Characterization of Materials Using X-Ray Diffraction Powder Diffraction

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1 Praktikum III, Fall Term 09 Experiment P1/P2; Characterization of Materials Using X-Ray Diffraction Powder Diffraction Authors: Michael Schwarzenberger Philippe Knüsel Participants: Michael Schwarzenberger and Philippe Knüsel Assistants: Taylan Örs, Jürgen Grässlin

2 1. Abstract The topics of the two experiments were the theory about the emission of x-ray, the Bragg s law and the Scherrer equation. With that knowledge, materials were characterized by X-ray diffraction analysis in P1. Furthermore peak positions were compared with powder diffraction in order to identify the phases in the sample. In P1 the symmetry and the orientation of a crystal could be found. Furthermore the texture of a material gave information about production processes. In P2, by comparing the peaks in the powder diffraction diagram with a databank, basic information of the crystal structure of the sample was found. 2. Introduction Fig. 1: Spectrum of an X-ray tube. The two peaks are the characteristic radiation. The photons of the bremsstrahlung can have every energy between 0 kev and the original kinetic energy (here 45 kev). Source: X-rays have a wavelength range of 100 Å to 0.1 Å (10-9 m to m). Radiation is generated with a socalled X-ray-tube. It consists of a cathode and an anode. The former is a metal-filament (often tungsten) that is heated up to 2000 C through electric current. That causes the metal to emit electrons that are accelerated by a voltage of kv. When striking the anode, which consists of a fine metal plate (for example beryllium), the electrons are decelerated. As electrons have an electrical charge, their deceleration will cause emission of radiation. The energy of an emitted photon is equal to the continuous loss of kinetic energy of the electron. This type of radiation is called bremsstrahlung. Some electrons can strike out an electron in the inner shells of an atom of the anode. Another electron will then transition to this shell. Since this shell has a lower energy, this transition causes the emission of a photon to balance the energy difference between the two shells. The difference of energy between the shells is characteristic for every element and thus, this type of radiation is called characteristic radiation. When an X-ray-photon interacts with a bonded electron, the oscillating electric field of the photon causes the latter to emit a spherically-moving secondary wave. Since the distance between the atoms in a crystal and the wavelength of X-rays are within the same range, the lattice of the crystal acts like a 3-dimensional diffraction grating (fig. 2). This means that there will be specific constructive and destructive interferences as a function of angle, used 1

3 wavelength and distance between the atoms (and therefore, as a result of different atom sizes, elements in the crystal). Fig. 2: X-rays interact with the electrons of the atom and cause the emission of spherical wave which interfere with each other. Source: X-ray characterisation of the crystal structure of materials is possible by the Bragg s law. If we look at the X-rays being reflected on the different lattice planes (Fig. 3), the condition for constructive interference can be deduced from trigonometric calculations: As the waves have to be in phase, the difference in the distance they have covered must be a multiple of the wavelength. This distance can be calculated from the distance between the planes and the reflecting angle, thus: =2 sin n: order of diffraction λ: wavelength d hkl : distance between crystal planes θ: angle between radiation and crystal plane Fig. 3: Approach which leads to the Bragg s law, where the x-rays are reflected at the crystal planes. Source: s/7/74/loi_de_bragg.png There are several methods that are used to analyze crystal structures through X-ray diffraction. Their common point is that one variable of Bragg s law is unknown and has to be determined while the others are fixed by experimental conditions. The important methods that were used in this laboratory class are explained in the following paragraph. For the Laue method, a whole spectrum of X-rays, so-called white X-ray-beam, is used. The sample consists of a single crystal that has to be oriented. In some cases where the orientation of the crystal planes is unknown, the Laue-methods can be used to align the singlecrystal. It is now clear that the angle between a specific crystal plane and the X-ray-beam is constant, therefore θ is fixed. Due to Bragg s law, every crystal plane with its characteristic distance d hkl has one specific wavelength that will interfere constructively when reflected on the plane. Practically spoken, this means that the angle can be measured in an experiment 2

4 and the distance between the crystal planes, and therefore the crystal plane itself, can be deduced from the former. Instead of a range of wavelength, monochromatic X-rays can be used. This implies that a qualitative analysis can only be done either by using a powder of statistically-oriented crystallites where every crystal plane has a number of crystallites oriented with an angle θ that meets Bragg s law or by using a single crystal and vary the position of the crystal with goniometers (different angles are changed). There are different types of the former that is called powder diffraction. The most known is the Debye-Scherrer method. With highperformance detectors, powder diffraction analysis can be expanded to qualitative phase analysis since the unit cell s atoms type and position influences the intensity of the diffracted beam. 3

5 3. Materials and Methods 3.1. P2: Powder Diffraction Settings Diffraction Transmission Monochromator Curved Germanium (111) Radiation Cu 1.54 Å Detector Linear PSD 1 PSD Mode Moving: Fixed Omega Scan Type 2 Theta Step 0.01 Measuring time 8 sec/step Generator 45 kv/45 ma Tab. 1: Settings of the powder-diffractometer for the structure analysis a) In the first part, we were given an unknown powder with the task to do a phase analysis. First it had to be pestled because agglomerates and too big crystallite would have worsened the results. The powder was then put in a capillary and shook to avoid air bubbles in the sample. The capillary was then broken at the fill line and closed by heating it with a lighter. The sample was then installed on the sample holder with wax. The whole sample was then put on the goniometer in the powderdiffractometer. It was aligned so that it rotated without wobbling. The measuring speed was adjusted so that the whole measurement was done in one hour (see tab. 1). Then the measurement was started by computer. After the measuring program was finished, we converted the data file into a ASCII file and made a graphic where the peak position and intensities could be determined. With help of a program, we then tried to interpret the peaks and find basic information about the crystal structure like unit cell dimensions and relative intensities. b) In the second part the size of the crystallite was determined with the Scherrer-equation: = cos Τ hkl : dimension of the crystallite along the direction [hkl] λ: wavelength of the x-rays (here: λ= Å) β hkl : full width at have maximum (FWHM) of the reflection hkl θ: diffraction angle A powder diffraction experiment was made again and the FWHM of chosen reflections were taken. For the instrumental broadening, the broadness of the peak of BaF 2 was taken. = 1 Position Sensitive Detector 4

6 1.1. P1: Characterization of Materials First, we installed a sample of a silicon single crystal on a goniometer and irradiated it for 3 min (35 kv/50 ma). An image plate was installed behind the crystal before. After the irradiation, the photo plate was scanned and the Laue picture saved. We used a device from the manufacturer Oxford Diffraction for all experiments of the next part. The samples that had to be analyzed were a piece from the neck resp. the body of a commercial PET-bottle, a piece of a shrinking tube and aluminum foil. The shrinking tube was analyzed first untreated an then heated. The aluminum foil was additionally scratched after having been heated for a third measurement. The same experiment was done with every sample. We installed the sample on the goniometer. Then we took two measurements of 10 sec each (50 kv/40 ma). The pictures were saved digitally. 5

7 2. Results 2.1. P1: Characterization of Materials Fig. 4: Laue picture of the silicon single crystal 6

8 Fig. 5: Aluminum foil, untreated Fig. 6: Aluminum foil, heated Fig. 7: Aluminum foil, scratched after having been heated 7

9 Michael Schwarzenberger/Philippe Philippe Knüsel X-Ray Ray Diffraction/Powder Diffraction Fig. 8: Body of a PET-bottle Fig. 9: Neck of a PET-bottle Fig. 11: Shrinking tube, untreated Fig. 10: Shrinking tube, heated 8

10 2.2. P2: Powder Diffraction a) Fig. 12: Powder diffraction diagram of the unknown sample with marked peak positions Fig. 13: Peaks of calcium carbonate/calcite (red) and those of the sample (green) 9

11 Fig. 14: Peaks of calcium carbonate/aragonite (red) and those of the sample (green) b) Fig. 15: A peak of the powderdiffraction pattern of CeGd-oxide β instrumental = 0.08 Peak 1 Peak 2 Peak 3 Average 2θ [ ] n/a β [rad] n/a τ [Å] Tab. 2: Peaks of CeGd-oxid 10

12 3. Discussion 3.1. Characterization of Materials Laue Diffraction In the Laue picture of the silicon single crystal (figure 4) a fourfold axis can be found. Furthermore it can be said that the single crystal has its {100}-set of planes orientated perpendicularly to the X-ray-beam because of the points. But the symmetry does not seem to be perfect. The reason is that the sample is not exactly vertical to the beam. Aluminium Foil The figure 5 (untreated aluminum foil) shows incomplete rings, while figure 6 (heated aluminum foil) shows only points. Figure 7 (scratched after being heated) shows partial that almost form rings. This leads to the conclusion that the aluminum foil already has a texture, which is partly destroyed when heated due to recrystallization. The reason for the texture in the untreated material is that a foil is produced by rolling a piece in a direction until it is thin. Scratching the foil textures the material again. After scratching, there are more defects again and therefore more texture. So the picture shows thin rings. Pet Bottle It can be seen that the rings in figure 9 are very thick in comparison to figure 8. It is therefore obvious that the body of the PET bottle has the higher orientation than the neck. The body is textured. As in figures 5-7 for the aluminum foil, the textured material shows partial rings in the diffraction pattern. The difference between aluminum and PET without texture (fig. 6 resp. 9) is that the polymer cannot be perfectly without orientation due to its long molecules. This explains the rings in the diffraction of the neck. On the other hand, aluminum is crystalline while PET is amorphous. That causes the differences in the pictures of the samples without texture (the neck resp. the heated aluminum foil). The PET bottle, an amorphous polymer, is produced by blowing a preform into the form of the bottle. The chains of the polymer are not oriented in the preform. After blowing up, the body is stretched so the chains are oriented. The form of the neck has not changed. That explains the differences in the picture. Shrinking Tube In picture 10, there are a lot of thin rings. After heating the tube, it shrinks and the orientation rises, so we got weaker signals. During the heating stresses between the chains are reduced and the microstructure is reorganized. 11

13 3.2. Powder Diffraction a) We take the conclusion by comparing the peaks and their positions with the data bank that the unknown substance has to be Calcium Carbonate, a substance which is found in washing machines, for example. Two different phases of calcium carbonate are in the sample: Calcite (fig. 13, red) and aragonite (fig. 14, red). The sample is a mixture of these two calcium carbonate phases. b) The averaged dimension of the crystallites is about 249 Å. 4. Conclusion The two experiments were very interesting and showed some methods to analyze unknown substances. With the help of powder- and X-ray diffraction, conclusions about the composition and processing of a material can be gave. Furthermore, we have learned how to handle with X-ray safely and achieved some knowhow for future work in material science. On the other hand the experiments showed the problems of these methods. For example, we had some problems with the diffractometer because of a 2θ-misalignment. 5. References Fig. 1: Source: Fig. 2: ion.png Fig. 3: [1] : Laboratory course introduction P1 Materialcharakterisierung mit Röntgendiffraktion, Fall Term 09:, Materials Science BSc, ETH Zurich. [2] : Laboratory course introduction P2 Pulverdiffraktometrie, Fall Term 09:, Materials Science BSc, ETH Zurich. [3] : Steurer, Walter (2008): Kristallografie ; Course Script, Materials Science BSc, ETH Zurich. 12

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