KTaO3 has the space group of Pm-3m . K atom occupies Wyckoff position 1a, Ta ato

Question

KTaO3 has the space group of Pm-3m. K atom occupies Wyckoff position 1a, Ta atom occupies 1b, and Oxygen atoms occupy 3c. Lattice constants of the unit cell is a = 0.3989 nm. Calculate the diffraction intensities of the first 5 diffraction peaks of this crystal. You should include the structure factor, multiplicity factor, and Lorentz-Polarization factor. Go to the website “http://it.iucr.org/Cb/ch6o1v0001/sec6o1o1.pdf” to look at the table of atomic form factor. (You can only access the website using the IP within the university.) The X-ray used for the problem is Cu Ka radiation.

Explanation / Answer

From the data

with,

a = 0.3989 nm

   = 3.989 angstrom

d = a/sq.rt.(h^2 + k^2 = l^2)

For a 100 plane,

d = 3.989/sq.rt.(1) = 3.989 angstrom

So,

sin(theta) = l/2d

                 = 1.54/2 x 3.989

Theta = 11.13 degrees

2theta = 22.26 degrees                

For a 110 plane,

d = 3.989/sq.rt.(2) = 2.820 angstrom

So,

sin(theta) = l/2d

                 = 1.54/2 x 2.820

Theta = 15.84 degrees

2theta = 31.68 degrees                

Similarly we could calculate 2theta value for the 111 plane

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