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(1)Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. AGH University of Science and Technology, Krakow Faculty of Physics and Applied Computer Science Department of Solid State Physics. D I S S E RTAT I O N. Wojciech Szczerba. Chemical and Nano-Structural Study of Magnetoresistive Iron Fine Particles by Means of X-Ray Absorption Spectroscopy. Supervised by: Prof. dr hab. Czesław Kapusta. Krakow 2009.

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(3) To my wife Dorota.

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(5) The research presented in this Dissertation has been carried out in international collaboration within the Project MUNDIS (European Commission Grant No. 027827), Competitive Contact-Less Position Sensor Based on Magnetoresistive Nano-Contacts, coordinated by the Instituto de Nanociencia de Aragon de la Universidad de Zaragoza, Spain..

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(7) Acknowledgements The work was supported by the European Commission, Grant No. 027827, STREP – MUNDIS and by the Polish Ministry of Science and Higher Education, Grant No. 60/6.PR UE/2007/7. I would like to thank Dr. Janusz Przewoźnik for providing the XRD data and Dr. Jan śukrowski for providing the MS data, as well as Maciej Szczerba for his kind help with the SEM study. Thanks are due to Dr. Damian Rybicki for his assistance at the NMR measurements and Andrzej Lemański for keeping the NMR spectrometer alive. Special thanks are due to Dr. Marcin Sikora for his guidance in synchrotron experiments and bright ideas in the data interpretation. I would also like to thank all my colleagues from Prof. Kapusta’s research group especially Dr. Dariusz Zając and Dr. Marta Borowiec, for their help and support during the long lasting XAFS experiments in Hamburg and Trieste. I am sincerely grateful to Prof. Czesław Kapusta for his scientific guidance and advice, as well as for the possibility to perform research at state of the art research facilities around Europe and the possibility to get in touch with top scientific research..

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(9) Contents Chapter 1 Motivation .............................................................................................15 Chapter 2 Material Properties...............................................................................17 2.1. Iron and Iron Oxides...............................................................................17. 2.1.1. Electronic and Magnetic Properties of Iron Oxides ...............................18. 2.1.2. Wüstite....................................................................................................19. 2.1.3. Hematite .................................................................................................19. 2.1.4. Magnetite ................................................................................................20. 2.1.5. Maghemite ..............................................................................................21. 2.2. Magnetoresistance in Granular Materials...............................................22. Chapter 3 X-ray Absorption Spectroscopy ..........................................................25 3.1. Introduction ............................................................................................25. 3.2. Synchrotron Radiation............................................................................26. 3.3. X-ray Absorption Fine Structure ............................................................29. 3.4. FEFF .......................................................................................................34. 3.5. Experimental Set-up for XAFS ..............................................................37. 3.6. Data Handling.........................................................................................39. Chapter 4 Sample Preparation and Preliminary Characterization...................45 4.1. Sample Preparation.................................................................................45. 4.2. Magnetoresistance Measurements..........................................................47. 4.3. Morphology ............................................................................................50. 4.4. Further Characterization .........................................................................55. Chapter 5 Chemical and Structural Analysis.......................................................59 5.1. Hard X-ray Experiment ..........................................................................59. 5.1.1. Transmission XAFS Results – Iron K-edge............................................60. 5.1.2. TEY XAFS Results – Iron K-edge .........................................................62. 5.2. Soft X-ray Experiment ...........................................................................67. 5.2.1. Iron L-edges XANES .............................................................................68.

(10) 5.2.2. Oxygen K-edge XANES ........................................................................ 76. 5.2.3. Oxygen K-edge EXAFS ......................................................................... 83. 5.3. Summary of XAFS Results .................................................................... 91. Chapter 6 Summary ............................................................................................... 93 Chapter 7 Conclusions ........................................................................................... 95 Appendix A FEFF Calculations............................................................................. 97 A.1. Hematite (α-Fe2O3)................................................................................. 97. A.2. Magnetite (Fe3O4), Fe at tetrahedral site................................................ 98. A.3. Magnetite (Fe3O4), Fe at octahedral site ................................................ 98. A.4. Iron (α-Fe) .............................................................................................. 98. Appendix B XAFS Spectra .................................................................................... 99 B.1. Linear Combination Fits for XANES at Oxygen K-edge ...................... 99. B.2. Linear Combination Fits for XANES at Iron L2, 3-edges ..................... 103. B.3. FEFF Fits for EXAFS at Oxygen K-edge ............................................ 106. Streszczenie ...............................................................................................................111 References .............................................................................................................. 115.

(11) Acronyms bcc – body centered cubic BMR – Ballistic Magneto-Resistance CFSE – Crystal Field Stabilization Energy CMR – Colossal Magneto-Resistance DW – Debye – Waller factor EAY – Elastic Auger electron Yield EDS – Electron Dispersive x-ray Spectroscopy EXAFS – Extended X-ray Absorption Fine Structure fcc – face centered cubic FFT – Forward Fourier Transform GMR – Giant Magneto-Resistance GUI – Graphic User Interface HASYLAB – HAmburger SYnchrotronstrahlungsLABor HRTEM – High Resolution Transmission Electron Microscope INA – Instituto de Nanociencia de Aragon de la Universidad de Zaragoza, Spain LCF – Linear Combination Fit LDOS – Local Density Of States MR – Magneto-Resistance / Magneto-Resistivity MS – Mößbauer Spectroscopy NMR – Nuclear Magnetic Resonance PFY – Partial Fluorescence Yield RF – Radio Frequency SCF – Self Consistent Fit SE – Secondary Electrons SEM – Scanning Electron Microscope STXM – Scanning Transmission X-ray Microscope TEY – Total Electron Yield TMR – Tunneling Magneto-Resistance UHV – Ultra High Vacuum VUV – Visual light and UltraViolet XAFS – X-ray Absorption Fine Structure XANES – X-ray Absorption Near-Edge Structure XAS – X-ray Absorption Spectroscopy XPS – X-ray Photoelectron Spectroscopy XRD – X-Ray Diffraction.

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(13) I N T R O D U C TI O N.

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(15) Chapter 1 Motivation The continuous technological pursuit for high sensitivity, fast, durable, and inexpensive magnetic sensors for a variety of applications has stimulated an extensive research effort in the field of magnetic sensing world-wide. These applications include magnetic recording, medical instrumentation, consumer electronics, as well as position, rotation and speed sensing in machinery, robotics and vehicles, and for applications on different scales from large scale sensors installed in railroad bogies to nanoscale read-heads in hard disk drives. This interdisciplinary research ranges from basic quantum-mechanical aspects of the magnetotransport properties through solid state physics and chemistry to materials science aspects and fabrication of such sensors, and is aimed on a better understanding of magnetoresistive phenomena in the matter, as well as on the improvement and engineering of the magnetoresistive properties of these materials. The great impact of the magnetoresistive effects on the modern technology and society found its great expression in the recent award of the Nobel Prize in Physics, in 2007, to Albert Fert and Peter Grünberg for their discovery of the giant magnetoresistance (GMR) (Baibich 1988, Binasch 1989, Fert 2008) which has successfully been exploited e.g. in the hard disk drive read-heads, since the early 1990s. Most of the research has been focused on layered thin film structures exhibiting a significant magnetoresistance (MR) at room temperature (GMR effect), where the MR phenomena arise from perturbation of the interfacial spin-dependent scattering by an applied magnetic field, described by the so-called spin-valve model (Binasch 1989). MR phenomena include also the tunneling magnetoresistance (TMR) (Moodera 1999) and the colossal magnetoresistance (CMR) (van Helmolt 1993, Ramirez 1997). The CMR is associated with bulk magnetic phase transitions and is observed in oxides such like manganese perovskites (Jonker 1950) or double perovskites of d-transition elements (Serrate 2007)..

(16) Motivation. All the above mentioned MR phenomena exploit intrinsic physical properties of the materials and require quite sophisticated high-tech production methods. However, the magnetotransport properties depend also strongly on the geometry of the given sample (Solin 2007). The geometric enhancement effect plays a significant role in the ballistic magnetoresistance (BMR) (García 1999) which occurs in nano-contacts between ferromagnetic materials e.g. in iron granular materials prepared by milling. These materials can be used in magnetoresistive position sensors for applications in e.g. automotive industry. The devices have to work in a wide range of temperatures of –40 to 125 °C, with voltages appropriate for car power supplies and in moderate magnetic fields. They are expected to have a mechanical durability of at least 107 cycles. Moreover, their MR properties have to be reproducible within a small tolerance in order to comply with the requirements of mass production. The latter issue has been one of the motivations for the present study, as for the reproducibility of the physical properties of a system it is crucial to know and control the conditions of the occurrence of the effect of interest. For the MR properties of devices based on ball milled fine iron particles the interfaces between metallic grains play a pivotal role. The surfaces of the particles are covered with a thin oxide layer, thus it is important to know the structure, chemical composition and thickness of such a layer. For the purpose of the present study X-ray absorption spectroscopy (XAS) has been chosen as the primary analytic tool owing to its outstanding sensitivity, element selectivity and the ability to distinguish between chemical compounds consisting of the same elements. Furthermore, XAS provides information on the local structure surrounding a given element site. These properties of XAS will ensure a detailed and deep insight into the properties of the samples studied, particularly into the structure and chemistry of the oxide layer. The BMR effect is still novel and not fully understood, and there are still controversies concerning its experimental evidence (Egelhoff 2005). Therefore, the study of the interfacial oxide layer which plays a crucial role in the magnetotransport is of major importance for the understanding of MR effects in granular materials, as well as for their successful exploitation in future magneto-sensitive devices.. 16.

(17) Chapter 2 Material Properties The powder samples investigated in the study presented are based on metallic iron; therefore this chapter treats structural, electronic and magnetic properties of iron and iron oxides. The second part of this chapter is devoted to the magnetoresistive phenomena found in granular materials. Ballistic magneto-resistance and the spin filtering effect in thin oxide layers as well as magnetotransport phenomena in multiple nanocontacts, as they are observed in granular materials, are briefly discussed.. 2.1 Iron and Iron Oxides Metallic iron is known to mankind since ancient times – the Iron Age began ca. 1000 BC. Nowadays it is still the most important functional material used in form of steel and cast iron. Iron oxides used as pigments are known to mankind even longer. Moreover, iron plays a very important role in biology as it is an active element in chlorophyll and hemoglobin. Iron has atomic number 26 and atomic weight 55.847 u. It has four stable isotopes: 54 (5.9%), 56 (91.6%), 57 (2.2%) and 58 (0.33%). The electronic configuration of free iron atoms is [Ar]3d64s2. The main oxidation states of iron are Fe2+ and Fe3+. At room temperature the only stable metallic iron phase is ferrite, denoted also as α-Fe. It has a body centered cubic structure with the lattice constant of 2.87 Å and the density of 7.874 g/cm3. At 1183 K iron transforms into a face centered cubic phase called austenite (γ-Fe). Above 1663 K, up to the melting point at 1812 K, the bcc phase called δ-ferrite is again the more stable one. In metallic iron there are in average 0.6 effective free-electrons per atom (Slater 1936). Owing to its metallic nature iron has a very high electrical and thermal conductance; at room temperature the electrical resistivity is 96.1 nΩ m. The α phase is ferromagnetic up to.

(18) Material Properties. 1042 K with 2.22 µ B per atom at 0 K. Pure elemental iron is a soft magnetic material which gets easily magnetized and demagnetized, showing almost no remanent magnetization. Iron is highly reactive to oxygen. In dry atmosphere it is covered by a thin protective and self-healing oxide layer. However, at moist air and acid environment it corrodes. The corrosion product is rust consisting mainly of iron hydroxides. Due to the porosity of rust it does not protect the metal from further corrosion. Iron oxides1 are widespread in nature. Generally, iron oxides consist of close packed arrays of oxygen anions, either in hexagonal close packing or face centered cubic structure in which the octahedral and, in some cases, the tetrahedral interstices are partly filled with trivalent and/or divalent iron cations. Four main iron oxides are found in nature: FeO (wüstite), Fe3O4 (magnetite), α-Fe2O3 (hematite), γ-Fe2O3 (maghemite) 2.1.1 Electronic and Magnetic Properties of Iron Oxides For the iron oxides the Fe 3d electrons determine most of the electronic and magnetic properties, hence orbitals containing these electrons are of interest. In iron oxides they possess a significant degree of covalent bonding, therefore the 3d electrons are, to large extend, localized on the Fe atom and its coordination site. Thus the electronic structure can be described in terms of molecular energy levels of simple atomic clusters. FeO69–. for Fe3+ in octahedral coordination. FeO610–. for Fe2+ in octahedral coordination. FeO45–. for Fe3+ in tetrahedral coordination. The molecular orbitals are constructed by a linear combination of atomic orbitals of appropriate symmetry; in the case of the iron oxide clusters these are the d orbitals of Fe and p orbitals of O. Orbitals of similar character and energy are grouped into bands. The molecular t2g band contains the set of orbitals dxy, dyz and dzx, and the eg band includes the orbitals d x2 and d x2 − y 2 . In the Fe bound in solids the t2g and eg bands are split due to the presence of electrostatic interactions of the crystal field into two molecular orbitals. Due to electrostatic repulsion the eg band lies above the t2g band in the octahedral coordination, and in the tetrahedral coordination the situation is reversed. Electrostatic interactions resulting in the crystal field stabilization energy (CFSE), are also responsible for the preference of Fe2+ ions to 1. This and the following sections concerning iron oxides are based on (Cornell 1996).. 18.

(19) Material Properties. occupy octahedral sites, whereas trivalent Fe, which has one electron less, occupies octahedral and tetrahedral sites with equal energetic preference, since in both cases the CSFE of Fe3+ is zero. Fe ions on adjacent sites interact with each other via exchange interaction which tends to cause parallel or antiparallel alignment of the spins. In iron oxides the Fe3+ are surrounded by O2– ions, so the exchange interactions proceed via the intervening ligand. This is the so-called super-exchange (Anderson 1950). Unpaired electrons in the eg orbitals of Fe3+ interact magnetically with electrons on the p orbitals of the O2– ions and a chain coupling effect occurs, which can extends over the crystal if the cation and ligand are close enough to provide sufficiently large energy of the coupling. The exchange integrals depend on the Fe-O bond length and on the bond angle; for bond angles 120° – 180° the interactions are strong, whereas for 90° they are much weaker. In the case of Fe2+ clusters the super-exchange interactions are similar to those of Fe3+. When Fe2+ and Fe3+ are present at adjacent sites, as in magnetite, electron delocalization can occur as a result of the so-called double-exchange interaction (Zener 1951). 2.1.2 Wüstite Wüstite is a black iron oxide which contains only divalent iron ions. The structure is that of rock salt and is based on a face centered cubic oxygen anion array. It is usually nonstoichiometric (cation deficient) and can only be obtained at temperatures above 843 K. At lower temperatures it decomposes into Fe and Fe3O4 when cooled slowly. The nonstoichiometric form can exists as a metastable phase at room temperature when rapidly quenched. 2.1.3 Hematite Hematite is widespread in soils and minerals; it is also the oldest known iron mineral. It is extremely stable and is often the end product of transformation of other iron oxides. Its color is red, if present as fine powder and black or sparkling grey, if coarsely crystalline. Hematite has the corundum structure which is based on a hexagonal close packed oxygen anion array. The lattice constants are a = 5.034 Å, c = 13.752 Å (Blake 1966). The trivalent iron cations occupy two thirds of the octahedral interstices which are arranged regularly in the (001) plane; two filled sites are followed by one vacant, therefore the FeO6 octahedra form six-fold rings around the vacant sites.. 19.

(20) Material Properties. Hematite is an n type semiconductor with a commonly accepted value of the energy gap of 2.2 eV, though there is some controversy upon this value (Cornell 1996, p. 110). The conduction band is composed of empty Fe3+ d states and the valence band consists of fully occupied t2g Fe3+ orbitals. Hematite has a low carrier mobility of about 10–2 cm2 V–1 s–1, thus its resistivity is high. Above 956 K hematite is paramagnetic. Below that temperature is usually regarded as antiferromagnetic. However, above 260 K (the Morin temperature) the spins are not exactly antiparallel and exhibit a small canting angle of 0.1°, hence it is weakly ferromagnetic at room temperature. Below TM the alignment is exactly antiparallel. Table 2.1 Crystallographic data of hematite (Blake 1966). x. y. z. Fe1. 0. 0. 0.3553. O. 0.30590. 0. 0.25. Space group: D16 2h -R3c. a = 5.038 Å c = 13.772 Å. Fig. 2.1 Unit cell of α-Fe2O3, black spheres – iron, white spheres – oxygen.. 2.1.4 Magnetite Magnetite is ferrimagnetic, containing both Fe2+ and Fe3+ ions. It is the oldest known magnetic material, lodestone. Magnetite is black and has the structure of an inverse spinel with divalent and trivalent Fe in the octahedral sites and trivalent Fe in the tetrahedral sites. Thus, its formula can be written as Fe3+[Fe2+ Fe3+]O4, where the brackets denote the octahedral coordination. The unit cell is based on 32 O2– ions and has a face centered cubic symmetry with lattice constant a = 8.396 Å (Wechsler 1984). Magnetite is an n and p type semiconductor with a very small energy gap of 0.1 eV at room temperature. Due to the double-exchange interaction it is almost metallic and has a relatively high conductivity of 102 – 103 Ω–1 cm–1.. 20.

(21) Material Properties. Below 850 K (the Curie temperature) magnetite is ferrimagnetic. The spins of Fe ions at tetrahedral sites are antiparallel to those at octahedral sites. The antiparallel alignment of the Fe3+ spins compensates their magnetic moments and the Fe2+ with their 4 µ B per ion give rise to the net magnetic moment of magnetite. Table 2.2 Crystallographic data of magnetite (Wechsler 1984). x. y. z. Fe1. 0.125. 0.125. 0.125. Fe2. 0.5. 0.5. 0.5. O. 0.2547. 0.2547. 0.2547. Space group: O7h -Fd3m. a = 8.3958 Å. Fig. 2.2 Unit cell of Fe3O4, black spheres – iron, white spheres – oxygen.. 2.1.5 Maghemite Maghemite is a red-brown, ferrimagnetic material, containing only Fe3+ cations. It is isostructural with magnetite, but with cation deficient sites which compensate for the oxidation of Fe2+. Each unit cell contains 32 O2– anions in fcc ordering, 21 ⅓ Fe3+ cations and 2 ⅔ vacancies. The cations are distributed randomly over the tetrahedral and octahedral sites, but forms of synthetic maghemite often display superlattices of ordered vacancies. Maghemite is usually formed by a solid state transformation from another iron oxide or iron compound and almost always adopts the habit of its precursor. Thus its unit cell parameter, though usually given as a = 8.34 Å, may range from 8.338 Å to 8.389 Å. Maghemite is an n type semiconductor with the energy gap of 2.03 Å and electric properties similar to hematite. At room temperature maghemite is ferrimagnetic. The Curie temperature lies above the temperature of the phase transition into hematite, 713 K. As in the case of magnetite the spins in the tetrahedral sublattice are antiparallel to the spins in the octahedral sublattice, hence, the uncompensated spins at the octahedral sites give rise to the net magnetic moment.. 21.

(22) Material Properties. 2.2 Magnetoresistance in Granular Materials The magnetoresistive effect in granular materials such as the ball-milled iron powders under investigation is mainly a geometry induced MR effect2. Ferromagnetic particles of the powder are pressed together but the contact surfaces are rather small, of some nanometers in diameter. These point contacts act as waveguides for electrons when an electric potential is applied. Due to the small dimensions of the waveguide the conductance through the nano-contact is quantized. In addition, the ferromagnetic particles serve as ferromagnetic leads and the transport through the point contact is a spin-dependent process in which electrons of a preferred spin polarization are conducted due to the difference in the density of the two spin states at Fermi level. When the magnetization vectors of the two contacting grains are antiparallel, the electrons suffer from spin scattering. This is because of the small dimensions of the nanocontact and the ballistic transport in which the spins cannot accommodate adiabatically when passing through the contact region containing a domain wall. The domain wall is very thin due to the geometry of the junction and the magnetization gradient is high, preventing the electrons from adiabatic flipping, thus some of the electrons are repelled. When the alignment of the magnetization vectors is parallel, e.g. due to an externally applied magnetic field, the domain wall is not present and the junction is in high conductance state. This effect is termed ballistic magnetoresistance (BMR) and was first reported by N. García et al. (1999) on Ni-Ni nanocontacts. The BMR is defined as [BMR] =. I ↑↑. ∆R R↑↓ − R↑↑ = R R↑↑. I ↑↑ > I ↑↓. (2.1). I ↑↓. Fig. 2.3 Schematic illustration of the BMR effect on a single nanocontact. The grey areas depict the ferromagnetic leads, the white arrows show the magnetization vector alignment. The shaded areas represent the spin polarized nanocontact area consisting of a semiconducting ferrimagnetic oxide layer. In the parallel alignment of the magnetization due to external field the electrons of one spin polarization propagate by ballistic transport through the nanocontact to the other ferromagnetic lead. In the antiparallel alignment without external field a domain wall is present at the junction and the electrons suffer from spin scattering which leads to a higher resistance.. 2. A detailed review on BMR can be found in (Solin 2007). 22.

(23) Material Properties. The BMR effect due to domain wall scattering is enhanced if the nanocontact is made of a semiconducting material with fully polarized spin states, as it is in the case of the iron oxides where the conduction band consists of unfilled Fe2+ or Fe3+ 3d states with spin down only. In this case the thin oxide layer serves as a spin-polarizer not allowing the spins to flip before reaching the domain wall (grain boundary). This prevents the electron spins from accommodating adiabatically to the magnetization of the other grain and enhances the spin scattering at the domain wall, hence, leading to a higher MR (García 2002a). Experimentally measured MR values on electrodeposited granulates vary from few hundred to few thousand percent (Chopra 2002, García 2004, García 2005). Unfortunately, in most cases nanocontacts are not stable in time. The high currents at the junction cause a degradation of the nanocontact mainly through heating and resulting oxidation. A solution is to exploit multiple nanocontacts like they are present in powders (García 2002, García 2005); which reduces drastically the current at a single junction. In the case of ferromagnetic powders artifacts which mimic the BMR effect can also occur during the experiment, i.e. a clumping together of the powder particles in response to the applied field (Egelhoff 2005). This can be avoided by use of single domain particles, or multi domain particles exhibiting net magnetic moments, which already are clumped together and/or by the application of pressure onto the particle assembly. The BMR effect still lacks an unambiguous theoretical interpretation and has not yet been applied in technology in contrast to the GMR and TMR effects, though the experimental results are very promising.. 23.

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(25) Chapter 3 X-ray Absorption Spectroscopy This Chapter gives a brief introduction into the main experimental method used, the Xray Absorption Spectroscopy3. In this part the basic properties of synchrotron radiation and the methods of its production are discussed. Furthermore, basic theoretical aspects of X-ray Absorption Near Edge Structure and Extended X-ray Absorption Fine Structure spectroscopies are given. They are followed by a practical description of the sophisticated abinitio calculations used for the absorption spectra modeling, which make use of the multiple-scattering theory. Also, the practical aspects of X-ray absorption spectroscopy, like the experimental set-up and data handling are discussed.. 3.1 Introduction X-rays can interact with matter through scattering, refraction and absorption. The scattering process has successfully been exploited in diffraction techniques for almost a century now. Though powerful, X-ray diffraction is not always capable of providing nanostructural information, since the diffraction process to occur needs a periodic lattice of certain size – crystallites of at least 10 nm. Moreover, it has no chemical sensitivity, which is of great importance when site selectivity of elements in the system has to be studied. In these cases the Extended X-ray Absorption Fine Structure (EXAFS) can be applied, which carries structural information about the local surrounding of the absorbing element encoded in oscillations of the absorption spectrum above the absorption edge. Analyzing the absorption edge itself in the X-ray Absorption Near-Edge Structure (XANES) spectroscopy allows a determination of the electronic state and local coordination symmetry of the element probed, making it a valuable analytical tool for providing information about the 3. A detailed review on XAS can be found in e.g. (Fontaine 1993) and (Lengeler 2006).

(26) X-ray Absorption Spectroscopy. chemistry of the studied material. Most often both spectroscopies are combined in the Xray Absorption Fine Structure (XAFS) experiment. Fig. 3.1 An exemplary XAFS spectrum (metallic iron measured at the iron K-edge). The extensive EXAFS oscillations are clearly visible in this case. They extend several hundreds electron volts above the absorption edge. EXAFS carries structural information about the local environment of the absorber, whereas XANES provides chemical information about the absorber itself.. Though already discovered in the 1930s by Krönig, XAFS was of little interest until the early 1970s. The main reason for that was that no white X-ray source powerful enough was available to collect data systematically with a reasonable energy resolution and within a reasonable time. The advent of synchrotron light sources in the 1970s boosted the development of both experimental methods and theoretical models, providing the experimentalists with appropriate analytical tools. By now XAFS has proven to be a very valuable experimental technique in fields such as solid state physics, chemistry, especially catalyst chemistry, materials science, engineering, geo sciences and life sciences.. 3.2 Synchrotron Radiation Synchrotrons4 are circular particle accelerators, where charged particles travel on circular trajectories at ultra-relativistic velocities (γ >> 1) within the accelerator ring. The particles while moving round the storage ring are emitting very intensive light, called synchrotron radiation, in a very broad band ranging from far infrared do hard X-rays. In synchrotrons designed as light sources electrons or positrons are used owing to their favorable charge to mass ratio which allows a high acceleration at relatively low energies. Electrons coming from an electron source are initially accelerated by a linear accelerator and injected into a booster synchrotron, which provides the electrons appropriate energies, so they can feed the storage ring. Periodically, new portions of electrons have to be injected into the storage ring in order to compensate operational losses. During a normal synchrotron radiation run usually two or three injections per day are necessary. The inter4. A detailed review on synchrotrons and synchrotron radiation can be found in e.g. (Raoux 1993) and (Freund 1993). 26.

(27) X-ray Absorption Spectroscopy. val between injections is related to the mean life time of electrons in the storage ring, which depends very much on the machine design. Newer designs such as the Canadian Light Source have a continuous electron injection, which has the advantage of a quasiconstant ring current, but might bear some difficulties for experiments needing high beam position stability. Electrons traveling along the storage ring emit radiation, so that they lose energy which has to be compensated by RF-cavities. The RF-cavities shape the electron beam into a specific bunch structure, which can be varied and used in time resolved experiments. In order to keep the particles on a circular orbit bending magnets are used, dividing the trajectory into several straight sections. At a bending magnet the electron suffers acceleration towards the center of the storage ring. This is a result of the Lorentz force (F = ev×B). The radius of curvature ρ depends on the ratio of the relativistic γ-factor to the magnetic field B perpendicular to the orbital plane as follows. ρ=. me γc eB. (3.1). According to the classical laws of electrodynamics an accelerated charge emits electromagnetic radiation. The energy flux of the field is emitted isotropically around the acceleration vector in a large solid angle. But, when being accelerated at relativistic energies, the radiation pattern in the laboratory frame becomes sharply peaked in the direction of motion of the charged particle due to the relativistic Doppler shift in accordance with Lorentz transformations of space-time. The typical opening angle of the radiated beam is of 1/γ = (1 – v2/c2)1/2 in the laboratory frame. Since for electrons γ = 1957 E (GeV) in practical unit, at a medium size machine like ELETTRA operating at E = 2 GeV the opening angle is of about 0.25 mrad. Due to the natural collimation of the synchrotron light an external observer sees only a very short light burst when the electron traverses on the bending arc. Such a short pulse has a very broad frequency band, which explains the broad white spectrum of synchrotron radiation. The maximum of the intensity of the radiation usually corresponds to the X-ray range. The critical energy ħωc, defined as a value for which a half of the total power is radiated at frequencies lower than the critical one, ωc, for a bending magnet is given as 3 γ 2 eB ωc = 2 me. (3.2). 27.

(28) X-ray Absorption Spectroscopy. Synchrotron radiation is thus highly collimated and therefore synchrotron light sources are extremely bright, as the whole photon flux is emitted in a very small solid angle. Thus, synchrotron light produced by a bending magnet outperforms a classical X-ray tube in terms of photon flux intensity by at least five orders of magnitude. This photon output can be increased dramatically if special insertion devices, such as wigglers and undulators, are mounted in the straight sections of the storage ring. These are multipole devices consisting of two arrays of magnets with alternating polarity, producing magnetic fields perpendicular to the synchrotron plane. The electron, when passing through such a device, starts to wiggle on a quasi-sinusoidal trajectory. Each wiggle causes the electron to emit synchrotron light. The optical properties of a multipole device are characterized by the dimensionless parameter K, defined as K=. eλu B0 2 π me c. (3.3). Multipole devices can work in the incoherent regime, the ‘wiggler’ regime (K >> 1), where the deviation angle of the electron trajectory is larger than the natural opening angle 1/γ of the photon beam and the individual photon bursts do not interfere. Thus, the total photon flux is increased by a factor of 2N, N being the number of wiggles. But, if the deviation angle is smaller than 1/γ, as in the case of the ‘undulator’ regime (K ≈ 1), the individual photon pulses can interfere with each other giving very high resonant peaks at certain wavelengths. These resonant wavelengths can be tuned by varying the intensity of the magnetic field most conveniently by changing the gap between the magnet arrays. Another important property of the synchrotron radiation is its polarity. Radiation emitted in the storage ring plane is completely linearly polarized, whereas radiation emitted off plane has a circular component, which increases with the deviation angle. The helicity of the circular polarization observed above the storage ring plane is opposite to the one observed from below. This property is largely exploited in the X-ray absorption spectroscopy and imaging techniques based on magnetic dichroism effect, as well as in investigations of chiral systems.. 28.

(29) X-ray Absorption Spectroscopy. 3.3 X-ray Absorption Fine Structure5 In the absorption process X-rays passing through matter are attenuated according to the Lambert-Beer law (Eq. 3.4), where I0 is the intensity of the impinging beam, I1 is the intensity measured behind the absorber, and d is the absorber thickness.. I 1 ( E ) = I 0 ( E ) e − µ ( E )d. (3.4). The linear absorption coefficient µ depends on the photon energy and the absorbing material. In the X-ray spectral range, defined usually as 300 eV to 30 keV, the absorption coefficient is not the only one contributing to the total cross section of matter. However, the other contributions to the total cross section, i.e. Thomson and Compton scattering, are changing far less with energy than absorption. For nuclear absorption and electron-positron pair creation the considered photon energies are far too low to contribute. A commonly accepted approximation for the mass absorption coefficient µ/ρ in the X-ray range is. µ ZZ = const N a   ρ A E . 3. (3.5). Basically, the absorption process is a consequence of the photoelectric effect. An impinging photon can only lose energy by exciting a bound electron into a higher unoccupied energy level or into an unbound state in the continuum. Due to the energy and momentum conservation rules a free electron cannot absorb a photon. When the photon energy ħω equals the binding energy of an electron in the atom, the quantum can be absorbed. This explains the occurrence of absorption edges – sharp step-like jumps of the absorption coefficient at certain energies. In this case a new absorption channel opens and the absorption coefficient increases drastically. According to Eq. (3.5) absorption is more efficient for elements with higher atomic number Z, simply due to the fact that heavier elements contain more electrons and therefore more absorption channels are available. The absorption edges are denoted by the shell the photoelectron is excited from, e.g. 1s electrons are excited at the K-edge, 2s, 2p1/2 and 2p3/2 electrons at L1, L2 and L3 edges respectively. These edges are like fingerprints for a given element allowing identifying it unambiguously, as the energy of the edge corresponds directly to the binding energy of the excited electron. Since the absorption process is a microscopic effect, the interaction between the photon and electron has to be described quantum-mechanically. In the theoretical description of the photoabsorption process the Fermi Golden Rule plays a central role, which states that 5. This section is based on the reviews by B. Lengeler (2006), F.M.F. de Groot (2006) and A. Fontaine (1993). 29.

(30) X-ray Absorption Spectroscopy. the transition probability Wfi between a system in its initial state ψi and final state ψi is given by. W fi =. 2π ψ f T ψi h. 2. δ (E f − Ei − hω ). (3.6). The squared matrix element gives the transition rate. The initial and final state functions contain an electron part and a photon part which describe the annihilation of a photon in absorption process. The delta function takes care of the energy conservation. The transition operator T contains all possible transitions, but in the description of the X-ray absorption process the single-photon approximation is used. An additional assumption is that in the transition induced by the X-ray photon only one electron does participate. Then the transition operator reduces to the first order term T1 only, which is equivalent to the first order term of the interaction Hamiltonian H1. The interaction Hamiltonian describes the interaction between X-rays and electrons and in the approximation of the perturbation theory the first order term can be expressed as. H1 =. e p⋅A mc. (3.7). This term describes the action of a vector field A on an electron with a momentum operator p. The vector field describes the electromagnetic wave of the impinging X-ray beam and is given as a plane wave, where êq is a unit vector of the polarization q A = eˆ q A0 e i (kx −ωt ). (3.8). The electric field E is collinear with the vector field, so one can understand the Hamiltonian H1 as an interaction between the electric field E and the electron momenta. In the dipole approximation one can find that the transition operator can be expressed as. T1 ∝ ∑ (eˆ q ⋅ p ) q. (3.9). The delta function in Eq. (3.6) implies that only densities of empty states ρ(E – EB) can be observed, EB being the electron binding energy. Assuming that the absorption coefficient µ(E) is proportional to the transition probability W and denoting the squared matrix element as Mif 2 one gets the familiar form of the Fermi Golden Rule for XAFS. µ (E ) ∝ M if ρ (E − E B ) 2. (3.10). In the dipole approximation the matrix element Mif is non-zero only if the difference of the orbital quantum number between the initial state and the final state is 1 and the spin is. 30.

(31) X-ray Absorption Spectroscopy. conserved. This gives the following selection rules for the excitation process expressed in eigen-values of the orbital momentum l and the total momentum j. l f − li = 1. (3.11 a). j f − ji = 0 vel 1. (3.11 b). This means that for the K and L1 edges s electrons are excited into empty p states, whereas for the L2 and L3 edges the p electrons are excited into empty s and d states. The shape of the absorption edge should be a projection of the partial density (∆l = 1) of empty states convoluted with a Lorentzian broadening due to the finite core-hole lifetime, which leads to an energy uncertainty according to the Heisenberg principle. Using in the calculations a density of states in the presence of a core-hole instead of an unperturbed one and adding a quadrupole term (∆l = 2) to the transition operator gives even better results, but only in the case when the interaction between the electrons and the final state is relatively low. This is for example the case for K-edge excitation (1s → 4p) in 3d transition metals. But the one-electron interaction approximation does not hold for systems, like 3d metal ions and rare earths where the interactions between electrons are strong. In these cases one has to account for many-body effects. There are several approaches in this matter, like the multiplet approach or the multiple-scattering theory used for simulating near-edge XAFS (XANES) spectra. In experimental practice a comparative analysis of XANES spectra is used when possible. Experimental data are compared with measured reference spectra of compounds where the absorbing element has a known formal valence and local structure. One can observe distinct differences in shape and position of edges. A shift of the edge towards higher energies with increasing formal valence can be observed. The shift is explained qualitatively by the fact, that ions with higher valences have fewer electrons. This means that the screening of the attracting potential of the nucleus is weaker, resulting in a slightly higher binding energy of the core levels. The shape of the edge itself is closely related to the local symmetry of the surrounding atoms. The octahedral coordination can be easily distinguished from the tetrahedral coordination, since in the case of the latter one a quite distinctive pre-edge feature can be observed. The differences in the edge shape can be understood, when bearing in mind that according to Eq. (3.10) XANES probes unoccupied electronic states around the Fermi level. These states of course are very sensitive to the local symmetry.. 31.

(32) X-ray Absorption Spectroscopy. Extended X-ray Absorption Fine Structure spectroscopy investigates the oscillatory part of the XAFS spectrum above the absorption edge. These oscillations extend to approximately 1 keV above the edge and are a characteristic feature for bound atoms. They contain information about the local structure around the absorbing atoms. The oscillatory structure is caused by the backscattering of the excited photoelectron on the surrounding atoms in the lattice or molecule. In this case one has to add a backscattering part to the final state wave function of the outgoing photoelectron. ψ f = f 0 + f bsc. i 2 kr j   iβ j e 2 iδ 1  2  = 1 + i3 cos (θ j )F j (k ) e e f   0 kr j2  . (3.12). describes the spherical wave of the outgoing photoelectron; it is the unperturbed. f0. term for an isolated atom, whereas f bsc is the backscattered wave originating from a scatterer at the position rj. The scattered wave has the same symmetry as the incoming wave but is modified in the following way: •. phase factor e 2iδ1 takes care of the phase shift suffered by the photoelectron within the potential of the absorbing atom. •. the term kF j (k ) e. iβ j. describes the complex amplitude for backscattering by the. neighboring atom at position rj •. e. ikr j. is the geometrical phase shift suffered by the photoelectron with the wave. number k on its trajectory to the neighbor and back. •. the term 3 cos 2 θ j takes care of the angular dependence of the photoelectron emission in the absorption process. Preferentially, the photoelectron is emitted along the direction of the electric field vector E; θj is the angle between E and rj.. Inserting Eq. (3.12) into the expression for the transition probability Wfi gives a modified absorption coefficient which is a convolution of the atomic absorption coefficient for an isolated atom µ 0 and the normalized oscillatory part χ.. µ = µ 0 (1 + χ ). (3.13). The expression for a XAFS oscillation originating form a single backscattering event on an atom in position rj has then the following form. χ j (k ) = 3 cos 2 θ j F j (k ). 32. [. ]. 1 sin 2kr j + Φ j (k ) kr j2. (3.14).

(33) X-ray Absorption Spectroscopy. This is the basic EXAFS equation. In order to derive it the spherical wave has been approximated by a plane wave. The interpretation of this equation is the following. The photoelectron emitted form the absorbing atom in the absorption process propagates as a spherical wave. If other atoms are located in the vicinity of the absorber the photoelectron is scattered by these atoms. In this place the plane wave approximation is applied. One assumes that the curvature of the wave front of the impinging spherical photoelectron wave is small enough to be replaced in the calculations by a plane wave. Then the scattered wave may interfere with the incoming primary wave. If constructive interference occurs, the probability to find the photoelectron is increased compared to a photoabsorption process on an isolated atom, hence µ > µ 0 for constructive and µ < µ 0 for destructive interference. Due to the inference character χ is expected to vary periodically with k. One period is then 2krj. The photoelectron experiences energy dependent phase shifts both in the absorber when emitted and at the backscatterer. These phase shifts are taken into account in the total energy shift Φj(k). The factor Fj(k) describes the scattering strength of the scattering atom at position rj. The above EXAFS equation concerns a situation with only one backscatterer. For atoms in a lattice Eq. (3.14) has to be summed over neighboring shells.. χ = ∑ χ j (k ) j. (3.15). Additionally, for a polycrystalline sample with no texture the equation has to be averaged over the angle θj. The angular dependence is replaced by the coordination number of the j-th shell.. 3∑ cos 2 θ j = ∑ N j j. j. (3.16). The above assumptions concern a perfect lattice without defects and thermal vibrations. Defects may generate static displacements from the ideal lattice position. These static and dynamic displacements reduce the EXAFS amplitude. Assuming that the atoms in the j-th coordination shell have a Gaussian distribution with a standard deviation σj around the average shell distance rj, the EXAFS amplitude is damped by the Debye-Waller factor. e. −2σ 2j k 2. . The mean square average σj2 of the difference of the displacement uj of the scat-. terer relative to the displacement u0 of the absorber is defined as. σ 2j = [r j ⋅ (u j − u 0 )]2. (3.17). 33.

(34) X-ray Absorption Spectroscopy. An additional damping factor Dj(k) has to be added to the EXAFS equation, in order to account for inelastic scattering processes of the photoelectron with other electrons which reduce substantially the coherence length, thus reducing the number of the shells contributing to the interference to the very few nearest shells. D j (k ) = e. −2 r j. Λ. (3.18). Λ(k) is the mean free path of the photoelectron. Finally, the EXAFS equation for the K-edge absorption in polycrystalline samples can be written as. χ (k ) = ∑ j. N j F j (k ) kr j2. e. − 2 k 2σ 2j. −2rj. e. Λ. sin (2kr j + Φ j ). (3.19). A Fourier transform of χ(k) gives a quasi-radial electron density distribution function giving information about local structure around the absorber, which has already been shown in the early 1970s by Sayers, Stern and Lytle (Sayers 1971). For the data analysis of EXAFS it is interesting to evaluate the interatomic distances rj and their spread σj, as well as the coordination numbers Nj of the nearest neighbor shells. These parameters can be extracted from the oscillatory part χ of the measured absorption coefficient µ, provided the scattering amplitudes Fj(k) and the phases Φj are known. Nowadays, scattering amplitudes, phases and other parameters of importance are calculated by computer codes, which employ ab initio calculations and more sophisticated theories, e.g. multiple scattering theory, like the FEFF code used in this thesis.. 3.4 FEFF The FEFF code exploits the multiple-scattering theory6 and abandons the small atom approximation in favor for the curved wave model. The curved wave corrections are implemented by keeping the EXAFS formula, but replacing the complex backscattering amplitude F(k)eiΦ(k) by an effective scattering amplitude Feff, which is a function of k and rj. Though the interference of the photoelectron wave is mainly contributed by its direct backscattering on the neighboring atom to the absorber – also called single-scattering – a neighboring atom may scatter the wave to the original absorber on a more complex trajectory by reflecting the photoelectron wave via other neighbors. This is a multiple-scattering process, which is completely neglected in the basic EXAFS formula. For the analysis of the first coordination shell the single scattering model is sufficient to interpret the EXAFS 6. An introduction into the multiple-scattering theory for XAFS can be found in (Sainctavit 2006). 34.

(35) X-ray Absorption Spectroscopy. spectrum. For further shells in many cases also multiple-scattering paths have to be taken into account in order to interpret the spectrum properly, although their contributions are usually at least one order of magnitude weaker than those of single scattering amplitudes. However, they should not be neglected in certain configurations of three atoms in a row, where shadowing and lens effects may occur, which increase the amplitude of the multiple scattering paths drastically (Lee 1975). FEFF calculates the curved-wave multiple-scattering contribution to XAFS with use of formalism similar to the plane wave-approximation, but with scattering amplitudes replaced by distant-dependent scattering matrices, based on an exact, separable representation of the free propagator matrix elements in an angular momentum and site basis (Rehr 1990). For the construction of the scattering potential electron densities and atomic potentials are needed. These are calculated with use of a relativistic self-consistent code for the exchange potential; in the case of EXAFS the default Hedin-Lundqvist code (Hedin 1971) is usually sufficient (Rehr 2000). The atomic potentials are approximated by the muffin tin model. The FEFF code calculates also the complex partial wave phase shifts for the simulation of EXAFS spectra. Because of the huge number of scattering paths to be calculated FEFF. uses path filters, which cut off paths with longer distance and lower amplitude than. defined. FEFF also includes into the calculation the multi-scattering Debye-Waller factor based on radial disorder approximated by an isotropic Debye model. FEFF uses a single input file with a list of atoms and their Cartesian coordinates within the cluster. The atomic cluster is constructed upon the crystallographic data of the expected model structure. The header of the input contains information about the scattering potentials and several control flags, which allow varying calculation parameters, like exchange potential algorithms, muffin-tin overlapping, output options etc. A full list of the control flags, as well as a description of calculation strategies for different problems is given in the FEFF. manual and the official website of the FEFF project hosted by the University of Wash-. ington, Seattle, WA, USA. A thorough theoretical description of the. FEFF. code is given in. the paper by J.J. Rehr and R.C. Albers (2000). From the practical point of view of an experimentalist interested in the interpretation of standard XAFS spectra there are only few control flags of interest in the. FEFF. input file.. These are for example flags deciding whether XANES or EXAFS shall be calculated, whether to calculate the scattering amplitudes explicitly, or to use the self-consistent calculation algorithm, which for example gives better results for oxides. 35.

(36) X-ray Absorption Spectroscopy. For the fitting of the model spectra calculated by. FEFF. to the experimental data. (Newville 2001) is used, which is an interactive fitting algorithm for. FEFF. IFFEFIT. IFEFFIT. comes. with GUI programs ATHENA and ARTEMIS (Ravel 2005). ATHENA allows convenient XAFS data handling, where the background removal for extraction of the oscillatory part and Fourier transformation can be performed almost automatically. Nevertheless, it allows changing almost all parameters at any stage of the data processing procedure. It comes also with many additional tools useful in the experimental data analysis practice. ARTEMIS is the program for fitting the calculated spectrum to the experimental spectrum previously processed in ATHENA. The. FEFFIT. fitting model used by ARTEMIS represents the model χ func-. tion as a sum of χ functions of individual scatterings paths.. χ model (k ) =. ∑χ. (3.20). path. paths. Where χpath is defined as.  Amp(k ) × Ndegen × S02. χ path ( k ) = Im  . k ( Reff + delR ). 2. 2   exp  −2 p′′Reff − 2 p 2sigma2 + p 4fourth  3  .     sigma2  4 3 × exp i 2kReff + phase ( k ) + 2 p  delR − 2 − p third   Reff  3      . (3.21). The parameters p’ and p” are the real and imaginary parts of the complex momentum with respect to E0 – the bottom level of the conduction band, and are evaluated 2.  2me i  p = p′ − ip′′ =  Re ( p ( k ) ) −  − iei 2 λ (k )  h . (3.22). k is the real momentum with respect to the Fermi level, evaluated as  2m  2 k = kFEFF − e0 2 e   h . (3.23). The quantities Amp, phase, Re(p), and λ in the above equations are all functions of kFEFF, and are taken from path data files generated by the FEFF calculation, as is kFEFF itself. Ndegen – degeneration number of the path – and Reff – the effective path length – are also taken from these files. The path parameters in the above equation are as follows:. 36. e0. – shift of energy origin. ei. – imaginary energy shift (responsible for additional broadening).

(37) X-ray Absorption Spectroscopy. S02. – constant amplitude factor. delR. – change in half path length (1st cumulant, added to Reff). sigma2. – mean-square displacement (2nd cumulant), or Debye-Waller factor. third. – third cumulant. fourth. – fourth cumulant. A full description of the features and possibilities of. IFFEFIT. and its components. ATHENA, ARTEMIS, as well as XAFS data analysis tutorials can be found in the manual and the official website of the. IFEFFIT. IFEFFIT. project hosted by The Consortium for Ad-. vanced Radiation Sources, Argonne, IL, USA.. 3.5 Experimental Set-up for XAFS For recording a XAFS spectrum one needs to tune the energy of the incoming beam at a range of about 1 keV. Most commonly bending magnets are used as light sources for XAFS experiments, as their beam intensity is sufficient and almost constant within this energy range. Then, in order to get an energy tunable lights source, one needs only to use and control an appropriate monochromator. In some cases, where higher beam intensities are required, wigglers or undulators are used as sources. But then the control system becomes far more complicated, as one has not only to control the monochromator but also the undulator or even an array of undulators in order to stay tuned at the high intensity harmonic of the undulator. Monochromators exploit the effect that light of different wavelengths is diffracted at different angles. For hard X-rays they consist most commonly of a double Si crystal. For energies of 2 to 10 keV a Si(111) cut is used, for the range from 10 to 20 keV Si(311) is the optimum, whereas for energies above 20 keV Si(511) crystals are used. When a better energy resolution is needed, four-crystal systems can be used. Silicon single crystals are used because they are available in large pieces, have a very low density of defects and allow easy mechanical processing. For soft X-rays gratings are widely used for monochromatization. The monochromatized beam passes through an ion chamber or a transmitting photodiode, in order to measure the initial beam intensity I0. Then it enters the sample chamber, which may vary very much in its form and content, depending on the experimental needs. It may contain cryostats, furnaces, vacuum systems etc. Generally, in the case of soft Xrays (below 2 keV), the whole experimental set-up has to be confined in a UHV system, because of the high absorption in air. For energies above 7 keV the absorption in air be37.

(38) X-ray Absorption Spectroscopy. comes low enough to let the beam pass through air gaps bridging the experimental set-up. A higher penetration at larger photon energies allows also performing environmental XAFS in the presence of gases or liquids. In the classical X-ray absorption spectroscopy experiment a second ion chamber is placed behind the sample. This is the transmission mode, in which the absorption coefficient is measured directly according to the Beer-Lambert law. µ ∝ − ln. I1 I0. (3.24). Though simple, this detection mode needs some precautions to be undertaken during sample preparation. The sample has to have an appropriate thickness; if too thin, the absorption signal will be too weak for analysis; if too thick, the absorption signal will be out of the linear range of the detector or will not be measurable at all. The sample prepared should also have uniform thickness with no pinholes in it. In the case of too thick samples that cannot be made thinner, like samples on substrates or diluted samples, the fluorescence yield mode can be used. This is also a photon-in photon-out technique, where the characteristic fluorescent radiation originating from the relaxation of the core-hole level is detected. In the relaxation process the core-hole induced by the photo-absorption process is filled by an electron from a higher shell and a photon is emitted with an energy equal to the energy difference between the levels. This characteristic radiation is detected usually with solid state Si or Ge detectors. The florescent signal intensity is directly proportional to the absorption coefficient.. µ∝. I1 I0. (3.25). For non-diluted samples the self-absorption effect, which significantly damps the XAFS spectrum in comparison to XAFS spectra measured in transmission mode, has to be taken into account. Another detection technique is the total electron yield measurement. In this technique the primary photoelectrons, secondary electrons and Auger electrons originating from the non-radiative relaxation of the core-hole are detected. Only the contribution of the Elastic Auger Yield (EAY) is directly proportional to the absorption coefficient, but by applying appropriate background subtraction procedures one can get rid of the inelastic contribution. 38.

(39) X-ray Absorption Spectroscopy. from the TEY signal (Stöhr 1984). Then, the relation (3.25) is also valid for the TEY detection mode, which is a far simpler technique than EAY. Thus, the TEY detector consists of a plate electrode on a positive potential connected to an electrometer, whereas the EAY detector needs an electron energy discriminator. The AUTOBK algorithm (Newville 1993) implemented in. IFFEFIT. is such a background subtraction procedure, in which the part be-. hind the absorption edge is taken into account. Samples for TEY measurements have to be conducting and connected to the ground, in order to not to get charged by the continuous electron loss. This would lead to a decay of the TEY signal with time. Filling the sample chamber with some helium gas allows improving the detection yield, by reducing the work function. One of the major drawbacks of the TEY detection mode is the need of a high vacuum due to the interaction of electrons with matter. On the other hand, the high crosssection of electrons interaction with matter results in the fact that the TEY signal originates from a region of only few nanometers thickness below the surface, making it an excellent technique for surface analysis (Abbate 1992, Stöhr 1984, Vogel 1994).. 3.6 Data Handling In this Section, the practical XAFS data handling procedure is presented on the example of an α-Fe spectrum. The data were measured in transmission geometry. Data recorded by the detectors and stored e.g. in appropriate columns in ASCII raw data files have to be processed according to the expression (3.24) or (3.35), depending on the detection mode used, in order to get the energy dependent function proportional to the X-ray absorption cross-section µ (solid line in Figure 3.2). Fig. 3.2 Absorption cross-section function of metallic iron at Fe K-edge after preprocessing of raw data. The absorption edge-step and the EXAFS oscillation in the post-edge region are pronounced. After normalization, preedge line and post-edge should be parallel.. The second step is the normalization of the spectrum to the edge step. To do it ‘manually’ one has to determine the edge energy and to fit a straight line to the pre-edge region and subtract it form the data. Then one has to fit a first or second order polynomial to the post edge region and to divide the data set by its value at the edge energy. When using 39.

(40) X-ray Absorption Spectroscopy. IFFEFIT. the normalization is done automatically by one of the background subtraction algo-. rithms for EXAFS, e.g. AUTOBK, which mimics the quasi-atomic contribution µ 0 into µ by backward Fourier transform, minimizing the χ(R) oscillations below Rmin (usually around 1 Å). Fig. 3.3 Normalized absorption function of metallic iron at Fe K-edge. The background function cuts through the middle of the EXAFS oscillations. In the next step it is subtracted from the spectrum to give the χ(k) function.. After normalization one has to define the edge-step energy E0 for the further EXAFS analysis and for a comparative determination of formal valence states in XANES. The determination of E0 is somewhat arbitrary. There are two most commonly used methods to define it: E0 as a maximum of the first derivative and E0 as a half of the edge-step. Our research group tends to use the half edge-step method, as it gives in our opinion a better estimation of the chemical shifts. For EXAFS one has to extract the oscillatory part of µ (see Eq. (3.13)). In. IFFEFIT. this. is done by subtracting one of the background functions (preferably AUTOBK) from the normalized absorption cross-section function. The extracted oscillatory part, χ, is rescaled into the wave vector space k according to the equation. k=. 1 2me ( E − E0 ) h. (3.26). Figure 3.4 shows the χ(k) function for metallic bcc iron measured at the iron K-edge. Fig. 3.4 EXAFS oscillations after background removal and normalization. The oscillations are a consequence of interference of outgoing and backscattered photoelectron waves, which slightly alter the photoelectron density at the absorber. Therefore the absorption crosssection is also modified.. 40.

(41) X-ray Absorption Spectroscopy. The next step is the preparation of the χ(k) function for the forward Fourier transform (FFT) into the R space. First, the χ(k) data set is multiplied by an appropriate power of k in order to make the oscillations approximately symmetric within the desired transformation window; usually k or k2 is sufficient. Fig. 3.5 The χ(k) function prepared for FFT. The window defines the k range to be transformed into the R space. It should include as much information as possible, but without the noisiest parts, which would introduce artifacts into the real space EXAFS function.. This procedure emphasizes the higher k oscillations which contribute to the lower R features in the real space EXAFS function. Beside this, the FFT parameters have to be set, like: k range to be Fourier transformed, type of the window function and window slopes. The application of window function is necessary, since the Fourier transform runs from negative infinity to infinity, and the data set corresponds of course to a finite k-range. There is no simple recipe of how to choose the parameters. The choice depends strongly on the given spectrum, the experimentalist’s experience and preferences, as well as the information to be derived. Fig. 3.6 Real space EXAFS function of metallic bcc iron. As it is a result of the Fourier transformation it consists of real part harmonics and imaginary part harmonics. The magnitude resembles the quasi-radial electron density function around the absorber, averaged over all absorber sites in the sample.. The obtained EXAFS function corresponds to the quasi-radial electron density function in the surrounding of the absorbing element averaged over all absorber sites in the sample set off by the phase shifts suffered by the photoelectron in the photoabsorption and the scattering events. In order to interpret the data it is necessary to have additional information like XRD data, or possible models of the structure studied. These models can then be used in ab-intio calculations and verified in EXAFS data analysis. 41.

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(45) Chapter 4 Sample Preparation and Preliminary Characterization In this Chapter the sample preparation and the preliminary sample characterization are described. A brief presentation of results and the conclusions upon them are given for the experiments conducted including magneto-resistivity measurements and scanning electron microscopy along with energy dispersive X-ray spectroscopy study. NMR and Mößbauer spectroscopy results as well as XRD data are also presented.. 4.1 Sample Preparation The samples were prepared at Instituto de Nanociencia de Aragon de la Universidad de Zaragoza, Spain (INA). The main batch (batch be – see below) was prepared by the Author in November 2006. The samples were fabricated by ball-milling of spherical < 10 µm high purity Fe powder of Goodfellow-ALFA. The vibrating ball mill is a modified Pulverisette model by Fritsch and can work at following pressures: ambient atmosphere, 10–1 mbar, 10–5 mbar, 10–7 mbar depending on the pumping apparatus. It was found that the optimum pressure for Fe powders is 10–5 to 10–7 mbar. Poorer vacuum of less than 10–3 mbar results in a significant oxidation of the Fe particles. Previous experiments have shown that the milling time should last for at least some tens of hours to get the desired magnetoresistive properties. In order to avoid overheating of the milled powders a sequence of 20 min milling time followed by a 10 min pause was used. Post-milling treatment was applied to tune the nano-contact transport properties. The powders were annealed in a tube furnace for durations shown in the list below and then left to cool down for 24 h under given vacuum conditions in the furnace..

(46) Sample Preparation and Preliminary Characterization. Below, a list of the Fe powders produced at INA is shown. The following notation is used: Fexh-bn-TTt, where x is the milling time under 10–6 mbar, n is the batch number and t is the label that indexes the kind of thermal treatment (TT) of the sample after milling. Batch 01: Fe16h-b01, Fe224h-b01 Batch 02: Fe16h-b02 Batch 03: Fe16h-b03-TT0: no thermal treatment Fe16h-b03-TT1: 350 °C at 10–5 mbar for 3 h Fe16h-b03-TT2: 350 °C in air for 5 min Fe16h-b03-TT3: 200 °C at 10–1 mbar for 2 h Batch 04: Fe56h-b04, Fe112h-b04, Fe168h-b04, Fe237h-b04 and Fe336h-b04 Batch 05: Fe8h-b05, Fe16h-b05, Fe32h-b05, Fe56h-b05, Fe112h-b05, Fe168h-b05 and Fe224h-b05 The pristine spherical Fe micro-powder is denoted as Fe0h. Of the above listed samples, XAFS, NMR and Mößbauer spectroscopy (MS) experiments have been performed on the following powders: Fe0h, Fe224h-b01, Fe16h-b03TT0, Fe16h-b03-TT1, Fe112h-b04, Fe336h-b04 and the entire b05-batch. In order to enhance the sensitivity and resolution of NMR and MS measurements conducted in parallel with the XAFS experiments, an additional 57Fe enriched batch was prepared at INA. Commercial 96%. 57. Fe isotope powder by CHEMGAS was mixed with the. Fe0h powder of natural abundance of 57Fe in a mass ratio of 1:4 in order to obtain samples containing approximately 20% of 57Fe. The following isotropically enriched samples were prepared by ball milling at 2×10–6 mbar and subsequent thermal treatment: Batch e:. Fe1h-be Fe16h-be-TT0: no thermal treatment Fe16h-be-TT1: 300 °C at 2×10–6 mbar for 1 h Fe16h-be-TT4: 300 °C in air for 1 h. The pristine 57Fe isotope powder was denoted as Fe57. In the course of this Work the results of the following samples are presented Fe0h, Fe1h-be, Fe16h-be-TT0, Fe16h-be-TT1, Fe16h-be-TT4, Fe16h-b03-TT0, Fe16h-b03-TT1, Fe112h (Fe112h-b04), Fe336h (Fe336h-b04), since this samples followed the whole ex-. 46.

(47) Sample Preparation and Preliminary Characterization. perimental cycle. The magnetoresistance results presented in the following Section are an exception, where only the results for the be-batch are given.. 4.2 Magnetoresistance Measurements Directly after the preparation the be-batch samples were characterized concerning their magnetoresistive properties. The measurements were conducted on an INA home made experimental set-up for MR measurements in alternating magnetic fields (Fig. 4.1).. N. S. A. B. CONTROLLER. Ω. . Fig. 4.1 Scheme of the experimental set-up for MR measurements. The powder is put into a plastic vessel (zoom) with electrical contacts. Uniaxial pressure is applied to enhance the junctions between the grains. The device is placed in an electromagnet which is supplied by a programmable stabilized power supply (B). The magnetic field intensity is measured by a Hall probe (A). The resistance is measured by means of 2-point sensing. The controller provides connection to the PC, acquires data from the sensors and controls the power supply. (INA home design). Below, the results of the MR measurements are presented. The measurements were carried out for four cycles of alternating magnetic field. Uniaxial pressure was applied to the device by use of a micrometer. The standard pressure applied was corresponding to 210 µm compression.. Fig. 4.2 MR measurements of the pristine 57Fe isotope powder, Fe57. The zero field resistivity shows a good cycling stability. The non-zero field resistivity increases with number of cycling but has a saturation tendency. The last cycle has a MR response of about 84%.. 47.

(48) Sample Preparation and Preliminary Characterization. The resistance was measured by 2-point sensing and the magnetic field intensity was controlled by a Hall probe. All the data were acquired on a PC via a digital controller. The experiments were conducted at room temperature in the magnetic field of up to 4.5 kOe.. Fig. 4.3 MR measurements of the pristine 57Fe isotope powder mixed with Fe0h powder. The MR response is approximately constant with cycling. The last cycle has a MR response of about 43%. The overall resistivity of the device is relatively high.. Fig. 4.4 MR measurements of the 1 h milled sample Fe1h-be. The MR response shows a very good cycling stability. The MR response in the last cycle amounts to ca. 66%. The overall resistivity of the sample is significantly higher than for the other milled samples Fe16h-be-TT0 and Fe16h-be-TT1.. Fig. 4.5 MR measurement of the 16 h milled samples Fe16h-be-TT0. The resistance exhibits an unstable character in the first two cycles. The next two cycles have a tendency to converge around a MR response value of about 75%. The overall resistivity is very low. The instability is most probably a result of mechanical instability of the particles due to insufficient pressure and a resultant movement of the particles in the alternating applied field.. 48.

(49) Sample Preparation and Preliminary Characterization. Fig. 4.6 MR measurement of the 16 h milled and subsequently vacuum annealed sample Fe16h-be-TT1. The overall MR behavior is similar to that of Fe16h-be-TT0, but without the instabilities of the previously presented case. The zero field resistance decreases asymptotically to a constant value, as does the increasing non-zero field resistance. The last cycle has a MR response of about 90%. The resistivity of the sample is of the same order of magnitude as this of Fe16h-be-TT0.. Fig. 4.7 MR measurement of the 16 h milled and subsequently air annealed sample Fe16h-be-TT4. The resistivity behavior is very unstable. The overall resistance is very high in the MΩ range. The MR response increases with cycling. Such effects may result from mechanical instabilities of the powder particles; therefore the pressure applied was doubled.. Fig. 4.8 MR measurement of the 16 h milled and subsequently air annealed sample Fe16h-be-TT4 after doubling of uniaxial pressure. The resistivity is significantly reduced, but the MR response disappeared almost completely.. The pristine iron powders show a very high MR response, though they lack the MR stability exhibited by the milled powders. Longer milling lowers the resistivity of the samples. Vacuum annealing improves the cycling stability, whereas air annealing destroys the MR response almost entirely. 49.