Trascendencia de la Rebelión de Túpac Amaru II

copper, molybdenum and cobalt. The wavelength of X-rays emitted from a target

A P PEN D IX-

by electron bombardment decreases with the atomic number of the target material.

hkl

Figure A2 - Bragg reflection from crystal planes with spacing dhki

In figure A2 a parallel beam of X-rays of wavelength X is depicted as reflecting from a crystal plane with a spacing of dhkl- The condition for constructive interference of X-rays reflected at an angle 9 is ,

nA, = 2dhki sinO

where n is an integer called the scattering order, for the respective plane and h,k and I are the are integers defining the many possible planes within a crystal and are called the Millar indices. Analysis of the spacing between the many possible crystal planes allows the structure to be established and the intrinsic properties of the material can be inferred.

From a physical standpoint, the sample under analysis is fixed on a rotating platen which is placed in a diffractometer normally with the geometry shown in figure A3. The 20 scans presented in chapter 7 are obtained by scanning the

APPENDIX

tiny fractions of an Angstrom due to the highly monochromatic nature of the X-ray source and the diffractometer geometry.

If the material under investigation is in the form of small randomly oriented crystals, (or a ‘powder’ ) then all the possible crystal planes will be presented to the X-ray source at all possible angles leading to a 20 spectrum with a peak corresponding to each crystal plane. On the other hand a highly oriented crystalline material will only have a 20 spectrum with peaks corresponding to the crystal planes which lie in the plane of the substrate holder.

This is useful from the point of view of gauging the degree of alignment of a material for which the material properties are sensitive to crystal orientation such as the ferroelectric materials discussed in chapter 2. The disadvantage of course is that limited information can be gained about the crystal structure without the complete diffraction fingerprint.

focussing circle detector focus X-ray source sample

Figure A3 -The parafocussing geometry of an X-ray diffractometer

A 2.2 EDX (energy dispersive X-ray analysis)

The technique of EDX is used to gain information on the stoichiometric composition of a material. A beam of electrons, with energies of tens of keV, is

APPENDIX

focused on sample so that X-rays are emitted in much the same way as the X-ray generation in the XRD source. As with the XRD source, the X-rays have clearly defined output peaks with wavelengths which are characteristic of the target and with an intensity proportional to the concentration of the particular element concerned. In EDX, the energies of the X -rays and their intensities are measured simultaneously in a solid state detector so that an X-ray spectrum is obtained for the target material with energy peaks for K,L and M transitions in the targets electron shells. For a quantitative measure the measured intensities are modified by a factor called the ZAP correction factor. This factor allows for,

a) the absorption of X-rays from within the bulk of the sample by other elements in the sample of lower atomic number (proportional to the atomic number, Z, of elements in the sample),

a) the absorption volume of the of the electrons in the sample, (inversely proportional to the atomic weight. A), and

c) X-rays emitted by fluorescence, (F), as a result of the absorption of X-rays of a shorter wavelength.

The advantage of this method is that the composition of a sample can quickly be obtained with the equipment which is normally used in conjunction with a scanning electron microscope, so features visible on the SEM can be quickly analysed for elemental composition.

The disadvantages are that the energy sensitive detector is limited in its ability to distinguish between closely spaced wavelengths and the accuracy of elemental compositional readings is only to within 10%.

A 2.3 Electron probe microanalysis EPMA

This technique is essentially the same as EDX except that X-rays are distinguished by their peak positions after diffraction in perfect crystals as in a diffractometer in reverse. This method of analysing X-ray spectra is known as wavelength dispersive to distinguish it from the energy dispersive method of

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The disadvantages are the sensitivity of the system which is much lower than for EDX, dictating long measurement times and individual analysis of each element. The simplest way to increase the sensitivity of the system would be to increase the current of the electron probe, but the maximum current is limited by the heating effect on the sample and the fact that the probe must be focused to small spot to maintain wavelength resolution.

In addition ZAP corrections are not exact for complicated compositions and accurate measurements require calibration of the system with a standard sample of similar composition to the sample. In addition the geometry requires that the sample have a flat surface, ideally a polished one.

APPENDIX

A.3 INDEX OF ACRONYMS

A M U B IS C C O CM A EDX EP M A FWHM IV D K.E. LIMA LIP MBE M O C V D NdrYAG PLD PZT Q M S 8 S E M TE TOP X R D C C D

Atomic Mass Units BiSrOaCuO

Cylindrical Mirror Analyser

Energy Dispersive X-Ray Analysis Electron Probe Microanalysis Full Width Half Maximum Ionised Vapour Deposition Kinetic Energy

Laser ionisation Mass Analysis

Laser Induced Fluorescence Spectroscopy Molecular Beam Epitaxy

Metal-Organic Chemical Vapour Deposition Neodymium YAG, (Yttrium Aluminium Garnet ) Pulsed Laser Deposition

PbZrxTi(i-x)0 3 (Lead Zirconate Titanate) Quadrupole Mass Spectrometer

Sputtering

Scanning Electron Microscope Thermal Evaporation

Time Of Flight X-ray Diffraction