Unit Cell - Linear Density - BCC & FCC

[General_Sax]

Unit Cell -- Linear Density -- BCC&FCC

Homework Statement

Calculate the linear density for the most densely packed directions in BCC and FCC. Note the difference in linear density. Note the difference in linear density.

Homework Equations

LD = #of atoms/length

The Attempt at a Solution

I arrive at an answer, however my answers for BCC and FCC are the same. I chose vector [110] for the BCC and got this for the LD equation: LD = 2/4R

For FCC I chose vector [101] ... LD = 2/4R

I was hoping someone could see my error.

 

[Astronuc]

One should find diagrams and discussion in W.D. Callister, Materials Science and Engineering, An Introduction, 7th Ed., John Wiley and Sons, 2007, or later editions.

In BCC, the close-packed planes are the {110} planes, and the close-packed directions are the <111>
In FCC, the close-packed planes are the {111} planes, and the close-packed directions are the <110> direction
Ref: http://monoceros.physics.muni.cz/~j...xty/Krystaly/CrystalStructures&Properties.pdf

Other notes
https://faculty.ksu.edu.sa/sites/default/files/chapter3.pdf

https://chem.libretexts.org/Bookshe...iquids/7.08:_Cubic_Lattices_and_Close_Packing

Problems with planar densities of fcc and bcc are found in this assignment.
http://maecourses.ucsd.edu/~jmckittr/mae20-wi11//Assignment 4 solutions.pdf