What is Primitive unit cells
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A primitive cubic unit cell is a unit cell in which the atoms are present only at the corners of the cube. 1 / 8 is the contribution per corner atom in a cubic unit cell. In other words, each atom at the corner of the cube is shared by 8 unit cells. Hence, each atom at the corner contributes 1/8 to the unit cell. To understand how the contribution per atom is 1/8, consider the following cube
If we consider an arrangement of cubes, such that they form layers stacked one on top of the other, then we will find that in one layer of cubes, one corner is shared by three other cubes. Also this corner would be shared by four cubes in the layer of cubes above this layer. Thus there are are 4 + 4 = 8 cubes sharing one corner. As in a primitive unit cell, the atoms are placed at the corners, therefore the contribution per unit cell would be 1 / 8.
If we consider an arrangement of cubes, such that they form layers stacked one on top of the other, then we will find that in one layer of cubes, one corner is shared by three other cubes. Also this corner would be shared by four cubes in the layer of cubes above this layer. Thus there are are 4 + 4 = 8 cubes sharing one corner. As in a primitive unit cell, the atoms are placed at the corners, therefore the contribution per unit cell would be 1 / 8.
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a primary cell has particle at all the corner of unit cell
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