Activation energies for nucleation and growth and critical cluster size dependence in JMAK analyses of kinetic Monte-Carlo simulations of precipitation

Molnár, Dávid; Niedermeier, Christian A.; Mora, Alejandro; Binkele, Peter; Schmauder, Siegfried

doi:10.1007/s00161-012-0258-5

Cited by 9 publications

(9 citation statements)

References 19 publications

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“…This leads to a slower transformation rate compared to Eq. (1) as interfering nuclei will hinder each other from growing further, similar to Ostwald ripening as described and illustrated by Molnar et al [44]. However, if the nuclei are positioned far from each other with less risk of interfering, the impingement is weak with a faster transformation rate as compared to Eq.…”

Section: Kinetic Analysismentioning

confidence: 82%

In situ X-ray scattering study of the cubic to hexagonal transformation of AlN in Ti1−xAlxN

et al. 2014

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In the present work, we have studied the decomposition of arc-evaporated Ti 0.55 Al 0.45 N and Ti 0.36 Al 0.64 N during heat treatments in vacuum by in situ synchrotron wide-angle X-ray scattering primarily to characterize the kinetics of the phase transformation of AlN from the cubic (c) NaCl structure to the hexagonal (h) wurtzite structure. In addition, in situ small-angle X-ray scattering measurements were conducted to explore details of the wavelength evolution of the spinodal decomposition, thus providing information about the critical size of the c-AlN-rich domains prior to the onset of the transformation to h-AlN. We report the fractional cubic to hexagonal transformation of AlN in Ti 1Àx Al x N as a function of time and extract activation energies between 320 and 350 kJ mol À1 depending on the alloy composition. The onset of the hexagonal transformation occurs $50 K lower in Ti 0.36 Al 0.64 N compared to Ti 0.55 Al 0.45 N where the high Al content alloy also has a significantly higher transformation rate. A critical wavelength for the cubic domains of $13 nm was observed for both alloys. Scanning transmission electron microscopy shows a c-TiN/h-AlN microstructure with a striking morphology resemblance to the c-TiN/c-AlN microstructure present prior to the hexagonal transformation.

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Section: Kinetic Analysismentioning

confidence: 82%

In situ X-ray scattering study of the cubic to hexagonal transformation of AlN in Ti1−xAlxN

et al. 2014

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“…However, this model is not often the best choice for hydrothermal reactions (Lasaga, 1998;Kasioptas et al, 2010) because the JMAK model assumes that the activation energy and reaction order are not time dependent. This presumption follows from the following constraints for the JMAK model: 1) uniform nucleation at random sites in an infinite system with isotropic growth; 2) no change in nucleation, crystallization, and dissolution mechanisms or activation energies; and 3) high supersaturation (Lasaga, 1998;Molnar et al, 2012;Rheingans and Mittemeijer, 2013). In hydrothermal systems, the availability of nucleation sites may decrease; the types of nucleation sites and reaction mechanisms may change; and the saturation level will decrease due to precipitation (De Blanco et al, 1986;Molnar et al, 2012).…”

Section: Background For Jmak Analysismentioning

confidence: 99%

“…This presumption follows from the following constraints for the JMAK model: 1) uniform nucleation at random sites in an infinite system with isotropic growth; 2) no change in nucleation, crystallization, and dissolution mechanisms or activation energies; and 3) high supersaturation (Lasaga, 1998;Molnar et al, 2012;Rheingans and Mittemeijer, 2013). In hydrothermal systems, the availability of nucleation sites may decrease; the types of nucleation sites and reaction mechanisms may change; and the saturation level will decrease due to precipitation (De Blanco et al, 1986;Molnar et al, 2012). For instance, in their study of the replacement of aragonite by apatite in aqueous solutions from 80 to 190 °C, Kasioptas et al (2010) report that the activation energies increase linearly while the reaction order increases exponentially with increasing temperature.…”

Section: Background For Jmak Analysismentioning

confidence: 99%

A kinetic analysis of the transformation from akaganeite to hematite: An in situ time-resolved X-ray diffraction study

2016

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The nucleation and growth of akaganeite and its transformation to hematite under hydrothermal conditions were monitored over a temperature range of 80 to 200 °C using time-resolved synchrotron X-ray diffraction. In each experiment, akaganeite was the first phase to form and hematite was the final phase. No intermediate phases were identified.The induction time to akaganeite nucleation was ~5525 s and 537 s at 80 °C and 100 °C, respectively, yielding an activation energy of 129 ± 15 kJ/mol. However, akaganeite nucleated at a constant temperature of 123 ± 5 °C when the heater set point was 150 °C or higher, suggesting an activation energy for akaganeite nucleation of 0 kJ/mol between 150 -200 °C. Hematite nucleation induction times decreased with increasing temperature from 1723 s to 110 s between 150 and 200 °C. Based on a JMAK analysis, the activation energies for the crystal growth and dissolution of akaganeite were 74 ± 8 kJ/mol and 125 ± 7 kJ/mol, respectively. Our calculated activation energies for hematite nucleation and crystal growth were 80 ± 13 kJ/mol and 110 ± 21 kJ/mol, respectively.

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“…This is generally not fulfilled in most cases but owing to the simplicity of the KJMA equation it is widely used among experimentalists for transformations in, e.g., steel [25][26][27], polymers [28], and ceramic coatings [29]. Due to the prerequisites of a homogenous nucleation there are modified versions of the KJMA equation to account for grain boundary nucleation [30,31]. In Paper V, Eq.…”

Section: Nucleation and Growthmentioning

confidence: 99%

Microstructural evolution of TiAlN hard coatings at elevated pressures and temperatures

Norrby¹

2014

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LINKÖPING 2014The cover image shows nine two-dimensional x-ray diffractograms of TiAlN merged into one quarter circle. Going counterclockwise from an as-deposited sample, the parts show different stages of annealing. The color scheme is chosen to represent the motto "Stort hjärta, hårt arbete".Niklas Norrby, unless otherwise stated ISBN: 978-91-7519-372-4 ISSN: 0345-7524 Printed by LiU-Tryck, Linköping, Sweden, 2014 i Abstract A typical hard coating on metal cutting inserts used in for example turning, milling or drilling operations is TiAlN. At elevated temperatures, TiAlN exhibits a well characterized spinodal decomposition into coherent cubic TiN and AlN rich domains, which is followed by a transformation from cubic to hexagonal AlN. Using in-situ synchrotron x-ray radiation, the kinetics of the second transformation was investigated in this thesis and the strong temperature dependence on the transformation rate indicated a diffusion based nucleation and growth mechanism. The results gave additional information regarding activation energy of the transformation and the critical wavelength of the cubic domains at the onset of hexagonal AlN. After nucleation and growth, the hexagonal domains showed a striking resemblance with the preexisting cubic AlN microstructure.During metal cutting, the tool protecting coating is subjected to temperatures of ~900 ºC and pressure levels in the GPa range. The results in this thesis have shown a twofold effect of the pressure on the decomposition steps. Firstly, the spinodal decomposition was promoted by the applied pressure during metal cutting which was shown by comparisons with annealed samples at similar temperatures. Secondly, the detrimental transformation from cubic to hexagonal AlN was shown to be suppressed at elevated hydrostatic pressures. A theoretical pressure/temperature phase diagram, validated with experimental results, also showed suppression of hexagonal AlN by an increased temperature at elevated pressures.The spinodal decomposition during annealing and metal cutting was in this work also shown to be strongly affected by the elastic anisotropy of TiAlN, where the phase separation was aligned along the elastically softer <100> directions in the crystal. The presence of the anisotropic microstructure enhanced the mechanical properties compared to the isotropic case, mainly due to a shorter distance between the c-AlN and c-TiN domains in the anisotropic case. Further improvement of the metal cutting behavior ii was realized by depositing individual layers with an alternating bias. The individual bias layers exhibited microstructural differences with different residual stress states. The results of the metal cutting tests showed an enhanced wear resistance in terms of both crater and flank wear compared to coatings deposited with a fixed bias.iii Populärvetenskaplig sammanfattningI den här avhandlingen presenteras forskningsresultat på en keramisk beläggning, TiAlN (titanaluminiumnitrid), som ligger som ett skyddande skikt på svarvskär. Tjockleken på beläggni...

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Activation energies for nucleation and growth and critical cluster size dependence in JMAK analyses of kinetic Monte-Carlo simulations of precipitation

Cited by 9 publications

References 19 publications

In situ X-ray scattering study of the cubic to hexagonal transformation of AlN in Ti1−xAlxN

In situ X-ray scattering study of the cubic to hexagonal transformation of AlN in Ti1−xAlxN

A kinetic analysis of the transformation from akaganeite to hematite: An in situ time-resolved X-ray diffraction study

Microstructural evolution of TiAlN hard coatings at elevated pressures and temperatures

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