Bonds broken at atomically flat crystal surfaces—II

Surface atomic structures, surface energies, and equilibrium crystal shape of molybdenum

“…From our calculations, the ratio of the surface energies per unit area ␥ hkl /␥ 100 are 1.0, 0.97, 0.93, and 0.87 for the ͑100͒, ͑111͒, ͑211͒, and ͑110͒ surfaces, respectively, compared with the values 1.0, 0.87, 0.80, and 0.71 obtained from a bond-cutting model. 34 We see that even the simplest bond-cutting models predict correctly the trend of the surface energies. When we compare the numbers, we see that the bond-cutting model overestimates the surface energies of less compact orientations relative to the most compact ͑110͒ orientation.…”

The Surface Energy and Contact Angles of a Liquid Foam

“…The volume of the Kelvin cell is 8 √ 2a 3 and the area of the hexagonal section is 4 √ 2a 2 . The volume of the wall cell is thus 4 √ 2a 3 + 4 √ 2a 2 x.…”

“…This approach was previously used (1) to calculate the surface energies of 2D clusters of identical bubbles and proved to be quite accurate. The broken bond method was used in the past to estimate the surface energy of simple crystalline solids (2,3).…”

“…where we used the value [31b] for ( ε w ) 3 . Introducing [34] to relate r with a and dividing by the length (area) per pool bubble ( √ 3a in 2D and (3 √ 3/2)s 2 in 3D), we obtain…”

Free energy of the bcc–liquid interface and the Wulff shape as predicted by the phase-field crystal model

“…Apparently, the {100} faces have decreasing importance with increasing , whereas the {111} face does not show up at all. These differences in the Wulff shape may be attributed to the fact that the Wulff shape is known to be sensitive to the interaction potential [18,19,20]. A recent work suggests that in the PFC model the effective pairpotential has a repulsive peak at ≈ r 0 √ 2, where r 0 is the radius corresponding to the main minimum of the potential [41], which potential differs from the potentials expected for noble gases and metals.…”