A series of atomistic calculations is performed in order to evaluate the effects of several physical factors on dislocation emission in a model hexagonal lattice. The method of calculation is the lattice Green's-function method, together with several pair potentials with variable parameters. The physical factors of interest are the dislocation width (or, more precisely, maximum strain) and ''unstable stacking energy'' suggested by several continuum-based calculations, as well as the mode-I loading. We find that the continuum theories are surprisingly accurate, provided that some modifications are made. Typical discrepancies are of order 10% in the emission stress intensity. However, the atomistic calculations indicate that several of the assumptions underlying the continuum theories are inaccurate. In addition, we find strong mode-I-mode-II interactions, which are summarized in the form of a crack-stability diagram.