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Pavol Jozef Šafárik University in Košice, Faculty of Science

Pavol Jozef Šafárik University in Košice, Faculty of Science. Supportive Textbooks in Course: Methods of Condensed Matter Spectroscopy – M ö ssbauer Spectroscopy Teacher: Pavol Petrovič Study programme: Physics of Condensed Matter The ESF project no. SOP HR 2005/NP1-051 , 11230100466.

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Pavol Jozef Šafárik University in Košice, Faculty of Science

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  1. Pavol Jozef Šafárik University in Košice, Faculty of Science Supportive Textbooks in Course: Methods of Condensed Matter Spectroscopy – Mössbauer Spectroscopy Teacher: Pavol Petrovič Study programme: Physics of Condensed Matter The ESF project no. SOP HR 2005/NP1-051, 11230100466 The project is cofinanced with the support of the European Union

  2. Contents of shortened instructional materials Physical principles of the Mössbauer effect. Methodology of experiments. Hyperfine interactions - electrical monopole, electrical quadrupole and magnetic dipole interactions. Physical information involved in hyperfine spectrum parameters. Processig and evaluation of Mössbauer spectra. Results obtained at the study of properties of new materials by means of Mössbauer spectroscopy. Note: all spectra presented in the abridged materials have been published in scientific publications in which the author of these materials has participated as an coauthor.

  3. Recommended references • Dickson D.P.E, Berry F.J.: Mössbauer Spectroscopy. Cambridge University Press, Cambridge, 1986. • Goldanskij V.I., Herber R.H.: Chemical Applications of Mössbauer Spectroscopy. Academic Press, New York, 1968. • Gonser U.: Mössbauer Spectroscopy. Springer Verlag, Berlin, 1975. • Long G.J., Grandjean F.: Mössbauer SpectroscopyApplied to Magnetism and Materials Science. Vol. 2. Plenum Press, New York, 1996. • Maddock A.G.: Mössbauer Spectroscopy. Principles and Applications of the Techniques. Horwood Publishing, Chichester, 1997. • Ovchinnikov V.V.: Mössbauer Analysis of the Atomic and Magnetic Structure of Alloys. Cambridge Inter. Sci. Publ., Cambridge, 2006. • Vértes A., Korecz L. Burger K.: Mössbauer Spectroscopy. Akadémiai Kiadó, Budapest, 1979. • Wertheim G.K.: MössbauerEffect – Principles and Applications. Academic Press, New York, 1964.

  4. Nuclear resonance fluorescence The process of nuclear resonance absorption followed by the nuclear resonance emission of  - radiation. Nuclear resonance fluorescence – the method of investigating condensed matter. Preferences of the method: • deep penetration of -radiation into condensed substances, • small relative width of absorption and emission lines, • high spectrum parameters sensitivity to the internal and external factors of the examined substance.

  5. The nature width of absorption/emission line Heisenberg uncertainty principle: - inaccuracy in measuring energy, - time interval disposed to the measurement of one energy value, - modified Planck´s constant. Basic energetic nucleus state: Excited nucleus state: Γ– natural width of absorption/emission line

  6. L(W) 1  1/2 W W0 W0 -/2W0 + /2 Analytical form of elementary absorption/emission line Dependence of the number of emitted/absorbed γ-quanta by certain isotope per time unit on energy or frequency of γ-radiation. Lorentz shape: C L(W) – density of probability of γ-quanta absorption or emission by the W energy of the given isotope.

  7. Absorption/emission lines of resonant nucleus • Free nucleus emission line, • fixed nucleus absorption/emission lines, • fixed nucleus absorption line.

  8. Selected action parameter Atomic fluorescence (in general) Nucleus fluorescence (57Fe isotope) W0 [eV] ~ 10 14,4·103 τex [ns] ~ 4,5 97,0 Γ[eV] ~ 10-7 4,5·10-9 Γ/ W0 ~ 10-8 3,1·10-13 WR [eV] ~ 5·10-10 1,9·10-3 WR / Γ ~ 5·10-3 4·105 Comparison of the atomic and nucleus fluorescence parameters The nucleus reverse reflection energy: Observation: good difficult

  9. Rudolf Mössbauer discovery 1955 – Max Planck Institute, Heidelberg post-graduate study devoted to nucleus fluorescence 191Ir 1958 – publishing PhD results in Zeitschrift für Physik 151 (1958), 124-143, (Kernresonzflureszenz von Gammastrahlung in Ir191) and Naturwissenschaften 45 (1958), 538. 1961 – Nobel prize award for Physics Mössbauer explained his experimental results by the manifestation of recoil-free nuclear resonance fluorescence whose existence was justified by the analogy with the existence of elastic scattering of X-rayand slow neutrons in crystal (Lamb 1939). The efficient cross-section of X-ray scattering by the atomic nucleus lattice is substantially influenced by the energy WBof an elastic atomic bond in a crystalline lattice of solid. - absorbing/emitting nucleus atom is ejected from the lattice, 1. • momentum accepted from the absorbed/emitted photone • is transferred to the crystal by the nucleus. 2.

  10. Probability of the process of recoil-free absorption/emission of -quantum Recoil-free process – photone absorption by an absorber as a whole, without any change of its internal energy. Probability of this process is given by Mössbauer-Lamb factor: - modified wave length of -quantum, x - nucleus oscillation amplitude in the direction of-quantum spreading. Mössbauer-Lamb factor for Debye’s model of a solid: A solid – isotropic flexible medium capable of performing internal oscillations; system of 3N bound quantum oscillators  internal crystal energy is quantized probability of recoil-free process is no-zero.

  11. Mean energy of j-th oscillator: N – number of crystal atoms Mean photone number with ħωj energy: Mean atom shift from all oscillators: Debye’s distribution function of oscillator frequencies: substitution: Probability of recoil-free -quantum absorption/emission process:

  12. Mössbauer-Lamb factor – low-teperature approximation or Influence of recoil-free f fraction by a choice of: 1. isotopeas a source and an acceptor of radiation (M, W), 2. host substance involving the isotope (D).

  13. isotope host W[keV] f 57Fe Fe 14,4 0,91 191Ir Ir 129 0,06 Mössbauer isotopes There are approximatelly 200 nucleartransitions with parameterssuitablefor the application in Mössbauer spectroscopy: 1. transition energy less than the energy of an elastic atomic bond in a lattice, 2. life span of an excited nuclear level within range of 10-5 s up to 10-13 s. So far 110 isotopes have been examined; their application in Mössbauer spectro-scopy is as follows (according to MEDC UNC, April 2007, 46 028 publications): 1. 57Fe – 64% papers, 3. 151Eu – 3% papers, 2. 119Sn – 18% papers, 4. 197Au – 2% papers, 5. other 106 transitions – 13% papers. Comparison of the properties of the most applied isotope and the isotope on which Mössbauer’s discovery was performed:

  14. absorbator  - source velocity control unit detector multichannel analyser vibrator amplifier a 0 t v +vmax 0 t -vmax Transmission arrangement of Mössbauer spectrometer Doppler effect: Activity mode with constant acceleration

  15. Numeric processig and evaluation of Mössbauer spectra Theoretical model of a complex Mössbauer spectrum: - teoretical number of impulses scanned in the k-th spectrometer channel, - average Doppler velocity assigned to the k-th spectrometer channel, - background; the number of impulses scanned at the velocity far from resonance absorption (v→ ∞), • theoretical model of the l-th non-distributed • subspectrum, - vectors of unknown non-distributed parameters of all subspectra,

  16. - teoretical model of the only distributed subspectrum • distribution function of distributed parameter x satisfying • a normalisation condition: Distribution function is searched by fitting process as a table of values: equidistant nodes: Modified teoretical model of Mössbauer spectrum:

  17. optimalisation procedure step: minimalization of the functional given by the weighted sum of residue squares and a smoothing member: In order to estimate the unknown parameters: Frank-Wolfe quadratic programming method has been applied. 2. optimalisation procedure step: functional minimalization: ( Tabulated values of the distribution function are given in the preceding step.) In order to estimate the unknown parameters: Levenberg-Marquardt optimalisation method has been applied.

  18. Combined method for the analysis of complex Mössbauer spectra including a distribution in hyperfine interactions. Nuclear Instruments and Methods in Physics Research B72 (1992), 462-466. Examples of applying the method: • Sharp absorption lines of crystalline iron with admixture (Fig.2). • Broaded absorption line of the amorphous alloy with one distributed parameter (Fig.3). • Spectrum decomposition of the nanocrystalline alloy into subspectra - six sharp sextets and one distributed sextet (Fig.4).

  19. Attention is given to the three types of hyperfine interactions: electrical monopole, electrical quadrupole, magnetic dipole. Elektrical and magnetic hyperfine interactions • Additional interactions between the nucleus and its charged surrounding result from the fact that the nucleus is not any structureless body, but a set of very close, moving charged and neutral particles having a certain spatial arrangement in a final volume. • Mössbauer effect facilitated visualisation and quantification of hyperfine interaction parameters.

  20. Energy of electrical interaction of a nucleus with its charged environment V - charged nucleus volume, - nuclear charge density in position • electrical field potential of a charged • surrounding of nucleus. Decomposition of the electrical field potential into the Taylor series:

  21. For a nuclear charge, it holds: • Total nuclear charge: • Dipole nuclear moment vector – law of parity conservation: • Quadrupole nuclear moment tensor: • Effective nuclear charge radius R:

  22. Electrical monopole interaction – shift of energy levels of nuclei The energy of electrical nuclear interaction in approaching the first three members of a series: For an electron charge, the Poisson equation holds: - superposition of wave functions of surrounding charges with density, forming the field having potential. Energy increase of nuclear states: Energy change of a nuclear shift:

  23. v v [mm / s] + v + v - v - v 0 1/2 1/2 v 0 Electrical monopole interaction – isomer shift of spectrum Difference in energies of the same W0 transition in a source (S) and in an absorbator (A): nuclear factor atomic-molecular factor vδ – isomer shift of spectrum

  24. Isomer shift (IS)  provides valuable physical-chemical information about absorber properties. • It is influenced by: • electron structure of an atom, • atom valency, chemical bond, • charge states Fe2+ and Fe3+ (they are differ significantly in ). Mössbauer spectroscopy of hydrogenated Fe91Zr9 amorphous alloys. → Journal of Magnetism and Magnetic Materials 128 (1993), 365-368.

  25. Electrical quadrupole interaction The nucleus with non-spheric distribution of a charge in a non-homogeneous electrical field. A tensor of an electrical field gradient at the proper choice of coordinate system: For diagonal non-zero elements the Poisson equation hold: ← quadrupole nuclear moment asymmetry parameter → Parameter of non-homogeneous electrical field at nucleus:

  26. Electrical quadrupole interaction energy Hamiltonian of an electrical quadrupole interaction: Proper energy values: Magnetic quantum number of a nucleus: Spin quantum number of a nucleus: - multiple degeneration of energetic levels

  27. mI=±3/2 I=3/2 mI=±1/2 mI=±1/2 I=1/2 1/2 AQ v Quadrupole splitting of Mössbauer spectrum

  28. Transition from the excited to ground state Angular dependence of lines intensities Relative lines intensities polycrystal monocrystal 1 3 3 1 1 5 Quadrupole interaction – angular dependence of lines intensities • - angle between the direction of-quantum emission and the main axis of a crystal symmetry

  29. Quadrupole splitting of spectrum – physical information The existence of quadrupole splitting of spectrum is evidence that at the place of the Mössbauer atom with non-zero quadrupole moment there is a non-homogeneous electric field. There are two principal sources of non-homogenity of the internal electric field at nucleus: • electron charges of incompletely occupied electron levels in a particular atom, • ion charges surrounding the nucleus, if their symmetry is lower then cubic. Quadrupole splitting provides highly valuable information about: • the structure of an electron shell, • chemical bond, • overall crystal or molecule architecture, …

  30. Anions → [Fe(CN)5NO]2- [Fe(CN)6]3- [Fe(CN)6]4- Room temperature transmission Mössbauer spectra of new boronium cyano complexes. Cations ↓ Na+, K+, K+ [dipyPhBCl]+ Proceedings of 7-th European Symposium on Thermal Analysis and Calorimetry – ESTAC 7, Balatonfüred 1998. [(Et2N)2PhBCl]+ [Me2PhS]+

  31. Magnetic dipole interaction Nucleus with non-zero magnetic moment in an effective magnetic field. Dipole magnetic nuclear moment: - nuclear magnetone, - gyromagnetic factor Effective magnetic field at the nucleus: - hyperfine field. - local field, Main sources of a hyperfine field: contact Fermi nuclear interaction with s-electrons, dipole-dipole nuclear interaction with electrons having non-zero charge density at nucleus.

  32. Energy of magnetic dipole interaction Hamiltonian of magnetic dipole interaction: Corresponding proper energy values: - gives the energy change of a nuclear state, if a nucleus is found in the magnetic field. Studying condensed substances, the magnetic hyperfine spectrum strukture provides valuable physical information about: • magnetic structure, • magnetic phase changes, • phase analysis, …

  33. mI +3/2 2/3exH +1/2 I=3/2 -1/2 -3/2 14,4keV -1/2 I=1/2 +1/2 v 0 Zeeman splitting of Mössbauer spectrum

  34. Transition angular dependence of a line intensity 3 3 3 2 0 4 1 1 1 Dipole interaction – angular dependence of lines intensities • - angle between the direction of emitting -quantum and a vector of an effective magnetic field at the nucleus: relative intensity relative intensity

  35. [B]-okta (A)-tetra Structure and properties of the ball-milled spinel ferrites. Materials Science and Engineering A226-8, (1997), 22-25. Redistribution of cations Fe3+ induced by high energetic mechanical milling

  36. Hydrogen induced changes on the hyperfine magnetic field of amorphous Fe-Ni-Zr alloys. Key Engineering Materials 81-83 (1993), 357-362. → Influence of hydrogenation on the magnetic properties of amorphous Fe-Co-Zr alloys. Journal of Magnetism and Magnetic Materials 112 (1992), 334-336. ↓

  37. The Structure and Magnetic Properties of Fe-Si-Cu-Nb-B Powder Prepared by Mechanochemical Way. Physica status solidi 189 (2002), 859-863. Coexistence of three phases containing Fe: 1. -Fecrystalline grains, 2. granule bounds and intergranule area, 3. superparamagnetic particles.

  38. Properties of the nanocrystalline Finemet alloys prepared by mechanochemical way. Acta physica slovaca 48 (1998), 703-706. Initial material for milling: nanocrystalline tape, alloy in the atomic relation of elements: Fe : Cu : Nb : Si : B 73,5 : 1 : 3 : 13,5 : 9, pure elements in the given atomic relation.

  39. Influence of annealing on the crystallographic structure and some magnetic properties of the Fe-Cu-Nb-U-Si-B nanocrystalline alloys. Journal of Materials Science 33 (1998), 3197-3200. Phase analysis of nanocrystalline system Fe73.5Cu1Nb3-xUxSi13.5B9 (x=1, 2, 3 at.%) by decomposition of complex spectrum into subspectra.

  40. Extraterestrial Applications of Mössbauer Spectroscopy MIMOS on the Mars Exploration Rovers – Spirit and Opportunity Images Credit: NASA/JPL-Caltech Rover Traces on the Martian Surface

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