A06_Diffraction_activity_S2022

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Nov 24, 2024

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1 Last Name First Name Section Number Instructor Name Wang Nancy 6 j. shi ENGR1600: Materials Science for Engineers Interactive Activity 06 Identify Single Element Crystal Structures Objective : Understand how to identify crystal structure using powder diffraction patterns. Only pure elements in cubic crystal structures are included here. Use Mathematica simulation to looked for allowed powder x-ray diffraction peaks. Materials : Laptop, Tablet (supplied) or Android Phone (7 or later) with Xray Vision App loaded from LMS, barcode (LMS). Due date : In approximately one week. Procedure : Step 0: Augmented Reality App activity a) Either download the App from LMS onto Android phone OR borrow a tablet in class. b) You will need a copy of the bar code also on LMS. c) Aim the camera of your android phone at the bar code. You should see a crystal lattice on screen. d) Scroll between cubic, bcc, fcc e) Scroll between laue, powder, and angle diffraction types. f) Go to angle diffraction and vary the temperature. What happens to the diffraction peaks? Repeat by increasing and decreasing the wavelength of the incoming x-rays. Step 1: In Table 1 (next page) take the 2 values for the powder diffraction patterns of each cubic crystal type (Figure 1) and use Bragg’s Law to calculate the d-spacing and then the signatures, d i /d 1st . Figure 1: The powder diffraction pattern for three unknown cubic crystals are given below. The wavelength of the X-ray is 1.54 Angstrom (0.154 nm). Note the x-axis is 2θ, not θ . Crystal A Crystal B
2 Crystal C Crystal D Table 1: Signatures for up to first 8 diffraction peaks from powder diffraction patterns in Figure 1. Use Bragg’s Law to calculate d. The shaded cell is your d 1st . A θ 14.22 23.65 28.06 34.565 38.19 d (nm) 0.313 0.192 0.164 0.132 0.125 d/d1 st 1 0.613 0.522 0.422 0.397 B θ 19.27 5 27.83 34.875 41.315 47.575 53.96 60.855 69.02 d 0.233 26 0.1649 0.13466 0.1166 0.1043 0.09522 0.08816 0.082467 d/d1 st 1 0.706936 466 0.577295 722 0.499871 388 0.447140 53 0.408214 01 0.377947 355 0.353541 113 C θ 19.16 22.27 32.41 38.94 41.03 d 0.234 6 0.20318 0.14366 0.1225 0.11729 d/d1 st 1 0.866069 906 0.612361 466 0.522165 388 0.499957 374 D θ 13.29 5 18.975 23.46 27.38 30.94 34.28 40.57 d 0.334 8 0.2368 0.1934 0.1674 0.14976 0.1367 0.11839 d/d1 st 1 0.707287 933 0.577658 303 0.5 0.447311 828 0.408303 465 0.353614 098
3 Step 2: Calculate the normalized d- spacing’s in sequence for SC, BCC, FCC in Table 2 below (d/a columns). Excel is recommended. 2 2 2 l k h a d hkl + + = Step 3: Use the CDF App (02_RPI-ENGR1600-Crystal-Structure-Demo) to determine forbidden x-ray reflections in Table 1. If there are extra atoms laying uniformly outside the planes (such as two images below), there will be no diffraction peak, mark X in that hkl’s d/a column. Shortcut: All hkl reflections are allowed in SC. Step 4: Calculate the “signatures” d i /d 1st for four cubic structures using the first allowable reflection as d 1st . (Table 2) Table 2: Possible d- spacing’s, forbidden reflections, and signatures (d i /d 1 ) for 4 cubic systems. “X” denotes forbidden (hkl) reflections from CDF simulation. d 1st is the shaded cell Reflections (hkl) Index SC BCC FCC DC (diamond) d/a d i /d 1st d/a d i /d 1st d/a d i /d 1st d/a d i /d 1st (100) 1 1 X - X - X - (110) 0.707 0.707 0.707 1 X - X - (111) 0.577 0.577 X .577 1 .577 1 (200) 0.5 0.5 0.5 0.707 .5 .866 X (210) 0.447 0.447 X X X (211) 0.408 0.408 .408 .573 X X (220) 0.354 0.354 .354 .5 .354 .612 .354 .612 (300)/(221) 0.333 0.333 X X X (310) 0.316 0.316 .316 .447 .316 .547 X (311) 0.302 0.302 X .302 .522 .302 .522 (222) 0.289 0.289 .289 .409 .289 .5 X (320) 0.277 0.277 X X X (321) 0.267 0.267 .267 .377 X X (400) 0.25 0.25 .25 .354 .25 .433 .25 .433 Step 5: Compare the signatures (d/a ratio’s) from Tables 1 and 2 to determine the crystal structure of each crystal A-C in Table 3 below. Based on the crystal structure identified. Label the first peak of each crystal. Calculate the corresponding lattice constant.
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4 Table 3: Identification of crystal structure for each diffraction pattern (A, B, C, D). Compare signatures in Tables 1 and 2. Crystal Crystal Structure First Peak θ First Peak Plane Miller Index Lattice constant A DIAMOND 14.22 111 .5421 B BCC 19.27 110 .3299 C FCC 19.16 111 .4063 D SC 13.29 100 .3348 Step 6: Using the AR App, for each diffraction pattern in Figure 1, label the peaks with their hkl values. For example, for the pattern you assigned to the simple cubic structure, label the (001), (110), (111), etc. peaks directly on the pattern (Figure 1). Do these match the hkl values in Table 2? They do match the hkl values in table 2. They do match the hkl values in the table