Types of Packing in Solids

A crystal lattice is a diagrammatic depiction of the three-dimensional groupings of component particles in a crystal, in which each particle is portrayed as a point in space. This representation is known as a representation of a crystal in three dimensions. The atoms that make up a crystal lattice are packed extremely densely, which results in very little space being left between them. The following topics will be explored about close packing in solids in three dimensions:

Tight Packing of Solids Across All Three Dimensions

The development of three-dimensional tight packing from square close-packed layers in two dimensions:

In this particular form of tight solid packing, the second layer is stacked on top of the first layer in such a manner that the spheres that make up the higher layer are precisely positioned above those that make up the lower layer. That is to say, the spheres that make up both layers are exactly aligned in both the horizontal and the vertical planes. Since the spheres in all of the levels have the same arrangement, the lattice can be seen to follow a pattern denoted by the letters A, B, C, etc., so let’s call the arrangement of the spheres in the first layer the “A” type. This particular type of lattice is most commonly referred to as a simple cubic lattice.

Close packing in three dimensions derived from close packing in two dimensions of hexagonal layers:

Creating a three-dimensional structure that is densely packed can be accomplished by stacking layers one on top of the other.

Putting the second layer on top of the first layer: This type of tight packing involves placing a second layer that is comparable to the layer below it on top of the first layer in such a manner that the spheres of the second layer are positioned in the depressions of the first layer. Because the spheres in the first layer and the second layer are not aligned in the same way, the first layer may be referred to as “A,” and the second layer can be referred to as “B.” It has come to our attention that a tetrahedral void is created every time a sphere from the second layer is placed on top of the vacuum from the first layer (or vice versa). Whereas at other locations, we see that the triangular voids in the second layer are located above the triangular voids in the first layer, which causes the triangular forms of these to not overlap with one another. These kind of voids are referred to as octahedral voids, and they are encircled by six spheres.

We are able to determine with relative ease the total number of these two categories of vacancies. Let’s say the number of spheres crammed together is N. In that case:

N is equal to the number of octahedral voids that are produced.

The formula for calculating the number of tetrahedral voids created is 2N.

Because each sphere is in communication with twelve other spheres, each of them have the same coordination number of 12.

In this manner of tight packing, 74% of the available space within the crystal has been occupied.

The Basics of Solid Packing Principles

1. In a crystal, each individual particle—whether it be ions, atoms, or molecules—is connected to a lattice point through a lattice point pair.
2. To achieve the most densely packed and tightly closed structure possible, the component particles do all in their power to be jammed up against one another.
3. The packing is done in such a way that the amount of space that is not occupied by component atoms, molecules, or ions is kept to a minimum.
4. Due to the configuration of these crystals, the highest potential crystal density has been achieved.
5. Crystals are more stable when their packing is more dense.

Voids

In the instance of a crystal lattice that was generated by a simple cubic unit cell, the amount of space that is occupied by component particles is around 52.4 percent, and the term “void” is used to refer to the 47.6 percent of space that is unoccupied and empty. In a body-centered cubic construction, the amount of space that is occupied is around 68 percent, while the amount of space that is vacant is approximately 32 percent.

Packing Proceeding in Stages

It’s possible to put the arrangement together in three distinct steps. A linear arrangement of the constituent particles in a row forms the basis of the first step of the process. The arrangement of particles in this manner produces a one-dimensional structure. A planar two-dimensional structure can be created by repeatedly arranging linear elements in one dimension in a succession of different ways. Finally, in the third step, the planar arrangement of the particles is extended to a three-dimensional configuration by arranging the planar layers in such a way that they are readily placed one on top of the other.

Conclusion 

However, in the case of a face-centered cubic construction, the amount of space that is occupied is up to 74 percent, while the amount of vacant space is decreased to 26 percent. The term “closest packing” refers to the most effective way of arranging spheres such that they occupy the majority of the space that is available while also keeping the amount of free space in the crystal lattice to a minimum.