Two-Dimensional Grain Growth Simulation by Local Curvature Multi-Vertex Model

2012 ◽  
Vol 715-716 ◽  
pp. 551-556 ◽  
Author(s):  
Teruyuki Tamaki ◽  
Kenichi Murakami ◽  
Hotaka Homma ◽  
Kohsaku Ushioda
Keyword(s):  
Grain Boundary ◽  
Boundary Energy ◽  
Two Dimensional ◽  
Vertex Model ◽  
Triple Junctions ◽  
Local Curvature ◽  
Misorientation Distribution ◽  
Grain Boundary Character ◽  
Random Microstructure ◽  
Physical Principles

A local curvature multi-vertex model was developed. This model is the straightforward two-dimensional topological network model based on the physical principles which are the curvatures of grain boundaries and the grain boundary tensions at triple junctions. The model was applied to the artificial random microstructure under some conditions of grain boundary characters. The misorientation distribution was changed very little under constant grain boundary energy and mobility, but it was change much under grain boundary character dependent on misorientation. Therefore, in order to discuss actual textures, it is important to take grain boundary characters into account.

The Effect of Variability Among Grain Boundary Energies on Grain Growth in Thin Film Strips

1994 ◽  
Vol 338 ◽  
Author(s):  
H.J. Frost ◽  
Y. Hayashi ◽  
C.V. Thompson ◽  
D.T. Walton
Keyword(s):  
Thin Film ◽  
Grain Boundary ◽  
Grain Growth ◽  
Boundary Energy ◽  
Strip Width ◽  
Grain Boundary Energy ◽  
Triple Junctions ◽  
Interconnect Reliability ◽  
Bamboo Structure ◽  
Grain Boundary Pinning

ABSTRACTGrain growth in thin-film strips is important to interconnect reliability because grain boundary structures strongly effect the rate and mechanism of electromigration-induced failure. Previous simulations of this process have indicated that the transformation to the fully bamboo structure proceeds at a rate which decreases exponentially with time, and which is inversely proportional to the square of the strip width. We have also reported that grain boundary pinning due to surface grooving implies that there exists a maximum strip width to thickness ratio beyond which the transformation to the bamboo structure does not proceed to completion. In this work we have extended our simulation of grain growth in thin films and thin film strips to consider the effects of variations in grain boundary energy. Boundary energy is taken to depend on the misorientation between the two neighboring grain and the resulting variations in grain boundary energy mean that dihedral angles at triple junctions deviate from 120°. The proportionality between boundary velocities and local curvatures, and the critical curvature for boundary pinning due to surface grooving also both depend on boundary energy. In the case of thin-film strips, the effect of boundary energy variability is to impede the transformation to the bamboo structure, and reduce the width above which the complete bamboo structure is never reached. Those boundaries which do remain upon stagnation tend to be of low energy (low misorientation angle) and are therefore probably of low diffusivity, so that their impact on reliability is probably reduced.

Correlation between Boundary Energy and Grain Boundary Character Distribution in Fe-Based Polycrystals

2007 ◽  
Vol 558-559 ◽  
pp. 879-884 ◽  
Author(s):  
Patricia Gobernado ◽  
Roumen H. Petrov ◽  
Leo Kestens
Keyword(s):  
Surface Energy ◽  
Grain Boundary ◽  
Boundary Energy ◽  
Annealing Treatment ◽  
Grain Boundary Character Distribution ◽  
Grain Boundary Energy ◽  
Boundary Character ◽  
Grain Boundary Character ◽  
Character Distribution ◽  
Boundary Character Distribution

The grain boundary energy anisotropy in BCC Fe-based polycrystals is considered. The correlation between the energy in BCC random grain boundaries and the distribution of grain boundary planes in the bulk was examined with a special attention on the presence of low index (low surface energy) planes in the internal surfaces. For a BCC structure, {100} and {110} planes are known to be the lowest energy planes dominating the equilibrium crystal shapes. Experimental evidences demonstrated that these planes were predominant in the texture of surfaces controlled by surface energy [2]. Moreover, the relation between the grain boundary character distribution and the crystallographic dependence on the grain boundary energy in the bulk after annealing treatment was studied. The grain character boundary distribution (GCBD) was calculated using the crystallographic information obtained from OIM-EBSD maps from samples showing columnar grains. Preliminary results showed no particular distribution trend within the standard stereographic triangle (001-101-111).

Singularities at Grain Triple Junctions in Two-Dimensional Polycrystals With Cubic and Orthotropic Grains

1996 ◽  
Vol 63 (2) ◽  
pp. 295-300 ◽  
Author(s):  
R. C. Picu ◽  
V. Gupta
Keyword(s):  
Grain Boundary ◽  
Plane Strain ◽  
Anisotropic Elasticity ◽  
Symmetric Case ◽  
Elastic Plane ◽  
Two Dimensional ◽  
Triple Junctions ◽  
Stress Singularities ◽  
Plane Strain Deformation ◽  
Singular Configuration

Stress singularities at grain triple junctions are evaluated for various asymmetric grain boundary configurations and random orientations of cubic and orthotropic grains. The analysis is limited to elastic plane-strain deformation and carried out using the Eshelby-Stroh formalism for anisotropic elasticity. For both the cubic and orthotropic grains, the most singular configuration corresponds to the fully symmetric case with grain boundaries 120 deg apart, and with symmetric orientations of the material axes. The magnitude of the singularities are obtained for several engineering polycrystals.

scholarly journals Extracting the Grain Boundary Character/Free Energy Relationship from the Microstructure: Pure and Tilt Boundaries

1997 ◽  
Vol 472 ◽  
Author(s):  
B. Adams ◽  
D. Kinderlehrer ◽  
S. Ta'asan ◽  
W.W. Mullins ◽  
S. Costiner
Keyword(s):  
Free Energy ◽  
Grain Boundary ◽  
Excess Free Energy ◽  
Free Energy Function ◽  
Triple Junctions ◽  
Grain Boundary Character ◽  
Classical Work ◽  
Tilt Boundaries ◽  
Lattice Misorientation ◽  
Two Parameter

ABSTRACTAnalysis is described to extract the excess free energy of grain boundaries from the mesotexture of well-equilibrated polycrystalline samples. The approach is based upon the force and torque balances at triple junctions described in the classical work of Herring [1]. The main advantage of the approach is that the free energy function is obtained over the full fundamental zone of grain boundary types. For the purposes of exposition, the method is described for specified two-parameter hypersurfaces in the fundamental zone for cubic polycrystals (the sets of pure <100> and <111> tilt boundaries) and the free energy is assumed to depend only upon the lattice misorientation. Results from testbed simulations are presented.

scholarly journals Grain Boundary Properties and Grain Growth: Al Foils, Al Films

2004 ◽  
Vol 819 ◽  
Author(s):  
Katayun Barmak ◽  
Wayne E. Archibald ◽  
Anthony D. Rollett ◽  
Shlomo Ta'asan ◽  
David Kinderlehrer
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Grain Growth ◽  
Misorientation Angle ◽  
Driving Forces ◽  
Boundary Energy ◽  
Orientation Imaging Microscopy ◽  
Solute Drag ◽  
Grain Structure ◽  
Two Dimensional

AbstractRelative grain boundary energy as a function of misorientation angle has been measured in cube-oriented, i.e., <100> fiber-textured, 120 [.proportional]m-thick Al foil using orientation imaging microscopy and a statistical multiscale method. The energies of low-angle boundaries increase with misorientation angle, in good agreement with the Read-Shockley model. The relative energies of high-angle boundaries exhibit little variation with misorientation. Examination of the grain structure of <111> fiber-textured, 100 nm-thick Al films annealed at 400°C for 0.5-10 h shows 5 and 6 sided grains to be the most frequent, and the fraction of four-sided grains to be significant. The mean number of sides is slightly lower than the expected value of 6 for two- dimensional structures. Of lognormal, gamma and Rayleigh distributions, gamma gives the best fit to the grain size data in the films; however, the difference between gamma and lognormal is small. Grain growth is not self-similar and stagnates after one hour of annealing. The evolution of the grain size distribution with time indicates that the growth stagnation in the films is neither consistent with boundary pinning by grooving nor with conventional treatments of solute drag. Surface, elastic-strain and plastic-strain energy driving forces do not play a significant role in the grain growth and the subsequent stagnation since the films are strongly textured even in the as- deposited state. The steady-state distributions of reduced grain area for two-dimensional, Monte Carlo and partial differential equation based simulations show excellent agreement with each other, even when anisotropic boundary energies are used. However, comparison with experimental distributions reveals a significantly higher population of small grains in the experiments.

Structural Dependence of Grain Boundary Energy in Fe-Based Polycrystals Identified by OIM Measurements

2007 ◽  
Vol 550 ◽  
pp. 411-416
Author(s):  
Patricia Gobernado ◽  
Leo Kestens
Keyword(s):  
Grain Boundary ◽  
Boundary Energy ◽  
Initial Boundary ◽  
Geometrical Configuration ◽  
Grain Boundary Energy ◽  
Triple Junctions ◽  
High Angle ◽  
Orientation Contrast ◽  
Contrast Microscopy ◽  
Two Parameter

The (relative) grain boundary energy of random high angle boundaries has been measured in several Fe-based polycrystals. Crystallographic data obtained by orientation contrast microscopy (OIM) are combined with the geometrical configuration of grain boundaries at triple junctions. A two-parameter representation of the relative grain boundary energy in terms of misorientation angle and misorientation axis is presented. In the applied procedure a variation of the energy values assigned to one boundary was observed depending on the triangulation path chosen by the operator to connect the arbitrary initial boundary with the boundary under consideration. Results show no evidence of correspondence between the observed energy cusps and the presence of CSL boundaries.

Mesoscale Simulation of the Evolution of the Grain Boundary Character Distribution

2004 ◽  
Vol 467-470 ◽  
pp. 1063-1068 ◽  
Author(s):  
D. Kinderlehrer ◽  
Irene Livshits ◽  
Gregory S. Rohrer ◽  
Shlomo Ta'asan ◽  
Peng Yu
Keyword(s):  
Steady State ◽  
Grain Boundary ◽  
Boundary Energy ◽  
Grain Boundary Character Distribution ◽  
Grain Boundary Energy ◽  
Boundary Character ◽  
Grain Boundary Character ◽  
Character Distribution ◽  
Boundary Character Distribution ◽  
Lattice Misorientation

A mesoscale, variational simulation of grain growth in two-dimensions has been used to explore the effects of grain boundary properties on the grain boundary character distribution. Anisotropy in the grain boundary energy has a stronger influence on the grain boundary character distribution than anisotropy in the grain boundary mobility. As grain growth proceeds from an initially random distribution, the grain boundary character distribution reaches a steady state that depends on the grain boundary energy. If the energy depends only on the lattice misorientation, then the population and energy are related by the Boltzmann distribution. When the energy depends on both lattice misorientation and boundary orientation, the steady state grain boundary character distribution is more complex and depends on both the energy and changes in the gradient of the energy with respect to orientation.

Generalized Vertex Model - Study of Recrystallization in Copper

2007 ◽  
Vol 558-559 ◽  
pp. 1157-1162 ◽  
Author(s):  
Krystian Piękoś ◽  
Jacek Tarasiuk ◽  
Krzysztof Wierzbanowski ◽  
Brigitte Bacroix
Keyword(s):  
Grain Boundary ◽  
Texture Evolution ◽  
Boundary Energy ◽  
Annealing Treatment ◽  
Energy Difference ◽  
Primary Recrystallization ◽  
Recrystallization Process ◽  
Vertex Model ◽  
Stored Energy ◽  
Boundary Misorientation

Classical vertex model till now described only the grain growth stage and not the primary recrystallization. In the present work the vertex model is first extended in order to take into account the both stages of recrystallization process. The influence of the stored energy is taken into account and some phenomenological laws describing the evolution of grain boundary energy and mobility with misorientation angle are used. Nucleation is considered to be site-saturated. The experimentally determined stored energy values, crystallographic orientations and boundary misorientation distributions are used in order to characterize the initial microstructure. The model is tested to study the recrystallization of 70% and 90% cold rolled polycrystalline copper during an annealing treatment. In order to explain the texture evolution in both cases, it is necessary to introduce an energy threshold for grain boundary movement, i.e. a minimal value of the stored energy difference between a nucleus and the deformed material necessary to provoke grain boundary motion. The developed model is shown to predict texture evolutions in good agreement with experimental data.

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