Quadrupolar Spin Systems Research Articles

New double resonance technique for quadrupolar nuclei

New double resonance techniques for the resolution enhancement of nuclear magnetic resonanceof quadrupolar nuclei are presented which use population transfers between Zeemanlevels of a quadrupolar split spin system. Experiments on high temperature superconductorsare reported where a differentiation between overlapping lines due to different crystallographicsites and also different isotopes can be achieved. In addition, methods for selective measurementsof the spin-spin and spin lattice relaxation are shown.

2D Off-Resonance Nutation NQR Spectroscopy of Spin 3/2 Nuclei

Abstract The effects of off-resonance irradiation in nutation NQR experiments are demonstrated both experimentally and theoretically. The theoretical description of the off-resonance effects in 2D nutation NQR spectroscopy is given, and general exact formulas for the asymmetry parameter are obtained. It is shown that the outcome of the off-resonance nutation experiments depends on the data acquisition procedure, leading to one- or three-line nutation spectra. To explain this fact and to describe the off-resonance nutation experiment properly, the transient response theory of a quadrupolar spin system to an RF pulse was modified using the wave-function approach. The 2D separation of interactions technique has been applied to separate a static and a randomly time-fluctuating dynamic part of the quadrupole interaction in the antiferroelectric phase of poly-crystalline ammonium dihydrogen arsenate. Two-dimensional off-resonance nutation NQR spectroscopy has been used to determine the full quadrupolar tensor of spin-3/2 nuclei in several molecular crystals containing the 35Cl and 75As nuclei. The off-resonance phenomena in 2D NQR are very important from the practical point of view (determination of ƞ in multiple or broad-line spectrum) and also provide interesting information on the dynamic properties of a quadrupolar spin system.

Frequency stepped adiabatic passage excitation of half-integer quadrupolar spin systems

The excitation of half-integer quadrupolar spins by frequency stepped pulses is explored in powdered samples, under both static and magic angle spinning (MAS) conditions. The effects of sweep rate, sweep range, RF field strength, rotation and quadrupole frequency are investigated by numerical simulations and experiments. Using excitation by a frequency stepped half-passage it is possible to generate undistorted, quantitatively interpretable central-transition powder spectra in static samples, with an improved sensitivity compared with short-pulse excitation. Under MAS the duration of the half-passage must be shorter than 1/2 rotor period to get simple results. The conditions required for a quantitatively interpretable frequency stepped half-passage are formulated and subsequently tested on a number of model compounds. The conditions to bring about a complete inversion of the spin system by an adiabatic full-passage are more stringent than for excitation, and cannot be realized in most practical cases. Sel...

Frequency stepped adiabatic passage excitation of half-integer quadrupolar spin systems

The excitation of half-integer quadrupolar spins by frequency stepped pulses is explored in powdered samples, under both static and magic angle spinning (MAS) conditions. The effects of sweep rate, sweep range, RF field strength, rotation and quadrupole frequency are investigated by numerical simulations and experiments. Using excitation by a frequency stepped half-passage it is possible to generate undistorted, quantitatively interpretable central-transition powder spectra in static samples, with an improved sensitivity compared with short-pulse excitation. Under MAS the duration of the half-passage must be shorter than 1/2 rotor period to get simple results. The conditions required for a quantitatively interpretable frequency stepped half-passage are formulated and subsequently tested on a number of model compounds. The conditions to bring about a complete inversion of the spin system by an adiabatic full-passage are more stringent than for excitation, and cannot be realized in most practical cases. Selective excitation and inversion of a single transition is feasible, however.

Shaped pulse excitation in multi-quantum magic-angle spinning spectroscopy of half-integer quadrupole spin systems

Coherence excitation by shaped pulses in the multi-quantum magic-angle spinning spectroscopy of half-integer quadrupole spin systems was explored. A theoretical analysis shows there exists a class of shaped pulses that are superior to the rectangular pulses normally used in MQMAS studies. Significant sensitivity enhancement can be achieved without loss of resolution and quantification. This is verified by numerical simulations based on decaying triangular and exponential shaped pulses. 23Na multi-quantum magic-angle spinning spectra of polycrystalline anhydrous di-sodium hydrogen phosphate (Na 2HPO 4) are shown to be well-explained by the theoretical analysis.

A New Nuclear-Quadrupole Double-Resonance Technique based on Solid Effect

Abstract A new nuclear-quadrupole double-resonance technique is described. It has a higher sensitivity and a higher resolution than the conventional nuclear-quadrupole double-resonance technique based on solid effect. The new technique involves magnetic field cycling between a high and a low static magnetic field and simultaneous application of two rf magnetic fields when the sample is in the low static magnetic field. A strong rf magnetic field induces "forbidden" simultaneous transitions in a magnetic (usually 1H) and in a quadrupole spin system and thus couples the two spin systems. A weak rf magnetic field induces transitions between the energy levels of the quadrupole nuclei and simulates a fast spin-lattice relaxation of the quadrupole nuclei when its frequency matches an NQR frequency. The sensitivity and resolution of the new technique are discussed and test measurements in tris-sarcosine calcium chloride are presented.

One Pulse Spin-locking in NQR

Abstract The response of a quadrupolar spin system in zero applied magnetic field to a long rf pulse, for both single crystal and polycrystalline samples possessing broad Lorentzian-shaped resonance lines has been studied. The dependencies of magnetization on frequency offset, linewidth and power are investigated both theoretically and experimentally. The problem of the effective field direction in both single crystal and polycrystalline samples is also discussed. For a polycrystalline cuprous oxide (Cu2O) sample it is observed that the magnetization after a long pulse in on-resonance condition does not become zero for time t ≫ T2 , in agreement with theoretical results. It has also been shown that the magnetization increases with increase in the width of the resonance line as well as with the decrease in the excitation power.

Use of computer algebra for the study of quadrupole spin systems

Analytical computation of the effect of radiofrequency pulses and free evolution between pulses are studied in a spin system dominated by the nuclear electric quadrupole interaction using ‘symbolic computer algebra’. The program MAPLE is used to compute spin density matrices for single spin systems with spin magnitude I = 1, 3/2, 2 and 5/2. In all cases except I = 5/2, the pure nuclear electric quadrupole Hamiltonian with arbitrary asymmetry parameter η is used to obtain results for a single pulse and an evolution period following the pulse. In the spin 5/2 system η is set to zero. The calculations are done using a simple matrix representation of the density operator and the Baker-Campbell-Hausdorff formula. In addition, the validity of dropping non-secular (i.e., time-dependent) terms from the Hamiltonian for the pulse in the quadrupole interaction frame is examined for the spin 1 case using a truncated Magnus expansion.

Magnetic field dependence of internal interactions in nuclear spin systems

AbstractThe internal interactions in spin systems depend on the magnetic field strength, since the latter perturbs the electronic wave functions. The changes in the interaction tensors are approximately proportional to the applied magnetic field. This effect is experimentally most significant for quadrupolar spin systems, since the quadrupolar interaction is usually the strongest. This field dependence of internal interactions, seldom considered before, may lead to an ambiguity in the explanation of nuclear magnetic resonance (NMR) experiments of quadrupolar spin systems.

Zeeman Effect of Pure NQR in a Rotating Frame (CW and Pulsed Excitation)

Abstract The Zeeman effect in a rotating frame is considered for the case when the quadrupolar nuclear spin system is acted on by two radio-frequency fields.

NQR in the Effective Fields of a Multiple-Pulse Sequence

Abstract We discuss a new form of resonant response for a quadrupolar nuclear spin system subjected to applied alternating magnetic fields.

Relaxation Processes in NQR Multiple-Pulse Spin-Locking

A theory of the spin-lattice and spin-spin relaxation processes in quadrupole spin systems with I > 1/2 in the situation of the multiple-pulse NQR spin locking is proposed for the pulse sequence MW-4. The theory is based on the assumption that for t ≳ T2 the change of the spin system is a quasi-equilibrium process. Rate equations for inverse generalized temperatures are obtained and the kinetic coefficients calculated for the case o f exponential correlation functions. The above assumption was confirmed for some substances containing the 35Cl and 123Sb, and the time constant T1e characterizing the spin echo signal decay was investigated and compared with the time constant T1q, in the case of continuous spin locking.

On spin-spin reservoir relaxation in NQR

An attempt is made to discuss in a preliminary manner the question of the possible influence of absence of the inner equilibrium in the quadrupole spin system on the nuclear quadrupole spin-lattice relaxation. A general approach is proposed and special situations considered: small percentage of the quadrupole nuclei on the one hand and the paramagnetic impurity relaxation mechanism on the other. In the case of spin 5 2 and zero asymmetry parameter the spin-lattice relaxation time of the “quadrupole spin-spin reservoir” is calculated and compared with the “usual” quadrupole spin-lattice relaxation time.

Triple quantum NMR on spin systems with I = 3/2 in solids

Pulsed NMR experiments are developed for the excitation and the detection of triple quantum coherences in quadrupolar spin systems with I = 3/2. Two experimental methods are used: For systems with small quadrupolar frequencies direct triple quantum excitation and detection is accomplished by weak rf irradiation pulses. For large quadrupolar frequencies modulated rf pulses are applied to create and to monitor triple quantum coherences. Modulated rf pulse techniques are also used to search for quadrupolar frequencies and to excite selectively center frequency spectral lines of I = 3/2 nuclei. Applications of these techniques are demonstrated by 23Na(I = 3/2) NMR experiments on an oriented single crystal of sodium ammonium tartarate tetrahydrate.

Nuclear double resonance interferometric spectroscopy

A double resonance technique designed to allow study of quadrupolar interactions in nonintegral spin systems is described using both theoretical calculations and experimental data. The interferometric technique involves indirect detection of quadrupolar-broadened satellites by observation of only the central 1/2↔−1/2 transition. Changes in the phase factor of one wavefunction in a multilevel quadrupolar split spin system are monitored by observation of the free-induction decay of the central transition, while a 360° pulse at a second (search) frequency is applied. Particular consideration is given to the accurate reproduction of an inhomogeneously broadened satellite, and several spectroscopic schemes are compared theoretically and tested experimentally using the 23Na satellites in single-crystal sodium nitrate. Emphasis was placed on the important roles of H1 broadening and coherence transfer to the double quantum states.

Determination of relative intramolecular configuration by nuclear quadrupole double resonance

The influence of a nuclear quadrupole spin system B on the spin echo of a nuclear quadrupole system A is governed by a 1/r6 law. This relation was used to determine relative intramolecular arrangements within molecules and complex ions in solids. By heteronuclear double resonance 81Br [graphic omitted] 27Al in KAl2Br7 the bridging bromine has been determined and also the Br frequencies have been assigned to certain Br—Al bonds. Homonuclear double resonance 35Cl [graphic omitted] 35Cl was applied to molecular compounds of Cl3CCO2H and the close-lying frequencies of two molecules in the asymmetric unit were split-up into the appropriate groups. Finally, from isotopic 81Br [graphic omitted] 79Br double resonance in 3,5-dichlorophenoxy aluminiumdibromide and 4-chlorophenoxy aluminiumdibromide a structure is proposed for these molecules. The aluminium atoms in these dimeric compounds are connected by bridging oxygen atoms, whereas the bromine atoms are in terminal positions.

Transient response of a quadrupolar spin-system in zero applied field

The response of a system of nuclear spins I = 3 2 experiencing electric quadrupole couplings in zero externally applied field to two pulse sequences is examined using time-dependent perturbation theory. One sequence consists of a single pulse of duration t w applied Δω from resonance, with the other sequence of this single pulse followed by a short, resonant 90° pulse. The duration of the first pulse is assumed, in general, to be comparable to T 2 ϱ , where T 2 ϱ is a time-constant characterizing the rate of approach of the system to a new equilibrium in the presence of the r.f. field H 1( t). The response of the system as a function of Δω is markedly dependent upon the relative values of t w and T 2 ϱ . For the two limits t w ⪢ T 2 ϱ and t w ⪡ T 2 ϱ , very different variations in response of the system to the first pulse are predicted, and amply verified experimentally. The response of the I = 3 2 system in zero static applied field to these pulse sequences is analogous to that previously found for a purely magnetically coupled system of spins I = 1 2 in a large static applied field, and this is so irrespective of the value of the asymmetry parameter η or of the orientation (θ,φ) of the r.f. coil axis in the principal axis system. The whole experimental sequence is performed in a time very much less than that characteristic of spin-lattice relaxation processes, so that the spin-system may be considered effectively isolated from the lattice.

Response of a quadrupolar spin system in zero applied field to a long, off-resonant radio-frequency pulse

The response of a system of nuclear spins I=3/2 experiencing electric quadrupole couplings in zero applied field to a long, off-resonant radio-frequency pulse is investigated using simple time-dependent perturbation theory. It is found that the height of the transient following such a pulse varies with the distance from exact resonance, Δω, in the same manner as previously found for the case of a purely magnetically coupled spin system in high field, in which the rf pulse is of sufficient duration to allow the magnetization to become aligned along the effective field when viewed from the rotating frame. We find, in addition, that if a short resonant ``sampling'' pulse is applied after the transient from the long pulse has died down, the maximum height of the transient following this second pulse varies with Δω in the same manner as the response of the Zeeman system to this pulse sequence. Furthermore, with this two-pulse sequence, an echo-type transient is predicted to appear at a time 2τ, where τ is the time at which the sampling pulse is applied. We assume that the whole sequence is over in a time very much less than that characteristic of spin-lattice relaxation processes. The theory, which is extended to cover the general case of a nonaxially symmetric electric field gradient, is verified semiquantitatively by experiment.

Scheme for Sensitive Nuclear Double-Resonance Detection: Deuterium and 13C

An experiment which involves the participation of three nuclear spin species is carried out to accomplish sensitive double-resonance detection of nuclei. An ordered nuclear quadrupole spin system (A) is used to establish and monitor a metastable ordered state of a second abundant spin system (B). A double-resonance coupling is brought about between the B spin system and a third rare or weakly interacting system (C) to accomplish the detection of the C resonance. The usefulness of this scheme lies in the choice of an A system with a short spin–lattice relaxation time (T1A) and a B system with a long spin–lattice relaxation time (T1B). The choice of a long T1B increases the sensitivity of the experiment in that a long time is available during which effective nuclear dipole–dipole cross relaxation can occur between the B and C systems. With a short T1A, the cycling rate at which information is gathered to detect the C system is enhanced by a factor ∼T1B / T1A over that of the earlier two species double-resonance method. For increased sensitivity T1B can be chosen arbitrarily long, while for the purposes of an increased rate of data acquisition, T1A can be chosen arbitrarily short, thus producing an efficient double-resonance scheme. This scheme is applied to a 12% deuterium enriched sample of paradichlorobenzene. The nuclear quadrupole coupled Cl35 reservoir acts as the A system. The zero field nuclear quadrupole resonance system (at 34.78 mHz at 77°K) supplants the usual high field stabilized magnet and power supply required in an NMR double-resonance experiment. The B proton system has a zero field lifetime of 46 sec, and approximately a 1 h lifetime at 135 G. The C systems investigated are (1) deuterium and (2) the naturally abundant 13C nuclei in paradichlorobenzene. An analysis of double-resonance detection of I = 1 spin systems is given and shows that for a well resolved nuclear quadrupole asymmetry η splitting, a double resonance cannot be detected because of the nonsecular character or quenching of cross-relaxation interaction terms. The analysis is extended to include the unquenching effect of constant magnetic fields and the integer I > 1 quadrupole system is discussed. The observation of the 13C resonance is the first reported observation through the nuclear magnetic resonance techniques of the 1.1% naturally abundant 13C in a solid.

Nuclear quadrupole spin-lattice relaxation in solids

Nuclear quadrupole spin-lattice relaxation in solids has been investigated using pulsed nuclear induction techniques. By selective excitation of the quadrupolar spin system, several new modes of relaxation are observed. Measurements of these modes are used to determine the individual transition probabilities W 1 and W 2 associated with Δ m = ± 1 and ± 2 quadrupole spin-lattice relaxation. W 1, W 2, and the spin-lattice relaxation time T 1 of the Cl 35 pure quadrupole resonance in p-C 6H 4Cl 2, KClO 3, and NaClO 3 have been measured in the temperature range 77–300°K. The B ayer theory of quadrupole spin-lattice relaxation is applied to p-C 6H 4Cl 2 to calculate W 1 and W 2. From the B ayer theory and the separate measurement of W 1 and W 2, information is obtained about the lifetime of excited torsional states and the mode of torsional oscillation which provides the dominant relaxation contribution in p-C 6H 4Cl 2. Measurements of the spin-lattice relaxation in NaClO 3 and KClO 3 are compared with C hang's theory of quadrupole relaxation. The experimental results suggest that the model used by C hang to describe the fluctuating internal electric field gradient in NaClO 3 responsible for the Cl 35 relaxation is inadequate.