Basic knowledge of crystals

In the visible light spectrum, there are a large number of highly transparent glass types, which can be selected according to their dispersion n (λ). The conditions in the ultraviolet (UV) and infrared (IR) spectral regions are completely different. There are only a few glass types, so , Need to use optical crystals to make some supplements.

1. Design and structure

Crystals are solids in which structural units (atoms, ions, or molecules) are approximately periodically arranged in a three-dimensional structure. The deviation from strict periodicity is due to the limited expansion of the crystal and construction errors.

The crystal is described by the unit cell of the lattice, and is composed of basic vectors a1, a2, and a3 with angles α, β, and γ, respectively. The crystal lattice is based on a suitable coordinate system that represents the macroscopic position of the crystal surface and the line of intersection. There are infinite ways to select a unit cell. However, in general, the unit cell with the smallest volume or the shortest basis vector is selected. The length of the basis vector is called the lattice constant. This kind of crystal can be obtained by continuously increasing the unit cell in the direction of the basis vector.

There are various forms of crystals, according to their shape and internal structure, will show a unique symmetry. Due to the regular arrangement and symmetry of the surface, the crystals can be divided into 32 levels or point groups, and these levels can be reduced to 7 crystal systems. The basis of this classification is the form of the unit cell, the basic unit cell All crystals of the same form belong to the same crystal system.

Different grades of crystals of the same crystal system are distinguished according to the degree of symmetry. The cubic crystal system has the highest degree of symmetry, and the corresponding symmetry operations are:

●It can be translated near any lattice point, that is, all lattices have translational symmetry;

●The reflection on the plane is marked by two translation vectors, that is, not all lattices are mirror-symmetrical;

●According to a lattice point inversion;

●Rotate with a lattice vector as the rotation axis, in other words, all lattices have at least one rotational symmetry [Kleb90]

When a crystal is based on molecules or atomic groups instead of individual atoms, it is possible to obtain more than 230 different types of arrangements. The special order in the unit lattice has been taken into account here. In fact, all crystals are different from their ideal structure to varying degrees. Many factors affect the three-dimensional periodicity of the crystal lattice, including (of course, there are other factors):

●Structural defects;

●Electronic defects

●Surface defects

● Thermal and other oscillations of the lattice structure block;

●The uneven distribution of mixed crystals;

●Clots and secretions;

●Micro-crystalline, sub-microcrystalline

●Internal stress

These actual structural defects are interdependent, so they cannot be considered in isolation. They include general and special contents. Structural defects play a major role, including the deviation of all crystal structural units from the ideal regular arrangement of the crystal lattice. Since its extended dimension is larger than that of the atom, it can be divided into the following categories

●Zero-dimensional defects (point defects), that is, atoms are located in the wrong lattice positions, non-ideal impurity atoms;

●Dimensional defects (line defects, dislocation), or asymmetry along a line that is not necessarily a straight line

●Two-dimensional defects (surface defects), such as grain boundaries, twin boundaries, phase boundaries, stacking faults;

●Three-dimensional defects (body defects), such as cavities, secretions.

2. Related properties

The physical and chemical properties of the crystal can be expressed by its chemical composition and structure, that is, according to the type and density of the structural unit and the spatial arrangement. The misalignment of the crystal structure and actual structural defects play a decisive role in this. In addition, an important fact is that the crystal is a uniform anisotropic body, and its physical properties are generally directional. Therefore, related properties all specify a direction. There are exceptions, such as mass, density, and specific heat. Use tensors to express the anisotropic properties.

Hardness is a very important property of crystals, indicating the ability of the crystal to withstand mechanical damage. At this time, various anisotropic properties, such as elasticity, plasticity, and strength, work at the same time. As with glass and other materials, different hardness types are an important distinction, such as scratch, abrasion, and indentation hardness. The anisotropy of hardness mainly depends on the solvability. Once subjected to mechanical shocks, such as pressure, tension, or sudden blows, many crystals will split along a certain crystal lattice plane, and the resulting surface will appear atomically smooth in a large area. The cleavage plane can easily identify a lattice plane with very small atomic structural unit intervals and extremely dense atoms.

Generally, the lattice planes with the densest atoms are the furthest away from each other, and the cohesion between such lattice planes is the smallest. As the lattice plane splits, gaps are generated, and the bonding force decreases. From the morphological point of view, it is often important that these lattice planes are used as growth planes.

For the crystal surface where the position of the cleavage plane is widened, as the cracks are formed, the cleavability becomes obvious. These cracks, especially when considering the optical properties, indicate the primary crystal reference direction. The relationship between cleavability and structure of many crystals is completely different.

Generally, the density of crystals is higher than the corresponding amorphous material (amorphous), the hardness is greater, but it is also more brittle. Due to its optical properties, the selected crystal can very well complement the technical requirements of materials used in the optical field.

The crystal material is particularly suitable for the ultraviolet and infrared spectral regions, and has a high transmittance τ (λ). For most applications, only isotropic materials can be used, and anisotropic crystals are mainly used in polarized optics. Optically isotropic crystals are crystals whose propagation speed, light absorption, and other optical phenomena are independent of the angle between the beam direction and the crystal axis. This is completely correct for cubic crystals. It should be noted that although these crystals are optically isotropic, some properties, such as growth rate, X-ray diffraction and cleavage, exhibit anisotropic properties.

The application of crystal materials has greatly expanded the scope of optical applications, including:

●Extend the optical medium's spectral transmission range in the ultraviolet (LiF, CaF2 and quartz) and infrared spectral regions (KBr, KRS-5 and CsJ);

●Ge and ZnSe special infrared optical elements and light windows;

●CaF2 and glass lens are combined to design microscope and photographic objective lens to better correct chromatic aberration;

●Using calcite (calcium carbonate), gypsum and mica with strong birefringence, and materials with low birefringence, such as quartz (SiO2), corundum (Al2O3) and ammonium dihydrogen phosphate (ADP) to make polarizing optical elements;

●Optical filter;

●Electro-optical and non-linear optical components;

●Acousto-optic components [Naum92]

Crystals can also be used as laser crystals, scintillators, luminescent materials and detectors, and optical data storage in optical applications.

To sum up, it can be concluded that optical materials must be carefully selected. According to the relevant nature and technical requirements of the system, low-cost production can be achieved.