Distribution and Energies of Grain Boundaries in Magnesia as a Function of Five Degrees of Freedom

Abstract

The multiplicity of distinct grain boundary configurations in polycrystals has made it difficult to determine the relative frequency with which each configuration is adopted. As a result, the physiochemical properties of each boundary and the influence of the distribution of boundaries on macroscopic materials properties are not well understood. Using a semiautomated system, we have measured all five macroscopically observable degrees of freedom of 4.1 × 106 boundary plane segments making up 5.2 × 106μm2 of grain boundary interface area in a magnesia polycrystal. Our observations demonstrate that not all grain boundary configurations occur with the same frequency and that the relative free energies of the different interfacial configurations influence the population distribution. Furthermore, the results indicate that relative grain boundary energies can be estimated based on the free surface energies.

Grain boundary energy anisotropy: a review

“…This is illustrated in Fig. 13, which compares free surface energies with grain boundary populations for MgO (cubic) [42][43][44], TiO 2 (rutile, tetragonal) [60], and Al 2 O 3 (corundum, trigonal) [61]. On average, rather than seeking high symmetry configurations, grain boundaries tend to favor configurations in which at least one side of the interface can be terminated by a low index plane [62].…”

“…However, the development of automated electron backscatter diffraction orientation mapping in the scanning electron microscope has made it possible to characterize the crystallography of 10 4 -10 5 triple junctions in a reasonable amount of time [39][40][41]. When coupled with serial sectioning, it is possible to determine the complete geometry for triple lines involving all boundary types and apply the Herring equation [42][43][44].…”

Grain boundary energies in body-centered cubic metals

“…In annealed polycrystals, the grain boundary energy distribution (GBED) is known to be inversely correlated to the grain boundary character distribution (GBCD), defined as the relative areas of grain boundaries distinguished by lattice misorientation and grain boundary plane orientation [5,6]. Morawiec [7] developed a technique to determine the GBED from three-dimensional electron backscatter diffraction (3D-EBSD) data, and this has been applied to measure grain boundary energies in a number of ceramics and metals including MgO [8,9], Y 2 O 3 [10], Ni [11], a Ni-based alloy [12], a ferritic steel [13], and an austenitic steel [14]. This method requires large amounts of data because there are no assumptions about the functional form of the GBED, and the number of unknown energies scales with the discretization of the system.…”

The effect of SiO2 addition on the development of low-Σ grain boundaries in PTC thermistors

“…The particular structures that are favoured depend on the system: for example SrTiO 3 shows a strong tendency to form 1 0 0 type grain boundary planes at 15 • grain misorientation 25 , in MgO [1 0 0] planes occur preferentially at all misorientations 26 , and in alpha-brass asymmetric 1 1 0 tilt boundaries and 1 1 1 twist boundaries were found to predominate 27 . The driving force is an overall energy reduction through the preferential formation and retention of low energy grain boundary structures, and has been validated by the derivation of an approximately inverse relationship between the energy of a particular grain boundary structure and its frequency of occurrence in the microstructure 28 .…”