“…G RAIN boundaries of hill-and-valley (h&v) shapes with alternating parallel segments or kinked shapes (as observed at cross sections) with flat or curved segments intersecting at joints have been observed in many metals (Au, [1][2][3] Ni, 4,5 Al, 2,6,7 Ag, 8 -10 Cu, 11 Zn, 12,13 316L stainless steel, 14,15 a Ni-base superalloy, 16 Si-Fe, [17][18][19] Cu-Bi, 20 -22 and Fe-Te 23,24 ) and some oxides (MgO, 25 MgO⅐2Al 2 O 3 , 26 NiO, 27 Al 2 O 3 , 28 -34 and BaTiO 3 35-39 ) with both special and general misorientation angles between the grains. Some flat segments of the h&v boundaries were parallel to low-index planes of one or both of the grain pairs 1,3,28,32,34 -39 and likely to be singular corresponding to cusps in the polar plot of the boundary energy ␥ against the normal direction.…”