structure of the columnar, metallic thin films over a macroscopic substrate area. In the diffractometer, the X-ray radiation is generated by electrons from a cathode that are accelerated to a copper anode, where on the one hand the electrons are strongly decelerated (bremsstrahlung) and on the other hand electrons from the shells of the atoms of the specimen material are removed, thereby creating characteristic X-rays. The X-ray radiation is parallelized by a multilayer gradient mirror. The selection of the Cu Kα1 radiation (wavelength λ = 0.15405 nm) is performed by a dual crystal monochromator. The parallel, monochromatic X-ray beam reaches the lattice plane of the sample under a Bragg angle θ.
For parallel planes of atoms with a space distance dhkl between the planes (hkl are the Miller indices), constructive interference occurs if the Bragg condition is fulfilled:
2𝑑ℎ𝑘𝑙sin 𝜃 = 𝑛𝜆, (3.2.3)
where n is a positive integer and λ is the wavelength of the incident wave. The diffracted beam enters an aperture system that limits the beam divergence. Afterwards, the beam is detected by a scintillation detector. For the θ-2θ measurement, the sample moves by the angle θ and the detector simultaneously moves by the angle 2θ, while the X-ray tube is stationary. A fulfilled Bragg condition results in a characteristic diffraction maximum (“Bragg peak”). The position of the Bragg peak in the θ-2θ diffraction diagram depends on the lattice spacing. Such a peak is only observed if the lattice plane normal is parallel to the diffraction vector u, which is the vector that bisects the angle between the incident and diffracted beam. Thus, a θ-2θ measurement only contains information about one family of
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Bragg peaks. A SEIFERT XRD 3003 PTS diffractometer is applied for the θ-2θ measurements presented in this study, because it enables to align the position of sample and detector (and accordingly the diffraction vector u) so that the other families of Bragg peaks in the sample can also be detected.
The texture of the samples is investigated by in-plane pole figure (IPPF) measurements.
For this purpose, a certain Bragg reflection is chosen from a powder diffraction file database. During the IPPF measurement, the half-sphere above the sample is scanned with a fixed Bragg reflection geometry by varying two geometrical parameters. Firstly, the sample rotates around its normal by the azimuthal angle Φ [0°; 360°]. Secondly, the diffraction plane is tilted with respect to the sample normal by the polar angle χ [0°; 90°].
The step sizes for both motions are 2°. If the Bragg condition (equation (3.2.3)) is fulfilled, a pole density maximum can be obtained. Eventually, the resulting diffracted intensity distribution, measured as a function of these two angles Φ and χ, is plotted in stereographic projection to obtain the pole figure of the chosen Bragg reflection. The projection center is the south pole of the pole sphere as illustrated in Figure 3.7. The center of the pole figure is defined as χ = 0°, while χ = 90° denotes the outer edge of the pole figure. A pole density maximum at χ = 0° means that the lattice direction is parallel to the substrate normal, and a pole density maximum located at χ = 90° indicates that the lattice direction is perpendicular to the substrate normal. The azimuthal angle Φ = 0° is located at the top of the pole figure (12 o´clock), and is circularly coordinated clockwise, meaning that Φ = 90°
corresponds to 3 o´clock, Φ = 180° corresponds to 6 o´clock, etc. The position of the pole density maxima of a crystallite oriented perpendicular to the sample surface (reference plane) differs from those crystallites that are tilted with respect to the substrate surface, as indicated in Figure 3.7 (a) and (b), respectively.
The IPPF measurements are performed in an Ultima IV X-ray diffractometer (RIGAKU), because this diffractometer enables XRD measurements with more intensity compared to the SEIFERT diffractometer since there is no monochromator on the incident optics side. The incorporated cross beam optics technology facilitates to select between the permanently mounted and aligned parallel and focusing geometries. In the RIGAKU diffractometer, a copper anode is utilized for X-ray radiation as well. The X-ray generator has a maximum rated output of 3 kW, a rated tube voltage between 20 – 60 kV, and a rated tube current between 2 – 60 mA. The RIGAKU diffractometer is equipped with an automatic alignment of tube height, goniometer, optics, and detector. The horizontal beam divergence is controlled by a Soller slit inserted in X-ray beam path. The in-plane parallel slit collimator (PSC) on the incidence optics side and the in-plane parallel slit analyzer (PSA) on the receiving optics side control the vertical beam divergence and define the covering 2θ-range. In contrast to the Soller slits, the PSC and the PSA determine the
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Figure 3.7: Schematic illustration of the pole figure measurement exemplarily for the <100> direction in a bcc crystal oriented perpendicular to the substrate surface (a) and tilted with respect to the substrate surface (b). The red dots illustrate the pole density maxima and the grey plane is the reference plane.
χ denotes the polar angle and the Ф is the azimuthal angle.
measurement resolution and reduce the measurement intensity. The PSA collects only the parallel component of the diffraction signal from the sample surface. If the diffraction peak of interest is close to another diffraction peak, a PSA with sufficiently small aperture should be used to avoid detecting intensity from the other diffraction peak. Optionally, a dual position graphite diffracted beam monochromator for Cu can be inserted on the incident beam side, but this reduces the measured intensity significantly. The detector is a scintillation counter.
For all IPPF measurements in this study, the parallel beam geometry produced by a multilayer gradient mirror and collimated primary Cu Kα X-ray radiation (wavelength λ = 0.15405 nm) is used. Further, a Soller slit of 2.5°, PSC = 2.5°, and a slit that limits the horizontal footprint of the sample (divergence height limiting slit DHL = 5 mm) are applied. As the intensity of the IPPF measurements in the present work is typically lower than 103 cps, neither a monochromator nor a PSA are used. Each IPPF is measured for at least 24 h up to several days. Notice that a quantitative analysis of the IPPF measurements requires various corrections such as absorption-, background-, and defocusing-corrections [112]. However, because all IPPF measurements in the present work are evaluated exclusively on a qualitative basis, such corrections are not applied, meaning that all shown IPPFs appear as-measured.
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