Elsevier

Acta Materialia

Volume 49, Issue 15, 3 September 2001, Pages 2981-2991
Acta Materialia

On misorientation distribution evolution during anisotropic grain growth

https://doi.org/10.1016/S1359-6454(01)00207-5Get rights and content

Abstract

In order to study the development of texture and boundary character during annealing, three-dimensional grain crystallography and crystallographically mediated grain boundary properties were incoporated into a finite temperature Monte Carlo model for grain growth. Randomly textured microstructures evolve normally, with growth exponent n=0.96. While texture remains random, the steady-state boundary misorientation distribution favors low-angle boundaries. To first order, low-angle boundaries increase by lengthening, not by proliferating. In contrast, microstructures with a strong single-component texture develop four-grain junctions and highly curved grain boundaries, which alter evolution. The boundary misorientation distribution narrows and shifts to low angles, and no steady state is observed. The accompanying decrease in mean boundary mobility causes growth to slow, resulting in a growth exponent n=0.62. The dependence of the growth exponent on average boundary mobility may explain experimental observations of exponents less than unity.

Introduction

It is well known that crystallographic texture plays an important role in determining the physical, electrical and magnetic properties of polycrystalline materials. Some properties (e.g., plasticity) are affected by the bulk texture; others (e.g., high-temperature superconductivity) are influenced by the distribution of grain boundary types, which is texture-mediated. Controlling both texture and grain boundary character is therefore very important during processing of metal alloys.

Grain boundary engineering [1] is an ambitious application of thermomechanical processing to optimize both texture and boundary character. Tantalizing evidence of the effectiveness of this approach has been provided by Palumbo et al. [2], [3], who have developed processing routes that dramatically improve the corrosion resistance of certain alloys by increasing the fraction of coincident site lattice (CSL) boundaries present in the microstructure. During grain boundary engineering, an increase in CSL boundaries is often accompanied by a decrease in intensity of the bulk texture, illustrating the complex relationship between texture and boundary character.

Traditional X-ray analysis has long been used to measure the global frequency distribution of grain orientations in a polycrystal [i.e., the orientation distribution function (ODF) or texture], and grain misorientation distribution functions (MDFs) have been derived in various ways from the ODF. Recent advances in orientation imaging microscopy (OIM) [4] produce detailed, spatial maps of crystallographic orientations. This allows, for the first time, easy calculation of the frequency distribution of actual grain boundary misorientations in real polycrystals. This grain boundary MDF is not derived from the ODF, but rather is directly measured for each boundary in a microstructure and so depends explicitly on neighbor grain correlations. In fact, there is no unique relationship between an ODF and its grain boundary MDF; a given ODF can result in very different MDFs, depending on grain correlations [5]. In this paper, all referenced MDFs are of the directly measured, grain boundary type.

Automated OIM techniques enable detailed investigations of the influence of microstructural evolution on both the ODF and the MDF. However, because there is yet little understanding of the fundamental mechanisms that control the evolution of boundary character, annealing schedules to optimize the MDF continue to be developed empirically.

Polycrystalline microstructures include a menagerie of microstructural features: grain boundaries, second-phase particles, dislocations, solute, etc. Since microstructural evolution depends upon the local topology and connectivity of these features, mesoscale computer simulations for microstructural evolution can provide valuable insight. The most successful mesoscale grain growth models include Potts models [6], front tracking models [7], vertex models [8], phase field models [9], and cellular automata [10]. The kinetics and topological characteristics of isotropic grain growth have been exhaustively investigated using these methods.

Relatively little work has been done to investigate the effects of anisotropic boundary properties on the evolution of texture and the MDF. Grest et al. [11] used the Potts model to simulate the effect of misorientation-dependent boundary energy on grain growth. In that study, crystal orientations were not three-dimensional, but rather were scalar tilt angles, which unconstrains the formation of low-energy boundaries. In addition, the results suffered from simulation lattice pinning, which affected both microstructure and evolution kinetics. Subsequent Potts model studies of anisotropic grain growth have also attempted to incorporate crystallography [12], [13], [14], [15], [16], [17], usually to probe the coupling between texture development and abnormal grain growth [12], [13], [14], [15], [17]. Most of these simulations utilize scalar crystallography [12], [13], [15], [17]. Some restrict the effects of crystallography to boundary mobility (not energy) [15], [17], or do not weight boundary mobility by energy [12], [13], [14], [16]. Others operate on non-statistical system sizes and simulation times [16] or may be affected by lattice pinning [14]. In addition, most of these studies specify an initial condition tailored to initiating the phenomenon of interest (e.g., seeding the microstructure with special grains) [12], [13], [15], [17]. Thus the aim of this paper is twofold: (1) to discuss the incorporation of misorientation-dependent boundary properties in Potts model simulations, and (2) to investigate the development of texture and MDF during grain growth.

The paper is set out in the following way. First we examine the crystallography of polycrystalline microstructures and review the experimental measurements of energetic and kinetic parameters required to characterize the microstructure. Then we discuss how these parameters can be implemented into the Potts model simulation. Finally we describe two examples of anisotropic grain growth, the evolution of a random texture and the evolution of a strong single-component texture. When discussing these examples we focus on the changes in the MDF caused by grain growth.

Section snippets

Orientation and misorientation

The orientation of the axes of a crystal with respect to an external frame of reference (the specimen axes) can be specified by a rotation in three-dimensional space (posessing three degrees of freedom). As such it can be represented by a (3×3) rotation matrix O. The misorientation between two grains is the rotation that rotates one grain's orientation into that of the other. If the orientation of grain A is represented by the rotation matrix OA, and that of grain B by OB, then the

The algorithm

A continuum microstructure is bitmapped on to a discrete lattice. Each lattice site is allocated an index si so that all sites within a grain have the same index, and grain boundaries are represented by interfaces between neighboring sites of unlike index. Each index is also assigned a discrete crystallographic orientation Oi using a method that allows both the initial texture and MDF of the ensemble to be defined from experimental measurements [5]. The misorientation angle between grains i and

Anisotropic grain growth: random texture

For the first examination of texture and boundary character evolution, we choose the simplest system: a randomly textured, single-phase polycrystal. Each grain in the initial structure is assigned a crystallographic orientation from a list of 999 orientations, randomly distributed in Euler space. The grain boundary MDFs of these initial structures match the analytical solution for the MDF of a randomly textured polycrystal, known as the Mackenzie distribution (shown as the solid line in Fig. 4)

Grain growth of a single-component texture

To contrast with the randomly textured case, we selected a system with a high degree of bulk texture. Each grain in the initial structure is assigned an orientation from a Gaussian distribution of orientations around {111}〈100〉. Because all orientations are close to a common reference axis, it is easy to form a boundary at or below the mean misorientation, but it is harder to find grains that can form a high-angle boundary with each other. Thus, although the orientation distribution is Gaussian

Conclusions

In order to study the development of texture and boundary character during annealing, full three-dimensional grain crystallography and realistic, crystallographically mediated grain boundary properties were incoporated into a finite temperature Monte Carlo Potts model for grain growth.

Systems with similar initial microstructures but different textures exhibit markedly different behavior during grain growth. Microstructures with random textures maintain normal grain topology and evolve in a

Acknowledgements

Thanks to Dr A. W. Godfrey for discussions and providing orientation handling subroutines. MAM is grateful for support through a Newman Scholarship at University College Dublin, Ireland. GNH appreciates support from Kettering University and Sandia National Laboratories for sabbatical leave. This work was performed at Sandia National Laboratories, supported by the US Department of Energy under contract number DE-AC04-94AL85000 and by the Office of Basic Energy Sciences New Initiative program.

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