:

Abstract The crystallization process of a bioactive silicate glass with 47.5SiO2-10Na2O-10K2O-10MgO-20CaO-2.5P2O5 molar composition was investigated by using nonisothermal differential t hermal a nalysis (DTA). T he DTA plots recorded at different heating rates exhibited a single crystallization peak. The activation energy for crystallization was estimated by applying the equations proposed by Kissinger and Matusita-Sakka. The Johnson-Mehl-Avrami exponent (n) was assessed by using the Ozawa and Augis-Bennett methods. The analyses suggest that a surface crystallization mechanism with one-dimensional crystal growth is predominant. The activation energy for viscous flow was also assessed (176 kJ/mol) and was found lower than the activation energy for crystallization (271 kJ/mol). This confirms the stability of 47.5B against crystallization and its good sinterability, which is a highly attractive feature for producing glass products of biomedical interest, such as bioactive porous scaffolds for bone repair.

APA, Harvard, Vancouver, ISO, and other styles

Liu, Yuyang, Zhihao Zhao, and Gaosong Wang. "Effect of Over-Aging Degree on Microstructures, Precipitation Kinetics, and Mechanical Properties of an Ultra-High-Strength Al-Zn-Mg-Cu Alloy." Coatings 14, no. 11 (2024): 1415. http://dx.doi.org/10.3390/coatings14111415.

Full text

Abstract:

The effect of over-aging on the precipitation behavior and mechanical properties of an ultra-high-strength Al-Zn-Mg-Cu alloy was investigated using various over-aging treatment regimes. To reveal the influence of over-aging on matrix precipitation, nucleation and coarsening mechanisms were analyzed based on thermodynamic models and calculated precipitation data. Precipitation kinetics at different over-aging degrees were determined through differential scanning calorimetry analysis and the Johnson–Mehl–Avrami–Kolmogorov equations, revealing the activation energy required to precipitate the η’ phase precipitates ranging from 166.08 to 343.28 kJ/mol, and the activation energy required to precipitate the η phase precipitates ranging from 802.03 to 288.42 kJ/mol from the T6 to T73 conditions. In conjunction with a quantitative microstructure analysis, a highly accurate model was developed by systematically calculating the strengthening components of the ultra-high-strength Al-Zn-Mg-Cu alloy under various aging conditions.

APA, Harvard, Vancouver, ISO, and other styles

Low, It-Meng. "An Overview of Parameters Controlling the Decomposition and Degradation of Ti-Based Mn+1AXn Phases." Materials 12, no. 3 (2019): 473. http://dx.doi.org/10.3390/ma12030473.

Full text

Abstract:

A critical overview of the various parameters, such as annealing atmospheres, pore microstructures, and pore sizes, that are critical in controlling the decomposition kinetics of Ti-based MAX phases is given in this paper. Ti-based MAX phases tend to decompose readily above 1400 °C during vacuum annealing to binary carbide (e.g. TiCx) or binary nitride (e.g. TiNx), primarily through the sublimation of A elements such as Al or Si, forming in a porous MXx surface layer. Arrhenius Avrami equations were used to determine the activation energy of phase decomposition and to model the kinetics of isothermal phase decomposition. Ironically, the understanding of phase decomposition via exfoliating or selective de-intercalation by chemical etching formed the catalyst for the sensational discovery of Mxenes in 2011. Other controlling parameters that also promote decomposition or degradation as reported in the literature are also briefly reviewed and these include effects of pressure and ion irradiations.

APA, Harvard, Vancouver, ISO, and other styles

Im, Sang Hyeok, Nam Jin Kim, Dong Hwan Kim, et al. "Sintering and Crystallization Behavior in Li₂O-Al₂O₃-SiO₂ (LAS) Glass." Advanced Materials Research 129-131 (August 2010): 753–58. http://dx.doi.org/10.4028/www.scientific.net/amr.129-131.753.

Full text

Abstract:

The study investigated the crystallization and sintering behavior in Li2O-Al2O3-SiO2 (LAS) glass powder. The sintered sample was produced with a glass particle (Φ=44㎛). The relative density and transmittance of the sintered samples showed the highest value at the temperature of 650°C. In the higher temperature than 650°C, the crystal growth occurred to decrease the densification of Li2O-Al2O3-SiO2 (LAS) glass powder. Main crystalline phase was β-spodumene in the glass powder. From the non-isothermal differential thermal analysis, the crystallization of the particles (Φ=44㎛) was observed at 640~684°C with respect to the heating rate. The activation energy of crystallization (EC) and Avrami constant (n) calculated by Kissinger and Ozawa equations indicated that the surface and the bulk crystallization occurred simultaneously in the glass. The optimum sintering condition of this glass powder was 650°C without crystal growth of β-spodumene, although a nucleation or nano-crystal growth occurred.

APA, Harvard, Vancouver, ISO, and other styles

Li, Ting, Kui Zhang, Zhi Wei Du, Jia Wei Yuan, and Xing Gang Li. "Deformation Behavior of Mg-7Gd-5Y-1Nd-0.5Zr Alloy during Hot Compression." Applied Mechanics and Materials 633-634 (September 2014): 108–15. http://dx.doi.org/10.4028/www.scientific.net/amm.633-634.108.

Full text

Abstract:

The hot deformation behavior of Mg-7Gd-5Y-1Nd-0.5Zr alloy was investigated by compression tests at temperatures of 673 K, 713 K, 753 K, and 793 K and strain rates of 0.001 s-1, 0.01 s-1, 0.1 s-1, and 1s-1. The stress-strain curves exhibit typical dynamic recrystallization behavior with a single peak stress followed by a gradual fall toward a steady-state stress. The apparent activation energy of deformation and constitutive equations for the alloy were determined through regression analysis for conventional hyperbolic sine equation. The apparent activation energy of DRX and dynamic kinetics model for alloy were determined using the regression analysis for Avrami equation. Optical microscope and electron backscattered diffraction were employed to investigate the microstructure evolution of Mg-7Gd-5Y-1Nd-0.5Zr alloy during hot compression. The results suggested that the grain boundary is the main nucleation sites of dynamic recrystallization, and (0001) basal fiber texture has formed during hot compression.

APA, Harvard, Vancouver, ISO, and other styles

Volpe, M., M. Tomellini, and M. Fanfoni. "Rate equations and Johnson–Mehl–Avrami–Kolmogoroff method for modelling the coverage–time dependence in thin film growth at solid surfaces." Surface Science 423, no. 2-3 (1999): L258—L264. http://dx.doi.org/10.1016/s0039-6028(99)00003-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Siwek, Aleksander. "CFD-based modelling of phase transformation in laser welded low-carbon steel." Welding in the World 65, no. 7 (2021): 1403–14. http://dx.doi.org/10.1007/s40194-021-01130-2.

Full text

Abstract:

AbstractThis paper presents a numerical model of the laser welding of steel, taking into account the heat and mass flows, as well as thermal effects associated with phase transformations. It was assumed that the heat source is a laser with a symmetrical power distribution of the TEM10 beam in two welding condition variants: a stationary heat source and a source moving at a constant speed along the sample. After reaching the melting temperature, the movement of the liquid phase was forced by the Marangoni effect acting on the surface of the welding pool. For the laser power applied, the surface of the welding pool was assumed to be flat. It was proposed an algorithm for the forecasting of the phase changes during heating and cooling. Diffusive phase transformations during cooling were modelled using Johnson-Mehl-Avrami-Kolmogorov (JMAK) equations. Diffusionless transformations occurring when cooling rates exceed the critical ones were modelled using Koistinen-Marburger (KM) equations. Calculations were made for a rectangular sample welded in air and cooled spontaneously in the atmosphere. The boundary conditions were simulated assuming a constant coefficient of heat exchange and radiation to the environment. The start and end time of the changes occurring in the cooling phase were calculated based on the average cooling rate in the temperature range 800–500°C (v8/5). The model was tested for the test material: S355J2 steel.

APA, Harvard, Vancouver, ISO, and other styles

Teodorescu, Mihaela, Patrice Lasne, and Roland E. Logé. "Modeling Recrystallization for 3D Multi-Pass Forming Processes." Materials Science Forum 558-559 (October 2007): 1201–6. http://dx.doi.org/10.4028/www.scientific.net/msf.558-559.1201.

Full text

Abstract:

The present work concerns the simulation of metallurgical evolutions in 3D multi-pass forming processes. In this context, the analyzed problem is twofold. One point refers to the management of the microstructure evolution during each pass or each inter-pass period and the other point concerns the management of the multi-pass aspects (different grain categories, data structure). In this framework, a model is developed and deals with both aspects. The model considers the microstructure as a composite made of a given (discretized) number of phases which have their own specific properties. The grain size distribution and the recrystallized volume fraction distribution of the different phases evolve continuously during a pass or inter-pass period. With this approach it is possible to deal with the heterogeneity of the microstructure and its evolution in multi-pass conditions. Both dynamic and static recrystallization phenomena are taken into account, with typical Avrami-type equations. The present model is implemented in the Finite Element code FORGE2005®. 3D numerical simulation results for a multi-pass process are presented.

APA, Harvard, Vancouver, ISO, and other styles

Meng, Weixiao, Xiaojie Zhang, Xiuli Hu, et al. "Mechanical Properties and Non-Isothermal Crystallization Kinetics of Polylactic Acid Modified by Polyacrylic Elastomers and Cellulose Nanocrystals." Polymers 15, no. 18 (2023): 3767. http://dx.doi.org/10.3390/polym15183767.

Full text

Abstract:

In this paper, a polyacrylic elastomer latex with butyl acrylate (BA) as the core and methyl methacrylate (MMA) copolymerized with glycidyl methacrylate (GMA) as the shell, named poly(BA-MMA-GMA) (PBMG), was synthesized by seeded emulsion polymerization. Cellulose nanocrystal (CNC) was dispersed in the polyacrylic latex to prepare PBMG/CNC dispersions with different CNC contents. The dried product was mixed with polylactic acid (PLA) to fabricate PLA/PBMG/CNC blends. The addition of PBMG and PBMG/CNC improved the mechanical properties of the PLA matrix. Differential scanning calorimetry (DSC) was used to investigate the non-isothermal crystallization kinetics. The Avrami equation modified by the Jeziorny, Ozawa and Mo equations was used to analyze the non-isothermal crystallization kinetics of PLA and its blends. Analysis of the crystallization halftime of non-isothermal conditions indicated that the overall rate of crystallization increased significantly at 1 wt% content of CNC. This seemed to result from the increase of nucleation density and the acceleration of segment movement in the presence of the CNC component. This phenomenon was verified by polarizing microscope observation.

APA, Harvard, Vancouver, ISO, and other styles

Жукова, М. М., П. Н. Столяров, Ю. А. Мисюрин, В. Н. Алфимов, И. А. Базуров, and А. А. Костерова. "MODELS OF ALANE DECOMPOSITION UNDER DYNAMIC HEATING." Южно-Сибирский научный вестник, no. 5(51) (October 31, 2023): 89–94. http://dx.doi.org/10.25699/sssb.2023.51.5.011.

Full text

Abstract:

Исследование твердофазных процессов в условиях динамического нагрева образца представляет значительный интерес в связи с возможным изменением кинетической модели, по сравнению с разложением в условиях постоянной температуры. Для обработки экспериментальных данных твердофазных процессов используют как модели одностадийных реакций, таких как модели Киссинджера, Фридмана, Озава-Флина, Аврами-Ерофеева и ряд других, а также модели многостадийных реакций. Для многостадийных моделей для каждой стадии используются уравнения типа Аврами- Ерофеева. Кроме простых моделей используется изоконверсионный метод, позиционируемый как универсальный метод, не требующий предположения о лимитирующих стадиях процесса. Экспериментальные данные процесса разложения алана в условиях отсутствия кислорода удовлетворительно описываются либо уравнением автокатализа первого порядка (по потере массы), либо двухстадийной кинетикой (данные ДСК или волюмометрия). Разложение в присутствии кислорода требует более сложной модели (трехстадийной) с учетом появления окисной пленки на поверхности алана. The study of solid-phase processes under conditions of dynamic heating of a sample is of considerable interest. Will there be a change in the kinetic model, that is, limiting processes, in comparison with decomposition under conditions of constant temperature? To what extent will the kinetic parameters of the processes change? For processing experimental data of solid-state processes, both models of single-stage reactions are used, such as the models of Kissinger, Friedman, Ozawa-Flyn, Avrami-Erofeev and a number of others, as well as models of multi-stage reactions. For multi-stage models, Avrami-Erofeev-type equations are used for each stage. In addition to simple models, the isoconversion method is used, which is positioned as a universal method that does not require assumptions about the limiting stages of the process. Experimental data on the decomposition of alane in the absence of oxygen are satisfactorily described either by the first-order autocatalysis equation (in terms of mass loss) or by two-stage kinetics (DSC data or volumetrics). Decomposition in the presence of oxygen requires a more complex model (three-stage) taking into account the appearance of an oxide film.

APA, Harvard, Vancouver, ISO, and other styles

Henrichsen, L. K., and A. J. McHugh. "Analysis of Film Blowing with Flow-enhanced Crystallization." International Polymer Processing 22, no. 2 (2007): 179–89. http://dx.doi.org/10.1515/ipp-2007-0009.

Full text

Abstract:

Abstract An analysis of the steady-state film blowing process based on a two-phase constitutive model that accounts for flow-enhanced crystallization is presented. The amorphous melt phase is represented by a multi-mode Giesekus constitutive equation with a transformation-dependent relaxation time and the semi-crystalline phase is represented by a rigid rod model. The relaxation times in the two constitutive equations are linked by an Avrami, temperature-dependent rate expression which contains a term in the Helmholtz free energy to account for flow-enhancement. Comparisons are made to experimental data for film blowing of linear low density (LLDPE) and low density (LDPE) polyethylenes. Excellent fits for the bubble radius, temperature, and crystallinity are shown. It is also shown that the ratio of amorphous stress to total stress at the “lock-in” point provides an excellent correlating variable for the elongation to break and yield strength properties of the as-blown film. Inclusion of multiple relaxation times in the Giesekus model offers insights on the controlling role of the maximum relaxation time in the stress profiles and locking-in behavior due to crystallization.

APA, Harvard, Vancouver, ISO, and other styles

Kim, Young Seok, Kyu Ho Lee, Tae Ho Kim, Young Joon Jung, S. H. Yim, and Bong Ki Ryu. "Crystallization Kinetics for Synthesis Hyper-Structure in P₂O₅-ZnO-B₂O₃-BaO-Al₂O₃-TiO₂ Glass Ceramic Composite." Materials Science Forum 569 (January 2008): 153–56. http://dx.doi.org/10.4028/www.scientific.net/msf.569.153.

Full text

Abstract:

The nucleation and crystallization kinetics of P2O5-B2O3-ZnO-BaO-Al2O3-TiO2 crystals in bulk glass in which this crystals were found to crystallize in the heating process of the glass, were studied by non-isothermal measurements using differential thermal analysis (DTA). A nucleation rate-temperature was determined by plotting either the reciprocal of the temperature corresponding to the crystallization peak maximum, 1/Tp, or the height of the crystallization peak, (*T)p, as a function of nucleation temperature, Tn. The temperature where nucleation can occur for this glass ranges from 700°C to 890°C and the temperature for maximum nucleation is 760±5°C. The correct activation energy for crystallization, Ec, for this glass is the same for surface and/or bulk crystallization, and is 533±15°CkJ/mol. The analysis of the crystallization data with the Kissinger equation and the Marotta equation yields the correct value for Ec only crystal growth occurs on a fixed number of nuclei. The crystallization process of a sample heat treated at the temperature of the maximum nucleation rate was fitted to kinetic equations with an Avrami constant, n ≈2 and a dimensionality of crystal growth, m ≈2.

APA, Harvard, Vancouver, ISO, and other styles

Sheng, I. C., and Y. Chen. "Modeling Welding by Surface Heating." Journal of Engineering Materials and Technology 114, no. 4 (1992): 439–49. http://dx.doi.org/10.1115/1.2904197.

Full text

Abstract:

A mathematical model has been developed in describing the temperature distribution, the flow of the molten fluid and the stress field in the solid during welding. In modeling the properties of the material during welding, the solid phase is assumed to behave as a thermoviscoplastic solid obeying Bodner-Partom/Walker type constitutive equation, whereas the fluid phase as a thermoviscous incompressible fluid. Three regions exist: pure solid, pure fluid, and the transition (solid-fluid mixture). In the formulation of the boundary value problem, the energy equation is coupled to the equation of motion through the terms of mechanical work and the latent heat of the phases, whereas the equations of motion of the solid and the fluid are decoupled. Appropriate thermal and traction boundary conditions are detailed in the text. Phase transformation activities during cooling are monitored by CCT diagram and Avrami equation. An arbitrary Lagrangian and Eulerian method is used to accommodate the kinematic description of both the solid and the fluid phases. A representative plane perpendicular to the moving heat source is analyzed. Results of sample calculations are presented to show the temperature and the stress evolution in time. Residual stress and microstructure patterns are presented.

APA, Harvard, Vancouver, ISO, and other styles

Winczek, J., and T. Skrzypczak. "Thermomechanical States in Arc Weld Surfaced Steel Elements." Archives of Metallurgy and Materials 61, no. 3 (2016): 1623–34. http://dx.doi.org/10.1515/amm-2016-0264.

Full text

Abstract:

AbstractThe paper presents a model of temperature, phase transformation and stresses fields in a steel element during single-pass Gas Metal Arc Weld (GMAW) surfacing.Kinetics of phase transformations during heating is limited by temperature values at the beginning and at the end of austenitic transformation, while the progress of phase transformations during cooling is determined on the basis of TTT-welding diagram and Johnson-Mehl-Avrami and Kolomogorov law for diffusive transformations and Koistinen-Marburger for martensitic transformation. Stress state of a bar subjected to thermo-mechanical loads is described assuming the plane cross section hypothesis and using integral equations of stress equilibrium of a bar as well as simple Hook’s law. Stresses in the elastic-plastic state are determined by iteration using solutions with a variable elastic modulus of elasticity, conditioned by tensile curves. Dependence of stresses on strains is assumed on the basis of tensile curves of particular structures, taking into account the influence of temperature. There were performed calculations of the temperature field, phase transformations, strains and stresses for GMAW surfacing of a cuboid element made of S235 steel. Authors’ programs, made in Borland Delphi, were used for calculations.

APA, Harvard, Vancouver, ISO, and other styles

Kubiak, Marcin, Zbigniew Saternus, Tomasz Domański, and Wiesława Piekarska. "Modeling of Yb:YAG Laser Beam Caustics and Thermal Phenomena in Laser–Arc Hybrid Welding Process with Phase Transformations in the Solid State." Materials 17, no. 10 (2024): 2364. http://dx.doi.org/10.3390/ma17102364.

Full text

Abstract:

This paper focuses on the mathematical and numerical modeling of the electric arc + laser beam welding (HLAW) process using an innovative model of the Yb:YAG laser heat source. Laser energy distribution is measured experimentally using a UFF100 analyzer. The results of experimental research, including the beam profile and energetic characteristics of an electric arc, are used in the model. The laser beam description is based on geostatistical kriging interpolation, whereas the electric arc is modeled using Goldak’s distribution. Hybrid heat source models are used in numerical algorithms to analyze physical phenomena occurring in the laser–arc hybrid welding process. Thermal phenomena with fluid flow in the fusion zone (FZ) are described by continuum conservation equations. The kinetics of phase transformations in the solid state are determined using Johnson–Mehl–Avrami (JMA) and Koistinen–Marburger (KM) equations. A continuous cooling transformation (CCT) diagram is determined using interpolation functions and experimental research. An experimental dilatometric analysis for the chosen cooling rates is performed to define the start and final temperatures as well as the start and final times of phase transformations. Computer simulations of butt-welding of S355 steel are executed to describe temperature and melted material velocity profiles. The predicted FZ and heat-affected zone (HAZ) are compared to cross-sections of hybrid welded joints, performed using different laser beam focusing. The obtained results confirm the significant influence of the power distribution of the heat source and the laser beam focusing point on the temperature distribution and the characteristic zones of the joint.

APA, Harvard, Vancouver, ISO, and other styles

Rusu, Lăcrămioara, Cristina-Gabriela Grigoraș, Andrei-Ionuț Simion, Elena-Mirela Suceveanu, Bogdan Istrate, and Maria Harja. "Biosorption Potential of Microbial and Residual Biomass of Saccharomyces pastorianus Immobilized in Calcium Alginate Matrix for Pharmaceuticals Removal from Aqueous Solutions." Polymers 14, no. 14 (2022): 2855. http://dx.doi.org/10.3390/polym14142855.

Full text

Abstract:

Two types of biosorbents, based on Saccharomyces pastorianus immobilized in calcium alginate, were studied for the removal of pharmaceuticals from aqueous solutions. Synthetized biocomposite materials were characterized chemically and morphologically, both before and after simulated biosorption. Ethacridine lactate (EL) was chosen as a target molecule. The process performance was interpreted as a function of initial solution pH, biosorbent dose, and initial pharmaceutical concentration. The results exhibited that the removal efficiencies were superior to 90% for both biosorbents, at the initial pH value of 4.0 and biosorbent dose of 2 g/L for all EL initial concentrations tested. Freundlich, Temkin, Hill, Redlich-Peterson, Sips, and Toth isotherms were used to describe the experimental results. The kinetic data were analyzed using kinetic models, such as pseudo-first order, pseudo-second order, Elovich, and Avrami, to determine the kinetic parameters and describe the transport mechanisms of EL from aqueous solution onto biosorbents. Among the tested equations, the best fit is ensured by the pseudo-second-order kinetics model for both biosorbents, with the correlation coefficient having values higher than 0.996. The many potential advantages and good biosorptive capacity of Saccharomyces pastorianus biomass immobilized in calcium alginate recommend these types of biocomposite materials for the removal of pharmaceuticals from aqueous solutions.

APA, Harvard, Vancouver, ISO, and other styles

Atapek, Ş. Hakan, İrfan Eker, Fulya Kahrıman, and Şeyda Polat. "Homogenization effect on precipitation kinetics and mechanical properties of an extruded AA7050 alloy." Materials Testing 64, no. 10 (2022): 1455–64. http://dx.doi.org/10.1515/mt-2022-0190.

Full text

Abstract:

Abstract In this study, effect of homogenization on precipitation kinetics and mechanical properties during aging in AA7050 alloy was investigated. The billet material produced by direct chill method was homogenized at 470 °C for 12–20 h and then extruded to form T-profile. The electrical conductivity of the alloy aged at 120 and 185 °C for 0–36 h were measured and precipitation kinetics were calculated based on the relationship between increased electrical conductivity and amount of precipitates during aging. Time dependent precipitation fraction change curves using Avrami equations revealed that precipitation accelerated as the homogenization time increased due to increased nucleation and growth rates of precipitates. Peak hardness values in aging were reached depending on the increase in homogenization time, however, lower peak hardness (∼185 HV) was determined at 185 °C aging compared to the obtained ones (195–197 HV) at 120 °C aging. Depending on the increase in homogenization time, an increase trend in strength was detected in peak aged alloys. The application of longer time homogenization and subsequent aging caused an increase in strengths. The studied homogenization and aging conditions could be a useful guide for achieving the highest strength and ideal elongation values in commercial practice for the AA7050 alloy.

APA, Harvard, Vancouver, ISO, and other styles

Ahmad, Ibrahim, Hyun-Kyung Kim, Suleyman Deveci, and R. Kumar. "Non-Isothermal Crystallisation Kinetics of Carbon Black- Graphene-Based Multimodal-Polyethylene Nanocomposites." Nanomaterials 9, no. 1 (2019): 110. http://dx.doi.org/10.3390/nano9010110.

Full text

Abstract:

The effect of carbon black (CB) and microwave-induced plasma graphene (g) on the crystallisation kinetics of the multimodal high-density polyethylene was studied under non-isothermal conditions. The non-isothermal crystallisation behaviour of the multimodal-high-density polyethylene (HDPE), containing up to 5 wt.% graphene, was compared with that of neat multimodal-HDPE and its carbon black based nanocomposites. The results suggested that the non-isothermal crystallisation behaviour of polyethylene (PE)-g nanocomposites relied significantly on both the graphene content and the cooling rate. The addition of graphene caused a change in the mechanism of the nucleation and the crystal growth of the multimodal-HDPE, while carbon black was shown to have little effect. Combined Avrami and Ozawa equations were shown to be effective in describing the non-isothermal crystallisation behaviour of the neat multimodal-HDPE and its nanocomposites. The mean activation energy barrier (ΔE), required for the transportation of the molecular chains from the melt state to the growing crystal surface, gradually diminished as the graphene content increased, which is attributable to the nucleating agent effect of graphene platelets. On the contrary, the synergistic effect resulting from the PE-CB nanocomposite decreased the ΔE of the neat multimodal-HDPE significantly at the lowest carbon black content.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!