Close Packing in Two Dimensions
Two dimensional close packed structure can be generated by stacking (placing) the rows of close packed spheres.
The second row can be placed in contact with the first row in such a way that the spheres of second row are exactly above the first row.
- The spheres of the two rows are aligned horizontally as well as vertically.
- Let the first row be ‘A’ type row and the second row is also of ‘A’ type due to its similarity with the first one.
- Similarly, we may place more rows to obtain AAA type of arrangement.
- Each sphere is in contact with four of its surrounding atom. Thus, the two dimensional coordination numbers is 4.
- If the centers of these 4 immediate surrounding spheres are joined, a square is formed. Due to which this packing is known as square close packing in two dimensions.
- The second row can be placed above the first row in a staggered manner in such a way that the spheres fit in the depressions of the first row.
- Let the first row be ‘A’ type row, and the second row be ‘B’ type row.
- When the third row is placed adjacent to the second in staggered manner, its spheres are aligned with those of the first layer. Hence this layer is also of ‘A’ type.
- The spheres of similarly placed fourth row will be aligned with those of the second row (‘B’ type). Hence this arrangement is of ABAB type.
- This arrangement provides less free space and is more efficient than the square close packing.
- Each sphere in this arrangement is in contact with six of surrounding spheres and the two dimensional coordination numbers is 6.
- The centers of these six spheres are at the corners of a regular hexagon due to which this packing is also known as two dimensional hexagonal close packing.
- These are triangular in shape. In one row, the apex of the triangles is pointing upwards and in the next layer the apex of the triangles is pointing downwards.