In: Other
The formula to determine the indices of the planes using XRD data is,
where, = diffraction angle
= wavelength of X- rays in nm
a = lattice parameter of a crystal in nm
h,k,l = the indices of the peaks
procedure to calculate the indices of the peaks,
1. Calculate for different values of 2
Peak no. | 2 | 1x / | 2x/ | 3x/ | hkl | |||
1 | 30.7301 | 0.0702 | ||||||
2 | 35.6406 | 0.0937 | ||||||
3 | 51.1984 | 0.1867 | ||||||
4 | 60.9706 | 0.2574 | ||||||
5 | 64.0327 | 0.2811 | ||||||
6 | 75.4344 | 0.3743 |
2. Find out the minimum value of (here it is 0.0702) and divide all the values of using this minimum value.Multiply the final result by 1, 2 and 3 and tabulate the results. This is done to get a rounded-off figure for our values.
Peak no. | 2 | 1x / | 2x/ | 3x/ | hkl | |||
1 | 30.7301 | 0.0702 | 1 | 1 | 2 | 3 | ||
2 | 35.6406 | 0.0937 | 1.3348 | 1.3348 | 2.6696 | 4 | ||
3 | 51.1984 | 0.1867 | 2.6595 | 2.6595 | 5.319 | 8 | ||
4 | 60.9706 | 0.2574 | 3.6667 | 3.6667 | 7.3334 | 11 | ||
5 | 64.0327 | 0.2811 | 4.0043 | 4.0043 | 8.0086 | 12 | ||
6 | 75.4344 | 0.3743 | 5.3319 | 5.3319 | 10.6638 | 16 |
The following values of h,k,l are predetermined indies for specific unit cell systems;
Primitive = 1,2,3,4,5,6,8,9,10,11,12,13,14,16.....
Body-centered = 2,4,6,8,10,12,14,16,....
Face-centered = 3,4,8,11,12,16,19,20,24,27,32,.....
Diamond Cubic = 3,8,11,16,19,24,27,32,....
From the table, 3x/ shows the rounded-off values matching closely with the indices. The indices closely match with the values of Face-centered cubic crystal system. The corresponding h,k,l values of FCC system are listed that would yield the values of .
Peak no. | 2 | 1x / | 2x/ | 3x/ | hkl | |||
1 | 30.7301 | 0.0702 | 1 | 1 | 2 | 3 | 3 | 111 |
2 | 35.6406 | 0.0937 | 1.3348 | 1.3348 | 2.6696 | 4 | 4 | 200 |
3 | 51.1984 | 0.1867 | 2.6595 | 2.6595 | 5.319 | 8 | 8 | 220 |
4 | 60.9706 | 0.2574 | 3.6667 | 3.6667 | 7.3334 | 11 | 11 | 311 |
5 | 64.0327 | 0.2811 | 4.0043 | 4.0043 | 8.0086 | 12 | 12 | 222 |
6 | 75.4344 | 0.3743 | 5.3319 | 5.3319 | 10.6638 | 16 | 16 | 400 |