visual epr · a, b, c* coordinate system for monoclinic crystals: c* is perpendicular to ab plane...
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Visual EPRInteractive programs for paramagnetic resonance
The package consists of several complementary programs devoted to help researchers to
treat experimental spectra of Electron Paramagnetic Resonance, EPR, to simulate observed
spectra and their angular dependences, to obtain spectroscopic characteristics of
paramagnetic spices, and to prepare representative figures for publication.
Valentin Grachev
Visual EPR
Contents Page 1
Content
Preface 2
Definitions and notations 4
Files and their extensions 6
Spin-Hamiltonian 7
Destination of programs 8 Viewer for spectra for Windows (View_spw.exe) 8
Simulation resonance fields and EPR spectra (Fields.exe) 10
Fields-Angles-Intensities-Widths dependencies (FAIW.exe) 12
Obtaining spin-Hamiltonian parameters by fitting angular dependences
(Params.exe) 12
Interrelations of programs of the Visual EPR package 13
References 14
Make better, who can
Preface The “Visual EPR” package consists of several complementary programs devoted to help
researchers and students to treat experimental spectra of Electron Paramagnetic Resonance, EPR
or Electron Spin Resonance, ESR, to simulate observed spectra and their angular dependences, to
obtain spectroscopic characteristics, and to prepare representative figures for publication.
The programs were developed during many years in closed collaboration with experimenters in
the labs where main manpower is undergraduate and graduate students. Therefore, they have
simple and convenient interface, are flexible enough to solve most of everyday tasks, and do not
require additional programming. For instance, a change of point group symmetry, values of
electron and nuclear spins, number of equivalent centers or any parameters of spin-Hamiltonian
takes a few clicks only.
A balanced combination of exact numerical diagonalization of spin-Hamiltonian matrices and
perturbation theory allowed creating algorithms, which are fast enough to calculate spectra of the
Gd3+
or Mn2+
in a few minutes using conventional desktops and laptops. The programs have a lot
of unique useful findings inside, which help you to manage with many difficulties of spectra
treatment.
Since the first distribution of DOS versions in 1992, the programs have been successfully used in
dozen spectroscopic groups from different countries. Beginning 2005 programs for Windows
operational system (from Windows XP to Windows 7) are available.
At present, the “Visual EPR” package includes following programs designed to facilitate various
aspects of EPR spectra treatment:
Fields.exe – to calculate energy levels and resonance magnetic fields, simulate spectra,
and compare experimental and calculated angular dependencies,
Params.exe – to determine spin-Hamiltonian parameters by fitting experimental data,
View_spc.exe – to view and compare measured spectra, treat them (filtering, peak-
picking…) and collect angular dependence of resonance line positions, intensities and
widths in a file,
FAIW.exe – to represent on one plot four-dimensional table of angular dependences of
resonance magnetic field, line intensities and widths (Fields-Angles-Intensities-Widths
dependencies), to compare observed and calculated dependencies, and to prepare the
picture for publication,
Cos_Eul.exe – to find principal values and directions of principal axes of general
Cartesian and irreducible tensors of second rank.
Visual EPR
Preface Page 3
These everyday programs can accelerate experimental data treatment, enhance trustworthiness of
obtained results, improve accuracy of determined characteristics, and increase efficiency of
conducted research in laboratories, which need in characterization of magnetic properties. Due to
visual representation of calculation results, they can also be used for educational purposes.
Acknowledgement. Findings and solutions of several generations of researchers have been used
for the program development. I have a very great respect to authors of numerous publications,
which made direct or indirect influence on the program features (a short list at the end of the
tutorial cites only some of them [1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
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27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40,
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48,
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62]).
Valentin Grachev (Valentyn Grachov)
Definitions and notations
Coordinate systems a, b, c Crystallographic coordinate system
a, b, c* Coordinate system for monoclinic crystals: c* is perpendicular to ab
plane
x, y, z Local coordinate system related to one paramagnetic center. High
symmetry crystals may have several electrically identical, but
magnetically non-equivalent centers with different coordinate systems.
For instance, x, y, z and -x, y, z if a crystal has mirror plane bc.
1, 2, 3 Coordinate system related to principal axes of g-tensor (“magnetic”
axes system)
X, Y, Z Laboratory coordinate system related to external magnetic field B
Vectors and Tensors Apq; p, q = x, y, z Cartesian components of second rank tensor of hyperfine interaction
Akq; k=0, 2; q=-k,…, k Irreducible components of second rank tensor of hyperfine interaction
B, Bp; p = x, y, z Cartesian vector of external magnetic field; mainly in SI units, mili
Tesla (or mT), sometimes in Gauss (or G) for a compatibility with
measured spectrum files
B1, B1p; p = x, y, z Cartesian vector of microwave magnetic field
bkq, ckq; Components of irreducible tensors described zero field splittings (ZFS)
k=2, 4, 6; q=-k,…, k
ekq, fkq; Components of irreducible tensors described Zeeman splittings of high
k=2, 4, 6; q=-k,…, k order (BS3 and BS
5)
gpq g-tensor. Sometimes, capital letter G is used in screen labels to
facilitate readability of subscripts: Geff is geff
ggpq Symmetrical g·g or g2 tensor
gn Nuclear g-factor
Visual EPR
Definitions and notations Page 5
I, Ip; p = x, y, z Vector of nuclear spin
J, Jpq; p, q = x, y, z Tensor of exchange interaction
Okq; q=0,…, k Irreducible tensor operators
Ωkq; q=1,…, k Irreducible tensor operators
Qpq; p, q = x, y, z Cartesian components of second rank tensor of quadrupole interaction
Qkq; k=0,2; q=-k,…, k Irreducible components of second rank tensor of quadrupole
interaction
S, Sp; p = x, y, z Vector of electron spin
Tkq; q=-k,…, k Irreducible tensor operators
Greek symbols
, , Alpha, Beta, Gamma - Euler angles for the description of magnetically
non-equivalent centers (English definition)
, , Xi, Eta, Zeta - Euler angles for the description of crystal misalignment
(German definition)
ν Microwave frequency (MHz)
µB Bohr magneton
µn Nuclear magneton
, Theta, Phi – polar and azimuthal angles characterized direction of
external magnetic fields.
Other terms ns1, ns2 numbers of states of the spin-Hamiltonian
Ms projection of electron spin on quantization axis ( sip quantum number)
Visual EPR
Definitions and notations Page 6
Files and their extensions Most files have the ASCII format. Their full description is placed in the Appendix.
.gem Output file for View_spw.exe program with experimental angular dependence
(road map). It contains angles defined directions of external magnetic field with
respect to crystal axes, resonance magnetic fields, intensities and line widths for
every EPR line.
.gep Input file for Fields.exe and Params.exe program. It contains all required
information about paramagnetic center symmetry, spin-Hamiltonian
characteristics, instrumentation parameters etc. The file can be created using the
spreadsheet in Fields.exe.
.gfm Output file of Fields.exe program with full angular dependencies of resonance
magnetic fields in three perpendicular planes - 180o degrees dependencies for zx,
xy and yz planes. FAIW.exe program can be used in order to view and compare
its content by special graphical representation of resonance magnetic fields,
intensities, line widths of EPR lines and angles characterized directions of
external magnetic field.
.grm Output file of Fields.exe program with angular dependencies of resonance
magnetic fields in three perpendicular planes - 90o degrees dependencies for zx,
xy and yz planes (road map). Input file for FAIW.exe.
.grt Output file of Fields.exe program with angular dependencies of resonance
magnetic fields in one selected plane defined by input angles. Similar file with
experimental data can be created by View_spw.exe. Input file for FAIW.exe.
.jdx Spectrum file in the format recommended by the Joint Committee on Atomic and
Molecular Physical Data Exchange (JCAMP-DX) for electron magnetic
resonance. Can be viewed and treated with the help of View_spw.exe.
.fls Spectrum file often used in computerized EPR spectrometers. Can be viewed and
treated with the help of View_spw.exe.
.dsc, .dta Bruker description and spectrum data files (BEST format). Input file for
View_spw.exe.
.par, .spc Bruker parameters and spectrum data files (binary format). Input file for
View_spw.exe.
Visual EPR
Quick start Page 7
Spin Hamiltonian
The following general spin-Hamiltonian is used in the Visual EPR programs:
( ) ( ) ( ) ( )
, 2,4,6 0,..., 1,...,
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
,
( ) ( )
0,..., 1,...,
( ) ( )
( , ) ( , )
i i q q i q q i
B p p p p p
i i p q p q p
i ik k i ij j j j j j j
n n
i k i j j j
q q i q q i
B p p p p
q p q p
H f b O c
e O f
B g S S S
S J S S A I I Q I B g I
B S B S, 2,4
.i p
Here
i, k = 1,…, 9 - electron spin numbers, j = 1,…, 99 - nucleus number;
µB – Bohr magneton, µn – nuclear magneton,
f2=1/3, f4=1/60, f6=1/1260;
B – vector of external magnetic field,
S, I – vectors of electron and nuclear spins,
g, gn – electron and nuclear g-tensors,
J, A, Q – tensors of exchange, hyperfine and quadrupole interactions;
Opq, Ωp
q – irreducible tensor operators;
bpq, cp
q – parameters of zero field splitting,
epq, fp
q – parameters of high-order Zeeman splitting (BS
3).
Visual EPR
Menu items Page 8
Destination of Programs
The aim of the Visual EPR programs is to help you to pass a whole way from measurements of
spectra to publication of physical results without losses and in shortest time. The programs cover
most aspects of spectra treatment and presentation.
Viewer for spectra for Windows (View_spw.exe)
View_spw.exe is the program developed for viewing and preliminary treatment of EPR,
ENDOR and other spectra. The program allows:
1. To browse all spectra in directory (or, selectively, EPR or ENDOR only) - it helps you in
a few seconds to find the spectrum needed;
2. To convert the spectrum from one format to another - the program recognizes several
different formats: two binary formats - byte (BRUKER) and single (WIN-EPR), two ASCII
formats - one column (Y) format with signal intensities only and two column (X and Y)
format with sweeping parameter values and intensities (the last are usually used for
graphical programs, like “ORIGIN”, “GRAPHER”,...), *.sta, *.fls and *.jdx -formats;
3. To view a spectrum with “ZOOM” along X or Y or both directions;
4. To estimate line positions (g-factor, resonance magnetic field or frequency) and distance
(splitting) between any points in the spectrum;
5. To carry out filtering of the spectrum using one of 9 filters with variable width:
convolution with Gram polynoms, Gaussian and Lorentzian, as well as fast Fourier
transformation and moving average;
6. To carry out baseline correction using smoothed line, Fourier cut of high harmonics or
manual polynom.
7. To carry out peak-peaking of the spectrum - efficient auto-peaking procedure with double
filtering recognizes both absorption and derivative shapes of resonance lines;
8. To carry out resolution enhancement for spectra in derivative form using subtraction of
unknown background
9. To carry out pipeline processing of many spectra in one folder or in a 3D spectral file.
Visual EPR
Menu Page 9
Viewer for spectra for Windows (View_spw.exe)
10. To decompose complicated spectrum with overlapped lines to separate Gaussian and
Lorentzian derivatives;
11. To estimate positions, intensities and widths of constituent lines, their effective
g-factor value or in the case of ENDOR spectrum - Larmor frequency;
12. To compare several spectra on one screen, for instance experimental and calculated
spectra;
To carry out algebraic operations with discrete spectra of different resolution:
R = A + k1*B+k2*C…;
13. To view thumbnails of all spectra in a folder and to print them on a page together with
the spectrum parameters;
14. To prepare a high quality picture for publication;
15. To edit the files with parameters of your spectra adding polar and azimuthal angles of
magnetic field direction, temperature, microwave frequency and so on;
16. To create a file with four-dimensional tables of angular dependences of resonance
magnetic field, line intensities and widths (Fields-Angles-Intensities-Widths dependences),
which can be used by Fields.exe for comparison with calculated angular dependences, and
by Params.exe for fitting angular dependencies of the spectra, i.e. to collect the positions
and intensities of resonance lines (from all peak-files) and the values of polar and azimuthal
angles (from corresponding parameter files) and automatically sort them. You can view and
treat these angular dependencies with the help of FAIW.exe program;
17. To create a file with a dependence of spectra on other parameters, which were varied at
experiments, like temperature, microwave power etc. The file can also be viewed by
FAIW.exe program.
No one known program does grant you most of these possibilities
Visual EPR
Menu items Page 10
Simulation resonance fields and EPR spectra (Fields.exe)
FIELDS_w calculates angular dependencies of resonance magnetic fields and intensities of
EPR lines for the rotation of magnetic field in any plane. The program imitates a sweep of
the static magnetic field from Bmin to Bmax. Near resonance it uses a small field steps with
cubic interpolation of energy level dependencies on magnetic field; far from resonance it
increases this step.
The program has a spreadsheet for the input of all characteristics of a paramagnetic ion or
defect (we shall call it a center) required for simulation of EPR spectra and their
dependencies:
Information about crystal structure, its space group, possible electrically equivalent,
but magnetically different centers, symmetry group of the center, Euler angles for
magnetically non-equivalent centers (if present),
Spin-Hamiltonian, electron part (number of spins, spin values, parameters of Zeeman
interactions, the parameters of zero-field splitting (crystalline field),
Interactions for exact diagonalization (exchange or strong hyperfine interactions)
S-I interactions, perturbation part (weak hyperfine interactions with isotopes with
non-zero magnetic moments – natural abundances of the isotopes are used for
calculation of relative intensities of EPR lines)
Instrumental part (microwave, frequency, initial and final orientations of the static
magnetic field relative to the coordinate system which are characterized by polar and
azimuthal angles, steps on angles, range of the field sweep, threshold level separated
allowed and forbidden transitions, temperature etc.)
Spectrum attributes (initial line width, broadening mechanisms)
The above information allows to build automatically corresponding matrices of spin-
Hamiltonian.
The input parameters can be saved in <*.gep> file for further use.
The program was designed for users of different levels. Students can use templates and
change minimal sets of Spin-Hamiltonian and instrumentation parameters. Professionals
receive nearly unrestricted possibilities for analysis and simulation of EPR spectra of real
crystals.
Visual EPR
Menu Page 11
Simulation resonance fields and EPR spectra (Fields.exe)
.
The “Step by step form” allows to obtain the following dependencies:
1. Positions of energy levels on magnetic field;
2. Differences of energy levels on magnetic field;
3. Transition intensities on magnetic field;
4. Electron Paramagnetic Resonance (EPR) spectrum shape
• on line width and line shape (Gaussian, Lorentzian and their derivatives),
• on azimuthal or polar angles,
• on any parameter of Spin-Hamiltonian,
• on microwave frequency,
• on temperature.
These dependencies are drawn on screen, written into output file and can be saved as a high
resolution picture.
The calculated wave functions of the spin-Hamiltonian can be also written into file if
required.
The “Simulation form” allows to simulate interactively resonance fields for given spin-
Hamiltonian parameters and to compare and adjust simulated and experimental spectra and
their angular dependence. This helps to a great extent to decipher complicated angular
dependencies created by several equivalent and non-equivalent centers in crystals, and to
determine spectroscopic characteristics of observed paramagnetic defects including
parameters of their spin-Hamiltonians and initial line width. The form uses two panels
allowing to treat simultaneously spectra and/or angular dependencies measured at different
conditions (for instance, at different microwave frequencies, like X- and Q-bands).
The program has a tutorial designed to illustrate capabilities of Fields.exe program for users
of different levels, which helps to build up understanding of its features.
Visual EPR
Menu items Page 12
Obtaining spin-Hamiltonian parameters by fitting angular dependences
(Params.exe)
Params.exe uses experimental angular dependencies edited with the help of FAIW.exe for
refinement of obtained spin-Hamiltonian parameters by fitting.
Fields-Angles-Intensities-Widths dependencies (FAIW.exe)
FAIW.exe is powerful tool for viewing, comparing and transformation of 2-3-4 dimensional
arrays of EPR, ENDOR or other data. It is developed mainly to represent four-dimensional
tables of angular dependences of resonance magnetic field, line intensities and widths
(Fields-Angles-Intensities-Widths dependencies) on one graph. It visualizes experimental or
calculated angular dependencies of resonance magnetic fields (EPR) or resonance
frequencies (ENDOR) and converts into special symbols the information about other
resonance line characteristics - intensity and width.
The program has large sets of symbols for the representation of experimental data and sets of
color lines for the representation of calculated angular dependencies. This allows convenient
comparison of observed and calculated dependencies (including multi-frequency EPR data),
and preparation of the graph for publication.
FAIW.exe is designed also to prepare a data file for adjustment angular dependencies with
the help of Fieds.exe and for fitting angular dependence by Params.exe using extraction and
erasing corresponding visual data on the graph instead of strings in the text file.
It allows editing angular dependence, extracting the points, what you need, from array of
experimental data measured for real crystal containing several paramagnetic dopants and
trace impurities. It can shift all points on definite angle and save the result. It helps to
exclude from experimental data those points, which are close to calculated angular
dependencies. It has many other useful visual procedures, which transform the data in the
table of the treated file. For instance, a possibility to change wrong angles in *.grt-file, to
insert or delete data for one angle, to change line intensities for one plane, to create of road
map file from three files with angular dependencies for separate planes.
It works with special ASCII files. These files are output files of View_spw.exe
(experimental angular dependencies, <*.grt> or <*.gem> ) or Fields_w.exe (calculated
angular dependencies, <*.grt> or <*.grm> ).
Visual EPR
Menu Page 13
Interrelations of programs of the Visual EPR package
View_spw.exe is the basic program, which you can use immediately after measurements for
the spectrum treatment. It prepares spectra and files with four-dimensional tables for other
programs.
View_spw.exe can be used for preparation of spectral files for Fields.exe (filtering, baseline
correction, and algebraic procedures).
View_spw.exe must be used to prepare angular dependencies of experimental spectra for
comparison with calculated dependencies with the help of Fields.exe and for refinement of
obtained spin-Hamiltonian parameters by fitting with Params.exe.
FAIW.exe can be used for editing experimental angular dependencies obtained with the help
of View_spc.exe.
View_spw.exe must be used to prepare angular dependencies of experimental spectra for
comparison with calculated dependencies.
Fields.exe must be used to prepare calculated angular dependencies for comparison with
experimental ones.
Params.exe can be used for refinement of obtained spin-Hamiltonian parameters by fitting
experimental angular dependencies. It uses angular dependencies edited with the help of
FAIW.exe.
CosEul.exe can be used for a conversion of spin-Hamiltonian parameters from Cartesian to
irreducible tensor components, as well as for evaluation of principal values and principal axes
of second rank tensors.
Visual EPR
Page 14
References 1 A. Abraham, B. Bleaney. Electron Paramagnetic Resonance of Transition Ions (Clarendon Press,
Oxford, 1970). 2 S. A. Altshuler, B. M. Kozirev. Electron Paramagnetic Resonance in Compounds of Transition Elements
(Science, Moscow, 1972; Wiley, New York, 1974). 3 V.G.Grachev. Correct expression for generalized spin-Hamiltonian for non-cubic paramagnetic centers.
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Visual EPR
References Page 15
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