J. Baum

Multiple‐quantum dynamics in solid state NMR

Recently developed solid state multiple‐quantum NMR methods are applied to extended coupling networks, where direct dipole–dipole interactions can be used to create coherences of very high order (∼100). The progressive development of multiple‐quantum coherence over time depends upon the formation of multiple‐spin correlations, a phenomenon which also accompanies the normal decay to equilibrium of the free induction signal in a solid. Both the time development and the observed distributions of coherence can be approached statistically, with the spin system described by a time‐dependent density operator whose elements are completely uncorrelated at sufficiently long times. With this point of view, we treat the distribution of coherence in a multiple‐quantum spectrum as Gaussian, and characterize a spectrum obtained for a given preparation time by its variance. The variance of the distribution is associated roughly with the number of coupled spins effectively interacting, and its steady growth with time refl...

NMR studies of clustering in solids

The authors present a time-resolved multiple-quantum NMR experiment which allows us to determine the spatial distribution of atoms in materials lacking long-range order; in particular, they study the size and extent of atomic clustering in these materials. Multiple-quantum NMR is sensitive to the distribution of spins in a solid. At the two extremes, uniformly distributed spins absorb radio-frequency quanta continuously, whereas clustered groups of N spins can absorb only up to N quanta. Model experiments are demonstrated on the hydrogen distribution in selectively deuterated organic solids and in hydrogenated amorphous silicon.

Broadband population inversion by phase modulated pulses

We present a class of continuously phase modulated radiation pulses that result in coherent population inversion over a large range of transition frequencies. The continuously modulated pulses can be approximated by sequences of discrete phase shifted pulses. Simulations of the inversion properties of the continuously modulated pulses and of the discrete pulse sequences are given.

NMR imaging in solids by multiple-quantum resonance

NMR imaging is now a well-established technique for studying biological systems (1). In its most general form, an imaging method uses a magnetic field gradient to encode the positions of the nuclear spins with a spatially varying Larmor frequency. Once the variations in resonant frequency have been decoded appropriately, an image of the nuclear spin density or, more generally, of any mix of NMR parameters can be created. In a linear magnetic field gradient, g, the spread of frequencies across a thickness AZ is ghz. If features on the order of AZ are to be resolved, then the externally imposed field, gAz, must itself be resolved relative to any background or internal field. For solids, the dominant background field is usually the local dipolar field, BL. In biological systems familiar from ‘H imaging, rapid isotropic molecular motion often averages these internal dipolar fields to zero. However, in a strongly protonated solid, where molecular motion is restricted, a typical value for BL might be 5 G so that a gradient greater than 50 G/cm (0.5 T/m) would be needed to achieve a resolution of 1 mm. One approach (2-4) to this problem is to reduce the effective local field by a multiple-pulse line-narrowing sequence (5, 6). The alternative approach is to leave the local field untouched, but to impose a gradient large enough to meet the condition g % &/AZ. In this communication, we demonstrate a prototype imaging experiment for solids based in spirit on this “brute force” method of increasing the gradient, but which relies instead on the properties of multiplequantum NMR transitions (7, 8) to increase the effective gradient strength by an order of magnitude. Specifically, we intensify the effect of the gradient upon the evolution of the spin system by creating high-order multiple-quantum coherences and following their development in the static field gradient. A multiple-quantum coherence of order n = Mi Mj, where Mi and Mj are the magnetic-quantum numbers for high-field states Ii) and lj), evolves n times more rapidly in an inhomogeneous field than the usual single-quantum coherence. That is, if a singlequantum transition in the presence of a field gradient appears with resonance offset AU, then an n-quantum transition appears at nAo. The effective local dipolar fields are, however, roughly comparable for highand low-order coherences in very large

Phase-incremented multiple-quantum NMR experiments

Time-resolved multiple-quantum (MQ) NMR is a useful tool for determining the spatial distribution of atoms in materials lacking long-range order. Recently, proton MQ NMR using time proportional phase incrementation (TPPI) (1-3) has been applied to NMR imaging of solids (4), the study of hydrogen distribution in solids (5, 6), and hydrogenated amorphous silicon (7). By use of a modification of the conventional MQ experiment suggested by Emid (a), it is possible to improve the sensitivity and efficiency for clustering studies. Related ideas have appeared in the context of NMR imaging (9, 10). We explain herein experimental details of this modification, called “phase-incremented MQ NMR,” and show results of spin clustering studies in solid and liquid crystalline samples. To appreciate how phase-incremented MQ NMR works (8), it is useful to review the time-domain MQ experiment described schematically in Fig. la. As usual, the sequence can be partitioned into four distinct periods; namely the preparation (T), evolution (tl), mixing (T’), and detection (tz) periods. The pulse sequence applied during the preparation period determines the multiple-quantum excitation. For example, the eight-pulse sequence shown in Fig. lb generates the following average dipolar Hamiltonian (13):

Multiple quantum NMR excitation with a one-quantum hamiltonian

Abstract Excitation of multiple quantum coherence in dipolar coupled spin systems is usually accomplished with a two-quantum multiple pulse sequence which can be time reversed by means of a 90° phase shift. The application of such an excitation scheme to a spin system in thermal equilibrium excites only even orders of multiple quantum coherence. We demonstrate here time reversible pulse sequences that excite all orders of coherence by creating a pure one-quantum average hamiltonian. We also describe pulse schemes which can be used to create pure one- or two-quantum average hamiltonians with variable scaling between +1 and −1. These excitation schemes are relevant to the study of spin clustering by multiple quantum NMR.

Iterative maps with multiple fixed points for excitation of two level systems

Iterative schemes have been used in NMR to generate pulse sequences which excite spin systems over narrow or broad ranges of transition frequencies and radio frequency amplitudes. Mathematical methods employing iterative maps and related concepts from nonlinear dynamics have been applied in the analysis of these schemes. The effect of transforming a pulse sequence by an iterative procedure can be represented as an iterative map on a quantum statistical propagator space, with fixed points in this space corresponding to certain desired responses of the spin system. The stability of these points with respect to variations of parameters, such as amplitudes or energies, determines the bandwidth characteristics of the corresponding sequence; broadband behavior results from stable fixed points, and narrowband behavior from unstable fixed points. This paper examines schemes which produce maps with more than one stable fixed point. Such schemes are shown to generate sequences which exhibit bistable or selective, b...

Spatially selective NMR with broad-band radiofrequency pulses

Abstract The problem of non-invasive spatial localization in NMR is approached by constructing a spatially selective composite pulse sequence and incorporating it into a recently developed difference scheme. The composite sequence described, which requires nine phase-shifted π pulses, functions only over a narrow range of radio-frequency (rf) field strengths while remaining effective over a broad range of resonance frequencies. Relying upon the field gradient of a surface coil to label regions in space by local rf amplitudes, the pulse inverts all nuclear spins at a selected distance from the coil across a broad range of chemical shifts. This approach will allow the observation of chemically shifted NMR signals from specific regions of a material or organism. Computer simulations are presented, and the method is demonstrated experimentally on a phantom sample using a surface coil.

Multiple Quantum NMR Study of Hydrogen Clustering in Amorphous Silicon

Because Multiple Quantum NMR coherences occur only between spins which are coupled together by the dipole interaction, this technique has been used to study the clustering of hydrogen in amorphous silicon. The clustered hydrogen was found to be associated with the broad line of the single quantum NMR spectra. For device quality films, the average cluster size is approximately six protons. The concentration of these five to seven atom defects increases with increasing hydrogen content until, at very high hydrogen content, the clusters are replaced by a continuous network of silicon-hydrogen bonds.