Effect of a weak static magnetic field on nitrogen-14 quadrupole resonance in the case of an axially symmetric electric field gradient tensor

Highlights

• A doublet in the N-14 Quadrupole Resonance spectrum may appear.

• It requires a weak static magnetic field B₀ in addition to the usual rf field B1.

• Furthermore, it requires an electric field gradient tensor of axial symmetry.

• It depends on the amplitudes and relative orientation of B0 and B1.

Abstract

The application of a weak static B₀ magnetic field (less than 1 mT) may produce a well-defined splitting of the ¹⁴N Quadrupole Resonance line when the electric field gradient tensor at the nitrogen nucleus level is of axial symmetry. It is theoretically shown and experimentally confirmed that the actual splitting (when it exists) as well as the line-shape and the signal intensity depends on three factors: (i) the amplitude of B₀, (ii) the amplitude and pulse duration of the radio-frequency field, B₁, used for detecting the NQR signal, and (iii) the relative orientation of B₀ and B₁. For instance, when B₀ is parallel to B₁ and regardless of the B₀ value, the signal intensity is three times larger than when B₀ is perpendicular to B₁. This point is of some importance in practice since NQR measurements are almost always performed in the earth field. Moreover, in the course of this study, it has been recognized that important pieces of information regarding line-shape are contained in data points at the beginning of the free induction decay (fid) which, in practice, are eliminated for avoiding spurious signals due to probe ringing. It has been found that these data points can generally be retrieved by linear prediction (LP) procedures. As a further LP benefit, the signal intensity loss (by about a factor of three) is regained.

Introduction

Normally, pure Nuclear Quadrupole Resonance (NQR) is run in zero static magnetic field. In order to improve sensitivity, it may however happen that static magnetic fields (denoted thereafter by B₀) are used for polarizing high gyromagnetic ratio nuclei (e.g. protons), the quadrupolar resonance of the nucleus of interest, e.g. nitrogen-14 (the subject of the present work), being observed by double resonance techniques [1]. However, in that case, even if one is dealing with field cycling procedures, both magnetic fields are relatively high. By contrast, NQR experiments in the presence of weak static magnetic fields were envisaged very early [2] but seldom considered since then. In fact, a long time ago, in double resonance experiments carried out for increasing sensitivity, satellites of the main resonance were observed when a small magnetic field was applied during nitrogen-14 quadrupole resonance observation [3]. These satellites were however attributed to the presence of protons directly bound to nitrogen. Later, nitrogen-14 quadrupole resonance of hexamethylenetetramine (HMT, which, because its electric field gradient (efg) tensor is of axial symmetry, exhibits a single resonance) was proposed to serve as a gauss-meter for weak magnetic fields [4]. Quite recently, it was shown that a static magnetic field produces line-shapes specific to each of the two high frequency lines of sodium nitrite [5] (sodium nitrite possesses an electric field gradient tensor devoid of any symmetry). The interpretation of all these experiments rests on the addition of a Zeeman term to the NQR Hamiltonian. This term may lead to the observation of a Zeeman doublet in the degenerate situation of an axial symmetry electric field gradient tensor. In that case, first order perturbation theory applies. By contrast, in the general case (electric field gradient tensor without any symmetry), one has to rely on second order perturbation theory with, as a result, distorted and complicated line-shapes and, in addition, the requirement of larger magnetic fields.

However, in none of these previous works, the radio-frequency (rf) field was not explicitly taken into account although it appears as being of prime importance in the case of pulsed NQR [6]. We shall present here a complete theory for the case of a powder sample and of an axially symmetric efg tensor which accounts for experimental observations carried out as a function of the magnetic field amplitudes, $B_0$ and $B_1$respectively, and of the rf pulse duration. It will be shown, among other things, that, according to experimental conditions and contrary to simplistic expectations, symmetrical doublets, dubbed in the following Zeeman doublets, may or may not be observed yet with line-shapes and splittings (when a doublet is actually observed) depending strongly on both $B_0$ and $B_1$ amplitudes and on the pulse duration. It is the purpose of this study to fully understand this peculiar behaviour. It will be shown, in particular, that the Zeeman splitting does not generally provide directly the value of the $B_0$ field. It will also be shown that the relative orientation of the two magnetic fields is decisive as far as signal intensity is concerned. Beyond its academic interest, this latter finding should permit to avoid sensitivity losses due to the fact that most experiments are carried out in the earth magnetic field.