Question

Question 2. A primitive tetragonal crystal has lattice parameters of a=b=3 Å and c=4 Å and is placed in an x-rays powder diffraction system and irradiated with X-rays of wavelength 2.5 Å. (i) Use Bragg’s law to determine the scattering angle for the (001), (100), and (111) reflections (n=1). (ii) Is it possible in this apparatus to observe the (111) reflections from this crystal using X-rays of wavelength 5 Å.? Why not?

Answer 1

2 A Primitive tetragonal crystal. Lattice Panameters a = b = 3^* E l CE 4 The X- rays of wavelength n=2.5A ☺ The interplannar spacing for (hk, l) plane is, A = 41 The interplannan spacing for (001) Plane is dan a potom n zun The condition for observe the reflection from a crystal tot i in a is wavelength of x-nay. 2x 4 Ao > 2.5 possible. Sine Use Bragg's law adsino = ni neol, 2d sine =D Sing = = ? ambis 0 = sin(25) ∞ 1818. 2° .. Scattering angle for (601) plane is 18.2. 2.5 m 2 x 4 Ao Similarly The interplannan spacing for 100) plane is, do toto 19 = 3

a 2x 3 n° > 2.5 Ao - possible. use Bragg's law for not, for n=1, adsino =D 1. Sino = Sing = 2 2 0 = sin(2-5) = 24.6 scattering angle for (100) plane is 24. 6 interpeanan spacing for (111) pleme is - - The The (en) du hos o dont fait sätant partie ✓ 16x9 e zdou > a possible. so, n=1, 2d, sino = 7 Sino = 2 sino = 2.54 0 = sin( 3035787 41.90 ~ 42° The seattering angle fon (111) plane is 42 ou

( If the x-nay wavelength is n = 54 For (111) plane, di, = 1.87 À a adi = 2x1.87 = 3.74% so Hene, zdili in = 3.740 < 5 * So, 2dil * This condition is not satisfied so it is not possible.