Vegard's 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 non-statistical 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. Vegard's 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.
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Ceramics and Composites
- Condensed Matter Physics
- Physical and Theoretical Chemistry
- Inorganic Chemistry
- Materials Chemistry