The unit cell of the crystal lattice is used to describe the microstructure of materials. Many physicochemical properties of a substance depend on its parameters: hardness, melting point, electrical and thermal conductivity, ductility, and others. The types of these elementary structures were described as early as the 19th century. One of the varieties is a primitive cell. To select a unit cell in the material structure, a number of conditions must be observed.
Crystal cell
All solids by their internal structure can be classified into two forms: amorphous and crystalline. A distinctive feature of the latter is a specific organized particle structure.
The crystal lattice is a simplified three-dimensional model of solid crystals, which is used to analyze their properties in physics, chemistry, biology, mineralogy, and other sciences. Outwardly, it looks like a grid. At its nodes are atoms of matter. This array of points has a certain, regularly repeating order, specific for each type of substance.
What is a unit cell?
The unit cell of the crystal lattice is the smallest part of a solid that allows characterizing its properties. It serves as the basis of the lattice and is duplicated in it countless times.
This model is used to simplify the visual description of the internal structure of crystals. In this case, a system of 3 crystallographic coordinate axes is used, which differ from ordinary orthogonal axes in that they are finite segments of a certain size. The angles between the axes can be equal to 90 ° or be indirect.
If you densely fill a certain volume with unit cells, you can get the perfect single crystal. In practice, polycrystals consisting of several spatially limited regular structures are more common.
Kinds
In science, 14 types of elementary cells of lattices with a unique geometry are distinguished. They were first described by the French physicist Auguste Brave in 1848. This scientist is considered the founder of crystallography.
These types of elementary structures of the crystal lattice are grouped into 7 categories, called syngonies, depending on the ratio of side lengths and equal angles:
- cubic;
- tetragonal;
- orthorhombic;
- rhombohedral;
- hexagonal;
- triclinic.
The simplest and most common in nature of them is the first category, which in turn is divided into 3 types of lattices:
- Simple cubic. All particles (and they can be atoms, electrically charged particles or molecules) are located at the vertices of the cube. These particles are identical. Each cell has 1 atom (8 vertices × 1/8 atom = 1).
- Body-centered cubic. It differs from the previous model in that there is another particle in the center of the cube. Each cell contains 2 atoms of the substance.
- Face centered cubic. Particles are contained in the vertices of the unit cell, as well as in the center of all faces. Each cell has 4 atoms.
Primitive cell
A unit cell is called primitive if its particles are located only at the vertices of the lattice and are absent in other places. Its volume is minimal compared to other types. In practice, it often turns out to be low-symmetric (an example is the Wigner-Seitz cell).
In non-primitive cells, the atom in the center of the volume divides them into 2 or 4 identical parts. In a face-centered structure, there is a division into 8 parts. In metallography, they use the concept of an elementary rather than a primitive cell, since the symmetry of the former allows a more complete description of the crystal structure of the material.
Signs
All 14 types of unit cells have common properties:
- they are the simplest repeating structures in a crystal;
- each center of the lattice consists of one particle, called the lattice node;
- the nodes of the cell are interconnected by straight lines that form the geometry of the crystal;
- opposite faces are parallel;
- the symmetry of the elementary structure corresponds to the symmetry of the entire crystal lattice.
When choosing a unit cell structure, they are guided by some rules. She should have:
- smallest volume and area;
- the largest number of identical edges and angles between them;
- right angles (if possible);
- spatial symmetry, reflecting the symmetry of the entire crystal lattice.
Volume
The unit cell volume is determined depending on its geometric shape. For cubic syngony, it is calculated as the length of the face (the intercenter distance of atoms) raised to the third degree. For hexagonal syngony, the volume can be determined by the formula below:
where a and c are the lattice parameters measured in angstroms.
In practice, the crystal lattice parameters are calculated so that in the future it is possible to determine the structure of the compound, the mass of the atom (based on the weight of a given volume and Avogadro number) or its radius.