Precession Signal Research Articles

An improved method for measuring the order parameter in nematic liquid crystals

We present here an improved method for measuring the order parameter S in nematic liquid cyrstals. The mehtod is based on measuring the centers of gravity (CG) of two groups of lines, generally unresolved or partially resolved, of the magnetic resonance spectrum of ring protons. The CG are defined from the spectral center and the separation between them is used to obtain S. The method is applied to measure S in para−azoxyanisole at different temperatures and the results are compared with earlier ones. In obtaining the spectrum, use has been made of the Fourier transform of the proton free−precession signal. The advantages of using this procedure over the commonly used continuous−wave technique are also discussed.

A Pulsed NMR System for Nuclear Thermometry Below 2 K

A pulsed NMR system for platinum nuclear spin thermometry and for measurements of the nuclear spin-lattice relaxation time τ1 has been developed. The nuclear free precession signal is detected with a fast linear detector and an RC integrator. The τ1 measurements were performed by the transient recovery method with the aid of automated circuitry multiplexing of the linear detector output into four separate integrators. The thermometer was tested between 10 mK and 2 K using a powdered platinum sample. Within the experimental accuracy of about 2% the amplitude of the nuclear free precession signal was found to be proportional to 1/T. The thermometer could be calibrated with the aid of the Korringa relation τ1T=κ, with κ=29.6 msec K. Thermal equilibrium problems of the τ1 measurements are discussed in detail.

Damped magnetization oscillations in Ni-Fe thin films

Damped free oscillations of the magnetization have been clearly observed at the completion of 180° flux reversal along both the easy and the hard axis in Ni-Fe thin films. The frequency of these oscillations, as well as their damping, was studied as a function of the applied pulse field and compared to the results obtained by ferromagnetic resonance. Excellent agreement was found for oscillations excited by reversals along the hard axis when the frequency was measured after the amplitude had damped to small amplitudes. Along the easy axis, the free precession frequency was higher than the resonance frequency. An inconclusive attempt was made to associate the strength of the free precession signal with dispersion.

Construction and use of a pulsed copper nuclear magnetic resonance thermometer

A pulsed nuclear magnetic resonance thermometer, constructed for temperature measurements below 0.5 K, is described. The nuclear free precession signal of copper nuclei is recorded with a gated low noise amplifier and with a phase sensitive detector gated to integrate the signal over an adjustable number of periods. The physical significance of the signal is discussed. A comparison of the resonance thermometer against a slurry type cerium magnesium nitrate (CMN) thermometer for the temperature region 10 mK to 100 mK is presented. The deviation Δ = T NMR − T CMN, representing the departure of the CMN thermometer from a Curie law behaviour, was measured as (0.5 ± 0.2) mK. In experiments with a nuclear refrigeration cryostat the resonance thermometer was calibrated against a nuclear orientation thermometer which provided an independent absolute temperature standard. At the low temperature end, from 1 mK to 10 mK, the linearity of the thermometer in T −1 was confirmed by measurements of the nuclear spin-lattice relaxation time.

Sensitivity in Fourier transform NMR spectroscopy of slowly relaxing systems

Several techniques of pulsed NMR are analyzed with respect to their effectiveness in eliciting NMR spectra from noise for cases (e.g., 13C spectroscopy) for which T 1 ⪢ T 2 ∗ . These include the free induction decay, multiple spin echoes, and a modified “DEFT” procedure. It is found that among them the most effective is likely to be a spin-echo method in which a 90° pulse is applied at the maximum of an even-numbered echo. This procedure offers an improvement in measurement time as compared with the repeated-free-induction-decay technique of the order of 0.3 T 1 τ , where τ is the time during which the nuclear precession signal is recorded. Given currently available apparatus, this improvement is likely to be of the order of 20-fold in 13C spectroscopy.

A Proton Precession Magnetometer

A simple portable proton precession magnetometer designed and constructed for Kodaikanal Observatory is described. Except for the signal amplifier, the instrument is transistorized. The accuracy of measurement of a absolute value of the earth's total field with the magnetometer is ±1 gamma. The precession signal voltage from the sampling coil is amplified and squared by a Schmitt trigger circuit, the output of which drives 10 stages of binary dividers. T4e first pulse in the output of the chain of dividers opens a gate allowing pulses from a 100 Kc crystal oscillator to pass to a pulse counter. The pulse immediately following -the opening pulse closes the gate. By suitable feed back of this closing pulse any following pulse is prevented from opening the gate again. For the next observation, a manual resetting is necessary. The number of 100 Kc Is pulses counted are used to compute the scalar field.

Input Circuits for Pulsed NMR

A detailed comparative analysis of several possible input circuits for observing NMR free precession signals is given. Special attention is paid to the case of signals having short decay time constants. Here the presence of a large initial ringing transient makes it necessary to consider possible modifications in the design of the receiver system. The analysis indicates that an untuned transformer coupled input circuit is potentially superior to the traditional parallel resonant circuit in this case.

A transistorized rocket-borne proton magnetometer and associated data processing equipment

The design and construction of a complete system for the accurate determination of the earth's magnetic field in a rocket vehicle are described. The flight equipment utilizes the principle of proton-free precession to produce a frequency analogue of the intensity of the geomagnetic field; this frequency is independent of the attitude of the rocket. Some special features of the instrument which are necessary to make it perform satisfactorily in the severe environmental conditions of a rocket flight are discussed in detail. During play-back of the telemetered and recorded precession signals the ground equipment described improves the quality of the data and converts them to a form more suitable for analysis and interpretation. The results of the first instrument-proving flight are presented and briefly discussed

Nuclear Transfer Effects in Nuclear Magnetic Resonance Pulse Experiments

The Bloch equations for the nuclear magnetic resonance of a single nuclear species which is transferred between state environments having different relaxation times (T1 or T2) and different resonance frequencies have been solved for rf pulse experiments. Expressions have been obtained for the free precession signals in two-pulse experiments. A theoretical study of the signal envelopes has been made for several specific instances. In particular, the effect of the frequency difference between the two states on transverse (T2) relaxation has been investigated; the predicted effect is large in some cases. The longitudinal (T1) relaxation is independent of the frequency separation. A reduction of phase dispersion by the second pulse which is similar to that in molecular diffusion is also predicted.

Transient Excitation of Nuclei in Ferromagnetic Metals

Free precession signals and spin echoes have been observed from Fe57, Co59, and Ni61 nuclei in finely divided multidomain iron,cobalt, and nickel, respectively. Spin-lattice relaxation has been studied in all three metals from temperatures in the liquid helium range to room temperature or above. Although the relaxation is not strictly exponential, the rate of recovery of the magnetization appears to be proportional to the absolute temperature. Spin-spin relaxation has been studied in natural cobalt and in both natural and enriched samples of iron and nickel. The spin-spin coupling is very much stronger in cobalt than in iron or nickel, as expected,because of the very much larger nuclear magnetic moment of Co59. Spin diffusion through the frequency spectrum of cobalt has been investigated at 4.2 and 77°K by the stimulated echo technique. The results are consistent with a theory of one-dimensional diffusion with exchange rate and exchange distance of the order of 1/T2. The spin-echo technique has also been used in all three metals to study the effect of domain wall motion on the nuclear resonance. A dc pulse, which displaces the domain walls by a controllable amount, is placed between the first rf pulse and the echo. This study confirms that the induction signals arise from nuclei in domain walls and further suggests a connection between line broadening and domain wall processes. A weak free-precession signal, arising from domain rotation, has been observed from cobalt in high magnetic fields. The sign of the precession has been determined, confirming that the hyperfine field is directed opposite to the magnetization.

A new absolute instrument: the proton vector magnetometer

At the Fredericksburg Magnetic Observatory, of the Coast and Geodetic Survey, the proton-precession magnetometer has been successfully adapted, through a method conceived by the writer, for measuring the horizontal and vertical components of the earth's magnetic field. Results thus far obtained are preliminary, for there has not been sufficient time to make a series of observations for complete comparison with the existing observatory standards. The proton vector magnetometer employs the well-known proton free-precession principle for measurement of the field intensity.1,2,3 As operated at Fredericksburg, the sensing head is a bottle of water, 7 cm in diameter and 10 cm long, on which is wound a multilayer coil, serving both for polarizing the hydrogen nuclei and for picking up the precession signal. The axis is approximately horizontal and in the magnetic prime vertical. In the Z measurement, a pair of Helmholtz coils (spacing 41.3 cm) is used to nullify approximately the horizontal component of the field. The remaining (nearly vertical) component is then measured with the proton-precession magnetometer. Similarly, a second Helmholtz pair (spacing 48.6 cm) is used to nullify the vertical component, leaving only the horizontal to be measured.

Audio-frequency Nuclear-resonance Echoes

THE principal expense and source of difficulty in equipment for nuclear magnetic resonance is the magnet to provide the large magnetic field. It has been shown that a nuclear-resonance signal can be obtained using only the Earth's field1,2. This is the so-called free-precession experiment, in which the nuclear system is first polarized at right angles to the Earth's field by means of a simple current-carrying coil. After removal of this field, the nuclear magnetization precesses about the Earth's field (approximately 0.48 gauss) and induces an alternating voltage in the same coil at a frequency of about 2 kc./s., which may be observed after suitable amplification. The polarizing field serves the double purpose of producing a nuclear magnetization appropriate to a large field and hence a stronger signal to be observed in the smaller field, and also produces this polarization at right angles to the small field. The signal is attenuated by loss of phase-coherence of the precessing nuclei, due both to interactions between them with a time constant T 2, and to inhomogeneity in the Earth's field (T 2 *). The method can be used for measuring the decay time, T 2, which is a property of the material, by observing the decay of the precession signal, provided the inhomogeneity of the Earth's field is sufficiently small for T 2 * ≫ T 2. In many cases, for example, in liquids such as water containing mobile protons, T 2 may be several seconds and the corresponding field mhomogeneity must be less than 10 microgauss/cm. in order to measure T 2. This implies that the experiment cannot be performed in the laboratory and usually requires the sample coil to be placed out of doors away from all buildings (we have found a brick wall to be unacceptably magnetic in this sense).

Free Magnetic Induction in Nuclear Quadrupole Resonance

The free precession of an ensemble of nuclear quadrupole moments in an axial electric field gradient is studied by the pulsed nuclear induction method. A quantum-mechanical analysis describes the free precession and spin echo signals which result from the application of single and double pulses of radio-frequency field at the condition of zero-field quadrupole resonance. Beat modulation effects exhibited by free precession signals in a small constant external magnetic field are predicted by analysis. An alternative semiclassical description of quadrupole precession is given, which is analogous to the macroscopic nuclear induction equations of Bloch. Theory is verified by observation of free precession signals of chlorine in NaCl${\mathrm{O}}_{3}$.