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4-3: Consider a hypothetical element whose structure can be based on either of the following: Cell A: base-centered tetragonal containing two atoms per cell at 000 and ½ ½ 0, for which a = 2 Å and c = 3 Å. Cell B: simple tetragonal with one atom per cell at 0 0 0, for which a = 2 Å and c = 3 Å. (a) Determine simplified structure-factor equations for each cell. (b) Determine the positions (20 values) of the first four lines that would be observed ($F^2 \ne 0$) on the powder pattern made with Cu $K\alpha$ (c) Plot the 20 values of these lines in the manner of the Figure below, and label each line with its indices relative to Cell A and Cell B. (d) Draw the two cells in the proper relation to one another and show that the indices of any one observed line, other than the obvious ones of the form 001, refer to the same plane of atoms. DISTANCE ON FILM OR CHART CUBIC HEXAGONAL simple body- face- centered centered diamond close- packed $2\theta$ = 0° 1 2 hkl 100 110 111 200 210 211 220 300, 221 310 311 222 320 321 400 410, 322 411, 330 331 420 hkl 100 10-1 102 110 10-3 200 11-2 20-1 20-2 10-4 20-3 21-0 21-1 11-4

          4-3: Consider a hypothetical element whose structure can be based on either of the following:
Cell A: base-centered tetragonal containing two atoms per cell at 000 and ½ ½ 0, for which a = 2 Å and c = 3 Å.
Cell B: simple tetragonal with one atom per cell at 0 0 0, for which a = 2 Å and c = 3 Å.
(a) Determine simplified structure-factor equations for each cell.
(b) Determine the positions (20 values) of the first four lines that would be observed ($F^2 \ne 0$) on the powder pattern made with Cu $K\alpha$
(c) Plot the 20 values of these lines in the manner of the Figure below, and label each line with its indices relative to Cell A and Cell B.
(d) Draw the two cells in the proper relation to one another and show that the indices of any one observed line, other than the obvious ones of the form
001, refer to the same plane of atoms.
DISTANCE ON FILM OR CHART
CUBIC
HEXAGONAL
simple body- face-
centered centered diamond close-
packed
$2\theta$ = 0°
1
2
hkl
100
110
111
200
210
211
220
300, 221
310
311
222
320
321
400
410, 322
411, 330
331
420
hkl
100
10-1
102
110
10-3
200
11-2
20-1
20-2
10-4
20-3
21-0
21-1
11-4

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4-3: Consider a hypothetical element whose structure can be based on either of the following:
Cell A: base-centered tetragonal containing two atoms per cell at 000 and ½ ½ 0, for which a = 2 Å and c = 3 Å.
Cell B: simple tetragonal with one atom per cell at 0 0 0, for which a = 2 Å and c = 3 Å.
(a) Determine simplified structure-factor equations for each cell.
(b) Determine the positions (20 values) of the first four lines that would be observed (F^2 0) on the powder pattern made with Cu Kα
(c) Plot the 20 values of these lines in the manner of the Figure below, and label each line with its indices relative to Cell A and Cell B.
(d) Draw the two cells in the proper relation to one another and show that the indices of any one observed line, other than the obvious ones of the form
001, refer to the same plane of atoms.
DISTANCE ON FILM OR CHART
CUBIC
HEXAGONAL
simple body- face-
centered centered diamond close-
packed
2θ = 0°
1
2
hkl
100
110
111
200
210
211
220
300, 221
310
311
222
320
321
400
410, 322
411, 330
331
420
hkl
100
10-1
102
110
10-3
200
11-2
20-1
20-2
10-4
20-3
21-0
21-1
11-4

Added by Donna F.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

09/27/2023

Step 1

- **Cell A (Base-centered tetragonal):** - Atoms at positions: (0,0,0) and (1/2,1/2,0). - Structure factor \( F(hkl) = f[1 + e^{i\pi(h+k)}] \). - Simplified: \( F(hkl) = 2f \) if \( h+k \) is even, \( F(hkl) = 0 \) if \( h+k \) is odd. - **Cell B (Simple Show more…

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4-3: Consider a hypothetical element whose structure can be based on either of the following: Cell A: base-centered tetragonal containing two atoms per cell at 000 and 1(1)/(2)(1)/(2)0, for which a=2angstrom and c=3angstrom . Cell B: simple tetragonal with one atom per cell at 000 , for which a=2angstrom and c=3angstrom . (a) Determine simplified structure-factor equations for each cell. (b) Determine the positions ( 2 heta values) of the first four lines that would be observed ) on the powder pattern made with CuKalpha (c) Plot the 2 heta values of these lines in the manner of the Figure below, and label each line with its indices relative to Cell A and Cell B. (d) Draw the two cells in the proper relation to one another and show that the indices of any one observed line, other than the obvious ones of the form 00I, refer to the same plane of atoms. 4-3: Consider a hypothetical element whose structure can be based on either of the following: Cell A:base-centered tetragonal containing two atoms per cell at 000 and 0.for which a =2Aand c=3A Cell B:simple tetragonal with one atom per cell at 000.for which a=2 A and c =3A (a) Determine simplified structure-factor equations for each cell. (b) Determine the positions (20 values) of the first four lines that would be observed (F2 O) on the powder pattern made with Cu K (c) Plot the 20 values of these lines in the manner of the Figure below, and label each line with its indices relative to Cell A and Cell B. (d) Draw the two cells in the proper relation to one another and show that the indices of any one observed line, other than the obvious ones of the form 0 OI, refer to the same plane of atoms. CUBIC HEXAGONAL simple body- centered face- centered packed hAt 100 110 111 200 210 211 220 300, 221 DISTANCE ON FILM OR CHART 310 - 311 222 320 14 321 16 400 17 410, 322 411, 330 19 331 102 110 10-3 20-2 104 203 21-1 11-6 420

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