The atomic structure of the (310) symmetric tilt grain boundary in Nb
and of an interface between Mo and Re is calculated. The calculations
are done within the tight binding (TB) approximation to quantum mechan
ics and are checked carefully against some accurate first-principles c
alculations in the local density approximation to density functional t
heory. A non-orthogonal spd electron TB model is tested, but is found
to be no improvement on the much simpler orthogonal d-electron model;
in particular there is no improvement in the volume dependence of the
total energy. The structure of the Nb grain boundary is compared to th
at obtained by other authors using high resolution electron microscopy
. The comparison enables some statements to be made about the nature o
f the interatomic interactions and especially about the opposing force
s that are balanced at the equilibrium grain boundary expansion. The p
aper includes the first quantum mechanical calculation of a dissimilar
metal interface with a view to obtaining the structure of a misfit di
slocation and a value for the theoretical strength of the interface. I
t is concluded that the misfit dislocation in this case has a widely s
pread core and that the theoretical strength is considerably reduced r
elative to the bulk crystal.