What is the contribution of particle at the edge centre of a particular unit cell is?

The smallest repeating unit of a crystal lattice, or the building block of the crystal, is called a unit cell. A crystal lattice is the three-dimensional arrangement of atoms, molecules, and ions inside a crystal. A crystal lattice is formed by the joining of several unit cells.

The contribution of each atom to that unit cell is determined by the number of unit cells with which it is shared. If it is present in only one unit cell, such as the body-centered atom, its contribution is 1, if it is shared by two unit cells, it contributes 12, and if it is shared by four unit cells, it provides 14.

Now consider the contributions of atoms at various lattice locations. Because atoms at the body’s center aren’t totally present in a single unit cell, their contribution will be equal to one. For atoms at the unit cell’s corners:

  • The corners of eight unit cells meet at one location when several unit cells unite to create a crystal lattice.
  • It would appear as four unit cells above it and four unit cells below it, sharing the corner in the middle.
  • As a result, one atom in the corner is shared by eight unit cells, resulting in a contribution of 18.

Each face is always shared by two unit cells for atoms at the face centres. As a result, each atom in the face’s centre will be shared by two unit cells, resulting in a contribution of 12. An edge of the cubic unit cell is always shared across four unit cells for an atom at the edge centre. As a result, one atom at the edge centre is shared by four unit cells, and its contribution to one unit cell is 14.

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