Solid Packing

The constituent particles in crystalline solids are arranged in a regular and repeating pattern. The crystal lattice is a diagrammatic representation of three-dimensional arrangements of constituent particles in a crystal, where each particle is represented as a point in space. The atoms in a crystal lattice are packed so closely together that there is very little space between them. As a result, the cubic form of a lattice's unit cell. There will still be some empty spaces in the cell as we stack the spheres. The arrangement of these spheres must be very effective in order to eliminate these empty spaces. To avoid empty spaces, the spheres should be placed as close together as possible.

The definition of Coordination Number is also related. In a crystal lattice structure, the coordination number is the number of atoms that surround a central atom. As a consequence, there are three directions in which the constituent particles are tightly packed. Let's take a look at each of them individually.

The following sections discuss close packing in crystals in solids in various dimensions:

Close Packing in One Dimension

Packing in one dimension involves arranging spheres in a row such that neighbouring atoms are in contact. The number of nearest neighbour particles is known as the coordination number. The coordination number is two in the case of one-dimensional close packing.

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Close Packing in Two Dimension

A row of closed packed spheres is stacked to create a two-dimensional pattern in two-dimensional close packing. There are two methods for stacking:

Square Close Packing:

In a close packing, the second row can be put exactly below the first row. As a result, if we call the first row a "A" type row, the second row, which is organized identically to the first, is also an "A" type row. Each sphere is in contact with four other spheres in this configuration. As a result, it has a four-coordination number. We note that when the centres of the four closest spheres are joined, a square is formed. In crystalline solids, this type of packing is known as square close packing in two dimensions.

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Hexagonal Close-Packing (ABAB Type Arrangement): 

The second row can be staggered below the first row, with its spheres fitting into the depressions of the first row. As a result, if we refer to the first row as an "A" type row, the second row, which is organized differently, can be referred to as a "B" type row. The third-row displays as “A” form once more. The “ABAB” sort of packing is what it's called. Each sphere is in contact with six other spheres in this configuration. As a result, it has a teamwork number of six. When the centres of the six closest neighbouring spheres are connected, a hexagon is formed. Hexagonal close packing in two dimensions is the name given to this type of solid packing. In contrast to square close packing, it has less free space and thus higher packing efficiency.

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Three Dimensional Close Packing

True lattices and structures are formed by packing three-dimensionally close together. They're created by piling two-dimensional sphere layers on top of each other. This can be accomplished in two ways:

1. Close packing in three dimensions derived from two-dimensional square close-packed layers

2. Close packing in three dimensions derived from two-dimensional hexagonal close packing layers

Three-Dimensional Close Packing from Two-Dimensional Close-Packing in Crystals: 

By putting the second square closed packing exactly above the first, three-dimensional close packing in solids can be created. The spheres are properly positioned horizontally and vertically in this tight packing. Similarly, we can make a simple cubic lattice by stacking more layers one on top of the other. The primitive cubic unit cell is the unit cell of the basic cubic lattice.

Three-dimensional Close Packing from Two-Dimensional Hexagonal Close-Packing in Crystals:

Close packing in three dimensions derived from two-dimensional hexagonal close packing layers

With the support of two-dimensional hexagonal packed layers, three-dimensional close packing can be shaped in two ways:

1. Stacking the second layer on top of the first

2. Stacking the third layer on top of the second

Stacking the Second Layer Over the First Layer

Assume that we take two hexagonal tight-packed layers ‘A' and position them over the second layer B (because the spheres in both layers are aligned differently) such that the spheres of the second layer are positioned in the depressions of the first layer. When a sphere from the second layer is positioned directly above the void (space) from the first layer, a tetrahedral void is created. We also note octahedral voids at the points where the second layer's triangular voids are placed next to the first layer's triangular voids in such a way that triangular space does not overlap. Six spheres surround the octahedral voids.

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By Stacking the Third Layer Over the Second Layer

1. By covering tetrahedral voids 

2. By covering octahedral voids

Did You Know?

The spheres of the third layer are aligned directly above the spheres of the first layer in three-dimensional packing. If we give the first layer the letter A and the second layer the letter B, the pattern would be ABAB... and so on. The resulting structure is known as a hexagonal close-packed structure, or HCP.

Spheres are not put with either the second layer or the first layer in this form of packaging. The pattern would be ABCABC if we call the first layer A, the second layer B, and the third layer C (as it is now a separate layer). The resulting structure is also known as a cubic close packed (ccp) structure or a face-centred packed cubic structure (fcc). Metals such as copper and iron, for example, crystallize in the structure. Since each sphere in the system is in direct contact with 12 other spheres, the coordination number in both cases would be 12. The packing is extremely effective, with approximately 74% of the crystal being fully occupied.