Vegards Rule Revisited in BaxPb1-x(NO3)2 by NMR and XRD

Vegardʹs rule, originally based on powder X-ray diffraction data from BaxPb1-x(NO3)2, is reevaluated through the application of nuclear magnetic resonance (NMR) spectroscopy. Solid state 207Pb NMR and 15N NMR spectra of BaxPb1-x(NO3)2 (0.93>x>0.08) were recorded. The chemical shift dispersions for each magnetic nucleus are remarkable for their sensitivity to the nearest neighbor Pb2+ and Ba2+ distributions. The intensities of the peaks in the 207Pb spectra and their deviations from a simple binomial dependence reveal a nonstatistical incorporation of Ba2+ and Pb2+ in the bulk crystals. Complementary analyses were performed by powder X-ray diffraction and with electron spectroscopy for chemical analysis that reveal bulk heterogeneities varying with crystal growth conditions. Vegardʹs original determination of a linear correlation between lattice constants and composition in BaxPb1-x (NO3)2 is shown to have been a favorable consequence of the low resolution X-ray film methods available in the 1920s, but his additivity relationship is restored locally in the linear correlation of chemical shift with composition of the first metal coordination sphere.