  We derive a theory that describes homogeneous nucleation of grain boundary
(GB) phases. Our analysis takes account of the energy resulting from the GB
phase junction, the line defect separating two different GB structures, which
is necessarily a dislocation as well as an elastic line force due to the jump
in GB stresses. The theory provides analytic forms for the elastic interactions
and the core energy of the GB phase junction that, along with the change in GB
energy, determine the nucleation barrier. We apply the resulting nucleation
model to simulations of GB phase transformations in tungsten. Our theory
explains why under certain conditions GBs cannot spontaneously change their
structure even to a lower energy state.
