~(207)Pb nmr and monte carlo studies of ionic solid solutions

摘要

Lead, strontium and barium nitrates, like the titanates of the same cations, form a continuous set of solid solutions. ~(207)Pb NMR spectra of mixed crystals of lead/strontium nitrate and lead/barium nitrate each show up to 13 lines, arising from lead ions with from zero to twelve Pb~(2+) nearest-neighbor cations replaced by Sr~(2+) or Ba~(2+). In the case of (Pb,Sr)(NO_3)_2 these shifted lines are further split by the multiplicity of inequivalent nearest-neighbor replacements. The average shift per Sr~(2+) ion is 21.8 ppm; that for Ba~(2+) is smaller. Using Monte Carlo/Metropolis calculations, the intensities of the resonances can be fit to statistical models of Pb~(2+) and Sr~(2+) ion distributions, and used to probe the microenergetics of solid solution formation. The data can be satisfactorily fit by distributions in which the cations are slightly clustered, with like pairs of nearest neighbors being favored by 120 J/mol over unlike pairs. Interestingly, this finding is inconsistent with the conventional interpretation of powder diffraction results for the mixed crystals, where the dependence of lattice parameter on composition shows a slight positive curvature, generally hed to indicate a favorable interaction between unlike ions.