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Slides from 2012 in videos assigned for lectures on 8 and 10 November
2012-Lecture 10 starting from 0:33 until the end, all of lecture 11 and
lecture 12 from start to 1:02.
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2
SAME SUBSHELL COUPLING +
TOTAL L,S”MONOPOLE”
(N-1)e- SHAKE-UP/
SHAKE-OFF
”MONOPOLE” 1e- DIPOLEd/d
"Basic Concepts of XPS"
Chapter 3
tot
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3
SAME SUBSHELL COUPLING +
TOTAL L,S”MONOPOLE”
(N-1)e- SHAKE-UP/
SHAKE-OFF
”MONOPOLE” 1e- DIPOLEd/d
"Basic Concepts of XPS"
Chapter 3
tot
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4
SAME SUBSHELL COUPLING +
TOTAL L,S”MONOPOLE”
(N-1)e- SHAKE-UP/
SHAKE-OFF
”MONOPOLE” 1e- DIPOLEd/d
"Basic Concepts of XPS"
Chapter 3
tot
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5
SAME SUBSHELL COUPLING +
TOTAL L,S”MONOPOLE”
(N-1)e- SHAKE-UP/
SHAKE-OFF
”MONOPOLE” 1e- DIPOLEd/d
"Basic Concepts of XPS"
Section 3.D.
tot
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6
SAME SUBSHELL COUPLING +
TOTAL L,S”MONOPOLE”
(N-1)e- SHAKE-UP/
SHAKE-OFF
”MONOPOLE” 1e- DIPOLEd/d
"Basic Concepts of XPS"
Section 3.D.
Section 6.D.
tot
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v0 e inc
(c)
fK
fk
0 = reference
wave
j = object
wave
(a) (b)
CO
C1s
500 eV
ref. intens.
I0 |0|2
Photoelectron Diffraction
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0.65 Å
Forward Scattering
X-ray Photoelectron Diffraction:1ML FeO on Pt(111)
(a) (b)
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9
PLUS SPIN:
()= msi
= +½ =
()= msi
= -½ =
()
()
()
()
ms
=
msf
- msi
= 0 !
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10
- = antibonding
1sa - 1sb
+ = bonding
1sa + 1sb
The quantum mechanics of covalent bonding in molecules:
H2+ with one electron
=R
Total
Energy antibonding
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11 a.u. = -16.16 eV
(Compare – 13.61 for H atom 1s)
a.u. = +7.21 eV
negative (occupied)
positive (unoccupied)
Bonding
Anti-Bonding anti
MO 1sa - 1sa
bondingMO 1sa + 1sa
Ha Hb
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12 36
The LCAO or tight-binding picture for CO:
Chemist’s picture (no core):
C O x
x X
x
NON/WEAKLY CORE:
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13
THE ELECTRONS
IN HF (OR HCl):
ionic molecules
F H
1 E = -25.6 a.u.
F 1s core
12
HF: F1s222321x2 1y
2
1 e- 9 e-
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14 "Basic Concepts of XPS"
Chapter 3
PLUS SPIN:
()= msi
= +½ =
()= msi
= -½ =
()
()
()
()
ms
=
msf
- msi
= 0 !
PLUS SPIN:
()= msi
= +½ =
()= msi
= -½ =
()
()
()
()
ms
=
msf
- msi
= 0 !
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15
The free-electron solid at absolute zero 2 2
2
e
kE(k ) 3.81(k( in )) ( in eV )
2m Å-1
= the density of states
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NEARLY-FREE ELECTRONS IN A WEAK PERIODIC POTENTIAL—1 DIM.
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17
L
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18
Aluminum—fcc,
a = 4.05 Å
1s22s2 2p63s2 3p1
Electronic bands and density of states for “free-electron” metals -
Rydberg = 13.605 eV
a
0
2/a
=1.5
5Å
-1
Lithium—bcc, a = 3.49 Å
1s22s1
a
2/a
=1
.8Å
-1
kx
0
2 2
xx
(k )E(k )
2m
2 2
xx
(k )E(k )
2m
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19
Electronic bands and density of states for a semiconductor-Germanium—
1s22s2 2p63s2 3p63d104s24p2
Bonding
(filled at
T = 0)
Anti-
Bonding
(empty at
T = 0)
EF
Vacuum
Level Work
Function,
= 4.8 eV
Inner
Potential,
V0 4.8+0.3+12.6
= 17.7 eV
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20
V0,Cu
=13.0eV
- 8.6 eV
Vacuum level
The electronic structure of a transition metal —fcc Cu Cu = 4.4 eV = work function
Experimental
points from
angle-resolved
photoelectron
spectroscopy
(more later)
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21
1x
3
4
1y
5
–+
++–
+
Atomic orbital makeup
,( ) ( )MO AO
j Ai j Ai
Atoms AOrbitals i
r c r
1x
3
4
1y
5
–+
++–
+
Atomic orbital makeup
1x
3
4
1y
5
–+
++–
+
1x
3
4
1y
5
–+
++–
+
Atomic orbital makeup
,( ) ( )MO AO
j Ai j Ai
Atoms AOrbitals i
r c r Solid state tight-binding approach
j
j
BF
k
ik R AOAi jAi ,k1/ 2
Ai= basis set of AOsj = 1.....N unit cells at Rin unit cell
φ (r ) = a Bloch function
1 e c φ (r R )
N
Crystal potential-1D
Tight-binding wave function
Atomic orbitals
j-1j j+1
jR
Bonding
Anti-
Bonding
Ej
Molecular
orbital
approach
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22
And the same thing for the d orbitals:
e g
t 2g 3z 2 - r 2 x 2 - y 2
yz zx xy
x
y z
e g
t 2g 3z 2 - r 2 x 2 - y 2
yz zx xy
x
y z
eg and t2g not
equivalent in
octahedral (cubic)
environment
Transition
Metal (e.g. Mn)
Ligand
(e.g. O)
eg and t2g not
equivalent in
octahedral (cubic)
environment
Transition
Metal (e.g. Mn)
Ligand
(e.g. O)
Face-centered cubic—
12 nearest neighbors
x
y
z
xy
yz
zx
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23
Copper densities of states-total and by orbital type:
~Bonding ~Anti-Bonding
More localized 3d-like
Delocalized free
electron-like
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24
The electronic
structures of the 3d
transition metals—
“rigid-band
model”
3s23p6 filled + 3d,4s CB 3d24s2 3d34s2 3d54s1 3d64s2
3d74s2 3d84s2 3d104s1 3d104s2
+ Flat “core-
like” Zn 3d
bands at -0.8
Rydberg
+ Flat “core-
like” Ar 3s, 3p
bands at -1.0-
1.5 Rydbergs
+ Exchange!
+ Exchange!
+ Exchange!
+ Exchange!
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25 k = 0 k = 0
Spin-down (Minority)
Spin-up (Majority)
The electronic bands and densities of states of ferromagnetic iron
Exchange
splitting S = 2.2 Bohr
magnetons
(Atomic iron:
2.0 Bohr
magnetons)
4 x ½ = 2
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26
Hathaway et al., Phys. Rev. B 31, 7603 (’85)
Eexch
V0,Fe
=12.4 eV
Vacuum level
Fe = 4.3 eV
-8.1 eV
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Fe: ANGLE AND
SPIN-RESOLVED
SPECTRA AT POINT
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28
And the same thing for the d orbitals:
e g
t 2g 3z 2 - r 2 x 2 - y 2
yz zx xy
x
y z
e g
t 2g 3z 2 - r 2 x 2 - y 2
yz zx xy
x
y z
Face-centered cubic—
12 nearest neighbors
x
y
z
xy
yz
zx
-
+
- +
-
+
- +
+
-
+
-
+
+
-
+
- + eg and t2g not
equivalent in
octahedral (cubic)
environment
Transition
Metal (e.g. Mn)
Ligand
(e.g. O)
eg and t2g not
equivalent in
octahedral (cubic)
environment
Transition
Metal (e.g. Mn)
Ligand
(e.g. O)
yz plane
-
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29
E.g.—Crystal field in Mn3+ & Mn2+ with negative octahedral ligands
Mn3+ 3d4
Bonding-
Delocalized
Non/Weakly-Bonding-
Localized
10 Dq Xstal fld.
JH > 0 Exchange
Jahn-
Teller
x
y
z
Mn2+ 3d5
High-spin*
High-spin*: 10Dq << JH
/Low-spin*
Low-spin*: 10Dq >> JH
+
-
A1
B1
E
B2
Group theoretical symmetry
bonding
+ -
+
bonding +
-
+
-
-
+
+
-
O2pz
O2pz
-
yz plane
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Chikamatsu et al.,
PRB 73, 195105 (2006);
Plucinski, TBP
Plucinski, TBP
with expt’l. band offset
Zheng, Binggeli, J. Phys.
Cond. Matt. 21, 115602 (2009)
Plucinski, TBP
La0.67Sr0.33MnO3- Half-Metallic
Ferromagnet
SrTiO3 and La0.67Sr0.33MnO3 band structures and DOS
Projected DOSs
Spin-down
Spin-up Spin-down
Mn eg
Mn t2g Expt’l. band offset 3.0 eV
Expt’l. bandgap 3.3 eV
dxz+dyz
dxy
dz2 dx2-y2
O 2p
Spin-up
dxz+dyz
dxy
SrTiO3-band insulator
No spin down!
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Experiment- spin-resolved PS
La0.70Sr0.30MnO3 as thin film
Park et al., Nature, PRB 392, 794 (1998)
T << TC T > TC
Half-Metallic Ferromagnetism O 2p
O 2p Egap
JH
Mn 3d
EF
O 2p
O 2p
FM : T << TC
PM : T > TC
Mn 3d
t2g eg
Energy (eV) Pickett and Singh, PRB 53, 1146 (1996)
O 2p
La 4f
Egap
JH
LDA theory- FM La0.75Ca0.25MnO3
t2g t2g
t2g
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33
SURFACE ELECTRONIC STATES
(d character, localized)
(s,p character, delocalized)
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34
Shockley
surface
State:
s,p makeup
Tamm
surface
state:
3d makeup
Surface states
on Cu(111)
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“The UPS Limit”
Vary to scan
,|| ,||f fK k
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The Nobel Prize in Physics 2010
Andre Geim, Konstantin Novoselov
…"for groundbreaking experiments
regarding the two-dimensional
material graphene"
Bostwick et al., Nature Physics 3, 36 - 40 (2007)
Photoelectron spectroscopy
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38
The Soft X-Ray Spectroscopies
Core
VB
EF
CB
e-
e- Valence PE
PE = photoemission = photoelectron spectroscopy
XAS = x-ray absorption spectroscopy
AES = Auger electron spectroscopy
XES = x-ray emission spectroscopy
REXS/RIXS = resonant elastic/inelastic x-ray scattering
h
h
Electron-out:
surface
sensitive Core PE
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39
hv
i(bound)
f(free)
Vacuum
MATRIX ELEMENTS IN THE SOFT X-RAY SPECTROSCOPIES: DIPOLE LIMIT
Photoelectron spectroscopy/photoemission:
2ˆ (1) (1)f iI e r
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40
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41 "Basic Concepts of XPS"
Figure 1
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42
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43
NO. ATOMS QUANTITATIVE SURFACE ANALYSIS
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44 36
The LCAO or tight-binding picture for CO:
Chemist’s picture (no core):
C O x
x X
x
NON/WEAKLY CORE:
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45
Valence-level
Photoelectron
spectra of CO
adsorbed on
various
transition
metal
surfaces
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– +
Ni 3dxy
“back
bond”
+
+
–
–
Zangwill,
p. 307, plus
PRL 55, 2618 (’85)
Theoretical
Calculations
of charge
density for
CO bound to
Ni(001)- “on-
top”:
O
|
C
|
Ni
CO 5
Ni 3dz
bond
+
–
–
–
–
+
CO 2 = *
Density
gain
Ni
2
+ –
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Vibrational
fine structure
Kimura et al.,
“Handbook of HeI
Photoelectron Spectra”
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SAME SUBSHELL COUPLING +
TOTAL L,S”MONOPOLE”
(N-1)e- SHAKE-UP/
SHAKE-OFF
”MONOPOLE” 1e- DIPOLEd/d
"Basic Concepts of XPS"
Chapter 3
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VIBRATIONAL
STRUCTURE IN
VALENCE-LEVEL (MO)
SPECTRA
Diatomic A-B example
(Also applies to core-
level emission if
equilibrium distance
changes on forming
core hole)
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VIBRATIONAL STRUCTURE IN VALENCE-LEVEL (MO) SPECTRA
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SAME SUBSHELL COUPLING +
TOTAL L,S”MONOPOLE”
(N-1)e- SHAKE-UP/
SHAKE-OFF
”MONOPOLE” 1e- DIPOLEd/d
"Basic Concepts of XPS"
Chapter 3.D.
spin-orbit +