Calculation of nearest neighbours up to 6th coordination number for an atom located at body centre in CCP structure

Body-centred cubic (BCC) or cubic close-packed (CCP) structures are commonly found in metals. In a CCP structure of compound XY, X atoms are present at octahedral voids. Let's calculate the number of nearest neighbours up to 6th coordination number for an atom located at the body centre.

1. Calculation of the number of nearest neighbours up to 1st coordination number

The atom located at the body centre is surrounded by 8 atoms in the first coordination shell. These 8 atoms are present at the corners of the cube.

2. Calculation of the number of nearest neighbours up to 2nd coordination number

The atoms present at the corners of the cube are surrounded by 6 atoms in the second coordination shell. These 6 atoms are present at the faces of the cube. Therefore, the atom located at the body centre is indirectly surrounded by 6 atoms in the second coordination shell.

3. Calculation of the number of nearest neighbours up to 3rd coordination number

The atoms present at the faces of the cube are surrounded by 12 atoms in the third coordination shell. These 12 atoms are present at the corners of the adjacent cubes. Therefore, the atom located at the body centre is indirectly surrounded by 12 atoms in the third coordination shell.

4. Calculation of the number of nearest neighbours up to 4th coordination number

The atoms present at the corners of the adjacent cubes are surrounded by 6 atoms in the fourth coordination shell. These 6 atoms are present at the faces of the adjacent cubes. Therefore, the atom located at the body centre is indirectly surrounded by 6 atoms in the fourth coordination shell.

5. Calculation of the number of nearest neighbours up to 5th coordination number

The atoms present at the faces of the adjacent cubes are surrounded by 24 atoms in the fifth coordination shell. These 24 atoms are present at the corners of the adjacent cubes. Therefore, the atom located at the body centre is indirectly surrounded by 24 atoms in the fifth coordination shell.

6. Calculation of the number of nearest neighbours up to 6th coordination number

The atoms present at the corners of the adjacent cubes are surrounded by 12 atoms in the sixth coordination shell. These 12 atoms are present at the faces of the adjacent cubes. Therefore, the atom located at the body centre is indirectly surrounded by 12 atoms in the sixth coordination shell.

Therefore, the total number of nearest neighbours up to 6th coordination number for an atom located at the body centre in CCP structure is:

8 + 6 + 12 + 6 + 24 + 12 = 68

Conclusion

The number of nearest neighbours up to 6th coordination number for an atom located at the body centre in CCP structure is 68.