Pascal P. Man

Analytical expression for the spin-5/2 line intensities

The density matrix of a spin I = 5/2 excited by a radiofrequency pulse is calculated. The interaction involved during the excitation of the spin system is first order quadrupolar. Consequently, the results are valid for any ratio of the quadrupolar coupling, θQ to the pulse amplitude θRF. The behaviour of the central and the two satellite line intensities versus the pulse length is discussed. The aluminium nuclei (27Al) in a single crystal of corundum (Al2O3) are used to illustrate some results.

Solid-state interaction between NaY zeolite and vanadium pentoxide, molybdenum trioxide, or tungsten trioxide

Abstract When mixtures of NaY zeolite with V 2 O 5 or MoO 3 are calcined in air at atmospheric pressure within well-defined temperature and composition ranges, the oxides migrate into the pores of the zeolite lattice. In contrast to these oxides, WO 3 does not diffuse into the pores of NaY after treatment under the same conditions. The differences in the behavior of each of these oxides with NaY are related to their dissimilar physical properties (melting point and solubility in hot water). Beyond certain temperature and oxide concentrations, the NaY lattice is destroyed and new phases are formed. These interactions and reactions in the solid state have been followed by X-ray diffraction and 29 Si n.m.r. and 129 Xe n.m.r. of adsorbed xenon.

Aluminium-27 Solid-state NMR Study of Aluminium Coordination Complexes of Alizarin

The structures of complexes obtained by the reaction of alizarin (C14H8O4) and Al3+ in basic media depend upon the reaction solvent and the nature of the base. With aqueous or methanolic solutions of sodium hydroxide abinuclear complex [Al2(μ‐OH)2(C14H6O4)4(Na)4(H2O)4] was obtained, which is stable as the tetrahydrate and isobserved even in the gas phase by electrospray mass spectrometry. With potassium hydroxide the monohydrate form is obtained. These two products are distinguishable by 27Al NMR in the solid state by means of their chemical shifts (+23.1 and 0.0 ppm) and their linewidths Δν1/2 (1200 and 4000 Hz). The chemical shifts of these binuclear complexes or similar derivatives are discussed in relation to possible chelation of the four molecules of water with alizarinate entities according to the bulk of the cation. The results are illustrated by two types of structure, named ‘closed structure’ (with strongly chelated H2O molecules and dibenzene sandwich Na+) and ‘open structure’.

Determination of the quadrupolar coupling constant in powdered samples with a two in-phase rf pulse sequence in solid-state NMR

Abstract We propose a new method for the determination of the quadrupolar coupling constant e2qQ/h of a spin I = 3 2 in powdered samples. It is suitable for characterizing a nucleus with a featureless central transition line shape where it is difficult to extract the value of e2qQ/h from the spectrum. The pulse sequence is a two in-phase rf pulse with a short delay between them. The method consists of measuring the central transition line intensity for increasing lengths of the second pulse and comparing it to calculated data. We illustrate the method with the sodium nuclei 23Na in powdered NaNO3.

Measurement of quadrupolar coupling with a two-pulse sequence in solid-state N.M.R.

The intensity of the central transition of a spin-3/2 system following excitation by two in-phase rf pulses is calculated using the fictitious spin-1/2 operator formalism. Measurement of this line intensity as a function of the duration of the second rf pulse enables the quadrupolar coupling to be determined. The method is illustrated with a study of 7Li nuclei in a single crystal of LiTaO3. For polycrystalline samples the powder average is computed numerically in order to obtain the quadrupolar coupling constant and the asymmetry parameter.

Study of a spin system by a spin-echo sequence

The density matrix describing the evolution of a spin system excited by a spin-echo sequence is calculated from the equilibrium state to the acquisition period by taking into account only the first-order quadrupolar interaction. The formation of an echo due to the two satellite transitions is predicted, and the line intensity of the central transition and a satellite transition of the free induction decay following the second pulse are obtained for any ωQ/ωrf ratio. Sodium nuclei in powdered NaNO3 and lithium nuclei in a single crystal of LiTaO3 are used to illustrate three experimental conditions: the interpulse delay is smaller, comparable or larger than the duration of the free induction decay.

Exact expression for the spin 7/2 line intensities: Application to solid state 59Co(III) NMR

The density matrix of a spin I = 7/2, excited by a radiofrequency pulse, is calculated in taking into account the first order quadrupolar interaction during the excitation. Therefore, the results are valid for any ratio of the quadrupolar coupling ωQ to the pulse amplitude ωRF. The behaviour of the central line intensity versus the pulse length is discussed both in time and frequency domains. The quadrupolar coupling constant e 2 qQ/h = 8·24 MHz of the 59Co(III) nucleus in a polycrystalline sample of Na3[Co(NO2)6] is determined using this one-dimensional nutation method, and the lineshape reveals mainly the presence of chemical shift anisotropy with axial symmetry.

Numerical analysis of Solomon echo amplitudes in static solids

For the first time a numerical procedure for computing the Solomon echo amplitudes of half-integer quadrupole spins (I=3/2, 5/2, 7/2, and 9/2) has been derived from a detailed analysis of the evolution of the spin system using the density operator formalism. As the first-order quadrupole interaction is taken into account throughout the experiment, consisting in exciting the spin system with two pulses either in phase or in quadrature phase and separated by a delay τ2, the results are valid for any ratio of the quadrupole coupling, ωQ, to the amplitude of the pulses, ωrf. These results are applicable to light nuclei at high magnetic field, for which the second-order quadrupole interaction and the chemical shift anisotropy are negligible. We predict (4I2−1)(2I−1)/16 echoes and their positions in the detection period τ4, (I−1/2)2 of which are allowed echoes, the others being forbidden echoes. All of these echoes are satellite-transition signals, which are superimposed on the free induction decay (FID) of the...

Study of a spin-3/2 system by a quadrupolar-echo sequence: suppression of spurious signals

The density matrix describing the evolution of a spin-3/2 system excited by a quadrupolar-echo sequence consisting of two rf pulses in quadrature phase, (X)-tau 2-(Y)-tau 4-[acquisition(y)], is calculated from the equilibrium state to the acquisition period. The interactions involved are the first-order quadrupolar interaction throughout the experiment and a local heteronuclear magnetic dipolar term between the two pulses and during the acquisition period. Three echoes, one due to a satellite transition at tau 4 = tau 2 and two due to the central transition at tau 4 = tau 2 and tau 4 = 3 tau 2, are predicted. They have similar expressions than those obtained with two rf pulses of the same phase, (X)-tau 2-(X)-tau 4-[acquisition(y)], except the signs. Moreover, it is shown experimentally that a combination of these two sequences, namely: (X)-tau 2-(X)-tau 4-[acquisition(y)]-recycle delay-(X)-tau 2-(-X)-tau 4-[acquisition(y)]-recycle delay-(X)-tau 2-(Y)-tau 4-[acquisition(-y)]-recycle delay-(X)-tau 2-(-Y)-tau 4-[acquisition(-y)]-recycle delay, cancels the spurious piezo-electric signals when studying a ferro-electric material in the single-crystal form.

Determination of spin-5/2 quadrupolar coupling with two-pulse sequences.

The density matrix of a spin-5/2 system excited by two in-phase pulses separated by a delay tau 2 is calculated from the equilibrium state to the end of the second pulse. The interaction involved throughout the computation is the first-order quadrupolar interaction. Consequently, the results are valid for any ratio of the quadrupolar coupling to the amplitude of the radio-frequency pulse. It is shown that single- and multi-quantum coherences developed during the first pulse are detected at the end of the second pulse through single-quantum coherences. Other two-pulse sequences with various phase cyclings as well as the rotary echo sequence are also discussed and illustrated with the nuclei 27Al in a single crystal of corundum Al2O3.