Experimental Method for Determining Surface Energy Anisotropy and Its Application to Magnesia

Abstract

An experimental technique has been developed to determine the surface energy anisotropy of crystalline solids. The technique is based on atomic force microscopy measurements, which are used to quantify the geometry of thermal grooves, and electron backscattered diffraction pattern measurements, which are used to specify crystallographic orientations. Observations are made at circumferential thermal grooves, where it is assumed that Herring's local equilibrium condition for a triple junction holds and that the grain-boundary energy is independent of its boundary plane. A truncated double Fourier series is used to approximate the surface energy, and the unknown coefficients of the series are determined by fitting the observations to the local equilibrium condition. The method, which should be applicable to most polycrystalline materials, has been tested on magnesia that has been thermally grooved at 1400°C in air. The maximum of the best-fit surface energy function is at (111) and the minimum is at (100). The relative surface energies of the low-index planes are ␥ 110 /␥ 100 ‫؍‬ 1.040 ؎ 0.008 and ␥ 111 /␥ 100 ‫؍‬ 1.072 ؎ 0.010.

Grain boundary plane populations in minerals: the example of wet NaCl after low strain deformation

“…NaCl and MgO have the same crystal symmetry, and structure (space group Fm " 3mÞ; which has a minimum surface energy for {100} planes (Hartman 1973;Saylor et al 2000). The grain boundary plane populations for NaCl found in this study are very similar to those reported for magnesia (MgO) (Saylor et al 2003a): both materials show a preference for {100} planes when plane normals are averaged over all misorientations.…”

“…In a material that is not strongly anisotropic, like NaCl, the development of facetted grain boundaries, often forming square shaped grains in NaCl, is taken as evidence for the presence of intergranular fluids (Urai 1983;Spiers et al 1986), although some highly anisotropic minerals, like micas, always have facetted grain boundaries (Vernon 2004). The NaCl sample contained about 32 ppm of water and the MgO sample studies by Saylor et al (2000), about 0.3% of impurities. Water and impurities predominantly segregate at grain boundaries (Yan et al 1983;ter Heege et al 2004), although the main impurity in MgO, calcium, is reported to show anisotropic segregation, with the most frequently observed boundaries showing the least calcium accumulation (Saylor et al 2003b).…”

The distribution of internal interfaces in polycrystals

“…The tendency for grain boundaries in MgO to form on {100} planes is thought to be related to its surface energy anisotropy, c(n). The favored planes, {100}, have the lowest surface energy and those that occur with the lowest frequency, {111}, have the highest surface energy [80,81]. The distribution of grain boundary planes in SrTiO 3 is also well correlated to the surface energy anisotropy (see Fig.…”

Surface equilibrium angle for anisotropic grain growth in SnO2 systems

“…The determination of materials structures in polycrystals ceramics with high surface area are being facilited microscopy techniques [13][14][15]. The liquid phase formed during sintering process is found by means of determination of dihedral angle [16,17].…”