Is the calculation of percentage of each atom within a Body centered cubic cell AKA volume of the BCC cell same as the atomic packing factor for the BCC unit cell.
The BCC % is 68%. the atomic packing factor is just 0.68. Am I completely wrong?
And also how do i calculate the lattice constant given Fe is the atom and it's radius is 0.124nm.
I know the lattice constant is a, b, c
would a, b,c be all the same because it's a cube?
No. The bcc is 68% and the factor is, of course, 0.68.
Fe is a bcc, also, and if you know r, then 4r = a(3)2 and you can calculate a.
Here is a site that gives a,b,c and much more information about iron. a, b, and c are about 286 something pm. The volume would, of course, be a3 for the unit cell.
4r = a(3)1/2
The calculation of the percentage of each atom within a Body Centered Cubic (BCC) cell is not the same as the atomic packing factor for the BCC unit cell. The percentage of each atom within a BCC cell refers to the fraction of the total atoms that are located within the cell. In the case of BCC structure, there is one complete atom at the center of the cell along with eight partial atoms at the eight corner positions.
To calculate the percentage of each atom in the BCC cell, you can use the following formula:
Percentage of complete atom = (1/total atoms) x 100%
Percentage of partial atom = (number of partial atoms/total atoms) x 100%
However, the atomic packing factor (APF) represents the fraction of space occupied by atoms within the unit cell. APF is given by the formula:
APF = (volume of atoms in the unit cell) / (total volume of the unit cell)
For a BCC structure, there is one complete atom at the center and eight partial atoms at the corners. The volume of atoms in the unit cell is the sum of the individual atom volumes, while the total volume of the unit cell is calculated as the cube of the lattice constant.
Now, regarding the lattice constant calculation for Fe within a BCC structure, you can determine it by considering the atomic radius of Fe. In a BCC structure, the lattice constant (a, b, c) is the distance between the centers of two adjacent BCC unit cells.
Since a BCC unit cell is a cube, the lattice constant will be the same for all three directions (a = b = c). To calculate the lattice constant, you can use the formula:
Lattice constant (a) = 4 * Atomic radius of Fe
So in this case, if the atomic radius of Fe is given as 0.124 nm, you can calculate the lattice constant (a) by multiplying the atomic radius by 4.
Keep in mind that these calculations assume ideal conditions and may not account for any deviations or interactions that occur in real-world scenarios.