Lawrence Berkeley National Laboratory

Significant efforts can be found throughout the literature to optimize the current carrying capacity of Nb$_3$Sn superconducting wires. The achievable transport current density in wires depends on the A15 composition, morphology and strain state. The A15 sections in wires contain, due to compositional inhomogeneities resulting from solid state diffusion A15 formation reactions, a distribution of superconducting properties. The A15 grain size can be different from wire to wire and is also not necessarily homogeneous across the A15 regions. Strain is always present in composite wires, and the strain state changes as a result of thermal contraction differences and Lorentz forces in magnet systems. To optimize the transport properties it is thus required to identify how composition, grain size and strain state influence the superconducting properties. This is not accurately possible in inhomogeneous and spatially complex systems such as wires. This article therefore gives an overview of the available literature on simplified, well defined (quasi--)homogeneous laboratory samples. After more than 50 years of research on superconductivity in Nb$_3$Sn, a significant amount of results are available, but these are scattered over a multitude of publications. Two reviews exist on the basic properties of A15 materials in general, but no specific review for Nb$_3$Sn is available. This article is intended to provide such an overview. It starts with a basic description of the Niobium--Tin intermetallic. After this it maps the influence of Sn content on the the electron--phonon interaction strength and on the field-temperature phase boundary. The literature on the influence of Cu, Ti and Ta additions will then be briefly summarized. This is followed by a review on the effects of grain size and strain. The article is concluded with a summary of the main results.