Doc: Number of Atoms in a Unit Cell Notes | EduRev

Chemistry Class 12

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Class 12 : Doc: Number of Atoms in a Unit Cell Notes | EduRev

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Introduction to Number of Atoms in a Unit Cell
That a crystal lattice comprises of several unit cells. In a unit cell, every constituent particle( atom, molecule or ion ) has a specific and fixed position called lattice site. We can calculate a number of atoms/molecules and ions in a unit cell easily by analyzing the nature and position of constituent particles in unit cells.

Doc: Number of Atoms in a Unit Cell Notes | EduRev

Image 1: Types of Unit Cell

(a) Primitive Cubic Unit Cell
In the primitive cubic unit cell, the atoms are only located on the corners. That means 8 atoms are located on 8 corners of the lattice. Each atom located on the corner contributes 1/8th of the original volume of the cell. So since there are total 8 atoms in a primitive cubic
unit cell, the total number of atoms in the primitive cubic unit cell.
Doc: Number of Atoms in a Unit Cell Notes | EduRev 
So there is only 1 atom in a primitive cubic unit cell.

Doc: Number of Atoms in a Unit Cell  Notes | EduRev

Image 2: The corners get only 1/8th part of atom

(b) Body- centred Cubic Unit Cell
In a body-centred unit cell, 8 atoms are located on the 8 corners and 1 atom is present at the center of the structure. So total atoms in the body-centred unit cell will be:
Since 8 atoms are present at the corners, each will contribute 1/8th of the original volume of the cell. Thus in the body-centred cubic unit cell:
  • There are 8 corners and 1 corner shares 1/8th volume of the entire cell, so
    Doc: Number of Atoms in a Unit Cell  Notes | EduRev
  • Also, the atom at the centre is wholly present at the centre of the cell and can’t be shared
    1 × 1 = 1 atom
    So there are total 2 atoms present in a body centred unit cell.

Doc: Number of Atoms in a Unit Cell  Notes | EduRev

Image 3: Atoms in body-centrd unit cell

(c) Face-centred Cubic Unit Cell
In face-centred cubic unit cell atoms are present on 8 corners and center of all the faces. Also, each atom located on the centre of the unit cell is shared by two adjacent unit cells. Therefore only half atom belongs to a single unit cell.
Thus in Face-centred cubic unit cell
• There are 8 atoms present on 8 corners, therefore, each corner will get 1/8 part of atom
Doc: Number of Atoms in a Unit Cell  Notes | EduRev
• There are six faces and each face gets 1/2 part of atom then

Doc: Number of Atoms in a Unit Cell  Notes | EduRev
Total atoms present in a face-centred unit cell = 1 + 3 = 4 atoms

(d) End-centred Cubic Unit Cell
In end-centred cubic unit cell, 8 atoms are located on 8 corners of the cube and 1 atom each is present on two opposite faces of the cube.
Therefore in end-centred cubic unit cell

  • There are 8 atoms present on 8 corners, therefore each atom contributes 1/8th portion of the cell
    Doc: Number of Atoms in a Unit Cell  Notes | EduRev
  • There are 2 atoms located  at the center of the cell and each atom contributes 1/2 portion of the cell
    Doc: Number of Atoms in a Unit Cell  Notes | EduRev
    Total atoms present in a end-centred cubic unit cell = 1 + 1 = 2 atoms

Doc: Number of Atoms in a Unit Cell  Notes | EduRev

Image 4: Contribution of Atom in different unit cells

The table given below summarizes a total number of atoms present in a unit cell.
Doc: Number of Atoms in a Unit Cell  Notes | EduRev

Doc: Number of Atoms in a Unit Cell  Notes | EduRev

Image 5: Types of unit cells

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