1 / 40

Zoltán Klencsár

TRANSMISSION INTEGRAL ANALYSIS OF MÖSSBAUER SPECTRA DISPLAYING HYPERFINE PARAMETER DISTRIBUTIONS WITH ARBITRARY PROFILE. Zoltán Klencsár. Budapest, Hungary. http://www.mosswinn.hu. z.klencsar@mosswinn.hu. MSMS 201 4 - Hlohovec u Břeclavi – Czech Republic 26-30 May, 2014.

carney
Download Presentation

Zoltán Klencsár

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. TRANSMISSION INTEGRAL ANALYSIS OF MÖSSBAUER SPECTRA DISPLAYING HYPERFINE PARAMETER DISTRIBUTIONS WITH ARBITRARY PROFILE ZoltánKlencsár Budapest, Hungary http://www.mosswinn.hu z.klencsar@mosswinn.hu MSMS 2014- Hlohovec u Břeclavi – Czech Republic 26-30 May, 2014

  2. Aim: tocombinethecalculation of arbitraryprofilehyperfineparameterdistributionswithtransmissionintegralfitting

  3. Outline • Introductioneffectivethickness, thicknesseffects, transmissionintegral • The problem of combiningarbitraryprofiledistributioncalculationmethodswithtransmissionintegralfitting • Solution of theproblem, algorithmworkflow • Test cases, demonstration of thecapabilitiesofthealgorithm • Relatedissuesinthe MossWinn program

  4. Introduction „The broadening of an absorption line in the Mossbauer effect due to finite absorber thickness has first been treated by W.M.Visscher (unpublished notes).” H. Frauenfelder: The Mössbauer Effect, New York: W.A. Benjamin, Inc., 1962 The shape of the Mössbauerspectrumto be expected in a transmission-type experimentwastreatedbyMargulies et al. forvariousexperimentalconditionsincludingthick and thinas well as split and unsplitsource and absorber: S. Margulies, J.R. Ehrman, Nucl. Instr. Meth.12, 131-137 (1961). S. Margulies, P. Debrunner, H. Frauenfelder, Nucl. Instr. Meth.21, 217-231 (1963). The thickness dependence of the apparent Mössbauer line / spectrum parameters were widely investigated and approximate formulas were derived among others for line intensity and line width parameters. See, e.g., J.M. Williams, J.S. Brooks, Nucl. Instr. Meth.128, 363-372 (1975). and references therein.

  5. 1. H. Frauenfelder, The Mössbauer Effect, New York: W.A. Benjamin, Inc., 1962, pp. 45- 2. S. Margulies, J.R. Ehrman, Nucl. Instr. Meth.12, 131-137 (1961). 3. R.E. Meads, B.M. Place, F.W.D. Woodhams, R.C. Clark, Nucl. Instr. Meth.98, 29-35 (1972). 4. S.A. Wender, N. Hershkowitz, Nucl. Instr. Meth.98, 105-107 (1972). 5. N. Hershkowitz, R.D. Ruth, S.A. Wender, A.B. Carpenter, Nucl. Instr. Meth.102, 205-217 (1972). 6. G. Hembree, D.C. Price, Nucl. Instr. Meth.108, 99-106 (1973). 7. G.K. Shenoy, J.M. Friedt, Phys. Rev. Lett.31, 419-422 (1973). 8. G.K. Shenoy, J.M. Friedt, Nucl. Instr. Meth.116, 573-578 (1974). 9. S. Mørup, E. Both, Nucl. Instr. Meth.124, 445-448 (1975). 10. R. Zimmermann, R. Doerfler, Hyperfine Interactions12, 79-93 (1982) 11. D. Gryffroy, R.E. Vandenberghe, Nucl. Instr. Meth.207, 455-458 (1983). 12. O. Ballet, Hyperfine Interactions23 (1985) 133-177. 13. D.G. Rancourt, Nucl. Instr. Meth. Phys. Res. B 44, 199-210 (1989). 14. S. Margulies, P. Debrunner, H. Frauenfelder, Nucl. Instr. Meth.21, 217-231 (1963). 15. J.D. Bowman, E. Kankeleit, E.N. Kaufmann, B. Persson, Nucl. Instr. Meth.50, 13-21 (1967). 16. J. Heberle, Nucl. Instr. Meth.58, 90-92 (1968). 17. B.T. Cleveland, J. Heberle, Physics Letters36A, 33-34 (1971). 18. J.M. Williams, J.S. Brooks, Nucl. Instr. Meth.128, 363-372 (1975). 19. P. Jernberg, Nucl. Instr. Meth.B4, 412-420 (1984). 20. J.G. Mullen, A. Djedid, G. Schupp, D. Cowan, Y. Cao, M.L. Crow, W.B. Yelon, Phys. Rev. B37, 3226-3245 (1988). 21. J.G. Mullen, A. Djedid, D. Cowan, G. Schupp, M.L. Crow, Y. Cao, W.B. Yelon, Physics Letters A127, 242-246 (1988). 22. M.C. Dibar-Ure, P.A. Flinn, A Technique for the Removal of the “Blackness” Distortion of Mössbauer Spectra, in Mössbauer Effect Methodology 7, edited by I.J. Gruverman, New York–London: Plenum Press, 1971, pp. 245-262. 23. T-M. Lin, R.S. Preston, Comparison of Techniques for Folding and Unfolding Mössbauer Spectra for Data Analysis, in Mössbauer Effect Methodology 9, edited by I.J. Gruverman, C.W. Seidel, D.K. Dieterly, New York–London: Plenum Press, 1974, pp. 205-224. 24. G.K. Shenoy, J.M. Friedt, H. Maletta, S.L. Ruby, Curve Fitting and the Transmission Integral: Warnings and Suggestions, in Mössbauer Effect Methodology 9, edited by I.J. Gruverman, C.W. Seidel, D.K. Dieterly, New York–London: Plenum Press, 1974, pp. 277-305. 25. D.L. Nagy, Physical and Technical Bases of Mössbauer Spectroscopy, in Mössbauer Spectroscopy of Frozen Solutions, edited by A. Vértes & D.L. Nagy, Budapest: AkadémiaiKiadó, 1990, pp. 34-39. 27. S.S. Hanna, R.S. Preston: Phys. Rev.139, A722-725 (1965). 28. R.M. Housley, R.W. Grant, U. Gonser: Phys. Rev.178, 514-522 (1969). 29. J.M. Williams, J.S. Brooks: Nucl. Instr. Meth.128, 363-372 (1975). 30. U. Gonser, H. Fischer: Hyp. Int.72, 31-44 (1992).

  6. The effective thickness, t Surfacenumberdensity (in 1/cm2) of Mössbauer nuclei, e.g. 57Fe. the probability of recoilless nuclear resonance absorption of resonant g radiation by Mössbauer nuclei in the absorber. Maximum cross section for the resonant absorption per Mössbauer nucleus (e.g. 0 ≈ 25610−20 cm2 for 57Fe). • Ieand Ig are the nuclear spin quantum numbers of the excited and ground state of the Mössbauer transition, •  = /2where is the wavelength of the resonant radiation,and • is the internal conversion coefficient associated with the nuclear transition.

  7. Effective thickness, t “Clearly, the thin absorber limit will not normally be valid in Fe-57 work.” D.G. Rancourt: Nucl. Instr. Meth. Phys. Res. B 44, 199-210 (1989). Thin absorber approximation is considered to be valid. ( t < 1 ) Natural Fe surface density,mg / cm2

  8. Typical thickness effects • Compared to the thin absorber case: • broadening of lines • change of relative line widths • change of relative line intensities • change of relative line amplitudes • change of relative subspectrum areas (in case of multiple components) • change of line shape profile Transmission thin thick (t = 20)

  9. For s = a = 0: • Considering the 57Fe Mössbauer spectrum of a random powder sample displaying a full-blown sextet, the six individual absorption peaks “share” the total  effective thickness in proportion to their “ideal” thin-absorber intensity ratios, and in the absence of polarization effects they display intensity and peak width values that to a good approximation correspond to the effective thicknesses 1,6 = 3/12, 2,5 = 2 /12 and 3,4 = /12 for the 1-6, 2-5 and 3-4 peaks of the sextet, respectively.  = 8 I0 and I1 denote modified Bessel functions of the first kind: (see, e.g., D.L. Nagy, Physical and Technical Bases of Mössbauer Spectroscopy, in Mössbauer Spectroscopy of Frozen Solutions, edited by A. Vértes & D.L. Nagy, Budapest: Akadémiai Kiadó, 1990, pp. 34-39.)

  10. The transmission integral absorption shape Mössbauerradiation emittedfromthesourcewith recoil. (non-resonant) mass absorption Mössbauer  radiation emitted from the source without recoil, subject to nuclear resonant absorption. The counts of the experimental spectrum will scatter around the curve: Background fraction of detected countsduetoradiationotherthantheMössbauerradiationemittedfromthesource (e.g. X-rays, -raysadmittedthroughthe SCA window). Baseline For Lorentzian as well as forsplit and/ornon-Lorentzian absorption shapes: • Scope: • - Thin, single-line, unpolarized source. • Unpolarized, uniform absorber (or polarization and granularity effects may be neglected) R.M. Housley, R.W. Grant, U. Gonser: Phys. Rev.178, 514-522 (1969). J.D. Bowman, E. Kankeleit, E.N. Kaufmann, B. Persson: Nucl. Instr. Meth.50, 13-21 (1967). Natural line width of the Mössbauer transition. (e.g. G0= 0.097 mm/s for 57Fe) G.K. Shenoy, J.M. Friedt, H. Maletta, S.L. Ruby, Curve Fitting and the Transmission Integral: Warnings and Suggestions, in Mössbauer Effect Methodology 9, edited by I.J. Gruverman, C.W. Seidel, D.K. Dieterly, New York–London: Plenum Press, 1974, pp. 277-305.

  11. To calculate the transmission integral weneed to be able to calculate An(u): • This is straightforward for • models for crystalline phases („crystalline subspectra”) that can be fully parameterized, i.e. their shape is fully determined by the corresponding elements of the parameter vector p under evaluation. • But how to handle hyperfine parameter distributions? • Assume a certain shape for the distribution, e.g. Gaussian, binomial etc., that can be fully parameterized just like a crystalline subspectrum. Use one of the “model-independent” distribution evaluation methods, that make use of the measured spectrum data to derive arbitrary profile distributions. B. Window, J. Phys. E: Sci. Instrum.4, 401-402 (1971). J. Hesse, A. Rübartsch, J. Phys. E: Sci. Instrum.7, 526-532 (1974). G. Le Caër, J.M. Dubois, J. Phys. E: Sci. Instrum.12, 1083-1090 (1979). C. Wivel, S. Mørup, J. Phys. E: Sci. Instrum.14, 605-610 (1981). L. Dou, R.J.W. Hodgson, D.G. Rancourt, Nucl. Instr. Meth.Phys. Res.B100, 511-518 (1995). There is a problem though: all of these methods assume that the measured spectrum can be modeled with a fit envelope calculated as the weighted sum of elementary subspectra, and make use of the measured spectrum data accordingly in order to derive the elementary subspectrum weights in question. Such use of the measured data is not justified when the spectrum is subject to thickness effects. • But what if the distribution shape is not known in advance? • Do successive approximation by adding up more and more of the fully parameterized distributions, and hope that their shape is suitable for a fast convergence, or …

  12. Use one of the “model-independent” distribution evaluation methods, that make use of the measured spectrum data to derive arbitrary profile distributions. B. Window, J. Phys. E: Sci. Instrum.4, 401-402 (1971). J. Hesse, A. Rübartsch, J. Phys. E: Sci. Instrum.7, 526-532 (1974). G. Le Caër, J.M. Dubois, J. Phys. E: Sci. Instrum.12, 1083-1090 (1979). C. Wivel, S. Mørup, J. Phys. E: Sci. Instrum.14, 605-610 (1981). L. Dou, R.J.W. Hodgson, D.G. Rancourt, Nucl. Instr. Meth.Phys. Res.B100, 511-518 (1995). Hesse & Rübartsch: Smoothing matrix

  13. A possible general solution to the problem of thickness effects: Extract and fit the absorption shape: An(u) M.C. Dibar-Ure, P.A. Flinn, A Technique for the Removal of the “Blackness” Distortion of Mössbauer Spectra, in Mössbauer Effect Methodology 7, edited by I.J. Gruverman, New York–London: Plenum Press, 1971, pp. 245-262. - used discrete Fourier transformation (FFT) - in conjunction with Gaussian noise filtering - to extract the An(u) absorption shape from spectra. D.G. Rancourt, Accurate Site Populations From Mössbauer Spectroscopy, Nucl. Instr. Meth. Phys. Res. B 44, 199-210 (1989). - suggested a clever (fitting-based) noise filtering and deconvolution procedure to extract t An(u) from spectra without numerical calculation of the Fourier transform of measured data.

  14. A possible general solution to the problem of thickness effects: Extract and fit the absorption shape: An(u) • Problems • The selection of the noise filter function has a degree of arbitrariness. • No clue concerning the “best” filter function for a particular spectrum & fit problem. • The effect of the unwanted spectral deformation/broadening (appearing in An(u) due to the combined effect of the deconvolution and noise filtering) on the final fit parameters is dubious. • The deconvolution and noise filtering will change the spectrum and statistics of the spectral noise, whose effect on the final fit parameters is dubious. Fitting of An(u) is not an optimal solution.

  15. Measurement, or a quantity calculated on the basis of the measurement. Theoretical quantity that can be calculated with arbitrary precision. Doppler velocity values corresponding to the actual measured counts. 2k equidistantly spaced velocity values. (2048)

  16. range of wj > range of vi P D.L. Nagy, U. Röhlich, Hyp. Int.66, 105-126 (1991). An extension of the H-R distribution calculation method to the case of thick absorbers. Subtract crystalline Hesse & Rübartsch ℱ−1 = 1exp(Ãn(wj)) Interpolation Convolution

  17. Preparation of test spectra t = 5, 10, 20, 30, 40, 50 b = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.95 Spectra with singlet: t = 5, 10, 20, 30, 40, 50 b = 0.8 • To examine the effectiveness of the outlined algorithm, a typical 57Fe hyperfine magnetic field distribution, sampled in 70 equidistantly distributed points spanning the range of 0…35 T, was created by the addition of three Gaussians, and corresponding N(vi) 57Fe Mössbauer spectra were created for various values of b and  by calculating the transmission integral via direct numerical integration with a relative precision of 10−8. Sextets with equal (a = 0.097 mm/s) line widths and relative line areas of 3:2:1:1:2:3 were used as the elementary pattern of the distribution, with a correlation ( = 0.4 mm/s − 0.02 mms−1 T−1 Bhf) between the isomer shift  and hyperfine magnetic field (Bhf), and with zero quadrupole splitting. The single-line Mössbauer source was assumed to have a recoilless fraction of fs = 0.7 and a line width of ΓS = 0.11 mm/s. • Model spectra were then created by adding normally distributed random spectral noise to the spectra. Whereas the N() = 106 baseline and therefore the variance of the noise distribution are the same in all of the spectra, the S/N ratio of the Mössbauer signal depends on b as well as on . The algorithm, as realized in the MossWinn program, was used to fit the spectra by fixing the (above given) theoretical value for all the parameters in p with the exception of fc,r (“Filter cutoff”) and l (“Smoothing factor”). These were fitted to their optimal values that provided the lowest 2. t = 20, b = 0.8

  18. range of wj > range of vi Subtract crystalline Hesse & Rübartsch ℱ−1 = 1exp(Ãn(wj)) Interpolation Convolution

  19. AlgorithmWorkflow Stages Ãn(wj) An(wj) under- smoothed over- smoothed

  20. Optimal value of the cutoff frequency Ãn(wj) An(wj)  = 10, b = 0.3 GIF animations were created with http://gifmaker.me/

  21. Automatic adaptation to the S/N ratio

  22. Ãn(wj) An(wj)

  23. Optimal S/N Ratio of Ãn(w)  = 5, b = 0.1  = 5, b = 0.9

  24. Broadening due to filtering The effect of the relative cutoff frequency of the applied filter function (with Gs = 0.11 mm/s) on the width of a Gaussian with original FWHM of GG = 0.1 mm/s. Q(f) filter before filtering after filtering I. Vincze, Nucl. Instr. Meth.199, 247-262 (1982). GG (FWHM) For S/N = 16 … 64 : GG≳ Gs fc,r = fc / (250 s/mm)

  25. Effect of the cutoff frequency fc,r(optimal)  0.27

  26. The effect of the number of distribution data points (t = 10, b=0.8) t = 10 b = 0.8 n, Number of distribution data points n, Number of distribution data points

  27. The effect of the number of distribution data points (t = 40, b=0.9) t = 40 b = 0.9 n, Number of distribution data points n, Number of distribution data points

  28. Comparison of results obtained with thin absorber approximation and with transmission integral fitting • Distribution shape • Relative area fraction of the crystalline component • Goodness of the fit t = 5, 10, 20, 30, 40, 50 b = 0.8 singlet

  29. t = 5 t = 10 t = 20 t = 30 t = 40 t = 50 b = 0.8 Thin absorber approximation

  30. t = 5 t = 10 t = 20 t = 30 t = 40 t = 50 b = 0.8 Transmission integral

  31. Thin absorber approximation Transmission integral Fit result Theory b = 0.8

  32. Transmission integral Thin absorber approximation

  33. Handling unfolded spectra

  34. How to take into account both parts of an unfolded spectrum Ũ- +(wj) Ũ- +(wj) + Ũ+ -(wj) Ũ+ -(wj) 2

  35. Fitting unfolded spectra

  36. Mössbauer line sharpening where for 57Fe Distribution of singlets. includesneitherthesourcenortheabsorberintrinsic line width.

  37. t = 40, b = 0.6 t = 5, b = 0.2 t = 20, b = 0.5 t = 5, b = 0.2 t = 20, b = 0.5 t = 40, b = 0.6

  38. t = 20, b = 0.8 t = 20, b = 0.8 t = 20, b = 0.8 singlet t = 20, b = 0.5

  39. The algorithm can be applied… • for 57Fe as well as other Mössbauernuclidesavailablein MossWinn. • to fit multiple distributions to the same spectrum. • with various elementary patterns selected for the distribution, including patterns calculated via the numerical diagonalization of the static Hamiltonian for powder samples, as well as patterns displaying dynamic (relaxation) effects. • in conjunction with the simultaneous fitting of several spectra allowing the application of constraints among the distribution and transmission integral parameters associated with the spectra fitted together.

  40. Conclusions • An algorithm has been developed that successfully combines the model-independent distribution evaluation method of Hesse and Rübartsch with the calculation of the transmission integral for unpolarized absorbers, and enables the extraction of arbitrary-profile hyperfine parameter distributions from Mössbauer spectra of thin as well as of thick samples. • An automatic treatment of noise filtering was successfully realized on one hand by binding the cutoff steepness of the applied filter function to the FWHM width of the source Lorentzian, on the other hand by treating the filter’s  relative  cutoff frequency as a fit parameter. • As the algorithm handles the required noise filtering quasi automatically, the fit of arbitrary-profile hyperfine parameter distributions to Mössbauer spectra of unpolarized thick absorbers becomes straightforward in practice.

More Related