  A hexagonal columnar crystal undergoes a shear-melting transition above a
critical shear rate or stress. We combine the analysis of the shear-thinning
regime below the melting with that of synchrotron X-ray scattering data under
shear and propose the melting to be due to a proliferation of dislocations,
whose density is determined by both techniques to vary as a power law of the
shear rate with a 2/3 exponent, as expected for a creep model of crystalline
solids. Moreover, our data suggest the existence under shear of a line hexatic
phase, between the columnar crystal and the liquid phase.
