Body Centered Cubic Unit Cell - Online Tutor, Practice Problems & Exam Prep

The body-centered cubic (BCC) unit cell is a fundamental structure in crystallography, featuring a cube with one atom at each of its eight corners and a single atom at the center. This arrangement results in a total of two atoms per unit cell. The corner atoms are shared with adjacent cells, each contributing 1/8 to the unit cell, while the central atom is not shared. The edge length (a) of a BCC unit cell is calculated using the formula:

$a=\frac{4r}{\sqrt{3}}$

where r is the atomic radius. The BCC structure has a packing efficiency of 68% and a coordination number of 8, indicating each atom is surrounded by eight nearest neighbors. These characteristics are crucial for understanding the properties of materials with a BCC lattice structure.

Body Centered Cubic Unit Cell Concept 1

The body center cubic unit cell is composed of a cube with an atom at each corner and one atom in the center. So we would say that when it comes to a bodysuit or cubic unit cell, we have a total of 2 atoms involved. And remember one of those atoms is found in the center of our structure.

Now remember each one of these red spheres? It is shared by other unit cells around. So each one of these only accounts for 1/8 of an atom. And if you took them all into consideration, 1/8 * 8 corners gives us 1 atom here. And then we have this one atom in the very center. So that's how we come up with two total atoms for body centered cubic unit cell.

Now we can say here that when it comes to a simple cubic unit cell, we knew that the MDA or edge link was equal to two R. That's because the atoms touched one another. But when it comes to a body centered cubic in itself, there's a small little gap here. As a result of this small gap, that means our edge link now changes. Our edge link now is equal to four times your radius divided by 3. So a here equals 43r.

Now as we become more and more complex, our packing efficiency will increase. Here for body centered cubic unit cell it becomes now 68% and as we become more complex our coordination number also increases. Here for body centered cubic unit cell it now becomes the value of eight. So when dealing with a body centered cubic unit cell, remember these key ideas and key values for any one of them.

Body Centered Cubic Unit Cell Example 1

Iron adopts a body centered cubic unit cell illustrate how the number of atoms per unit cell for the ion atom are obtained. So remember for any cubic unit saw we have 18 atom for every corner and that shared between 8 atoms. So for all of them it's one atom right off the bat.

But remember for a body center cubic unit cell, we also have an additional atom within the center of our cube. So we add that in. So taking those both into consideration, that's how we come up with two atoms per one unit cell for a body centered cubic unit cell.

Tungsten possesses a body-centered cubic structure. If its density is 19.28 g/cm3, what is its radius in pm?

• A. 910 pm
• B. 316 pm
• C. 137 pm
• D. 3.18 pm

Vanadium has a body-centered cubic structure. If the atomic radius of vanadium is 134 pm, calculate the density of solid vanadium.

• A. 5.33 g/cm3
• B. 4.29 g/cm3
• C. 5.71 g/cm3
• D. 0.52 g/cm3

The edge of a body-centered cubic unit cell of an element Z was found to be 2.88 x 10-8 cm. The density of the element is 7.2 g/cm3. What is the approximate molar mass of Z?

• A. 101.7 g•mol-1
• B. 39.107 g•mol-1
• C. 10.291 g•mol-1
• D. 51.996 g•mol-1
  

Here’s what students ask on this topic:

How many identical atoms are in a body-centered (bcc) cubic unit cell?

In a body-centered cubic (bcc) unit cell, there are two atoms in total. Here's how it breaks down: At each corner of the cube, there's a fraction of an atom that belongs to the unit cell since each corner atom is shared with eight other unit cells. Since there are eight corners, you have:

8 × ¹⁄₈ = 1 atom from the corners.

Additionally, there is one full atom at the very center of the cube, which is not shared with any other unit cell. When you add the one atom from the corners to the one atom in the center, you get a total of 2 atoms in a body-centered cubic unit cell.