Kinetics Of Normal Grain Growth Research Articles

Recrystallization Kinetics of Niobium with Submicrocrystalline Structure

Abstract—Transmission and scanning electron microscopy have been used to study the kinetics of recrystallization at 400 and 700°C of niobium in which a submicrocrystalline structure was created as a result of high-pressure torsion. It has been shown that the recrystallization at 700°C occurs in accordance with the kinetics of normal grain growth. A decrease in the rate constant with an increase in the duration of annealing to more than 1 h is due to textural changes, rather than the completion of primary recrystallization. Upon the low-temperature recrystallization (400°C), a stable fine-grained structure is formed, which remains almost unchanged with increasing duration of annealing.

Cellular automata simulation for high temperature austenite grain growth based on thermal activation theory and curvature-driven mechanism

Based on the thermal activation theory and curvature-driven mechanism, a 2D cellular automaton model with different state transition rules was built. Validity of the model was proved by the shrinking of circular grains. Grain growth of high temperature austenite was simulated by this model; the morphology, grain size distribution, topological aspects, and local kinetics of austenite grain growth were analyzed under different simulation time. Among the grains with different sides, the 6-sided grains are the most common and 5-sided grains are the second most common. The grains with more than six sides will grow and grains with less than six sides will shrink, while the 6-sided grains will neither grow nor shrink. The kinetics of normal grain growth follows the Burke equation and the growth exponent at different temperatures and activation energies has been researched.

Shedding some light on the early grain growth regime: About the effect of the initial microstructure on normal grain growth

In the present paper the effect of the initial microstructure on the coarsening kinetics of normal grain growth is investigated. To that aim, two microstructures characterized by two distinctively different grain size distributions—one following a normal and the other one following a bimodal distribution—are analyzed as they undergo coarsening by means of Monte Carlo Potts model simulations showing different behaviors at early relaxation times but reaching the same quasi-stationary self-similar growth regime for long-time annealing.

Grain Growth in Nb-Alloyed Stainless Steel of AISI 347 during Heating

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.

Effect of Matrix Size and Neighbour Sites on Microstructure Evolution in 3D Monte Carlo Grain Growth Simulation

Grain size is an important microstructural feature of materials; it contributes to its mechanical and physical properties. Quantitative information of three-dimensional topological evolution during the three-dimensional normal grain growth process is very rare. In this work, an isothermal Monte Carlo procedure is applied to study the kinetics of normal grain growth in three dimensions using the Monte Carlo technique. Monte Carlo simulation of the grain growth in polycrystalline materials employed maps the microstructure onto a discrete lattice. It consists in evaluation of potential energy of a lattice point. Therefore, the choice of the simulation parameters can affect the grain growth characteristics. We attempted to define specific simulation parameters for the three dimensional MC simulation of grain growth using theses lattices. The parameters include the choice of the lattice symmetry, the pixels number and the number of the nearest neighbor lattice sites in the calculation of the system energy. The goal of these computer simulations is to provide insights on the simulated structure and to analyze the grain growth kinetics for the 3D domain through several 2D cross-sections. Compact microstructures were developed and the first results show that the lattice symmetry and the neighbours number have a fundamental influence on the results of grain growth simulation. The saturation is too rapid with only the consideration of the 1st neighbours while acceptable similar evolutions are obtained for the 2nd or 3rd neighbours consideration. Grain size evolution obeys the power law kinetics for the 2D cross-section confirming the quasi-steady state of the 3D normal grain growth. The highest grain growth velocity and grain size were obtained at the cross-sections of the heart of microstructures. One other noted information is the existence of a minority of grains which continue to grow slowly leading up to the abnormal grain growth.

On the Monte Carlo simulation of normal grain growth

The microstructures and their kinetics of normal grain growth are simulated using different Monte Carlo (MC) algorithms. Compared with the relative figures and the theoretical normal grain growth exponents of n=0.5, the effects of some factors of MC algorithm, i.e. the lattice types, the methods of selecting lattice sites, and the neighbors selection for energy calculations, on the simulation results of grain growth are studied. Two methods of regression were compared, and the three-parameter nonlinear regression is much more suitable for fitting the grain growth kinetics. A better model with appropriate factors included triangular lattice, the attempted site randomly selected, and the first and second nearest neighbors for energy calculations is obtained.

Computer simulation of 2D grain growth using a cellular automata model based on the lowest energy principle

The morphology, topology and kinetics of normal grain growth in two-dimension were studied by computer simulation using a cellular automata (CA) model based on the lowest energy principle. The thermodynamic energy that follows Maxwell–Boltzmann statistics has been introduced into this model for the calculation of energy change. The transition that can reduce the system energy to the lowest level is chosen to occur when there is more than one possible transition direction. The simulation results show that the kinetics of normal grain growth follows the Burke equation with the growth exponent m = 2. The analysis of topology further indicates that normal grain growth can be simulated fairly well by the present CA model. The vanishing of grains with different number of sides is discussed in the simulation.

小さい結晶粒の粒径分布に依存する粒成長の動力学

A theoretical relationship is derived between the kinetics of normal grain growth and the size distribution of small grains. When the distribution of the normalized grain size r is proportional to rm around r=0 in a steady state, the grain growth exponent n is revealed to be m+1. The same relationship is also derived from the analysis of the mean field model. The validity of this relationship is confirmed from the consistence with existing grain-growth models and numerical simulations. Experimental consistence is observed with the size distribution on sectional surface. It is found that a log-normal function is not a steady-state size distribution for normal grain growth with n=2, even though it may approximate experimental size distributions. The obtained relationship is also shown to be applicable to particle coarsening by Ostwald-ripening.

Kinetics of Normal Grain Growth Depending on the Size Distribution of Small Grains

m þ 1. The same relationship is also derived from the analysis of the mean field model for particle growth. The validity of this relationship is confirmed from the consistence with existing grain-growth models and numerical simulations. Experimental consistence is observed for the size distribution on sectional surface. It is found that a log-normal function is not a steady-state size distribution for normal grain growth with n ¼ 2, even though it may approximate experimental size distributions. The obtained relationship is also shown to be applicable to particle coarsening by Ostwald-ripening.

Microstructural evolution during sintering of TiO 2/SiO 2-doped alumina: mechanism of anisotropic abnormal grain growth

Microstructural changes that occurred during the sintering of alumina doped with TiO 2 and SiO 2 have been investigated. The kinetics of normal grain growth at the initial stage is retarded by the dopant segregation at the grain boundaries. However, due to the accumulation of dopants at the grain boundaries during grain growth, its concentration at the boundaries ultimately exceeds the solubility limit and an intergranular liquid film emerges. The appearance of the liquid and the resulting increase in boundary mobility are confirmed to be the main cause of abnormal grain growth. For the abnormal grains, a liquid phase is observed at the basal surface in most cases, while the edges of these grains were partially wetted. Anisotropic or directional growth of the abnormal grains is explained in terms of the enhanced growth kinetics due to the re-entrant edges formed by grain boundaries at the non-basal planes.

Investigation of the normal grain growth kinetics in pure metals without hard texture

A theoretical analysis on the application of Beck's and Burke's equations for an estimation of the kinetics of grain growth in polycrystalline materials is performed. Applying Monte Carlo simulation for the normal grain growth the relationship between the mean diameter, area, and velocity of growth of polycrystalline grains is obtained for a large annealing interval. Using the simulation procedure it is possible to obtain the accurate function reflecting the dependence of the kinetic factors n and A on the annealing time. It is shown that the deviation of n from the value 0.5 in pure metals without hard texture is more an rule than an exception. Es wird eine theoretische Analyse uber die Anwendung der Gleichungen von Beck und Burke zur Berechnung der Kinetik von Kornwachstum in polykristallinen Materialien durchgefuhrt. Unter Verwendung der Monte-Carlo-Simulation fur das normale Kornwachstum wird fur einen grosen Temperungsbereich eine Beziehung zwischen dem mittleren Durchmesser, der Flache und der Wachstumsrate polykristalliner Korner erhalten. Mit dem Simulationsverfahren ist es moglich, die genaue Funktion zu erhalten, die die Abhangigkeit der kinetischen Faktoren n und A von der Temperungszeit wiedergibt. Es wird gezeigt, das die Abweichung von n vom Wert 0,5 in reinen Metallen ohne harte Textur mehr die Regel als die Ausnahme ist.

Effect of size distribution on the kinetics of normal grain growth and of particle coarsening

A simple model is presented to describe the kinetics of normal grain growth. The final expression incorporates a factor which depends on the grain size distribution but no assumption is made on the distribution function. A similar expression is also derived for particle coarsening.

A Diffusion‐Compensation Relation for Normal Grain Growth and Grain‐Boundary Diffusion of Oxygen in Oxides

Values of D0/δ and Q for grain‐boundary diffusion, derived from published studies of normal grain growth in Al2O3, BeO, CaO, MgO, SiO2, and CaSiO3, are fit by the linear compensation equation log D0/δ=0.03170Q ‐7.6792 (r2=0.9384). Comparison of grain‐boundary diffusion coefficients derived from grain growth in oxides with those obtained by direct experimental measurement suggests that the kinetics of normal grain growth are controlled by grain‐boundary diffusion of oxygen.

The kinetics of normal grain growth

The relationship between the quasistationary distribution functions in normal grain growth and the corresponding grain-growth velocities is investigated. The restrictions imposed by volume conservation lead to a simple differential equation which describes quasistationary grain growth. This equation allows us to express the reduced growth velocity (dR/dt)/(dR*/dt), where R* is the scaling grain size, in terms of the corresponding distribution function and to express the distribution function by means of the reduced growth velocity. General conclusions about the shape of distribution functions can be drawn from these expressions.

Grain growth and secondary recrystallization in iron

The effect of impurities and of slight deformations as factors modifying the kinetics of normal grain growth after primary recrystallization in pure iron is investigated. Samples of pure iron and Armco iron, each with or without a content of precipitated oxides, were examined. Inclusions inhibit grain growth up to high temperatures, whilst the influence of strain depends on its amount: very low deformations (∼2%) generally block grain growth; for deformations around 5%, secondary recrystallization takes place; higher deformations (∼10%) accelerate the early stages of growth, leading to not very large final grain dimensions. 2.0% elongation has been found to be, in our conditions, the critical strain limit for secondary recrystallization.