This thesis describes application and development of advanced solid-state nuclear magnetic resonance techniques for complex materials, in particular organic-inorganic nanocomposites and thermoelectric tellurides. The apatite-collagen interface, essential for understanding the biomineralization process in bone and engineering the interface for controlled bio-mimetic synthesis and optimized mechanical properties, is buried within the nanocomposite of bone. We used multinuclear solid-state NMR to study the composition and structure of the interface. Citrate has been identified as the main organic molecule strongly bound to the apatite surface with a density of 1/(2 nm)², covering 1/6 of the total surface area in bovine bone. Citrate provides more carboxylate groups, one of the key functional groups found to affect apatite nucleation and growth, than all the non-collagenous proteins all together in bone; thus we propose that citrate stabilizes apatite crystals at a very small thickness of ∼3 nm (4 unit cells) to increase bone fracture tolerance. The hypothesis has been confirmed in vitro by adding citrate in the bio-mimetic synthesis of polymer-hydroxyapatite nanocomposites. The results have shown that the size of hydroxyapatite nanocrystals decreases as increasing citrate concentration. With citrate concentrations comparable to that in body fluids, similar-sized nanocrystals as in bone have been produced. Besides the dimensions of the apatite crystals, the composition of bone also affects its bio-functional and macroscopic mechanical properties; therefore, our team also extended its effort to enhance the inorganic portion in our bio-mimetic synthesis from originally 15 wt% to current 50 wt% compared to 65 wt% in bovine bone, by using Lysine-Leucine hydroxyapatite nucleating diblock co-polypeptide, which forms a gel at very low concentration.

In this thesis, various advanced solid state NMR techniques have been employed to characterize nanocomposites. Meanwhile, we have developed new methods to achieve broadband high resolution NMR and improve the accuracy of inter-nuclear distance measurements involving quadrupolar spins. Broadband high resolution NMR of spin-1/2 nuclei has been accomplished by the adaptation of the magic angle turning (MAT) method to fast magic angle spinning, termed fast MAT, by solving technical problems such as off-resonance effects. Fast MAT separates chemical shift anisotropy and isotropic chemical shifts over a spectral range of ∼1.8 γB₁ without significant distortions. Fast MAT ¹²⁵Te NMR has been applied to study technologically important telluride materials with spectra spreading up to 190 kHz. The signal-to-noise ratio of the spectra is significantly improved by using echo-matched Gaussian filtering in offline data processing. The accuracy of the measured distances between spin-1/2 and quadrupolar nuclei with methods such as SPIDER and REAPDOR has been improved by compensating for the fast longitudinal quadrupolar relaxation on the sub-millisecond with a modified S₀ pulse sequence. Also, the T_1Q effect on the spin coherence and its spinning speed dependency has been explored and documented with analytical and numerical simulations as well as experimental measurements.