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Build intuition之: 常见晶体结构类型再谈

已有 25129 次阅读 2013-11-4 08:53 |个人分类:物质结构及其预测|系统分类:科研笔记

关注:

1)Pearson symbol标记

2) typical  或well known结构




参考网址:

!! http://jcrystal.com/steffenweber/gallery/StructureTypes/st4.html

 

http://icsd.ill.eu/icsd/help/structuret.html


该网站给出了Structure type,Space Group, Wyckoff Symbol, Pearson Symbol 等十分有用的信息,如

Structure
Type
Prototype
CC Code
Space
Group
SG
Num.
ANX
Form.
Wyckoff
Symbol
Pearson
Symbol
c/a
Min
c/a
Max
AET
Pearson
Note
Description
(Bi7Pb)Pt458336PNMA

c3oP1222.5
CeF34P3-c1

g f d ahP24


LaF3, Cu3P, HoH3, tysonite

CeMn6Ni5102223P4/MBM

k j g c atP240.500.90
U(Ni.68Si.32)11tP24, P4/mbm, 1.5-1.9, k j g c a, 102223

CeNi12B660771Cmc2136
b7 a5oS76





CeNi3102230P63/MMC

k f d c b ahP242.903.80
LaF3(P63mc)27089P63cm

c3 b ahP24
YF326595PBNM
AX3d c2oP161.001.25



YF326595PNMA
AX3d c2oP160.600.80
"isopointal with Fe3C AX3, must contain F, Cl, Br oder I enthalten"
Al3Pu58141P63/mmc194
k h f bhP242.22.5
Na3As26883P63/MMC

f c bhP81.552.00
Al3Ir, SB: D0(18)

Na3As26883P63/MMC

f d bhP81.552.00
Al3Ir, SB: D0(18)
Ni3Sn105357P63/MMC

h chP80.700.90
Mg3Cd, Pt3U, SB: D0(19)Aristotype is Mg

Ni3Sn105357P63/MMC

h dhP80.700.90
Mg3Cd, Pt3U, SB: D0(19)Aristotype is Mg
Ni3Ti30216P63/MMC

h g c ahP161.451.85
Pd3U, SB: D0(24)D0(24)-Type

Ni3Ti30216P63/MMC

h g d ahP161.451.85
Pd3U, SB: D0(24)




题记:Thanks to Huayun

In the PBE calculations, we tried to include all possible candidates for post-cotunnite phases, and the following structures were considered:

fluorite(space group Fm-3m, Z = 4),

cotunnite (Pnma, Z= 4),

pyrite or modified fluorite (Pa-3,Z = 4),1

brookite (Pbca, Z= 8),1[H2O2的相]

post-PbCl2 (P1121/aor P21/a, Z = 8),

2 -US2 or Fe2P (P62m, Z = 3),3–6

 post-cotunnite phase of TeO2(P21/m, Z = 4),7,8

Co2Si (Pnma, Z = 4),9

Ni2In or _-Ni2Si (P63/mmc, Z = 2),3,10–13

 distorted Ni2In (Cmcm, Z = 4),3and

AlB2(P6/mmm, Z =1).14

The Cmc21 (Z =4, CN= 11) and P63mc (Z =2, CN= 11)phases

were captured by the structural search in PSO evolutionary calculations.S

imilar to Cmcm phase, both of these two structures are also adistortion of the hexagonal Ni2In phase



post-cotunnite phases



cotunnite (Pnma, Z= 4)




brookite (Pbca, Z= 8),

板钛矿

The brookite structure is built up of distorted octahedra with a titaniumion at the center and oxygen ions at each of the six vertices. Each octahedron shares three edges with adjoining octahedra, forming an orthorhombic structure.[8]


Crystal structure of brookite

Brookite is orthorhombic, and one of the four naturally occurring polymorphs (minerals with the same composition but different structure) of titanium dioxide, TiO2, approved by the International Mineralogical Association (IMA). The others are akaogiite (monoclinic), anatase (tetragonal) and rutile (tetragonal). Brookite is rare compared to anatase and rutile and, like these forms, it exhibits photocatalytic activity.[5] Brookite has a larger cell volume than either anatase or rutile, with 8 TiO2 groups per unit cell, compared with 4 for anatase and 2 for rutile.[6]Iron Fe, tantalum Ta and niobium Nb are common impurities.[3]

  • pyrite or modified fluorite (Pa-3,Z = 4),FeS2 type

http://en.wikipedia.org/wiki/Pyrite

黄铁矿 Space group: Pa3


Crystallography[edit]

Crystal structure of pyrite. In the center of the cell a S22− pair is seen in yellow.

Iron-pyrite FeS2 represents the prototype compound of the crystallographic pyrite structure.


The structure is simple cubic and was among the first crystal structures solved by X-ray diffraction.

[22] It belongs to the crystallographic space groupPa3 and is denoted by the Strukturbericht notation C2.

Under thermodynamic standard conditions the lattice constanta of stoichiometric iron pyrite FeS2 amounts to 541.87 pm.[23] 


The unit cell is composed of a Fe face-centered cubic sublattice into which the S ions are embedded. 


The pyrite structure is also used by other compounds MX2 of transition metalsM and chalcogensX = O, S, Se and Te. Also certain dipnictides with X standing for P, As and Sb etc. are known to adopt the pyrite structure.[24]


In the first bonding sphere, the Fe atoms are surrounded by six S nearest neighbours, in a distorted octahedral arrangement. The material is a diamagneticsemiconductor and the Fe ions should be considered to be in a low spindivalent state (as shown by Mössbauer spectroscopy as well as XPS), rather than a tetravalent state as the stoichiometry would suggest.

The positions of X ions in the pyrite structure may be derived from the fluorite structure, starting from a hypothetical Fe2+(S)2 structure.



Whereas F ions in CaF2 occupy the centre positions of the eight subcubes of the cubic unit cell (¼ ¼ ¼) etc., the S ions in FeS2 are shifted from these high symmetry positions along <111> axes to reside on (uuu) and symmetry-equivalent positions. Here, the parameter u should be regarded as a free atomic parameter that takes different values in different pyrite-structure compounds (iron pyrite FeS2: u(S) = 0.385 [25]).


The shift from fluorite u = 0.25 to pyrite u = 0.385 is rather large and creates a S-S distance that is clearly a binding one. This is not surprising as in contrast to F an ion S is not a closed shell species. It is isoelectronic with a chlorine atom, also undergoing pairing to form Cl2 molecules. Both low spin Fe2+ and the disulfide S22− moeties are closed shell entities, explaining the diamagnetic and semiconducting properties.

The S atoms have bonds with three Fe and one other S atom. The site symmetry at Fe and S positions is accounted for by point symmetry groupsC3i and C3, respectively. The missing center of inversion at S lattice sites has important consequences for the crystallographic and physical properties of iron pyrite. These consequences derive from the crystal electric field active at the sulfur lattice site, which causes a polarisation of S ions in the pyrite lattice.[26] The polarisation can be calculated on the basis of higher-order Madelung constants and has to be included in the calculation of the lattice energy by using a generalised Born–Haber cycle. This reflects the fact that the covalent bond in the sulfur pair is inadequately accounted for by a strictly ionic treatment.

Arsenopyrite has a related structure with heteroatomic As-S pairs rather than homoatomic ones. Marcasite also possesses homoatomic anion pairs, but the arrangement of the metal and diatomic anions is different from that of pyrite. Despite its name a chalcopyrite does not contain dianion pairs, but single S2− sulfide anions.

Crystal habit[edit]

Dodecahedron- shaped crystals from Italy.

Pyrite usually forms cuboid crystals, sometimes forming in close association to form raspberry-like framboids. However, under certain circumstances, it can form anastamozing filaments or T-shaped crystals.[27] Pyrite can also form dodecahedral crystals and this suggests an explanation for the artificial geometrical models found in Europe as early as the 5th century BC.[28]

Varieties[edit]

Cattierite (CoS2) and vaesite (NiS2) are similar in their structure and belong also to the pyrite group.

Bravoite is a nickel-cobalt bearing variety of pyrite, with > 50% substitution of Ni2+ for Fe2+ within pyrite. Bravoite is not a formally recognised mineral, and is named after Peruvian scientist Jose J. Bravo (1874–1928).[29]






post-PbCl2 (P1121/aor P21/a, Z = 8),


γ-US2 or Fe2P (P62m, Z = 3)



post-cotunnite phaseof TeO2(P21/m, Z = 4)



Co2Si(Pnma, Z =4)



Ni2In or θ-Ni2Si (P63/mmc, Z = 2)


distortedNi2In (Cmcm, Z = 4)


a distortion of the hexagonal Ni2In phase:AlB2(P6/mmm, Z = 1)


a distortion of the hexagonal Ni2In phase:Cmc21(Z =4, CN= 11)








BiF3结构


    α-BiF3属于立方晶系结构(皮尔逊符号:cF16,空间群:Fm-3m, No. 225)。

    β-BiF3具有YF3型结构,其中铋原子采取了变形的9配位三冠三棱柱构型。[4]这种结构一般被认为是离子型的,与同族其他元素的三氟化物不同。因为三氟化磷(PF3)、三氟化砷(AsF3)和三氟化锑(SbF3)中固态时都存在着MX3分子。[4]

 

晶体结构正交晶系oP16,空间群:Pnma, No. 62(β相)


plumbum

http://en.wikipedia.org/wiki/Barium_chloride

 

BaCl2 crystallizes in two forms (polymorphs). One form has the cubicfluorite (CaF2) structure and the other the orthorhombiccotunnite (PbCl2) structure. Both polymorphs accommodate the preference of the large Ba2+ ion for coordination numbers greater than six.[4] The coordination of Ba2+ is 8 in the fluorite structure[5] and 9 in the cotunnite structure.[6] When cotunnite-structure BaCl2 is subjected to pressures of 7–10 GPa, it transforms to a third structure, a monoclinic post-cotunnite phase. The coordination number of Ba2+ increases from 9 to 10.[7]




PbCl2 adopt the cotunnite structure (Pnam, Z = 4)

参考网址:

http://www.sciencedirect.com/science/article/pii/0022369795000607

The high pressure behaviour of PbCl2 and SnCl2 has been investigated by angular-dispersive X-ray diffraction.


Under ambient conditions, these two compounds adopt the cotunnite structure (Pnam, Z = 4) for which the cation has the highest coordination number found among the ionic AX2 compounds.


A crystallographic transition was observed at 16 GPa for both compounds. The structure of the high pressure phase is a distorted orthorhombic Co2Si structure: it is monoclinic (&amp;lt;img&nbsp;height=&quot;30&quot;&nbsp;border=&quot;0&quot;&nbsp;style=&quot;vertical-align:bottom&quot;&nbsp;width=&quot;62&quot;&nbsp;alt=&quot;&quot;&nbsp;title=&quot;&quot;&nbsp;src=&quot;http://origin-ars.els-cdn.com/content/image/1-s2.0-0022369795000607-si1.gif&quot;&amp;gt;, Z = 8) and the coordination number has increased to ten.

The mechanism of the transition occurs in two minimal steps: &amp;lt;img&nbsp;height=&quot;50&quot;&nbsp;border=&quot;0&quot;&nbsp;style=&quot;vertical-align:bottom&quot;&nbsp;width=&quot;190&quot;&nbsp;alt=&quot;&quot;&nbsp;title=&quot;&quot;&nbsp;src=&quot;http://origin-ars.els-cdn.com/content/image/1-s2.0-0022369795000607-si2.gif&quot;&amp;gt;. The pressure dependence of the cell constants, volume and the equation-of-state parameters are given.


In the cotunnite phase, B0 and B0 are 34 GPa and 7.4, and 31 GPa and 4.9, for PbCl2 and SnCl2, respectively. The bulk moduli of both compounds triple above the transition.


The same monoclinic structure accounts for the high pressure phases of all the cotunnite-structured compounds investigated up to now.


This structure type was previously unknown for AX2 compounds and is now the final step for the high pressure sequence of the phase transitions in these compounds. It is probable that the AO2 dioxides adopt this structure in the megabar range. 


2011 Jul 22;107(4):045701. Epub  2011 Jul 22.

Theoretical and experimental evidence for a new post-cotunnite phase of titanium dioxide with significant optical absorption.

Abstract

  We report the discovery of a post-cotunnite phase of TiO2 by both density-functional ab initio calculations and high-pressure experiments.

   A pressure-induced phase transition to a hexagonal Fe2P-type structure (space group P62m) was predicted to occur at 161 GPa and 0 K and successfully observed by in situ synchrotron x-ray diffraction measurements at 210 GPa and 4000 K with a significant increase in opacity.

  This change in opacity is attributed to a reduction of band gap from 3.0 to 1.9 eV across the phase change. The Fe2P-type structure is proved to be the densest phase in major metal dioxides.


三氧化铼结构




化合物的晶体结构[编辑]

参考网址:http://zh.wikipedia.org/wiki/%E6%99%B6%E4%BD%93%E7%BB%93%E6%9E%84 

化合物的晶体结构
名称英文名代号晶格结构晶系配位举例示意图(点击可放大)
氯化钠结构NaCl structureB1型面心立方晶格立方晶系[6][7]NaCl-estructura cristalina.svg
氯化铯结构CsCl structureB2型简单立方晶格立方晶系[8][9]CsCl crystal.png
立方硫化锌闪锌矿)结构zinc blende structureB3型类金刚石晶格立方晶系[10][11]Sphalerite-unit-cell-3D-balls.png
六方硫化锌纤锌矿)结构wurtzite structureB4型简单六方晶格六方晶系[12][13]Wurtzite-unit-cell-3D-balls.png
砷化镍结构NiAs structureB8型
六方晶系[14][15]Nickel-arsenide-3D-unit-cell.png
碘化镉结构CdI2 structureC6型
三方晶系

Cadmium-iodide-3D-balls.png
萤石结构fluorite structureC1型面心立方晶格立方晶系

Fluorite-unit-cell-3D.png
萤石结构antifluorite structureC2型
立方晶系

Fluorite-unit-cell-3D.png
金红石结构rutile structureC4型简单四方晶格四方晶系

Rutile-unit-cell-3D.png
钙钛矿结构perovskite structureE21
立方晶系

Perovskite.jpg
三氧化铼结构ReO3 structureDO9
立方晶系

Rhenium-trioxide-unit-cell-vdW.png


1.Pearson symbol标记

http://zh.wikipedia.org/wiki/皮尔逊符号

 

皮尔逊符号英语Pearson symbol)又称皮尔逊记号,是晶体学中描述晶体结构的一种方法,由里奥·布鲁尔·皮尔逊创立。[1]这种符号由两个字母和一个数字组成,例如:

根据2005年IUPAC无机化学命名法,两个斜体字母具体指定布拉维点阵,其中小写字母表明晶体的类型,大写字母表明点阵的类型。最后的数字表示一个晶胞内原子的个数。[2]

符号对照表[编辑]

晶族
a三斜
m单斜
o正交
t四方
h六方和三方
c立方
点阵类型
C侧面心
F面心
I体心
R菱方
P简单

十四种可能的布拉维点阵可以通过前两个字母来区别:

晶族点阵符号皮尔逊符号的字母
三斜PaP
单斜PmP
单斜CmC
正交PoP
正交CoC
正交FoF
正交IoI
四方PtP
四方ItI
六方和三方PhP
菱方RhR
立方PcP
立方FcF
立方IcI

皮尔逊符号和空间群[编辑]

皮尔逊符号不能唯一地表示晶体结构的空间群,例如氯化钠型结构(空间群:Fm3m)和金刚石型结构(空间群:Fd3m)的皮尔逊符号都是cF8。




2. 英文介绍

The Pearson symbol, or Pearson notation, is used in crystallography as a means of describing a crystal structure, and was originated by W.B. Pearson.[1] 

  The symbol is made up of two letters followed by a number. For example:

  • Diamond structure, cF8

  • Rutile structure, tP6

The two (italicised) letters specify the Bravais lattice.

  The lower case letter specifies the crystal class, and

  the upper case letter the lattice type.

  The figure gives the number of the atoms in the unit cell. IUPAC (2005) [2]

Crystal class
atriclinic
mmonoclinic
oorthorhombic
ttetragonal
hhexagonal and rhombohedral
ccubic
Lattice type
S,A,B,CSide face centred
FAll face centred
IBody centred (from innenzentrierte (German))[3]
RRhombohedral
PPrimitive

The letters A, B and C was formerly used instead of S. When centering had a pair of opposite faces along the X-axis it was called A-centered. Equivalent centering along the Y- and Z-axes were called B- and C-centered, respective.[3]

The fourteen possible Bravais lattices are identified by the first two letters:

Crystal classLattice symbolPearson symbol letters
TriclinicPaP
MonoclinicPmP

SmS
OrthorhombicPoP

SoS

FoF

IoI
TetragonalPtP

ItI
Hexagonal (and trigonal)PhP
RhombohedralRhR
CubicPcP

FcF

IcI

Pearson symbol and space group[edit]

The Pearson symbol does not uniquely identify the space group of a crystal structure, for example both the NaCl structure, (space group Fm3m) and diamond (space group Fd3m) have the same Pearson symbol cF8.

References[edit]

  1. Jump up^ W.B. Pearson, A Handbook of Lattice Spacings and Structures of Metals and Alloys,Vol. 2, Pergamon Press, Oxford, 1967

  2. Jump up^ Nomenclature of Inorganic Chemistry IUPAC Recommendations 2005; IR-3.4.4, pp.49-51; IR-11.5, pp.241-242

  3. ^ Jump up to:a b page 124 in chapter 3. Crystallography: Internal order and symmetry in Cornelius Klein & Cornelius S. Hurlbut, Jr.: Manual of Mineralogy, 21st edition, 1993, John Wiley & Sons, Inc., ISBN 0-471-59955-7

Further reading[edit]

2. Cu3As arrangement -----I-43d

Nb3Sn-type   ---- Pm-3n



http://jcrystal.com/steffenweber/gallery/StructureTypes/st4.html


VF3

Strukturbericht                - ?

           

V F3 
         Vanadium fluoride

R-3c (167) [hR8]
         5.168 5.168 13.438 90 90 120
         V at 0,0,0
         F at 2/5,0,1/4

 

ZrI3

Strukturbericht - ?

           

Zr I3 
         Zirconium iodide

P63/mcm (193) [hP8]
         7.25 7.25 6.64 90 90 120
         Zr at 0,0,0
         I  at 0.325,0,1/4






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