Ta-Nb alloys are shown to form random solid solutions by x-ray diffuse scattering measurements. These alloys have equal size atoms in their pure state with lattice parameters that are invariant in composition, obey Vegard's law, and exhibit an absence of solid solution hardening and an absence of fracture embrittlement at high solute concentrations. Ta-Mo atoms of about 5% difference in atomic size form short range ordered solid solutions with large atomic displacement effects. The Ta-Mo, and Ta-W, Nb-Mo and Nb-W alloys have in common a lattice parameter that varies in composition with a negative deviation from Vegard's Law. There is also a negative heat of mixing which is well correlated with short range order. In addition, all these alloys show linear solid solution hardening to high solute concentrations at room temperature and fracture embrittlement at high solute concentrations. Diffuse ex-ray scattering measurements on Ta-Mo alloys give the short range order parameters and atomic size displacements. The hardening is attributed to a combination of size effect induced substitutional solid solution hardening and short range order induced hardening.