Question

Powder diffraction for a pure metal yields the following dhkl spacings values (nm): 0.2088, 0.1808, 0.1278, 0.1090, 0.1044, 0.09038, 0.08293, and 0.08083. A monochromatic x-radiation having a wavelength of 0.1542 nm was used. Use this information to find the following: a) Is the pure metal FCC or BCC? b) Determine the lattice parameter. (c) Determine the atomic radius and the metal using the values listed in Table 3.1 (or from the list in the front cover of Callister)

Answer 1

d_hkl                        sin²ϴ=λ²/4d_hkl²                   (sin²ϴ/0.04543)=h² + k² + l²          

0.2088                  0.1363                                 3

0.1808                  0.1818                                 4

0.1278                  0.3639                                 8

0.1090                  0.5003                                 11

0.1044                  0.5454                                 12

0.09038               0.7277                                 16

0.08293               0.8643                                 19

0.08083               0.9098                                 20

These correspond to hkl values of (111),(200),(220),(311) so on..

The reflection maxima thus observed from planes for which hkl are either all odd or all even. So the unit cell belongs to the FCC arrangement.

b.

The larger Bragg angles can be measured more accurately than the smaller one, so more accurate value for sin²ϴ is 0.9098.

For this the corresponding d_hkl value is 0.08083

So, d_hkl² = λ²/4 sin²ϴ = 4a²/h² + k² + l²

or, (0.08083² = 4a²/20

or, a = 0.1807 nm = 180.7 pm

c. Table is not given in the question.