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Planar density

by asdf1
Tags: density, planar
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asdf1
#1
Oct28-06, 09:55 AM
P: 738
HOw od you calculate the planar density for {100}, {110}, {111} for FCC?
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Swapnil
#2
Oct29-06, 01:42 AM
P: 460
Lets start with [100] plane which is a plane parallel to a face of the unit cell and it looks like a square. There is one atom at the center of the square and a total of 4*1/4 atoms on the coners of the plane. Hence there are a net total of 2 atoms inside the square. Now the area is just the area of the square which is a^2 (where a is the lattice constant). So the suface density is 2/a^2 atoms per unit area.

The [110] plane is the plane which cuts the unit cell diagonally in half and it looks like a square. There are just 4*1/4 atoms on the corners of the square - a net total of 1 atom inside the square. The length of one of the sides of the plane is a*sqrt(2). Hence the surface density is 1/(a*sqrt(2)) atoms per unit area.

The [111] plane is a plane that touches the three far corners of the unit cell and it looks like a triangle. There are then a total 1/6*3 atoms that make up the vertices of the triangle and there are a total of 1/2*3 atoms that make up the three edges of the triangle. So you have a net total of 2 atoms inside the triangle. The triangle is an equlilateral triangle with a leg of length a*sqrt(2). The area of an equilateral triangle is s^2*sqrt(3)/4 which then gives us a^2*sqrt(3)/2 as the area of that trinagle. Hence the density is 2/(a^2*sqrt(3)/2) atoms per unit area.
asdf1
#3
Oct29-06, 08:59 AM
P: 738
^_^
Thank you very much for explaning that very clearly!!!

rrc83
#4
Jun4-08, 03:05 PM
P: 1
Planar density

how do you find the planar density for the (2 0 0) FCC unit cell
Defennder
#5
Jun4-08, 10:37 PM
HW Helper
P: 2,616
First of all, can you picture the (200) plane in the FCC unit cell? Secondly, across how many atoms does it cut?
davidalbertos
#6
Jan24-10, 09:25 PM
P: 1
Just in case, in Si diamond structure, the plane (110) includes a total of 4 atoms, which increases the density to 9.6*10^(14).
nour halawani
#7
Dec25-11, 07:49 AM
P: 5
I need to know the number at surface atoms in a cube of a FCC lattice of gold atoms knowing that R= 144.2 pm with respect to L( length of the cube) and a ( length of a unit cell )


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