Abstract
An expression is derived for the displacements in an isotropic elastic medium which contains an edge dislocation moving with uniform velocity c. When c=0 the solution reduces to that given by Burgers for a stationary edge dislocation. The energy density in the medium becomes infinite as c approaches c2, the velocity of shear waves in the medium; this velocity therefore sets a limit beyond which the dislocation cannot be accelerated by applied stresses. The atomic structure of the medium is next partly taken into account, following the method already used by Peierls and Nabarro for the stationary dislocation. The solution found in this way differs from the one in which the atomic structure is neglected only within a region of width ζ which extends not more than a few atomic distances from the centre. ζ varies with c and vanishes when c=cr, the velocity of Rayleigh waves. It becomes negative when cr< c<c2. Thus cr rather than c2 appears to be the limiting velocity when the atomic nature of the medium is taken into account. Since cr similar, equals 0.9c2 the difference is not of much importance.
The same method applied to a screw dislocation gives, in the purely elastic case, the expression already derived by Frank. The corresponding Peierls-Nabarro calculation shows that the width ζ is proportional to (1 - c2/c22)½. This "relativistic" behaviour is analogous to Frenkel and Kontorowa's results for their one-dimensional dislocation model.