Carbon Inhomogeneity and Superconducting Properties of Mg(B,C)$_{2}$

Mg and B$_{4}$C mixtures (molecular ratio of [1:2]) were reacted in a single step in stainless steel from 850\r{ }C to 1300\r{ }C to produce nominal MgB$_{1.8}$C$_{0.2}$ as estimated from unit cell volumes. Reactions from 850 to 1100\r{ }C produced an inhomogeneous superconducting phase despite the initial atomic B$_{4}$C compound, suggesting that carbon segregation is an important part of these reactions. For reactions above 1100\r{ }C, the critical temperature T$_{c}$ increased from 18 to 28 K as the strain (as estimated from x-ray diffraction peak broadening) decreased at nominally constant carbon content, suggesting that structural order is also important. These changes will be discussed with regard to the formation and coarsening of amorphous and crystalline impurity phases observed by electron microscopy, which affect electron scattering and connectivity. Since only scattering affects the upper critical field, whereas both scattering and connectivity affect the transport properties, optimization of these reactions is crucial to understanding the potential for Mg(B,C)$_{2}$ as a high-field superconductor.