| dc.description.abstract | In the present investigation, we have used nuclear quadrupole resonance (NQR) as a local probe to study the structural and dynamical aspects of Group V trihalides. For this purpose, we have set up a pulsed NQR spectrometer integrated with a low?temperature assembly. We have measured the quadrupole resonance frequencies and relaxation times of different nuclei from room temperature down to liquid?helium temperatures. Spin systems with I = 3/2, 5/2, 7/2, and 9/2 have been studied in this investigation.
For I > 3/2 spin systems, we have evaluated the relaxation matrices for various ratios of the transition probabilities W? and W?. Numerical diagonalization of these matrices has yielded expressions that describe the magnetization recovery for I > 3/2 systems. We show that, in general, there will be I – 1/2 components for the nuclear quadrupole spin–lattice relaxation. The pre?exponential factors that determine the weightage of the various components are not equal. Some of them are small enough to be neglected, allowing simpler expressions to be used for analyzing the magnetization?recovery plots.
The halogen sites in all these compounds show chemical inequivalence, giving rise to separate NQR signals. The site assignments that we have made on the basis of intensity considerations agree with earlier studies. Within experimental error, the NQR frequencies of ³?Cl, ¹²¹Sb, ¹²³Sb, and ²??Bi could be fitted to fourth?order polynomials. These fits are not exact at very low temperatures (< 30 K), where the NQR frequencies remain constant. The inaccuracy of the polynomial fit appears as an overshoot of the calculated temperature coefficient (obtained by differentiation) toward the positive side below 30 K.
Structural and Raman spectroscopic investigations indicate the presence of intermolecular bonding in all these compounds. We found that these intermolecular interactions impart a positive temperature coefficient to the NQR frequencies of halogen atoms involved in the bonding. We provide a qualitative explanation for this effect in terms of electron populations in the intermolecular bond. Usual motional effects, which lead to an increase in NQR frequency with decreasing temperature, are also present. For the Cl sites not involved in significant intermolecular bonding, we analyzed the NQR frequencies using Bayer’s theory and obtained torsional?frequency values that compare well with Raman data.
Thus, there is an interplay between motional and bonding effects. When intermolecular interactions are weak, as in SbCl? and SbBr?, motional effects dominate and a negative temperature coefficient is observed, though reduced in magnitude by the positive contribution. In BiCl?, the intermolecular bonding is so strong that Cl sites involved in more extensive bonding show a positive temperature coefficient.
For the ²??Bi NQR in BiCl?, we have measured the NQR frequencies of two transitions, (1/2 ? 3/2) and (3/2 ? 5/2), simultaneously to obtain the temperature dependence of the quadrupole coupling constant (QCC) and the asymmetry parameter (?) of the electric field gradient (EFG). Since ? at the Bi site is high (> 0.6), the QCC and ? values were evaluated using a graphical method. The asymmetry parameter varies essentially linearly with temperature down to about 30 K.
In all three compounds studied, the NQR signals of Sb and Bi nuclei show a gradual increase in linewidth with decreasing temperature. This enabled us to record low?temperature NQR spectra by monitoring the spin?echo amplitude as a function of frequency. All spectra have linewidths in the range 70–80 kHz. The exact origin of this broadening is unclear; however, we speculate that it arises from freezing of the MX? pyramid motions, resulting in orientational disorder and hence a distribution of EFG values at the metal sites.
Relaxation times were measured using conventional magnetic?resonance pulse sequences. ³?Cl relaxation times become greater than 20 s by about 30 K, preventing measurement below this temperature. The large T? values indicate high sample purity. For Sb and Bi nuclei, the magnetization recovery was multiexponential as expected. Using our numerically derived recovery laws, we extracted a representative relaxation time for these nuclei.
³?Cl relaxation data were analyzed using semiclassical models available in the literature. When the torsional frequencies obtained from the Bayer?type analysis were used, the torsional level lifetimes (??) turned out to be imaginary, likely due to limitations of the single?mode approximation used in Bayer’s model. Nevertheless, the torsional frequencies agree with Raman spectra.
The T? values obtained using two different models (Woessner–Gutowsky and Kessel–Korchemkin) differed not only in magnitude but also in temperature dependence. The torsional lifetimes from the Kessel–Korchemkin model (which imposes an explicit temperature dependence) decreased with decreasing temperature, whereas those from the Woessner–Gutowsky model increased with decreasing temperature.
We attempted to fit the ³?Cl T? values to an expression of the form
AT² + B,
and the fit was good. However, the activation energies obtained were too small to be attributed to reorientation of MX? pyramids. Attempts to fit the data to a power law (AT?) showed that n > 2 for ³?Cl as well as for ¹²¹/¹²³Sb and ²??Bi NQR.
Finally, we applied the Zamar and González (Z–G) model to the relaxation data. According to the Z–G model, the relaxation rate in molecular crystals follows
AT² + BT?.
We found that our relaxation data for all compounds fit this expression well, particularly at higher temperatures. It is evident that the T? term becomes dominant at higher temperatures. Zamar and González proposed that this term arises from an interaction process. Therefore, we conclude that in these molecular crystals, the interaction process significantly influences the temperature dependence of nuclear quadrupole spin–lattice relaxation at higher temperatures. | |
