Local structure in ball-milled and Ni substituted Nd$_y$Fe$_{4-x}$Ni$_x$Sb$_{12}$

We report EXAFS measurements at the Nd L$_{\rm III}$, Fe, and Sb K edges in Nd$_y$Fe$_{4-x}$Ni$_x$Sb$_{12}$. Recent measurements show that ball-milled Nd$_y$Fe$_4$Sb$_{12}$, with $\sim$ 150 nm size particles, significantly improved the figure of merit (ZT) by 22 \%, compared to material with 10 $\mu$m sized particles. Since ball milling can produce significant disorder and even amorphization, which would lower the thermal conductivity, we compared the local structure for ball-milled and hand ground samples. We find that the average local structure is essentially unchanged by ball milling; the reduced particle size reduces the phonon mean free path, thereby reducing the thermal conductivity. When Ni is substituted on the Fe site, together with a decreased concentration of Nd, we find the largest changes in disorder are about the Nd atoms; there is little disorder of the first few neighbors about the Fe site. Further the local distortions are not uniform; the lattice constant decreases with Ni concentration, but the Nd-Sb bond length slightly expands while the Sb-Sb contracts more than expected. Some consequences are discussed.