We report on the dependence of the lattice parameter on thickness (t) and grain size (D) in
nanogranular Nb thin films deposited on Si (100) substrates by using dc magnetron
sputtering. The lattice parameter is found to exponentially increase with decreasing
thickness as well as grain size. We analyze the lattice expansion in terms of the excess free
volume in the grain boundaries, which is found to decrease with the grain size in large
thickness limit. The thickness dependence of the lattice expansion and the grain size …