  The energetically optimal position of lattice defects on intrinsically curved
surfaces is a complex function of shape parameters. For open surfaces, a simple
condition predicts the critical size for which a central disclination yields
lower energy than a boundary disclination. In practice, this transition is
modified by activation energies or more favorable intermediate defect
positions. Here it is shown that these transition characteristics (continuous
or discontinuous, first or second order) can also be inferred from analytical,
general criteria evaluated from the surface shape. A universal scale of
activation energy is found, and the criterion is generalized to predict
transition order as symmetries such as that of the shape are broken. The
results give practical insight into structural transitions to disorder in many
cellular materials of technological and biological importance.
