WinNormos-for-Igorphysics-astronomy-manuals.wwu.edu/WinNormos3-Manual.pdf · 1.2 Introduction to WinNormos-for-Igor WinNormos-for-Igor is a group of two least-squares ﬂtting programs

WinNormos-for-IgorUsers ManualVersion 3.0

Written by:R.A. BrandLaboratorium fur Angewandte PhysikUniversitat DuisburgD-47048 DuisburgGermanyTel.: [..49] (0) (203)379-2389FAX.: [..49] (0) (203)379-3601Internet: [email protected]://www.uni-duisburg/FB10/LAPH

Sold by:Dr. U. KleinWissenschaftliche Elektronik GmbHWurmstr. 8D-82319 StarnbergGermanyTel.: [..49] (0) (8151)-9025-0FAX.: [..49] (0) (8151)-9025-10Internet: [email protected]

Date: May 14, 2009

ii

Contents

1 User’s Guide 11.1 What is New in Version 3 . . . . . . . . . . . . . . . . . 11.2 Introduction to WinNormos-for-Igor . . . . . . . . . . . . 1

1.2.1 Site and Dist: . . . . . . . . . . . . . . . . . . . . 41.2.2 Site: . . . . . . . . . . . . . . . . . . . . . . . . . 51.2.3 WDist: . . . . . . . . . . . . . . . . . . . . . . . . 61.2.4 Stack plot: . . . . . . . . . . . . . . . . . . . . . . 8

1.3 Possible types of evaluation . . . . . . . . . . . . . . . . 81.3.1 Main possibilities and some special cases . . . . . 8

DIST . . . . . . . . . . . . . . . . . . . . . . . . . 101.4 Using SITE . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.4.1 Introduction: SITE . . . . . . . . . . . . . . . . . 111.4.2 Some simple cases . . . . . . . . . . . . . . . . . . 12

A general starting procedure for fitting . . . . . . 121.5 Using DIST . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.5.1 Introduction: DIST . . . . . . . . . . . . . . . . . 14Crystalline sites . . . . . . . . . . . . . . . . . . . 15

1.5.2 Allowed variable and constant combinations . . . 16

2 Input Parameters 192.1 DATA Parameters, SITE and DIST . . . . . . . . . . . . 19

2.1.1 Control of the experimental spectrum input . . . 19Velocity scale . . . . . . . . . . . . . . . . . . . . 19Folding . . . . . . . . . . . . . . . . . . . . . . . . 19FIT, Max calls and mode buttons . . . . . . . . . 20

2.2 SITE PARAM-Parameters . . . . . . . . . . . . . . . . . 212.2.1 Constant Parameters . . . . . . . . . . . . . . . . 21

General parameters . . . . . . . . . . . . . . . . . 21Hamiltonian method parameters . . . . . . . . . . 21Transmission integral parameters . . . . . . . . . 23Isotropic EFG with magnetic field parameters . . 23

2.2.2 Variable parameters . . . . . . . . . . . . . . . . 24Variables which refer to the whole spectrum . . . 24Transmission integral variables . . . . . . . . . . . 24Hamiltonian fit variables . . . . . . . . . . . . . . 25

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iv CONTENTS

Hamiltonian: Excited state property variables . . 25Variables which refer to one sub-spectrum . . . . 263/2-1/2 transitions . . . . . . . . . . . . . . . . . 27Quadrupole sub-spectra: NLINE(i) = 2 . . . . . . 27Magnetic sub-spectra: NLINE(i) = 6 or 8 . . . . 27Hamiltonian method variables . . . . . . . . . . . 28Hamiltonian solution: angular variables . . . . . . 28Hamiltonian: Goldanskii-Karyagin effect variables 29Hamiltonian: Wegener relaxation variables . . . . 30VOIGT line profile variables . . . . . . . . . . . . 30

2.2.3 Special cases and routines: variables . . . . . . . 31Polarised-source spectra variables . . . . . . . . . 31EFGB routine variables . . . . . . . . . . . . . . 31

2.3 DIST &PARAM-Namelist . . . . . . . . . . . . . . . . . 312.3.1 Short list of parameters and variables . . . . . . . 31

Fit parameter related to spectrum . . . . . . . . . 31Constant parameters related to distribution blocks 32Constant parameters related to distribution blocks:

(DIST = 1 only) . . . . . . . . . . . . . 32Variable parameters related to distribution block(s) 32Constants related to the crystalline sub-spectra . 32Variables related to the crystalline sub-spectra . . 33

2.3.2 Long list of parameters and variables . . . . . . . 33Constant parameters . . . . . . . . . . . . . . . . 33DISTRI = Histogram: pure histogram only . . . 36

Variables referring to the spectrum . . . . . . . . 36Variables referring to a certain block i . . . . . . 36Parameters related to the asymmetry effects . . . 37Gaussian distribution . . . . . . . . . . . . . . . . 38Polarised magnetic spectrum . . . . . . . . . . . . 38Parameters for crystalline sub-spectra . . . . . . . 38Variables for crystalline sub-spectra . . . . . . . . 38

List of Figures

1.1 Starting panel. The left hand site is used to enter newspectra, fold them and possibly store spectra with fits.On the right hand side, the name of the spectrum, an op-tional isomer shift offset, temperature and magnetic fieldcan be entered. On the left hand side, pull-down list con-trols which spectrum is to be treated. Folding is done withthe next button, eventually linearising the velocity scale,adding neighbouring channels, setting the proposed fold-ing point, maximum velocity and setting transmission oremission spectrum. . . . . . . . . . . . . . . . . . . . . . 2

1.2 Panel for reading-in spectra. . . . . . . . . . . . . . . . . 31.3 Site-Data panel. Results of fitting with SITE. . . . . . . 61.4 Site-Para panel. Panel for setting number and kind of

subspectra as well as starting values. . . . . . . . . . . . 71.5 Graphic panel for hooking on peaks and estimating start-

ing values. . . . . . . . . . . . . . . . . . . . . . . . . . . 81.6 Dist-Data panel for DIST. . . . . . . . . . . . . . . . . . 91.7 Panel for defining the blocks of distribution in DIST. . . 101.8 Panel for defining the crystalline subspectra. . . . . . . . 111.9 Panel for defining the stack plot to be created. Many

options available from panel and others from Igor pull-down menues. . . . . . . . . . . . . . . . . . . . . . . . . 12

1.10 Plot created by Stack Plot. . . . . . . . . . . . . . . . . . 131.11 Typical spectrum, here fitted with SITE. . . . . . . . . . 131.12 Typical distribution fit to a magnetic metglas sample fitted

with DIST. At the right, the distribution is shown. . . . 141.13 Typical Mossbauer calibration spectrum. We will use this

as a demonstration. . . . . . . . . . . . . . . . . . . . . . 15

v

vi LIST OF FIGURES

List of Tables

1.1 Line numbering for 3/2-1/2 transitions . . . . . . . . . . 91.2 Possible Mossbauer isotopes for SITE . . . . . . . . . . . 141.3 Possible isotopes and allowed fit possibilities . . . . . . . 15

2.1 Possible isotopes and hyperfine properties: I . . . . . . . 232.2 Possible isotopes and hyperfine properties: II . . . . . . . 242.3 Line numbering for 3/2-1/2 transitions . . . . . . . . . . 272.4 Goldanskii-Karyagin coefficients . . . . . . . . . . . . . . 29

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Chapter 1

User’s Guide

1.1 What is New in Version 3

In version 3 the Graphical User Interface (GUI) has been extensivelyre-designed, most significantly on the right hand side of each card. Thisnew GUI is for Igor 6.0 and later since many features not found in Igor5 are used. On the CD, both old (for Igor 5) and the new templates areincluded. This now looks like a table of values, with a few check boxes.Initial values can be inserted in the first numeric column. Clicking onthe results column puts the result value into the start value.

A major change in the XOP is that an error was corrected. This errorconcerned quadrupole subspectra and led to small errors in relative areasfor quadrupole compared to sextets or single lines.

It is now possible to set an offset for the isomer shift. All fitting andgraphing is done relative to this offset.

1.2 Introduction to WinNormos-for-Igor

WinNormos-for-Igor is a group of two least-squares fitting programs usedto evaluate Mossbauer spectra, SITE and DIST. This user’s guide hasbeen written to introduce these programs with the help of some simpleexamples. In Chapter 2 there is a complete list of parameters for thosealready familiar with these programs. The programs are structured ina similar manner, so that a maximum of compatibility is maintainedbetween them. They are meant for solving two different common typesof problems encountered in Mossbauer spectroscopy.

The program SITE is designed to evaluate a series, usually short, ofdifferent sub-spectra, each representing a different environment (for ex-ample metallurgical phase). These different sites (thus the name SITE)are assumed distinguishable by the values of the isomer shift ISO, thequadrupole splitting DEQ or VZZ, and hyperfine magnetic field BHF,line width WID, etc. The sub-spectrum area is then proportional to

1

2 CHAPTER 1. USER’S GUIDE

Figure 1.1: Starting panel. The left hand site is used to enter new spec-tra, fold them and possibly store spectra with fits. On the right handside, the name of the spectrum, an optional isomer shift offset, tempera-ture and magnetic field can be entered. On the left hand side, pull-downlist controls which spectrum is to be treated. Folding is done with thenext button, eventually linearising the velocity scale, adding neighbour-ing channels, setting the proposed folding point, maximum velocity andsetting transmission or emission spectrum.

the quantity, and we want to find the best values of these different pa-rameters. The program SITE will find the optimum values of theseparameters for a given model (Mossbauer isotope; number and type ofsub-spectra; which parameters are to vary, and which are constants; val-ues of the constants). This program uses nonlinear optimisation withleast-squares statistics (a χ2-method).

There is a special type of very common problem in Mossbauer spec-troscopy where the above type of program is not very convenient. Thisis when there is a continuous distribution of hyperfine parameters for atleast part of the spectrum. A typical example would be a magnetic amor-phous metallic glass. In this case, the hyperfine field varies in a smoothway over a certain range of values. The program DIST is intended totreat such problems (and thus the name). The distribution can be eitherin hyperfine magnetic field BHF, quadrupole splitting QUA, or centre(isomer) line shift ISO. The possible applications of this program range

1.2. INTRODUCTION TO WINNORMOS-FOR-IGOR 3

from very simple to very complex and specialised.The basic method uses nonlinear least-squares optimisation as in SITE,combined with linear regression for finding the areas of each sub-spectrumin order to gain in speed and accuracy. This latter part is also called thehistogram method, since we define a range of the distributed parame-ter, say the magnetic hyperfine field, and find the optimum histogramof sub-spectra areas for the spectrum. The resulting distribution P(x)(where x = BHF, QUA or ISO) is restricted to positive values and canbe smoothed, thus avoiding the oscillations common in distribution pro-grams.SITE and DIST are combined into one Igor c© Experiment includingspectrum folding. This Introduction, and the user’s guide has been writ-ten to introduce these programs with the help of some simple examples.To set-up WinNormos-for-Igor, first install Igor as per Igor manual.Then add the file WinNormos.xop to the correct Igor folder (or createa link to it, as explained in the Igor manual). Then start Igor and load theWinNormos-for-Igor experiment template WinNormos-for-Igor.pxt(or directly an experiment). When finished, you store the new Experi-ment under a different name, either as packed or unpacked experiment,including all data and calculations. You can then re-start this experimentlater. The basic starting panel is given in Figure 1.1.

Figure 1.2: Panel for reading-in spectra.

The Experiment contains a graphical panel with a series of tab cards.The first tab card Spectrum seen in Fig. 1.1 is for reading-in spectraand folding (as necessary) as well as defining the velocity scale. Thepanel shows a demonstration file (DISTDEMO.MOS) loaded into Igor.The top left shows a pull-down menu of possible spectra being fitted.


The current spectrum is shown below. The raw spectrum is shown onthe lower left. Any number of different spectra (with different names)can be read-in using the Read-in New Spectrum tab. The Read-in NewSpectrum tab creates the panel shown in Fig. 1.2. After selecting a file,the panel looks as above. If the number of lines of text is incorrect, thenadjust and re-plot the spectrum. You should also set type of velocityscale and the value of VMAX (if not already set). After accepting thespectrum, we return to the first card page including the new spectrum.After reading in the spectrum, the GUI reverts to 1.1 you can set themaximum velocity, possible folding point (PFP) and fold the spectrum.If the check-box Linearize is checked, the velocity scale will be linearisedwhen folding (presently, spectra which are folded on disk cannot be lin-earised). If you change the maximum velocity, you will be warned tore-fold to obtain the correct velocity scale. On folding, if the sign ofthe geometry effect disagrees with the sign of the maximum velocity, awarning panel will also be issued.Below the button to enter new spectra, there are two buttons markedSave Spec and Load Spec. These can be used to store a spectrum andits fits to HD storage, and recover everything again in a different Exper-iment. The Erase button is used to erase a spectrum from the currentexperiment (not from disc storage).On the right side, final values of the folding point (PFP), as well as esti-mated geometry effect, background and resonant area are shown. Thesetwo latter values will be used later in setting up the fit. In the graph be-low, the raw as well as the folded spectrum is shown. The latter includesthe assumed velocity profile.

1.2.1 Site and Dist:

Here we present controls common to all Site and Dist cards. Both pro-grammes have one card names Data. This card is for properties commonto all possible model fits. There are then one (Site) or two (Dist) addi-tional cards which define the model fit. They all look similar. At the topof the left hand side the name of the current spectrum is shown, and tothe right a button (rarely needed) to browse through the data folders.There is a collection of common controls at the bottom. The Helpbutton displays a help page for that card. The Done button is when youare finished and will erase the GUI and ask you to save the experiment.The Graph button generates a simple graph similar to the one shownon the lower part of the panel. The Save button is at the present timeunnecessary. The Do Report button generates a HTML-format reportas well as text-format files of the spectrum and fit which can be saved andviewed with any browser. Fitting is started by clicking the Do Zero-Fitor Do Fit buttons.There is a panel showing the state of the convergence flag as well as the


number of iterations necessary. The resulting chi-2 parameter defined asthe normalised sum of square differences is also shown.The names of the parameters are the same as used before in the DOSversion, making a transition easier. In the list of variables, checking thecheck-box will select that as to be varied. If the check-box is absent, thecorresponding parameter cannot be varied, but perhaps changed beforethe fit.On the right side of each panel card, there is a tabular list of the relevantsubspectrum variables. Relevant variables (or constants) have namesgiven in the second column. If there is a check box in the first column,these can be set variable (checked). The empty positions are not used forthe current subspectrum type. The starting values in the first numericalcolumn (the 3rd column of the table) can be changed. Results and errorbars are shown in columns 2 and 3 respectively. By clicking on a resultingvalue, this will be inserted as a starting value. Thus a good way toproceed is to fit only a few variables, setting the fit value as the newstarting one, and gradually allowing more variables to vary.For other than the first subspectrum, there is a check box in the columnafter the error values which can be used to link the current variable tothe same variable in a different subspectrum. In the case that this ischecked, the constant values and variable index can be entered in theappropriate columns.The resulting fit is shown in the area below, including the deviationsbetween theory and experiment.

1.2.2 Site:

The program for treating a discrete set of subspectra, each represent-ing different values of the hyperfine constants, is accessed through thetab cards Site-Data and Site-Para. The Site-Data card is shown inFig. 1.3. On the left panel the maximum number of iteration calls canbe set (default is usually enough), as well as the choice between thinabsorber and transmission integral. Constant parameters concerning thenuclear transition are on the right side of the left hand panel, and possiblyvariable parameters on the right panel as discussed above.The next tab panel Site-Para, Fig. 1.4, defines the different subspec-tra. Note that both the total number of subspectra (NSUB), and thecurrently displayed subspectrum (currentSub) can be chosen indepen-dently (1 ¡= currentSub ¡= NSUB). The subspectrum type can also bechosen from a list on the left panel.There is a series of button commands on the left hand panel. The firstCalibrate Vmax can be used for a iron sextet spectrum of bcc iron atroom temperature to recalculate VMAX given that the hyperfine fieldshould be 33.1 T. The Search Peaks Panel is explained below. SaveModel and Load Model are used to save fitting models (number and


Figure 1.3: Site-Data panel. Results of fitting with SITE.

type of subspectra etc.) to be used (Loaded) for other spectra.

By clicking the Search Peaks Panel button, you get the panel givenin Fig. 1.5. First click the start button once. (This becomes the Finishbutton for exiting.) Then the hook-cursor function is activated. Click atthe maximum (minimum here) of a spectral line, holding the left mousetaste down. Then pull-out a Lorentzian line which approximates theexperiment. (See help file within WinNormos-for-Igor experiment formore details.)

1.2.3 WDist:

The Dist-Data, Dist-Block and Dist-Xls panels are for using the Dis-tribution program. This program is intended to treat problems includinga distribution of hyperfine parameters (and thus the name) mainly use-ful for metallic glasses, etc. The distribution can be either in hyperfinemagnetic field Bhf , quadrupole splitting EQ, or centre (isomer) shift δ.The possible applications of this program range from very simple to verycomplex and specialised. The main possibilities are:

• 1/2-3/2 Mossbauer transitions (57Fe , 119Sn , 197Au standard).

• Distributions in BHF , EQ or ISO. Any combination is acceptable.


Figure 1.4: Site-Para panel. Panel for setting number and kind of sub-spectra as well as starting values.

• Including separate sub-spectra for crystallised components usefulfor partially crystallised amorphous or nano-crystalline materials.

• Including different correlation effects between hyperfine parameterssuch as hyperfine field Bhf and isomer shift ISO, or hyperfine fieldand quadrupole effect EQ.

• Different types of distribution profiles and line forms includingGaussian and Voigt form distributions.

• Polarised source experiments with spin-texture evaluation.

The main Dist-Data panel sets the constants applying to the wholespectrum. This is shown in Fig. 1.6.

The panel Dist-Block shown in Fig. 1.7 is used for defining the blocksof subspectra constituting the distribution. One or more can be de-fined. Set the number of subspectra and type for each block. Lambda isthe smoothing value.

The Dist-Xls tab is used to define one or a series of separate crystallinesubspectra. For each subspectrum, set type and eventually other relevantparameters.


Figure 1.5: Graphic panel for hooking on peaks and estimating startingvalues.

1.2.4 Stack plot:

The tab Stack Plot is used for creating a plot file of one or more ofthe spectra treated in the current experiment. The panel is shown inFig. 1.9.The selection is done on the left. The plot button produces the plotshown in Fig. 1.10. This plot then can be saved to disk using the built-infeatures of Igor.

1.3 Possible types of evaluation

Below are listed the main possibilities for SITE and DIST.Many different Mossbauer isotopes are possible and can be chosen atrun-time. Most common isotopes are pre-defined and can be chosen byusing a simple command at run-time which sets all nuclear parameters.

1.3.1 Main possibilities and some special cases

The main possibilities of SITE are:

• 1/2-3/2 Mossbauer transitions (57Fe, 119Sn, 197Au): single lines,quadrupole doublets, magnetic sextets and octets. The lines arenumbered 1 to 6 for sextets, 1 to 8 for octets. The lines are num-bered according to the transition:

1.3. POSSIBLE TYPES OF EVALUATION 9

Figure 1.6: Dist-Data panel for DIST.

3/2 state -3/2 -1/2 +1/2 +3/2 -3/2 -1/2 +1/2 +3/21/2 state -1/2 -1/2 -1/2 -1/2 +1/2 +1/2 -1/2 -1/2

line 1 2 3 8 7 4 5 6area 3 2 1 0 0 1 2 3

Table 1.1: Line numbering for 3/2-1/2 transitions

• Any Mossbauer isotope: exact solution of the static Hamiltonian,either single crystal, powder or texture.

• Transmission integral fit.

Special cases possible including:

• Special line forms (Lorentzian, Gaussian, Voigt).

• Exact solution for a powder EFG (random directions) + magneticfield.

• Some simple relaxation profiles.

• Polarised source experiments.

A typical spectrum is given in Figure 1.11.


Figure 1.7: Panel for defining the blocks of distribution in DIST.

DIST

The program DIST is intended to treat problems including a distributionof hyperfine parameters (and thus the name) mainly useful for metallicglasses, etc. The distribution can be either in hyperfine magnetic fieldBHF, quadrupole splitting DEQ, or isomer shift ISO. The possibleapplications of this program range from very simple to very complex andspecialised. The main possibilities of DIST are:

• 1/2-3/2 Mossbauer transitions (57Fe, 119Sn, 197Au standard).

• Distribution in BHF, DEQ or ISO.

• Combination of two (or more) different distribution blocks includ-ing different distributed hyperfine parameters.

• Including separate sub-spectra for crystallised components usefulfor partially crystallised amorphous or nano-crystalline materials.

• Including different correlation effects between hyperfine parameterssuch as hyperfine field BHF and isomer shift ISO, or hyperfine fieldand quadrupole effect DEQ.

• Different types of distribution profiles and line forms includingGaussian and Voigt form distributions.

1.4. USING SITE 11

Figure 1.8: Panel for defining the crystalline subspectra.

• Polarised source experiments with spin-texture evaluation.

A typical distribution spectrum is given in Figure 1.12.The number of built-in isotopes has been greatly extended for SITE.These can be chosen by changing the character ISTYPE from the default’57FE’ to one of the below (Upper case letters only):

1.4 Using SITE

1.4.1 Introduction: SITE

SITE can be used to treat Mossbauer spectra in the case of a discreteseries of different hyperfine sites. Many different possible isotopes arealready built-in to the program. In the case of the most common 3/2-1/2transitions, there are many different choices for fitting the spectra. Thereis a first order perturbation model where the sub-spectrum is specifiedby the number of lines NLINE. It is also possible to treat these, or anyisotope, using the usual full static Hamiltonian for the exact digitalisationof the mixed BHF - VZZ interactions: HAMILT. Below is a table ofallowed combinations of isotopes and methods.


Figure 1.9: Panel for defining the stack plot to be created. Many optionsavailable from panel and others from Igor pull-down menues.

1.4.2 Some simple cases

Included with the program are a series of demonstration spectra. Theseare discussed here and later on in this manual. They spectra can be usedto study different types of fits.

A general starting procedure for fitting

• The background counting rate does not have to be initialised. Theprogram estimates a good starting value which almost always issufficient. You will only have trouble with this if a resonant linehappens to be at the edge of the spectrum (almost never the caseand very bad practice).

• Generally do not start with the transmission integral.

• Start by setting ZROFIT to get an idea how various possibilitiesfit.

• Check various reasonable combinations of relevant angles betweenVZZ and Γ, between VZZ and BHF, the values of η, and sign ofVZZ.

1.4. USING SITE 13

Figure 1.10: Plot created by Stack Plot.

Figure 1.11: Typical spectrum, here fitted with SITE.

• Unless the spectrum contains several different sub-spectra with verydifferent resonant areas, the parameters ARE(i) do not have to beinitialised: the default values will do.

• When the starting values of the other parameters are reasonable,the spectrum can be fitted in the thin-absorber approximation,without the transmission integral.

• If the fitted values differ very much from these initial values, thesecan be updated for the next step.

• If the transmission integral is to be used, first set FSO and WDSto the correct values. Then using ZROFIT again, set the value ofTAB so as to agree at least fairly well with the spectrum. ( ARE= 1. for first sub-spectrum)

• A final fit can now be performed after resetting ZROFIT. Theseshould give the final best values and error bars of the parameters.

• The results can be typed out using P and MBPLOT.


Figure 1.12: Typical distribution fit to a magnetic metglas sample fittedwith DIST. At the right, the distribution is shown.

ISTYPE EGAMMA(KeV)

remarks

57Fe 14.413 default isotope119Sn 23.871197Au 77.345121Sb 37.150127I 57.6129I 27.77133Cs 80.997 excited state quadrupole

unknown125Te 35.4667Zn 93.32161Dy 25.655170Yb 84.3237Np 59.5

Table 1.2: Possible Mossbauer isotopes for SITE

1.5 Using DIST

1.5.1 Introduction: DIST

DIST is a hyperfine distribution version which an be used for eithermagnetic, quadrupole and/or isomer shift distributions, but usually isrestricted to 3/2-1/2 Mossbauer transitions. In the case of magnetic dis-tributions, it is possible to include the correlation of the magnetic fieldwith isomer shift and with quadrupole effect. In certain cases, it is possi-ble to calculate the latter to higher than first order perturbation theory.Different types of distributions are possible: either a histogram (includ-ing smoothing), or a Gaussian distribution, a binomial distribution, ora fixed distribution (user-defined) can be used. Several different typesof line forms can be defined. The program can also be used with themaximum entropy method to calculate the distribution.

Method used in calculating the hyperfine distribution: The same routinefor the nonlinear least squares problem as in SITE is used. In addition,within the loop of this routine, the sub-spectra areas are found using thelinear least squares solution, including the condition that the areas mustbe positive. Smoothing of the distribution is included by incorporating amatrix of coefficients (as in the method of Hesse and Rubartsch [7]). Bysetting ZROFIT , it is possible to only perform the latter linear problem,that of finding the areas for the given values of ISO etc. and the estimatedvalue of BKG. This is a good way of finding the distribution very rapidly.

1.5. USING DIST 15

ISTYPE HAMILT NLINE EFGB57Fe yes 1,2,6,8 yes119Sn yes 1,2,6,8 yes197Au yes 1,2,8 no151Eu yes no no121Sb yes no no127I yes no no129I yes no no

133Cs yes no no125Te yes no no67Zn yes no no161Dy yes no no170Yb yes no no237Np yes no no

Table 1.3: Possible isotopes and allowed fit possibilities

Figure 1.13: Typical Mossbauer calibration spectrum. We will use thisas a demonstration.

When the other non-linear variables, ISO, etc., are approximately correct,then they can be improved by resetting back to FIT, and finding thecomplete minimisation.

Crystalline sites

It is possible to define crystalline sub-spectra which are treated sepa-rately from the distribution blocks. Such spectra are either single lines,quadrupole or sextets.Forms of distributions given by DISTRI = Dist Type:

• Dist Type = Histogram: Histogram method with smoothing. Asimple histogram of sub-spectra is calculated including both a smooth-ing parameter as well as the possibility of pinning the distributionto go smoothly to zero at the lower and upper ends. NormallyLorentzian line form is used, but other possibilities include us-ing VOIGT-form lines which simulates a smooth distribution usingfewer sub-spectra.

• Dist Type = Gaussian: Gaussian distribution (also double distri-bution). A Gaussian form of P(BHF) is assumed, characterisedby an average value and a standard deviation. It is also possibleto assume a double Gaussian distribution including a negative part(useful for quadrupole distributions of VZZ).

• Dist Type = Random Quadrupole: not yet tested.


• Dist Type = Fixed: not yet tested.

Types of line profiles given by METHOD = Subspec Type:

• Hyperfine magnetic field:

– Subspec Type = Hyperfine field distribution: simple hyperfinefield distribution. Magnetic sextets are calculated.

– Subspec Type = Asymmetry: Calculation a la Brand (seereferences). Asymmetry effects due to the correlation of hy-perfine parameters are explicitly calculated. The simple lineform given in [8, 9] is used.

– Subspec Type = B&C Asymmetry: Calculation a la Billard& Chamberod [6]. The more exact method given in [6] is usedfor the asymmetry effects.

– Subspec Type = Polarised source: Calculation for polarisedsource. A fully magnetically-split source is assumed.

• EFG quadrupole distributions:

– Subspec Type = doublet: Simple distribution. A distributionof symmetric quadrupole doublets is assumed. Asymmetryeffects can be treated by letting the isomer shift ISO varylinearly over the DEQ distribution.

• Isomer shift distribution.

– Subspec Type = Singlet: Simple isomer shift (single line) dis-tribution.

1.5.2 Allowed variable and constant combinations

a For quadrupole distributions, QUA is the starting value, and DTQthe step value for the distribution. For histogram distributionsDISTRI = Histogram, these must be both held fixed. For fixedform distributions, DISTRI greater than 1, they can be varied.

b For magnetic hyperfine distributions, BHF is the starting value,and DTB the step value. For histogram distributions, both mustbe fixed. For fixed form distributions, they can be varied.

c For isomer shift distributions, ISO is the starting value, and DTIis the step value. For histogram distributions, both must be fixed.For fixed form distributions, they can be varied.

1.5. USING DIST 17

d The average fields for the different blocks are calculated separately,including the root-mean-square average, and the mean value. Fromthis, the standard deviation of the distribution (roughly the distri-bution width) is calculated. The form of the distribution is com-pared to the Gaussian distribution using the higher moments: Neg-ative SKEW means a tail at smaller field values. Positive SKEWmeans a tail at larger field values. Negative KURTOSIS meansthe distribution is flatter than a Gaussian distribution is. PositiveKURTOSIS means the distribution is more pointed than a Gaus-sian is.

e It is possible to divide the distribution into several different blocks,and treat each block separately (relative line areas, etc.). In thisway, the type of the distribution (histogram and smoothing, Gaus-sian, etc.) can be chosen separately for each block, as well as thetype of line form (magnetic, quadrupolar, isomer shift).


Chapter 2

Input Parameters

2.1 DATA Parameters, SITE and DIST

2.1.1 Control of the experimental spectrum input

Velocity scale

• Velocity scale: Specify the type of drive form

If set to triang, then triangular drive form. Otherwise, sine-driveform assumed.

• VMAX: Specify the maximum velocity

The maximum velocity of the drive. The sign of VMAX will de-termine whether or not the spectrum will be reversed (spectrumshould always be in order of increasing velocity, negative to leftand positive to right).

Because of certain features in the folding routine, the correct signof VMAX will depend on which range is used for the folding pointPFP. PFP can either be about equal to ND (usually = 512), orequal to ND/2 (usually = 256). If sign of VMAX does not agreewith the sign of the geometry effect, a warning will be printed.Reversing sign of VMAX should then give the correct velocity.

• Linearize: Linearize the velocity scale

This produces a linear scale independent of the previous velocityscale. Interpolation is done using a cubic spline between the firstand the last velocity. This must be used when the velocity scale isnonlinear, and transmission integrals are to be calculated.

Folding

• VMAX: Maximum velocity in mm/s.

19

20 CHAPTER 2. INPUT PARAMETERS

The velocity scale will be calculated from VMAX at folding orlater. Note that the sign of VMAX is important, as it can be usedto reverse the velocity scale at folding or later.

• PFP: The trial folding point.

Two different ranges are allowed for PFP. This can either be equalto about ND ( = 512), or to about ND/2 ( = 256), but the correctsign of VMAX will be different in each case. In order to hold PFPfixed in value, give the desired value but with sign set negative.

• ND: The number of channels in the unfolded spectrum.

The final number of channels in the spectrum is NP, and is cal-culated from ND. If spectrum folded, then NP = ND/2, otherwiseNP = ND. In the case of a simulation NP = ND.

FIT, Max calls and mode buttons

• FIT: the spectrum will be fitted.

• SIMULT: only a simulated spectrum will be calculated; no exper-imental spectrum will be read-in or used. If TRAING .FALSE.,a sinus velocity form will be used, otherwise a linear form will beused. In both cases, VMAX determines the velocity scale. SIMULTcan be used both with SITE and DIST. In both cases, the areasof the sub-spectra must be given. For DIST, these are given inAREREL(i), i = 1, .. NSUB and DISTRI = Histogram. For SITE,these are given in ARE(i), i = 1, .. NSUB.

• ZROFIT: The theoretical spectrum will be calculated from thestarting values only, and compared with the experimental spec-trum. This can be used in order to see if the fit is possible. In thecase of DIST, the distribution will be calculated, so that the areasdo not have to be given.

• MXCFUN Maximum number of calls to CALFUN, the subroutinewhich calculates the momentary theoretical sub-spectra and result-ing spectrum. This has the effect of limiting the maximum CPUtime, depending on the complexity of the theoretical function used.

• EMSPEC: Emission spectrum, area is added to background.

2.2. SITE PARAM-PARAMETERS 21

2.2 SITE PARAM-Parameters

2.2.1 Constant Parameters

General parameters

• NSUB: Number of sub-spectra.

• NLINE Number of lines in sub-spectrum i

– NLINE = singlet: single line.

– NLINE = doublet: quadrupole doublet with line separationQUA.

– NLINE = sextet: magnetic sextet or octet (but first ordercalculation).

Hamiltonian method parameters

For HAMILT, then the other parameter values must be given as well:PHS, MIX, QMR, PARITY and ST. These will be usually set by thechoice of isotope, ISTYPE. Note that for HAMILT = .TRUE., the num-ber of lines does not have to be set, and will always be set for the maxi-mum number for the transition. For variables, see page 25 and 28.

• HAMILT: If set, then full Hamiltonian method will be used tocalculate the sub-spectrum. In this case, the ground state spin SG,the excited state spin SEX, and the angular momentum quantumnumber of the radiation ST must all be specified. In addition, thelogical condition PARITY and the values for mixed radiation MIX,the nuclear g-factor ratio GFR and the nuclear quadrupole ratioQMR should be set for the transition. Usually, these will all be setby choosing the name of the isotope in ISTYPE.

The value input for NLINE will have no effect, since this optioncalculates the number of lines from the spin values of the excitedand ground states.

See the parameters: ISTYPE, PARITY, IFSC, IFGK, SEX, SG,ST.

See the variables: WID, ARE, ISO, QUA, BHF, PHS, MIX, GFR,QMR, AKS, ETA, RTH, PHI, BEX, GAX, G11, G20, G21, G22,STG, STQ and STI.

Cannot be used for sub-spectra calculated using EFGB, or the re-laxation or polarised source routines.

• EGAMMA Gamma ray energy in keV.


• GFACTGyromagnetic factorsee ISTYPE Gyromagnetic factor =magnetic moment in units of nuclear magnetons. This is for theground state unless the ground state spin is zero; then it is theexcited state value.

• PARITY If .TRUE., then transition with parity change is assumed,otherwise no parity change. Will be set by program if ISTYPE isset to one of the pre-set isotopes (161Dy only = .TRUE.).

• IFSC For HAMILT = .TRUE.: a single crystal or oriented sampleis assumed. The angles BEX and GAX define the orientation of thegamma ray in the EFG basis system. If .FALSE., then a powdersample is assumed. If IFSC is set to .TRUE., then for example theangle BEX cab be used to calculate the magnetic texture.

• IFGK If HAMILT = .TRUE., then Goldanskii-Karyagin or textureeffects assumed. The coefficients G11 (dipole transition), or G21and G22 (quadrupole transition, ST = 2) or G11, G20, G21 andG22 (mixed transition, MIX > 0) describe the GK or texture co-efficients. These parameters replace the relative line depths A23,etc., used in the case of a sextet for the 3/2-1/2 transitions.

• SEX The excited state spin (0., 0.5, etc.) in units of h.(example:57Fe SEX = 1.5)

• SG The ground state spin in units of h. (example: 57Fe SG = 0.5)

• ST The smallest value of the gamma ray angular momentum inunits of h. ST = 1 (dipole) or ST = 2 (quadrupole; rare but seealso MIX if ST = 1). (example: 57Fe ST = 1.0)

Preset values of the nuclear constants used are given in 2.1 and 2.2.

• Temperature The absorber temperature. If zero, then this param-eter is ignored. Otherwise a Boltzmann distribution population iscalculated for the ground state sublevels and the line intensities ad-justed for this effect. Useful when the temperature is low comparedto the ground state splitting.


ISTYPE EGAMMA SG SEX PARITY GFACT GFR57Fe 14.413 1/2 3/2 0 0.090604 -0.571423119Sn 23.871 1/2 3/2 0 -1.0461 -0.20162197Au 77.345 3/2 1/2 0 0.1448 8.6186151Eu 21.532 5/2 7/2 0 3.465 0.53329121Sb 37.15 5/2 7/2 0 3.3591 0.52662127I 57.6 5/2 7/2 0 2.8091 0.64602129I 27.77 7/2 5/2 0 2.6174 1.4963

133Cs 80.997 7/2 5/2 0 -2.5786 -1.86947125Te 35.46 1/2 3/2 0 -0.8872 -0.22689867Zn 93.32 5/2 1/2 0 0.8755 3.29884161Dy 25.655 5/2 5/2 1 -0.479 -1.235128170Yb 84.2529 0 2 0 0.669 1237Np 59.54 5/2 5/2 1 2.51 0.53777

Table 2.1: Possible isotopes and hyperfine properties: I

Transmission integral parameters

The transmission integral assumes a non-polarised single-line source.

• Mode: If set to transmission, then the transmission integral willbe calculated in SITE (not in DIST!). The area parameter ARE isin units of effective absorber thickness (absorber thickness = TAB* ARE(i) for sub-spectrum i).

Note on the calibration of the sub-spectra for the plot: In the caseof a transmission integral, the sum of the sub-spectra does not equalthe theory spectrum. The normalisation for the plots is made asfollows. First the sub-spectra are normalised to the relative areain the thin absorber approximation: WDS * ARE * TAB * FSO.If then at any point the sum of the sub-spectra exceeds the theoryspectrum, then they are all re-scaled down (the sub-spectra). Thisavoids ’strange’ looking plots.

In addition, as of now, the transmission integral method is re-stricted to LINEAR velocity scales. If this is not the case, thenthe velocity scale can (and should) be linearised.

Isotropic EFG with magnetic field parameters

In the case of an isotropic distribution of VZZ directions in space, witha fixed external field BHF of given direction, the exact solution is alsoknown [4]. Variables are: WID(i), ARE(i), ISO(i), QUA(i), and BHF(i)as well as the angle RTH and asymmetry parameter ETA. The Gaussiandistribution can now be used as well.


ISTYPE QMR WID ST MIX PHS57Fe 1 0.194 1 0 0119Sn 1 0.647 1 0 0197Au 0 1.882 1 0.11 0151Eu 0.6272 1.31 1 0 0121Sb 6.491 2.1 1 0 0127I 0.4272 2.49 1 0 0129I 2.591 0.586 1 0 0

133Cs 0 (?) 0.535 1 0 0125Te 1 5.208 1 0 067Zn 0 0.00032 1 0 0161Dy 0 0.98551 0.378 1 0170Yb 1 2.02 2 0 0237Np 0.995 2.0 1 0 0

Table 2.2: Possible isotopes and hyperfine properties: II

• Sub-spectrum calculated assuming a fixed direction for the hyper-fine magnetic field, and an isotropic distribution of the EFG prin-ciple axis system. The parameter RTH is the angle between theGamma ray and BHF. In the case of an isotropic distribution ofBHF, use the magic angle RTH = 54.

2.2.2 Variable parameters

Variables which refer to the whole spectrum

• The background, in counts. This is always to be fitted, and thestarting value is normally that which is calculated internally. It isthe average of the first three and last three channels.

• BKi, i = 1, 4Coefficient of the power ith for the background cor-rection. Background function calculated from (Bki is BKi):

1 + Σi(Bki/1000) ∗ (Vi/V1)i

Transmission integral variables

The following three variables are for transmission integral fits only. Theyrefer to the source, and thus to the whole spectrum.

• FSO: Source Debye Waller factor.

Uncorrected source Debye Waller factor for transmission integralfits only. This is given by FSO = fso NM/Ntot where NM is theMossbauer counting rate, and Ntot is the total counting rate within


the pulse height spectrum window (both have to be measured off-resonance if correct fso values are to be calculated from FSO!

• TAB: Absorber thickness for transmission integral runs only.

The absorber thickness of each sub-spectrum will be calculatedfrom ARE(i) * TAB. ARE(1) should NOT be used as a variable,and should be equal to 1. For multi-sub-spectrum fits, ARE(2),etc can be used and are the relative effects for the sub-spectrumcompared to sub-spectrum 1. The total tab for the sample absorberis given by tab = TAB Σ ARE(i) over the sub-spectra.

• WDS:Source line width.Default value:WIDNAT/2

Hamiltonian fit variables

• PHS: Relative phase between the different gamma ray components(see MIX and ST). If there is mixed angular momentum compo-nents in the radiation, MIX > 0.0. Then if the absorber is a singlecrystal, PHS gives the relative phase.

Equal to ηl−ηL where l = radiation with larger angular momentum.Only useful for single crystal absorbers (see IFSC, BEX and GAX).Defined in the same way as in Equation 12 of the reference; see andensuing discussion.

• MIX: Amplitude of the mixed radiation component (see PHS andST).

Only useful for a single crystal absorber (see IFSC, PHS, BEX andGAX). PHS and MIX only have to be set for nonstandard isotopes.

• AKS: Interference term between internal conversion and photo-effect.

Leads to a skew-effect on the line form. Defined in the same wayas in Equation 7 of the reference. If AKS = 0 then and only thencan a VOIGT line profile be used!!

Hamiltonian: Excited state property variables

The following two parameters are used to calculate the magnetic dipoleand electric quadrupole splitting of the excited state from those for theground state. Normally these are known and held constant for the givenisotope.

• GFR: Ratio of the excited to ground state g-factors:

µe

µg

Sg

Se


If SEX = Se or SG = Sg is zero, then set GFR = 1.0. See BHF.GFR can only be a variable in the case of a Hamiltonian fit, but itis used in the case of 3/2-1/2 transitions for the magnetic sextetsor octets to calculate line positions.

• QMR: Ratio of the excited to ground state nuclear quadrupolefactors:

Qe

Qg

Sg(2Sg + 1)

Se(2Se + 1)

For SG = Sg is equal to 0 or to 1/2, then GFR = 1.0. See QUA.

Variables which refer to one sub-spectrum

Unless otherwise noted, in addition to the variables connected with a cer-tain method, WID(i), ARE(i), ISO(i), QUA(i), and BHF(i) are all rel-evant variables for one sub-spectrum. One exception is for transmissionintegral spectra, where ARE = 1 for the first sub-spectrum is constant(see page 25).

• WID: FWHM line width in mm/s.

If ISTYPE not a standard type, WID must be given a value, other-wise the default value will be the natural line width, depending onISTYPE. In the case of a transmission integral fit, WID(i) is theabsorber width. Otherwise, it is the sum of absorber and sourcewidths. The default value is adjusted for this.

• ARE: Resonant AREA in units of mm/s of the complete sub-spectrum.

In the case of a transmission integral, this is the effective absorberthickness for sub-spectrum i, and in relative units. The defaultvalue is taken from an estimation of the experimental spectrum,where the total area is estimated and then divided by the numberof sub-spectra. In most cases, this is a good starting value.

In the case of a transmission integral, then ARE(i) is a relativenumber, with ARE(1) = 1.0 a fixed value. See discussion on trans-mission integral.

• ISO: Isomer shift, in mm/s, with respect to the zero velocity of thesource (found from the folding routine).

• QUA:

1. For any sub-spectrum except singlet: Quadrupole splitting.

2. For HAMILT = .TRUE., given by eQVzz/2.


3. For NLINE = 2, given by DEQ = line separation.

4. For NLINE = 6, given by 2ε.

5. For NLINE = 8, given by eQVzz/2 (isotropic EFG with fixedBHF: EFGB = .TRUE.)

• BHF: Hyperfine magnetic field in Tesla.

3/2-1/2 transitions

In the case of a 3/2-1/2 transition, the lines are numbered 1 to 6 forsextets, 1 to 8 for octets. The lines are numbered according to the tran-sition:

3/2 state -3/2 -1/2 +1/2 +3/2 -3/2 -1/2 +1/2 +3/21/2 state -1/2 -1/2 -1/2 -1/2 +1/2 +1/2 -1/2 -1/2

line 1 2 3 8 7 4 5 6area 3 2 1 0 0 1 2 3

Table 2.3: Line numbering for 3/2-1/2 transitions

For the case of quadrupole doubles and magnetic sextets (and octets),in the case of the first-order perturbation fit (HAMILT = .FALSE.), thedifferent lines can have different line widths. These are controlled by therelative line widths using WID as the line width for line 1 (quadrupole)or line 3 (magnetic). The relative widths are given by W21, etc. Theseare given below.

Quadrupole sub-spectra: NLINE(i) = 2

• W21:Relative line width

Relative line width of line 2 with respect to line 1.

• A21:Relative area1.0

Relative area of line 2 with respect to line 1.

Magnetic sub-spectra: NLINE(i) = 6 or 8

• W13: Default = 1.0




Relative line widths of lines 1/6, 2/5 and 7/8 with respect to lines 3/4.For a sextet, W73(i) is set equal to 0.0, and cannot be fitted.

• A13: Default = 3.0



Relative areas of lines 1/6, 2/5 and 7/8 with respect to lines 3/4. For asextet, A73(i) is set equal to 0.0, and cannot be fitted.

Hamiltonian method variables

Here, QUA = eQVzz/2, so that the asymmetry parameter η is a separatevariable.

• ETA: Asymmetry parameter.

Option only for the cases of a Hamiltonian or a random EFG + field:Asymmetry parameter for the quadrupole effect. Defined in the usualway, but not limited to the range of 0 to 1. In the case that the fit-ted η lies outside this standard range, the co-ordinate system should betransformed.

Hamiltonian solution: angular variables

The orientation of the magnetic field BHF within the EFG basis systemis described by the angles RTH = θ and PHI = φ.

• RTH: Angle θ between the direction of the magnetic field BHFand VZZ, in degrees.

• PHI: Angle φ between the direction of Vxx and the magnetic fieldBHF. In degrees.

The orientation of the gamma ray within the EFG basis system is de-scribed by the angles BEX = β and GAX = γ. The third angle α is notspecified as this is a dummy parameter (non-polarised source ). To usethese angles, set IFSC = .TRUE. as well.

• BEX: Angle between the direction of VZZ and the gamma raydirection. In degrees.

• GAX: Angle between the direction of Vxx and the gamma ray di-rection. In degrees.


Hamiltonian: Goldanskii-Karyagin effect variables

If IFGK = .TRUE., then there are a series of Goldanskii-Karyagin coeffi-cients which describe the texture or the asymmetry of the Debye-Wallerfactor.

• G11

• G20

• G21

• G22

GlM parameter dipoleST = 1

quadrupoleST = 2

mixedMIX > 0

G11 X - XG20 - X X

G11,G22 - X X

Table 2.4: Goldanskii-Karyagin coefficients

X = this parameter can be used.

GlM = GlM can be written as:

1

2l + 1GlM =

∫ 2π

0dα

∫ 2π

0dγ

∫ π

0dβ sin β

DkMl(αβγ)DkM

l∗(αβγ)g(αβγ)g∗(αβγ)

In this expression, |g(αβγ)|2 is the recoilless fraction in the direction(αβγ). The rotation matrix elements are defined in the usual way:

DkMl(αβγ) = eikαdkM

l(β)eiMγ.

GlM is different from 1 for either texture in the sample, or anisotropy inthe recoilless fraction.

For a complete discussion of angular momentum addition, see the bookby Edmonds [3] which is exceptional in this area as it contains no errors.


Hamiltonian: Wegener relaxation variables

Two new variables are introduced for the Hamiltonian method only.

• ST2: Quadratic Wegener relaxation effect broadening on the linewidth.

The anomalous broadening ∆γij for the line from the nuclear transitionij is calculated as:

∆γij = (µimi/ji − µjmj/jj)2

⟨(∆B)2

⟩τ2

where⟨(∆B)2

⟩is the average square fluctuating field and τ2 is the atomic

spin fluctuation constant and ST2 =⟨(∆B)2

⟩τ2.

Ref: H. Wegener, Z. f. Physik 186 (1965) 498.

• ST3: Ternary Wegener relaxation shift of the line positions.

The anomalous line shift ∆δij for the line from the nuclear transition ijis calculated as:

∆δij = 2(µimi/ji − µjmj/jj)3

⟨(∆B)3

⟩τ3

similar to the line width broadening but depending on the cubed averagefield fluctuation

⟨(∆B)3

⟩and corresponding correlation time τ3. The fit

parameter ST3 = 2⟨(∆B)3

⟩τ3.

VOIGT line profile variables

There are three variable parameters which describe the Gaussian stan-dard deviations σ of BHF, VZZ and ISO. In the case of the first orderperturbation expression, the standard deviations of the line positions arecalculated directly. In the case of HAMILT = .TRUE., this is done bysolving the Hamiltonian (and so line positions) for σ-shifts in the vari-ables (i.e., for BHF + STG, for QUA + STQ, etc.), giving an exactexpression for the variation in line positions.

• STB:Gaussian width

Gaussian standard deviation of the proposed distribution of BHF.Units are in Tesla. The average value is of course, BHF. Can beused together with the other Gaussian widths. Old name was STG.

• STQ:Gaussian width

(Presently not included in Hamiltonian method. Replaced withST2 = Wegener anomalous line width contribution from magneticrelaxation.)

2.3. DIST &PARAM-NAMELIST 31

Gaussian standard deviation of the proposed distribution of theEFG. Units are in mm/s. The average value is of course, QUA. Canbe used together with the other Gaussian widths. For 2-line sub-spectrum, distribution of DEQ,; for a six-line sub-spectrum (1storder perturbation theory), distribution of 2ε, and for HAMILT =.TRUE., distribution of VZZ.

• STI:Gaussian width

(Presently not included in Hamiltonian method. Replaced withST3 = Wegener anomalous line shift contribution from magneticrelaxation.)

Gaussian standard deviation of the proposed distribution of ISO.Units are in mm/s. The average value is of course, ISO. Can beused together with the other Gaussian widths.

2.2.3 Special cases and routines: variables

Polarised-source spectra variables

(Presently not implemented but can be done on request. Will be includedin Version 3.0.)

EFGB routine variables

In addition to below, variables are: WID(i), ARE(i), ISO(i), QUA(i),and BHF(i). Note that QUA is equal to eQVzz/2.

• ETA:Asymmetry parameter

The asymmetry parameter. It is not assured that ETA is restrictedto the range of 0 to 1, so that care must be used when this parameteris allowed to vary.

• RTH:Angle θ

The angle θ between the gamma ray and the hyperfine magneticfield. Note that this is different from the θ = RTH defined forHAMILT = .TRUE.

2.3 DIST &PARAM-Namelist

2.3.1 Short list of parameters and variables

Fit parameter related to spectrum

• BKG Background counts

• BKi, i = 1, .. 4 Correction coefficients for baseline.


Constant parameters related to distribution blocks

• NSUB Number of sub-spectra to be included.

• NSB Number of sub-spectra in block i.

• WID Line width FWHM.

• A13 Relative area of lines 1 and 6 to 3 and 4.

• A73 Relative area of lines 7 and 8 to 3 and 4.

• ETA Asymmetry parameter for QUP.

• BHS Source magnetic field, polarised source.

Constant parameters related to distribution blocks: (DIST = 1only)

• LAMBDA Smoothing parameter (usually = 1).

• BETA1 Limits distribution values at lower limit.

• BETA2 Limits distribution values at upper limit.

Variable parameters related to distribution block(s)

• ISO Isomer shift (centner shift) of the first sub-spectrum.

• A23 Relative area lines 25 to 34.

• RTH Average value of θ in sin1 θ.

• QUA Quadrupole line shift. 2ε.

• DTQ Quadrupole change pro sub-spectrum.

• DTI Isomer shift change pro sub-spectrum.

• STI Standard deviation of the isomer shift distribution.

• AVG Average field for DISTRI = Gaussian

• STG Standard deviation.

• BHF Starting hyperfine field.

• DTB Change in hyperfine field pro sub-spectrum.

Constants related to the crystalline sub-spectra

• NXLS Number of crystalline sub-spectra.


Variables related to the crystalline sub-spectra

• ARX Resonant area of the sub-spectrum in units of mm/s.

• ISX Isomer shift (centner shift).

• WIX FWHM line width.

• A2X Area 2nd to the 1st line for a quadrupole sub-spectrum or tothe 3rd for a magnetic sextet.

• QUX Quadrupole line shift. (equals DEQ for doublet, or 2ε forsextet).

• A1X Area 1st to 3rd line for sextet only.

• BHX Magnetic hyperfine field.

2.3.2 Long list of parameters and variables

Constant parameters

The DOS-program METHOD parameter is the method of calculating theLine profile.

• METHOD = Hyperfine field distribution: fast fit using only verysimple asymmetry. Basically a histogram of sextets, with a possi-ble linear change in isomer shift. EXACT = .TRUE. now works(distribution of octets): includes line position, width and area cor-rections for random EFG only, in the variable QUP (QUA is theline shift).

• METHOD = Asymmetry: Fit using asymmetry correlation pa-rameters from the limit of very small asymmetry try (Brand et al.1983). Either CONC or PROB(i) must be set in order to calculatethe correlation corrections. See IMETHOD = B&C Asymmetry aswell. This method is only correct when the asymmetry is smallerthan the line width.

• METHOD = B&C Asymmetry: Fit using the expression from Bil-lard and Chamberod [6] for the asymmetry parameters. The sumover next neighbours is explicitly calculated, while the average overangular orientation is simulated using the approximate expressiongiven by Billard and Chamberod. Either CONC or PROB(i) mustbe set in order to calculate the averages. The effective standard de-viation of the line width for a configuration of p nearest neighboursis S2(p) = p*(12p)/22, where p = number nearest neighbours 0, 1,2 .. 12:


STD(p) = WID*SQRT(1+S2*(H2P+QUP)**2/WID).

In this way, the pseudo-Voigt line form is used. This is an improve-ment over the expression used in Billard and Chamberod, who useLorentzian form lines [6].

The program DIST now has the possibility to have as inputs boththe fields PROB and the structure factors S2, which are used inthe asymmetrical calculations, METHOD = Asymmetry or B&CAsymmetry.

• METHOD = Polarised source:

(Presently not implemented but can be done on request. Will beincluded in Version 3.0.)

Simple hyperfine distribution using a magnetic polarised source.THETAS and PHIS are the angles between gamma ray and thesource hyperfine field vector, BHS is the source hyperfine field. EX-ACT can be used. See SITE for an explanation of the spin texturecoefficients D10 and D20. (The coefficients D2P and D2N have notbeen implemented here as yet.)

• METHOD = Doublet distribution: simple quadrupole distribution.QUA is used as the starting quadrupole value, and sub-spectra arecalculated in steps of DTQ. Similar to METHOD = Hyperfine fielddistribution, except for quadrupole sub-spectra.

The old DOS-parameter DISTRI is the type of distribution profile used.

• DISTRI = Histogram:

Histogram method. Sub-spectra relative areas are calculated us-ing linear regression plus damping. Either magnetic or quadrupolesub-spectra can be calculated. Smoothing parameters LAMBDA,BETA1 and BETA2 are effective.

• DISTRI = other than Histogram:

Different types of distributions with fixed form are possible. Inthese methods, the histogram step width can also be varied. Sincein this case, a distribution width smaller than the step width mustbe avoided, the value of the standard deviation used is adjusted inorder to avoid a narrower distribution than the step width used inthe histogram. The real standard deviation is calculated from:

√STG2 + DTX2

where DTX is either DTB for magnetic histograms, or DTQ forquadrupole histograms.


• DISTRI = Gaussian: Gauss method.

Relative sub-spectra areas are calculated using the Gauss distribu-tion:

P (x)dx =dx√2πσ

exp

−1

2

[x− 〈x〉

σ

]2

where for magnetic distributions, 〈x〉 = 〈Bhf〉, for quadrupole dis-tributions, DEQ and for isomer shift distributions, ISO. The pa-rameter used is AVG. For the standard deviation of BHF, DEQor ISO, σ, STG is used.

For the case of a quadrupole distribution, it is possible to include asymmetrical negative Gauss distribution of relative height PNEG:

P (x)dx =

dx√2πσ

(1− Pn) exp

−1

2

[x− 〈x〉

σ

]2

+Pn exp

−1

2

[x + 〈x〉

σ

]2

where P − n is given by the parameter PNEG.

• DISTRI = Fixed is a new distribution method. NOT YET IN-STALLED.

The relative distribution is held fixed, and only the position andtotal area are changed. The lower limit is defined by BHF forIMETHOD = B&C Asymmetry, or QUA for IMETHOD = Doubletdistribution or 7. In order to allow the lower limit to vary in theformer case, there is now a new parameter BHFFIT(i), which ifset .TRUE., will allow this point to vary. The profile is input inthe variable AREREL(i), i = 1, .. NSUB for a single distributionblock, or i = 1, .. NSB(k) for the k’th block. If CONC > 0 andDISTRI = Fixed (fixed distribution method), AREREL(i) will becalculated for a binomial distribution, where in the case of severaldistribution blocks, this will be taken to be the same in all blocks.

• DISTRI = Random quadrupole

(Presently not implemented but can be done on request. Will beincluded in Version 3.0.)


DISTRI = Histogram: pure histogram only

• LAMBDA: Smoothing parameter

Smoothing parameter which should usually be set to 1.0. The spec-trum is fitted with an additional condition on the change in slopeof the distribution. The larger LAMBDA is, the smoother is thedistribution found, but the poorer is the fit. As a criterion forLAMBDA, the Hesse Rubartsch parameter [7] should not be toomuch larger than 1 (see results printout: the Hesse - Rubartsch pa-rameter is approximately equal to the χ2 fit criterion). Only usedfor DISTRI = Histogram.

If several distribution blocks are being used to fit the spectrum, andLAMBDA(2) has not been set by user, the same value will be usedas in the first block. (The same holds for BETA1 and BETA2.)

• BETA1: Lower edge of P(x)

This parameter minimises the area of the first sub-spectrum of thei’th distribution block. This makes the distribution to go smoothlyto zero at the beginning.

• BETA2: Upper edge of P(x)

This parameter minimises the area of the last sub-spectrum in thei’th distribution block. This makes the distribution go to zerosmoothly at the upper edge.

• VOIGT: Voigt line profile

If nonzero, then Voigt profile calculated for the line form, usingWID as the Lorentzian line width, and STD as the Gaussian stan-dard deviation.

Variables referring to the spectrum

• BKG: Background counts.

• BK1 .. BK4: Coefficients

Coefficient of the power i for the background correction. Back-ground function calculated from (Bi is BKi):

1 + Σi(Bi/1000) ∗ (Vi/V1)i

Variables referring to a certain block i

• A23: Area ratio

Relative line areas lines 2 and 7 to lines 3 and 6.


• RTH:⟨sin2 θ

⟩

⟨sin2 θ

⟩is used as the relative line area parameter.

• ISO: Isomer shift

Centner shift (Isomer shift) of the first sub-spectrum in the distri-bution block.

• DTI: Isomer shift change

Isomer shift change pro sub-spectrum. Can be used for magneticand quadrupole splitting to change the isomer shift for each sub-spectrum. For isomer shift distributions, DTI is the change inisomer shift pro sub-spectrum. In the case of DISTRI = Fixed,this can be set as variable.

• STI: Standard deviation

Standard deviation of the isomer shift distribution. A Gaussianform is assumed, and spectra added at isomer shifts which are givenby ISO ± n*STI where n = 0, 1, 2 and ISO is the average isomershift.

• QUA: Quadruple line shift

First order quadrupole line shift 2ε in mm/s.

• DTQ: Quadrupole shift change

Quadrupole line splitting change pro sub-spectrum. Used for quadrupolesplitting distributions only.

• BHF: Starting BHF

For magnetic hyperfine field distributions, this is the starting fieldfor distribution block i.

• DTB: BHF change

Hyperfine field step pro sub-spectrum.

• STD: Standard deviation

Standard deviation of the Gaussian form in the VOIGT-profile. Formagnetic sub-spectra, units used are Tesla, otherwise in mm/s.

Parameters related to the asymmetry effects

Correlation between the magnetic hyperfine field and the local isomershift:(Presently not implemented but can be done on request. Will be includedin Version 3.0.)


Gaussian distribution

• AVG: Average hyperfine effect

For the Gaussian, Czjzek or Le Caer distributions only. The unitsdepend on the method (Tesla for magnetic, and mm/s for quadrupoledistribution)

• STG: Standard deviation

Standard deviation of the Gaussian distribution (in units of Teslaor mm/s). Also used in the Czjzek and Le Caer distributions as thedistribution width parameter (units mm/s). Note the difference toSTD: STD is the standard deviation used in calculating the lineform, and STG is that used in calculating the distribution form.

Polarised magnetic spectrum

(Presently not implemented but can be done on request. Will be includedin Version 3.0.)

Parameters for crystalline sub-spectra

• NXLS: Number of crystalline sites

Number of crystalline sites to be considered.

• XLS type: Type of sub-spectrum.

Number of lines of the crystalline sub-spectrum i. Allowed arevalues of singlet, doublet and sextet.

Variables for crystalline sub-spectra

• ISX: Isomer shift

Isomer shift of the i’th crystalline sub-spectrum.

• WIX: Line width

Line width (FWHM) of the i’th crystalline sub-spectrum.

• STX: Standard deviation

If STX non-zero, standard deviation of the Gaussian form in theVOIGT-profile. For magnetic sub-spectra, in Tesla, otherwise inmm/s.

• A2X: Relative line area

Relative area of the line 2 / line 3 (6 line magnetic sub-spectrum),or line 2/line 1 (2 line quadrupole sub-spectra).


• QUX: Quadrupole effect

Quadrupole line shift of the i’th crystalline sub-spectrum. Equalto DEQ for doublets, 2ε for sextets.

• D1X: Relative area

Relative line area of line 1 / line 3 for 6-line magnetic sub-spectra.

• BHX: Hyperfine field BHF

Hyperfine field BHF of the i’th crystalline sub-spectrum.

• ARX: Area

Area of the i’th crystalline sub-spectrum, in units of mm/s.


Bibliography

[1] J. Pelloth et al., Phys. Rev. B 52 (1995) 15372.

[2] Mossbauer Isomer Shifts, eds. G.K. Shenoy and F.E. Wagner (NorthHolland Amsterdam 1978).

[3] A.R. Edmonds, Angular Momentum in Quantum Mechanics(Princeton University Press, Princeton 1974)

[4] Blaes et al. Nucl. Instr. and Methods B9 (1985) 201.

[5] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling,Numerical Recipes, The Art of Scientific Computing (CambridgeUniversity Press)

[6] Billard and Chamberod, Solid State Comm., 17 (1975) 113.

[7] J. Hesse et al., J. Physique Coll. 40 C2 161.

[8] R.A. Brand et al., J. Phys. F 13 (1983) 675.

[9] R.A. Brand, Nuclear Instruments and Methods B, 28 (1987) 398,and ibid., 417.

[10] A. Mohammad Djafari and G. Demoment, Applied Optics, 26 1987.

[11] The Maximum Entropy Formalism, eds. R.D. Levine and M. Tribus,(MIT Press 1978).

[12] R.A. Brand and G. Le Caer, Nuclear Instruments and Methods B34 (1988) 272.

[13] J.N. Kapur and H.K. Kesavan, Entropy Optimization Principles andApplications (Academic Press Boston 1992)

[14] Maximum Entropy in Action, eds. B. Buck and V.A. Macaulay (Ox-ford University Press 1992).

[15] D.S. Sivia, Data Analysis: A Bayesian Tutorial (Oxford UniversityPress 1996).

41

42 BIBLIOGRAPHY

[16] G. Larry Bretthorst, Bayesian Spectrum Analysis andParameter Estimation, in Lecture Notes in Statis-tics Vol. 48 (Springer Verlag Berlin 1988), availableon the WWW at htp://www.astro.psu.edu/statcodes/ andhtp://astro.tu.cornell/staff/loredo/bayes

[17] E.T. Jaynes, Probability Theory: The Logic of Sci-ence to be published, actual version available onthe WWW at htp://www.astro.psu.edu/statcodes/ andhtp://astro.tu.cornell/staff/loredo/bayes

[18] R. Fletcher, Practical Methods of Optimization 1 and 2, (Wiley,1980).

[19] Michael Metcalf, Fortran Optimization (Academic Press 1982).

[20] W.I.F. David, J. Appl. Cryst. 19 (1986) 63.

[21] K. Ruebenbauer and T. Birchall, Hyperfine Interactions, 7 (1979)125.

[22] G.K. Shenoy et al. in Mossbauer Effect Methodology vol. 9 (PlenumPress) 277.

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