Computer Simulations and Statistical Theory of Normal Grain Growth in Two and Three Dimensions

A modified Monte Carlo algorithm for single-phase normal grain growth is presented, which allows one to simulate the time development of the microstructure of very large grain ensembles in two and three dimensions. The emphasis of the present work lies on the investigation of the interrelation between the local geometric properties of the grain network and the grain size distribution in the quasi-stationary self-similar growth regime. It is found that the topological size correlations between neighbouring grains and the resulting average statistical growth law both in two and three dimensions deviate strongly from the assumptions underlying the classical Lifshitz- Sloyzov-Hillert theory. The average local geometric properties of the simulated grain structures are used in a statistical mean-field theory to calculate the grain size distribution functions analytically. By comparison of the theoretical results with the simulated grain size distributions it is shown how far normal grain growth in two and three dimensions can successfully be described by a mean-field theory and how stochastic fluctuations in the average growth law must be taken into account.

Download Full-text

The Correlation Theory of 2D Normal Grain Growth

Materials Science Forum ◽

10.4028/www.scientific.net/msf.467-470.1081 ◽

2004 ◽

Vol 467-470 ◽

pp. 1081-1086 ◽

Cited By ~ 1

Author(s):

M.W. Nordbakke ◽

N. Ryum ◽

Ola Hunderi

Keyword(s):

Grain Size ◽

Size Distribution ◽

Grain Growth ◽

Grain Size Distribution ◽

Computer Simulations ◽

Mean Field Theory ◽

Mean Field ◽

Grain Structures ◽

Spatial Grain ◽

Kinetics Of

Computer simulations of 2D normal grain growth have shown that size correlations between adjacent grains exist in 2D grain structures. These correlations prevail during the coarsening process and influence on the kinetics of the process and on the grain size distribution. Hillert’s analysis starts with the assumption that all grains in the structure have the same environment. Since computer simulations contradict this assumption, the mean-field theory for normal grain growth needs to be modified. A first attempt was made by Hunderi and Ryum, who modified Hillert’s growth law to include the effect of spatial grain size correlations. In the 1D case the distributions derived by means of the modified growth law agreed well with simulation data. However, the distribution derived for 2D grain growth retained unwanted properties of the Hillert distribution. We review some recent progress in developing a mean-field statistical theory. A paradox related to curvilinear polygons is shown to support the expectation that the grain size distribution has a finite cutoff.

Download Full-text

Normal Grain Growth in Three Dimensions: Monte Carlo Potts Model Simulation and Mean-Field Theory

Materials Science Forum ◽

10.4028/www.scientific.net/msf.550.589 ◽

2007 ◽

Vol 550 ◽

pp. 589-594 ◽

Cited By ~ 1

Author(s):

Dana Zöllner ◽

Peter Streitenberger

Keyword(s):

Field Theory ◽

Grain Size ◽

Monte Carlo ◽

Distribution Function ◽

Grain Growth ◽

Mean Field Theory ◽

Mean Field ◽

Size Distribution Function ◽

Three Dimensions ◽

Self Similar

A modified Monte Carlo Potts model algorithm for single-phase normal grain growth in three dimensions in presented, which enables an extensive statistical analysis of the growth kinetics and topological properties of the microstructure within the quasi-stationary self-similar coarsening regime. From the mean-field theory an analytical grain size distribution function is derived, which is based on a quadratic approximation of the average self-similar volumetric rate of change as a function of the relative grain size as it has been determined from the simulation. The analytical size distribution function is found to be in excellent agreement with the simulation results.

Download Full-text

Normal Grain Growth in Three Dimensions: Monte Carlo Potts Model Simulation and Mean-Field Theory

Materials Science Forum - Fundamentals of Deformation and Annealing ◽

10.4028/0-87849-434-0.589 ◽

2007 ◽

pp. 589-594

Author(s):

Dana Zöllner ◽

Peter Streitenberger

Keyword(s):

Field Theory ◽

Monte Carlo ◽

Grain Growth ◽

Potts Model ◽

Model Simulation ◽

Mean Field Theory ◽

Mean Field ◽

Three Dimensions

Download Full-text

Mean Field Analysis of Orientation Selective Grain Growth Driven By Interface-Energy Anisotropy

MRS Proceedings ◽

10.1557/proc-343-65 ◽

1994 ◽

Vol 343 ◽

Cited By ~ 2

Author(s):

J. A. Floro ◽

C. V. Thompson

Keyword(s):

Grain Size ◽

Size Distribution ◽

Grain Growth ◽

Texture Evolution ◽

Mean Field ◽

Orientation Distribution ◽

Interface Energy ◽

Abnormal Grain Growth ◽

Field Analysis ◽

Energy Anisotropy

ABSTRACTAbnormal grain growth is characterized by the lack of a steady state grain size distribution. In extreme cases the size distribution becomes transiently bimodal, with a few grains growing much larger than the average size. This is known as secondary grain growth. In polycrystalline thin films, the surface energy γs and film/substrate interfacial energy γi vary with grain orientation, providing an orientation-selective driving force that can lead to abnormal grain growth. We employ a mean field analysis that incorporates the effect of interface energy anisotropy to predict the evolution of the grain size/orientation distribution. While abnormal grain growth and texture evolution always result when interface energy anisotropy is present, whether secondary grain growth occurs will depend sensitively on the details of the orientation dependence of γi.

Download Full-text