| dc.description.abstract | The detection of quadrupole resonance absorption requires application of a radio frequency magnetic field H? of suitable frequency. The rf field H? should be such that ?H?T?T? ? 1 to avoid saturation, but not be so small that the absorption becomes too small to be detected. In general, nuclear quadrupole resonance (NQR) experiments require relatively large rf power than the nuclear magnetic resonance (NMR) experiments as the spin-lattice relaxation times T? involved are small. The detection apparatus must have sufficient sensitivity to provide a nuclear signal that would exceed oscillator and amplifier noise.
The quadrupole frequencies range from a few megahertz to about a thousand megahertz. In order to search for resonance absorption, the applied rf frequency must be changed continuously over a certain frequency range and yet, the apparatus must maintain reasonable stability and sensitivity. In NMR, the oscillator frequency may be held fixed while the Larmor frequency can be varied by changing the magnetic field. This is not possible in pure quadrupole resonance since the frequencies are determined by the internal electric field gradients which depend on the crystal structure of the compound.
The theory of nuclear quadrupole resonance transitions induced by an rf magnetic field perturbation predicts, in its steady state, the following expression for the net power absorbed per second, for the transition m ? m+1:
Pm?m+1=6NA(2m+1)4?2H12(I+m)(I?m+1)T2/[KT(2I+1)2+12?2H12(I+m)(I?m+1)T1T2]P_{m \to m+1} = \frac{6NA(2m+1)}{4} \gamma^2 H_1^2 (I+m)(I-m+1) T_2 \Big/ \Big[ K T (2I+1)^2 + \frac{1}{2} \gamma^2 H_1^2 (I+m)(I-m+1) T_1 T_2 \Big]Pm?m+1?=46NA(2m+1)??2H12?(I+m)(I?m+1)T2?/[KT(2I+1)2+21??2H12?(I+m)(I?m+1)T1?T2?]
where:
N = Total number of resonant nuclei
A = e²qQ / 4I(2I?1)
? = gyromagnetic ratio
H? = amplitude of the rf field
K = Boltzmann constant
T = temperature
T? = inverse line width
T? = spin-lattice relaxation time
The magnitude of P? ? P??? is measured in terms of the change in the voltage across the tank coil of the oscillator circuit. This change reaches a maximum for an rf magnetic field of amplitude H? determined by the saturation condition:
?2H12T1T2(I+m)(I?m+1)=1(2.2)\gamma^2 H_1^2 T_1 T_2 (I+m)(I-m+1) = 1 \tag{2.2}?2H12?T1?T2?(I+m)(I?m+1)=1(2.2)
The apparatus used for quadrupole resonance detection are usually oscillator-detectors. The early circuits of this type were developed by Pound and Knight and by Roberts. The sample is placed in the volume of an inductance L which is tuned to the transition frequency by means of a capacitor C. By using the LC circuit as the oscillating element with electronic feedback, the voltage level of oscillation becomes a function of nuclear absorption.
The principle common to all continuous wave type oscillator-detectors is that the nuclear absorption reduces the resonant impedance Z? of the LC circuit from the value:
Z0=L/CR(2.3)Z_0 = L / C R \tag{2.3}Z0?=L/CR(2.3)
to the value:
CR(1+{m p QP/?0H1})C R \big(1 + \{\text{m p QP}/\omega_0 H_1\}\big)CR(1+{m p QP/?0?H1?})
where:
R = series resistance of the tank circuit
P = sample filling factor
?? = resonance frequency
Q = Quality factor of the resonant circuit
H? = amplitude of the effective rf field
The reduction in resonant impedance is given by:
(Z0?Zr)=Z0??pQP/?0H12(2.5)(Z_0 - Z_r) = Z_0 \cdot \pi p Q P / \omega_0 H_1^2 \tag{2.5}(Z0??Zr?)=Z0???pQP/?0?H12?(2.5)
If V? is the operating voltage level of the oscillator, and (?V?/?Z) is the slope of the characteristic curve of V? versus Z for the detector, the signal due to nuclear absorption is given by:
?V=(?V0/?Z)(Z0?Zr)=(?V0/?G)(Gr?G0)(2.6)\Delta V = (\partial V_0 / \partial Z)(Z_0 - Z_r) = (\partial V_0 / \partial G)(G_r - G_0) \tag{2.6}?V=(?V0?/?Z)(Z0??Zr?)=(?V0?/?G)(Gr??G0?)(2.6)
where G = 1/Z is conductance.
Optimum absorption of power by the nuclei occurs according to the condition governed by equation (2.2). However, the characteristic slope (?V?/?G) is not always large enough for a given V? to give a sufficient signal because T? and T? are small. Consequently, one will have to operate in the region close to point C in Fig. 2.1. In cases where T?·T? is large, it is difficult to prevent saturation by making V? very small, as this will bring the operating point close to B and make the oscillations unstable. If these limitations become serious, one has to use super-regenerative quenched oscillators (SRO) when searching for new resonances.
In all the methods for measuring line shapes and detecting resonances, a means for modulating the response at some low frequency is necessary. The signal may be presented on an oscilloscope if the modulation amplitude is greater than the line width. If a low modulation depth is used, the signal can be recorded with the help of a lock-in amplifier.
PART II
2.1 The Principle of SRO Detector
In super-regenerative oscillators, the oscillations are periodically quenched either externally or internally (self-quenching). The frequency at which the oscillations are quenched is called the quench frequency, which is of the order of 1/1000th of the oscillator frequency. The quenching action drives the oscillator into and out of oscillations. During the transition back to the oscillatory state, the oscillator is extremely sensitive to external signals.
There are two modes of detection of NQR signals in the super-regenerative oscillators:
(a) Incoherent mode – oscillations are allowed to decay below the noise level before the next rf burst is initiated. Thus, the oscillations are initiated by noise and there is no phase coherence between individual rf bursts.
(b) Coherent mode – the next cycle of oscillation is initiated by the trail of the preceding one before it decays below noise level and hence, phase coherence is maintained. This effect gives rise to an increased integrated signal response. Dean suggests that the second mechanism is more appropriate for quadrupole resonance detection by the SRO method.
The quenching produces sidebands centered around the fundamental carrier frequency spaced at integral multiples of the quench frequency. This property can cause confusion in the assignment of the correct resonance frequency because any of the sidebands of sufficient intensity can excite a quadrupole resonance as the oscillator carrier frequency is scanned. The actual frequency is identified by varying the quench frequency and noting the line that does not shift.
In the application of SRO for NQR/NMR detection, the SRO has to act not only as a receiver but also as the transmitter. If the quench frequency and other circuit constants are so arranged that the decay of the rf due to quench pulse is made to start only after the rf oscillations have been built up to the equilibrium amplitude (limited by nonlinear device characteristics), then the detector output voltage is found to be proportional to the logarithm of the amplitude. Signal voltage. This mode of detection is called the Logarithmic mode of detection. In contrast to this is the Linear mode of detection, where the decay of the rf oscillations starts before the equilibrium amplitude is reached. Under these circumstances, the detector output is directly proportional to the signal voltage. Fig. 2.2 shows the oscillation envelope of SRO and Fig. 2.3 shows the power spectrum of SRO.
The first instrument to be successfully employed for the detection of NQR was the SRO used by Dehmelt and Kruger. Several versions of the SRO for NQR detection are described, among others, by Dean, Dean and Pollack, Graybeal and Croston, Narath, Petersen and Bridenbaugh, Tongh and Smith, O'Konski and Scheffer, and Carter et al. Some of the later versions incorporate automatic coherence and gain control and sideband suppression circuitry. But the circuits employing sideband suppression have generally been shown to result in about 50 percent loss of signal detection sensitivity.
Tong has discussed the phenomenon of super-regenerative oscillator locking, or synchronization to an external generator, in relation to NQR detection. SRO spectrometers incorporating injection and phase-locking techniques have been discussed by Graybeal and Cornwell, Linzer, Read, and Ostabinet et al. in an attempt to improve the line shape response of the SRO detector. A variety of field-effect transistor oscillator circuits, employed with success in NQR spectroscopy, have been reported by Klein, though with no extra detection sensitivity in comparison with hard-wired valve oscillator spectrometers.
Thus, the super-regenerative technique has the advantage of large rf fields sufficient to excite those resonances with large line widths, namely with short T? and T?. The maintenance of conditions for high sensitivity in continuous-wave oscillator-detectors is relatively difficult. The voltages at various points of the electronic circuit must be maintained at proper values such that any small change of the resonance impedance of the LC circuit produces a detectable change in its voltage level of oscillation. The quenched oscillator effectively passes through such a condition periodically, eliminating the need for stable critical adjustment. In addition, when nuclear resonance occurs, the oscillation bursts are initiated by the nuclear signal rather than by noise. This accounts for the observation that the super-regenerative circuit gives a large S/N ratio. Just before the onset of oscillations, the gain of the circuit is of the order of 10?. This gain applies more to signal than it does to noise, since it is the signal that initiates the grid current flow, which restores the feedback necessary to sustain oscillations. | |
