In solids, particles are arranged as closely as possible to minimize empty space and maximize packing efficiency. The arrangement of these particles, often represented as spheres, is known as close packing. This concept is vital in understanding the structural arrangement of atoms in crystals.
Two-dimensional close-packed structures can be generated by arranging particles in two different ways: square close packing and hexagonal close packing.
In square close packing, particles are arranged in a grid where each particle touches four other particles, forming a square arrangement. The coordination number in this structure is 4, meaning each particle has four immediate neighbors.
In hexagonal close packing, the second row of spheres is placed in the depressions of the first row in a staggered manner. This arrangement allows each sphere to be in contact with six neighbors, giving a coordination number of 6.
Did You Know?
In a two-dimensional hexagonal arrangement, each particle is surrounded by six others. This type of packing is common in nature, such as in honeycombs.
Common Misconception:
Some students confuse the number of layers with the coordination number. Remember, the coordination number indicates how many immediate neighbors a particle has, not the number of layers.
Real-world crystal structures are three-dimensional, which can be achieved by stacking two-dimensional layers of close-packed particles.
When square close-packed layers are stacked on top of one another, the particles in the second layer are directly above the first layer. This arrangement leads to a simple cubic lattice, where each particle is surrounded by six others, with a coordination number of 6. This type of lattice is inefficient in packing.
Three-dimensional close packing can be achieved by stacking hexagonal close-packed layers in different manners. There are two major types:
In the hcp structure, the third layer is placed directly above the first, creating an ABAB... pattern. This arrangement leads to an efficient packing with a coordination number of 12, meaning each sphere touches 12 others.
The ccp structure is formed by placing the third layer above the second in a way that its spheres cover the octahedral voids of the second layer. This results in an ABCABC... pattern. The ccp structure also has a coordination number of 12 and occupies 74% of the space, similar to hcp.
NEET Tip:
Both hcp and ccp structures are common in questions related to coordination numbers and packing efficiency. Always remember that both have a coordination number of 12 and occupy 74% of the space.
Real-Life Application:
The structural efficiency of hcp and ccp packing is used in various engineering materials to optimize strength and durability, such as in alloys for aircraft construction.
When particles are close-packed, they leave empty spaces known as voids. There are two types of voids in these structures:
Tetrahedral voids occur when three particles from one layer and one particle from the adjacent layer form a tetrahedron. For every particle in a close-packed structure, there are two tetrahedral voids.
Octahedral voids occur when two sets of three particles from adjacent layers form an octahedron. There is one octahedral void for every particle in the structure.
Did You Know?
In ionic solids, smaller cations like Na⁺ in NaCl occupy octahedral voids within the larger close-packed anions (Cl⁻), explaining the structure of many ionic compounds.
Packing efficiency refers to the percentage of space occupied by particles in a structure. For different close-packed structures, the efficiency is:
In a cubic close-packed structure, each unit cell contains 4 atoms. The packing efficiency can be calculated using the formula:
The packing efficiency is then calculated as:
Volume of the unit cellVolume of spheres×100%=74%