How to calculate the lattice sums of BCC?

In summary, the conversation is about calculating the lattice sums A12 and A6 for a BCC structure. The person has already calculated A12 and is asking for help to check for any mistakes and confirm the values of the nearest neighbors. They also mention the distance for the second nearest neighbors and the coefficient for the second term in the calculation of A12.
  • #1
ilovecubes
1
0
How do I calculate the lattice sums A12 and A6 for a BCC structure?

I have calculated the following so far:

A12 = 8(1/1)^12 + 6(1/root2)^12 + 12(1/2)^12 + 16(1/root5.5)^12 + 8(1/root6)^12 = 8.097.

Have i made any mistakes? Are my nearest neighbour values correct? Please help! o:)
 
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  • #2
ilovecubes said:
How do I calculate the lattice sums A12 and A6 for a BCC structure?

I have calculated the following so far:

A12 = 8(1/1)^12 + 6(1/root2)^12 + 12(1/2)^12 + 16(1/root5.5)^12 + 8(1/root6)^12 = 8.097.

Have i made any mistakes? Are my nearest neighbour values correct? Please help! o:)

Second nearest neighbors distance is a (lattice constant).
First n.n. distance is a*sqrt(3)/2 (half body diagonal)
So the coefficient in the second term should be (sqrt(3)/2)^12.
 

Related to How to calculate the lattice sums of BCC?

1. How do you determine the lattice constant for BCC structure?

The lattice constant for BCC (Body-Centered Cubic) structure can be calculated by using the following formula: a = 4r/√3, where a is the lattice constant and r is the atomic radius of the BCC unit cell.

2. What is the formula for calculating the lattice sums of BCC?

The formula for calculating the lattice sums of BCC is given by: Σ = 8πn/(V*λ^3), where Σ is the lattice sum, n is the number of unit cells, V is the volume of the unit cell, and λ is the Debye wavelength.

3. How do you determine the number of unit cells in a BCC crystal?

The number of unit cells in a BCC crystal can be determined by using the formula: N = (8*Na)/a^3, where N is the number of unit cells, Na is Avogadro's number, and a is the lattice constant.

4. What is the significance of calculating lattice sums for BCC?

Calculating lattice sums for BCC is important for understanding the behavior of atoms in a crystal lattice. It can also provide information about the electronic, thermal, and mechanical properties of materials.

5. How do you account for defects in the lattice sums of BCC?

Defects in the lattice structure of BCC can be accounted for by using the formula: Σ = Σ0*(1-ρ/ρ0), where Σ0 is the ideal lattice sum, ρ is the concentration of defects, and ρ0 is the concentration of defects in an ideal crystal.

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