Coordination Number Of Bcc

The coordination number in the bcc lattice structure is 8. Explanation: BCC is known as a body-centered cubic (bcc) and has a coordination number of 8. There are 2 atoms per unit cell present in this pattern. The simple cubic has a coordination number of 6 and contains 1 atom per unit cell. Every single atom is connected to 8 other atoms at the. With more than 80 years of service and 8 million members across Illinois, you can trust Blue Cross and Blue Shield. Our Medicaid plan offers a comprehensive benefit package including medical, prescription, vision and dental services. It is said to have a coordination number of 8. The bcc unit cell consists of a net total of two atoms; one in the center and eight eighths from corners atoms as shown in the middle image below (middle image below). The image below highlights a unit cell in a larger section of the lattice.

  1. Coordination Number Of Ccp
  2. Coordination Number Of Bcc Crystal Lattice
Volume of bcc unit cell

Key Difference – BCC vs FCC

The terms BCC and FCC are used to name two different arrangements of crystalline structures. BCC stands for body-centred cubic structure whereas FCC stands for face-centred cubic structure. These are forms of cubic lattices. Therefore, these arrangements have spheres (atoms, molecule or ions from which the lattice is made of) arranged in cubic structures. The unit cell of BCC has spheres in the corners of a cube and one sphere in the centre of the cube. Since there are eight corners in a cube, the total number of spheres present in a BCC unit cell is 9. The unit cell of the FCC has spheres in each corner of a cube and also in the centre of each cubic face. Then the unit cell of FCC has 12 spheres. The key difference between BCC and FCC is that the coordination number of BCC is 8 whereas the coordination number of FCC is 12.

CONTENTS

1. Overview and Key Difference
2. What is BCC
3. What is FCC
4. Similarities Between BCC and FCC
5. Side by Side Comparison – BCC vs FCC in Tabular Form
6. Summary

What is BCC?

The term BCC stands for the body-centred cubic arrangement of spheres (atoms, molecule or ions from which the lattice is made of). In this arrangement, the spheres are located in each corner of a cube and one sphere in the middle of the cube. A unit cell of a lattice is the smallest unit that resembles the whole structure of the lattice. Since a cube has 8 corners, there is a total of 9 spheres in a BCC structure (eight in the corners plus on in the middle).

However, each sphere in the corner of the unit cell of BCC is a member of the neighbouring unit cell. That is because the lattice is made of many unit cells packed together. Since there are 8 spheres in a unit cell which are the corners of other unit cells, the coordination number of the BCC structure is known to be 8. Then, when considered the net total of spheres in a BCC unit cell, it has 2 spheres because one corner has 1/8th of spheres. The eight corners together form one sphere, and there is one sphere in the middle, together with results in two spheres.

The packing of spheres in BCC arrangement is not tight. That means the packing of spheres in BCC is not a close packing as in FCC (face-centred cubic) or HCP (hexagonal close packing). The packing factor of BCC is 0.68. Packing factor is the volume of spheres per the volume of the unit cell. Examples of metals that have the BCC structure include Lithium (Li), Sodium (Na), Potassium (K), Chromium (Cr) and Barium (Ba).

What is FCC?

The term FCC stands for the face-centered cubic arrangement of spheres. In this arrangement, the spheres are located in each corner of a cube (unit cell) and in the centres of each cubic face. Here also, each sphere in the corners is a member of the neighbouring unit cell. Apart from that, each sphere in the centre of the cubic face is shared with the adjacent unit cell.

The coordination number of FCC is 12. That is because there are 12 spheres per unit cell that are shared with other unit cells. The net total of spheres present in FCC unit cell is 4. It can be calculated as follows.

Total spheres in corners = (1/8) x 8 = 1

Total spheres in cubic faces = (1/2) x 6 = 3

Then the total spheres per unit cell = 1 + 3 = 4

The FCC structure has more packing of spheres than that of BCC (the spheres pack closer together). The packing factor of FCC structure is 0.74. This means the ratio between the volume occupied by spheres and the total volume of the unit cell is 0.74. Some examples of the metals having FCC structure are Aluminum (Al), Copper (Cu), Gold (Au), Lead (Pb) and Nickel (Ni).

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What are the Similarities Between BCC and FCC?

  • Both BCC and FCC are forms of arrangement of cubic lattices.
  • The unit cell of both BCC and FCC structures is a cube.

What is the Difference Between BCC and FCC?

BCC vs FCC

The term BCC stands for the body-centered cubic arrangement of spheres (atoms, molecule or ions from which the lattice is made of).The term FCC stands for the face-centred cubic arrangement of spheres.
Arrangement of Spheres
BCC has spheres in the eight corners of a cube and one sphere in the centre of the cube.FCC has spheres in the eight corners of a cube and also in the centres of the cubic faces.
Coordination Number
The coordination number of the BCC structure is 8.The coordination number of the FCC structure is 12.
Packing Factor
The packing factor of BCC is 0.68The packing factor of FCC is 0.74
Number of Spheres in a Unit Cell
A unit cell of BCC has a net total of 2 spheres.A unit cell of FCC has a net total of 4 spheres.
Examples
Some examples of metals that have the BCC structure include Lithium (Li), Sodium (Na), Potassium (K), Chromium (Cr) and Barium (Ba).Some examples of the metals having FCC structure are Aluminum (Al), Copper (Cu), Gold (Au), Lead (Pb) and Nickel (Ni).

Summary – BCC vs FCC

BCC stands for the body-centred cubic arrangement. FCC stands for the face-centred cubic arrangement. These arrangements are used to describe the location of atoms, molecules or ions and the empty spaces present in a lattice structure. The difference between BCC and FCC is that the coordination number of BCC is 8 whereas the coordination number of FCC is 12.

Reference:

1.Primary Metallic Crystalline Structures. Available here
2.“FCC and BCC.” BINDT. Available here

Image Courtesy:

1.’CCC crystal cell (opaque)’By Daniele Pugliesi (CC BY-SA 3.0) via Commons Wikimedia
2.’FCC crystal structure’By User:ARTE – Own work, (Public Domain) via Commons Wikimedia

Related posts:

The term 'closest packed structures' refers to the most tightly packed or space-efficient composition of crystal structures (lattices). Imagine an atom in a crystal lattice as a sphere. While cubes may easily be stacked to fill up all empty space, unfilled space will always exist in the packing of spheres. To maximize the efficiency of packing and minimize the volume of unfilled space, the spheres must be arranged as close as possible to each other. These arrangements are called closest packed structures.

The packing of spheres can describe the solid structures of crystals. In a crystal structure, the centers of atoms, ions, or molecules lie on the lattice points. Atoms are assumed to be spherical to explain the bonding and structures of metallic crystals. These spherical particles can be packed into different arrangements. In closest packed structures, the arrangement of the spheres are densely packed in order to take up the greatest amount of space possible.

Types of Holes From Close-Packing of Spheres

When a single layer of spheres is arranged into the shape of a hexagon, gaps are left uncovered. The hole formed between three spheres is called a trigonal hole because it resembles a triangle. In the example below, two out of the the six trigonal holes have been highlighted green.

Once the first layer of spheres is laid down, a second layer may be placed on top of it. The second layer of spheres may be placed to cover the trigonal holes from the first layer. Holes now exist between the first layer (the orange spheres) and the second (the lime spheres), but this time the holes are different. The triangular-shaped hole created over a orange sphere from the first layer is known as a tetrahedral hole. A hole from the second layer that also falls directly over a hole in the first layer is called an octahedral hole.

Closest Pack Crystal Structures

Hexagonal Closest Packed (HCP)

Coordination Number Of Ccp

In a hexagonal closest packed structure, the third layer has the same arrangement of spheres as the first layer and covers all the tetrahedral holes. Since the structure repeats itself after every two layers, the stacking for hcp may be described as 'a-b-a-b-a-b.' The atoms in a hexagonal closest packed structure efficiently occupy 74% of space while 26% is empty space.

Cubic Closest Packed (CCP)

The arrangement in a cubic closest packing also efficiently fills up 74% of space. Similar to hexagonal closest packing, the second layer of spheres is placed on to of half of the depressions of the first layer. The third layer is completely different than that first two layers and is stacked in the depressions of the second layer, thus covering all of the octahedral holes. The spheres in the third layer are not in line with those in layer A, and the structure does not repeat until a fourth layer is added. The fourth layer is the same as the first layer, so the arrangement of layers is 'a-b-c-a-b-c.'

Coordination Number and Number of Atoms Per Unit Cell

A unit cell is the smallest representation of an entire crystal. All crystal lattices are built of repeating unit cells. In a unit cell, an atom's coordination number is the number of atoms it is touching.

  • The hexagonal closest packed (hcp) has a coordination number of 12 and contains 6 atoms per unit cell.
  • The face-centered cubic (fcc) has a coordination number of 12 and contains 4 atoms per unit cell.
  • The body-centered cubic (bcc) has a coordination number of 8 and contains 2 atoms per unit cell.
  • The simple cubic has a coordination number of 6 and contains 1 atom per unit cell.
Unit CellCoordination Number# of Atoms Per Unit Cell% space

Simple Unit Cell

6

152%

Body-Centered Cubic

8268%

Face-centered Cubic

12474.04%

Cubic Closest Packed

12474.04%

Hexagonal Closest Packed

126* (2) see note below74.04%

Note

*For the hexagonal close-packed structure the derivation is similar. Here the unit cell consist of three primitive unit cells is a hexagonal prism containing six atoms (if the particles in the crystal are atoms). Indeed, three are the atoms in the middle layer (inside the prism); in addition, for the top and bottom layers (on the bases of the prism), the central atom is shared with the adjacent cell, and each of the six atoms at the vertices is shared with other five adjacent cells. So the total number of atoms in the cell is 3 + (1/2)×2 + (1/6)×6×2 = 6, however this results in 2 per primitive unit cell.

References

  1. Conway, J. H. and Sloane, N. J. A. Sphere Packings, Lattices, and Groups, 2nd ed. New York: Springer-Verlag, 1993.
  2. Krishna, P. and Verma, A. R. Closed Packed Structures, Chester, UK: International Union of Crystallography, 1981.
  3. Petrucci, Ralph H., William S. Harwood, F. Geoffrey Herring, and Jeffry D. Madura. 'Crystal Structures' General Chemistry: Principles & Modern Applications, ninth Edition. New Jersey: Pearson Education, Inc., 2007. 501-508.

Contributors and Attributions

Coordination Number Of Bcc Crystal Lattice

  • Brittanie Harbick, Laura Suh, Jenny Fong