crysto book

Table: crystal systems and their examples: system unit cell dimensions lattice examplesTriclinicMonocinicRhomboheral/trigonalHexagonalOrthorhombicTetragonalCubic

a≠b≠c α≠β≠γ≠900

a≠b≠c α=γ=900; β≠900

a=b=c α=β=γ≠900

a=b≠c α=β=900;γ=1200

a≠b≠c α=β=γ=900

a=b≠c α=β=γ=900

a=b=c α=β=γ=900

PP,CR(P)PP,F,I,C(A,B)P,IP,F,I

Pred,K2S2O8,turquoiseβS,Se,As4S4,KNO2,feldsparHg,Sb,rubyZn,Co,NiAs,berylI,Ga,Fe3C,topazIn,TiO2,zirconPo,Au,Mo,NaCl,diamond

Table: Symmetry elements in crystal systems:system Symmetry elements ZTriclinicMonoclinicRhombohedral/trigonalHexagonalOrthorhombicTetragonalCubic

1, -1m, 2, 2/m3, -3, 3m, -3m, 326, 6/m, -6, 6m, -6m, 62, 62mmm2, 222, mmm, 4, 4/m,-4, 4m, -4m, 42, 42m23, m3, -43m, 432, m3m

1,22, 2, 4

4, 4, 8

Gas liquid and solid are the phyical states of matter, which exist at ordinary temperature and pressure. Stability of any sate depends upon a) interatomic/inter molecular forces, b) the forms of energy possesed by these atoms /molecules.

Wavelengths* of different Targets Target

Z Kβ1 Kα1 Kα2 Kᾱ Abs.Edge

β-filter

CrMnFeCoNiCuZnMoRhPdAg

2425262728293042454647

2.084801.910161.756531.620751.500081.392171.295200.632250.545590.520520.49701

2.289622.101741.935971.788901.657831.540501.435100.709260.613200.585450.55941

2.293512.105701.939911.792791.661681.544341.438940.713540.617620.589820.56381

2.290922.103061.937281.790211.591131.541781.436380.710690.614670.586910.56083

2.07011.89541.74291.60721.46891.3802 1.28310.61970.53410.50900.4855

VCr MnFeCoNiCuZrRuRh or RuPd or Rh

Note:- Kᾱ = 2Kα1 + 1Kα2 * wavelengths are expressed in Å

Madelung Constants(M.C.)

Compd. C.N. M.C. Compd. C.N. M.C.

NaClCsClCaF2(Fluorite)TiO2(Rutile)CdCl2

α-quartzPdF3

6:68:88:46:3

1.747561,762672,519392.4082.4454.4038.860

ZnS(Zn.blende)ZnS(Wurtzite)Al2O3(Corundum)ZnS(sphalerite)CdI2

Cu2OReO3

4:44:46:46:4

1.638061.641324.17191.6382.19154.4438.962

YF3

Y2O3

La2O3

8.89925.1024.18

LaF3

Al2O3

9.11124.24

Hermann Mauguin symbols of 32 Point Groups

Full Short Full Short Full Short

1īm22/mmm22222/m2/m2/m44/m

1īm22/mmm22mmm44/m

2m4mm4224/m2/m2/m33m322/m-66

m4m424/mmm33m32i m-66

6/m-6m26mm6226/m2/m2/m232/m 3m4324/m32/m

6/m-6m6m626/mm23m -43m43m3m

Point group equivalence:[m ≡ -2 ≡ 1/m];[-1m ≡ 2/m];[12≡2][1/mm ≡ 2m ≡ mm];[-2m ≡ 2m];[22≡222];[2/mm≡mmm];[3/m≡-6] [3/mm ≡-6m];[4m≡4mm];[m ≡2m];[4/mm ≡4/mmm];[6m≡ 6mm];[-6m≡-62m];[6/mm≡ 6/mmm];[-23≡ 2/m3];[2/m3≡ m3];[2m3 ≡ 3m]; [432≡ 43];[4/m3m≡ m3m]

Hermann Mauguin symbols of 32 Point Groups in crystal systems

Crystal Systems Laue Groups Point Groups Space

groups

Triclinic -1 or ī (2) 1, or -1 or ī 2

Monoclinic 2/m (3) 2,m,2/m 13

Orthorhombic mmm (3) 222,mm2,mmm 59

Tetragonal 4/m ,4/mm (7) 4, ,4/m,422,4mm, 2m,4/mmm 25

Hexagonal 6/m,6/mmm (7) 6,-6,6/m,622,6mm,-62m,6/mmm 68

Trigonal/Rhombohedral , m (5) 3,,32,3m, m 27

Cubic m3,m3m (5) 23,m3,432, 3m,m3m 36

Total 7 11 32 230

Radii of elements(3) with cubic primitive lattice

Element/Z

At.No.

a (Ǻ) ionic R

v.d.W.R.

at.R.

cov.R.

O/8F/9Po/84

8984

6.836.673.352

1.331.42.3

1.52 0.6 0.66

Radii of elements(17) with cubic body centered (bcc) lattice at.r = (√3/4)a or at.r = 0.433 a

Element at.no. a(Ǻ) ionic r. at.r.cal v.d.W. at.r.exp Cov.r.

LiNaKVα-CrMnγ-FeRbNbMoCsBaEuTaWFrRa

311192324252637414255566373748788

3.50924.29065.3283.0282.88468.91393.5915.703.0063.14696.145.0194.5783.30263.165n.d.5.15

0.761.021.380.590.520.460.6451.520.690.651.671.351.170.640.621.81.43

1.51951.8582.3041.3111.2491.611.5552.4681.3021.902.982.532.312.01.93

1.822.272.75n.d.2.443.032.623.03ndnd3.432.68ndndnd3.482.83

1.521.8582.2721.3111.2491.3671.2412.4751.461.392.652.221.801.461.392.1743.5

1.341.541.961.251.271.391.252.111.371.452.251.981.981.381.462.62.21

Radii of elements(24) with cubic face centered lattice at.R. = (√2/4) a = 0.35355 a

Element at.no. a(Ǻ) Ionic at.rcal at.rexpv.d.W.

cov.r

NeAlArCaScCrMnNiCuSrRhPdAgXeLaCeYbIrPtAuPbRnAcThPuAm

1013182021242528293845464754575870777879828689909495

4.4294.04955.2565.58843.5243.6154.0863.9244.0794.95

1.121.431.251.281.441.391.441.75

0.380.5350.990.7450.520.461.120.680.861.261.0611.0340.8580.6250.6250.851.191.1190.9720.8870.982

1.94 1.542.051.88n.d.1.631.401.722.161.751.662,021.96

0.691.911.74

Radii of elements with cubic primitive lattice

Element At.No. Ionic/ charge

Covalent v.d.Waals

F

Cl

Br

I

O

9

17

35

53

8

1.33/1-

0.08/7+

1.81/1-

0.34/5+

0.27/7+

1.96/1-

0.47/5+

0.39/7+

2.19/1-

0.62/5+

0.50/7+

1.40/2-

0.10/6+

1.85/2-

0.37/4+

0.30/6+

1.47

1.75

1.85

1.98

1.52

S

Se

Te

N

P

Mn

Po

16

34

52

7

15

25

84

1.96/2-

0.78/3+

0.50/4+

0.42/6+

2.18/2-0.70/4+0.56/6+0.16/3+0.13/5+0.44/3+0.35/5+

2.20/1-

1.40/2-

1.84/2-

1.98/2-

2.21/2-

1.71/3-12/3-0.80.660.60

1.80

1.90

2.06

1.55

1.80

0.46

0.67

Radii of elements(37) with hexagonl lattice

Element at.No a,c/Z ionic R.

at.R.exp at.R.cal vdW

BeMgTiCoZnZrCd

4122227304048

2.2856;3.5832/3.2094;5.2105/2.9506;4.6788/2,507;4.069/2.6649;4.9468/3.2315;5.1477/2.9788;5.6167/

1.131.61.471.251.331.601.49

0.911.38

1.46

Radii of elements() with tetragonl latticeRadii of elements() with orthorhombic latticeRadii of elements() with rhombohedral/trigonal latticeRadii of elements() with monoclinic latticeCalculation of Density and other parameters for cubic primitive elements (3) [V=a 3 ]

At. At.wt. a(Ǻ)/Z t0C V ρexp ρcal

β-F

βMn

γ-O

Pwhite

α-Po

18.998

54.938

15.9994

30.974

209.98

6.67/16

6.3116/10

6.83/24

7.17/12

3.34/1

85K

-225

20

296.741

251.43

318.612

368.602

37.260

1.516

3.16

2.0

1.82

9.32

1.700

3.62

2.001

1.674

9.355

Calculation of Density and other parameters for f.c.c. elements (28) V=a 3

at. at.wt. a/Z t0C V ρexp ρcal

Ac

Ag

α-Al

β-Am

227.03

107.87

26.982

241.06

5.311/4

4.0857/4

4.04959/4

4.894/4

20

25

25

>769/5

149.806

68.202

66.41

117.217

10.066

10.49

2.698

13.69

10.062

10.502

2.698

13.655

α-Ar

Au

β-Bk

C(dia

α-Ca

αCe

γ-Ce

βCf

βCm

α-Co

βCr?

βCs

39.948

196.967

249.08

12.011

40.078

140.116

140.116

252.08

244.06

58.9332

51.996

132.91

5.3109/4

4.0786/4

4.997

3.5669/8

5.5884/4

4.85/4

5.161/4

5.473 nd

4.382

3.5447/4

3.68/4

6.465/4

-233

25

>977

20

77 K

25

20

RT

25/2.6

149.797

67.847

124.775

45.3809

174.527

114.084

137.468

163.937

84.143

44.663

49.836

270.213

1.656

19.302

13.25

3.51

1.55

8.16

6.771

10.170

13.52

8.70

7.20

1.87

1.771

19.277

13.255

3.5148

1.525

8.155

6.768

10.21

11.865

8.76

6.928

3.266

Cs

β’Cs

Cu

βEs

γ-Fe

αGe

αH

βHe

Ir

Kr

β-La

β‘La

132.91

132.91

63.546

252.08

55.845

72.61

1.0079

4.0026

192.217

83.798

138.91

138.91

5.984/2

5.8/2

3.6146/4

5.75/4

3.6467/4

5.6574/8

5.338/8

4.24

3.8392/4

5.796/4

5.303/4

5.17

25/4

25/4.17

20

1100

25

25

-157

310

214.277

195.112

47.226

178.393

48.495

181.072

152.102

76.225

56.588

194.709

149.13

138.188

1.87

1.93

8.92

8.84

7.648

5.324

0.088

0.18#

22.5

2.823

6.186

6.17#

2.059

2.262

8.935

9.38

7.646

5.325

0.088

0.349

22.555

2.858

6.185

6.675

γLi

γMn

γNd

Ne

Ni

α-Pb

Pd

γPr

Pt

δ-Pu

Rh

Rn

6.941

54.938

144.24

20.1797

58.6934

207.2

106.42

140.91

195.083

239.05

102.905

222.02

4.388

3.863/4

4.80

4.462/4

3.5238/4

4.9502/4

3.8903/4

4.88/4

3.9236/4

4.6371/4

3.8035/4

No data

1100

-248

25

20

25

25

>320/atm

25

-61.7

84.489

57.647

110.592

88.836

43.7556

121.302

58.8775

116.214

60.421

99.7102

55.0238

No data

0.53#

7.43#

7.0#

1.444

8.902

11.35

12.02

6.77#

21.45

16.254

12.41

4.4

3.786

6.328

8.660

1.5083

8.907

11.342

12.002

8.051

21.455

15.92

12.418

β-Sc?

αSi

α-Sn

α-Sr

α-Th

γTl

Xe

β-Yb

44.956

28.086

118.71

87.62

232.038

204.38

131.293

173.04

4.541/4

5.4306/8

6.4892/8

6.0849/4

5.0843/4

4.778/4

6.309/4

5.4848/4

320

r.t./atm

<18

20

20

25/3.67

58K

798

93.6385

160.156

273.258

225.300

131.4297

109.078

251.120

164.657

3.00

2.33#

5.75

2.54

11.72

11.85#

3.54

6.977

3.188

2.3289

5.769

2.5823

11.723

12.441

3.472

6.978

Calculation of density and other parameters for b.c.c. elements(36) V=a 3

At. At.wt a(Ǻ)/Z=2 t0C V ρexp ρcal

γ-Am

α-Ba

241.06

137.33

?

5.025

>1077

20 126.884

13.67

3.594 3.593

βBe?

β-Ca

δ-Ce

α-Cr

α-Cs

βDy

αEu

α-Fe

β-Fe?

δ-Fe

Fr

βHf

9.0122

40.078

140.115

51.9961

132.905

162.503

151.96

55.845

55.845

55.845

223.02

178.49

2.5515/2

4.48

4.12

2.8846

6.141

4.03

4.5827

2.86645

2.86645

2.9346

No data

3.610

>12700

500

730

20

20

1381K

20

20

800

1425

20

1743

16.611

89.915

69.935

24.0025

231.47

65.451

96.198

23.5535

23.5535

25.272

No data

47.046

1.848?

1.55

6.67

7.19

1.873

8.54#

5.243

7.875

7.875

7.357

1.87

11.4

1.801

1.584

6.652

7.192

1.906

8.243

5.245

7.872

7.872

7.336

12.6

βGd

K

K

γ-La

β-Li

α-Mn

δMn

Mo

β-Na

Nb

β-Nd

γ-Np

157.25

39.098

39.098

138.906

6.9417

54.938

54.938

95.94

22.9898

92.906

144.24

237.048

4.06

5.334

5.247

4.26

3.5093

8.9139/58

3.081

3.1468

4.2906

3.2986

4.13

3.518/2

1265

20

78K

868

20

25

1140

20

25

20

868

>600

66.923

151.760

144.455

77.309

43.2436

708.277

29.247

31.1607

78.9867

35.8913

70.445

43.54

7.87

0.862

0.86

5.98

0.534

7.44

7.43#

10.22

0.967

8.57

6.80

18.0

7.801

0.855

0.899

5.965

0.533

7.468

6.236

10.22

0.966

8.594

6.798

18.075

β-Pm

β-Pr

ε-Pu

Ra

αRb

β-Sc

γSi

β-Sm?

β-Sr

Ta

βTb

β-Th

146.92

140.908

239.05

226.025

85.468

44.956

28.086

150.36

87.62

180.95

158.93

232.038

10.99/36

4.13

3.6361/2

5.148

5.705

3.752

6.636/16

4.07

4.85

3.306

4.07

4.11

890

798

<483

20

75K

1350

917

614

25

1289

1450

1327.373

70.445

48.0737

136.591

185.681

52.819

292.226

67.419

114.084

36.133

67.419

69.427

6.77

6.64

16.856

5.0

1.532

3.73

2.3296

7.40

2.6

16.654

8.267

11.5

6.615

6.641

16.509

5.494

1.528

2.826

2.553

7.404

2.55

16.626

7.826

11.096

β-Ti

β-Tl

γ-U

V

W

β-Y

γ-Yb

β-Zr

47.88

204.383

238.029

50.9415

183.85

88.906

173.04

91.224

3.307

3.882

3.524/2

3.0278

3.1652

4.11

4.44

3.609

900

25

805

19

25

1478

763

>862

36.166

58.501

43.763/2

27.7575

31.7111

69.427

87.528

47.438

4.43

11.85

18.06

6.1

19.254

4.405

6.54

6.49

4.395

11.599

18. 058

6.093

19.248

4.252

6.564

6.443

Calculation of Density and other parameters of elements of orthorhombic system (7) [V=abc]

At. At.wt. a,b,c/Z t0C V ρexp ρcal

γAm

δAm

241.06

241.06

10.115,5.67,3.116/6

3.063,5.968,5.169/8

25/10

25/>15

178.709

94.489

13.6

4.05

13.435

3.953

Am

γB

Br

α'Ce

Cl

Cs

Cs

F

Ga

I

αNp

Pblack

241.06

10.811

79.904

140.12

35.453

132.91

132.91

18.9984

69.723

253.81

237.05

30.974

5.093,4.679,3.028/2

5.054,5.612,6.966/28

6.737;4.548;8.761/8

3.0143,5.8935,5.1603/3

6.24;4.48;8.26/8

9.2718,13.3013,34.2025/84

11.205,6.626,6.595/4

5.50,3.28,7.28/8

4.5186;7.657;4.526/8

7.2647;4.786;9.791/8

4.723;4.887;6.663/8

3.314,4.376,10.4877/8

25/16

-150

113K

25/4.3

25/10

20

20

20

72.158

197.577

268.436

91.672

230.91

4218.091

489.641

131.331

156.588

340.394

153.791

152.093

13.6

2.544

2.03

6.8

5.907

1.90#

1.90#

1.696

4.93

20.25

20.487

2.69

5.546

2.543

2.04

7.612

5.913

2.6468

1.802

1.921

4.949

20.47

20.469

2.704

γPu

α16S8

2S12

4S18

4S20

αU

239.05

32.066

32.066

32.066

32.066

238.029

3.1587,5.7682,10.162/8

10.465;12.866;24.486/128

4.73,9.14,14.7474/24

21.152,11.441,7.581/72

18.58,13.181,8.6/80

2.8548;5.8589;4.9576/4

>215

25

20

185.152

3296.861

637.563

1834.602

2106.166

82.921

17.506

2.06

2.036

2.09

2.018

19.067

17.146

2.067

2.004

2.089

2.0219

19.060

Calculation of Density and other parameters of elements of hexagonal system (43) [V=0.866a 2 c]

At. At.wt. a,c/Z t0C V ρexp ρcal

β-Al

α-Am

As

βBa

26.982

241.06

74.922

137.33

2.693,4.398/2

3.4681,11.241/4

3.76,10.548/6

3.901,6.154/2

25/>20.5

20/atm

25/>5.33

27.621

117.069

129.141

81.101

2.70

13.67

5.778

3.76#

3.243

13.673

5.778

5.622

αBe

Bi

αBk

Cbuck

γ-Ca

Cd

βCe

αCf

αCm

εCo

γ-Cr

Cs?

9.012

208.98

249.08

12.01

40.0784

112.41

140.12

252.08

244.06

58.933

51.996

132.91

2.2855,3.5832/2

4.5495;11.8623/6

3.416,11.069/4

2.4612,6.7078/4

3.98,6.52/2

2.9794,5.6186/2

3.681,11.857/4

3.390,11.015/4

3.496,11.331/4

2.5071,4.0686/2

2.722,4.427/2

3.011,4.855/2

25

25

20

450

20

20

25/72

16.209

212.615

111.857

35.1878

89.44

43.192

139.131

109.623

119.93

22.1466

28.4056

38.118

1.848

9.747

14.78

1.848

1.55

8.642

6.893

15.1

13.51

8.832

8.56

1.90#

1.846

9.79

14.786

1.846

1.488

8.641

6.687

15.269

13.513

8.835

9.061

11.576

αDy

αEr

εFe

αGd

H

3He?

4He

α-Hf

αHo

In

αLa

αLi

162.5

167.26

55.845

157.25

1.00794

4.0026

4.0026

178.49

164.93

114.82

138.91

6.941

3.591,5.6475/2

3.5588,5.5874/2

2.485,3.99/2

3.6336,5.781/2

3.776;6.162/2

3.501;5.721/2

3.47,5.54/4

3.1946,5.0511/2

3.5778,5.6178/2

3.2517,4.9459/2

3.774,12.171/4

3.111,5.093/2

20

25

>13GPa

25

11K

3.48/.163

3.95/.129

25

25

25

78K

63.0674

61.2823

21.3375

66.099

76.0858

60.726

57.768

44.6404

62.2358

45.288

149.658

42.687

8.55

9.066

7.9004

7.901

0.076

0.126

0.468

13.276

8.795

7.286

6.145

0.53

7.886

8.689

8.6892

7.8983

0.088

0.207

0.460

13.275

8.7983

8.417

6.163

0.5398

αLu

Mg

N

αNa

αNd

Ni

Os

αPm

αPr

Re

Ru

Sb

174.97

24.305

14.0067

22.990

144.24

58.693

190.2

146.92

140.91

186.23

101.07

121.75

3.5031,5.5509/2

3.2094,5.2103/2

4.02;6.601/4

3.767,6.154/2

3.6582;11.7966/4

2.65,4.33/2

2.7343;4.32/2

3.6721;11.8326/4

3.6725;11.835/4

2.7609;4.457/2

2.7058;4.2811/2

4.307;11.273/6

25

20

21K

5K

20

20

25

25

20

20

25

25

58.9911

46.476

92.3804

68.3545

136.721

26.333

27.9801

138.174

138.232

29.4235

27.1434

181.095

9.84

1.738

1.026

0.971

7.007

8.90

22.59

7.22

6.773

21.02

12.37

6.697

9.8473

1.7362

1.007

1.117

7.0052

7.400

22.576

7.060

6.769

21.009

12.362

6.696

αSc

α-Se

Se

βSi

Si

βSm

δSm

β-Sr

α'Tb

Tc

Te

αTi

44.956

78.96

78.96

28.086

28.086

150.36

150.36

87.62

158.93

98.906

127.603

47.867

3.3049;5.273/2

4.3656;4.959/3

3.308,5.2653/1

4.686,2.585/4

3.8,6.28/4

3.663,5.845/2

3.618,11.66/2

4.32,7.06/2

3.601;5.6936/2

2.743;4.40/2

4.4565,5.9268/3

2.9503;4.6831/2

25

20

1000

25/1atm

25/>16

450

25/4GPa

248

248

25

25

25

49.9999

81.8465

49.897

49.157

78.532

67.917

132.176

114.101

63.9368

28.6696

101.9356

35.3007

2.989

4.79

2.992

2.33#

2.3

2.6/75

7.5?

2.6

8.229

11.5

6.232

4.507

2.9851

4.8044

2.627

3.794

2.375

2.549

7.350

2.549

8.2526

11.454

6.234

4.502

αTl

αTm

βTm

αY

αYb

Zn

αZr

204.38

168.93

168.93

88.905

173.04

65.39

91.224

3.4566;5.5248/2

3.5375;5.5546/2

3.327,23.48/8

3.6474;5.7306/2

3.8799,6.3859/2

2.6646;4.9469/2

3.2321;5.1477/2

18

20

20/>9GPa

25

25

25

25

57.1653

60.1954

225.072

66.0214

83.249

30.4169

46.5694

11.85

9.35

9.3#

4.469

7.0

7.133

6.506

11.87

9.317

9.967

4.498

6.901

7.137

6.5035

Calculation of Density and other parameters of elements of rhombohedral/trigonal system(7)[V=a 3( 1- 3cos 2 α +2cos 3 α )1/2 ]

At. At.wt. a;α/Z t0C V ρexp ρcal

As 74.922 4.1318;54.1670/2 25 36.589 5.78 5.772

αB

βB

αBi

Hg

β-Po?

Sb

Sm

10.811

10.811

208.98

200.59

209.98

121.76

150.36

5.057;58.0670/12

10.12,65.4670/108

4.5494;57.23670/1.5

3.005;70.520/1

3.36;98.2170/1

4.30841;57.10830/1.5

8.996;23.2130/2.5

20

31

25

20

87.397

819.995

53.281

24.277

36.638

45.096

81.4309

2.447

2.35

9.807

13.546

9.3#

6.685

7.52

2.464

2.364

9.7663

13.716

5.731

6.723

7.6629

Calculation of Density and other parameters for elements of monoclinic system (2) [V=abcsinβ]

At. At.wt. a;b;c;β/Z t0C V ρexp ρcal

Am? 241.06 3.025,11.887,2.83,106.110/2 97.7655 13.7# 8.186

Bi

Ce ?

α''Ce

F

O

Pviolet

αPu

βPu

β4S8

Smo

Se

208.98

140.12

140.12

18.998

15.9994

30.974

239.05

239.05

32.066

32.066

78.96

6.674,6.117,3.304,110.30/

3.135,3.173,4.798,91.920/4

5.813,3.145,5.612,113.100/4

5.5;3.28;7.28;900/8

5.403;3.429;5.086;132.530/4

9.21,9.15,22.6,106.10/84

6.1835;4.8224;10.973;101.790/16

9.284,10.463,7.859,92.130/34

10.778,10.844,10.924,95.80/32

8.442,13.0259,9.356,124.980/32

9.054;9.083;11.601;90.810/32

25

25

150

20

126.507

47.701

94.372

131.331

69.439

1829.838

319.96

762.884

1270.224

845.116

953.942

9.808#

6.67#

6.67#

1.7

1.495

2.36

20.262

17.553

1.96

2.19

4.809

10.969

19.542

9.859

1.921

1.53

2.360

20.255

17.685

1.341

2.016

4.397

Calculation of Density and other parameters for elements of tetragonal system(5)[V=a 2 c]

At. At.wt. a;c/Z t0C V ρexp ρcal

α'B

β'B

εCe

Cl2

Cs

In

βNp

Pa

δ'Pu

10.811

10.811

140.12

70.92

132.90543

114.82

237.05

231.036

239.05

8.75,5.06/50

10.12,14.14/192

2.92,4.84/

8.56;6.11/8

3.349,12.487/1

3.253;4.956/2

4.897,13.388/16

3.932;3.238/2

3.339,4.446/2

-185

25/8

20

313

20

>463

387.406

1448.14

41.268

447.702

140.052

52.444

321.052

50.06

49.568

2.28

2.36

6.757

2.03

1.873

7.31

19.379

15.322

16.0

2.316

2.379

5.636

2.104

1.573

7.269

19.611

15.32

16.011

βSn

γSn

Βu

118.69

118.69

238.03

5.832;3.1813/4

3.7,3.37/2

10.759,5.656/30

<18

>9

108.203

46.135

654.716

7.265

6.56

18.11

7.284

8.54#

18.105

Calculation of Density and other parameters for elements of triclinic system()[V=abc(1-cos 2 α-cos 2 β-cos 2 γ + 2(cosαxcosβxcosγ) 1/2 ]

At. At.wt. u.c.d./Z t0C V ρexp ρcal

Pred 30.974 11.45,5.503,11.261,71.840,90.370,71.560/28

635.228 2.16 2.26

Distribution of crystal structures of elements

Sc F.c.c.

B.c.c.

Tet.

Ortho.

Hex.

Rho. monoc. unknown

3 28 36 5 7 43 7 2 19

Examples of mineral elements in primitive cubic crystal system

Element At.wt. a/Z V ρexp Ρcal

Examples of mineral elements in bcc crystal system

Element At.wt. a/Z V ρexp Ρcal

ChromiumCrIronFeTantalumTa

51.996

55.85

180.95

2.8839/2

2.874/2

3.3058/2

23.99

23.74

36.13

7.2

7.6

16.29

7.2

7.81

16.63

Examples of mineral elements in fcc system

At. At.wt. a/Z V ρexp Ρcal

AluminumAlCopperCuDiamondCGoldAuLeadPbNickelNiSiliconSiSilverAgPlatimunPt

26.98

63.55

12.01

196.97

207.20

58.69

28.09

107.87

195.08

4.04/4

3.615/4

3.5668/8

4.0786/4

4.9505/4

3.5238/4

5.431/8

4.0862/4

3.9231/4

65.94

47.24

45.38

67.85

121.32

43.76

160.19

68.23

60.38

2.7

8.94

3.51

17.64

11.37

8.0

2.32

10.5

18

2.72

8.93

3.52

19.28

11.34

8.91

2.33

10.5

21.46

Examples of mineral elements in tetragonal crystal system

Element At.wt. a,c/Z V ρexp Ρcal

FulleriteC60

720.66 14.22;13.56/4 2741.95 1.95 1.75

IndiumInTinSn

114.82

118.71

3.25;4.95/2

5.831;3.182/4

52.28

108.19

7.31

7.31

7.29

7.29

Examples of mineral elements in orthogonal crystal system

Element At.wt. u.c.d./Z V ρexp Ρcal

ArsenolampriteAsPararsenolampriteAsSulpherS8

74.92

76.51

256.53

3.63;4.45;10.96/8

3.3633;10.196;10.314/18

10.45;12.845;24.46/16

177.04

353.69

3283.27

5.44

5.94

2.06

5.62

6.47

2.08

Examples of mineral elements in hexagonal system

At. At.wt. a;c/Z V ρexp ρcal

ChaoiteCCadmiumCdLonsdaleiteC

1201

112.41

12.01

8.948;14.078/168

2.979;5.617/2

2.52;4.12/4

976.17

43.17

22.66

3.38

8.6

3.41

3.43

8.65

3.52

RheniumReTitaniumTiZincZn

186.21

47.88

65.39

2.76;4.458

2.95;4.69/2

2.6591;4.9353/2

29.41

35.35

30.22

21.03

4.4

7.05

21.03

4.5

7.19

Examples of mineral elements in rhombohedral/trigonal crystal system


AntimonySbArsenicAsSeleniumSeTelluriumTe

121.75

74.92

78.96

127.60

4.299;11.25/6

3.768;10.574/6

4.366;4.954/3

4.447;5.915/3

180.06

130.01

81.78

101.30

6.66

5.7

4.81

6.2

6.74

5.74

4.81

6.27

Examples of mineral elements in monoclinic crystal system


Radii of elements of SC and unknown (UK) crystal systems:

Element

Atomic Ionic Covalent v.d.Waals Crystal

AtFrMnPmPoRnSi(dia)

1.273.481.612.051.351.201.11

1.27unkn1.401.851.901.201.10

1.52.601.39unknunkn1.451.11

2.023.482.052.432.02.202.10

0.761.940.811.281.08unkn0.40

Radii of elements of bcc crystal system:

Element Atomic Ionic covalent v.d.waals crystal

BaCrCsEu

2.531.662.982.31

2.151.402.601.85

1.981.272.25unkn

2.681.27n dn d

1.490.761.811.31

FeKLiMoNaNbRaRbTaVW

1.562.431.671.901.901.98unkn2.652.001.711.93

1.402.201.451.451.801.452.152.351.451.351.35

1.251.951.341.451.541.37unkn2.111.381.251.46

2.02.751.82n d2.27n dn dn dn dn dn d

0.691.520.900.791.160.781.621.660.780.680.74

Radii of elements of fcc Crystal system:

Element Atomic ionic Covalent v.d.Waals crystal

AcAgAlArAuCaCuGeHeIrKrNe

1.951.651.180.711.741.941.451.250.311.800.880.38

1.951.601.250.711.351,801.351.250.311.350.880.38

2.011.531.180.971.441.741.381.220.321.371.100.69

2.01.722.11.881.662.41.402.11.402.02.021.54

1.261.290.53unkn1.511.140.710.53unkn0.77unknunkn

NiPbPdPtRhSrThXeYb

1.491.541.691.771.732.191.801.082.22

1.351.801.401.351.352.001.801.081.75

1.211.471.311.281.351.921.651.301.74

1.632.021.631.752.052.552.402.152.28

0.701.490.780.740.811.321.090.621.13

Radii of elements of Tetragonal crystal system:

element Atomic ionic covalent v.d.Waals Crystal

InPaSn

1.561.801.45

1.551.801.45

1.44unkn1.41

1.93n d2.17

0.941.090.69

Radii of elements of Orthorhombic crystal system:

element Atomic ionic covalent v.d.Waals crystal

BrClGa

0.940.791.36

1.151.001.30

1.140.991.26

1.851.751.87

1.821.670.76

INpSU

1.151.750.881.75

1.401.751.001.75

1.33unkn1.02unkn

1.98n d1.801.86

2.06unkn0.430.87

Radii of elements of Hexagonal crystal system:

element Atomic ionic covalent v.d.Waals crystal

AmBeCCdCeCmCoDyErGdHHfHoLaLuMgNNd

1.751.120.671.611.85unkn1.522.282.262.330.532.082.261.952.171.450.562.06

1.751.050.701.551.85unkn1.351.751.751.800.251.551.751.951.751.500.651.85

unkn0.900.771.48unknunkn1.26unknunknunkn0.371.50unkn1.691.601.300.75unkn

n d n d1.701.58n dn dn dn dn dn d1.2n dn dn dn d1.731.55n d

1.120.410.290.921.151.110.541.051.031.080.10.851.041.361.000.860.301.30

OsPrReRuScTbTcTiTlTmYZnZr

1.852.471.881.781.842.251.831.761.562.252.121.422.05

1.301.851.351.301.601.751.351.401.901.751.851.351.55

1.28unkn1.591.261.44unkn1.561.361.48unkn1.621.311.48

n dn dn dn dn dn dn dn d1.96n dn d1.39n d

0.771.320.770.820.891.180.790.751.031.021.040.740.85

Radii of elements of Trigonal/Rhomohedral crystal system:

element Atomic Ionic covalent v.d.Waals Crystal

AsB(rhom)Hg(rhom)SbSmTe

1.140.871.711.332.381.23

1.150.851.501.451.851.40

1.190.821.491.38unkn1.35

1.85n d1.55n dn d2.06

0.720.250.830.901.101.11

Radii of elements of Monoclinic crystal system:

element Atomic Ionic covalent v.d.Waals crystal

BiFOPuSe

1.430.420.481.751.03

1.600.500.601.751.15

1.460.710.73unkn1.16

n d1.471.52n d1.90

1.171.191.211.000.56

Radii of elements of Triclinic crystal system:

Element Atomic Ionic covalent v.d.Waals Crystal

P 0.98 1.00 1.06 1.80 0.31

Examples of cubic compounds with unit cell edge length:

Comp. a(Ǻ) Comp. a(Ǻ) Comp. a(Ǻ)

FeS2

KClZnS

5.416.284.1

LiHMnOUO

4.084.434.92

NH4IAgBrMgO

7.245.774.20

SrTiO3 3.905 KBr 6.59 AgCl 5.55

Comp. a(Ǻ) Comp. a(Ǻ) Comp. a(Ǻ)

FeOTiCCdCl2

CeO2

Fe3O4

4.3074.3285

RbIPbSCaOMgSZnSThO2

MgAl2O4

7.335.92

MnSCuClZrO2

MgFe2O4

Calculation of density and other parameters of cubic compounds with NaCl type (f.c.c.) crystal lattice:

Comp. M.W. u.c.d. V ρexp ρcal

NaCl 58.44 5.6402 179.425 2.165 2.1627

ZnSPbSFeSeNiSbSMgOCaOSrOBaOTiOMnOFeOCoONiOCdOSnAsTiCUCMgSCaSSrSBaSMnSMgSeCaSeSrSeBaSeCaTeSrTeBaTeLiFLiCl

97.459239.267134.806212.5240.304456.0774103.62153.32663.866470.937471.84474.932674.6928128.41193.6159.89250.0456.37272.145119.687169.39787.005103.268119.041166.583216.293167.68215.223264.9325.93942.39

5.425.9365.415.914.2134.81055.1605.5394.1774.4454.3074.2604.17694.69535.72484.32854.9555.2005.69486.0206.3865.2245.4625.9246.2466.66.3566.667.04.03515.1396

159.22209.161158.34206.42574.778111.319137.388169.93972.87787.82479.89677.30972.872103.512187.62181.0984121.6553140.608184.687218.167260.427142.564162.95207.896243.672287.496256.774295.408343.065.7135.765

4.0907.604.726.853.583.354.705.724.955.375.7456.446.678.15

4.9313.632.682.593.74.253.994.23.574.385.134.874.8395.132.639052.64

4.0647.5965.6536.8363.5793.3455.0085.9915.8195.3635.9716.4366.8068.2376.8524.90413.6472.6622.5943.6434.3194.0524.2083.8024.5394.9954.3364.8085.1292.6222.637

LiBrLiILiHNaFNaBrNaINaHLaNNpN??PuNScNTiNUNZrNKFKClKBrKIRbFRbClRbBrRbIAgFAgClAgBrCsF

86.85133.857.94941.988102.894149.8923.998152.912251.057253.05758.96361.874252.037105.23158.096774.551119.9166.003104.466120.921165.372212.368126.868143.323187.774151.908

5.50136.004.0834.645.97726.4734.8905.29124.89794.9064.444.244.894.5375.3476.29316.59667.06555.65166.5816.8897.3424.925.5495.77466.014

166.493216.068.06799.897213.547271.217116.93148.137117.498118.08287.52876.225116.9393.391152.873249.226287.052352.719180.515285.02326.94395.77119.095170.861192.56217.516

2.073.464.0760.822.5583.213.671.396unkn14.43.65.414.42.481.9842.753.1233.123.5572.803.353.115.8525.566.4734.115

2.0733.4644.1150.7752.7913.1993.671.3636.854??14.234.4735.3914.3122.5231.9862.7733.1253.1253.8432.8173.3593.5647.073??5.576.4754.637

Examples of cubic compounds with ZnS (zinc blende) type (f.c.c.) crystal lattice:


CuFCuClγ –CuBrγ –CuIγ-AgIβ –MnSβ-MnSeBeSBeSeBeTeβ –ZnSZnSeZnTeβ –SiCβ-CdSCdSeCdTeHgSHgSeHgTeBNBPBasAlPAlAsAlSbGaPGaAsGaSb

82.54498.999142.586190.45234.7787.004133.89841.078287.975136.61597.459144.355192.99540.097144.477191.373240.013232.659279.555329.1824.81941.785585.73457.9552101.904148.742100.697144.645191.483

4.2555.4165.69056.0516.4955.605.884.86245.075.545.4065.6676.10264.3585.8186.0776.4815.85176.0856.4533.6164.5384.7775.4515.6626.13475.4485.65346.095

77.037158.868184.269221.555273.992175.616203.297114.961130.324170.031157.989181.995227.27182.768196.934224.423272.224200.376225.311268.71147.28193.453109.01161.968181.514230.877161.700180.688226.423

7.14.1454.715.675.6753.995.452.36unkn5.14.095.275.93.214.825.8166.28.18.38.13.452.95.222.853.724.264.1385.31765.614

7.1154.1385.1385.7085.68953.294.3732.3734.4825.3354.0965.2675.6393.2174.8715.6625.8547.7108.2398.1343.4862.9695.2222.3763.7284.2784.1355.3155.615

InPInAsInSb

145.794189.742236.58

5.8696.0586.4782

202.159222.325271.871

4.815.675.775

4.7895.6675.778

Examples of cubic compounds with bcc crystal lattice: V = a 3


Tl2O3

MgAl2O4

456.765142.27

10.5468/88.08/8

1173.173528.18

10.23.44

10.343.577

Examples of compounds of tetragonal crystal system: V = a 2 c

Comp. M.W. u.c.d./Z V ρexp ρcal

SnO2

TiO2

SnO2

MnO2

NH4BrTiO2(ruti)

150.70879.865150.70886.93697.942679.865

3.18;6.69/24.5937;2.9581/24.737;3.186/24.4;2.875.123;4.193/24.594;2.958/2

67.6562.42271.499655.563110.04662.428

6.954.24937.00965.12.4294.232

7.44.2486.9985.1952.9554.25

Examples of compounds of Orthorhombic Crystal Lattice:V=abc

Comp. M.W. u.c.d./Z V ρexp ρcal

CaSO4

Li2PdO2

CaCO3arag

AgNO3

KNO3

PbSO4

Al2O3

136.14152.3100.086169.874101.103303.262101.961

6.245;6.995;6.993/43.74;2.98;9.35/24.95;7.96;5.74/46.995;7.328;10.11/85.414;9.164;6.431/48.475,5.356,6.954.1,4.785,12.991/6

305.481104.208226.167518.232319.07315.475254.864

2.964.852.834.352.1096.293.98

2.9594.8522.9384.3532.1046.3833.985

Examples of compounds of Hexagonal Crystal SystemV=0.866 a 2 c

Comp. M.W. u.c.d. V ρexp/z ρcal

TiO2

CrO2

GeO2??IrO2

βMnO2

MoO2

NbO2

OsO2

PbO2

RuO2

SnO2

TaO2

WO2

CoF2

79.86583.994104.608224.21886.936127.938124.904222.228239.198133.068150.708212.948215.83896.929

4.5937,2.9581/24.41,2.91/24.395,2.859/14.49,3.14/24.396,2.871/24.86,2.79/24.77,2.96/24.51,3.19/24.946,3.379/24.51,3.11/24.7373,3.1864/24.709,3.065/24.86,2.77/24.6951,3.1796/2

62.42256.59447.82463.30255.48265.89967.34964.88582.66063.25871.50967.96556.6670.091

4.234.894.22811.665.036.475.911.49.386.976.959.9512.14.46

4.2484.9273.631??11.765.2026.44556.15711.3719.6076.9846.99710.40212.6474.591

FeF2

MgF2

MnF2

NiF2

PdF2

ZnF2

93.84162.30192.93496.689144.416103.386

4.6966,3.3091/4.623,3.052/4.8734,3.3099/4.6506,3.0836/4.931,3.367/4.7034,3.1335/

72.99265.22878.61066.69281.86869.319

4.093.1483.984.725.764.95

4.2683.1713.9254.8135.8574.952

Examples of compounds with rhombohedral crystal lattices: V = a 3 .(1- 3cos 2 α+2cos 3 α) 1/2


Al2O3

NaNO3

MgAl2O4

Fe2O3

101.9684.994169.874159.69

15.216.3247;47.270/27.1515.427;55.30/2

3518.744124.862

100.698

3.952.2573.645.242

2.26

5.265

Examples of organic compounds found as minerals

Compound m.wt. u.c.d./Z V ρexp Ρcal

DiniteC20H36

Evenkite

276.51

338.66

12.356;12.762;11.427/4

7.47;4.98;65.85/4

1801.89

2449.66

1.01

0.87

1.02

0.92

(CH3)2(CH2)22

FichteliteC19H34

HartiteC20H34

IdrialiteC22H36

KarpatiteC24H12

Kratochvilite(C6H4)2CH2

RavatiteC14H10

SimonelliteC19H24

262.48

274.49

278.35

300.36

166.22

178.23

252.40

10.706;7.458;10.824 105.850/211.407;20.952;7.40693.9410;100.750;80.4990/48.07;6.42;27.75/4

16.094;4.69;10.049;110.790/2

8.514;5.744;18.52/4

8.392;6.181;9.55898.480/2

9.231;9.134;36.01/8

831.39

1711.06

1437.71

709.12

905.71

490.36

3034.22

1.032

1.04

1.236

1.35

1.21

1.11

1.08

1.05

1.07

1.29

1.41

1.22

1.2071

1.10

Examples of Minerals of Cubic Crystal System: V=a 3

Mineral/Formula M.W. u.c.d./Z V ρexp ρcal

AlabanditeMnSAlmandineFe2

+3Al2(SiO4)3

Alum(K)KAl(SO4)2.12H2OAlum(Na)NaAl(SO4)2.12H2OAlumotungtite

87.00

497.75

474.39

458.28

216.36

5.214/4

11.526/8

12.133/4

12.214/4

10.2/8

141.75

1531.21

1786.095

1822.106

1061.21

3.99

4.19

1.71

1.67

2.71

4.08

4.32

1.76

1.65

2.71

(W,Al)(O,OH)3?ArsenoliteAs2O3

Aurostibite AuSb2

Avicennite Tl2O3

CalvertiteCu5Ge0.5S4

ChromiteFeCr2O4

CorderoiteHg3S2Cl2

CuperiteCu2OFluoriteCaF2

Franklinite(Zn,Mn2+,Fe2+)(Fe3+,Mn3+)2O4

GalaxiteMnMgFeO4

GalenaPbSGersdorffiteNiAsSGoldamalgum(Au,Ag)HgHaliteNaClHunchunite(Au,Ag)2Pb

197.84

440.49

661.15

495.06

223.84

736.81

143.09

78.07

236.54

172.72

239.27

165.68

375.28

58.44

556.58

11.0457/16

6.66/4

10.5468/10

5.337/1

8.36/8

8.94/4

4.2696/2

5.463/4

8.42/8

8.271/8

5.936/4

5.719/4

10.01/25

5.6402/4

7.933/8

1347.66

295.408

1173.173

152.0

584.28

714.52

77.83

163.04

596.95

565.81

209.16

187.05

1003.00

179.43

499.24

3.90

9.98

9.574

5.41

4.79

6.85

6.1

3.13

5.14

4.23

7.4

6.11

15.53

2.17

16.0

3.70

9.9

9.36

5.41

5.09

6.85

6.11

3.18

5.26

4.05

7.6

5.88

15.47

2.16

14.81

KobeiteY0.9U0.1Ti1.5Nb0.5O5(OH)LazuriteNa3CaAl3Si3O12SMagnetiteFe2

3+Fe2+O4

NabaphiteNaBaPO4.9H2OPericlaseMgOPetziteAg3AuTe2

PyriteFeS2

PyropeMg3Al2(SiO4)3

SilleniteBi12SiO20

SodaliteNa8Al6Si6O24Cl2

Sphalerite(Zn,Fe)SSperrylitePtAs2

SpinelMgAl2O4

SylviteKClWalfordite(Fe3+)0.65(Te6+)0.35(Te4+)3O8

Zhanghengite

319.1

498.31

231.54

417.43

40.30

775.77

119.98

483.13

2855.84

969.21

96.98

344.92

142.27

74.55

591.76

60.74

5.0210/1

9.105/2

8.391/8

10.711/4

4.203/4

10.38/8

5.417/4

11.459/8

10.184/4

8.85/1

5.406/4

5.967/4

8.08/8

6.2931/4

11.011/4

126.58

754.81

590.80

1228,83

74.25

1118.39

158.96

1504.67

1056.22

693.15

157.99

212.46

527.51

249.23

1335.0

4.6

2.4

5.15

2.3

3.78

8.92

5.01

3.74

9.3

2.29

4.05

10.58

3.64

1.99

2.53

4.19

2.19

5.21

2.26

3.67

9.21

5.01

3.56

8.98

2.32

4.08

10.78

3.58

1.99

2.94

(Cu0.6,Fe0.1,Zn0.2,Al0.05,Cr0.05) 2.952/1 25.72 3.92 3.92

Examples of Minerals of Tetragonal Crystal System: V= a 2 c

Mineral/Formula M.W. u.c.d./Z V ρexp ρcal

AbernathyiteK(UO2)(AsO4).3H2OAbswurmbachiteCuMn3+O8(SiO4)BellidoiteCu2SeBenleonarditeAg8Sb0.5As0.5Te2S3

ChalcopyriteCuFe2+S2

ChrombismiteBi16CrO27

CristobaliteSiO2

Formanite YTaO4

Leucite KAlSi2O6

Maucherite

502.0914

613.253

333.852

1312.68

183.53

3827.67

60.08

206.056

218.246

1244.96

7.176;18.926/4

9.406;18.546/8

7.75;11.41/9

6.603;12.726/2

5.28;10.41/4

8.649;17.24/2

4.971;6.918/4

11.52;11.74/32

13.09;13.75/16

6.868;21.8/4

933.40

1640.82

685.31

554.9

290.21

1289.6

170.95

1558.02

2356.04

1028.29

3.32

4.96

7.03

7.79

4.19

9.86

2.27

7.03

2.47

7.83

3.572

4.98

7.28

7.86

4.20

9.8

2.33

7.03

2.46

8.04

Ni11As8

Pinnoite MgB2O4.3(H2O)PiypiteK2Cu2(SO4)2OPotaritePdHgRutileTiO2

Scheelite CaWO4

SincositeCaV2

5+O2(PO4)25H2Otetra-auricuprideAuCuUreaCO(NH2)2

WeddelliteCa(C2O4)Wulfenite PbMoO4

ZirconZrSiO4

163.981

413.413

307.013

79.88

387.93

453.98

260.51

60.06

164.13

367.14

183.31

7.617;8.19/4

13.6;4.98/4

3.026;3.7062/14

594;2.959/2

5.242;11.373/4

8.895;12.727/4

3.96;3.67/2

5.646;4.701/2

12.33;7.353/8

5.435;12.11/4

6.607;5.982/4

475.17

921.101

33.918

62.43

312.49

1007.0

57.55

149.86

1117.87

357.72

251.13

2.29

3.1

14.88

4.25

6.01

2.99

15.03

1.33

1.95

6.75

4.714

2.29

2.98

15.039

4.25

6.12

2.97

15.03

1.33

2.02

6.82

4.65

Examples of Minerals of Orthorhombic Crystal System: V= abc

Mineral/Formula m.wt. u.c.d./Z V ρexp ρcal

AniliteCu7S4

AttikaiteCa3Cu2Al2(AsO4)4(OH)42H2OBarylite BaBe2Si2O7

BertossaiteLi2CaAl4(PO4)4(OH)4

BillingsleyiteAg7AsS6

BismuyhitniteBi2S3

Caledonite Pb5Cu2(CO3)(SO4)3(OH)6

Chelyabinskite(Ca,Mg)3Si(OH)6(SO4,CO3)29H2OCobaltite CoAsSEmpressiteAgTeHamergiteBeBO3(OH)KrenneriteAuTe2

LautiteCuAsSMckinstryite(Ag,Cu)2SMercalliteKHSO4

Pertsevite

573.09

944.79

323.52

609.8

1022.4

514.16

1613.34

574.77

165.92

235.27

93.84

452.17

170.53

212.34

136.17

130.82

7.89;7.84;11.01/4

10.01;8.199;22.78/4

9.82;11.65;4.673/4

11.48;15.73;7.23/4

14.96;14.99;10.56/8

11.13;11.27;3.97/4

20.088;7.143;6.564/2

19.01;20.93;22.45/18

5.57;5.582;5.582/4

8.882;20.1;4.614/16

9.76;12.23;4.43/8

16.54;8.82;4.46/8

3.79;5.43;11.42/4

14.043;150677;7.803/32

8.412;9.8;19.957/16

20.49;4.571;11.89/12

681.05

1869.6

534.61

1305.6

2368.08

497.98

941.86

8932.4

173.55

823.73

528.79

650.64

235.02

1727.85

1645.21

1113.61

5.68

3.36

4.04

3.10

5.92

7.0

5.05

1.92

6.33

7.55

2.372

8.53

4.9

6.61

2.33

2.31

5.59

3.2

4.02

3.1

5.74

6.86

5.69

1.91

6.35

7.59

2.36

9.23

4.82

6.57

2.20

2.34

Mg2(BO3)FPolaritePd(Bi,Pb)Sinoite Si2N2OSmirniteBi2Te4+O5 SpertiniiteCu(OH)2

StephaniteAg5SbS4

StibiocolumbiteSbNbO4

StiiotantaliteSbTaO4

Struvite-KKMg(PO4).6H2OThermonatriteNa2CO3H2O

314.96

100.18

625.56

97.56

789.36

278.65

366.70

266.47

124.0

7.191;8.693;10.681/16

5.473;8.84;4.835/4

16.447;5.513;11.579/8

2.951;10.592;5.257/4

7.793;12.295;8.506/4

4.929;11.797;5.559/4

4.9;11.79;5.57/4

6.903;6.174;11.146/2

10.72;5.249;6.469/4

667.68

234.00

1049.89

164.32

815.0

323.24

321.78

475.03

364.01

12.51

2.82

7.78

3.93

6.25

5.98

6.7

1.93

2.255

12.53

2.84

7.91

3.94

6.43

5.73

7.57

1.86

2.26

Examples of Minerals of Rhombohedral/Trigonal Crystal System:

Mineral/Formula M.wt. u.c.d./Z V ρexp ρcal

AcetamideCO (CH3)(NH2)Amakinite(Fe2+,Mg)(OH)2

59.07

83.46

11.44;13.5/18

6.917;14.52/12

1530.09

601.63

1.17

2.95

1.15

2.76

BernditeSnS2

BismuthBiBurtiteCaSn(OH)6

BelendoffiteCu7Hg6

CalciteCaCO3

Carlinite Tl2SCorundumAl2O3

Dolomite CaMg(CO3)2

EllisiteTl3AsS3

GordaiteNaZn(SO4)(OH)6Cl.6(H2O)HatruriteCaSiO5

HongshiitePtCuJarosite KFe3(SO4)2(OH)6

MagnesiteMgCO3

MilleriteNiSMonohydrocalcite

182.81

208.98

500.81

1648.36

100.09

440.83

101.96

184.4

784.27

626.2

228.32

258.63

184.4

84.31

90.76

119.10

3.639;5.868/1

4.537;11.838/6

7.21;17.03/3

13.36;16.161/12

4.989;17.062/6

12.12;18.175/27

4.751;12.97/6

4.842;15.95/3

12.324;9.647/7

8.363;13.018/2

7.15;25.56/9

10.703;13.197/48

4.842;15.95/3

4.633;15.15/6

9.62;3.149/9

10.566;7.573/9

67.30

211.03

766.68

2498.11

367.78

2312.12

253.54

323.85

1268.9

788.5

1131.63

1309.23

323.85

281.62

252.38

732.18

4.5

9.75

3.09

13.12

2.71

8.1

4.05

2.84

7.1

2.627

3.02

15.63

2.84

3.0

5.5

2.38

4.51

9.87

3.25

13.15

2.71

8.55

4.01

2.84

7.18

2.64

3.02

15.74

2.84

2.98

5.37

2.41

CaCO3.H2ORhodochcrositeMnCO3

SideriteFe2+CO3

Simpsonite Al4(Ta,Nb)3O13(OH)SphaerocobaltiteCaCO3

SpiokopiteCu39S26

StistaiteSnSbTelluriumTeTistariteTi2O3

TrechmanniteAgAsS2

ZlatogoriteCuNiS2

114.95

115.86

813.65

118.94

121.03

240.46

127.60

142.66

246.92

365.74

4.777;15.67/6

4.72;15.46/6

7.377;4.514/1

4.659;14.957/6

22.962;41.429/18

8.648;10.675/12

4.447,5.915/3

5.158;13.611/6

13.98;9.12/18

4.0489;5.1358/1

309.68

298.28

212.74

281.16

18917.1

691.4

101.30

313.61

1543.62

72.91

3.69

3.96

6.7

4.1

5.13

6.91

6.27

4.53

4.78

8.21

3.70

3.87

6.35

4.21

5.33

6.93

6.24

4.566

4.78

8.33

Examples of Minerals of Hexagonal Crystal System:

Mineral/Formula M.Wt. u.c.d./Z V ρexp ρcal

Afghanite(Na,Ca,K)8(Si,Al)12O24(SO4,Cl,CO3)H2OApatiteCa5(PO4)3ClBenitoiteBaTiSi3O9

Berborite Be2(BO3)(OH,F).(H2O)BerylBe3Al2(SiO3)6

Cancrenite Na6Ca2Al6Si6O24(CO3)2

ChaoiteCHematiteFe2O3

Hydroxy-cancrinite Na4(AlSiO4)3(OH).H2OKoutakiteCu5As2

MixiteBiCu6(AsO4)3(OH)6.3H2ONickelineNiAsOrceliteNi5-0.23As2

PenfielditePb2Cl3(OH)SobolevskeitePdBiStibiopalladinite

1200.45

520.76

413.46

112.35

537.5

1052.50

12.01

59.69

484.18

467.57

1163.10

133.61

429.81

537.77

315.4

775.60

12.77;21.35/4

9.598;6.776/2

6.641;9.76/2

4.433;10.638/2

9.215;9.192/2

12.7;5.15/1

8.948;14.078/168

5.0317;13.737/6

12.664;5.159/2

11.51;14.54/18

13.63;5.9/2

3.609;5.019/2

6.815;12.498/6

11.28;48.65/36

4.23;5.69/2

7.606;14.21/6

3015.2

540.59

366.3

181.04

675.98

719.36

976.17

301.2

716.54

1668.19

949.24

56.61

481.69

5360.83

88.17

711.93

2.64

3.20

3.6

2.2

2.76

2.45

3.38

5.3

2.32

8.48

3.8

7.79

6.5

5.82

11.88

9.5

2.59

3.15

3.75

2.06

2.64

2.43

3.43

5.28

2.24

8.38

4.07

7.84

8.5

6.0

11.88

10.85

Pd5Sb2

Vanadinite Pb5(VO4)3Cl VateriteCaCO3

WeissiteCu5Te3

ZinciteZnMnO

1416.27

100.09

700.53

80.34

10.317;7.338/2

7.135;16.98/12

12.54;21.69/15

3.242;5.176/2

678.72

748.61

2953.74

47.11

6.94

2.54

6.0

5.66

6.93

2.66

5.83

5.56

Examples of Minerals of Monoclinic Crystal System:

Comp./formula M.W. u.c.d./Z V ρexp ρcal

AcanthiteAg2SAcuminiteSrAlF4(OH)H2OAfwilliteCa3Si2O4(OH)6

AlacraniteAs8S9

AlamositePbSiO3

ArsenopyriteFeAsSArtiniteAg2(CO3)(OH)23H2OAschamalmite

247.80

225.62

342.45

887.962

238.28

162.83

196.68

1949.75

4.229;6.931;7.862; 99.610/413.223;5.175;14.251111.610/811.36;5.47;13.09 98.4330/49.942;9.601;9.178;101.940/211.209;7.041;12.22113.150 /125.74;5.68;5.79112.170/416.56;3.15;6.22990/213.71;4.09;31.43

227.21

906.64

806.73

857..12

886.78

174.82

320.47

1762.13

7.25

3.3

2.62

3.43

6.49

6.07

2.01

7.27

7.256

3.31

2.82

3.44

6.37

6.19

2.04

7.35

Pb6Bi2S9

AurivilliusiteHg+Hg2+OIBaddeleyiteZrO2

BakeriteCa4B4(BO4)(SiO4)3(OH)3H2OBarahonaiteAlCa,Cu,Na,Fe+3Al)12

BarytocalciteBaCa(CO3)2

BazhenoviteCaS5CaS2O3,6Ca(OH)2.20H2OBischofiteMgCl2.6H2OBoraxNa2B4O5(OH)4.8H2OBrezinaiteCr3O4

CannizzaritePb4Bi6S13

CaryopiliteMn+2MgZnFe+2)3(SiAs)2O5(OH,Cl)4

ChalcociteCu2SDatoliteCaBSiO4(OH)DiopsideCaMgSi2O6

EuclaseBeAlSiO4(OH)

544.088

123.22

623.65

2052.55

297.42

1157.48

203.30

381.37

284.25

2499.54

373.76

159.16

159.981

216.55

145.08

910/417.58;6.979;6.693101.720/85.1477;5.203;5.315699.380/44.85;7.627;9.65990.2550/110.161;22.39;10.54593.30/28.134;5.229;6.54773.8670/28.45;17.47;8.24; 119.50/19.9;7.15;6.193.70/211.858;10.67;12.67106.580 /45.96;3.425;11.27; 91.5330/24.13;4.9;15.4898.560/0.55.668;9.811;7.527104.520/211.881;27.323;13.491116.350 /969.66;7.64;4.83; 90.150/49.761;8.926;5.258; 105.80/44.763;14.29;4.618; 100.30/4

804.05

140.47

357.29

2395.1

267.5

1058.7

430.89

1537.46

229.97

309.78

405.2

3924.48

356.46

440.80

309.29

8.961

5.75

2.8

2.85

3.65

1.83

1.57

1.71

4.12

6.7

3.06

5.65

2.9

3.4

3.04

8.989

5.83

2.90

2.77

3.69

1.82

1.57

1.65

4.10

6.7

2.87

6.46

2.98

3.26

3.12

GrumipluciteHgBi2S4

GypsumCaSO42H2OHowliteCa2B5SiO9(OH)5

HoeliteC14H8O2(C6H4)2(CO2)HydroxylwagneriteMg2(PO4)(OH)JadeiteNa(AlFe3+)Si2O6

KainiteMgSO4.KCl.3H2OLazuliteMgAl2(PO4)2(OH)2

LeadhillitePb4(SO4)(CO3).(OH)2

Lutecite/MoganiteSiO2

MendoziteNaAl(SO4)2.11H2OMirabiliteNa2SO410H2OMontmoriloniteNaCaAl2Si4O10(OH)2(H2O)10

NavajoiteV2O5.3H2OPachnoliteNaCaAlF6.H2OPallodoarsenide

746.81

172.17

391.32

208.22

160.59

205.03

248.97

302.23

1078.9

60.08

440.27

322.20

549.07

235.93

222.06

287.76

14.164;4.053;13.967118.2830/45.68;15.18;6.29113.8330/412.78;9.33;8.6; 104.830/415.81;3.967;7.876102.670/29.656;12.859;12.069108.490/169.418;8.562;5.219;107.560/419.72;16.23;9.5394.920/167.1526;7.278;7.2334;89.2330/49.08;20.76;11.5689.80 /88.758;4.876;10.71590.090/1221.75;9.108;8.29892.470/412.82;10.35;11.48107.660/45.178;8.94;9.9599.90/134.94;3.597;11.7995.980/1012.12;10.414;15.6890.380/169.25;8.47;10.44

706.08

496.09

991.28

481.92

1421.21

401.23

3038.89

376.51

2179.06

457.57

1642.3

1451.46

453.04

1473.69

1979.05

815.96

6.998

2.3

2.58

1.42

3.??

3.3

2.1

3.05

6.4

2.54

1.74

1.49

2.35

2.56

2.98

10.42

7.02

2.31

2.62

1.43

3.00

3.39

2.18

2.67

6.58

2..62

1.78

1.47

2.01

2.66

2.98

10.54

Pd2AsParadocrasiteSb2(Sb,As)2

PhosphophyliteZn2(Fe2+Mn)(PO4)2

PoyarkoviteHg3ClOPyrrhotiteFe(1-x)S[x=0—0.17]QuenselitePbMn3+O2

RealgarAsSRosickyiteSRoxyiteCu1.78S(Cu9S5)SchoderiteAl2(PO4)(VO4).8H2OSphaerobertranditeBe3SiO4(OH)2

SpodumeneLiAlSi2O6

Staurolite(Fe3+Mg)2Al9(SiAl)4O20(O,OH)4

StringhamiteCaCuSiO4.2H2OTriploidite(MnFe2+)2(PO4)(OH)UralboriteCaB2O2(OH)4

463.59

448.4

653.22

85.12

311.14

106.99

32.07

145.18

408.0

152.62

186.09

811.89

231.74

222.31

161.73

940/187.252;4.172;4.431123.130/110.377;5.086;10.559;121.10/219.009;9.018;16.848110.820/246.865;11.9;22.7290.080/645.61;5.68;9.1693.30/49.29;13.53;6.57106.8830/168.5;13.16;9.29124.8170/3253.79;30.9;13.3690.00/51216.26;30.6;12.5591.770/185.081;4.639;17.664106.090/49.52;8.32;5.25 110.470/47.88;16.62;5.66900/45.03;16.135;5.343102.960/412.366;13.276;9.943108.230/166.881;12.305;9.79197.460/8

112.27

477.18

2699.55

929.51

291.4

790.22

853.15

22205.8

6241.35

400.04

389.576

741.27

422.59

1550.42

821.99

6.52

3.1

9.56

4.57

6.842

3.56

2.07

5.622

1.88

2.5

3.183

3.71

3.67

3.7

2.6

6.86

3.12

9.64

4.69

7.09

3.6

2.0

5.56

1.95

2.53

3.177

3.64

3.64

3.81

2.61

Wagnerite(Mg,Fe2+)2(PO4)FWolfeite(Fe3+Mn2+)2(PO4)(OH)XanthoconiteAg3AsS3

ZiesiteCu2V5+

2O7

162.71

223.22

494.72

340.97

9.644;12.679;11.957108.30/1612.2;13.17;9.79108.00/1616.98;6.21;11.99110.1670/87.689;8.029;10.106110.250/4

1388.11

1496.01

1186.78

585.33

3.1

3.79

5.55

3.86

3.11

3.96

5.54

3.87

Examples of Minerals of Triclinic Crystal System:

Name/formula M.Wt. u.c.d./Z V ρexp ρcal

AbelsoniteNiC31H32N4

AgrelliteNaCa2Si4O10FAlbiteNaAlSi3O8

BabintoniteCa2(Fe2+Mn)Fe3+Si5O14(OH)BaileychloreZn2.5Fe2

+3Al2Si3O10(OH)8

BikitaiteLi2[Al2Si4O12]12H2OBytownite(CaNa)(SiAl)4O8

Cejkaite

519.31

394.48

263.02

573.0475

709.44

408.21

275.01

546.35

8.44;11.12;7.2890.830;113.750;79.560/17.759;18.946;6.98689.880;116.650;94.320/48.144;12.787;7.1694.270;116.580;89.670/47.36;11.82;6.58;91.5160;93.850;104.0670/25.346;9.257;14.402900;97.120;900/28.606;4.9573;7.59789.890;114.420;89.960/18.17;12.85;13.16;93.150;116.0160;90.8330/79.28;9.295;12.864

614.98

915.25

664.4

539.76

707.2

295.11

1239.15

965.1

1.45

2.88

2.62

3.4

3.18

2.28

2.71

3.67

1.40

2.86

2.63

3.53

3.33

2.3

2.58

3.76

Na4(UO2)(CO3)3

KaoliniteAl2Si2)5(OH)4

GilmariteCu3(AsO4)(OH)3

InesiteCa2Mn7Si10O28(OH)2

KyaniteAl12OSiO4

MicroclineKAlSiO8

MurmaniteNa2Ti2(Si2O7)O2.2H2OOligoclaseNaAlSi3O8

RhodoniteMnSiO3

TridymiteSiO2

TurquoiseCuAl6(PO4)4(OH)8.4H2O

258.16

380.58

1317.65

162.05

278.33

750.89

265.42

129.13

60,08

813.44

90.290;91.120;119.550/45.14;8.93;7.3791.80;104.50;90.020/25.445;5.873;5.104115.00;93.050;92.00/18.889;9.247;11.975; 88.150;132.070;96640/17.112;7.844;5.574;90.120;101.10;105.90/48.577;12.967;7.22390.650;115.930;87.780/48.7;8.782;11.668;94.310;98.620;105.620/28.15;12.78;8.5;94.0160;116.330;88.6670/56.68;7.66;12.22;111.10;86.0160;93.2030/109.932;17.216;81.864900;900;900/3307.48;9.95;7.68;111.650;115.3830;69.4330/1

327.35

147.6

725.40

293.46

721.85

841.25

791.3

581.04

13997.87

449.39

2.6

4.21

3.06

3.61

2.56

2.855

2.65

3.6

2.3

2.7

2.62

4.21

3.02

3.67

2.56

2.96

2.78

3.69

2.35

3.01

Examples of Mineral Compounds in Cubic Crystal System:

Name/formula M.Wt u.c.d./Z V ρexp ρcal

Amalgum 817.51 9.9/10 970.3 13.92 13.99

Ag2Hg3

Atokite(Pd,Pt)3SnAuricuprideCu3AuAurostibiteAuSb2

BerzelianiteCu2SeChengdeiteIr3FeDamiaoitePtIn2

DanbaiteCuZn2

DieneriteNi3AsDomeykiteCu3AsDzharkeniteFeSe2

EugeniteAg11Hg2

Ferroskutterudite(Fe,Co)As3

FischesseriteAg3AuSe2

GaotaiiteIr3Te8

GeversitePt(Sb,Bi)2

504.47

387.6

440.47

206.05

632.51

424.72

194.33

250.99

265.56

213.77

1587.75

276.94

678.49

1597.46

482.20

3.991/1

3.753/11

6.66/4

5.739/4

3.791/1

6.364/4

7.762/12

9.45/16

9.611/16

5.783/4

10.02/4

8.17/8

9.967/8

6.413/1

6.44/4

63.57

615.08

295.41

189.02

54.53

257.75

467.65

843.91

887.78

193.4

1006.01

545.34

990.13

263.74

267.09

14.9

11.50

9.98

6.7

19.3

10.95

7.36

7.90

7.65

7.34

10.75

6.75

9.05

9.97

10.97

13.18

11.51

9.90

7.24

19.26

10.94

8.28

7.90

7.95

7.34

10.48

6.75

9.10

10.06

11.99

Goldamalgam(Au,Ag)HgHenryiteCu4Ag3Te4

Isoferroplatinum(Pt,Pd)3(Fe,Cu)Kerilite(Ag,Au)2(Te,Se,S)KrutaiteCuSe2

KrutoviteNiAs2

MaldoniteAu2BiMayingiteIrBiTeMoschellandsbergiteAg2Hg3

Rustenburgite(Pt,Pd)3SnTongxiniteCu2ZnTrogtaliteCo,Se2

TrustedtiteNi3Se4

YixunitePt3InZhanghengite(Cu,Zn,Fe,Al,Cr)Zvyagintsevite

375.28

1088.19

576.52

363.74

221.47

208.53

602.91

528.8

817.51

637.46

192.48

216.85

491.91

700.06

60.74

10.01/25

12.2/8

3.858/1

11.27/1

6.056/4

5.794/4

7.958/8

6.502/4

10.06/10

3.991/1

7.735/12

5.87/4

9.94/8

3.988/1

2.952/1

1003.0

1815.85

57.42

1431.44

222.1

194.51

503.98

274.88

1018.11

63.57

462.79

202.26

982.11

63.43

25.72

15.47

7.86

16.5

0.42

6.62

7.12

15.46

12.72

13.59

16.7

8.29

7.12

6.65

18.26

3.92

15.53

7.96

16.67

0.42

6.62

7.12

15.89

12.78

13.33

16.65

8.29

7.12

6.65

18.33

3.92

Pd3Pb 537.50 4.02/1 64.96 13.32 13.74

Examples of Mineral Compounds in Hexagonal Crystal System:


AlgodoniteCu6AsBohdanowicziteAgBiSe2

HedleyiteBi7Te3

Hexaferrum(Fe,Os,Ru,Ir)Hexamolybdenum(Mo,Ru,Fe,Ir,Os)Hexatestibiopanickelite(Ni,Pd)(Te,Sb)IMA.2008(Ni,Fe,Ir)JaipuriteCoSKochkaritePbBi4Te7

Langisite(Co,Ni)AsLuanheiteAg3Hg

456.2

474.77

1845.66

86.51

104.04

196.76

71.19

91.0

1936.32

133.79

524.19

2.6;4.228/0.3

4.2049;19.65/3

4.47;119.0/6

2.591;4.168/2

2.7506;4.4316/2

3.983;5.339/2

2.694;4.273/2

3.367;5.16/2

4.416;72.09/3

3.538;5.127/2

6.61;10.98/6

24.75

300.89

2059.17

24.23

29.04

73.35

26.86

50.66

1217.49

55.58

415.47

8.55

7.87

8.91

11.9

11.9

8.94

8.8

5.45

7.89

8.17

12.6

9.18

7.86

8.93

11.86

11.9

8.91

8.8

5.97

7.92

7.99

12.57

Osmium(Os,Ir)PlumbopalladinitePd3Pb2

Rutheniridosmine(Ir,Os,Ru)Ruthenium(Ru,Ir,Os)SorositeCu(Sn,Sb)VavriniteNi2SbTe2

VolynskiteAgBiTe2

Weishauite(Au,Ag)3Hg2

WeissiteCu2TeZlatogoriteCuNiSb2

190.23

733.66

182.5

101.072

183.02

491.04

572.05

925.26

246.962

365.74

2.7352;4.319/2

4.47;5.719/1

2.71;4.3/2

2.704;4.2817/2

4.217;5.12/2

3.909;15.682/2

4.468;20.755/3

2.9265;4.8178/0.25

8.3124;21.546/24

4.0489;5.1358/1

27.983

98.96

27.35

27.11

78.85

207.52

358.82

35.73

1289.289

72.91

22.48

12.4

22.2

12.368

7.75

7.79

8.01

10.8

7.381

8.21

22.573

12.31

22.16

12.382

7.71

7.86

7.94

10.75

7.633

8.33

Examples of Minerals of Compounds in Tetragonal Crystal System:


BelliodoiteCu2Se

206.05 11.52;11.74/32 1558.02 7.03 7.03

CameroniteAgCu7Te10

CuprostibiteCu2(Sb,Tl)EskeborniteCuFeSe2

FerronickelplatinumPt2FeNiLeadomalgamHgPb2

NielsenitePdCu3

NovodnepriteAuPb3

SelenojalpaiteAg3CuSe2

TulameenitePt2FeCuUrvantsevitePd(Bi,Pb)2

1828.69

248.853

277.31

504.70

614.99

295.63

818.57

544.63

509.55

523.49

12.695;42.186/16

3.99;6.09/2

5.518;11.048/4

3.871;3.635/1

3.545;4.525/1

3.7125;25.62/4

11.954;5.89/8

8.939;11.844/8

3.902;3.585/1

3.3628;12.902/2

6798.82

96.95

336.39

54.47

56.87

353.11

841.67

946.4

54.58

145.90

7.15

8.42

5.35

15.39

18.0

5.56

12.9

7.64

14.9

9.66

7.15

8.52

5.474

15.38

17.96

5.56

12.92

7.64

15.5

11.92

Examples of Minerals of Dimetallic Compounds in Orthorhombic Crystal System:


Anduoite(Ru,Os)As2

504.47 5.41;6.206;3.01/2 101.06 8.98 8.98

AntimonseliteSb2Se3

AthabascaiteCu5Se4

CabriitePd2SnCuCherepanoviteRhAsCupalite(Cu,Zn)AlDyscrasiteAg2SbEmpressiteAgTeEucairiteCuAgSeFerroseliteFeSe2

FrohbergiteFeTe2

HastiteCoSe2

KulleruditeNiSe2

LollingiteFeAs2

MattagamiteCoTe2

NaumanniteAg2SeNisbite

480.38

633.57

395.10

177.83

90.71

445.35

235.27

250.37

213.77

311.05

216.85

216.61

205.69

314.13

294.70

302.19

11.213;11.515;3.991/4

8.227;11.982;6.441/4

7.88;7.88;3.94/4

5.7;3.59;6./4

6.95;4.16;10.04/10

2.996;5.235;4.83/1

8.882;20.1;4.614/16

4.105;4.07;6.31/2

4.8001;5.776;3.585/2

5.28;6.26;3.85/2

3.6;4.84;5.72/2

4.89;5.96;3.67/2

5.25;5.92;2.85/2

5.31;6.31;3.89/2

4.336;7.067;7.753/4

5.16;6.3;3.84/2

515.31

634.93

244.65

122.78

290.28

75.75

823.73

105.42

99.4

127.25

99.67

106.96

88.58

130.34

237.57

124.83

5.88

6.63

10.7

9.72

5.19

9.69

7.55

7.69

7.21

8.055

7.22

6.72

7.4

8.0

7.25

8.0

6.19

6.63

10.73

9.62

5.19

9.76

7.59

7.89

7.14

8.12

7.23

6.73

7.71

8.0

8.24

8.04

Ni,Sb2

OeniteCoSbAsOmeiite(Os,Ru)As2

PaolovitePd2SnPararammelsbergiteNiAs2

ParaschachneriteAg3Hg2

RammelsbergiteNiAs2

RickarditeCu7Te5

Ruthenarsenite(Ru,Ni)AsSeinajokite(Fe,Ni)(Sb,As)2

VulcaniteCuTeWesterpeldite(Fe,Ni,Co)As

255.6

317.76

331.55

208.53

724.78

208.53

1082.82

165.40

276.64

191.15

131.93

3.304;6.092;10.258/4

5.409;6.617;3.02/2

8.11;5.662;4.324/4

5.77;5.838;11.419/8

2.961;5.13;4.83/0.8

4.78;5.78;3.53/2

4.0032;19.893;12.222/4

5.628;3.239;6.184/4

3.19;5.81;6.49/2

4.09;6.95;3.15/2

3.457;5.971;5.332/4

206.47

108.13

198.55

384.65

73.37

97.53

973.15

112.73

120.29

89.54

110.06

7.92

11.2

11.32

7.2

13.1

7.10

7.54

10.0

7.64

7.1

7.96

8.22

9.76

11.09

7.2

13.12

7.10

7.39

9.74

7.64

7.09

7.96

Examples of Mineral Compounds in Trigonal/Rhombohedral Crystal System:


Belendorffite 1648.36 13.36;16.161/12 2498.11 13.2 13.15

Cu7Hg6

CameroniteAgCu7Te10

MakineniteNiSe

1828.69

137.65

12.695;42.1860/16

10,01;3.28/9

6798.82

284.62

7.15

7.23

7.15

7.23

Examples of Mineral Compounds in Monoclinic Crystal System:


AcanthiteAg2SAlamositePbSiO3

BismiteBi2O3

BoraxNa2B4O5(OH)4.8H2OCalaveriteAuTe2

ClaudetiteAs2O3

Clinosafflorite(Co,Fe,Ni)As2

CoesiteSiO2

DoloresiteH8V4+

6O16

Dufrenoysite

247.8

283.28

465.96

381.37

452.17

197.84

207.83

60.08

569.70

724.57

4.229;6.931;7.862;99.610/4

11.209;7.041;12.22;113.150/12

5.83;8.14;7.48;67.0660/4

11.858;10.674;12.674;106.5830/4

8.76;4.41;10.15;125.20/4

5.339;12.984;4.5405;94.260/4

5.04;5.862;3.193;90.2130/2

7.17;12.38;7.17;1200/16

19.64;2.99;4.83;103.90/1

8.41;25.85;7.88;90.50/8

227.21

886.8

326.91

1537.46

320.41

313.89

94.33

551.18

275.33

1713.02

7.3

6.49

9.0

1.71

9.04

4.0

7.46

2.93

3.3

5.56

7.24

6.37

9.47

1.65

9.37

4.19

7.32

2.90

3.44

5.62

Pb2As2S5

EldfelliteNaFe3+(SO4)2

EuclaseBeAlSiO4

FarringtoniteMg3(PO4)2

FrooditePd,Bi2

HessiteAg2TeLoranditeTlAsS2

PalladoarsenidePd2AsVerbeekitePdSe2

WilkmaniteNi3Se4

270.96

145.8

262.86

524.38

343.34

343.44

287.76

264.34

491.91

8.022;5.135;7.123;92.150/2

4.763;14.29;4.618;100.30/4

7.6;8.23;5.08;94.060/2

12.75;4.29;5.67;102.8670/4

8.13;4.48;8.09;112.90/5

12.29;11.34;6.14;109.60/8

9.25;8.47;10.44;940/18

6.657;4.129;4.44;92.830/2

6.22;3.63;10.52;90.530/2

293.21

309.25

316.95

302.35

271.43

828.09

815.96

121.89

237.52

3.06

3.04

2.74

12.55

7.55

5.53

10.42

7.2

6.88

3.062

3.12

2.75

11.52

10.5

5.51

10.54

7.2

6.88

Examples of Minerals of simple salts in Triclinic Crystal System:


CaoxiteCa(C2O4).3H2OCattiite

182.144

659.66

6.076;7.174;8.46776.650;70.850;70.9170/26.932;6.925;16.154;

320.58

668.6

1.85

1.65

1.89

1.64

Mg3(PO4)2.22H2OChalcanthiteCuSO4.5H2OCopiapiteFe2+Fe3+

4(SO4)6(OH)2.20H2OCoquanditeSb6O8(SO4).H2OCornubiteCu5(AsO4)2.(OH)4

DoyleiteAl(OH)3

EzcurriteNa4B10O17.7(H2O)FairbankitePbTe4+O3

FroloviteCaB2(OH)8

HohmanniteF3+

2(SO4)2(OH)2.7H2OLimoriiteY2(SiO4)(CO3)IMA-2008-046MgZr(PO4)2.4H2OIMA2008-048Zn6(PO4)4.7H2OJogoweriteBaAl2(PO4)2(OH)2

JokokuiteMnSO4.5H2OKermesiteSb2S2O

249.686

1249.94

972.635

681.61

78.0

598.16

382.80

197.76

463.94

329.90

377.53

898.33

415.25

241.08

323.63

82.210;89.700;119.510/16.11;10.673;5.95;97.580;107.170;77.550/27.227;18.76;7.37991.460;102.180;98.950/111.434;29.77;11.31491.0730;119.2450;92.820/126.121;6.251;6.79092.930;111.30;107.470/15.002;5.175;4.9897.60;118.60;104.740/28.598;9.57;6.576102.750;107.50;71.50/17.81;7.11;6.96117.20;93.780;93.40/47.774;5.68;8.136113.150;101.670;107.870/29.148;10.922;7.18390.290;90.790;107.360/26.573;6.651;6.454116.440;92.340;95.630/25.3049;9.3372;9.628297.3480;91.5340;90.5120/28.299;9.616;12.17571.680;82.020;80.180/26.049;6.964;4.971116.510;86.060;112.590/16.37;10.77;6.1398.7670;109.9670;77.8330/210.84;4.07;10.2790.00;106.530;90.00/4

361.6

965.7

3355.64

227.109

108.52

477.31

342.39

307.89

675.201

251.21

472.81

900.04

172.60

381.88

443.09

2.286

2.105

5.78

4.64

2.48

2.053

7.45

2.14

2.255

4.47

2.76

3.22

4.01

2.03

4.55

2.279

2.15

5.77

4.823

2.478

2.049

7.43

2.13

2.50

4.36

2.65

3.31

3.99

2.10

4.85

KoritnigiteZnHAsO4

LishizheniteZnFe3+

2(SO4)4.14H2OLitidioniteKNaCuSi4O10

LopeziteK2Cr2O7

LudjibaiteCu5(PO4)2(OH)4

LudlockiteFe2+PbAs5+2O6

ManaksiteKNaMn2+Si4O10

McbirneyiteCu3(VO4)2

MeridianiiteMgSO4.11H2OMetarossiteCaV2

5+O6.2H2OMicroclineKAlSi3O8

MonetiteCaHPO4

ParadamiteZn2(AsO4)(OH)PectoliteNaCa2(Si3O8)(OH)SassoliteH3BO3

Sidrotil

223.33

813.55

397.97

294.18

575.7

309.25

389.36

420.52

318.537

273.99

278.33

136.06

286.71

332.40

61.83

241.99

7.948;15.829;6.66890.860;96.560;90.050/86.477;15.298;6.30990.20;101.110;93.970/19.8;8.01;6.97114.120;99.520;105.590/27.5;13.4;7.3898.00;90.850;96.2170/44.446;5.871;8.68103.90;90.30;93.20/110.11;11.95;9.86113.90;99.70;82.740/96.993;8.219;10.007105.110;100.760;114.790/25.3418;6.51;5.179888.610;68.110;69.220/16.7459;6.8173;17.279988.1370;89.4810;62.7190/26.215;7.065;7.76992.920;96.650;105.780/28.577;12.967;7.22390.650;115.9330;87.7830/46.9;7.0;6.6596.350;91.2670;76.10/45.83;6.711;5.648104.730;92.260;76.810/27.99;7.04;7.0290.050;95.00;102.4670/27.039;7.053;6.57892.5830;101.1670;119.8330/96.26;10.63;6.06

833.31

611.94

474.37

730.07

219.55

1064.91

495.24

156.22

705.89

325.64

721.85

309.80

207.92

384.09

277.65

363.85

3.54

2.206

2.75

2.69

4.36

4.37

2.73

4.354

1.499

2.45

2.56

2.929

4.55

2.86

3.4

2.15

3.56

2.21

2.79

2.68

4.354

4.34

2.61

4.47

1.50

2.79

2.56

2.92

4.58

2.87

3.33

2.21

Fe2+SO4.5H2OStranskiteZn2Cu2+(AsO4)2

TarbuttiteZn2(PO4)(OH)WeissbergiteTlSbSWeiditeCaHAsO4

Wollastonite-1ACaSiO3

472.16

242.76

390.27

180.01

116.16

97250;109.670;75.00/25.073;6.669;5.267109.850;112.140;86.880/15.657;6.432;5.521102.450;87.60;102.5670/211.9;6.4;6.1109.90;81.80;105.40/47.11;6.94;7.1594.320;101.60;87.370/47.94;7.32;7.07;90.0330;95.3670;103.4330/6

155.02

191.29

416.85

344.25

397.92

5.23

4.14

5.79

3.48

2.84

5.06

4.21

6.22

3.47

2.91

Examples of Minerals in Primitive Cubic Crystal System:


CupriteCu2OLazuriteNaCa(Al3Si3O12)SSodaliteNa8Al6Si6O24Cl2

143.09

498.31

969.21

4.2696/2

9.105/2

8.85/1

77.83

754.81

693.15

6.1

2.4

2.29

6.11

2.19

2.32

Examples of Minerals in body centered Cubic (bcc) Crystal System:


Goldamalgum(AuAg)HgKobeite(Y,U)(Ti,Nb)2(O,OH)6

ZhanghengiteCuZnFeAlCr

375.28

319.1

60.74

10.01/25

5.021/1

2.952/1

1003.0

126.58

25.72

15.47

4.6

8.324

15.53

4.19

3.92

Examples of Minerals of Dimetallic (1:1) Compounds in primitive Cubic Crystal System:

Name/formula At.r. M.wt. u.c.d./Z V ρexp ρcal

FesiliciteFeSiKamaciteα-Fe,NiSkaergraarditeCu,PdWairauiteCo,Fe

4.;1.63 <15%

83.93

114.781

173.19

114.78

4.48/4

2.856/1

3.0014/1

2.856/1

89.92

23.30

27.04

23.30

5.95

8.18

10.61

8.18

6.2

8.181

10.63

8.18

Examples of Minerals of Dimetallic (1:1) Compounds in Face centered Cubic (fcc) Crystal System:

Name/formula At.r. M.Wt. u.c.d./Z V ρexp ρcal

AltaitePbTeClausthalitePbSeColoradoiteHgTeStilleiteZnSeTiemanniteHgSeTaeniteγ-FeNi

2.02;2.06=1%

2.02;1.9<6%

1.7;2.06<18

1.39;1.9<27%

1.7;1.9<11%

2.0;1.63<19%

334.80

286.16

328.19

144.3724

279.555

56.42

6.452/4

6.147/4

6.448/4

5.6676/4

6.084/4

3.596/4

268.59

232.27

268.09

182.28

225.311

636.72

8.14

8.19

8.07

5.42

8.33

8.01

8.28

8.18

8.13

5.26

8.245

8.061

Examples of Minerals of Dimetallic (1:1) Compounds in Tetragonal Crystal System:

Name/formula at.r. M.Wt. u.c.d./Z V ρexp ρcal

PotaritePdHgtetra-uricuprite(de)

1.37;1.57

1.46;1.28<13%

307.01

260.51

3.02;3.706/1

3.96;3.67/2

33.80

57.55

14.88

15.03

15.08

15.03

AuCutetra-ferroplatinumPtFeTetrataeniteFeNi

1.39;1.26<10%

1.26;1.24<2%

250.93

57.27

3.84;3.72/2

2.533,3.582/2

54.85

22.98

14.3

8.275

15.19

8.28

Examples of Minerals of Dimetallic (1:1) Compounds in Orthorhombic Crystal System:

Name/formula

at. r. M.Wt. u.c.d./Z V ρexp ρcal

CherepanoviteRhAsEmpressiteAgTeVulcaniteCuTe

1.34;1.39 <4%

1.44;1.6 <11%

1.28;1.60 =20%

177.83

235.27

191.15

5.7;3.5;9.6/4

8.882;20.1;4.614/16

4.09;6.95;3.15/2

122.78

823.73

89.54

9.72

7.55

7.1

9.62

7.59

7.09

Examples of Minerals of Dimetallic (1:1) Compounds in Hexagonal Crystal System:

Name/formula

At.r. M.Wt. u.c.d./Z V ρexp ρcal

AchavaliteFeSeBreithauptiteNiSbCadmoseliteCdSeFrebolditeCoSeHongshiitePtCuImgreiteNiTeKlockmanniteCuSeNickelineNiAsNiggliitePtSnSchachneriteAgHgSederholmiteNiSeSobolevskitePdBiYuanjiangiteAuSnZincZn

1.26;1.4 =10%

1.24;1.59 =22%

1.54;1.4<10%

1.25;1.4< 11%

1.28;1.39 <8%

1.24;1.60<23%

1.24;1.39<11%

1.39;1.62<15%

1.44;1.57<9%

1.24;1.40<12%

1.37;1.70<20%

1.46;1.62<10%

134.81

180.44

191.37

137.89

258.63

186.29

142.51

133.61

313.79

299.19

137.65

315.40

315.68

65.39

3.636;5.946/2

3.93;5.13/2

4.271;6.969/2

3.61;5.28/2

10.703;13.197/48

3.937;5.354/2

3.938;17.25/6

3.609;5.019/2

4.111;5.446/2

2.976;4.842/1

3.65;5.34/2

4.23;5.69/2

4.316;5.51/2

2.6591;4.9353/2

68.08

68.62

110.09

59.59

1309.23

71.87

231.67

56.61

79.71

37.19

61.61

88.17

88.89

30.22

6.53

8.28

5.663

6.79

15.63

8.54

5.99

7.79

13.44

13.4

7.42

11.88

11.8

7.05

6.58

8.73

5.77

7.68

15.74

8.61

6.13

7.84

13.07

13.36

7.42

11.88

11.79

7.19

Examples of Minerals of Dimetallic (1:1) Compounds in Rhombohedral/Trigonal Crystal System:

Name/formula At.r. M.Wt. u.c.d./Z V ρexp ρcal

HongshiitePtCuMakineniteNiSeStistaiteSnSbTsumoiteBiTe

1.24;1.4<12%

1.7;1.6< 6%

258.63

137.65

240.46

336.583

10.703;13.197/48

10.01;3.28/9

8.648;10.675/12

4.422,24.05/6

1309.23

284.62

691.40

407.271

15.63

7.23

6.91

8.16

15.75

7.23

6.93

8.23

Examples of Minerals of Dimetallic (1:1) Compounds in Monoclinic Crystal System:

Name/formula

M.Wt. u.c.d./Z V ρexp ρcal

Examples of Minerals of Dimetallic (1:1) Compounds in Triclinic Crystal System:

Name/formula

M.Wt. u.c.d./Z V ρexp ρcal

Examples of Minerals of Trimetallic (1:1:1) Compounds in Primitive Cubic Crystal System:

Name/formula

rad.ratio M.Wt. u.c.d./Z V ρexp ρcal

EucairiteCuAgSeIMA2008-055(Ni,Fe,Ir)JolliffeiteNiAsSeKalungaitePdAsSeMaslovitePtBiSeMayingiteIrBiTeMilotaite

1.49;1.14;1.031.307 : 1 : 0.9041.69;1.14;1.031.482 : 1 : 0.9041.77;1.43;1.031.238 : 1 : 0.7201.80;1.43;1.231.259 : 1 : 0.8601.69;1.33;1.03

250.37

71.19

212.63

258.08

531.66

528.8

304.11

4.105;4.07;6.31/2

2.6941;4.2731/2

5.831/4

6.089/4

6.689/4

6.502/4

6.3181/4

105.29

26.86

198.26

225.78

299.28

274.88

252.21

7.7

7.99

7.1

7.637

11.63

12.72

8.09

7.91

8.80

7.12

7.59

11.80

12.78

8.01

PdSbSeOenditeCoSbAsPadmaitePdBiSe

1.271 : 1 : 0.774

1.69;1.43;1.031.182 : 1 : 0.720

255.6

394.36

3.304;6.092;10.258/4

6.448/4

206.87

268.09

7.92

9.86

8.22

9.77

The unit cell volumes

The volumes of unit cells (Vdirect lattice) of the seven crystal systems can calculated by formulae as given below:

System V =

Cubic

Tetragonal

Orthorhombic

a3

a2.c

a.b.c

Rhombohedral/Trigonal

Hexagonal

Monoclinic

Triclinic

a3.(1-3.cos2α +2cos3α)1/2 or 2a3.[sin(α/2).sin(3α/2)]1/2.sin(α/2)

3a2.sin600).c = √3/2.(a2c) = 0.866.a2.c

abc(1- cos2β)1/2 or abc.sinβ

abc.(1-cos2α –cos2 β–cos2 γ+ 2cosα .cosβ .cosγ )1/2 or

abc.(sin2α+sin2β+sin2γ-2+2cosα .cosβ .cosγ )1/2

Interplanar distances in crystal systems

crystal system 1/d2hkl =

Cubic

Tetragonal

Orthorhombic

Hexagonal

(h2 + k2 + l2)/a2

(h2 + k2)/a2 + (l2/c2)

(h2/a2) + (k2/b2) + (l2/c2)

[4/3(h2 + hk + k2)/a2] + (l2/c2)

(h2 + k2 + l2)sin2 α + 2(hk + kl + hl)(cos2 α + cos α)/a2(1 – 3 cos2 α

Rhombohedral

Monoclinic

Triclinic

+ 2cos3 α)

[h2/(a2 sin2 β)] + (k2/b2) + [l2/(c2 sin2 β)] – [(2hl cos β /ac sin2 β)]

1/V2(h2 b2c2sin2α+ k2c2a2sin2β +l2a2b2sin2γ) + 2hkabc2(cosα cosβ - cosγ) +2kla2bc(cosβ cosγ - cosα) + 2hlab2c(cosα cosγ - cosβ)

Relationships between direct and reciprocal lattice parameters

For triclinic crystal systems

Reciprocal lattice Direct lattice

a* = [b.c.sinα] /V

b* = [a.c.sinβ] /V

c* = [a.b.sinγ] /V and

a*=1/[a sin β* sin γ] =1/[a sin β sin γ*]

b*=1/[b sin γ*sin α] =1/[b sin γ sin α*]

a = [b*.c*.sinα*]/V*

b = [c*.a*.sinβ*]/V*

c = [a*.b*.sinγ*]/V* and

a=1/[a* sin β sin γ*] =1/[a* sin β* sin γ]

b=1/[b*sin γ sin α*] =1/[b* sin γ* sin α]

c*=1/[c sin α*sin β]=1/[c sin α sin β*]

a* :b*:c*=(sin α)/a : (sin β)/b: (sin γ)/c

V* = a*b*c* sin α* sin β* sin γ

V* = a*b*c* sin α* sin β sin γ*

V* = a*b*c* sin α sin β* sin γ*

V* = 1/V

d* =1/d

cos α* = [(cosβ.cosγ) – cosα]/sinβ.sinγ

cos β* = [(cosα.cosγ) – cosβ]/sinα.sinγ

cos γ* = [(cosα.cos β) – cosγ]/sinα.sinβ

[sin α*/sinα]=[sinβ*/sin β]=[sinγ*/sinγ]

c=1/[c* sin α sin β*]=1/[c* sin α* sin β]

a :b:c=(sin α*)/a*: (sin β*)/b*: (sin γ*)/c*

V = abc sin α* sin β sin γ

V = abc sin α sin β* sin γ

V = abc sin α sin β sin γ*

V = 1/V*

d = 1/d*

cos α = [(cosβ*.cosγ*) – cosα*]/sinβ*.sinγ*

cos β = [(cosα*.cosγ*) – cosβ*]/sinα*.sinγ*

cos γ = [(cosα*.cos β*) – cosγ*]/sinα*.sinβ*

[sin α /sin α*]=[sin β /sin β*]=[sin γ /sin γ*]

Relationships between direct and reciprocal lattice parameters

R.C. Monocl Ortho Hexa Rhombo Tet Cubic

a* = λ/a sin β λ/a (λ2/a)/√3) λ/a[sin α/(1-3cos2α + 2 cos3α)1/2]

λ/a λ/a

b* = λ/b λ/b (2λ/a)/√3) λ/a[sin α/(1-3cos2α +2 cos3α)1/2 ]

λ/a λ/a

c* = λ/c sin β λ/c λ /c λ/a[sin α/(1-3cos2α +2 cos3α)1/2 ]

λ/c λ/a

α* = 900 900 900 cos-1[-cosα/(1+cosα)] 900 900

β* = 1800- β 900 900 cos-1[-cosα/(1+cosα)] 900 900

γ* = 900 900 600 cos-1[-cosα/(1+cosα)] 900 900

For a rhombohedral system, α = β= γ and α* = β* = γ* therefore the cosin formulae can be written as:

cos α* = [(cosα.cosα)-cosα]/sinα.sinα or cos α* = [(cos2α - cosα)]/sin2α ; which is

= [cosα(cosα - 1)]/1 – cos2α or = cosα(cosα - 1)/(1 - cosα) (1 + cosα)

After simplification the equation can be reduced to:

cosα* = cosα/(1 + cosα)

Calculation of sin 2 θ by Bragg’s equation for crystal systems

Crystal system sin2θ =

Cubic

Tetragonal

Orthorhombic

Rhombohedral

Hexagonal

Monoclinic

Triclinic

[λ2(h2 + k2 + l2)]/4a2

λ2/ 4a2[(h2 + k2) + (λ2/4c2) l2]

λ2/ 4a2(h2) + λ2/4b2(k2) + λ2/4c2(l2)

λ2/ 4a2(p2+q2+r2)sin2α+2(pq+qr +rp)(cos2α –cos α) / (1+2 cos3α- cos2α)

λ2/ 3a2(h2 + hk + k2) + λ2/ 4c2 (l2)

λ2/ 4a2sin2β(h2 + k2 + l2) / 4a2(h2 + k2 + l2)

λ2/ 4[ha*2 + k2 b*2+ l2 c*2+2klb*c*cosα*+2lhc*a*cosβ* +2hka*b*cosγ*]

Values of N = h 2 +k 2 + l 2 in latices of cubic system

N P F I Forbidden N

1

2

3

4

5

6

7

8

9

9

100

110

111

200

210

211

220

300

221

111

200

220

110

200

211

220

7

10

11

12

13

14

15

16

17

17

18

18

310

311

222

320

321

400

410

322

411

330

311

222

400

310

222

321

400

411

15

19

20

21

22

23

24

25

25

26

26

27

331

420

421

332

422

500

430

510

431

511

331

420

422

511

420

332

422

510

431

23

27

28

29

29

30

31

32

33

33

34

34

333

520

432

521

440

522

441

530

433

333

440

521

440

530

433

28

31

35

36

36

37

38

38

39

40

41

41

41

531

600

442

610

611

532

620

621

540

443

531

600

442

620

600

442

611

532

620

541

42

43

44

45

45

46

47

48

49

49

50

541

533

622

630

540

631

444

700

632

710

533

622

444

622

631

444

710

47

Radii of elements : Ionic radii(Ǻ) of elements in crystalline state

Ion Rad Ion Rad Ion Rad Ion Rad

Li+

Na+

K+

Rb+

Cs+

Cu+

Ag+

0.9

1.16

1.52

1.66

1.81

74/91b

129

Be2+

Mg2+

Ca2+

Sr2+

Ba2+

Fe2+

Zn2+

0.59

0.86

1.14

1.32

1.49

0.92

0.74/88b

B3+

Al3+

Ga3+

In3+

Tl3+

Fe3+

Sc3+

0.41

0.68

0.76

0.94

1.03

0.79

0.89

H-

OH-

F-

Cl-

Br-

I-

O2-

1.26

1.23

1.19

1.67

1.82

2.06

1.26

Au+ 151 Cd2+

Hg2+

109

116

Y3+

Lu3+

1.04

1.00

S2-

Se2-

Te2-

1.70

1.84

2.11

Rules for systematically present reflections

Reflections Presences Symmetry symbol

hkl h+k+l = 2nh+k = 2nh+l = 2nk+l = 2n

h+k=2n,k+l=2n,h+l=2n orhkl→ all are odd or even

-h+k+l=3n

h+k+l=3n

no systematic presences

body-centeredC-centeredB-centeredA-centered

Face-centered

Face-centered

Rhombohedral

Hexagonal

I C B A

F

F

R

P

Primitive P

0kl k=2n

l=2n

k+l=2n

k+l=4n

(100) glide plane to a with b/2 translation

(100) glide plane to a with c/2 translation

(100) glide plane to a with (b/2)+(c/2) translation

(100) glide plane to a with (b/4)+(c/4) translation

b

c

n

d

h0l h=2n

l=2n

h+l=2n

(010) glide plane to b with a/2 translation

(010) glide plane to b with c/2 translation

(010) glide plane to b with (a/2)+(c/2) translation

(010) glide plane to b with (a/2)+c/4

a

c

n

d

h+l=4n translation

hk0

hhl

-h=2n

k=2n

h+k=2n

h+k=4n

l = 2n

h = 2n

h + l = 2n

2h + l = 4n

(001) glide plane to c with a/2 translation

(001) glide plane to c with b/2 translation

(001) glide plane to c with (a/2) + (b/2) translation

(001) glide plane to c with (a/4) + (b/4) translation

(110) glide plane to c with c/2 translation

(110) glide plane to a with (a/4) + (b/4) translation

(110) glide plane to c with (a/4) + (b/4) + (c/4) translation

(110) glide plane to c with (a/2) +

a

b

n

d

c

b

n

d

(b/4) + (c/4) translation

h00 h=2n

h=3n

h=4n

h=6n

Screw axis ‖to a with a/2 translation




21, 42, 63

31, 32, 62, 64

41, 43

61, 65

0k0 k=2n

k=3n

k=4n

k=6n

Screw axis ‖to b with a/2 translation




21, 42, 63

31, 32, 62, 64

41, 43

61, 65

00l l=2n Screw axis ‖to c with a/2 translationScrew

axis ‖to c with a/3 translation

21, 42, 6331,

32, 62, 64

l=3n

l=4n

l=6n

Screw axis ‖to c with a/4 translation

Screw axis ‖to c with a/6 translation

41, 43

61, 65

If the unit cell edgelengths are known, one can determine:

1. Unit cell volume (V)

2. Atomic radius (r)

3. Number of atoms/molecules per unit cell (Z)

4. Density (ρ)

5. Avogadro’s number (A)

6. Molecular mass (M)

7. Size of the hole/void

8. Prediction of formation of a compound

The equation used is: ρ = ZM/VA or ρ = 1.6604 ZM/V

where Z = Number of atoms/molecule per unit volume

M = atomic mass/molecular mass (g)

V =Volume of unit cell (Å3) x 10-24 to get it in cm3.

A = Avogadro’s number (6.02252x1023

Packing Efficiency:

Simple cubic system: The packing of atoms in a two dimensional lattice is considered. In a simple cubic system, the atoms occupy the corners of the unit cell and each corner is shared by four unit cells (in two dimensional lattice). Therefore the number of atoms per unit cell = 4x1/4 = 1 e.g. one atom per unit cell and the edgelength, a = 2r (where r is the radius of the atom) and the volume of the unit cell is V=a3 =(2r)3 = 8r3 ∴ r3 = a3/8 or r = ∛a3/8 = a/2. but the Volume of an atom of radius r = 4/3 π r3. Since there is only one atom/u.c. the volume occupied by an atom = 4/3 π r3 and V(unoccupied) = a3 - 4/3 πr3 or = a3 - 4/3 πa3/8 V(unoccupied) = a3 - 4/24 π a3 = a3(1-1/6 π) = 0.4764a3 or unoccupied volume = 0.4764 of total volume or it is 47.64 % of total volume ≈ 48% of total volume is unoccupied or 52% of total volume is occupied.

Therefore the packing efficiency of a simple cubic system is approximately 52%. The same conclusion can be drawn as below: relationship V(unoccupied) = a3 - 4/3 πr3 [since r = a/2] therefore V(unoccupied) = a3 - 4/3 πa3/8 or V(unoccupied) = a3 - 1/6 πa3 = a3(1-1/6π) V(unoccupied) = a3(0.4764) = 0.4764a3 or ≈ 0.48a3 or ≈ 48% of a3 V(occupied) = 52% of the total volume of unit cell. or packing efficiency e.g. V(occupied) = [volume of an atom x No. of atoms/u.c.]/volume of unit cell = [4/3 πr3 x 1]/8r3 = 0.524 or = 52.4% ≈ 52 % and density ρ = [at. mass /6.02 x 1023]/(2r)3 in g cm-3 Body centered cubic system: Face diagonal = √(a2 + a2) = √(2a2) = √(2) a or a√(2)

But body diagonal = √(face diagonal2 + edge length2) or = √(2)1/2a)2 + a2) = √(2a2 + a2) = √(3a2) = (√ 3) a But this is also = 4r

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