A06_Diffraction_activity_S2022
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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