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kubisch flächenzentriert (fcc) hexagonal dichtgepackt (hcp)

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kubisch raumzentriert

bcc

hexagonal dichtgepackt

hcp

kubisch flächenzentriert

fcc

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kubisch flächenzentriertkubisch raumzentriert

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Periodic Table of Elements1

HHydrogen

1s

1.0079

13.59520.38

13.95

0.0899

2

HeHelium

1s2

4.0026

24.5814.1

3.3

0.126

3

LiLithium

2s

6.939

5.3901603

453.5

0.534

4

BeBeryllium2s2

9.01218

9.3202753

1556

1.87

5

BBoron

2s2 2p

10.811

8.2964173

2303

2.34

6

CCarbon

2s2 2p2

12.011

11.2564623

3923

2.24

7

NNitrogen

2s2 2p3

14.0067

14.54577.35

63.15

0.81

8

OOxygen

2s2 2p4

15.999

13.61490.18

54.36

1.14

9

FFluorine

2s2 2p5

18.9984

17.41885.05

53.55

1.505

10

NeNeon

2s2 2p6

20.183

21.55927.07

24.54

1.20

11

NaSodium3s

22.990

5.1381163.2

370.95

0.97

12

MgMagnesium

3s2

24.305

7.6441393

923

1.739

13

AlAluminium3s2 3p

26.98154

5.9842723

933.3

2.702

14

SiSilicon

3s2 3p2

28.086

8.1492628

1693

2.42

15

PPhosphorus

3s2 3p3

30.97376

10.484553.2w

317.2w

1.82w

16

SSulphur

3s2 3p4

32.064

10.357717.75

392.2

1.96

17

ClChlorine

3s2 3p5

35.453

13.01239.1

172.2

1.56

18

ArArgon

3s2 3p6

39.948

15.75587.29

83.77

1.784

19

KPotassium

4s

39.09

4.3391027

336.7

0.86

20

CaCalcium4s2

40.08

6.1111760

1123

1.55

21

ScScandium3d 4s2

44.956

6.543003

1811

2.99

22

TiTitanium

3d2 4s2

47.90

6.833503

1943

4.52

23

VVanadium3d3 4s2

50.942

6.743673

2003

5.96

24

CrChromium3d5 4s

51.996

6.7642913

2173

6.93

25

MnManganese

3d5 4s2

54.938

7.4323363

1517

7.2

26

FeIron

3d6 4s2

55.847

7.873008

1808

7.86

27

CoCobalt

3d7 4s2

58.933

7.863153

1765

8.9

28

NiNickel

3d8 4s2

58.71

7.6333073

1726

8.9

29

CuCopper

3d10 4s

63.54

7.7242863

1356

8.92

30

ZnZinc

3d10 4s2

65.37

9.3911180.2

692.66

7.14

31

GaGallium

3d10 4s2 4p

69.72

6.002503

302.93

5.910

32

GeGermanium3d10 4s2 4p2

72.59

7.883103

1232

5.35

33

AsArsenic

3d10 4s2 4p3

74.922

9.81889

5.72

34

SeSelenium

3d10 4s2 4p4

78.96

9.75958

490.6

4.82

35

BrBromine

3d10 4s2 4p5

79.909

11.84331.93

265.95

3.12

36

KrKrypton

3d10 4s2 4p6

83.80

13.996119.75

115.98

3.744

37

RbRubidium

5s

85.47

4.176973

311.85

1.532

38

SrStrontium5s2

87.62

5.6921643

1043

2.6

39

YYttrium

4d 5s2

88.905

6.3772903

1773

4.5

40

ZrZirconium4d2 5s2

91.22

6.8353900

2128

6.5

41

NbNiobium

4d4 5s

02.906

6.8815173

2773

8.55

42

MoMolybdenum

4d5 5s

95.94

7.105073

2893

10.21

43

TcTechnetium

4d5 5s2

7.228(4900)

2520

11.5

44

RuRuthenium4d7 5s

101.07

7.3654373

2773

12.6

45

RhRhodium

4d8 5s

102.9

7.4614233

2233

12.4

46

PdPalladium4d10

106.4

8.333473

1825

11.4

47

AgSilver

4d10 5s

107.87

7.5742473

1234

10.5

48

CdCadmium

4d10 5s2

112.40

8.9911038

594.18

8.65

49

InIndium

4d10 5s2 5p

114.82

5.7852323

429.76

7.362

50

SnTin

4d10 5s2 5p2

118.69

7.3422963

505.06

5.750

51

SbAntimony

4d10 5s2 5p3

121.75

8.6391910

903.7

6.69

52

TeTellurium

4d10 5s2 5p4

127.60

9.011263

723

6.25

53

IIodine

4d10 5s2 5p5

126.90

10.454456

386.8

4.93

54

XeXenon

4d10 5s2 5p6

131.30

12.127165.03

161.4

5.897

55

CsCesium6s

132.90

3.893958

301.79

1.873

56

BaBarium

6s2

137.34

5.2101910

983

3.5

57

LaLanthanum

5d 6s2

138.91

5.613743

1193

6.18

58

CeCerium

4f 5d 6s2

140.12

6.543743

1070

6.7

59

PrPraseodymium

4f3 6s2

140.91

5.483290

1208

6.7

60

NdNeodymium

4f4 6s2

144.24

5.513483

1297

6.9

61

PmPromethium

4f5 6s2

3473

1308

-

62

SmSamarium4f6 6s2

150.35

5.61943

1345

7.5

63

EuEuropium4f7 6s2

151.96

5.671703

1099

5.245

64

GdGadolinium4f7 5d 6s2

157.25

6.163070

1585

7.96

65

TbTerbium

4f9 6s2

158.92

6.742750

1629

8.25

66

DyDysprosium

4f10 6s2

162.50

6.822600

1680

8.45

67

HoHolmium

4f11 6s2

164.93

2760

1734

8.76

68

ErErbium

4f12 6s2

167.28

2690

1770

9.05

69

TmThulium

4f13 6s2

168.93

1990

1818

9.29

70

YbYtterbium

4f14 6s2

173.04

6.221590

1097

7.0

71

LuLutetium

4f14 5d 6s2

174.97

6.153270

1925

9.82

72

HfHafnium

4f14 5d2 6s2

178.49

7.05420

2495

13.36

73

TaTantalum

4f14 5d3 6s2

180.95

7.885670

3270

16.6

74

WTungsten

4f14 5d4 6s2

180.95

7.985770

3650

19.3

75

ReRhenium

4f14 5d5 6s2

186.2

7.875870

3453

20.53

76

OsOsmium

4f14 5d6 6s2

190.2

8.74670

2970

22.48

77

IrIridium

4f14 5d7 6s2

192.2

9.24620

2716

22.42

78

PtPlatinum

4f14 5d8 6s2

195.09

8.884570

2042.5

21.450

79

AuGold

4f14 5d10 6s

196.97

9.222970

1336.2

19.29

80

HgMercury

4f14 5d10 6s2

200.59

10.434629.73

234.28

13.546

81

TlThallium

4f14 5d10 6s2 6p

204.37

6.1061731

576.7

11.85

82

PbLead

4f14 5d10 6s2 6p2

207.19

7.4152023

600.5

11.34

83

BiBismuth

4f14 5d10 6s2 6p3

208.98

7.2871833

544.4

9.8

84

PoPolonium

4f14 5d10 6s2 6p4

8.431235

527

-

85

AtAstatine

4f14 5d10 6s2 6p5

650

570

-

86

RnRadon

4f14 5d10 6s2 6p6

10.745211

202

-

87

FrFrancium7s

593

298

-

88

RaRadium

7s2

5.2771800

973

5

89

AcActinium

6d 7s2

6.93600

1470

-

90

ThThorium

6d2 7s2

232.04

4470

2020

11.724

91

PaProtactinium5f2 6d 7s2

4470

1840

15.37

92

UUranium

5f3 6d 7s2

238.03

4.04091

1405

18.97

93

NpNeptunium5f4 6d 7s2

4175

912

20.45

94

PuPlutonium5f6 7s2

3503

912.6

19.737

95

AmAmericium4f7 7s2

2880

1267

13.67

96

CmCurium

5f7 6d 7s2

1610

13.51

97

BkBerkelium

5f8 6d 7s2

98

CfCalifornium5f9 6d 7s2

99

EsEinsteinium5f10 6d 7s2

100

FmFermium

5f11 6d 7s2

101

MdMendelevium

102

NoNobelium

103

LrLawrencium

n

Xxname

electrons

mass

IPTboil

Tmelt

!

fccbcc

hcp

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kubisch raumzentriert

bcc

hexagonal dichtgepackt

hcp

kubisch flächenzentriert

fcc

Dichtgepackte Strukturen

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( 1 1 0 )( 1 1 1 )

( 1 0 0 )

fcc single crystal : different surface terminationsfrom BALSAC, K. Hermann

siehe auch: http://www.phchem.uni-due.de/photochem/Crystal faces.pdf

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Pt(100) reconstructed

Rekonstruktion

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fcc(110)-(2x1)

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( 3 3 5 )

steps

( 11 13 19 )

kinks

BALSAC plotHigh Miller indexed fcc surface with steps / kinks from BALSAC, K. Hermann

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EdgeAtom

Adatom EdgeAdatom

EdgeVacancy Surface

Vacancy

SurfaceAtom

KinkAtom

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0123456

free atom in vapor

adatom, WA

ledge adatom, WLA

kink atom, WK

ledge atom, WL

surface atom, WT

bulk atom

BIND

ING

ENE

RGY

(NN

BOND

S)

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square

rectangular centred rectangular

hexagonal oblique

a2s

a2sa2s

a2s a2s

a1s

a1sa1s

a1s a1s

γ

γγ

γ γ

|a1s| = |a2s|

|a1s| = |a2s|

|a1s| ≠ |a2s|

|a1s| ≠ |a2s|

γ = 90°

γ = 90°

γ = 120° γ ≠ 90°

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fcc(110) + c(2x2)-Ad

fcc(100)+p(2x2)-Ad; ; ~+c(4x2)-Ad

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2 Surface Crystallography1-1. Bludau et at~Surface Science 342 (1995) 134-154 139

0.35 -

0.30

0.25

0.20

0.15

0 . 1 3 0.O

Ocs- O o -phase diagram

. "/ ~ffu i weak 3 + d i s e (2x2) ~I I I I

l l

~3 I l

w~"/3 I

,,31 i ,

~, 12~I I = I [diffuse) I [ • x I ~ r2x2~ ! 12~.,) "= I i (diffuse

/

( d i f f u s e )

( 2x2 ) ) 2q3 [ t

(2x2) [snlitl I '(2x21 I spI t

1 ~39

`/39 I I

I I

¢) [ -421 (3x2-~a)iffu I ~ - - ~. d - - se)-lD

I dllffuse

d i f f u s e 1"17 D. I I

d i f f u s e [ "/7 I D, I I I

J `/7 [diffuse 47 l I

I ~7 I I diffuse q7 --q~ I

diffuse (2x~) [ ",~39 I I I weak)

ring ! diffuse ring I B [

"~'7 idtffuse "/7

I `]7 lldifUSel ~

ring i diffuse ring I I I I ii (z~l I dif.se

r ing I (2x2) ] Idifftls e I

I 011 0.2 013 0 1 4

0o

I `/7 I

I P

o15

[ diffuse---------~

0.6 017 0.8

Fig. 6. Experimentally derived phase diagram for cesium and subsequently adsorbed oxygen on the Ru(0001) surface for T - 310 K (only for the (3 x 2vr3)rect structure annealing to 370 K was required in order to obtain sufficient long-range order). The oxygen coverages were determined by the exposure and using the calibration curve in Fig. 2. Dashed boundaries are approximate ones.

of the oxygen-sticking coefficient dependent on the Cs coverage.

3.2.2. Cs coverage Ocs = 0.33 We start a detailed description of the Cs -O

phases with a horizontal cut through this phase diagram for an initial coverage of one monolayer of cesium (Ocs=0.33), i.e. with a well-defined 6U3 x v~)R30 ° structure. The development of the Cs -O structures at elevated temperatures with in- creasing oxygen exposure can readily be monitored by the LEED intensity of a third-order beam, for example the (2/3, 1/3) beam (see Fig. 7). This is possible because all structures appearing, except

tn

v

' I ' I ' I ' I ' I ' I ' 1 ' I ' ' I ' ( 2 / 3 , 1 / 3 ) - b e a m . O c s = 0 . 3 3

T=310 K

I , , I , 0.0 0.2 0.4 0.6 0.8 t.O 1.2 1.4 t.a 1.g 2.0

O2-Exposure (L)

Fig. 7. L EED intensity of the (2/3, 1/3) superstructure spot as a function of the oxygen exposure at T= 310 K. Since the (2/3, 1/3) spot is common to all structures in this s~quence, the maxima are related to the optimum development of the different C s - O superstructures stated. The corresponding oxygen coverages are indicated.

the hexagonal rotated ones, are commensurate with respect to the (v~ x v~)R30 ° unit mesh.

As with lower temperatures, already the addition of small doses of oxygen (<0.05 L) led to the appearance of incommensurate, rotated struc- tures and the successive disappearance of the (v~xv~)R30 ° structure as visible in a rapid decrease of the intensity of its superstruc- ture beams. Between 0.1 L and 0 .2L the (v'-3 x v~)R30°-pattern vanished cOmpletely; instead, the t E E D screen showed spots of the rotated structures.

Further oxygen deposition gave rise to an increase of the (2/3, 1/3) beam intensity leading to the reappearance of a well-ordered (V-J × v~)R30 ° structure with maximum intensity a t 0.7 L of oxygen. This exposure corresponds to a coverage of 0 o = 0 . 3 4 , i.e. to a stoichiometry of Cs: O = 1 : 1. A t E E D structural analysis of this (v~ x v~)R30 ° Cs -O phase containing one Cs and O atom per unit cell clearly favored a model, in which both atoms reside in hcp sites with respect to the Ru(0001) substrate and where the oxygen atoms are located below the plane of the Cs a~oms [21] (Fig. 8). The reduced layer distance of the Cs atoms in the (v'-3 x ~U3)R30 ° Cs -O phase compared to the

Ertl & co, Surf. Sci. 342, 134 (1995)

Ru(001)

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EVakuum

EFermi\

Metall Halbleiter Isolator

Valenzband

Leitungsband

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f(E) =

⇤exp

�E � µ

kBT

⇥+ 1

⌅�1

Fermi-Dirac Statistic

Elektronen sind Spin = ½ Teilchen, sog. Fermionen

1.0

0.8

0.6

0.4

0.2

0.0

Bes

etzu

ng

86420

Energie [eV]

µ = 5.5 eV T = 0 K 300 K 4000 K

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• unendlicher großer Kristall

• positive Ladungsdichte:

• Fermi Energie

• effektiver Radius

• typischer Wert: rs = 0.15 nm

�+(r) = ne

�F =�2

2m(3⇥2n)2/3

4� r3s

3= n�1

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Element rs [nm] n [1022 cm-3]

Li 0.17 4.7Rb 0.27 1.2Cu 0.14 8.5Ag 0.16 5.9Be 0.10 24.2Ca 0.17 4.6Al 0.11 18.1Pb 0.12 13.2

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-1-12

1-10_K

_M

_Γ

Ag (111)5

0

-5

eV

_K

_Γ

_M

_K

A

E

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EgEF

Evac

p-Si Ag NO

E

eΦSB

Semiconductor Metal Adsorbat

CB

VB

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(+)

(-)

Stufenkante

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VOLUME 82, NUMBER 22 P HY S I CA L REV I EW LE T T ER S 31 MAY 1999

Figure 1 shows a constant current image of a Cu(111)step edge at V � 1.4 V in (a) and the dI⇧dV image takensimultaneously in (b). Since dI⇧dV is a quantity roughlyproportional to the surface LDOS [21] the clearly visiblespatial oscillations in Fig. 1(b) are a direct consequenceof Friedel oscillations in the LDOS of the 2D surfacestate electron gas which are induced by every staticscattering center (e.g., step edges and point defects). Forour experiment we have chosen straight step edges witha defect free area larger than 250 Å 3 250 Å on theadjacent upper terrace (Fig. 1). By doing so we are surethat the local elastic mean free path Lm is considerablylarger than the measured Lf [1], and thus the LDOSoscillations at the step are not influenced by other staticscattering centers. In order to evaluate the decay of thestanding waves away from straight step edges as shownin Fig. 1 the dI⇧dV images have been slightly rotated toalign the step edge vertically, and then we have averagedthe dI⇧dV data over several line scans. Typical averageddI⇧dV data are presented in Fig. 2(a).To interpret our data we use elastic tunneling theory, i.e.,

the tunneling current I is given by

I�V , T , x, z⇥ ~Z `

2`T �E, V , z⇥rs�E, x⇥rt�E 2 eV ⇥

3 ⇤ f�E 2 eV , T ⇥ 2 f�E, T ⇥⌅ dE , (1)

where T is the temperature, x characterizes the lateralposition, z is the distance between surface and tip, rsis the surface LDOS, and f�E, T ⇥ is the Fermi function.The tip LDOS rt is assumed to be a constant sincewe are interested only in lateral variations of dI⇧dV .The transmission factor T is given by T �E, V , z⇥ �

FIG. 1. (a) Constant current image of a Cu(111) step edge:280 Å 3 138 Å, V � 1.4 V, I � 7 nA. (b) dI⇧dV imagetaken simultaneously with (a) by lock-in technique (DV �135 mV). Standing wave patterns at static scatterers as stepsand impurities are clearly visible.

e2zp

2me⇧ h̄2�p

Wt2E1eV1p

2E�12m�⇧me⇥2m�⇧meE2D0 1Ws ⇥, where

m� and E2D0 are the effective mass and the band edge of the

surface state, respectively, and Wt is the work function ofthe tip [21]. (Energies are given with respect to the Fermienergy.) The work function of the sample, Ws, can beconsidered constant for our purposes since we have foundits reduction at steps due to the Smoluchowski effect to belocalized to63 Å around the step edge. As shown by ARP[8–10] and STM [18,19] the Shockley type surface stateson noble metals form a quasifree 2D electron gas. Thus,in the presence of a straight step edge extending infinitelyin y direction, rs is readily calculated to yield

rs�E, x⇥ � rb 12L0

p

Z kE

0dq

31 2 r�q⇥e22�xkE⇧qLf⇥ cos�2qx⇥p

k2E 2 q2

, (2)

FIG. 2. (a) Typical dI⇧dV data perpendicular to a descendingCu(111) step obtained by averaging over several line scans ofa dI⇧dV image as shown in Fig. 1(b). The data at 1 and 2 eVwere taken with a stabilizing current of 5 and 10 nA and a DVof 119 and 156 mV, respectively. The solid lines depict thefits with Eqs. (4) and (5). The significance of the deducedLf is demonstrated by the dashed line: neglecting inelasticprocesses by setting Lf � ` leads to a much slower decay ratethan observed. (b) Comparison between the full calculation ofdI⇧dV with Eqs. (1) and (3) and the result obtained by settingT constant (T ! 0, Lf ! `, typical Cu(111) parameters:Ws � Wt � 4.5 eV, r � 0.5 [23]).

4517

Bürgi et al., Phys. Rev. Lett. 82, 4516 (1999)

Strom

x

y

e-

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2 Surface Smearing & Fridel Oszillationen

Oszillationen je größer je größer rs

Distance

SurfaceFriedeloscillations

Exponentialdecay intovacuum

Elec

tron

dens

ity

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Fe/Cu(111)

Eigler, IBM

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Fe/Cu(111)Don Eigler, IBM, http://www.almaden.ibm.com/vis/stm/

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a a

jj -1 jj +1jj

j -1 j +1j

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2 Debye Temperatur

Element θD [K]

Ag 225

Au 165

C (Diamand) 2230

C (Graphit) 760

Ge 385

Pt 240

Si 645

W 400

�D =� ⇥D

kB

• Debye Frequenz, ωD, ist ein Maß für die Steifheit des Gitters der Atome

• Die Debye Frequenz der Oberfläche ist meist niedriger als die im Volumenz.B. für Pt(100): 110 K

• Die Vibrationsamplituden an der Oberfläche sind 1.4 bis 2.6 mal so groß wie im Volumen