H.A Buckmaster

Decomposition of Multicomponent Exponential Decays by Spectral Analytic Techniques

It is shown that multicomponent exponential decays can be analysed using a technique which produces a spectrum whose peaks correspond in amplitude and position to the various exponential components present in the data. This technique is analogous to the Fourier Transform which provides a spectrum of the frequency components (complex exponentials) of a signal. Three techniques—the Orthonormal Exponential Transform, the Inverse Laplace Transform and the Gardner Transform are examined and their relative effectiveness in producing the desired spectra from theoretically generated and experimental data is discussed. It is shown that the updated Gardner Transform can be Ilsed to analyse experimental multicomponent exponential decays.

Computer analysis of EPR data

Abstract An iterative, convergent, computing procedure has been developed for evaluating the “best-fit” g values and crystalline electric field parameters in phenomenological and generalized spin-Hamiltonians from the experimental data describing an observed electron paramagnetic resonance (EPR) spectrum. It provides a measure of the quality of fit at each stage of the calculation. This procedure is more useful than perturbation methods for interpreting experimental EPR data using phenomenological and generalized spin-Hamiltonians because it does not presuppose a knowledge of the relative magnitudes of the parameters and the accuracy of the input data. The calculation can be carried out for any orientation of the external magnetic field with respect to the crystal symmetry axis. The procedure described is completely general, unlike earlier procedures for performing this type of calculation, and is applicable to any generalized spin-Hamiltonian. It enables previously impossible calculations to be effected easily and accurately.

Generalized spin-hamiltonian for Eu2+ in the tetragonal crystalline electric field of CaWO4

Abstract The generalized spin-Hamiltonian for Eu 2+ [4ƒ 7 , 8 S 7 2 , I = 5 2 ] in the tetragonal crystalline electric field of the CaWO4 lattice is derived from the tensor decomposition algebra. This spin-Hamiltonian is derived to provide a specific example upon which to base a discussion of the physical interpretation of the various terms of this and other generalized spin-Hamiltonians and a comparison with those terms in the conventional spin-Hamiltonian of Abragam and Pryce (1951) . A systematic approach to the analysis of the EPR and the ENDOR spectra using the higher order terms of the generalized spin-Hamiltonian is proposed.

Anomalous splitting of the ground state of gadolinium ion in lanthanum ethyl sulfate

The 8S72 ground state splittings of [xGd, (1 − x)La]·(C2H5SO4)3·9H2O where x = 0.005, 0.01, 0.02 have been determined by linear extrapolation from measurements in 1.5–6.0 mT magnetic fields to an accuracy of ≈ ± 0.3 MHz using weak magnetic field variable frequency EPR at 290.5 and 77 K. An anomalous splitting of the 8S72 ground state ∥±12> doublet in zero magnetic field is inferred, which is found to be concentration- and temperature-dependent. This splitting is determined to be (16.0 ± 0.5) MHz at 290.5 K and (10.3 ± 1.0) MHz at 77 K for 0.5 % Gd concentration, whereas the ∥±32>, ∥±52> and ∥±72> doublets remain degenerate in zero magnetic field within present experimental accuracy. The unique features of a weak magnetic field variable frequency EPR spectrometer are described.

Determination of the generalized spin-hamiltonian parameters of Gd3+ in lanthanum ethylsulphate at 290°K☆

The generalized spin Hamiltonian for Gd3+ (4f7; 8S72) in lanthanum ethylsulphate with C3h site symmetry has been derived using tensor decomposition algebra. The parameters in this generalized spin Hamiltonian were determined from the 290°K EPR spectra measured at ∼35 GHz for the parallel, perpendicular, and intermediate directions to the crystal symmetry axis by solving the resulting secular matrices using a digital computer program of exact matrix diagonalization and least-squares fit. The linear-magnetic field dependent parameters associated with a third- or higher-rank tensor operator are found to be six orders of magnitude smaller than the parameter associated with the first-rank spin tensor operator (the g factor). However, the introduction of these parameters improves the sum of square deviations of the fit by an order of magnitude compared with that obtained using the conventional spin Hamiltonian.

The analysis of noisy exponential decays

Abstract There are many experimental situations in which the information has the form of a noisy exponential superimposed upon an unknown baseline. This paper details a method to calculate this baseline, or alternatively, to test the exponential nature of the information. It is not necessary to assume or calculate a value for the exponential time constant nor to use a statistical criterion to determine the baseline using this method. Comparison with the method of Moore and Yalcin shows that it gives a more accurate data analysis when used with their technique to determine the exponential time constant. A new criterion for determining the optimum measurement time for the time constant is given.

Determination of EPR spin-Hamiltonian parameters from experimental data

A general computer program for calculating the parameters in generalized and phenomenological spin-Hamiltonians from experimental EPR data is described. The program is completely general and can be employed to solve any secular matrix equation. The algorithm makes use of symmetry properties to achieve rapid and efficient convergence. The program will analyze EPR data sets consisting of any number of transition frequency-applied magnetic field pairs obtained at any combination of frequencies, applied magnetic fields, magnetic field-crystal symmetry axis orientations, and ΔM = ±1, ±2,… transitions.

Anomalous zero-field splittings and g values of Gd3+ in lanthanide ethyl sulfates: Theoretical considerations

The odd-order terms T3±3(S) and T5±3(S) are introduced into the C3h symmetry spin Hamiltonian for the Gd3+ [4f7;8S72] ion in lanthanum ethyl sulfate without violating time-reversal invariance by interpreting the ground-state eigenfunction as | Mz>′ = α|4f7, 5p6; Mz> + β|4f8, 5p5 ; Mz>. The weak-magnetic-field behavior of the resulting eigenvalues is examined to determine whether their behavior is consistent with the experimental results reported recently by Shing and Buckmaster (J. Magn. Resonance 21, 295 (1976)). It is found, in agreement with these results, that the apparent g values of the transitions differ in weak and strong magnetic fields, the g values of the |+m>′ ↔ |+m+1 >′ and |−m>′ ↔ |−m−1>′ transitions differ, and the extrapolated zero-field splittings of the various transitions differ from the true splittings. However, the sign of the zero-field splitting of the |+32>′ ↔ |+12>′ and |−32>′ ↔ |12>′ transitions is incorrect when the applied weak magnetic field is parallel to the crystal symmetry axis and a zero-field splitting of the same magnitude but opposite sign is predicted for the |+52>′ ↔ |+32>′ and |+−52>′ ↔ |−32>′ transitions which is not observed experimentally. Consequently it is concluded that the inclusion of these terms is unlikely to explain the anomalous zero-field splitting inferred from weak-magnetic-field variable-frequency EPR measurements.

Magnetic resonance lineshape distortion in weak magnetic fields in the presence of a zero-field splitting

Abstract It is shown that lineshape distortion and resonance position shifts occur in magnetic resonance experiments performed in weak magnetic fields in the presence of zero-field splittings. These distortions occur only if the resonance signal is observed by modulating the applied magnetic field and not when the frequency is modulated. It is shown that these resonance position shifts and those produced by relaxation mechanisms generate anomalous zero-field splittings more than an order of magnitude smaller than the inferred anomalous zero-field splitting of the |± 1 2 . energy levels for Gd 3+ (4f 7 ; 8 S) ions in various lanthanide ethyl sulfates and double-nitrate host lattices.

Optimum filtering for sensitivity enhancement in magnetic resonance

Abstract Various criteria to optimize sensitivity enhancement filters are discussed. The importance of defining the SIN ratio according to the information required is emphasized since different definitions lead to different filters. Continuous waveform criteria are discussed in detail because filters designed according to these criteria increase the sensitivity while producing minimum distortion of the signal shape. The literature describing the realization of optimum filters using digital computers is reviewed with particular emphasis on magnetic resonance applications.