How does an FCC structure have a coordination number of 12?

Thread starter anonymous99
Start date Oct 2, 2020
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Fcc Structure

In summary, an FCC (Face-Centered Cubic) structure is a common crystal structure found in many metals and alloys, with a unit cell that is a cube with atoms located at each corner and in the center of each face. It differs from other crystal structures in that it has a coordination number of 12, which allows for maximum packing efficiency and stability. This coordination number is determined by counting the number of nearest neighbors each atom has, and it has practical implications such as strong bonding between atoms and resistance to deformation, making FCC materials suitable for use in various applications such as construction and aerospace.

Oct 2, 2020

anonymous99

Homework Statement: I understand if we take the face atom, there's 4 atoms in the same plane and 4 behind and 4 in front to give 12 but when I try to do the same for the corner atom, I can see it's touching the face atom and 2 other corner atoms in the same cell. Since corner atoms are shared by 8 squares, shouldn't this sum to 24?

Relevant Equations: Picture is attached to show what I mean. Look at the bottom left corner of the grey square in the unit cell on the left. It has 12 neighbours from the plane it lies on, 3 more from the grey square and 9 more from the 3 omitted squares. What mistake am I making?

Edit: nevermind, I realized my mistake. Corner atoms don't touch in FCC, so there's just 4 neighbours in each plane which sums to 12.

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Oct 2, 2020

lippyka

A:FCC has 12 nearest neighbors.The number of neighbors is related to the coordination number, which for FCC is 12.

Related to How does an FCC structure have a coordination number of 12?

1. How is the coordination number of 12 determined in an FCC structure?

In an FCC (face-centered cubic) structure, each atom is surrounded by 12 nearest neighbors. This is because each atom is in contact with 6 atoms in its own layer, as well as 3 atoms above and 3 atoms below in the layers above and below. This results in a coordination number of 12.

2. How does the coordination number affect the stability of an FCC structure?

The coordination number of 12 in an FCC structure is a result of the efficient packing of atoms, which leads to a high degree of structural stability. This allows for strong interatomic bonding and makes FCC structures commonly found in metals and alloys.

3. Can the coordination number of an FCC structure be changed?

No, the coordination number of an FCC structure is a characteristic of the crystal structure and cannot be altered without changing the entire structure. However, other crystal structures, such as BCC (body-centered cubic) or HCP (hexagonal close-packed), have different coordination numbers.

4. What is the relationship between coordination number and atomic radius in an FCC structure?

The coordination number in an FCC structure is directly related to the atomic radius of the atoms. The larger the atomic radius, the larger the coordination number will be, as there is more space for neighboring atoms to pack around it. This is why FCC structures are commonly found in metals with larger atomic radii.

5. How does the coordination number affect the physical properties of an FCC structure?

The coordination number in an FCC structure plays a significant role in determining the physical properties of the material. The high coordination number of 12 results in a close-packed structure, leading to high density, high strength, and good ductility. These properties make FCC structures useful in various applications, such as in the construction of buildings and bridges.