Frank's rule ($|{\mathbf{b}}_3{|}^2<|{\mathbf{b}}_1{|}^2+|{\mathbf{b}}_2{|}^2$)

The energy criterion associated with Frederick Charles Frank states that, for dislocations of comparable length with approximately common line-energy factors, a reaction conserving Burgers vector is energetically favourable when the displayed inequality holds. The rule is an energy estimate, not a proof that the geometry or kinetic barriers permit the reaction. Edge/screw character, elastic anisotropy and changed lengths refine it.