3D MС Simulation of Grain Growth Kinetics and the Zener Limit in Polycrystals

2014 ◽  
Vol 598 ◽  
pp. 8-12
Author(s):  
K.R. Phaneesh ◽  
Anirudh Bhat ◽  
Gautam Mukherjee ◽  
Kishore T. Kashyap
Keyword(s):  
Monte Carlo ◽  
Grain Growth ◽  
Growth Kinetics ◽  
Large Scale ◽  
Volume Fraction ◽  
Growth Exponent ◽  
Cube Root ◽  
Second Phase ◽  
Two Phase ◽  
Second Phase Particles

Large scale Potts model Monte Carlo simulation was carried on 3-dimensional square lattices of 1003 and 2003 sizes using the Metropolis algorithm to study grain growth behavior. Simulations were carried out to investigate both growth kinetics as well as the Zener limit in two-phase polycrystals inhibited in growth by second phase particles of single-voxel size. Initially the matrices were run to 10,000 Monte Carlo steps (MCS) to check the growth kinetics in both single phase and two-phase poly-crystals. Grain growth exponent values obtained as a result have shown to be highest (~ 0.4) for mono-phase materials while the value decreases with addition of second phase particles. Subsequently the matrices were run to stagnation in the presence of second phase particles of volume fractions ranging from 0.001to 0.1. Results obtained have shown a cube root dependence of the limiting grain size over the particle volume fraction thus reinforcing earlier 3D simulation efforts. It was observed that there was not much difference in the values of either growth kinetics or the Zener limit between 1003 and 2003 sized matrices, although the results improved mildly with size.

Grain Growth in Materials with Mobile Second-Phase Particles

2007 ◽  
Vol 558-559 ◽  
pp. 1021-1028 ◽  
Author(s):  
Vladimir Yu. Novikov
Keyword(s):  
Grain Boundaries ◽  
Grain Growth ◽  
Growth Kinetics ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Second Phase ◽  
Particle Volume ◽  
First Case ◽  
Second Phase Particles ◽  
Material Volume

Grain growth controlled by particles able to move together with grain boundaries is investigated by means of numerical simulation. The particles either located on grain boundaries or randomly distributed over the material volume are shown to retard the growth process. In the first case the growth kinetics is described by a power law Dn −D0 n = kt with the exponent n≤ 3. Growth kinetics under the influence of randomly distributed mobile particles can be approximated by the same law with the exponent n increasing with an increase in the particle volume fraction.

Evaluation of grain growth exponent by Monte Carlo simulation in polycrystalline materials

2021 ◽  
pp. 2150024
Author(s):  
P. Rajendra ◽  
K. R. Phaneesh ◽  
C. M. Ramesha ◽  
Madeva Nagaral ◽  
V Auradi
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Grain Growth ◽  
Growth Exponent ◽  
Polycrystalline Materials ◽  
Second Phase ◽  
2D Simulation ◽  
Second Phase Particles ◽  
The Matrix ◽  
Grain Growth Kinetics

In metallurgy, the microstructure study is very important to evaluate the properties and performances of a material. The Monte Carlo method is applied in so many fields of Engineering Science and it is a very effective method to examine the topology of the computer-simulated structures and exactly resembles the static behavior of the atoms. The effective 2D simulation was performed to understand the grain growth kinetics, under the influence of second phase particles (impurities) is a base to control the microstructure. The matrix size and [Formula: see text]-states are optimized. The grain growth exponent was investigated in a polycrystalline material using the [Formula: see text]-state Potts model under the Monte Carlo simulation. The effect of particles present within the belly of grains and pinning on the grain boundaries are observed. The mean grain size under second phase particles obeys the square root dependency.

Simulations of Anisotropic Grain Growth Involving Two-Phase Nanocrystalline/Amorphous Systems Using Q-State Monte Carlo

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
J. B. Allen
Keyword(s):  
Monte Carlo ◽  
Grain Boundary ◽  
Grain Growth ◽  
Amorphous Phase ◽  
Volume Fraction ◽  
Critical Role ◽  
Boundary Surface ◽  
Binding Energies ◽  
Two Phase ◽  
Amorphous Systems

The present work incorporates an implementation of the two dimensional, Q-state Monte Carlo method to evaluate anisotropic grain growth in two-phase nanocrystalline/amorphous systems. Specifically, anisotropic grain boundaries are simulated via the use of surface energies and binding energies; the former attributable to the variation in grain orientation and assigned through a mapping process involving Wulff plots. The secondary, amorphous phase is randomly assigned to the lattice in accordance with a specified initial volume fraction. Among other findings, the results reveal that the grain boundary surface energy, as governed by the shape of the Wulff plot, plays a critical role in the resulting microstructure. Additionally, it was found that the addition of a secondary amorphous phase to an existing anisotropic grain boundary system evolves into primary grain microstructures characteristic of single phase isotropic systems.

An Upper Bound Approach on Deformation of Two-Phase Materials in Uniaxial Tension

1983 ◽  
Vol 105 (1) ◽  
pp. 39-44 ◽  
Author(s):  
Y. Tada ◽  
M. Oyane ◽  
S. Shima ◽  
T. Sato ◽  
M. Omura
Keyword(s):  
Upper Bound ◽  
Volume Fraction ◽  
Strain Curve ◽  
Second Phase ◽  
Strength Ratio ◽  
Stress Strain Curve ◽  
Two Phase ◽  
Second Phase Particles ◽  
Strength And Deformation ◽  
Good Agreement

Strength and deformation of two-phase materials are investigated by the upper bound approach in relation to the volume fraction of the second-phase particles, yield strength ratio and bond strength between the constituents, shape of the particles, and environmental hydrostatic pressure. The stress-strain curve of a two-phase material is estimated as an application of this method. The calculated results are in good agreement with experimental ones.

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

1992 ◽  
Vol 7 (12) ◽  
pp. 3194-3201 ◽  
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.

scholarly journals Grain growth kinetics for B2O3-doped ZnO ceramics

2015 ◽  
Vol 33 (2) ◽  
pp. 220-229 ◽  
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.

Simulation of the Effect of Second Phase Particles in Different Shapes on Grain Growth of Mg Alloy by Phase Field Methods

2017 ◽  
Vol 727 ◽  
pp. 159-165
Author(s):  
Yan Wu ◽  
Si Xia
Keyword(s):  
Grain Growth ◽  
Phase Field ◽  
Volume Fraction ◽  
Mg Alloy ◽  
Spherical Particles ◽  
Second Phase ◽  
Field Methods ◽  
Second Phase Particles ◽  
Different Shapes ◽  
Phase Field Methods

The effect of second phase particles in different shapes on grain growth of AZ31 Mg alloy has been simulated by the phase field methods under realistic spatial-temporal scales. The long-range orientation field variables are chosen to express the temporal microstructure evolution and crystal orientation. The expression of the local free energy density equation was modified by adding the expression term of second phase particles, and the simulated results show that the grain boundary migration is pinned by the second phase particles during the grain growth, which is agree with the Zener pinning observation. When the shape of particles is different and the volume fraction is 10%, the effect of refining grain is different too, the oval particles are the strongest, followed by the rod particles, and the effect of spherical particles are weaker. The research will help to understand the mechanisms of grain growth containing the second phase particles strengthening.

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