Register to reply 
Calculating the interplanar distance d111 for an FCC lattice 
Share this thread: 
#1
Feb2310, 01:02 PM

P: 14

1. The problem statement, all variables and given/known data
As a part of a lab report, I need to calculate the distance of the (111) planes of an FCC lattice made out of spheres with diameter D. 2. Relevant equations 3. The attempt at a solution The course assistant has given me the value of [LATEX]\frac{\sqrt{6}}{3}D[/LATEX]. I can understand where the [LATEX]\sqrt{6}D[/LATEX] comes from; it's the space diagonal of the cubic unit cell of the FCC lattice. But why is it divided by three? That means that there are three (111)planes in one unit cell, but I have no idea why is that. 


#2
Feb2310, 02:16 PM

Emeritus
Sci Advisor
PF Gold
P: 11,155

Your interpretation is more or less correct. The body diagonal of a single FCC unit cell intersects (or terminates at) 4 successive (111) planes, with 3 interplanar regions between them.
Perhaps this figure might help... However, to calculate the interplanar spacing for a set of planes in a cubic lattice there is a pretty straightforward formula based on the Miller Indices of the plane. If you know the definition of the Miller Indices in terms of intercepts along the crystal axes, you can derive this formula using simple geometry. 


Register to reply 
Related Discussions  
Distance between copper atoms in cubic crystal lattice  Introductory Physics Homework  2  
Interplanar spacing d using braggs law  Atomic, Solid State, Comp. Physics  3  
Q: Calculating gravitation inside a lattice  General Physics  0  
Interplanar spacing 'd'  General Physics  1  
Interplanar spacing  Introductory Physics Homework  0 