The technique of X-ray powder diffraction

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X-ray powder diffraction can be used to determine the structure of a crystal as well as the lattice parameter of a copper-aluminum sample. This is a quick analysis technique used largely for phase identification in crystalline materials. It also offers information on unit cell dimensions. Also, the sample material has been carefully powdered and homogenized. It also improves understanding of the average bulk composition (Suryanarayana and Norton 2013, p.86).

For X-ray wavelengths similar to crystal lattice plane spacing, crystalline solids behave like gratings of a three-dimensional diffraction. X-ray diffraction works from a monochromatic X-ray as well as constructive interference. A cathode ray tube generates the X-rays. The latter are filtered to ensure of monochromatic radiation production, concentrate as well as directed to the sample material. Constructive interference is yielded when the ray of incident interacts with the material sample upon satisfaction of the conditions of the Bragg Law. For instance, nλ=2d sin θ. In this law, there is a relationship between electromagnetic radiation wavelength as well as the angle of diffraction and the spacing of the lattice in a sample of a crystal. The X-rays that are diffracted are detected, processed, and also counted. Through sample scanning by a 2θ angles range, the directions of lattice diffraction ought to be achieved to the powdered copper-aluminium random orientation. The conversion of the diffraction peaks to d-spacing permits the copper-aluminium identification since each mineral has a d-spacing unique set.

Typically, the results are peak position presented at 2θ as well as X-ray counts in table form or else a graph of the relationship of counts per second against degrees (2θ). Intensity can either be reported as the intensity at peak height, above background intensity or else integrated intensity, the peak area. Each peak’s d-spacing by Bragg’s equation solution for λ appropriate value. After the determination of all d-spacing, the unknown’s ds is compared to that of the sample which is known. Unknown sample’s identification provides possible through matching the d-spacing. For the parameters of copper-aluminium to be determined, particular hkl has to be indexed to each reflection.

Crystalline structures are often determined by X-ray diffraction from a single sample crystal, although the determination of structure from powders that are polycrystalline is essential. Crystal ray diffraction provides the crystals’ internal structure information. The X-ray technique can be used, since it has a short wavelength of an equal magnitude order as a crystals’ lattice constant.

Question 2

The technique of heat treatment is used to alter certain metals as well as alloy characteristics as a result of making them more suitable for a particular application kind. Moreover, heat treatment is the technique employed to modify the metals’ physical properties through heating or else cooling. Heat treatment can influence the physical-mechanical properties of Iron including density, phase transformation as well as thermal conductivity.

A change in phase also changes the crystalline structure of metals. The former relates to temperature directly and happens in the crystalline structure of metals, for instance, Iron. Temperature controls the transformations, although stress, the rate of heating or else cooling as well as chemical composition can affect the temperature at which the changes happen. For instance, there can be changes in Iron from the crystalline structures of body-centred cubic to face-centred cubic despite the fact that it remains solid. Iron is at body-centred cubic when at temperatures of 910 degrees Celsius, but changes to face-centred cubic from 910 to 1391 degrees Celsius. The transition of an Iron from BCC to FCC results to an 8 to 9 percent density increase. It results in shrinking the size of the sample of Iron when heated above the temperature of transition. Mass being constant, it indicates a decrease in volume of Iron.

It is evident that the BCC unit cell atoms touch across the diagonals of the cube. Therefore, if the length of the edge of the cube is represented by a, then √ 3a = 4R where R is the Iron atom’s radius. For that reason, a = 4R = 4(0.1√24 nm) = 0.2864 nm. Similarly, the FCC unit cell atom touches each other across the face of the cubic diagonal; as a result, the lattice parameter is 0.3591. The volume of Bcc is a3 = 0.28643 while the volume of Fcc is 0.35913. Fcc’s single unit cell has four atoms, while Bcc’s single unit cell has two atoms, therefore change in volume, VFcc-2VBcc/2VBcc. It implies that (0.046307-0.046934/0.046934)*100 is equal to -1.34%.

(Source: Galasso 2016, p.121)

Engineers are involved in modern world’s aspects as well as strive for meeting current society’s needs in the way that is responsible environmentally through the process of products’ designing. The latter reduces wastes, maximizes the efficiency of energy, and increases performance as well as facility recycling. Metal products form the backbone of the technological world. Heat treatment to change the physical properties of metal is essential to new material development. Further, new methods as well as models to make also understand them are the critical points of an engineer today. Understanding crystalline structures give engineers the means to measure mechanical properties allowing access to growth. The high society dependence on metals gives the profession of engineering sustained importance in the world today.

Question 3

a) Grains refer to the aggregated small crystals in polycrystalline objects. Some objects that metallic including castings have the grains that are large while the others have tiny ones. For instance, figure 1 illustrates grains in a metal.

Figure 1 (Source: Smallman 2016, p.24)

b) In a polycrystalline material, the interface between two grains or else a crystallite is referred to the grain boundary. Grain boundaries are defects in the structure of a crystal and tend to decrease a material’s electrical as well as the thermal conductivity. It separates regions with a crystalline orientation that is different within a polycrystalline solid. Grain boundaries are caused by a crystallizing solid uneven growth.

Crystal 2

Grain boundary (atoms of impurity)

Crystal 1

c) A twin is referred to as an area defect in which a regular lattice’s mirror image is formed throughout the silicon ingot growth, usually as a result of perturbation. It represents a crystalline orientation change across a twin plane in such a way that a particular symmetry exists across a plane.

d) A precipitate is a volume defect. It refers to the small particles presented into the matrix through reactions of solid state. They are broadly used for various aims, although they are commonly used to increase the structural alloy strength through the action of obstacles to the dislocation motion. Precipitates act as the generation of dislocation site. They generate lattice strain, and as a result, dislocations arise to relieve the stress caused. For instance, the precipitates induced in the course of the wafer processing of silicon come from oxygen, impurities of metals as well as dopants including boron (Henderson 2013, p.20).

Metallographic etching refers to a chemical procedure for highlighting metal features at microscopic levels. Metallurgists can predict as well as explain the physical features and failures in performance of a sample metal, through the study of character, amount and different features’ distribution. To analyze some features, samples of minerals must be polished to resemble a fine finish of a mirror. It is for the reason that most of the metallurgical characteristics are microscopic and can only be analyzed with optical magnification. Etchants are used to create a contrast between the microstructure of an element of metal. The work of the etchant is to uncover the shape as well as the grain boundary size, metallic phases, tiny non-metallic amounts, cracks, issues as well as the uniformity and material thickness.

Question 4

Secondary electron imaging is more surface sensitive therefore possessing a resolution that is high. Instead of losing energy through exciting electrons in the material to be sampled electrons from the beam of the incident can even go through backscattering re-emerging from a surface of a sample. Backscattered electrons escape depth higher compared to that of secondary electrons, further surface topographical characteristics resolution suffering. For instance, to demonstrate SEM secondary as well as backscattered electron imaging a comparatively thick Nickel wire wrapped with a Titanium wire that is relatively thin. Low rounded bumps texture on the surface of the Nickel wire is visible on the secondary electron image. However, the surface of the Titanium wire appeared rougher as well as flaky in appearance. The secondary electron image possesses a good resolution and is detailed regarding surface morphology. Looking at the same specimen, in backscattered electron image the texture of the surface is less visible.

Backscattered electrons have greater energy compared to secondary electrons. It indicates that Backscattered electrons emanating from deeper in the volume of interaction can escape from the sample. Then, they can be collected by the detector of the backscattered electrons. Therefore, the images from the electrons have the spatial resolution that is low compared to secondary electron images. Moreover, the backscattered electrons can travel further in the sample and later come out. Therefore, they carry less restricted information to the surface detail hence reducing the resolution. In X-ray mapping, the spatial resolution is high as a result of a larger area of detection as well as lower mapping of keV.

Aluminium, copper as well as iridium produce different X-ray peaks. For instance, aluminium has very low X-ray peaks, while copper has high X-ray peaks. Moreover, the elements absorb X-ray photons’ number.

Question 5

Energy Dispersive X-ray Spectrometry uses a spectrum of an X-ray emanating from a sample of a solid exposed to electron beam bombardment aimed at acquiring a chemical analysis that is localized. Elements between Beryllium and Uranium can be recognized in principle. The beam is scanned in a television-like raster as well as displayed in an intensity of an X-ray line that is selected. Subsequently, it produces the distribution images of elements or else maps. The images provided by the electrons from the sample collected expose surface topography or other differences of the mean atomic number. A typical spectrum of Energy Dispersive X-ray Spectroscopy is represented on a graph of a relationship between X-ray counts against energy (keV). Peaks in energy resemble the various samples’ elements. The spectrums are narrow as well as resolved, although several elements yield multiple peaks. For instance, strong Kα as well as Kβ peaks are shown by Iron.

(Chen et at. 2016, p.7)

X-ray photoelectron spectroscopy is the surface analysis technique mostly used since its application is on broad-range materials. It also provides quantitative also chemical state depth for a measurement of XPS is nearly 5nm. The instruments of XPS can obtain a lateral spatial resolution spectrum of about 7.5µm. When the focused beam is scanned across the surface of a sample, spatial distribution data is attained. Information concerning the distribution of data can be accomplished through the combination of measurements of XPS with ion milling to characterize film structures that are thin. A sample’s surface with mono-energetic rays of Al kβ is excited to produce photoelectrons to accomplish XPS. The energy of the photoelectrons emitted is measured by an electron energy analyzer. The identity of the elements, chemical state, as well as detected element quantity can be known from the binding energy also photoelectron peaks’ intensity.

X-ray photoelectron spectroscopy technique is most suitable for characterizing a titanium oxide that is 7nm since it’s the depth of sampling is 3 to 10nm. The standard technique's depth of analysis is less than 5nm. Therefore, it is suited better for the ultra-thin layers compositional analysis as well as microscopic features of the sample that are thin (Halim et al. 2016, p.406).


Chen, Z., et al., 2016. Quantitative atomic resolution elemental mapping via absolute-scale energy dispersive X-ray spectroscopy. Ultramicroscopy, 168, pp. 7-16.

Galasso, F.S., 2016. Structure and properties of inorganic solids: International series of monographs in solid state physics (Vol. 7). Amsterdam: Elsevier.

Halim, J., et al., 2016. X-ray photoelectron spectroscopy of select multi-layered transition metal carbides (MXenes). Applied Surface Science, 362, pp. 406-417.

Henderson, B., 2013. Defects and their structure in nonmetallic solids (Vol. 19). New York: Springer Science & Business Media.

Smallman, R.E., 2016. Modern physical metallurgy. Amsterdam: Elsevier.

Suryanarayana, C. and Norton, M.G., 2013. X-ray diffraction: A practical approach. New York: Springer Science & Business Media.

May 02, 2023

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