wk05-06_HANDOUT_XRD_f23

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1 MSE 235: X-Ray Diffraction of Metals Lab Activity Instructions: This is a two-week lab activity comprised of four major tasks. Tasks 1-2 will be completed during the first week, and Tasks 3-4 will be completed during the second week. During the first week, you will meet in the XRD lab (ARMS 2093); during the second week, you will meet in the optical microscopy lab but may access the XRD lab. Please read this lab handout and complete the required background reading before coming to lab. There are also 5 pre-lab questions (see below) that you need to answer before coming to lab during the first week (worth 5 points). Because the XRD is a relatively fragile piece of equipment, only authorized and trained users can operate the XRD system; in lab, your TA will operate the XRD system, and will assist you with completing the assigned tasks. Report: To prepare your report, a lab report template is available on Brightspace. Download and use/edit this document, then submit it as a PDF through Brightspace using the appropriate assignment link. The report will be due in roughly two weeks, i.e., one week after the conclusion of the second week of XRD lab activities. Goal: To become familiar with x-ray powder diffraction as a method for identification of crystalline materials and specifically, metals. Objectives: Upon completion of this experiment the student is expected: • To understand how to carry out XRD spectrum analysis • To understand how powder diffraction may be used to differentiate between single-phase and multi-phase materials • To become acquainted with use of powder diffraction for identification of unknown materials Background Reading: Powder diffraction reading that begins on page 4 of this document; Sections 3.13-3.17 and Section 4.3 in Callister & Rethwisch. Activity References: Virtual XRD: https://envision-public-builds.s3.amazonaws.com/MSE235_Virtual_Lab/index.html Crystallography Open Database – Inorganic Phases: http://www.crystallography.net/cod/ Equipment & Materials: Powder diffraction files (raw data files available on Brightspace); X-ray diffractometer (Bruker D8 Focus); powder metal specimens of Cu and Zn powder (located in drawer near sample prep station in ARMS 2093); data analysis software (e.g., Excel); plotting software (e.g., Origin). Pre-Lab Questions: On a separate sheet of paper, please answer these questions before the start of your lab session. Your TA will check to make sure you have completed all these questions; they will then discuss the answers at the start of the lab session. 1. What is the relationship between the lattice parameter ( a ) of a crystalline material and its interplanar spacing ( d )? And how is this equation related to Brag g’s Law? 2. What diffraction peaks are typically present in the spectrum of a FCC metal? 3. What diffraction peaks are typically present in the spectrum of a BCC metal? 4. What is a solid solution (e.g., an alloy of Cu and nickel alloy; see section 4.3 in Callister & Rethwisch)? 5. What is an allotropic phase transformation (see section 3.6 in Callister & Rethwisch)?

2 WEEK 1 – TASKS 1-2 TASK 1: Identification of Diffraction Peaks 1.1 Collect the XRD spectra for Cu and Zn powders , then answer the following questions. a. Open the obtained .DQL data files using any text editor. The file headings contain metadata describing the XRD collection parameters. Below this metadata is a two- column data set of intensity as a function of angle (2  ). b. Plot and index both spectra, identifying the Miller indices. Calculate the atomic radius of Cu. (Hint: What equations relate lattice parameter with the Miller indices?) c. How does your Cu atomic radius compare with the literature value? Include the calculated atomic radii of Cu along with the indexed diffraction patterns of both Cu and Zn in your lab report (do not forget proper figure captions). d. Why can you not calculate the atomic radius of Zn using the same equations that you used for Cu? 1.2 Collect the XRD spectra for Annealed Brass (a 70 wt%Cu-30 wt% Zn alloy known as cartridge brass), then answer the following questions. a. Alloys of Cu and Zn form a continuous FCC-substitution solid solution alloy when mixed . In this case, the lattice parameter, a , of the solid solution alloy can be estimated by assuming a linear variation with respect to the pure components: ? 𝐶𝑢−?? ?𝑙𝑙?𝑦 = ?? 𝐶𝑢 + (1 − ?)? ?? where x is the atomic fraction of Cu. This formula is known as Vegard’s law. Using the above equation and the lattice parameters of Cu and Zn, calculate the lattice parameter for a 70 wt% Cu-30 wt% Zn solid solution alloy. Don’t forget to convert from wt% to at%. ??% 𝐶? = (??% 𝐶?)(𝑀𝑊 ?𝑓 ??) (??% 𝐶?)(𝑀𝑊 ?𝑓 ??) + (??% ??)(𝑀𝑊 ?𝑓 𝐶?) where MW Cu and MW Zn are the molecular weights of Cu and Zn, respectively. b. Calculate the 2 θ shift (i.e., the change in the 2 θ value) for the { 200} peak of the solid solution alloy when compared to that of pure FCC Cu. (Hint: U se Bragg’s law and the equation relating interplanar spacing with lattice parameter for cubic crystal structures). Check your answers with your TA. c. Do your answers make sense when you consider the atomic radii of Cu and Zn? d. Does the calculated 2 θ value correspond to the 2 θ value of the {200} peak found in the experimental spectrum? Explain possible reasons for a deviation. Show your work and include the diffraction spectrum in your lab report along with the proper figure caption.

3 TASK 2: Identification of an Unknown Element Collect the XRD spectrum for an unknown element that has either an FCC or BCC crystal structure. Calculate/determine the following to help you identify the unknown element: a. Determine the angle (2  ) corresponding to each x-ray diffraction peak. b. Determine the interplanar spacing ( d ) associated with each x-ray diffraction peak. c. Determine whether the crystal structure is FCC or BCC. d. Calculate the appropriate lattice parameter ( a ) and atomic radius ( R ) of the element. e. Determine the possible identity of the element. (Hint: The information on the inside front cover of Callister & Rethwisch may be helpful!) f. Plot the spectrum, index it, and include it in your lab report with an appropriate caption. g. Bring these results with you to the Friday lecture at the conclusion of Week 1 of XRD activities. NOTE: All spectra will be provided on BrightSpace.

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4 WEEK 2 – TASKS 3-4 TASK 3: Diffraction Pattern Analysis 3.1 Collect the XRD spectra for 90% cold worked (CW) brass (“Cold Rolled Brass”), then answer the following questions. a. Compare this CW sample to annealed brass (from Task 1, which has not undergone cold working) by plotting their spectra on the same plot. b. Note the differences between the patterns and explain why those differences occur. (Hint: Pay attention to the peak position and intensity.) Remember that cold working a material can develop texture in the form of a preferred crystallographic orientation. c. Compare the FWHM (full width at half maximum) values of the 90% CW sample with those of the annealed brass sample at 2 θ values of 43 ° , 50 ° , and 74 °. d. Determine what effect cold rolling has on the orientation of (111) and (200) planes relative to the surface of the sample? How does this affect the diffraction pattern, if at all? e. Include the comparative spectra in your lab report along with a relevant figure caption. 3.2 Collect the XRD spec tra for a “Mixture of Cu and Zn Powder”, then answer the following questions. a. Compare this Cu/Zn powder mixture sample to annealed brass by plotting the spectra on the same plot. b. Note the differences between the patterns and explain why those differences occur. Specifically, explain why the pattern for the Cu/Zn powder mixture contains two sets of peaks, while the pattern for the Cu-Zn alloy contains just one set of peaks. TASK 4: Collecting X-Ray Diffraction Data This portion of the lab activity focuses on understanding how various XRD operating parameters affect the obtained spectra. You will use the XRD Virtual Lab available at: https://envision-public-builds.s3.amazonaws.com/MSE235_Virtual_Lab/index.html Open the Virtual Lab. Select Cu as your material, with angle range 20-90º. You will then vary XRD collection parameters over ten trials listed in Table 1. Some troubleshooting notes on the Virtrual Lab interface: • After you click through the parameters, click “Begin Experiment”. The simulation will take the actual amount of time an equivalent experiment (given the angle range, step size, and time steps). You may “Fast Forward” the simulation without affecting your results.

5 • Once the simulation completes, click “Export Data” to show the plotted spectrum, then click “Export” to download the data in .CSV format (which can be opened in any text editor or Excel). • I n Table 1, values indicated with “~” mean approximate. The sliders on several parameters in the Virtual Lab are difficult to land precisely on desired values, so minor variations are acceptable and will have negligible influence on your final answers. For example, for a time step of ~1.5 sec, landing the slider on 1.45 sec is sufficient. Table 1. List of parametric variations to carry out in Virtual Lab for Cu. Trial # Entry Slit [º] Exit Slit [º] Step Size [º] Time Step [sec] Strain on Crystal 0 (Control) 2.5 2.5 ~0.1 ~1.5 0 1 0.5 0.5 ~0.1 ~1.5 0 2 2.5 2.5 ~0.02 ~1.5 0 3 2.5 2.5 ~0.2 ~1.5 0 4 2.5 2.5 ~0.5 ~1.5 0 5 2.5 2.5 ~1.0 ~1.5 0 6 2.5 2.5 ~0.1 ~0.2 0 7 2.5 2.5 ~0.1 ~10 0 8 2.5 2.5 ~0.1 ~1.5 0.1 9 2.5 2.5 ~0.1 ~1.5 0.2 4.1 What is the effect of the following XRD settings on the peak position, peak intensities, peak FWHM, and signal-to-noise ratio (i.e., ratio of peak intensity to background intensity) of the resultant spectra: a. Entry and exit slits b. Step size c. Time step d. Strain on crystal Generate one plot each for (a), (b), (c), and (d), which facilitate comparison across spectra to illustrate the key trends/effects. 4.2 Amongst the ten trials outlined in Table 1, select one “good” and one “bad” spectrum to show in your lab report. Discuss features and characteristics of these spectra that make them either “good” or “bad”. 4.3 Calculate the predicted spectrum collection time for each of the ten trials in Table 1. Provide those times in your lab report. Discuss how you might reduce collection time while maximizing the quality of your spectra.

6 BACKGROUND INFORMATION ON POWDER DIFFRACTION Since every crystalline substance has a unique structure, i.e. the periodic arrangement of its atoms, this unique characteristic can be used to identify the substance. In particular, the set of crystallographic interplanar spacings has been the basis for an identification data base. The data base is a consequence of a technique to measure interplanar spacings. This technique is "Powder" Diffraction and the data base is the Powder Diffraction File compiled by the International Centre for Diffraction Data. Powder diffraction is a method to measure all possible interplanar spacings. The name comes from the use of diffraction to measure a representative set of interplanar spacings from a sample of randomly oriented "small single crystals" (typically 1- 10 μm in diameter). These "small single crystals" may be grains in a polycrystalline sample or particles in a powder. In either case, random orientation is needed to ensure that all interplanar spacings are sampled equally. X-Ray Spectra The x-ray spectrum is part of the electro-magnetic spectrum covering a wavelength range from approximately 0.01 Å to 1000 Å (an Angstroms, Å, is a unit of measurement commonly used in x-ray diffraction. 1 Å is equal to 0.10 nm) . The energy, frequency, and wavelength relationship for x-rays are: 𝐸 = ℎ 𝜈 = ℎ𝑐 𝜆 , where E is energy, h is Planck's constant, 𝜈 is frequency, c is speed of light, and 𝜆 is the wavelength. A useful relationship in specific units is: E (keV) = 12.398 / 𝜆 (Å) The spectrum generated from electron bombardment of a solid (Fig. 1) is divided into two types. The continuous (or white or Bremstrahlung) spectrum is generated from electron-electron collisions. Rising up from the Bremstrahlung is a series of intense and narrow bandwidth lines called the characteristic spectrum. The characteristic spectrum is generated by electron energy transitions in an ionized atom, and the permissible energy transitions that produce the spectrum are dictated by quantum relations for the electronic structure of the specific target atom. This means that electron bombardment of different materials will produce x-rays of different characteristic wavelengths (Table 1).

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7 Fig. 1: Example spectrum of Mo from “Elements of X - Ray Diffraction”, 2 nd edition, B.D. Cullity. X-Ray Diffraction To perform x-ray diffraction, a beam of characteristic x-rays generated in an x-ray tube is directed at the sample to be examined (Fig. 2). The beam arrives and departs the sample at an angle theta that is varied by rotating the sample. A detector is positioned at an angle two theta to measure the intensity of the x-ray beam scattered by the sample.

8 A diffraction pattern is gathered by measuring the intensity of the scattered x-ray beam as a function of the diffraction angle two theta. At most two theta angles the intensity of the scattered beam is very small. However, under conditions satisfying Brag g’s law the intensity of the diffracted beam may be very intense (Fig. 3). Bragg’s law (eq. 1) states that for two parallel beams of the same wavelength to remain in phase after scattering from parallel atomic planes, the path difference of the scattered beams must be an integral multiple of the wavelength. In the Bragg equation, 𝜆 is the wavelength of the incident x-rays, 𝜃 is the diffraction angle, and d is the spacing 𝜆 = 2 𝑑 sin 𝜃 , between atomic planes. The target of the x-ray source is usually one of the following elements: Cu, Mo, Cr, or Fe and the K-radiations are the normal spectral lines used. The Cu source is the most common because of the intermediate wavelength that allows measurements of the most useful range of d-values and still provides adequate resolution of the measured 2 𝜃 values.

9 Note that the peaks in Fig. 3 vary in intensity. The intensity of the diffraction peaks provides information about the atomic structure. In fact, there are many cases in which Bragg’s law is satisfied for a certain set of atomic planes and yet no diffraction may occur because of a particular arrangement of atoms in the unit cell. The effect of the arrangement of atoms on the intensity of a diffracted beam satisfying Bragg’s law is quantified by calculating the “structure factor”. An example of structure factor effects are the selection rules used to differentiate between BCC and FCC metals. Considering atomic planes with Miller’s indices ( hkl ), only peaks with Miller’s indices having h,k, and l being all odd or all even will be present in the diffraction patterns of FCC metals, while only peaks with the sum of h,k, and l being even are present in the diffraction patterns of BCC metals. Effect of Cold Working Cold working is the plastic deformation of metals below the recrystallization temperature (the temperature at which new, dislocation-free grains nucleate and grow). In most cases of manufacturing, such cold forming is done at room temperature. Sometimes, however, the working may be done at elevated temperatures where the material’s yield strength is lower and ductility is higher . The major cold-working methods can be classified as squeezing or rolling, bending, shearing and drawing. When metals are cold worked, defects density is increased due to plastic deformation. The large majority of cold-worked defects are dislocations. Increased dislocation density inhibits further dislocation motion, and the metal becomes more resistant to further deformation. This is called work hardening. The resulting metal product has improved tensile strength and hardness, but less ductility.

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10 The Full Width Half Maximum (FWHM) of a diffraction peak is the width of the peak at the half maximum intensity (Fig. 4). This value provides information about the grain size of the material and also indicates residual strain and distortions of the lattice due to the presence of dislocations. Fig 4. Schematic of FWHM. Texture In materials science, texture is the distribution of crystallographic orientations of a polycrystalline sample or single crystal. A sample in which these orientations are fully random is said to have no distinct texture. If the crystallographic orientations are not random, but have some preferred orientation, then the sample has a weak, moderate or strong texture depends on the percentage of crystals having the preferred orientation. Texture is seen in almost all engineered metals and can have a great influence on materials properties. Texture can be developed in a material during plastic deformation, often in the form of rolling. When a material is rolled, one crystallographic plane becomes parallel to the surface and a direction within that plane becomes parallel to the rolling direction. For example, BCC alloys typically have a (110)[001] rolling texture. (Callister, p. 821) This texture can also cause some variation in diffraction peak intensities. One extreme case is a complete lack of texture: a solid with fully random crystallite orientation will have isotropic properties at length scales sufficiently larger than the size of the crystallites. The opposite extreme is a perfect single crystal, which likely has anisotropic properties by geometric necessity.