Class Activity4

1)The table on the back shows a series planes defined in terms of the hkl indexes of the conventional cubic lattice. For your information h2+k2+l2, h+k+l, and sqrt(h2+k2+l2)sin() are provided. Add a check mark by those planes that will produce a diffraction peak for each the sc, bcc, fcc, and diamond lattices. Hint: use extinction rules.

2)4 peaks are observed on a diffraction pattern of a crystal structure with a single type of atoms. The 4 peaks are observed for 21=44.388o, 21=64.580o, 21=81.728o, and 21=98.135o. If the incoming wave length is λ=1.2Å

a)if the crystal structure is known to be bcc, determine the index of the planes giving rise to each of the 4 peaks

b)Determine the lattice parameter a of the conventional square lattice

c)What other type of lattice would have given rise to the same 4 first peaks, what would the lattice parameters befor this other cell?

h / k / l / h2+k2+l2 / h+k+l / sin() / sc / bcc / fcc / diamond
1 / 0 / 0 / 1 / 1 / 1.00
1 / 1 / 0 / 2 / 2 / 1.41
1 / 1 / 1 / 3 / 3 / 1.73
2 / 0 / 0 / 4 / 2 / 2.00
2 / 1 / 0 / 5 / 3 / 2.24
2 / 1 / 1 / 6 / 4 / 2.45
2 / 2 / 0 / 8 / 4 / 2.83
3 / 0 / 0 / 9 / 3 / 3.00
2 / 2 / 1 / 9 / 5 / 3.00
3 / 1 / 0 / 10 / 4 / 3.16
3 / 1 / 1 / 11 / 5 / 3.32
2 / 2 / 2 / 12 / 6 / 3.46
3 / 2 / 0 / 13 / 5 / 3.61
3 / 2 / 1 / 14 / 6 / 3.74
4 / 0 / 0 / 16 / 4 / 4.00
4 / 1 / 0 / 17 / 5 / 4.12
3 / 2 / 2 / 17 / 7 / 4.12
3 / 3 / 0 / 18 / 6 / 4.24
4 / 1 / 1 / 18 / 6 / 4.24
3 / 3 / 1 / 19 / 7 / 4.36
4 / 2 / 0 / 20 / 6 / 4.47
4 / 2 / 1 / 21 / 7 / 4.58
3 / 3 / 2 / 22 / 8 / 4.69
4 / 2 / 2 / 24 / 8 / 4.90
4 / 3 / 0 / 25 / 7 / 5.00
4 / 3 / 1 / 26 / 8 / 5.10
3 / 3 / 3 / 27 / 9 / 5.20
4 / 3 / 2 / 29 / 9 / 5.39
4 / 4 / 0 / 32 / 8 / 5.66
4 / 4 / 1 / 33 / 9 / 5.74
4 / 3 / 3 / 34 / 10 / 5.83
4 / 4 / 2 / 36 / 10 / 6.00
4 / 4 / 3 / 41 / 11 / 6.40
4 / 4 / 4 / 48 / 12 / 6.93