2. Crystal Structure

BCC {110) and {200}sin 2 θ A h 2 A + k 2 A + l 2 A——— = ——————— = 0. 5sin 2 θ Β h 2 B + k 2 B + l 2 Bex. an element that has either BCC or FCCstructure shows diffraction peaks atfollowing 2θ angles: 40, 58, 73, 86.8, 100.4and 114.7. wavelength of x-ray λ = 0.154a. BCC or FCC?b. determine the lattice constant a.c. identify the element.(a) 2θ θ sinθ sin 2 θ40 20 0.3420 0.117058 29 0.4848 0.235073 36.5 0.5948 0.353886.8 43.4 0.6871 0.4721100.4 50.2 0.7683 0.5903first and second angles0.1170/0.3420 = 0.5 BCC structure(b) λ √h 2 + k 2 + l 2 0.154 √2a = — —————— = ——— ———2 sinθ 2 0.342= 0.318 nm(c) W23