An orthorombic cell with a = 0.82nm, b= 0.94nm and c = 0.75nm. Calculate the separation of the plane using miller indices given below.
1.if the separation (a)(133) and (b)(399)
2.if the separation of (a)(122) and (b)(244)
3.what is your conclusion to 1 and 2
To calculate the separation of the plane using the Miller indices given, we can use the formula:
d(hkl) = a / sqrt(h^2 + k^2 + l^2)
1. For plane (133):
h = 1, k = 3, l = 3
d(133) = 0.82nm / sqrt(1^2 + 3^2 + 3^2) = 0.82nm / sqrt(19) = 0.82nm / 4.3589 = 0.1881nm
For plane (399):
h = 3, k = 9, l = 9
d(399) = 0.82nm / sqrt(3^2 + 9^2 + 9^2) = 0.82nm / sqrt(99) = 0.82nm / 9.9499 = 0.0824nm
2. For plane (122):
h = 1, k = 2, l = 2
d(122) = 0.82nm / sqrt(1^2 + 2^2 + 2^2) = 0.82nm / sqrt(9) = 0.82nm / 3 = 0.2733nm
For plane (244):
h = 2, k = 4, l = 4
d(244) = 0.82nm / sqrt(2^2 + 4^2 + 4^2) = 0.82nm / sqrt(36) = 0.82nm / 6 = 0.1367nm
3. Comparing the results:
- For 1, the separation of plane (133) is larger than plane (399): d(133) > d(399)
- For 2, the separation of plane (122) is larger than plane (244): d(122) > d(244)
From the calculations, we can conclude that the separation of the planes is inversely proportional to the Miller indices. This means that as the Miller indices numbers increase, the separation decreases.