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Manuscript Title: POWDERSPEC 2, a library of new programs for efficient simulation of powder EPR spectra.
Authors: V. Beltran-Lopez, L. Gonzalez-Tovany
Program title: POWDERSPEC 2
Catalogue identifier: ACGX_v2_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 79(1994)533
Programming language: Fortran.
Computer: IBM PC/AT.
Operating system: DOS 3.0 or higher.
RAM: 320K words
Word size: 16
Peripherals: graph plotter.
Keywords: Crystallography, Powder pattern, Analytical and Semi-analytical powder Pattern and EPR spectra, Powder EPR spectra, Axial symmetry, Cubic symmetry.
Classification: 8.

Nature of problem:
The interpretation of electron paramagnetic resonance (EPR) spectra of randomly oriented paramagnetic ions is a difficult problem because the random orientation of the crystallites smears out of the spectral features which depend on the angular position. The main features in these spectra can be predicted from the corresponding absorption functions or powder patterns, and the EPR spectrum can be simulated by the convolution of these powder patterns with first-derivatives of adequate lineshape functions such as Lorentzian, Gaussian or Voigtian [1]. For the axial field, where the field is a function of only the angle theta, the simulated spectrum can also be obtained directly from an integral in this angle [2]. The field dependent transition probability of the spins can also be included in the integral and quite complete analytical expressions including the main effects can be obtained [3]. The program AXIPRO simulates in a PC, in a fast and precise form, the EPR spectrum of ions of any spin in an axial field. The simulation includes the angle-dependent transition probability for the important S=5/2 spin. For S=1/2 ions, also in an axial crystal field, but with axially anisotropic g and A tensors [4], the program AXIANI, simulates the powder pattern and the respective EPR spectrum by convoluting this powder pattern with adequate lineshape functions. For non-axial fields the powder pattern can be obtained from a single- variable integral, the powder pattern integral [1], and the simulated EPR spectrum from a convolution of this powder pattern with an appropriate lineshape function. The program CUBIC simulates the powder pattern and the EPR spectrum of S=5/2 ions in a cubic crystal field by this method. The calculations are based on the following basic conditions: (i) the paramagnetic ions are isotropically oriented. (ii) the values of the resonance magnetic field are given by second- order perturbation theory.

Solution method:
These programs generate the powder patterns of polycrystalline samples by direct computer evaluation of analytical solutions, or by Gaussian numerical quadratures of the single-variable integral appearing in a general method of calculation of these patterns [1]. The corresponding simulated EPR spectra are the convolutions of these powder patterns with appropriate shape functions. These convolutions are calculated numerically with first-derivative Lorentzian or Gaussian functions, except for the axial field with crystal field dependent transition probability, which is performed analytically for a Lorentzian shape function [2,3].

Since a perturbation calculation is used, the Zeeman energy must be greater than both, the hyperfine interaction and the interaction with the crystal field. Also, if the overall spectral lineshape will be dominated by the angular distribution of spins in the crystal field, the range of the interaction energy of the spins with the crystal field myst be greater than the width of the resonance line of any single crystallite. It is assumed that the tensors g and A are isotropic for the pure axial and the cubic fields (AXIPRO and CUBIC). The lineshape function is also assumed isotropic.

Running time:
200 CPU seconds, in an IBM-PC/AT with numeric coprocessor, or equivalent.

[1] V. Beltran-Lopez and L. Gonalez-Tovany, Comput. Phys. Commun. 69(1992)397.
[2] V. Beltran-Lopez and J. Jimenez M., J. Magn. Reson. 48(1982)302.
[3] Y. Siderer and Z. Luz, J. Magn. Reson., 37(1980)449.