**2. Grain boundary structure**

increases. Experimental results indicate that GB width (*δ*) is approximately 0.5 nm for facecentered cubic (fcc) NC alloys and slightly larger than 1.0 nm for body-centered cubic (bcc) NC alloys [3, 5, 6]. Assuming the grains have the shape of spheres, the volume fractions of intercrystal regions and GB as a function of grain size (*d*) are shown in **Figure 1**. It can be seen from **Figure 1** that for nanostructured materials with grain size of 5 nm, nearly 50% of atoms will reside in or near the GB [7]. Therefore, nanostructured materials can be considered to compose of two parts: the core crystallites and a network of intercrystal regions (grain boundaries, triple junctions, etc.) [8]. In NC materials, grain boundary mediated processes, such as emission and absorption of dislocations by grain boundaries, grain rotation, and GB sliding will dominate the plastic deformation as the grain size is smaller than a certain critical value [9]. The properties of the nanostructure materials are thus determined not only by their reduced microstructural length scale, but also by the nature of their GB structures [10, 11]. Due to high volume fraction of the GB in NC materials, thermodynamic driving force exists to drive GB migration which results in the low stability of NC materials. The main objective of this chapter is to provide a comprehensive review of the experimental and simulation results on the microstructure

This chapter is structured as follows: Section 2 describes the basic methods established in the field of GB structure to describe the GB structure. The section that follows addresses the GB

**Figure 1.** The contribution of different microstructural elements to the volume fraction as a function of grain size (*d*),

assuming a grain-boundary thickness (*δ*) of 1 nm.

instability of NC materials system under various deformation conditions.

144 Study of Grain Boundary Character

For understanding the properties of NC materials, it is a prerequisite to have a detailed knowledge of the GB structure from the atomic (local) scale to the microstructural scale. A considerable effort has been made to understand the GB structure of polycrystalline materials, since the 1950s. To describe the GB crystallographically, a number of parameters must be defined. From a macroscopic perspective, a planar GB between two adjacent grains has five degrees of freedom. Four degrees of freedom are accounted for the crystallographic orientation of the rotation axis and the normal of the GB plane. The fifth is defined as the misorientation angle (*θ*) [12]. There are several criteria to classify the GB. According to *θ* value, GBs are typically classified to low-angle boundaries with *θ* ≤ 15° and high-angle boundaries with *θ* > 15° [13]. The coherency of homophase low-angle GBs can be described through the dislocation model [14]. The degree of coherency is related to the spacing of misfit dislocations within the GB. Based on the relative orientation of the rotation axis and the GB plane normal, the GB can be classified as a tilt and twist boundary. If the rotation axis is perpendicular to the GB plane normal, this GB is called a tilt boundary, whereas if the rotation axis is parallel to the GB normal, the GB is defined as a twist boundary. Although tilt and twist GBs occupy only a small fraction of the GB phase space, they are frequently observed experimentally, which suggests that they are energetically favored over other types of GBs [15].

Numerous theoretical efforts have been made to characterize the GB structures. The widely used models to analyze and predict the atomistic structures of GB include the coincidence site lattice (CSL) model and the structural unit (SU) model. In the CSL model, a coincidence index (Σ) is the ratio of the volume of the CSL cell to that of the lattice unit cell. The reciprocal value of the Σ represents the fraction of the lattice points belonging to the abutting crystal. GB with lower value of Σ contains a higher density of coincident sites and is expected to have low energy. While in the SU model, those GBs with specific misorientation angles called favored GB is constituted only from one type of structural units. Any intermediary GB between two favored GBs can be described by a linear combination of SUs comprising one or several neighboring favored boundaries [16, 17]. Twenty-one <1 1 0> symmetric tilt GBs are investigated by Rittner and Seidman with atomistic simulations, using an embedded-atom method potential for low stacking-fault energy fcc metal [18]. They found that the favored boundaries are the Σ = 1 (0 0 1), Σ = 27 (1 1 5), Σ = 11 (1 1 3), Σ = 3 (1 1 1), Σ = 9 (2 2 1) and the Σ = 1 (1 1 0) interfaces. The structural units associated with each of these boundaries are denoted by A–E, as shown in **Figure 2**. To reduce the number of distinct SU, distortions exceeding 15% are occasionally permitted in the SU of the GB region.

The advent of transmission electron microscopy (TEM), especially in the development of highresolution transmission electron microscopy (HRTEM) has provided us with a very powerful tool to explore the atomic structure of internal interfaces. **Figure 3** shows the HRTEM

**Figure 2.** Equilibrium bicrystal interface structures of <1 1 0> symmetric tilt boundaries and two perfect crystal orientation [18]. The structures are viewed along the tilt axis [1 1 0], with the open and filled circles indicating atomic positions in alternate (2 2 0) planes [18].

**Figure 3.** HRTEM images of [0 0 0 1]-tilt grain boundaries in ZnO bicrystals. (a) 10.6 ± 0.1° boundary composed of a dislocation array. (b) 20.1 ± 0.2° near Σ = 7 boundary having a facet structure. (c) 20.0 ± 0.2° near Σ = 7 boundary with a symmetric structure. (d) Higher magnification image of (c) with the boundary core structural units represented by quadrilaterals [19].

micrographs of the atomic structure of ZnO thin films [19]. It is evident that the low-angle GB is composed of edge dislocation along the GB plane as shown in **Figure 3(a)**. **Figure 3(d)** is the higher magnification of **Figure 3(c)**, having a periodic and nearly mirror symmetric character as clarified by drawings of SUs. The HRTEM greatly contributes to the experimental verification of the basic concepts of atomic structure of the GB [12]. TEM characterization results indicate that the GB of NC material is essentially the same as that of the coarse-grained materials. It should be noted that GB structures of NC materials are highly dependent on the alloy composition and processing steps in the manufacturing of NC materials.
