Evolution of crystal morphologies to equilibrium by surface diffusion with anisotropic surface free energy in three dimensions

Phase-field model study of the effect of interface anisotropy on the crystal morphological evolution of cubic metals

“…7(b) shows round corners. The evolution of crystal geometry from the non-equilibrium to equilibrium has been studied by phase-field modelling as well as other methods [24,25].…”

“…where g (25) There are other suggestions for dealing with different systems [20,21]. The phase-field computation is solving Eq.…”

Specific surface free energy and etch pit density of synthesized quartz crystal

“…It is well know that specific surface free energy (SSFE) is a significant value to determine the morphology of a single crystal and there are many theoretical investigations discussing the relationships between SSFE and the morphology of the crystals [1][2][3]. However, experimental investigation for SSFE is very few.…”

Experimental study for the Wulff's relationship of ruby single crystals using contact angles of liquid droplets

“…Though this relationship was proposed in 1901 [1], experimental trials to confirm this relationship are very few, because the experimental measurement of surface energy was believed to be difficult. Even though a lot of theoretical studies on SSFE concerning the morphology of the crystals are reported [2,3], direct measurement of the SSFE of crystal surface has never been reported for the last hundred years, but only some indirect estimation for the the SSFE of crystals were performed. For example, Brace and Walsh [4] tried to measure the surface energy of a quartz crystal by introducing a crack into the quartz crystal.…”