The unit cell of the crystal lattice serves to describe the microstructure of materials. Many physical and chemical properties of a substance depend on its parameters: hardness, melting point, electrical and thermal conductivity, plasticity, and others. The types of these elementary structures were described as early as the 19th century. One of the varieties is the primitive cell. To isolate a unit cell in the material structure, a number of conditions must be met.
Crystal lattice
All solids according to their internal structure can be classified into two forms: amorphous and crystalline. A distinctive feature of the latter is the specific organized structure of the particles.
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 the atoms of matter. This array of points has a specific, regularly repeating order specific to each species.substances.
What is a unit cell?
The unit cell of the crystal lattice is the smallest part of a solid that allows us to characterize its properties. It serves as the basis of the grid 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 the usual orthogonal ones 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 elementary cells, you can get an ideal single crystal. In practice, polycrystals are more common, consisting of several regular structures limited in space.
Views
In science, there are 14 types of elementary cells of lattices with a unique geometry. They were first described by the French physicist Auguste Bravais 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 the lengths of the sides and the equality of the angles:
- cubic;
- tetragonal;
- orthorhombic;
- rhombohedral;
- hexagonal;
- triclinic.
The most simple and common in nature fromof 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 one more particle in the center of the cube. Each cell has 2 atoms of matter.
- Face-centered cubic. Particles are contained in the vertices of the elementary cell, as well as in the center of all faces. Each of the cells has 4 atoms.
Primitive cell
An elementary cell is called primitive if its particles are located only at the lattice vertices and are absent elsewhere. 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).
For non-primitive cells, the atom in the center of the volume divides them into 2 or 4 identical parts. In the face-centered structure, there is a division into 8 parts. In metallography, the concept of an elementary rather than a primitive cell is used, since the symmetry of the first cell allows a more complete description of the crystal structure of the material.
Signs
All 14 types of elementary cells have common properties:
- they are the simplest repeating structures in a crystal;
- each lattice center consists of oneparticles, called the lattice node;
- cell nodes 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 the structure of an elementary cell, some rules are followed. She must 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 volume of an elementary cell is determined depending on its geometric shape. For the cubic syngony, it is calculated as the length of the face (center-to-center distance of atoms) raised to the third power. For a hexagonal system, the volume can be determined using the formula below:
where a and c are the parameters of the crystal lattice, measured in angstroms.
In practice, the parameters of the crystal lattice are calculated in order to later determine the structure of the compound, the mass of an atom (based on the weight of a given volume and the Avogadro number) or its radius.
