12th chemistry solid state-Closed-Packed Structures

Closed-Packed Structures

Coordination number − The number of nearest neighbours of an atom

Close-Packing in One dimension

• Only one way of arrangement, i.e., the particles are arranged in a row, touching each other

• Coordination number = 2

Close-Packing in Two Dimensions

• Square close-packing in two dimensions

• AAA type arrangement

• The particles in the second row are exactly above those in the first row.
• Coordination number = 4

• Hexagonal close-packing in two dimensions

• ABAB type arrangement

• The particles in the second row are fitted in the depressions of the first row. The particles in the third row are aligned with those in the first row.
• More efficient packing than square close-packing
• Coordination number = 6

Close-Packing in Three Dimensions

Three-dimensional close-packing is obtained by stacking two-dimensional layers (square close-packed or hexagonal close-packed) one above the other.

• By stacking two-dimensional square close-packed layers

• The particles in the second layer are exactly above those in the first layer.
• AAA type pattern
• The lattice generated is simple cubic lattice, and its unit cell is primitive cubic unit cell.

• Coordination number = 6

• By stacking two-dimensional hexagonal close-packed layers

• Placing the second layer over the first layer

• The two layers are differently aligned.
• Tetrahedral void is formed when a particle in the second layer is above a void of the first layer.
• Octahedral void is formed when a void of the second layer is above the void of the first layer.

Here, T = Tetrahedral void, O = Octahedral void

Number of octahedral voids = Number of close-packed particles

Number of tetrahedral voids = 2 × Number of close-packed particles

• Placing the third layer over the second layer: There are two ways −

• Covering tetrahedral voids: ABAB … pattern. The particles in the third layer are exactly aligned with those in the first layer. It results in a hexagonal close-packed (hcp) structure. Example: Arrangement of atoms in metals like Mg and Zn

• Covering octahedral voids: ABCABC … octahedral voids. The particles in the third layer are not aligned either with those in the first layer or with those in the second layer, but with those in the fourth layer aligned with those in the first layer. This arrangement is called ‘C’ type. It results in cubic close-packed (ccp) or face-centred cubic (fcc) structure. Example: Arrangement of atoms in metals like Cu and Ag

• Coordination number in both hcp ad ccp structures is 12.
• Both hcp and ccp structures are highly efficient in packing (packing efficiency = 74%)