Composition gradients and their effects on superconductivity in Al-doped   MgB2
  (Abridged abstract) Alloyed MgB2 differs from pure forms in that diffusion is needed to distribute the alloying elements homogeneously. Williamson-Hall analyses of x-ray diffraction peaks showed that Mg1-xAlxB2 samples made by a typical reaction A had higher crystalline strain than when thoroughly annealed by reaction B. The strain and other analyses indicate that reaction A produced substantial Al gradients across the individual grains while reaction B did not. The gredients skew the apparent superconducting behavior: properties appeared to be distinct when plotted vs. x (e.g. two Tc(x) curves), but all of the data merged when analyzed in terms of the unit cell volume v (e.g. one Tc(v) curve). Since v is derived from x-ray diffraction, it captures the average Al content actually present inside the grains and better reflects the behavior intrinsic to the addition of Al. These analyses show that it is important to coordinate structural and property characterizations to remove artifacts of composition gradients and uncover the intrinsic trends. Because the standard characterizations of the superconducting properties above gave no clear indication that the two sample sets had different homogeneity, the structural information was vital to make a correct assessment of the effects of Al doping on superconductivity. 
A. J. Zambano, A. R. Moodenbaugh, and L. D. Cooley