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.

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.

Effect of Particle Size on the Zener Limit: A Monte Carlo Simulation Approach

2012 ◽  
Vol 560-561 ◽  
pp. 152-155 ◽  
Author(s):  
Kalale Raghavendra Rao Phaneesh ◽  
Anirudh Bhat ◽  
Gautam Mukherjee ◽  
Kishore T. Kashyap
Keyword(s):  
Monte Carlo Simulation ◽  
Particle Size ◽  
Grain Size ◽  
Monte Carlo ◽  
Grain Boundaries ◽  
Grain Growth ◽  
Second Phase ◽  
Particle Sizes ◽  
Second Phase Particles ◽  
Average Grain Size

2D Potts model Monte Carlo simulation was carried out on a square lattice to investigate the effects of varying the size of second phase particles on the Zener limit of grain growth, in two-phase polycrystals. Simulations were carried out on a 1000^2 size matrix with Q-state of 64, dispersed with second phase particles of various sizes and surface fractions, and run to stagnation. Different grain growth parameters such as mean grain size, largest grain size, fraction of second phase particles lying on grain boundaries, etc., were computed for the pinned microstructures. The pinned average grain size or the Zener limit increased with increase in particle size, as per the classic Smith-Zener equation. The Zener limit scaled inversely with the square root of the particle fraction for all particle sizes, while it scaled exponentially with the fraction of second phase particles lying on the grain boundaries (ϕ), for all particle sizes tested.

Grain Growth during Annealing: Experiments and Modelling

2012 ◽  
Vol 715-716 ◽  
pp. 611-616 ◽  
Author(s):  
M. Candic ◽  
Bao Hui Tian ◽  
Christof Sommitsch
Keyword(s):  
Grain Growth ◽  
Second Phase ◽  
Excellent Correlation ◽  
Grain Sizes ◽  
Second Phase Particles ◽  
Different Temperatures ◽  
Grain Growth Kinetics ◽  
Parameter Approach ◽  
Annealing Experiments ◽  
Two Parameter

In the present work, for the description of grain coarsening, a probabilistic and a deterministic 2D cellular automaton simulation setup were developed. The results of the simulation have been validated by solution annealing experiments of austenitic stainless steel 304L (Fe-18Cr-8Ni) at different temperatures and times. Both cellular automata models show an excellent correlation between the experimental determined data and grain growth kinetics based upon considerations of temperature and second phase particles. Additionally, a two parameter approach of the probabilistic model was implemented, resulting in determining the grain sizes limiting normal and abnormal grains and accurate description of grain growth.

Monte Carlo simulation of grain growth in polycrystalline materials

2006 ◽  
Vol 252 (11) ◽  
pp. 3997-4002 ◽  
Author(s):  
C. Ming Huang ◽  
C.L. Joanne ◽  
B.S.V. Patnaik ◽  
R Jayaganthan
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Grain Growth ◽  
Polycrystalline Materials

scholarly journals Mechanism of Orientation Selectivity During Grain Growth of Secondary Recrystallization in Fe-3%Si Alloy

1999 ◽  
Vol 32 (1-4) ◽  
pp. 137-151 ◽  
Author(s):  
Y. Ushigami ◽  
T. Kubota ◽  
N. Takahashi
Keyword(s):  
Grain Growth ◽  
Secondary Recrystallization ◽  
Orientation Distribution ◽  
Recrystallization Temperature ◽  
Second Phase ◽  
Average Deviation ◽  
Pinning Effect ◽  
Second Phase Particles ◽  
The Matrix ◽  
The Ideal

Selective growth of {110}〈001〉 grains in the temperature gradient annealing has been studied in Fe–3%Si alloy. As grains grow, the average deviation angle from the ideal {110}〈001〉 orientation becomes smaller and orientation distribution changes corresponding to that of coincidence grains in the matrix. Secondary recrystallization temperature depends on the orientation of secondary recrystallized grain and sharper {110} 〈001〉 grains grow preferentially at lower temperatures.These phenomena are explained by modified Hillert's model of grain growth. Interfacial energy of coincidence boundary is lower than that of general boundary. Therefore, sharper {110}〈001〉 grains, which have higher frequency of coincidence grains in the primary recrystallized matrix, suffer lower pinning effect from the second phase particles and thus grow preferentially at lower temperatures.

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.

scholarly journals Discussion on the Rate Controlling Process of Coarsening of Niobium Carbonitrides in a Niobium Microalloyed Steel

2005 ◽  
Vol 500-501 ◽  
pp. 703-710 ◽  
Author(s):  
David San Martín ◽  
Francisca García Caballero ◽  
Carlos Capdevila ◽  
Carlos García de Andrés
Keyword(s):  
Grain Growth ◽  
Volume Diffusion ◽  
Microalloyed Steels ◽  
Second Phase ◽  
Austenite Grain Size ◽  
Austenite Grain ◽  
The Matrix ◽  
Niobium Microalloyed Steel ◽  
Grain Growth Kinetics ◽  
Austenite Grain Growth

Austenite grain growth in microalloyed steels is governed by the coarsening of fine precipitates present at grain boundaries below the grain coarsening temperature. Zener model is widely used in metals to describe the pinning effect of second phase particles precipitated in the matrix. In this work it has been discussed whether grain boundary or volume diffusion is the rate controlling process for the coarsening of the niobium carbonitrides. Calculations on austenite grain growth kinetics, obtained coupling Zener theory and both rate controlling processes of precipitate coarsening, have been compared against experimental austenite grain size results under nonisothermal heating conditions. In this sense, it has been concluded that the coarsening of niobium carbonitrides is mainly controlled by volume diffusion of Nb in austenite.

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