  We propose a discrete lattice model of the energy of dislocations in
three-dimensional crystals which properly accounts for lattice symmetry and
geometry, arbitrary harmonic interatomic interactions, elastic deformations and
discrete crystallographic slip on the full complement of slip systems of the
crystal class. Under the assumption of diluteness, we show that the discrete
energy converges, in the sense of $\Gamma$-convergence, to a line-tension
energy defined on Volterra line dislocations, regarded as integral
vector-valued currents supported on rectifiable curves. Remarkably, the
line-tension limit is of the same form as that derived from semi-discrete
models of linear elastic dislocations based on a core cutoff regularization. In
particular, the line-tension energy follows from a cell relaxation and differs
from the classical ansatz, which is quadratic in the Burgers vector.
