Three phases, a, b, and 8 meet as shown in Figure 2.8a, forming three inter- phase interfaces-namely, a/b, a/, and /8. It can be shown that the following holds. Yo/B Ya/8 sino; sin 02 YB/8 sin Using this equation, determine the equation that relates the grain boundary grooving angle Ogh to the interface energy Yal and the grain boundary energy Yux (Figure 2.8b). Yap B 738 Liquid 9 'gb ya 03 8 a Ya8 (a) (b) Figure 2.8 (a) Three phases meeting at a point, showing the angles between their surfaces. (b) A grain boundary groove showing the equilibrium groove angle