The possibilities for the extension of spectroscopy to two dimensions are discussed. Applications to nuclear magnetic resonance are described. The basic theory of two-dimensional spectroscopy is developed. Numerous possible applications are mentioned and some of them treated in detail, including the elucidation of energy level diagrams, the observation of multiple quantum transitions, and the recording of highresolution spectra in inhomogenous magnetic fields. Experimental results are presented for some simple spin systems.

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Phosphorus-31 NMR spectra have been obtained from a variety of synthetic, solid calcium phosphate mineral phases by magic angle sample spinning. The samples include crystalline hydroxyapatite, two type B carbonatoapatites containing 3.2 and 14.5% CO3(2-), respectively, a hydroxyapatite in which approximately 12% of the phosphate groups are present as HPO4(2-), an amorphous calcium phosphate, monetite, brushite, and octacalcium phosphate. Spectra were observed by the standard Bloch decay and cross-polarization techniques, as well as by a dipolar suppression sequence, in order to distinguish between protonated and unprotonated phosphate moieties. The spectra of the synthetic calcium phosphates provide basic information that is essential for interpreting similar spectra obtained from bone and other calcified tissues.

Twodimensional nuclear magnetic resonance in rotating solids: Time reversal effects in chemical shiftdipolar spectra J. Chem. Phys. 78, 613 (1983); 10.1063/1.444816Twodimensional nuclear magnetic resonance in rotating solids: An analysis of line shapes in chemical shift dipolar spectra Two-dimen~ional .magic. angle N~R methods produce high resolution dipolar-chemical shift spectra of polycrystalhne sohds which permit determination of the mutual orientation and principle values of the two coupling tensors. This technique is applied to the amide ISN_ 1 H spin pair in the dipeptide GlyGly . Hel . H 2 0, and we find the nearly axially symmetric ISN shift tensor is tilted 25' away from the NH ~nd .. In ~any situations, however, only the magnitude of the heteronuc1ear dipolar coupling is required, and s~mphficatl?n of t~e spectrum would be desirable. An experiment that projects the dipolar information onto a sIng~e rotatJ?nal sl~eband p.attern for each magnetically inequivalent spin is proposed. The approach involves scahn~ the IsotropIc c~emlcal shifts with a multiple-pulse train, together with rotationally synchronized samphng. The method IS demonstrated with spectra of the above mentioned dipeptide.