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FINES will be charged if book is returned after the date stamped below. PLEASE NOTE: In all cases this material has been filmed in the best possible way from the available copy. Problems encountered with this document have been identified here with a check mark 4 . 3999993 5090 10. 11. 12. 13. 14. 15. 16. Glossy photographs or pages __ Colored illustrations, paper or print Photographs with dark background __ Illustrations are poor copy Pages with black marks, not original copy Print shows through as there is text on both sides of page lndistinct, broken or small print on several pages / Print exceeds margin requirements Tightly bound copy with print lost in spine Computer printout pages with indistinct print Page(s) lacking when material received, and not available from school or author. Pagels) seem to be missing in numbering only as text follows. Two pages numbered . Text follows. Curling and wrinkled pages Dissertation contains pages with print at a slant, filmed as received Other U-M-I OPTICAL PROPERTIES OF ORDERED AND DISORDERBD SYSTEMS by N. Kedarnath A Dissertation Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics and Astronomy 1987 77’ C“YE/‘72:! 0 ABSTRACT OPTICAL PROPERTIES OF ORDERED AND DISORDERED SYSTEMS BY N. KEDARNATH An experimental investigation of the effects of generalized order-disorder transitions (Hi the optical properties and electronic levels in three metallic systems is described. The three metallic systems studied were (1) atomically ordered and disordered Cul_thX alloys (x s 0.25), (2) metallic glass a-Fe0.8Bo.2 and (3) layered and laser quenched Ni-Ti alloys. Measurements of the optical reflectivity in the energy range 1 eV tx>53 eV and the electron energy loss spectra in the energy range 3 eV to 90 eV were undertaken to study electronic properties. Sample characterization was achieved by X-ray and electron diffraction for structure determination and X-ray energy dispersive spectroscopy for composition micro-analysis. In dilutel U( s 0.10) Cu1_.XPtX disordered alloys, an indirect evidence suggesting the formation of Pt derived impurity states (virtual bound states) was seen. In alloys with 0.175 s x s 0.25 certain order-disorder related effects were identified. These included (1) an overall lower N. Kedarnath reflectivity of the ordered phase compared to the disordered phase and (2) a structure in 52(w) at about 6 eV seen only in the disordered phase. Origins of these effects are discussed in detail. The electron energy loss spectra of the metallic glass a-Feo 8 EN).2 agree well with the results of other investigators. Certain features (at 2.5 eV and 4.0 eV) in the loss spectra attributed to volume excitations by other investigators were seen to be due to surface excitations. Directly measured and computed reflectivities agree well with published results; a significant difference between our computed 52(w) and that of other workers was seen. The energy loss spectra of layered NiTi was seen to be different from a simple superposition of the spectra of Ni and 1&4 In addition, a close resemblance between the EELS of layered Ni-Ti and crystalline NiTi alloy was seen. The processes of alloying and amorphization appeared to have no effect. 1500 A. The samples used in this study were thinner than 1000 A, as revealed by EELS measurements. The accuracy of the thin-film micro-analysis technique is in the 5% - 10% range. For higher accuracies, "k-factors" computed from standard thin-film samples of known composition are needed. A typical x-ray energy dispersive spectrum is shown in Figure 2.11 for the Cu3Pt ordered alloy. UI-UZCOC 27 LT-ZOS SECS 700”- 6000-: v- V—vwv—fi v—r—V v—v 50.0- i 4000‘] Jose—l r.—¢ fi—fis r—L ff- 0 . sea 2000-> - loan-J i 7‘ 20.000 Figure 2.11 X-EDS of Cu3Pt Alloy 28 MEASUREMENT OF ELECTRONIC PROPERTIES In this study of the order-disorder effects on the optical/electronic properties of metallic systems we chose the following two techniques to measure the electronic properties: 1. Electron Energy Loss Spectroscopy (EELS) 2. Optical Reflection Spectroscopy The EELS measurements were carried out in the electron energy loss range (electronic excitation energy range) 5 eV to 90 eV in the Vacuum Generators HB 501 FE-STEM of the MSU Analytical Electron Microscopy Lab. The optical reflectivity spectra were obtained using a measurement facility developed by us on a NSF equipment grant. The following two sections describe these two techniques in detail. 29 ELECTRON ENERGY LOSS SPECTROSCOPY Electron Energy Loss Spectroscopy (EELS) is the study. of momentum and energy distribution of electrons that have interacted with a solid [2.6]. This is a powerful micro- analytical tool to study various electron excitations in a solid. The incident electrons interact with the electrons in.tflu3 solid through electromagnetic interaction; hence, EELS provides us with a method to study quantitatively the bulk dielectric function of the solid. A brief description of this technique is given below. Consider a beam of fast electrons of energy E0 ( 100 KeV, for example) and intensity 10 incident on a thin ((1000 A) sample. .A large fraction of these electrons go through without interacting with the sample. The rest are elastically and inelastically scattered. The energy and momentum distributions of these scattered electrons yield informatitnt about the solid under investigation. The scattered electrons are detected over a solid angle d9 in the direction (e,¢). An energy analyze) is used to collect the energy spectrum. See Figure 2.12 for a schematic of the electron energy loss measurement process in the transmission geometry. The energy loss intensity I(E,e) for single interactions is given by [2.12, 2.13]: I(E,0) d=a(E,e) IO dEdQ 30 Incident beam Eo ANALYZER Figure 2.12 Transmission EELS in an AEM 31 where dzo/dEdQ is the differential scattering cross—section for an electron in the direction 6 and with an energy loss E. N is the number of atoms/unit area in the volume of the sample examined. The differential scattering cross-section is related to the macroscopic dielectric function 5(a)) as shown below [2.12, 2.13]: d30(E,0) Im (“l/6(a)) l dEdQ 2n=a0nE0 62 = 9; Here, 9E is the characteristic scattering angle defined E<< E0 Thus for a fixed a, we find that the energy loss probability is directly propositional to the imaginary part of the loss function, -1/e(w). Optical measurements, on the other luuui are proportional to 22, the imaginary part of e(w). The difference is due to the fact that the electrons in the solid respond to a transverse electromagnetic field in optical measurements and to a longitudinal electrical field in the case of electron energy loss experiments. By the same argument, optical experiments measure Strans and EELS measure along? but detailed studies indicate that these two functions agree very well [2.14]. 32 A typical energy loss spectrum has many features depending on the types of excitations present in the solid [2.14, 2.12, 2.13]. Commonly occurring excitations are interband transitions, collective oscillations and core excitations. The low energy end of the spectrum is dominated by the zero loss peak, the electrons that have lost little or no energy in traversing the solid. In addition to this, one may find features that are due to interband transitions and collective excitations (plasma oscillations). Both direct and indirect interband transitions can occur. Volume and surface plasma oscillations are the collective oscillations that occur in this energy range. The volume plasmons are oscillations in the electron charge density setup by the electric fields of the incident electrons. The energy Ep of the volume plasmon is a function of the electron density N (number/volume). The exact relationship is [2.13, 2.14, 2.151.: 41rNe2 me where me is the (effective) mass of the electrons. This energy Ep is determined by the condition e(w) = 0 at the plasma frequency. For a vacuum-metal interface the surface plasmons oscillations occur at the energy ES [2.14], ISI- ‘f-IZCCO 33 LT-Zl SECS NI'I'KSD/Sfll . O o 3 . O r' I ..- \ . - s a . . we -' ‘. 'I \ j ~ I I. . \ .r . . , '. ; \ I \ s Q Q be up, ‘ a ‘L . \ . ItitTrrrTrrlviivrrIU . 56.4 ENERGY IV ....‘4 5 0 U I - '. \. ‘AR TYTIIIIIVII . ' Irrrrrrirvirrrrrvvrt -J.6 16.4 Figure 2.13 EELS of NiTi Alloy 6.4 34 E5 = I With Evac = 1 For a system of free—electrons with very little scattering, the volume plasmons would show up as a sharp peak at Ep is the loss spectrum. In a real metal, this peak is broadened by the different scattering mechanisms present. Shifts in the location of this peak are possible due to changes in the electron density and the effective mass [2.14]. For most metals and alloys the collective excitations can be found below 35ev. For energy losses above 35ev, a different physical process is responsible. This is the excitation of a core electron of an atom to the continuum [2.12, 2.13]. These excitations are sensitive to the local chemical composition and atomic environment, and this is exploited in techniques such as EXAFS [2.16]. 35 MEASUREMENT OF OPTICAL REFLECTIVITY Band structure investigation of various elements and alloys using optical spectroscopic methods is well established. Some of these methods are photoemission spectroscopy (PES, XPS, UPS), ellipsometry and optical reflection spectroscopy. These techniques provide much needed information about the conduction and valence bands Density of States (DOS). In this study, we measured the total reflectivity of the samples in the photon energy range 1 eV to 5 eV. These measurements complement the electron energy loss measurements. The total (specular and diffuse) optical reflectivity of the various alloys were measured using a facility developed at MSU. This facility consists of a light source (IR and UV-VIS), a monochromator, an integrating sphere, a detector and associated electronics. See Figure 2.14 for a schematic of this facility. The heart of this facility is a 15 cm diameter integrating sphere made by Labsphere. The inner surface of the sphere is coated with a highly reflective material (barium oxide). The reflectivity of this material is accurately known over the energy range measured. Measurements of the absolute reflectivities of samples were avoided; instead, the sample's reflectivity was compared to that of a reference coated with barium oxide. Moreover the use of an integrating sphere made possible the measurement 36 HONOCHROHATOR SOURCES ( JFII to 0.1,..- ) I new-com INTEGRATING SPHERE PHASE SENSITIVE DETECTOR A: Reference mirror part 3: Sample port C: Detectors ( PbS cell or PHI ) D: Vibretlng lirrot Figure 2.14 Layout of Optical Reflectivity Measurement Systems 7 - im-“WZV.LK , 37 of the total reflectivity without extensive efforts to prepare the surface of the sample. The reflectivity measurements were made at near normal (~ 4°) incidence. The relative location of the inlet and detector ports were such that the detector only measured the uniform light level setup by multiple scattering off the sphere wall. Optical reflectivity measurements over the photon energy range 0.6 eV to 5.5 eV was possible. Two different light sources were used to accomplish this. A 150 W xenon arc lamp for the range 1.0 eV to 5.5 eV and a IR lamp for the range 0.6 eV to 1.0 eV. The lamps were operated by stabilized power supplies. Though reflectivity measurements in the photon energy range 0.6 eV to 5.5 eV were possible, noise considerations limited the range to 1 eV to 5.0 eV. It SPEX MINIMATE monochromator was for wavelength selection. This monochromator incorporates a diffraction grating i 1 the Czerney-Turner mount. A microprocessor controlled stepper motor drive ensured wavelength selection to within.l.1un. Three gratings were used -a 600 lines/mm 1250 nm blazed grating for the range 700 nm to 2000 nm (1.7 eV to 0.6 eV), a 1200 lines/mm 500 nm blazed grating for the range 400 nm to 700 nm (4 eV to 1.8 eV) and a 1200 lines/mm 250 nm blazed grating for the range 250nm to 400 nm (5.5 eV to 4.0 eV). Two order sorting filters (pass bands 400 nm to 1200 nm and 700nm to 1200 nm) were used to eliminate unwanted higher orders. The detectors used were a 38 photomultiplier and a PbS cell. The photomultiplier, with its quartz envelope had good sensitivity in the UV and visible spectrum. The PbS cell served as the IR detector. The incident light was chopped at about 200 Hz and the output of the detector at this frequency was measured using a lock-in amplifier. The incident light could be switched from the sample to the reference with help of a scanning mirror. Thus, one could see the intensities of light reflected by the sample or the reference. The ratio of these two intensities is the reflectivity of the sample. To obtain the absolute reflectivity this has to be corrected for the actual reflectivity of the reference. Pure metallic samples of known reflectivities such as Cu,Au, Pt and Ag were measured to check the accuracy of the system. The results obtained were within 5% of the published results. Hence, the error associated with the measurements obtained with our system was taken to be 5%. CHAPTER.3 Optical Properties of Ordered and Disordered Cu1.thx Many metallic alloys exhibit generalized order- disorder transitions with attendant changes in electronic and optical properties. Elsewhere in this dissertation, we have described the effects of topological disorder on electronic and optical properties. In this chapter an experimental study of the effects of atomic order-disorder transitions on electronic structures is described. In alloy systems where the constituent elements are very similar in their electronic structure (configuration), atomic order-disorder transitions produce minor perturbations in electronic levels of the alloys. The noble elements Cu and Au form a series of stoichiometric alloys that show very small changes in the properties due to order-disorder transitions. Apart from showing weak structures the reflectivity of cmdered Cu3Au differs by less than 3% from the reflectivity of the disordered phase [3.1]. The transition metal--noble metal alloy Cu1_thx was chosen for study in this investigation. The alloy was available in the ordered and disordered phases for x = 0.175, 0.20 and 0.25. For Pt compositions below 10% 39 40 (n = 0.10, 0.08, 0.06, 0.04 and 0.02) the alloy was available as cast (disordered). The systems Cu-Au, Cu-Pd and Cu-Pt are specially suited for investigating the effects of atomic order- disorder transitions because the order-disorder transitions occur over a range of compositions. For example, the alloy system Cu1.thx exhibits ordered phases [3.2] for x near 0.25, 0.50 and 0.75. For x near 0.25, the structure of the disordered phase is the FCC Crystal with each lattice site occupied by an 'average' atom ( (l-x) Cu + x Pt). In the ordered phase the Pt atoms occupy the cube-corners and the Cu atoms occupy the face centers of the FCC lattice. This selective occupation of the lattice sites by atoms of different species leads to extra Bragg lines in the X-ray diffraction pattern called 'Super lattice' lines [3.3]. The effect of ordering can also be seen by constructing reciprocal lattices of the ordered and disordered phases. For the ordered phases, there are extra Brillouin planes in the reciprocal K-space [3.4]. The presence of these extra planes are a potential source for structure in the optical properties. Figure 3.1 depicts the Wigner-Seitz cell for the FCC lattice with a cubic superlattice inscribed. We twill refer to Figure 3.1 and discuss the origin of extra structures in the Optical properties later in this chapter. The systems Cu-Au, Cu-Pd and Cu-Pt offer a few other advantages for the study of order-disorder transitions and 40 (n = 0.10, (3.08, 0.06, (3.04 and 0.02) the alloy was available as cast (disordered). The systems Cu-Au, Cu-Pd and Cu—Pt are specially suited for investigating the effects of atomic order- disorder transitions because the order-disorder transitions occur over a range of compositions. For example, the alloy system Cu1_thx exhibits ordered phases [3.2] for x near 0.25, 0.50 and 0.75. For x near 0.25, the structure of the disordered phase is the FCC Crystal with each lattice site occupied by an 'average' atom ( (1-x) Cu + x Pt). In the ordered phase the Pt atoms occupy the cube-corners and the Cu atoms occupy the face centers of the FCC lattice. This selective occupation of the lattice sites by atoms of different species leads to extra Bragg lines in the X-ray diffraction pattern called 'Super lattice' lines [3.3]. The effect of ordering can also be seen by constructing reciprocal lattices of the ordered and disordered phases. For the ordered phases, there are extra Brillouin planes in the reciprocal K-space [3.4]. The presence of these extra planes are a potential source for structure in the optical properties. Figure 3.1 depicts the Wigner-Seitz cell for the FCC lattice with a cubic superlattice inscribed. We will refer to Figure 3.1 and discuss the origin of extra structures in the optical properties later in this chapter. The systems Cu-Au, Cu-Pd and Cu-Pt offer a few other advantages for the study of order-disorder transitions and 41 Figure 3.1 Wigner Seitz Cells of Face Centered and Simple Cubic Unit Cells 42 their effect on the optical properties. In these systems, the order-disorder transitions are not accompanied by a large change in the crystal structure or the lattice constant. Ihn Cu3Au and Cu3Pt the change in the lattice constant is less than 1%. These systems are also free from the complications of magnetic effects. That the Cu-Au system has been a prototype for order-disorder studies should come as no surprise. There are some important differences between the Cu-Au and the Cu-Pt and Cu-Pd systems. The elements Cu and Au belong to the noble elements group and have similar electronic structure. These two elements have 11 outer electrons i1) the configuration dlosl. The noble metals (Cu, Au and Ag) are characterized by a sharp absorption edge in their optical reflectivity spectra. This sharp edge is caused by the onset of interband transitions and for'ChJ and Au this edge occurs at about 2 eV and 2.6 eV respectively; for Ag this edge is at about 4.0 eV. Below this edge, the reflectivity is very high (almost 1.0). This accounts for the characteristic colors of Cu, Au and Ag. The elements Pt and Pd are transition metals. They 'have a total of 10 outer electrons. Their electronic Structure is le-nsn. In contrast with the d-bands of the nOble metals which do not cross the Fermi level, the d- bands of these elements cross the Fermi level. Interband 43 transitions from the occupied d-levels start at very low energies. Investigations of the electronic and optical properties were carried out using electron energy loss spectroscopy (EELS) and optical reflection spectroscopy. Other analytical techniques employed were X-ray diffraction and electron diffraction for structure determination and X- ray energy dispersive spectroscopy (X-ray EDS) for composition analysis. These techniques are discussed in detail in Chapter 2. SAMPLE PREPARATION: Samples of Cu1.XPtx atomically ordered (denoted 'G') and disordered ('U') in the Pt concentration range 0.175 s x s 0.25 were supplied to us by E. W. Collings of the Battelle Memorial Institute. A measurement of the long range order (LRO) parameter by X-ray diffraction revealed that the LRO parameter of the ordered (G) phase was between 0.65 and 0.75 for the 3 compositions (x = 0.175, 0.20 and 0.25), studied. Atomically disordered samples made by quenching the alloy melt showed no superlattice Bragg lines in the diffraction pattern. Thin sheets (about 200 pm) of the sample were prepared for the reflectivity measurements by etching them in 15% KCN solution. A potential difference of 5 Vac was used for tfllis electro-chemical process. This procedure yielded Sttrfaces that were free of scratches and other surface dalnage. 44 After optical reflectivity measurements, 3 mm dia. discs were cut from the sample and mechanically polished to a final thickness of about 30 um. Using a South-Bay jet- etching unit and a 15% KCN solution, these discs were etched. This procedure produced perforations in the middle of the discs. Regions around the perforations were thin enough ( < 1000 A) to transmit the high energy electrons of the electron microscope. RESULTS AND DISCUSSION: Measurements of the optical reflectivities (1.0 eV to 5.0 eV) and the EELS were done for the phases (G) and (U) for Pt concentrations of 17.5%, 20% and 25%. For lower Pt concentrations (below 10%), the alloy exists in the disordered phase; reflectivity measurements alone were carried out on these samples. Figures 3.2 - 3.11 display the results of the reflectivity measurements. For low Pt concentrations, the absorption edge at 2 eV in pure Cu is well preserved, though diminished in magnitude. 1m: measurable shift in the position (2 eV) of the edge is observed. The magnitude of the drop in R decreases as the Pt concentration increases. By about 10% Pt, the edge has completely disappeared. For Pt concentrations of 17.5% and above the Elm) spectraresembles that of pure Pt. The reflectivity of the ordered phases is consistently below that of the disordered phase, in the energy range 1.0 eV to 5.0 eV. Apart from this difference, Pt 45 Illltlllllllr L- + +— + . +- + - ‘- + . + _ + + _ + .. + )- + -l + + ._ + _. + _ + - + + ._ + ... lllllLlllLllL OOOOOOO omeeeui‘t"? OOOOOOO AitAiiaaIIaJ Figure 3.2 Reflectivity of Pt 6.0 5.0 2.0 1 8V Cu 46 T 1 EU I ‘ | ' l l _ + _ + - +‘I1 + + ._ + _ + - + - _ + _ + _ + . + + i + — ++ L_+ - + l—l— _. l l l l l 1 l u l l L O O O O O O O O O m m e a m. a. a. V" O O O O O O O A11A113allaJ PiSure 3.3 Reflectivity of Cu eV 47 'l‘l‘l'lrl'l _ + ‘ + - + - + + ._ + " ... + o\,,_ + . £3 + + 44— + — [1 + ll. + _ 3 + C.) + l—+ -‘ + _+ - + + _+_ _. lijlljllllll oooooooo seeEEE‘f‘l HQOOOOOO AiiAtiaailaJ Figure 3.4 Reflectivity of CuO_93Pt0 02 1 EV 48 ++++ 4.0 CU-Pt (4%) + ++ + + 20 1 . 1 l 1 l l I l I L I L l l o O r\ LO O (D 5 <5 a 4114113aila O 0.90 0.40 3 o in o J Figure 3.5 Reflectivity of Cu0.96Pto 04 ——. 49 >m >mtmcm o.m o.v o.m O. m o. _ . _ . _ + + +¥rtl+ _ _ .lL DmLmULomflU £9 Dalso ow. om. ow. on. om. om. oo. AitAtiaailaa Figure 3.6 Reflectivity of Cu0.94Pto.05 50 >m >otmcm .o.m or. o.m o. N CA OYO AitAtiaatlaa ooé UmLmULomflU Axmv amino Figure 3.7 Reflectivity of CuO . 92Pt0 . 03 >m >mtmcm or. o.m 9m 0. 51 d — u d d d d umLmULomHU Axofiv udijo O a AllAtlaIJSH Figure 3.8 O Reflectivity of Cuo.9oPto 10 52 O I l I I I ' I l I I fiI ' (13 l. \ .. B T‘ E r: 4_m >mtmcm om. ow. 53 AVAVAVAV ++++<<<< +r. «a ++ a ++ a iiiumw Q + a IT. umtmnto 4 + mew toms + U U IT ++++++ ANONV palau o“ o“ o‘ AitAtioaIJau Figure 3.10 O Reflectivities of Ordered and Disordered CugoPt20 (25%). Cu—Pt 54 0.90 Figure 3.11 l l ' l ' l ' l ‘ l m U _ m _ L -33 o — ‘53-. is -- mU +4 LO _ SS +4 _ -+< -+< — -+< + a -—9 + a V _ -+< _ + a + 4 _ +< -—9 +—< m _ +4 - +< +4 0 _ + -—. +'§ + m _ $46] _ + __ age -0. l I l I l | l ng O O O O O O O O 00. t. L0. L”. V. m. N. O O O O O O O 411A11391496 Reflectivities of Ordered and Disordered Cu75Pt25 energy eV 55 there are IN) significant differences in R(w) of the two phases. The error associated with these reflectivity measurements is about 3%. Turning our attention to the Rim) spectra for low Pt concentrations (10% and below) alloys, we find that R(w) below the edge (at 2 eV) is high, but lower than that of pure (mu This should be expected because the addition of Pt impurities introduces electron states between the top of Cu d-bands and the Fermi level. Whether these are due to truly localized virtual bound states as suggested by Friedel [3.5] or a lowering of the Fermi level relative to the (hi d-bands by a decrease in the electron density (number/volume) is a question that must be addressed. Measurements of the transmission and reflection coefficients in thin films of Cu1_deX for low Pd concentrations have been made by H. P. Myers et a1 [3.7]. They have also studied AgPd and AuPd films. The optical absorption coefficients computed from these films clearly indicate the presence of extra peaks (relatively broad) in A91..dex and Au1_deX (x < 0.40). In Agl.deX this peak occurs at about 2.6 eV (below the 3.8 eV absorption edge of Ag); :ha Au1.deX this peak occurs at about 2.0 eV, still below the absorption edge of Au. These extra peaks in Ez/A of AgPd and AuPd are attributed to the formation of virtual bound states at Pd sites; these states have energies that are above that of the d-bands of the host but below EF. In 56 Cu1_dex these peaks are not resolved, probably due to copper's own strong peak at 2 eV. It is reasonable to expect a similar behavior in the Cu1.thX alloys. In the R(u) of Cu1_thX alloys, the absorption edge stays at 2 eV as the Pt concentration is increased. That the edge does not shift to lower energies is a strong argument against the rigid-band picture of the alloying process. The rigid band model suggests that when Pt (10 valence electrons/atom) is added to a Cu matrix, there is a reduction in the electron density. Thus the Fermi energy, determined mainly by the electron density, would decrease and lead to the onset of interband transitions (top of filled d-bands to states just above EF) at energies below the 2 eV threshold seen in these alloys. These reflectivities measurements may indeed be indirect evidences of the formation of virtual bound states in dilute Cu-Pt alloys. Rao et.al.[3.12] have calculated the band structure of copper rich Cu-Pd alloys and also conducted angle resolved photoemission studies on these alloys. Their studies show clearly the formation of two Pd derived bands at 1.7 eV and 5.0 eV. Figure 3.12 shows the results of their investigations. We now turn to a discussion of the expected order— disorder effects on the optical properties. The reciprocal lattice of the ordered Cu3Pt phase is different from that of the disordered phase. This is due to the extra ENERGY (eV) 57 (m 29+ & as --~— ; / . >-‘§“""-/ 7x" " ’7 .7 A? a -10‘ . . I t: x: m a, z m ~51: " ‘- . ”Leo , /, /’ " /I’/’/ I //.’//I/’/ ! I x' -ui F X M m 20 oeusmr or STATES «mm atan"ev"i r——1 . , m) xu (m (0 (d) I 2.0r- -‘ 2.0 bcconcan’ .......... . -------- 9 o r1: 0 5'5“- “1» k \. Q \ §§T\\ ZZZ§ZC%¥/f Ce L: '3 l .3 5‘ O 4.0 1 I X 00 10 20 ' DENSITY 0F STATESlstures atom"eV"l CU35Pd15 Figure 3.12 Band Structures of Cu Rich Cu-Pd Alloys 58 superlattice symmetry present in the ordered crystal. This can be visualized by inscribing the Wigner—Seitz cell of a simple cubic lattice with the Wigner-Seitz cell of the FCC lattice (see Figure 3.1). The faces of the cubic cell intersect the Brillouin zone in many k-directions. For example, in the F-X direction of the 1St Brillouin zone of the FCC lattice is bisected by a face of the cubic Wigner— Seitz cell. Thus the points between this face and the symmetry point X are 'folded' into the cube; the point X is now at I. Similar band folding along other directions are possible. Many sub-bands are thus formed for the original bands. This formation of extra bands (states) will change the DOS at these energies. Many more interband transitions are now possible resulting in new structures in the reflectivity spectra. The changes in the DOS is such that the total number of states (area under the DOS curve) does not change. A mere redistribution of the states at various energies occurs [3.11]. Differential reflectogram studies on ordered and disordered Cu3Au by R. E. Hummel [3.1] show structures at 2.17 eV and 3.85 eV due to 'band folding'. In the disordered phase of Cu3Pt, an entirely different set of energy absorption mechanisms are possible. The translational symmetry of the lattice of the ordered phase requires the conservation of crystal momentum, in addition to energy, in electronic transitions. For transitions induced by the absorption of a low energy 59 photon, only direct transitions are possible. This is due to the fact that the incident photon has a very small momentum (= 2w/A) compared to the dimensions of the Brillouin zone. The K-conservation requirement limits the number of transitions that can be induced by a photon of energy fiw. In the disordered phase, the translatnmufl symmetry of the lattice is reduced to that of an FCC lattice by random occupation of the lattice sites by Cu and Pt atoms and the K-conservation requirement is relaxed [3.11].. The disordered phase differs from an ideal FCC lattice due to the presence of an extra (Pt - Cu) potential at the Pt sites and the scattering due to this potential. The process just described and the increased absorption due to 'band-folding' in the ordered phase result in a decrease in the optical reflectivity. Without the aid of accurate E(K) calculations, it is not possible to predict which of the two absorption processes results in a larger reduction in the reflectivity. Our experimental measurements, however, suggest that the effects of band- folding seem to be relatively stronger. The R(w) of the ordered phase for Pt concentrations 17.5%, 20% and 25% are consistently lower than the R(w) of the disordered phase. Hummel has observed similar effects (Rorder(w) < Rdisorder(w)) in Cu3Au alloys [3.1]. In addition to optical reflectivity measurements, the transmission EELS of the ordered and disordered phases (Pt 60 concentrations of 17.5%, 20% and 25%) were measured. The results are displayed in Figures 3.13 - 3.20. We also measured the EELS of pure Cu and Pt. The spectra shown are the raw spectra, before the removal of double losses. Some of the prominent features in the EELS of Cul_thX alloys are those at about 5.0 eV, 8-12 eV, 20 eV and 27-30 eV. The accuracy and resolution associated with these measurements are 11.0 eV and 1.0 eV respectively. Though there is a superficial resemblance between the EELS of Cu and the alloys, the EELS of Cu has many sharp features not found in the spectra of the alloys. For example, in the spectrum of Cu there is a clearly defined step at 7.8 eV and a peak at 11.6 eV. In the spectra of the alloys (all Pt concentrations and phases) a broad step/shoulder is seen to extend from about 8.0 eV to as much as 11.5 eV. The EELS of the pure metals Cu and Pt agree very well with published measurements [3.8, 3.9]. Our spectra lack detail below about 3.0 eV; this region is dominated by the tail of the zero loss peak. The absence of the K-core losses of oxygen and carbon indicate that the surfaces were free of oxides and other contaminants. We will first turn our attention to the two welldefined peaks at about 20 eV and 28 eV, in the spectra of the alloys. In the EELS of pure Cu these peaks are at 20.6 ev and 28.6 eV. The peak at 20.6 is stronger than the peak at 28.6 eV in pure Cu. The 20.6 eV peak has been 61 VURC CU LT-lc SECS .$ ‘ O «a \ .... :1 o o. O 0‘. 0‘ o. 0.0 Ito. : . o o \oo \~ \c. P. .. I... c. o. o... .... O9 % a . : .. 93.2 7J.2 V‘IUIFIITtrrFrTTTIIrI I 53.2 IIUIIUITTUTIITITVTI 33.2 I 13.2 IIIIIIFI I?‘ "taonbllo'99‘1lollollfl9.’ O.$1.5Lilo-“4111171-?61.31.111.188“. . . n K . II. 4H0. 2000 COUNTS ENERGY EV Figure 3.13 EELS of Cu b ‘1 62 n c H U P LT-IO SECS oo.‘ 60.0 COUNTS 20$.- u I O '0'Q--.O“|o.lllftnuallolll-'O'031Iololl'... ‘tlll‘u'00ttt‘II'QF‘L . 1'1 T T 11 I r r II 92.8 I 71.8 I r’v I r r1 T I I 52.8 IT'IWTTIY I 32.! 12.8 "frllrIlII'rfrVIWTTI ‘702 IV lfllflCY Figure 3.14 EELS of Pt “4‘66“ 04.600 63 £709! SECS CUF‘IITS 05 l O was _ O .“ I . : 1 n I . 0 fl ; .’ . \. ‘II-r : ‘ O r . o 0 ‘ \ I \ \ - \ ' \ O 0 Jul > ‘g, \ \ > ‘L l s ‘5 \ 20!- Ill- .. - - ITFIIIII rrTfIrIVI TITWIr1Iv IVfIItrW rvtrrrtrt I -0.6 11.4 3!.4 51.0 11.4 9L. ENERGY (V Figure 3.15 EELS of CugzosPt17.5 Ordered LT-IO SCCS C071175008 ’5 ... 1' °° (A. j I : ‘I '~ I 3 . \ I \ I ‘K Q 3' N :u- ° ,‘ \, t O A 3‘ l . O ' rf??1??+?3rvvtvvrvvArtivlvrrvLv?vvvivr?irt111vrrvvw 4.2 ".3 3L. 5L. ".0 H. I"!'"' " Figure 3.16 EELS of Cu82.5Pt17.5 Disordered m-hlccn (04:60“ 63 LT-Sf SICS Curtl7$ 05 I SUR- . 0“ 1 . : 1 h I . : fl' 1 I; ‘o ‘ (I ‘ I o . \ f . o. C ' \ '. s a. - \ 1/ \ Juu-> ‘\ ‘0 ~ I \ \ Ion-l Iva-l . l RHINO? [V Figure 3.15 EELS Of Cu82.5Ptl7.5 Ordered no" sccs cunnsoos ’3 n- .' . :f‘: 3 t : V . I ‘- ; \ I ‘K ’ i 3’HP‘. 1‘ us— i I ‘3 3" 4‘. (ltlfl' CV Figure 3.16 EELS of Cu32.5Pt17.5 Disordered .4160“ U-O‘GOG ISI- 64 LYOIS IECI CU'? 2. 0‘ r ‘ 1' 1 x f\.! R : d ‘ I s .’ 3. I “:9. ha: A ' \ r \- a k ° .’ I \\ 9...-~ L, l A V -,.1;rT—ttvItfigrjvvrvvvvvfixvltt1111,x.ratvlI111§§5I??11111,;.3 ZIIIO' IV ' Figure 3.17 EELS Of CugoPtzo Ordered LE'I. SIC! CU'TII 00’ ISI- - o /q\ xv "°~ ’ '\ In- 1' I t I I/ I suuo’ ,/ L 3 "W 'C.‘ o .6 IIIIO' 2' Figure 3.18 EELS of Cu80Pt20 Disordered IQ‘CCfl IQICOO 65 I'D]. SIC! CU'TIS 0U 7800' soon- 5000- ...-v.‘ .5" : '. Ine- ( 3'5 ‘y I ’- I ... r' ‘6 nn- ~29 w.’ 0‘ :" J ‘% ' :~U‘fir§, . 1".- ” n “K ‘3‘ I...- .... ' .. I... 10.2 56.1 70.1 90.1 Figure 3.19 EELS Of CU75Pt25 Ordered LT'I. ICC, CU'T” NI Ccll- {0 I ‘. .' . 4" ... z b .- w ‘. ' ..~ ’II- o: \\ ' s .’ 3‘ ; \ f, \ I III- . : 2 o' J III- '1’.‘I I I I I I I I‘I.I.I I rI I I I 1):.I.l I rI I I I 1".Y.I I I II I I I’LI.I II I I I I rd). ZIIICY 8' Figure 3.20 EELS of Cu75Pt25 Disordered 66 associated with a volume plasma oscillation, corresponding to an effective electron density of about 4 electrons/atom. There are a total of 11 electrons in the 3d(10) and 45(1) bands of Cu. Assuming that all 11 electrons participate in the plasma oscillation, the energy of the plasmon is about 32 eV. The ineffectiveness of the free-electron model to describe accurately the transition/noble metals may be seen from this discrepancy in the measured and predicted plasmon energies. In the EELS of the alloys, the two peaks (at 20 eV and 28 eV) have changed significantly in intensities, but there is no appreciable shift in the position of the 20 eV peak. The 28 eV peak appears to have shifted by less than 2 eV in Cu3Pt alloy. The 28 eV peak is more intense than the 20 eV peak in the alloys; in pure Cu the 20 eV peak is stronger than the 28 eV peak. Ya Ksendzov [3.10] has done a review of the electron energy loss spectra of the 3-d transition metals and has attributed the 20 eV excitation to a collective oscillation of the 3-d electrons of a particular spin orientation. In pure Cu there are 5 electrons with spin up (or down). If the 20 eV peak in the EELS of pure Cu was assumed to be due to a free electron like plasma oscillation we arrive at an electron density of about 4.2 eflectrons/atom. This agreement between Ya Ksendzov's prediction and experimental observation must not be taken too seriously. This model is 67 just a phenomenological model that appears to explain the occurrence of various features in the EELS of the 3-d transition metals without giving a fundamental reason for the splitting of the electrons into two groups of opposite spins. The description given by Ya Ksendzov would appear to suggest a shift of the 20 eV peak to lower energies in the alloys. No such shifts in the position of these peaks are observed. This model also attributes the 28 eV excitation in pure Cu to a collective oscillation of all the 11 outer electrons. When Pt atoms are added to Cu to form the alloys the effective number of electrons per atom would decrease; hence the 28 eV peak should shift to lower energies. (hi the contrary these peaks have a small but systematic shift to higher energies as the Pt concentration is increased. This behavior defies simple explanations. These features also appear to be insensitive to the crystalline phase of the alloys. Extensive band structure calculations for the Cu-Pt alloys are needed before an attempt is made to explain these anamolies. Many of the sharp features seen at low energies in the EELS of Cu are missing from the EELS of the alloys. Notable among these changes are the presence of a broad step/shoulder between 8 eV and 11.5 eV in the EELS of the alloys. To study the changes in the valence band structure of Cu brought about by alloying, we computed the 68 dielectric function e(w) of the alloys by a Kramers-Kronig inversion of the energy loss spectra. The structures in e2(w) correspond to critical points in the band transitions. The computed optical functions 62(w) for the alloys Cul.thx are shown in Figures 3.21 - 3.27. Also shown is the computed optical function 52(w) of pure Cu. Unlike the energy loSs spectra, 52(w) spectra of the alloys are very much like that of pure Cu (in the energy range 5 eV to 30 eV). The 62(an m >mtmcm mm om mm om ma 0“ m «ddu—Jdud—dd4q—qu-duddddu4—J—Hfiu-— phrhb-hb—pth—prpp—bhpp_bLbb—b-nb— onlllm.hfi palzo mm.o om.o mud 004 mm.“ oméz? mm.“ oo.m mm.m om.m mud oo.m mm.m om.m Figure 3.22 82(w) of Cu82.5Pt17.5 Ordered 71 ov >m >mtmcm mm om mm om ma 0“ m o q ' dqdl—Jdd-—-J-—u-u-dqdddd‘q+d~d—A-u7 .1 L-.LbFL~F»_phPL...bp.L-_h._»_.L..F OO. ADVIIIm.ka pause Figure 3.23 22(w) of Cu32.5Pt17.5 Disordered 72 >m >mcmcm ov mm om mm om ma 2 m dddaflddud—~ddd—Juqq—dJ)JA—JJd4—qu44‘ ' Lb-lbbnkb-PbpbrblblpPlpbppPh——)P)h|pbbuhbb_ A9 Illom vQIDU 00. Figure 3.24 62(w) of CugoPtzo Ordered 0.» mm om mm om m« o« m o >m >mtmcm rl 73 JlfidudJ‘qdql—ldld—d-qq—qdfiu—Jd14444qql— 4 prLLL.L_#EFEB.br+_b.ppb..-bbrbL-b 0m. ADVIIION “also Figure 3.25 52(w) of CugoPtzo Disordered 74 CV >m >mtmcm mm om mm om ma 2 m qfifiq—dq4q—ddqfi—Jquq—q-qd—uqu—dqua— nbt—prpr—PbLLFbL—ppnp—hnthbth— Am: Illmm pulse Figure 3.26 62(w) of CU75Pt25 Ordered Cu-Pt 25—-(U) 75 l l l l l l N m L (0 CU a: H e1 0 CD ‘I C) (\J N CU z 9 Figure 3.27 22(w) of Cu75Pt25 Disordered 0.4 40 35 30 25 20 15 10 energy eV 76 about 2 eV in pure Cu and persist up to about 8 eV before falling off in strength. In pure Pt the onset of interband transitions is below 1 eV. Transitions are possible up to 10 eV. The systematic increase in 22“») at 6.0 eV as a function of the Pt concentration may be due to an increase in the DOS at about 6.0 eV below the Fermi level. The e2(w) spectra of pure Cu and the alloys are very similar at higher (7 eV and above). The loss of sharp features in Cu and the occurrence of a step at about 8 eV in the EELS of the alloys are not reflected in 52(w). Hence, these changes defy a simple explanation. The feature in 52(w) at about 26 eV appears to be sensitive to the structural phase of the alloys. The magnitude of e2(w) at this energy increases from 0.90 for CuPto.175 alloy to 1.1 for the CuPt0.25. This is seen only in the disordered phases. The 52(w) of pure Cu at 26 eV is 0.75. This difference in 22(w) of the two phases could be an order- disorder effect. CONCLUSION: Optical reflectivity R(w) and transmission EELS of Pt, Cu, and atomically ordered and disordered Cul_thx alloys (0.175 s )c 0.25) were measured. The reflectivity measurements were in the range 1.0 eV to 5.0 eV and the EELS measurements were in the range 3 eV to 90 eV. A few indications of order-disorder effects on the reflectivity and the EELS were identified, though further studies using 77 highly ordered (LRO > 0.95) samples are needed before arriving an: an accurate description of the processes involved. In the reflection spectra, the absorption edge of Cu at 2.0 eV was seen to disappear for Pt concentrations above 10%. The overall reflectivities of the disordered phases was higher than that of the ordered phase--an order- disorder effect. The optical functions were computed from the EELS by kk inversion. The imaginary part 62(w), of the dielectric function of the alloys showed a feature at 6.0 eV, that was sensitive to the structural phase of the alloy. 77 78 Chapter 4 Order-Disorder Effects in the Feo.380.2 System Topological disorders have a large influence on the electronic and other physical properties of solids. A class of topologically disordered systems called metallic glasses exhibit new and very interesting magnetic and electronic properties that are of great technological importance. ‘A desire txa understand and exploit the properties of metallic glasses partly explains the intense research activity this field has seen in recent years. Amorphous Fe1.xBx has long been a model for the study of magnetic and structural properties of metallic glasses [4.1]. Extensive investigations of the electronic structure have also been carried out [4.2, 4.3, 4.4]. In spite of the existence of a large body of information on the Fe1_xBx system, some controversial questions remain unanswered. For example, the work of Abd-Elmeguid et.al. [4.5] suggest that the short range order in crystalline Fe0.8B0.2 U: - Fe0.8B0.2)and amorphous Fe0.8BO.2 (a— Fe00830.2) are not very different. But the Mossbauer studies (n1 a-Feo.gBo.2 done by Eibschutz et a1 [4.6] and Chien and Unruh [4.7] indicate that the short range order and atomic coordination in c-Fe0.8BO.2 are different from 79 those of a'FeO.8BO.2' De Crescenzi et a1 [4.8] have conducted Auger anui EELS studies on the crystalline and amorphous phases of this alloy and found a similarity between c-Fe and c-Fe0.830.2 and a similarity between c-Ni and the the metallic glass. There exists a fair amount of data on the electronic properties of crystalline and amorphous Fe1_XBx for x near 0.2 [4.4, 4.8, 4.9]. But a quick review of the available data on the electronic structure does not yield a clear picture of the electronic excitations in bulk Fe1_XBX. The difficulty is partly due to the fact that some of the experimental information come from experiments that are sensitive to the condition of the surface of the sample. Thus, some of the excitations reported by various investigators may simply be surface excitations or due to the impurities on the surface. De Crescenzi et a1 [4.8] have carried out electron energy loss studies on the Fe0.8B0.2 system. They used low energy (120 eV) electrons for an EELS study in the reflection geometry. The mean free path of these electrons is about 10 A [4.10]. These electrons thus probe the surface and the top 20-25 A of the sample: Consequently the reflection EELS contains a significant contribution from the surface excitations. Moreover, it is not clear if the spectra were corrected for multiple scatterings. The effect of multiple scatterings are 'amplified' in the 80 derivative detection technique employed by De Crescenzi et al. In this investigation we have measured the transmission EELS of a-Fe0.880.2 using electrons of energy 100 keV. We believe the results reported here reflect the electronic properties of bulk a-Fe0.8Bo.2. SAMPLE PREPARATION: The amorphus Fe0.380.2 samples used in this study were provided by Denis Greig and were prepared by melt-spinning at the University of Leeds. This technique produced a thin long ribbon about 3 mm wide and 45 um thick. Samples for the electron microscope were prepared from this ribbon by punching out 3 mm discs and jet-etching these discs in a jet-etching unit. No attempt was made to measure the micro-composition of the specimen in the AEM because the characteristic X-rays of Boron are not detectable using the energy dispersive X-ray detector. X-ray diffraction pattern of these ribbons showed no Bragg lines. RESULTS AND DISCUSSION: Ray and Tauc [4.1] measured the Optical reflectivity of a-FeoogBo.2 in the photon energy range 0.05 eV to 6.0 eV (Figure 4.1). ENue reflectivity monotonically decreases from almost 1.0 at 0.05 eV to about 0.35 at 6.0 eV. The reflectivity spectrum is essentially featureless. Our reflectivity measurements (Figure 4.2) in the energy range REFLECTIVITY [.0 0.9 ' 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.! 0.0 81 . c-Fe (JOHNSON AND CHRISTY) o. ' O'Feeo 82° x "xxxxxxx 1 i 1 l l _l l I 2 3 4 5 6 6w (eV) Figure 4.1 R(w) of a-Fe0.8Bo.2, Reference [4.1] 82 I I I i f l I )- .J .- + _( + r- + - + L. i ._ + t + . CD + m 1 LL "'1 I + (U L '+ d + L- + +4} d + + )— + .4 1+ + + ._ + ..J I l 1 I l l I O O O O O h. .0 m. V “I O O O O O AitAtiaatlae Figure 4.2 R(w) of a-Fe0.3Bo.2, This Investigation 6.0 5.0 3.0 4.0 2.0 1 energy eV g!!!- 83 0.6 eV to 5.0 eV agree with the results reported by Ray and Tauc. In contrast, the reflectivity spectrum of crystalline Fe has a small broad increase in reflectivity (drop in absorption) at about 3.5 eV. Our measurements of the electron energy loss spectra of a-Fe0.8B0.2 are presented in Figures 4.3, 4.4 and 4.5. Spectra from sample regions of different thicknesses are also presented. As a measure of the thickness of the sample, the ratio t of the integrated loss spectrum (3 eV to 90 eV and the integrated zero loss peak was used. In the spectra from thin regions (t = 0.1 and 0.32) there appears a bump at about 4.0 eV (Figure 4.4). For larger sample thickness (t = 0.66 and 1.0) this feature disappears (Figure 4.5). In addition the 'tail' of the zero loss peak decreases for larger thicknesses. Loss features due to volume excitations increase in intensity as the sample thickness increases. Loss features due to surface excitations, on the other hand, stay the same in intensity; indeed, relative to the rest of the spectrum they seem to decrease in intensity. Using this guideline, we attribute the feature seen at about 4.0 eV to a surface excitation. In the energy loss spectra for all thicknesses, there is a broad loss feature at about 23 eV. One probable explanation for this feature is a collective excitation similar to the plasma oscillations of a free-electron 84 J. C . - K K . . . K K C 5 ..u 5 C n... .... 2 1 l U S CUUNIS 9b. 4 76.4 56.4 .4 16 o-EIIIIIUI'I'YIIIITTIIUIIIIIIr]l'lrIIIYIrT'IIIrTTYT'TY—Y -306 ENERGY EV Figure 4.3 EELS of a-Feo.3B0.2 EELS NORM. LO+ 05“ X taff'1o A A ‘A x X .x d. ‘ ‘ b a. ‘ " .- 5" X A X A JP * ‘ L A 5 ‘ i A A 6 O A 1:109 A. a 5 x A“"gx ‘5 «(I- .O ‘. 9 a m: ‘ ‘ I b “ l A I 1 I F I ‘ 85 20 AE}eV Figure 4.4 Normalized EELS of a-FeosgBO. 4O EELS NORM. 0.5 ‘ 86 toff=0.1 ten=°°32 '0‘? ’ + I. 4' . 9 f ... .. O ... a. h * o 4. ... I 1b + * r O [- O- '.'*¢"7§-. .1. «lb 1 l I " I fl A E, eV Figure 4.5 Normalized EELS of a-Fe0.8Bo.2 c—Fe 87 1 L0 V‘ S o ('B/F-) UJI Figure 4.6 EELS of c-Fe 20 30 4O 50 50 70 80 90 10 eV 88 metal, but any attempt to further compare this peak to the free-electron plasma must be resisted. Plasma oscillationsare not well-defined in a system such as this transitjxni metal-metalloid amorphus allay. Depending on the procedure used to locate its position (centroid or peak), this feature has shifted by about 1 eV to 3.5 eV relative to pure crystalline Fe. More significant is the absence of any sharp features in the spectrum of a-Fe0.8B0.2, that are normally found in the spectra of c-Fe. Many of these features are associated with interband transitions. Colavita et al [4.11] have done a comprehensive study of the excitations in ferromagnetic Fe and have identified many of the interband transitions iJi the energy loss spectra. The absence of these sharp features in the energy loss spectra of a-Fe0.880.2 may be explained by the lack of long range order in the amorphous phase. The loss of long range order also leads t1) the breakdown of the momentum conservation requirements for transitions between energy levels. Thus, one may conclude that in the amorphous Fe0_8BO.2 energy absorption is possible at energies forbidden in the c- Fe0.830.2 by the K-conservation requirement and would show In? as a broad dominant loss. In our EELS measurements of pure Fe and the metallic glass the dominant losses are about 20 eV wide (FWHM) indicating that the loss of long 89 range order has no appreciable influence on the dominant loss. At higher energies we see energy losses due to transitions from the inner shells. The feature at about 54 eV is the Fe M2'3 core loss (3P1/2,3/2 + allowed states above Fermi level) and the features near 708 eV and 721eV are the Fe L2'3 core losses (2P1/2'3/2 + allowed states above Fermi level). The shape and location of these loss features convey a great deal of information about the local chemical ordering (or the lack thereof) of the solid. In the spectra of a-Fe0.880.2, we find no shifts in the positions or changes in the shapes of these core losses. They resemble those in the spectra pure crystalline Fe. We did not measure the EELS of c-Feo.gBo.2. Hence, we report here measurements of other investigators for the sake of completeness and for comparison with our measurements. The studies of De Crescenzi et a1 [4.8] and Th Paul and Neddermeyer [4.4] need special mention. These two groups have done photoemission (XPS, UPS) reflection EELS (using second derivative detection technique) and Auger spectroscopy. Several features at 2.5 eV, 5.9 eV, 9.1 eV, 12.0 eV and 16.6 eV are reported by De Crescenzi et a1 [4.8], though some of these may be due to the surface and adsorbed atoms on the surface. These results should be compared with the features at 4.5 eV, 8.5 eV, 11.5 eV and 23.0 eV as 90 determined in this investigation. De Crescenzi et a1 [4.8] also found a similarity between the energy loss spectra of pure crystalline Fe and c-FeOO8B0.2 and a similarity between the spectra of pure crystalline Ni and a-Fe0.8B0.2. De Crescenzi et a1 [4.8] explained the above mentioned similarities 111 the energy loss spectra in terms of the changes in local chemical short-range ordering and the changes in atoms coordinations when a-Fe0.880.2 crystallizes to form c-Fe0.8B0.2 . Hricovini and Krempasy [4.3] have done XPS and UPS studies on Fe0.880.2 and conclude that the electronic structure of a-Fe0.8B0.2 is similar tn) the electronic structure of crystalline Fe3B. The 3d electrons of Fe are basically undisturbed by the addition of boron. They rule out transfer of charge from B to Fe to explain this similarity in the electronic structure of a—Fe0.3B0.2 and Fe. Instead, hybridization of the s-p orbitals of Boron and the d-orbitals of iron is cited as a possible explanation. Hybridization of the s-p orbitals and the d orbitals do result in the transfer of a small amount of charge between the two elements. The core-losses in EELS are sensitive 1x) small charge transfers. In our EELS studies of a-Fe0.3Bo.2, the M2'3 core-losses of Fe at about 54 eV resembles the core-losses found in pure Fe in terms of shape and position. Thus the absence of a change in core- losses le a-Fe0.880.2 may be taken as an evidence ruling 91 out even small amounts of charge transfer. Examination of the Fe L2’3 core losses (measurements not shown) also leads one to a similar conclusion. Optical functions such as 32(w) and R(w) were computed from the energy loss data. These results are presented in Figures 4.7 and 4.8. e2(w) and R(w) share some common features--the plateau at about 10 eV and the structure at about 54 eV. The structure of €2(w) is very sensitive to the normalization factor used in the Kramers-Kronig inversion. ILt must be mentioned that the two different curves of 52(w) differ significantly from that reported by Ray euui Tauc. Ray and Tauc measured the optical reflectivities in the photon energy range 0.05 eV to 6.0 er Using an extrapolation of their reflectivity measurements to higher energies, they computed 52(w) by a KK inversion of the reflectivity data. A procedure such as this does not always reveal useful information because the KK inversion procedure is very sensitive to the high energy extrapolation in reflectivity. In the 52(w) spectra of pure Fe and the metallic glass there is a structure at about 10 eV. In pure Fe this structure is a plateau; in the metallic glass this is a broad peak. The reason for the enhancement of this structure in the metallic glass is unclear; The photo--emission valence-band spectra of Hricovini and Krempasy [4.3] also indicates a weak structure at about 9 eV below the Fermi level. 0.2 ~ 0.02 92 A Reference [4.1] scale factor / lb /00 45, eV Figure 4.7 62(w) of Fe0.880.2 93 / .. A Refrence [4.1] scale factor 1.0 1.25 OJ» OOI" OOO/ I /O /OO AE,eV Figure 4.8 R(w) of Feo.gBo.2 94 CONCLUSION: We have measured the optical reflectivity and high energy transmission EELS of melt-spun a-Fe0.880.2. Using the Kramers-Kronig dispersion relations we have computed the imagery part of dielectric function e2(w) and the reflectivity R(w) in the energy range 2 eV to 90 eV. The dominant feature is the EELS is at 23.0 eV i 0.5 eV. This value is about 1 eV to 3.5 eV higher compared to that of pure, crystalline Fe, depending on the criterion used to locate the peak. Several other features were observed in the loss spectrum. Two features at 2.5 eV and 4.5 eV associated with volume excitations by other investigators was seen to be due to surface excitations. No significant changes in the shape or the position of the Fe M2,3 core- 1055 was seen, ruling out a transfer of charge between the metalloid and transition metal atoms. The computed dielectxfix: function 22(w) differs significantly from published results while the computed reflectivity agrees with published results in the energy range 2 to 10 eV. Beyond 10 eV the discrepancy is significant. CHAPTER 5 ORDER-DISORDER EFFECTS IN THE NITI SYSTEM To identify the effects of loss of long range order on time electronic properties, metallic systems with and without 'artificial' order were studied using electron energy loss spectroscopy. For systems with 'artificial' order we used layered Ni-Ti samples and for systems without long range order (and 'artificial' order) we used amorphous Ni-Ti alloys produced by laser quenching the layered Ni-Ti samples. To investigate the effects of amorphization on the electronic levels we also studied a crystalline Ni-Ti (c - Ni-Ti) alloy. Experimental studies on these three kinds of systems are still limited in number. Artificially layered metallic systems have been used as X-ray mirrors, among other applications. A sound knowledge of their electronic properties is thus essential. Although amorphous metallic alloys have received extensive attention for their interesting magnetic and structural properties, a reliable understanding of their behavior at the microscopic level has not been achieved. 95 96 SAMPLE PREPARATION: The NiTi samples for this study were prepared by using DC Sputtering techniques. Alternating layers of Ni and Ti were deposited on aluminum covered copper substrates. Three different guns were required for the process (A1, Ni and Ti). The sputtering was done in an atmosphere of ultra-pure (99.9999%) Ar; Ar pressure was 3 mtorr. A 1.0 um layer of Al was deposited on the Cu substrate before depositing Ni and Ti layers. The total thickness of Ni and Ti layers were about 500 A in samples that were made specifically for AEM studies. The samples for magneth: studies and laser-quenched amorphization were about 1400 A in total thickness. Though samples of different layer thicknesses were prepared and studied, we limit our discussion to the results for the 50.8 A Ni/58.5 A Ti system. Amorphization of these layered systems was accomplished by laser-quenching. Short duration ( ‘ 10 x 10‘9 sec) Q-switched laser pulses from a Nd-YAG laser was directed on different regions of the sample. The energy of these pulses were varied to yield fluences of 0.2 J/cm2 to 3 J/cmz. The region affected by each pulse was about 2 mm in diametemu. Optimum amorphization of the layers was obtained at fluences of 1-2 J/cm’. Analytical electron ndcroscope studies were done on small pieces of the layered and laser quenched samples that 97 were floated off the Cu substrates by etching the intermediate Al layer with 50% KOH solution. Composition analysis by X—ray EDS showed the presence of Al in small amounts in certain regions of the sample. These regions were avoided while making energy loss measurements. Discs of 3 mm diameter were cut from the crystalline Ni-Ti samples and electrochemically etched for study in the AEM. RESULTS AND DISCUSSION: Electron energy loss spectra from 3 eV to 90 eV for layered NiTi, laser quenched NiTi alloy and c - NiTi alloy are shown in Figures 5.1, 5.2 and 5.3 respectively. Preliminary measurement of the optical reflectivity of the layered system is shown in Figure 5.4. Efforts to obtain more accurate and reliable optical measurements are currently underway. We were unable to measure the reflectivity of the laser quenched alloys, due to the limited size of laser quenched regions. X—ray diffraction studies, using Cu-Ka radiation, of the 50.8 A/58.5 A layered NiTi systems showed fairly sharp Bragg peaks indicating layers of crystalline Ni and Ti. 'Satellite' Bragg peaks indicating good registry between successive layers of Ni and Ti were not seen. We attribute the lack of registry between successive layers to the roughness of the Cu substrates. See Figure 5.5 for the X- ray diffraction pattern. 97 were floated off the Cu substrates by etching the intermediate Al layer with 50% KOH solution. Composition analysis by X-ray EDS showed the presence of Al in small amounts in certain regions of the sample. These regions were avoided while making energy loss measurements. Discs of 3 mm diameter were cut from the crystalline Ni-Ti samples and electrochemically etched for study in the AEM. RESULTS AND DISCUSSION: Electron energy loss spectra from 3 eV to 90 eV for layered NiTi, laser quenched NiTi alloy and c - NiTi alloy are shown in Figures 5.1, 5.2 and 5.3 respectively. Preliminary measurement of the optical reflectivity of the layered system is shown in Figure 5.4. Efforts to obtain more accurate and reliable optical measurements are currently underway. We were unable to measure the reflectivity of the laser quenched alloys, due to the limited size of laser quenched regions. X-ray diffraction studies, using Cu-Ka radiation, of the 50.8 A/58.5 A layered NiTi systems showed fairly sharp Bragg peaks indicating layers of crystalline Ni and Ti. 'Satellite' Bragg peaks indicating good registry between successive layers of Ni and Ti were not seen. We attribute the lack of registry between successive layers to the roughness of the Cu substrates. See Figure 5.5 for the X- ray diffraction pattern. 98 171 58/50 I.’ LT-lo SECS I II II II I II 5 TIIIIII \ \ O s O - ‘ I II I II I II I“II I II I II I g 35.8 5 . 3 . 0 Q 0. O I 3 .' I'l'Il'ji d 2 C O O uh x A- n a 9‘ 1 408 30K- COUNTS ENERGY EV Figure 5.1 EELS of NiTi Layers 99 N17! nun l LT-ll SECS L a L 1* —L rI II II I‘II II’II‘rW rI’II I 16.2 a. I ~' . a; at. g a j... u. .... .o\ 0“ ‘ oo ...o o. \.\. ...o a w tax 0. I. 1... 'o" I. I ..a O o)! o 2 o o o o — O O VflflmnhuflnnfivnVMJflflflnnflflvfivflfloflflthhflvTX“MAALhAfiflfi#VHflfl$u . _ . . . . x x . . a . 2 c ' . o . l 1 U C O U I 6 C 2 II II f1 i1 I 2 96.2 TTTIVT—riiij I 76.2 I 56. 36.2 'TIIFUIIII -30. ENERGY EV Figure 5.2 EELS of c-NiTi UI-ilccn 100 LTOII SECS NITISO/Sll ‘— [SK-I I ‘ I I g u l $.30 I o z t : . : t I : :' 'L . ° 1 X I o 19I~‘ : g g I \ | C I i ~ | r '. I . \ ' f o o ' ... l : \ I \ ' \ a Q “ ...Ir ‘.’ *0. W '0 509,-” ‘- Q \ L G- \ I L ... rIVVUVV'I{VIIIVUiYTrTYITV'r'VUIYTYr'{YI'IVYIYIW‘l—rr' ‘Jo‘ 163‘ 360‘ 5‘0. 760‘ 960‘ ENIIGY IV Figure 5.3 EELS of Laser Quenched NiTi 101 o. o.v o.m o.m om.o l o v o l om.o mm\om mLm>mH flklfiz om.o AIIAIIDBIJBJ Figure 5.4 R(w) of NiTi Layers 102 Muzzm uuzom YHOH) 40 gp so 55 so as 1° as so 1 l A J 29-» Figure 5.5 X-ray Diffraction of NiTi Layers 103 The energy loss measurements for the layered NiTi system (Figure 5.1) shows some surprising results. Since the X-ray diffraction studies (Figure 5.5) show sharp Ni and Ti Bragg peaks, it is reasonable to assume that the EELS of this system is a superpostion of the loss spectra of pure Ni and Ti. The layered samples studied had at least 5 layers of Ni (and Ti) to as many as 15 layers. Thus the total thickness of Ni (or Ti) was comparable to the mean free path of electrons for inelastic scatterimg; chracteristic features of Ni and Ti would be expected to appear in the EELS measurements. Instead of featuring two plasmon peaks at about 17 eV and about 25 eV (the characteristic features of Ni and Ti), the EELS of layered NiTi shows a relatively sharp plasmon at ~ 20.5 eV. This indicates that there is just one 'sea of electrons' and not two - corresponding to Ni and Ti electrons. Lack of clearly defined interfaces between Ni and Ti layers could lead to an 'average' crystal potential and thus a different plasma oscillation. Further examination of the EELS of the layered, laser quenched (Figure 5.2) and crystalline (Figure 5.3) samples shows that there is no appreciable shift in the location of the plasmon peaks in these three systems. The plasmon occurs at about 21.0 i 1.0 eV in the three spectra, indicating that there is no significant change in the electron density. That the EELS of the layered NiTi and c - NiTi are similar is by itself 104 surprising, especially when X-ray diffraction studies indicate the presence of well defined regions of Ni and Ti. Using the free electron model and counting the outer s and d electrons only, the plasmon energy should be about 6 eV lower than the observed plasmon energy. However, electron diffraction (Figures 5.6 & 5.7) studies of the layered and amorphous systems show that there is a clear change in the crystal structure as a result of laser quenching. The layered NiTi sample has 3 sharp diffraction peaks whereas the laser quenched has only one broad peak in the diffraction pattern. The EELS of laser quenched NiTi alloy is similar to that of the transition metal-transition metal systems FeQZZrB and Nin [5.1).. These two alloys have a broad plasmon at 23-25 eV. The N23 core losses of Zr (40 eV) the M2'3 losses of Fe (55 eV) and Ni (65 eV) are also seen. A similarity between the spectra of NIZr and NiTi might be expected because Zr and Ti share common outer electronic structure. The spectra of NiTi and Fe922r8,superficially similar show some differences on closer examination. The 142,3 (3P3/2'1/2 + allowed states above EF) core losses of Ti clearly show the effects of amorphization. These features occur at about 45 eV (M2,3 of Ti). In the layered NiTi and c - NiTi samples the Ti core loss is a Ibroad feature extending from about 35 eV to about 55 eV; the M2,3 excitation of Ni is also clearly visible as a step 105 Figure 5.6 Electron Diffraction of NiTi Layers Figure 5.7 Electron Diffraction of Laser Quenched NiTi 106 at about 65 eV. In the EELS of the laser quenched alloy the Ti core loss is reduced to a slope change at about 43 eV whereas the Ni M2'3 excitation seems to have undergone very little change. This observation coupled with the earlier observation that the plasmon oscillations are not influenced by amorphization produces an intriguing puzzle. Typically, in the process of alloying, it is the outer electrons that are affected the most. In transition metals the electrons involved are the outer s and dshell electrons. Ln the 3d transition metals changes in the 4s and 3d bands on alloying can be expected to be observed in the plasma oscillations. Instead of a change in the jplasmon excitation, we find a drastic change in the M2’3 core excitation of Ti. The “2,3 core losses of Ni do not show significant changes. The M2'3 transitions of Ni and Ti share some of the same final states--those unoccupied levels above EF. In addition to these states the final states of the core losses may include localised states associated with the creation of excited but un-ionized Ni Iassociate the changes in the Ti M2’3 loss feature with changes in the Ti 3p levels. Such a change in the core state is rare and puzzling. To test this hypothesis, one must resort to experimental techniques that probe the core levels--methods like X-ray photoemission spectroscopy (XPS). In this technique monochromatic x-ray photons of sufficiently high energy ( hv a 50 eV ) are used to knock out electrons from core levels of the sample and the energy distribution of the electrons studied. This would allow the study of the density of states at energies of the 3p levels. CONCLUSION: Electron energy loss spectra of 50.8 A/58.5 NiTi layered samples, laser quenched amorphous NiTi alloy and crystalline NiTi alloy were measured. The EELS of the layered NiTi sample resembled the EELS of the crystalline sample and was significantly different from a spectnnn obtained by a simple superpostion of the spectra of Ni and Ti. No appreciable difference was seen between the EELS of layered and laser quenched sample in the low energy region ( < 35 eV). The spectra of laser quenched NiTi were 108 qualitatively similar to the spectra of a-Nin and a- FegzZr. Examination of the Ti M2,3 core losses at about 45 eV in the layered and amorphous NiTi samples revealed that amorphization by laser quenching had significantly changed the structure of this loss feature. These changes were not seen in the EELS of the crystalline phase of the alloy. A profound change in the Ti 3p bands upon amorphization is one possible explanation for this change. APPENDIX KRAMERS-KRONIG ANALYSIS AND THE OPTICAL FUNCTIONS In an electron energy loss measurement the quantity measured, I(E,e), is the intensity of electrons that have lost energy E and scattered in the direction (e,¢). Using the results of classical scattering theory the following expression relating I(E,e) and the macroscopic dielectric function e(E) of the scattering material may be derived [A.l, A.2]. l l 1 I(E,e) = ION . Im __ . _ ZuzaonEO e(E) 62 + 0g Here a0 is the Bohr radius, n the density of the solid in atoms/cm3 and N the number of atoms/area in the volume examined. In a typical EELS measurement the detector angle a is usually fixed and 6E varies over a small range. I(E:9) ¢ Im (‘l/(€(E)) The function 1/e(E) is the loss function and e(E) = 31(E) + i 52(E). In terms of $1 and $2 the loss function 1/e(E) is 109 l l () J 61(E) - 162(E) eIE) - (e1(E))= + (ezmnz The bulk dielectric function e(E) is a macroscopic description of the electronic response to external electric fields. The dielectric function contains all the essential features of the electronic excitation spectrum The structure iJl 22(E) corresponds to critical points in the band transitions. The ability to measure the dielectric function directly gives us an opportunity to test the results of theoretical calculations. KRAMERS-KRONIG DISPERSION RELATIONS: The response of electrons in a solid to external fields (such as the electric fields of high energy electrons) can be accurately described by the linear response theory [A.3]. An important result of the linear response theory is the causality relationship between the imaginary part of the dielectric function e and its real part”. These relations are the well known Kramers—Kronig dispersion relations [A.4]. 61(w) - l = —' Pf 1r -°° w'-w ’1 w [61 (w') - l] dw' 82(0)) = — Pf 1r -°° w' - an In addition el(w) and 52(w) also satisfy the followimg 111 properties e*(w) = e(-w) el(-w) = 61(w) and £2(-w) = -€2(w) The Kramers-Kronig relations may be rewritten as 2 @ w'€2(w') dw' 6101))" l = — Pf I -~ w'z - wz -2 0° [81 (w') - l] dw' 62“") = '— Pf n -w w'2 - wz The integrals in the expressions above are the Cauchy principal value integrals, avoiding the singularity at w'=w. A similar set of Kramers-Kronig dispersion relations exist for the loss function l/e(w). For example Re [l/e(w) - l II '1'! H H B m "5. If the Im (l/e(w)) is known over a wide range of energies .it is possible to compute numerically the functions Re(1/e(w)), 61(w) and 62(w). 112 QUANTITATIVE ANALYSIS : In the electron energy loss spectrum (EELS) of a real system, the contributions from surface excitations, multiple losses and the strong zero loss peak (elastically scattered primary electrons) make quantitative analysis of the spectrum difficult. Fortunately, a number of procedures are available to handle these problems. We discuss below some of these techniques adopted by us. SURFACE EXCITATIONS: In the EELS of a very thin sample (teff < 0.2 ) the contributitnl from surface excitations are relatively significant. Surface excitations do not scale with the thickness while the rest of the spectrum does. In our energy loss studies we confined our attention to regions that were thicker (0.4 < teff < 1.0) This ndnimized the errors due to the presence of surface excitations. No attempt was made to remove the contributions from surface excitations. MULTIPLE LOSSES: When the thickness of the sample is significant (2 50%) compared to the mean free path for inelastic scattering, the incident electrons loose energy to more than one excitation. Electrons that have lost energy by multiple scatterings give an abnormally high intensity at higher energies ( > 20 eV) in the energy loss spectrum. In 113 general, the effect of double losses is nmch more than other higher order losses. In this study we limited our efforts to removing double losses from the energy loss spectra. The procedure adOpted by us for computing the intensity of double losses is similar to the techniques described by Daniels et a1 [A.4] and R. F. Egerton [A.2]. This method is really an approximation of a more vigorous technique and is good for only low energy losses (under 100 eV). The intensity of double losses at a (total) loss energy E is 1 E 12 (E) s — f I(E') I(E'-E) dE' , E > 15 eV 210 5 13m; lower limit 6, of the integral ensures that the zero loss peak is avoided in this computation. In this approximation 5A:.is assumed that the region below about lSeV is free from double losses. Io is the zero loss peak intensity integrated over a few channels around 0 eV. This approximation also assumes that the instrumental resolution 1h; very narrow and symmetric. The double loss corrected spectrum is given by the following expression. 1 E Icorrect (E) = Iraw(E) -"" f Iraw (E-E)dE 210 5 E 2 15 eV 114 ZERO LOSS PEAK: At the low energy end of the spectrum is the intense peak due to elastically scattered electrons. The tail of this zero loss peak extends to about 3eV of 4eV; it is also a function of the thickness of the sample. For sample thickness teff = 0.5 this tail is fairly narrow and may be eliminated by linearly extrapolating the spectrum such that I(0 eV) = 0 and 1(3 eV) = Imeas. (3 eV). This method yields fairly accurate spectra for metals and metallh: alloys. A spectrum, stripped of the zero loss peak and corrected for double losses must be scaled down before being used as input for the Kramers-Kronig inversion routine. This step is necessary to obtain accurate Optical functions. KRAMERS-KRONIG INVERSION: The numerical integration technique used was the trapezoidal ruleu This technique proved adequate because the energy loss spectra were available in 512 channels at 0.2 eV/channel steps. Several spectra of pure metals were used to test the KK inversion routine. The output of the KK inversion routine was the real part of the loss function, Re(l/e(E)). The optical functions 31(E), 52(E) and reflectivity R(E) were computed using the following relations: 115 Re(1/e) - iIm(1/e) e(E)+ie(E)= l 2 |Re(l/e)|2 + IIm(1/e)|2 / /€E + 35 + 1 - /2(/3I + 65 + 61) R(E) = / /EE_:_E3 + 1 + /2(/;E_:_EE + 81) Optical reflectivity of the systems under study were also measured directly in the photon energy range 0.6 eV to 5.0 eV. The scaling factor for the EELS was adjusted (to within 10%) to yield a match between the directly measured and computed optical reflectivities. The computed optical functions were not very accurate for energies below 4.0 eV as revealed by tests on pure metals. [2.1] [2.2] [2.3] [2.4] [2.5] [2.6] [2.7] [2.8] [2.9] REFERENCES Elements of X-ray Diffraction Cullity, Addison Wesley Publishing Co., 1971. Solid State Physics, N.W. Ashcroft and N.D. Mermin, Holt, Reinhart and Winston, 1976. X-ray Diffraction, B.E. Warren, Addison Wesley Publishing Co., 1969. Constitution of Binary Alloys, M. Hansen, McGraw Hill Book Co., 1958. 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