Question

Simple Cubic (SC) Structure 1. Write the Miller indices for the family of close-packed directions in the SC crystal. <hkl>= 2. Write the expression for theoretical density of a material with SC structure in terms of atomic radius (R), atomic weight (A), and Avogadro's number (NA). (Show your work.) 3. Calculate the planar density for the most densely packed SC planes in terms of atomic radius (R). (Show your work.) PD Body-Centered Cubic (BCC) Structure 4. How many non-parallel close-packed directions exist in the BCC crystal? Write the Miller indices for this family of close-packed directions. # non-parallel close-packed directions <hk> 5. Write the expression for theoretical density of a material with BCC structure in terms of atomic radius (R), atomic weight (A), and Avogadro's number (NA). (Show your work.) 6. Write the Miller indices for the family of close-packed planes in the BCC crystal. {hkl)

Answer 1

<hki) =<100) 1 х М density a3XNA acer ZxM z=1 = (20) PxNA Z x M 8r² NA IxM lo = 8y3 XNA no.of. atoms. 3 PD = planar density Area of plane (x4) ar d = 1515 (2x) LI, - Ppeloos- uro 2 8- corners non-paralell close-packed directions =8 Chal) cilly

© ur=3a as Z XM Z=2 atoms 3 density a3XNA ur 64r3 a = 313 a = 12.32 g3 2 x M da 12.32r3 XNA 0.16248 r²XNA {hxr} = {ua Gfaces x2 = 12 independent close packed direction. &110) 12) 2010) d = 8 - Exam a3 XNA aa Vzo a² ar on a²=162r u XM 3 に 1652 r²XNA - 0.197-3 XN A {1}