synonymUnit lattice(unit cell) generally refers to unit cell
The most basic geometric unit that constitutes a crystal is called a unit cell, whose shape, size andSpatial latticeOfParallelepipedThe unit is the same, and all features of the whole lattice are retained.The unit cell can completely reflectcrystalInternal atoms or ionsthree-dimensional spaceThe smallest unit of parallelepiped with chemical structural characteristics of distribution.Which can not only maintaincrystal structureOfSymmetryThe volume is also called "unit unit cell", but it is also often referred to as unit cell.
The smallest component of various crystal structuresVolume unitIt is called unit cell.[1]
Chinese name
Unit cell
Foreign name
Unit Cell
Alias
Unit cell
Definition
The most basic geometric unit of crystal
Form
The parallelepiped units of spatial lattices are the same
sameSpatial latticeDifferent cells can be obtained due to different selection methods, so the requirements for selecting cells can best reflect the latticeSymmetry, the selection principle is[2]：
1. SelectedParallelepipedIt should reflect the highest symmetry of the lattice;
twoParallelepipedThe number of equal internal edges and angles shall be the most;
3. When there is a right angle between the edges of a parallelepiped, the number of right angles shall be the maximum:
4. If the above conditions are met, the unit cell shall have the smallest volume
Generally, the unit cell isParallelepiped。The whole crystal can be regarded as countless crystal cellsGapless juxtapositionAnd become.
Please note that:
Gapless——There is no gap between adjacent cells
Juxtaposition——All unit cells are in parallel arrangement with the same orientation
Two-dimensional lattice
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Unit cell
There are five types of Brave lattices in the two-dimensional plane, twoCrystal axisa1、a2. Included angle.Oblique lattice: Any crystal axisa1、a2. Only when rotating π or 2 π can it remain unchanged.squarelattice、Hexagonal lattice、Rectangular lattice、Centered rectangular lattice, but there is aLattice point, so there are two drawing methods.
ParallelepipedThe geometric characteristics of can be determined by the relationship between side length and included angle.The side length and included angle of Bravo cell are calledCell parameter。There are a total of 7 types of three-dimensional unit cells with different geometric characteristics, called the Bravis system. Their names, English names, symbols and geometric characteristics are as follows:
Cubic (c) a=b=c, α=β=γ=90 °, (only one cell parameter a)
Tetragonal (t) a=b ≠ c, α=β=γ=90 °, (with two cell parameters a and c)
Hexagonal (h) a=b ≠ c, α=β=90 °, γ=120 °, (there are two cell parameters a and c)
orthogonal(Italic) orthorhombic (o) a ≠ b ≠ c, α=β=γ=90 °, (there are three cell parameters a, b and c)
Monoclinic (m) a ≠ b ≠ c, α=γ=90 °, β ≠ 90 °, (there are 4 cell parameters a, b, c and β)
Triclinic anorthic (a) a ≠ b ≠ c, α ≠ β ≠ γ, (there are 6 cell parameters a, b, c, α, β and γ)
Rhombohedral (triangular) rhombohedral (R) a=b=c, α=β=γ ≠ 90 °, (there are two cell parameters a and α)
Prime polycrystal cell
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Unit cell
A unit cell is a descriptive crystalMicrostructureThe basic unit of, but not necessarily the smallest unit.The unit cell hasPrime cellandPolycrystal cellPoints.The prime unit cell, the symbol P, is the smallest unit in the crystal microscopic space, and cannot be smaller.The set of atoms in the prime unit cell is equivalent to the smallest set of atoms in the crystal micro space that make periodic translation, calledStructural primitive。
The polyunit cell is of primary unit cellpolyploid, there are three types:
A simple lattice consists of only one kind of atom. Each cell has only one atom, which is distributed on the top corner of the cellScattering intensityIt is equivalent to the scattering intensity of an atom.
There are n atoms of the same or different kinds in the complex lattice unit cell. In addition to occupying the top corner of the unit cell, they may also appear in the body center, face center or other positions.[3]
Complex lattice unicellularScattered waveamplitudeSingle expectedIntracellularAtomicScattering amplitudeVector synthesis of.Due to the interference of diffracted rays, the intensity in some directions will be strengthened, while the intensity in some directions will be weakened or even disappear.This rule is calledSystem extinction(or structureextinction）。
