晶体结构

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In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms in a crystal. A crystal structure is composed of a unit cell, a set of atoms arranged in a particular way; which is periodically repeated in three dimensions on a lattice. The spacing between unit cells in various directions are called its lattice parameters. The symmetry properties of the crystal are embodied in its space group. A crystal's structure and symmetry play a role in determining many of its properties, such as cleavage, electronic band structure, and optical properties.

目录 1 Unit cell 2 Crystal system 3 Classification of lattices 4 Point and space groups 5 Defects in crystals 6 Crystal symmetry 7 单质 7.1 金属铜结构(metallic copper structure) 7.2 金属钠结构(metallic sodium structure) 7.3 金属镁结构(metallic magnesium structure) 7.4 金刚石结构(diamond structure) 7.5 石墨结构(graphite structure) 8 化合物 8.1 氯化钠结构(NaCl structure) 8.2 氯化铯结构(CsCl structure) 8.3 立方硫化锌结构(zinc blende structure) 8.4 六方硫化锌结构(wurtzite structure) 8.5 砷化镍结构(NiAs structure) 8.6 碘化镉结构(CdI2) 8.7 萤石结构(CaF2 fluorite structure) 8.8 反萤石结构(anti-fluorite structure) 8.9 金红石结构(TiO2 rutile structure) 8.10 钙钛矿结构(CaTiO3 perovskite structure) 8.11 三氧化铼结构(ReO3 structure) 9 See also 10 External links

Unit cell

A unit cell is a spatial arrangement of atoms which is tiled in three-dimensional space to describe the crystal. The positions of the atoms inside the unit cell are described by the symmetric unit or basis, the set of atomic positions (x_i,y_i,z_i) measured from a lattice point.

For each crystal structure there is a conventional unit cell, usually chosen to make the resulting lattice as symmetric as possible. However, the conventional unit cell is not always the smallest possible choice. A primitive unit cell of a particular crystal structure is the smallest possible unit cell one can construct such that, when tiled, it completely fills space. A Wigner-Seitz cell is a particular kind of primitive cell which has the same symmetry as the lattice.

Crystal system

The crystal system is the point group of the lattice (the set of rotation and reflection symmetries which leave a lattice point fixed), not including the positions of the atoms in the unit cell. There are seven unique crystal systems. The simplest and most symmetric, the cubic (or isometric) system, has the symmetry of a cube. The other six systems, in order of decreasing symmetry, are hexagonal, tetragonal, rhombohedral (also known as trigonal), orthorhombic, monoclinic and triclinic. Some crystallographers consider the hexagonal crystal system not to be its own crystal system, but instead a part of the trigonal crystal system.

Classification of lattices

晶系	格子
三斜
单斜	简单	底心
正交	简单	底心	体心	面心
六方
菱方 （三角）
四方	简单	体心
立方 (等轴)	简单	体心	面心

A Bravais lattice is a set of points constructed by translating a single point in discrete steps by a set of basis vectors. In three dimensions, there are 14 unique Bravais lattices (distinct from one another in that they have different space groups) in three dimensions. All crystalline materials recognised till now (not including quasicrystals) fit in one of these arrangements. The fourteen three-dimensional lattices, classified by crystal system, are shown to the right.

The crystal structure is one of the lattices with a unit cell, which contains atoms at specific coordinates, at every lattice point. Because it includes the unit cell, the symmetry of the crystal can be more complicated than the symmetry of the lattice.

Point and space groups

The crystallographic point group or crystal class is the set of non-translational symmetries that leave a point in the crystal fixed. There are 32 possible crystal classes.

The space group of the crystal structure is composed of the translational symmetries in addition to the symmetries of the point group. There are 230 distinct space groups.

Defects in crystals

Real crystals feature defects or irregularities in the ideal arrangements described above and it is these defects that critically determine many of the electrical and mechanical properties of real materials. In particular dislocations in the crystal lattice allow shear at much lower stress than that needed for a perfect crystal structure.

Crystal symmetry

Crystal structures can be divided into 32 classes, or point groups, according to the number of rotational axes and reflection planes they exhibit that leave the crystal structure unchanged. Twenty of the 32 crystal classes are piezoelectric. All 20 piezoelectric classes lack a center of symmetry. Any material develops a dielectric polarization when an electric field is applied, but a substance which has such a natural charge separation even in the absence of a field is called a polar material. Whether or not a material is polar is determined solely by its crystal structure. Only 10 of the 32 point groups are polar. All polar crystals are pyroelectric, so the 10 polar crystal classes are sometimes referred to as the pyroelectric classes.

There are a few crystal structures, notably the perovskite structure, which exhibit ferroelectric behaviour. This is analogous to ferromagnetism, in that, in the absence of an electric field during production, the ferroelectric crystal does not exhibit a polarisation. Upon the application of an electric field of sufficient magnitude, the crystal becomes permanently polarised. This polarisation can be reversed by a sufficiently large counter-charge, in the same way that a ferromagnet can be reversed. However, it is important to note that, although they are called ferroelectrics, the effect is due to the crystal structure, not the presence of a ferrous metal.

Incommensurate crystals have period-varying translational symmetry. The period between nodes of symmetry is constant in most crystals. The distance between nodes in an incommensurate crystal is dependent on the number of nodes between it and the base node.

晶体结构：晶体的周期性结构，可用晶胞中原子的分布图形表示。

单质

金属铜结构(metallic copper structure)

• 国际上表达这种结构形式的记号为A1型。
• 为立方最密堆积(ccp)，属立方晶系，面心立方点阵型式；
• 每个原子周围都和12个相同原子配位连接；
• 属A1型结构的单质有近二十种，如钙(Ca)，锶(Sr)，铝(Al)，银(Ag)，金(Au)，镍(Ni)，钯(Pd)，铂(Pt)，铑(Rh)，铱(Ir)，铅(Pb)等。

金属钠结构(metallic sodium structure)

• 国际上表达这种结构形式的记号为A2型。
• 为体心立方密堆积(bcp)，属立方晶系，体心立方点阵型式；
• 每个原子周围都和8个相同原子配位连接；
• 属A2型结构的单质有十多种，如铁(Fe)和ⅠA族元素锂(Li)、钠(Na)、钾(K)、铷(Rb)、铯(Cs)，ⅤB族元素钒(V)、铌(Nb)、钽(Ta)，ⅥB族元素铬(Cr)、钼(Mo)、钨(W)等。

金属镁结构(metallic magnesium structure)

• 国际上表达这种结构形式的记号为A3型；
• 为六方最密堆积(hcp)，属六方晶系，简单六方点阵型式；
• 每个原子周围都和12个相同原子配位连接；
• 属A3型结构的单质有铍(Be)，钴(Co)，锌(Zn)，镉(Cd)，铊(Tl)和ⅢB族元素钪(Sc)、钇(Y)，ⅣB族元素钛(Ti)、锆(Zr)、铪(Hf)，镧系元素等。

金刚石结构(diamond structure)

• 国际上表达这种结构形式的记号为A4型；
• 属立方晶系，面心立方点阵型式；
• 每个碳原子和周围四个碳原子按四面体配位，形成C-C共价单键。
• 属A4型结构的单质有硅(Si)，锗(Ge)，灰锡(Sn)等。

石墨结构(graphite structure)

• 国际上表达这种结构形式的记号为A9型；
• 属六方晶系，简单六方点阵型式；
• 每个碳原子和周围三个碳原子按平面三角形配位，形成具有六元环的层型分子。

化合物

氯化钠结构(NaCl structure)

• 国际上表达这种结构形式的记号为B1型；
• 属立方晶系，面心立方点阵型式；
• Na⁺和Cl^-离子周围都由6个异号离子按八面体方式配位。
• 数以百计的二元化合物，如卤化物、氧化物、硫化物、硒化物、氮化物和碳化物中，许多都是B1型的。

氯化铯结构(CsCl structure)

• 国际上表达这种结构形式的记号为B2型；
• 属立方晶系，简单立方点阵型式；
• Cs⁺和Cl^-离子周围都由8个异号离子按八面体方式配位；
• 属B2型的化合物有溴化铯(CsBr)，碘化铯(CsI)，溴化铊(TlBr)，碘化铊(TlI)，氯化铵(NH₄Cl)，溴化铵(NH₄Br)，碘化铵(NH₄I)等盐类及AgCd，AgCe，AgMg，AgZn，AuMg，AuZn，CaTl，CdLa，MgLa，MgSr，TlBi等许多金属间化合物。

立方硫化锌结构(zinc blende structure)

• 国际上表达这种结构形式的记号为B3型；
• 属立方晶系，面心立方点阵型式；
• Zn²⁺和S^2-离子周围都由4个异号离子呈四面体方式配位；
• 这种结构也可看作S^2-作立方最密堆积，Zn²⁺填入四面体的空隙中；
• 或者，由于Zn-S间共价键占很大成分，可将它的结构看作立方金刚石结构中的C原子，交替地由Zn和S原子置换而得；
• 属于B3型的化合物有氯化亚铜(CuCl)，溴化亚铜(CuBr)，碘化亚铜(CuI)，碘化银(AgI)，碳化硅(SiC)，氮化硼(BN)，磷化硼(BP)，硫化铍(BeS)等。

六方硫化锌结构(wurtzite structure)

• 国际上表达这种结构形式的记号为B4型；
• 属六方晶系，简单六方点阵型式；
• Zn²⁺和S^2-离子周围都由4个异号离子呈四面体方式配位；
• 这种结构也可看作S^2-作六方最密堆积，Zn²⁺填入四面体的空隙中；
• 属于B3型的化合物有氧化锌(ZnO)，卤化铜(CuX,X=Cl,Br,I)，氧化铍(BeO)，硫化镉(CdS)，硒化镉(CdSe)，碘化银(AgI)，碳化硅(SiC)等。

砷化镍结构(NiAs structure)

• 国际上表达这种结构形式的记号为B8型；
• 属六方晶系，简单六方点阵型式；
• Ni化物As的配位数都是6，但Ni是处在As的八面体配位中，As则处在Ni的三方柱体配位中；
• 许多过渡金属的硫化物、硒化物、碲化物和锑化物属于B8型。

碘化镉结构(CdI₂)

• 国际上表达这种结构形式的记号为C6型；
• 属三方晶系，简单六方点阵型式。

萤石结构(CaF₂ fluorite structure)

• 国际上表达这种结构形式的记号为C1型；
• 属立方晶系，面心立方点阵型式。

反萤石结构(anti-fluorite structure)

• 国际上表达这种结构形式的记号为C2型；
• 属立方晶系，面心立方点阵型式。

金红石结构(TiO₂ rutile structure)

• 国际上表达这种结构形式的记号为C4型；
• 属四方晶系，简单四方点阵型式。

钙钛矿结构(CaTiO₃ perovskite structure)

• 国际上表达这种结构形式的记号为E2₁型；
• 属立方晶系，简单立方点阵型式。

三氧化铼结构(ReO₃ structure)

• 国际上表达这种结构形式的记号为DO₉型；
• 属立方晶系，面心立方点阵型式。

See also

• Crystal
• Crystallography
• Crystallographic point group
• Crystallographic defect
• Crystal growth
• Liquid crystal
• Cleavage (crystal)
• Seed crystal
• Quasicrystals

For more detailed information in specific technology applications see materials engineering, materials science, ceramic or metallurgy.

External links

• Appendix A from the manual for Atoms, software for XAFS
• Intro to Minerals: Crystal Class and System
• Introduction to Crystallography and Mineral Crystal Systems
• Crystal planes and Miller indices
• Interactive 3D Crystal models
• [1]wp:Crystal structure