Thermal Grooving:

  

Figure 3. covers all the cases for a normal GB. Note that above formula is free of tilt angle.

The first term on the  right side of  this expression is almost identical to the one obtained by Mullins (1957, Eq.36) for a surface layer of  infinite extent, using the small slope approximation in addition to the assumption that the dihedral angles are in equilibrium configuration.

The В parameter, which is introduced by Mullins (1957) in his paper for scaling purpose, is exactly equal to in our representation.

Mullins (1957) obtain a prefactor compared to our value 4/5.

figure 3
  

Applying the inverse scaling procedures to our analytical findings the following equation for the grain boundary  TJ displacement is obtained;