Study on the structural properties and relaxation mechanisms in LiRb(1-x)(NH₄)(x)SO₄ (x=0, 0.5, and 1) mixed crystals by ¹H, ⁷Li, and ⁸⁷Rb nuclear magnetic resonance

LiRb(1-x)(NH₄)(x)SO₄ (x=0, 0.5, and 1) mixed crystals were grown using the slow evaporation method, and their lattice constants were determined by X-ray diffraction. The effects of replacing ammonium ions with rubidium on the phase transitions of and dynamics of LiRb(1-x)(NH₄)(x)SO₄ mixed crystals were studied. We investigated the structural properties and phase transition temperatures of the LiRb(1-x)(NH₄)(x)SO₄ mixed crystals by performing ¹H, ⁷Li, and ⁸⁷Rb NMR relaxation and DSC. When a fraction of rubidium ions in the pure LiRbSO₄ crystal is partially replaced by ammonium ions, we compare the structural properties for LiRbSO₄, LiRb₀.₅(NH₄)₀.₅SO₄, and LiNH₄SO₄ single crystals. The ¹H, ⁷Li, and ⁸⁷Rb NMR relaxation mechanisms of LiRb₀.₅(NH₄)₀.₅SO₄ are different from those of pure LiRbSO₄ and LiNH₄SO₄; the sequence of the structural phase transitions of LiRb₀.₅(NH₄)₀.₅SO₄ is different, which might be related to the dynamics and orientation of the sulfate tetrahedral groups in the crystal structure.

Study of molecular dynamics and cross relaxation in tetramethylammonium hexafluorophosphate (CH(3))(4)NPF(6) by (1)H and (19)F NMR

(CH(3))(4)NPF(6) is studied by NMR measurements to understand the internal motions and cross relaxation mechanism between the heterogeneous nuclei. The spin lattice relaxation times (T(1)) are measured for (1)H and (19)F nuclei, at three (11.4, 16.1 and 21.34 MHz) Larmor frequencies in the temperature range 350-50K and (1)H NMR second moment measurements at 7 MHz in the temperature range 300-100K employing home made pulsed and wide-line NMR spectrometers. (1)H NMR results are attributed to the simultaneous reorientations of both methyl and tetramethylammonium groups and motional parameters are evaluated. (19)F NMR results are attributed to cross relaxation between proton and fluorine and motional parameters for the PF(6) group reorientation are evaluated.

Complex methyl group and hydrogen-bonded proton motions in terms of the Arrhenius and Schrödinger equations

Equations for the temperature dependence of the spectral densities J(is)(m)(momega(I) +/-omega(T)), where m=1, 2, omega(I) and omega(T) are the resonance and tunnel splitting angular frequencies, in the presence of a complex motion, have been derived. The spin pairs of the protons or deuterons of the methyl group perform a complex motion consisting of three component motions. Two of them involve mass transportation over the barrier and through the barrier. They are characterized by k((H)) (Arrhenius) and k((T)) (Schrödinger) rate constants, respectively. The third motion causes fluctuations of the frequencies (nomega(I)+/-omega(T)) and it is related to the lifetime of the methyl spin at the energy level influenced by the rotor-bath interactions. These interactions induce rapid transitions, changing the symmetry of the torsional sublevels either from A to E or from E(a) to E(b). The correlation function for this third motion (k((omega)) rate constant) has been proposed by Müller-Warmuth et al. The spectral densities of the methyl group hindered rotation (k((H)), k((T)) and k((omega)) rate constants) differ from the spectral densities of the proton transfer (k((H)) and k((T)) rate constants) because three compound motions contribute to the complex motion of the methyl group. The recently derived equation [Formula: see text] , where [Formula: see text] and [Formula: see text] are the fraction and energy of particles with energies from zero to E(H), is taken into account in the calculations of the spectral densities. This equation follows from Maxwell's distribution of thermal energy. The spectral densities derived are applied to analyse the experimental temperature dependencies of proton and deuteron spin-lattice relaxation rate in solids containing the methyl group. A wide range of temperatures from zero Kelvin up to the melting point is considered. It has been established that the motion characterized by k((omega)) influences the spin-lattice relaxation up to the temperature T(tun) only. This temperature is directly determined by the equation C(p)T=E(H) (thermal energy=activation energy), where C(p) is the molar heat capacity. Probably the cessation of the third motion is a result of the de Broglie wavelength related to this motion becoming too short. As shown recently, the potential barrier can be an obstacle for the de Broglie wave. The theoretical equations derived in this paper are compared to those known in the literature.