Proton modulation of the electron spin echo envelope in a Nd3+:aquo glass

Abstract

The electron spin echo envelope has been measured at 4.2 °K for a frozen solution of NdCl₃ in water and alcohol. Measurements were made at a frequency of 9.134 GHz and at Zeeman field settings of 2400, 3200, and 4000 G. At all these field settings the electron spin echo envelope showed a deep modulation associated with frequencies in the vicinity of ω_I and 2ω_I, where ω_I is the free proton precession frequency. The components at ?ω_I were clearly visible in the early portion of the envelopes, but components ? 2ω_I tended to predominate towards the end. These results have been interpreted by means of a model in which it is assumed that the protons lie on one or more concentric spheres about the Nd³⁺ ion. In the simplest form of calculation based on this model the proton distribution was taken to be uniform over each of the spherical shells, and the envelope modulation function was calculated by summing contributions weighted according to the area of elements on the surface and the number of protons in the shell. In an alternative approach, the coordinating protons were assumed to be added in a random and uncorrelated manner on the surface of the sphere (or spheres) and a product formula was used to derive the result. Although the main qualitative features of the modulation envelope could be explained in this way, neither form of calculation was sufficiently exact to interpret the data to within the limits of experimental accuracy. The approximation on which the linear sum calculation is based breaks down in the magnetic field regime concerned here. The product calculation is on the other hand inherently inaccurate because of the assumption regarding the random placement of successive protons. We obtain a best value r₁= 3.0 ±0.1 Å for the radius of the first proton shell in the Nd:aquo complex. A more accurate value could probably be obtained by working with a higher microwave frequency and higher values of H₀. The significance of these results in relation to the design of electron spin echo experiments in organic and biological materials is discussed.