230种晶体学空间群的记号

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2024年2月9日发(作者：)

230种晶体学空间群的记号

Symbols of the 230 Crystallographic Space Groups

空间群是点对称操作和平移对称操作的对称要素全部可能的组合。点群表示晶体外形上的对称关系，空间群表示晶体结构内部的原子及离子间的对称关系。空间群一共230个，它们分别属于32个点群。晶体结构的对称性不能超出230个空间群的范围，而其外形的对称性和宏观对称性则不能越出32个点群的范围。属于同一点群的各种晶体可以隶属于若干个空间群。

230种晶体学空间群的记号

Symbols of the 230 Crystallographic Space Groups

点群

(Point group)

晶系(Crystal

圣佛利斯system)

国际符号符号(HM)

(Schfl.)

三斜

晶系

单斜

晶系

1

空间群(Space group)

C1

Ci

P1

P

P21

Pc

P21/m

P2221

Pmc21

Cmm2

Imm2

Pnnn

Pbcm

Cccm

C2

Cm

C2/m

Cc

F222

Pmn21

Ama2

2

P2

Pm

P2/m

P222

Pmm2

m

2/m

222

P2/c

P21/C

C2/c

C222

Pnc2

P21212

P212121

C2221

Pcc2

Cmc21

Iba2

Pccm

Pnnm

Cmma

Pma2

Pca21

I222

I212121

Pba2

Pna21

Aba2

Fmm2

mm2

Pnn2

Fdd2

Pmmm

Ccc2

Amm2

Abm2

Ima2

正交

晶系

mmm

Pmna

Pnma

Immm

Pban

Pmma

Pnna

Pmmn

Pbcn

Pbca

Ccca

Fmmm

Fddd

Pcca

Pbam

Cmcm

Cmca

Ibam

Ibca

Pccn

Cmmm

Imma

P41

I

P42

P43

I4

I41

4

四方

P4

P

晶系

4/m

422

P4/m

P422

I4122

P4mm

P42/m

P4212

P4/n

P4122

P42/n

I4/m

I41/a

P41212

P4222

P42212

P4322

P43212

I422

P4bm

I41md

P42cm

I41cd

4mm

P42nm

P4cc

P4nc

P42mc

P42bc

I4mm

I4cm

P

c2

I

m2

2m

P

2m

P2c

P

21m

P21c

P

m2

P

b2

Pn2

Ic2

I

2m

I

2d

P4/mmm

P4/mcc

P4/nbm

P4/nnc

P4/mbm

P4/mnc

P4/nmm

P4/ncc

P42/mmc

4/mmm

P42/mcm

P42/nbc

P42/nnm

P42/mbc

P42/mnm

P42/nmc

P42/ncm

I4/mmm

I4/mcm

I41/amd

I41/acd

P32

R3

R32

Imm

3

P3

P

P31

R

三方

晶系

32

3m

P3112

P3c1

Pm1

P65

P312

P3m1

P1m

P6

P

P321

P31m

P

1c

P61

P3121

P3212

P3221

P31c

R3m

R3c

Ia3

m

6

Pc1

R m

R c

P62

P64

P63

6/m

P63/m

P6122

P6cc

P6522

P63cm

P6/m

P622

P6mm

六方

晶系

622

6mm

P6222

P6422

P6322

P63mc

I213

Im3

Pa3

m2

6/mmm

23

P m2

P c2

P

2m

P

2c

P6/mmm

P23

Pm3

P432

P6/mcc

F23

Pn3

P4232

P63/mcm

I23

Fm3

F432

P63/mmc

P213

Fd3

m

432

F4132

I432

P4332

P4132

I4132

I

3d

立方

晶系

3m

P

3m

F

3m

I3m

P3n

F 3c

Fd

c

m m

Pm m

Pn n

Pmn

Pn m

Fm m

Fm c

Fd m

Ia d

1. The product was a mixture of unidentified dark blue microcrystals and brown

crystals

2. The mixture was then heated at 180°C for four days in a Teflon-coated steel

autoclave. The product, consisting of clear single crystals of MAP-RHO1 and an

unidentified white powder, was recovered by filtration and washed with

deionized water.

3. Attempts to isolate this compound by removal of solvent (0

OC, l0-2 mmHg)

resulted in decomposition to unidentifiable products.

4. Strong hydrogen bonding occurs only when the hydrogen atom is collinear with

the bonded atoms.

5. The hydrogen atom is located closer to one atom or the other.

6. Here the substitutional hydrogen atom located in a surface vacancy or the

hydrogen at an interstitial position of surface is a half-confined atom which is

only weakly bound.

7. The ethylenediamine ligand was chosen for its ability to chelate copper ions

leaving two free positions translocated so that {Cu(en) 2 } 2+ can act as a linking

agent between two POMs, via bridging oxygen atoms [4] and (c. We have

studied the influence of the initial pH .

8.

The ions or molecules surrounding the central atom are called ligands. Ligands

are generally bound to the central atom by a coordinate covalent bond (donating

electrons from a lone electron pair into an empty metal orbital), and are said to

be coordinated to the atom. There are also organic ligands such

as alkenes whose pi bonds can coordinate to empty metal orbitals. An example

is ethene in the complex known as Zeise's salt, K+[PtCl3(C2H4)]−.

9.

One nickel ion is coordinated by three ligands (with low occupancy of a fourth ligand) and

the second is coordinated by five ligands.

10. The eleven tungsten centers of compound 1 have a distorted octahedral geometry.

11.

All the tungsten atoms have distorted octahedral geometry

the +6 oxidation state.

and

the bond-valence sum (BVS) model25 clearly indicates that all the tungsten atoms are in

12.

13.

14.

15.

(1) dispersion of the negative charge over many atoms of the polyanion and

Anal. Calc. For

which is not thought of as being novel.

be thought of as和 be considered as 和 be seen as作为 “……被视为/被看作……"的语义上讲，总体上3个表达一样, 类似还有：as.../ as.../ as.../ look

on ...as...,etc.

ions exhibits distorted octahedral geometry, with a single TFA – anion (not shown)

occupying the sixth coordination site in all cases.

16.

The coordination sphere around each of the six equivalent Zn(II)

17.

The coordination geometry of this cadmium ion displays a distorted octahedron, with

His143 N 2 , His153 N 2 , Wat359 and Wat416 forming an octahedral base plane, and

His147 N 2 and Wat418 being located at the vertices

18.

In these polymers the metal atom exhibits

octahedral geometry but only two coordination sites of transition metal were used to

propagate the network.

19.

The coordination geometry of this cadmium ion displays a distorted octahedron, with

His143 N

2 , His153 N 2 , Wat359 and Wat416 forming an octahedral base plane, and His147 N 2

and

Wat418 being located at the vertices

20.

receives contributions from four nitrogen donors belonging to two en

molecules, two oxygen donors from two cluster anions

21.

The coordination geometry around copper ions can approximately be described as

orthorhombically distorted octahedral

22.

Each Mn(1) atom is bridged with three symmetry- equivalent Mn(1) atoms through

O(1) atoms and each O(1) atom is linked with three Mn(1) atoms.

23.

Each metal ion in the square is six-coordinate; four of the coordination sites are occupied

by the nitrogen atoms of two of bpy ligands and the remaining cis coordination sites

are occupied by cyanide-carbon or cyanide-nitrogen atoms.

24.

cube- 50 shaped blocks having

parallel front and rear faces, parallel side faces and parallel upper and lower faces.

25.

the two molecules shown in cyan (!) and red (//) are related by a crystallographic

two-fold axis, perpendicular to the plane, likewise red (Hi) and ...

26. with its apex pointing in the direction of flow

27. The 690 (675) em -1 loss with a relatively strong intensity is ascribed to the SiC

symmetric stretching vibration, because the SiC stretching vibrations of organa-silicon

compounds are observed between -600 and 800 cm "!

28. The 1100–700 cm−1 range shows the As–O stretching modes of the (AsO3OH)2− and

(As2O7)4− groups. As already mentioned, the complexity of the crystal structure does not

allow to be more specific. The strong and sharp band in infrared and the weak one in

Raman spectra around 909 cm−1 could be attributed to the antisymmetric bridge

stretching vibration,

νas (As–O–As) of pyroarsenate groups [27]. The most intense

Raman bands around 876 cm−1 (very weak in IR) and 857 cm−1 correspond to the

symmetric stretching vibrations of (AsO3OH)2− and (As2O7)4− groups, respectively.

29.

Compound 2 has been synthesized with the same procedure with

Pb(OAc)2

.3H2O

30.

The geometry around Cu(1) has the square pyramidal coordination with 3NO donor

atoms in the basal plane and water oxygen atom at the apical position.

31. Each dca ligand adopting

the end-to-end coordination mode is μ-bonded to two MnII ions with an Mn···Mn separ-

32.

The two Cys S atoms bind to the copper ions in a distorted

square planar fashion, each S interacting with both copper ions. ..

33.

The vibrational results strongly suggest that methionine sulfur is

bound to copper in the proteins.

34.

35.

36.

37.

38.

and Nd was bonded to the COO- group of EAA.

the electrons are inter-shared between the different atoms.

The central atom or ion, together with all ligands comprise the coordination sphere.

is the neutral [Cu(bpca)(dca)(H 2 O)] complex in which the three bpca nitrogen atoms

and a terminal dca nitrogen bind to copper in equatorial positions

The XPS estimations obtained on the valence state values are in reasonable agreement with those calculated

from bond valence sum calculations of compounds 1-3.

39.

40.

41.

42.

43.

44.

45.

46.

47.

48.

Both Sn atoms exist in distorted octa- hedral geometries, each defined by two cis-CH .

The CuI

ion

is coordinated in a tetrahedral configuration

the ligand coordinates only via the phosphorus atom

half the dca ligands coordinate directly (through all three nitrogen atoms) to three Mn

atoms

W spectroscopic data of solutions of PCs in dimethyl sulfoxide were obtained with a

Beckmann DU-7 W-Vis spectrophotometer

The UV-vis-near I R spectra were recorded in N,N-di- methylformamide

(DMF) solution by using a Perkin-Elmer

the Sn atom exists in a distorted tetragonal geometry in which the basal plane

is defined by four S atoms and the axial positions are occupied by two butyl substituents

The same procedure was carried out with 2 ml of plant extract (10 g/l) instead of rutin

determinations were carried out in duplicates.

] the same procedure was carried out in the absence of ex- tracellular Na, with choline

used in place of Na,

Fe1 (Fe1A) with NO5 donor set, including one N atom together with three O

atoms from two L3-

ligands and two carboxylic-O atoms from two PhCO2-

groups

49.

The coordination sphere of Dy1 is completed by two nitrogen atoms (N1 and N7*),

two ... N4 and N5) from a planar pentadentate dihydrazone uni

50.

However, the

bond-valence sum calculated for Bi 3+ shows a 32% deficiency from its

ideal value of 3.0.

51.

The bond valence sums of oxygens in the polyanion are listed in Table 4, and fall

within the range 1.59-2.03 except for O(11), O(12), O(39), and O(40). The bridging

atoms, O(11) and O(12), have BVS values of 1.19 and 1.32, and are therefore

presumed to be hydroxo groups. T

52.

Copper(II) ions display a square-pyramidal coordination geometry (τ = 0.06) for the N 2

OCl 2 donor set, where the basal coordination sites are occupied by one of the bridging

chlorine atoms

and the three donor atoms of the tridentate ligand and the apical site is occupied by

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