Grain Growth Kinetics: The Grain Growth Exponent

Grain growth kinetics in an AISI 347 stainless steel with Nb content up to 0.7%wt was studied during the isothermal holding in the temperature range of 1100-1270°C for various periods. Abnormal grain growth was observed even in the presence of a large amount of precipitates. The kinetics of normal grain growth was tracked by metallographic measurements and fitted by the classical modeling, which led to two important parameters of activation energy Q and growth exponent n derived. Both of them are larger than the usual values for grain growth in the Nb-microalloyed steels due to the much larger content of Nb in the present steel.

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Computer simulation of grain growth kinetics with solute drag

Journal of Materials Research ◽

10.1557/jmr.1999.0147 ◽

1999 ◽

Vol 14 (3) ◽

pp. 1113-1123 ◽

Cited By ~ 35

Author(s):

D. Fan ◽

S. P. Chen ◽

Long-Qing Chen

Keyword(s):

Grain Boundary ◽

Grain Growth ◽

Growth Kinetics ◽

Driving Force ◽

Boundary Energy ◽

Solute Drag ◽

Lattice Diffusion ◽

Diffuse Interface ◽

Growth Exponent ◽

Grain Growth Kinetics

The effects of solute drag on grain growth kinetics were studied in two-dimensional (2D) computer simulations by using a diffuse-interface field model. It is shown that, in the low velocity/low driving force regime, the velocity of a grain boundary motion departs from a linear relation with driving force (curvature) with solute drag. The nonlinear relation of migration velocity and driving force comes from the dependence of grain boundary energy and width on the curvature. The growth exponent m of power growth law for a polycrystalline system is affected by the segregation of solutes to grain boundaries. With the solute drag, the growth exponent m can take any value between 2 and 3, depending on the ratio of lattice diffusion to grain boundary mobility. The grain size and topological distributions are unaffected by solute drag, which are the same as those in a pure system.

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Grain growth kinetics and microstructures of the high Tc GdBa2Cu3O7−δ superconductor

Journal of Materials Research ◽

10.1557/jmr.1992.3194 ◽

1992 ◽

Vol 7 (12) ◽

pp. 3194-3201 ◽

Cited By ~ 5

Author(s):

M.W. Shin ◽

T.M. Hare ◽

A.I. Kingon ◽

C.C. Koch

Keyword(s):

Aspect Ratio ◽

Grain Growth ◽

Growth Kinetics ◽

Boundary Energy ◽

Growth Exponent ◽

Second Phase ◽

High Tc ◽

Microstructure Observation ◽

Grain Aspect Ratio ◽

Grain Growth Kinetics

Grain growth in the GdBa2Cu3O7−δ high Tc superconductor was investigated. The composition Gd1.09Ba1.91Cu3O7−δ, within the solid solubility region, was selected for the present grain growth study. Differential thermal analysis did not reveal any thermal event except the incongruent melting point, which is indicative of the absence of a liquid second phase during grain growth. The final densities of isothermally annealed samples ranged from 91.3% to 93.7% of theoretical density. The microstructure observation showed a greater grain aspect ratio in this material than in YBa2Cu3O7−δ. The average grain aspect ratio was about 4.7. A very low grain growth exponent of 0.07 was found in the isothermal annealing temperature range from 965 °C to 1020 °C. By comparison with the results on the YBa2Cu3O7−δ system previously reported, it was concluded that the grain growth kinetics in these materials are strongly controlled by the anisotropy of the grain boundary energy. The activation energy of grain growth was calculated to be about 77 kJ/mole.

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Grain growth kinetics for B2O3-doped ZnO ceramics

Materials Science-Poland ◽

10.1515/msp-2015-0029 ◽

2015 ◽

Vol 33 (2) ◽

pp. 220-229 ◽

Cited By ~ 5

Author(s):

Berat Yuksel ◽

T. Osman Ozkan

Keyword(s):

Activation Energy ◽

Grain Growth ◽

Growth Kinetics ◽

Liquid Phase Sintering ◽

Growth Exponent ◽

Second Phase ◽

Growth Activation ◽

Doped Zno ◽

Grain Growth Kinetics ◽

Zno Ceramics

AbstractGrain growth kinetics in 0.1 to 2 mol % B2O3-added ZnO ceramics was studied by using a simplified phenomenological grain growth kinetics equation Gn = K0 · t · exp(-Q/RT) together with the physical properties of sintered samples. The samples, prepared by conventional ceramics processing techniques, were sintered at temperatures between 1050 to 1250 °C for 1, 2, 3, 5 and 10 hours in air. The kinetic grain growth exponent value (n) and the activation energy for the grain growth of the 0.1 mol % B2O3-doped ZnO ceramics were found to be 2.8 and 332 kJ/mol, respectively. By increasing B2O3 content to 1 mol %, the grain growth exponent value (n) and the activation energy decreased to 2 and 238 kJ/mol, respectively. The XRD study revealed the presence of a second phase, Zn3B2O6 formed when the B2O3 content was > 1 mol %. The formation of Zn3B2O6 phase gave rise to an increase of the grain growth kinetic exponent and the grain growth activation energy. The kinetic grain growth exponent value (n) and the activation energy for the grain growth of the 2 mol % B2O3-doped ZnO ceramics were found to be 3 and 307 kJ/mol, respectively. This can be attributed to the second particle drag (pinning) mechanism in the liquid phase sintering.

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Grain growth kinetics and microstructure in the high Tc YBa2Cu3O7−δ superconductor

Journal of Materials Research ◽

10.1557/jmr.1991.2026 ◽

1991 ◽

Vol 6 (10) ◽

pp. 2026-2034 ◽

Cited By ~ 19

Author(s):

M.W. Shin ◽

T.M. Hare ◽

A.I. Kingon ◽

C.C. Koch

Keyword(s):

Aspect Ratio ◽

Grain Growth ◽

Growth Kinetics ◽

Weak Link ◽

Boundary Energy ◽

Critical Currents ◽

Growth Exponent ◽

High Anisotropy ◽

Significant Difference ◽

Grain Growth Kinetics

The grain growth and microstructure development of YBa2Cu3O7−δ have been investigated utilizing two different starting particle size distributions (normal and bimodal). The grain growth exponent, n, was found to be about 0.21 for both normal and bimodal samples. An activation energy of 125 kJ/mole was calculated. The low value of n might be attributed to the high anisotropy of grain boundary energy in this system. Samples made from the bimodal powder were found to accelerate grain growth without introducing abnormal grain growth. Although most of the samples attained fractional densities greater than 0.95, the presence of various amounts of porosity (particularly in the case of the bimodal starting powder) did not affect the growth kinetics. The measured aspect ratio of grains did not significantly change during growth. A significant difference in aspect ratio was measured between samples made from the two different starting powders. Critical currents ranged from 10 to 120 A/cm2, but no concrete relationship with grain size was established. This implies that the grains produced by this experiment were in the size range where other factors, presumably microcracking, severely limited the current carrying capacity by the weak link effect.

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Grain Growth Kinetics of Accumulative Roll Bonded AZ61 Alloy

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.585.387 ◽

2012 ◽

Vol 585 ◽

pp. 387-391 ◽

Cited By ~ 2

Author(s):

H. Shivananda Nayaka ◽

Gajanan P. Chaudhari ◽

B.S. Sunder Daniel

Keyword(s):

Grain Growth ◽

Growth Kinetics ◽

Annealing Temperature ◽

Isothermal Annealing ◽

Arrhenius Equation ◽

Growth Exponent ◽

Az61 Magnesium Alloy ◽

Ultrafine Grained ◽

Grain Growth Kinetics ◽

Kinetics Of

A detailed study was performed on the grain growth kinetics of ultrafine-grained AZ61 magnesium alloy produced by accumulative roll bonding by carrying out isothermal annealing treatments on the roll bonded samples. Annealing treatments were carried out in the temperature range 423 to 573K for 2 to 120 minutes. As the annealing time and temperature increased, the grain size increased. The effect of annealing temperature and time, on the grain growth can be well explained by the kinetic equation and Arrhenius equation. Based on the experimental results of grain growth during annealing treatments, the grain growth exponent and the activation energy for grain growth were determined. The grain growth kinetic parameters were compared with other magnesium alloys processed by various methods.

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A Study on the Hall–Petch Relationship and Grain Growth Kinetics in FCC-Structured High/Medium Entropy Alloys

Entropy ◽

10.3390/e21030297 ◽

2019 ◽

Vol 21 (3) ◽

pp. 297 ◽

Cited By ~ 14

Author(s):

Yung-Chien Huang ◽

Che-Hsuan Su ◽

Shyi-Kaan Wu ◽

Chieh Lin

Keyword(s):

Grain Size ◽

Grain Growth ◽

Growth Kinetics ◽

Lattice Distortion ◽

Kinetic Constant ◽

Growth Exponent ◽

Hardness Variation ◽

Modulus Difference ◽

Cold Rolled ◽

Grain Growth Kinetics

The recrystallization behavior, grain growth kinetics, and corresponding hardness variation of homogenized and 80% cold-rolled FeCoNiCrPd, FeCoNiCrMn, and their quaternary/ternary FCC-structured high/medium entropy alloys (H/MEAs) annealed under different conditions were investigated. Experimental results indicate that the grain size and hardness of these H/MEAs follow the Hall–Petch equation, with the Hall–Petch coefficient KH value being mainly dominated by the alloy’s stacking fault energy and shear modulus. The FeCoNiCrPd alloy exhibits the highest hardness of the H/MEAs at the same grain size due to the largest Young’s modulus difference between Cr and Pd. The grain growth exponent n, kinetic constant k, and activation energy for grain growth QG of all H/MEAs are calculated. The k can be expressed by the Arrhenius equation with QG, which is attributed to the diffusion rate. The results demonstrate that the QG values of these H/MEAs are much higher than those of conventional alloys; most notable is FeCoNiCrPd HEA, which has an unusually lattice distortion effect that hinders grain growth.

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Microstructural Features of the ZnO-Bi2O3 Binary System

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.545.8 ◽

2013 ◽

Vol 545 ◽

pp. 8-13 ◽

Cited By ~ 1

Author(s):

Niti Yongvanich ◽

Visuttipitukul Patama ◽

Wassa Kijsiri ◽

Nawarat Pancharoen

Keyword(s):

Activation Energy ◽

Grain Growth ◽

Growth Kinetics ◽

Transport Processes ◽

Liquid Phase Sintering ◽

Growth Exponent ◽

Size Difference ◽

Rapid Improvement ◽

New Findings ◽

Grain Growth Kinetics

Grain growth in ZnO with Bi2O3 addition of up to 1 mol% was examined in great detail for sintering in air. The results are analyzed and compared with previous reports in the context of the simplified phenomenological grain growth kinetics equation along with the physical properties of the sintered ceramics. In spite of the eutectic temperature at 735 °C, high density (> 90%) was not achieved at all Bi2O3 contents; this finding was contradictory to the well-known liquid-phase sintering. At 800 °C, rapid improvement in sintering occurred when increasing the content of Bi2O3 from 0.125mol% to 0.25mol%. Schematic study on weight loss also demonstrated an insignificant level of Bi2O3 volatilization under certain content. Analysis of the grain growth kinetics from isothermal sintering (900 °C - 1,000 °C) revealed strikingly different results in both grain growth exponent (n) and activation energy previously reported in literature. The n values ranged from 3.2 to 5.6 whereas the activation energy from 335 to 598 kJ/mol. Such large disparities were believed to be associated with various mass transport processes. The grain sizes in this study were much smaller than those published in literature (> 10 μm). This size difference, along with other microstructural features, was discussed and correlated in order to explain such anomalies and new findings obtained from the grain growth kinetics results.

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β Grain Growth Kinetics of a New Metastable β Titanium Alloy

Materials Science Forum ◽

10.4028/www.scientific.net/msf.747-748.844 ◽

2013 ◽

Vol 747-748 ◽

pp. 844-849 ◽

Cited By ~ 4

Author(s):

Yue Fei ◽

Xin Nan Wang ◽

Zhi Shou Zhu ◽

Jun Li ◽

Guo Qiang Shang ◽

...

Keyword(s):

Titanium Alloy ◽

Grain Growth ◽

Kinetic Equations ◽

Type Equation ◽

Growth Exponent ◽

Solution Treated ◽

Growth Activation ◽

Grain Growth Kinetics ◽

Kinetics Of ◽

Strength And Ductility

Ti-Mo-Nb-Cr-Al-Fe-Si alloy is a new metastable β titanium alloy with excellent combination of strength and ductility. The β grain-growth exponent and the activation energies for β grain growth for the investigated alloy at specified temperature were computed by the kinetic equations and the Arrhenius-type equation. The rate of β grain growth decreases with elongating solution treated time and increases with the increasing solution-treated temperature. The β grain-growth exponents, n, are 0.461, 0.464 and 0.469 at 1113, 1133 and 1153K, respectively. The β grain growth activation energy is determined to be 274 KJ/mol.

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