Question

The plots below represent X-ray diffraction data of intensity vs. angle. Use the wavelength and peak position information in the Figure to determine the lattice spacing of the materials investigated. Rank the lattice spacing of the materials measured in plots A-F, breaking ties alphabetically. (A) 2 = 2 nm (D) 1= 4 nm 12.5° 12.5° 25° 25° -20 -10 30 -30 -20 -10 0 10 20 30 (B) 2= 4 nm (E) 2= 3 nm 8.35° 8.35° m 16.7° m 16.7° n -30 -20 -10 10 20 -20 -10 10 20 30 (C)2 = 3 nm (F) 2= 2 nm 6.3° 6.3° 12.6° 12.6° -30 -20 - 10 10 20 30 -20 -10

Answer 1

If d is the lattice spacing,

using Brag's equation,

for first maxima, 2*d*sin(theta) = lamda

d = lamda/(2*sin(theta)

A) d = 2*10^-9/(2*sin(12.5))

= 4.62*10^-9 m

B) d = 4*10^-9/(2*sin(8.35))

= 1.38*10^-8 m

C) d = 3*10^-9/(2*sin(6.3))

= 1.37*10^-8 m

D) d = 4*10^-9/(2*sin(12.5))

= 9.24*10^-9 m

E) d = 3*10^-9/(2*sin(8.35))

= 1.03*10^-8 m

F) d = 2*10^-9/(2*sin(6.3))

= 9.11*10^-9 m

Ranking from lowest to highet value of lattice spacing.

A < F < D < E < C < B