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Multi-dimensional NMR of relaxation and diffusion has been an area undergoing rapid development in recent years. Compared to the 1D counter part, 2D experiments offer higher resolution to understand complex and natural materials that are often a mixtures of multiple molecular species and in complex physical states. Many of the materials exhibit internal structural complexity, micro-structures, both in natural materials such as rocks and soils, food stuff, and biological tissues. The materials properties are often strongly determined by such micro-structure. The multi-dimensional experiments allow us to obtain correlation functions of several NMR parameters, such as T1, T2 and diffusion coefficient to enhance the ability to identify different components, but they also encode more specific diffusion physics so that new phenomena can be observed. This chapter reviews the recent development of 2D NMR of diffusion and relaxation and its applications.

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