kubisch flächenzentriert (fcc) hexagonal dichtgepackt (hcp) iv/lecture_2.pdf · ruthenium 4d7 5s...
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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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2 Diamantstruktur
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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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2 Missing row reconstruction
fcc(110)-(2x1)
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2 Si(111)-(7x7)
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2 Si(111)-(7x7)
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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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2 Metall, Halbleiter und Isolator
EVakuum
EFermi\
Metall Halbleiter Isolator
Valenzband
Leitungsband
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2 Fermi-Verteilung
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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2 Jellium
• 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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2 rs & n Werte
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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2 Bandstruktur
-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