Кубтық кристалдық жүйелер

Crystallographic system where the unit cell is in the shape of a cube

In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals. There are three main varieties of these crystals:
Primitive cubic (abbreviated cP and alternatively called simple cubic)
Body centered cubic (abbreviated cI or bcc)
Face centered cubic (abbreviated cF or fcc)
Note: the term fcc is often used in synonym for the cubic close packed or ccp structure occurring in metals. However, fcc stands for a face centered cubic Bravais lattice, which is not necessarily close packed when a motif is set onto the lattice points. E. g. the diamond and the zincblende lattices are fcc but not close packed. Each is subdivided into other variants listed below. Although the unit cells in these crystals are conventionally taken to be cubes, the primitive unit cells often are not.

As a rule, since atoms in a solid attract each other, the more tightly packed arrangements of atoms tend to be more common. (Loosely packed arrangements do occur, though, for example if the orbital hybridization demands certain bond angles.) Accordingly, the primitive cubic structure, with especially low atomic packing factor, is rare in nature, but is found in polonium. The bcc and fcc, with their higher densities, are both quite common in nature. Examples of bcc include iron, chromium, tungsten, and niobium. Examples of fcc include aluminium, copper, gold and silver. Another important cubic crystal structure is the diamond cubic structure, which can appear in carbon, silicon, germanium, and tin. Unlike fcc and bcc, this structure is not a lattice, since it contains multiple atoms in its primitive cell. Other cubic elemental structures include the A15 structure found in tungsten, and the extremely complicated structure of manganese.

Compounds that consist of more than one element (e. g. binary compounds) often have crystal structures based on the cubic crystal system. Some of the more common ones are listed here. These structures can be viewed as two or more interpenetrating sublattices where each sublattice occupies the interstitial sites of the others.

One structure is the "interpenetrating primitive cubic" structure, also called a "caesium chloride" or B2 structure. This structure is often confused for a body centered cubic structure because the arrangement of atoms is the same. However, the caesium chloride structure has a basis composed of two different atomic species. In a body centered cubic structure, there would be translational symmetry along the [111] direction. In the caesium chloride structure, translation along the [111] direction results in a change of species. The structure can also be thought of as two separate simple cubic structures, one of each species, that are superimposed within each other. The corner of the chloride cube is the center of the caesium cube, and vice versa. It works the same way for the NaCl structure described in the next section. If you take out the Cl atoms, the leftover Na atoms still form an FCC structure, not a simple cubic structure. In the unit cell of CsCl, each ion is at the center of a cube of ions of the opposite kind, so the coordination number is eight. The central cation is coordinated to 8 anions on the corners of a cube as shown, and similarly, the central anion is coordinated to 8 cations on the corners of a cube. Alternately, one could view this lattice as a simple cubic structure with a secondary atom in its cubic void. In addition to caesium chloride itself, the structure also appears in certain other alkali halides when prepared at low temperatures or high pressures. Generally, this structure is more likely to be formed from two elements whose ions are of roughly the same size (for example, ionic radius of Cs+ = 167 pm, and Cl− = 181 pm). The space group of the caesium chloride (CsCl) structure is called Pmm (in Hermann–Mauguin notation), or "221" (in the International Tables for Crystallography). The Strukturbericht designation is "B2". There are nearly a hundred rare earth intermetallic compounds that crystallize in the CsCl structure, including many binary compounds of rare earths with magnesium, and with elements in groups 11, 12, and 13. Other compounds showing caesium chloride like structure are CsBr, CsI, high temperature RbCl, AlCo, AgZn, BeCu, MgCe, RuAl and SrTl.

The Heusler structure, based on the structure of Cu2MnAl, is a common structure for ternary compounds involving transition metals. It has the space group Fmm (No. 225), and the Strukturbericht designation is L21. Together with the closely related half Heusler and inverse Huesler compounds, there are hundreds of examples.

A Weaire–Phelan structure has Pmn (223) symmetry. It has three orientations of stacked tetradecahedrons with pyritohedral cells in the gaps. It is found as a crystal structure in chemistry where it is usually known as a "type I clathrate structure". Gas hydrates formed by methane, propane, and carbon dioxide at low temperatures have a structure in which water molecules lie at the nodes of the Weaire–Phelan structure and are hydrogen bonded together, and the larger gas molecules are trapped in the polyhedral cages.