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Optics and spectroscopyon (complex) hydrides
Andreas Borgschulte [email protected]
ContentsTechniques:
Photoemission spectroscopyUV-VIS spectroscopyIR/Raman spectroscopy
Physics:Band structure of electronsVibrations in solids
2
Schrödinger equation starts from interactions…and gives energies
( ) ( )[ ] ( )[ ] ( ) ( ) iiieffeffeffeffeffeff EpAAppBp Ψ=Ψ
⋅+⋅×∇+⋅×∇+−∇⋅∇+⋅+− σσφαφασφ 21
22
21
2
212
21
44
How to measure the Electronic Structure of Solids
Chem. interaction
magnetic interaction
Darwin-term
Dipole interactionSpin-orbit-coupling
Landau-term
UV IR RF
Chem. enthalpy: 0.1...10 eV
Exchange interaction: 0.1...5 eV Magn. anisotropy: 1...1000 µeV
Phonons: 1...100 meV
Photoemission Spectroscopy: 10 meV...10 keVUV-VIS spectroscopy: eVsIR-/Raman-Spectroscopy: 10 meV…1 eV
4
30 40 50 60 70 80 90 100
-70 -60 -50 -40 -30 -20 -10 0
inte
nsity
(cou
nts)
kinetic energy (eV)Pt
4f 5/
2Pt
4f 7/
2
Pt 5
p
Cr 3
p
valence bondhν = 120 eV
binding energy (eV)
LVE
E
K
L1
2,3
vac
F
)( Fvacbind EEEh −−+= ν
The Photoeffect
light: photons E= hνelectrons
Ekin
Momentum is also conserved
5
Elemental Composition on the surfaceCore-level shifts hint at electronic
changesComposition of desorbing speciesvalence bond spectroscopy?
Combined XPS and desorption mass spectrometry
95 90 850.30.40.50.60.70.80.91.0
540 535 530 525
0.30.40.50.60.70.80.91.0
100 90 80 70 60 50
0.2
0.4
0.6
0.8
1.0
Mg 2s
inte
nsity
(1)
O 1s
O2-OH-
oxmet
Mg 2s Mg KLL
Mg 2p
inte
nsity
(1)
binding energy (eV)XPS
50 100 150 200 250 30010-14
10-13
10-12
10-11
10-10
10-9
10-8
10-71.45
1.50
1.55
1.60
1.65
1.70
1.75
9x104
1x105
1x105
50 100 150 200 250 300
mass 2 (H2) mass 18 (H2O)
T =
175
deg
C
MS
-Sig
nal
(mba
r)
time (min) = temperature (deg C)
O1s
/ M
g2s
- Sig
nal
(1)
O1s
-sig
nal
(cou
nts)
MSA. Borgschulte et al., Appl. Surf. Sci., 254 (2008) 2377–2384
6
Important property is d/a
)/2()( akk π+Ψ=Ψ
Largest wavelength => infinity (k=0), smallest => a (k=π/a), because
k-vector = 2πd/aCan be understood as a wave with wave length a
kidadi eeadd ⋅=∝Ψ⇒+Ψ=Ψ /2)()( π
k-space and electronic structure
8
Band structure: Bloch functions
( )airRr /2exp)()( 0 πΨ=Ψ⇒Ψ=+Ψ
Schrödinger equation
ÜberlappAtom hHH +=
Tight-binding electronic bandstructure
k = 0
k = /aπ
k = 0
k = 0 k = /aπ
E(k)
E0
Example s-orbitals
9
3d-Element with bcc-structureE.g.. Cr
Tight-binding electronic bandstructure
More orbitals…
Hume-Rothery rules: f.c.c. vs. b.c.c.
s-electrons
10
( )[ ] [ ]∑∫ −⋅−−∝if
fiffi kEEkEkEMkdEN,
23 )()(),( δωδω hh
Momentum conservation in photoemission
Changing the exit angle θ
11
Bandstructure of yttrium dihydride probed by UPS
Ref. J. Hayoz et al., Phys. Rev. Lett. 90, 196804 (2003).
13
( )
( )
mfexx
dtxdmxxfF
xxfV
ti =⇒∝−
=−⋅−=
−⋅=
00
2
2
0
202
1
ωω
xx0
V
Molecular vibrations
f m
xx0
V
Real potential
causes anharmonicity
021 )( ωh+= nEωh
Quantum mechanics
9.01111
=+=− HBHB mmm
fmB mH
Reduced mass
14
ερ /=∇Er
0=∇Br
EjB &rrrµεµ +=×∇
BE &rr−=×∇
ρ&r
−=jdiv
EPED r
rrrrεεε 00 =+=
HMHB r
rrrrµµµ 00 =+=
Fundamentals: The Maxwell equations
( )
Et
Et
jt
Ht
E
2
2
∂∂
−=
∂∂
+∂∂
−=
×∇∂∂
−=×∇×∇
µεεµ
µ
( )
0002
2
22
2
111,1εµεµ rr
cn
cEtc
E
EE
==∂∂
=∇
−∇=×∇×∇
rn ε=
( )nc
nnr
0
2
222
1
21
42,
ωελπκωα
κεκε
εεεε
==
=−=
+=→
15
( )ωγωω
γω
ω
imeeEx
eeEfxxmxmti
ti
+−=
=++
20
0
0&&&
(Ne)-
x(Ne)+
( )
( ) ( )( )
( ) ( ) 222220
2
222220
220
1
220
1
1
/1
γωωωωγωε
γωωωωωωε
ωγωωωε
ε
+−=
+−
−+=
+−+=
+==
s
s
is
EPNexP
Drude-Lorentz model
0 1 2 3 4 5 6-10
-5
0
5
10
ω
ε 1, ε 2
( )
( ) ( )22
2
2
22
2
1
0
1
γωωγωωε
γωω
ωε
γ ω
+=
+−=
=++
p
tieeEfxxmxm &&&
Metals:
ω0
ωp
mNes /2=Oscillator strength
16
J. H. Weaver, D . W. Lynch, Phys. Rev. B 7, 4737 (1973).J. H. Weaver, C. G. Olson, Phys. Rev. B 15, 590 (1977).
yttrium
How to measure optical constantsEllipsometry => ε1, ε2 directly
Transmission:
λπκαα /4,0 == − xeIIReflection:
( )( ) 22
22
11
κκ
+++−
=nnR
Mind the sample
geometry!
All properties are interrelated via theKramers-Kronig relation
( ) ( )∫∞
−⋅
⋅+=0
22 ''
''21 ωωωωω
πω dkPn
17
A. T. M. van Gogh et al. Phys. Rev. B 63, 195105 (2001)Huiberts et al. Nature 380 (1996) 231
Optical properties of YHx
During hydrogen uptake of yttrium,
a metal-insulator transitionoccurs
YH2: metalYH3: insulator
Pure yttrium
YH2
YH3
18
P. van der Sluis et al. Appl. Phys. Lett. 70, 3356 (1997)
Optical Transmission of metal hydrides defines color
Band gap EG
19
Band gap EG
( ) ( ) 222220
2γωωω
ωγωε+−
=s
( ) ( )ωωδε
πωε hh −⋅= ficV
M
00
2
2
2
fiωh
00
→
→
γ
ωω fi
0ωh
Indirect band gapOptical constants and band structure of MgH2
J. Is
idor
sson
et a
l. Ph
ys. R
ev. B
, 68,
115
112
(200
3)
20
0 2 4 6 8 10-8
-6
-4
-2
0
2
4
6
8
10
ε 1,ε
2
photon energy [eV]
ε1ε21 2
34
Optical constants and band structure of YH2
J. Schoenes et al., J. All. Compds. 404–406 (2005) 453–456
22
Stability =>
100
101
102
103
104
105
0.0 0.2 0.4 0.6 0.8 1.0
470 K
433 K
363 K
313 K
log(T/T0)
p(H
2) [Pa]
295 K
c)
2.7 2.8 2.9 3.0 3.1 3.2
103
104370 360 350 340 330 320 310
p eq [P
a]
1/Temperature [10-3 K-1]
∆H = -40 kJ (mol H2)-1
Mg0.69Ni0.26Ti0.05
Temperature [K]
Mg at. fraction y0.4 0.5 0.7 0.8 0.9 1 MgTi 0.6
Ni0.
1
0.2
0.3
0.4
0.5
0.6
Enthalpy∆H
[kJ(m
ol H2 ) -1]
-70-65
-60-55
-50-45
-40-35
d)
Gremaud et al. Adv. Mater. 19 (2007) 2813
Hydrogenography: An Optical Combinatorial Method
Pressure range: >10 orders!
( ) HH NNTN ∝⇒∝ lnα
23
electron beam evaporator
Effusion cell,atomic H-source
Pumps
Manipulator
PC
spectrometer
light source
bifu
rcat
or
fibre
Westerwaal et al. J. Appl. Phys. 100, 063518 (2006)
UV-VIS Spectroscopy for in-situ Characterization of Hydrides
10-12…1 bar
24
In-situ synthesis of Mg2NiH4
Westerwaal et al. J. Appl. Phys. 100, 063518 (2006)
Simulation of n, k
Sensor!Slaman et al., Sensor Actuat. B-Chem 123, (2006) 538.Investigation of surface phenomena Westerwaal et al., Thin solid films, in press (2008).
26
Vibrations of ensembles
Vibrations of a linear chain
Plot of the frequencies along high symmetry lines
N (N large) of two atoms with different mass
Longitudinal waves: coupling constant C, transversal: coupling constant C’
27
kkmax
ω
TALA
TO
LO
k = 2π 1/λ
DISPERSION of a LINEAR CHAIN with TWO ATOMS
LO: ω = (2C(1/M + 1/m))1/2
TO: ω = (2C’(1/M + 1/m))1/2
LA = TA
TO
TO: ω = (2C’(1/m))1/2
TA: ω = (2C’(1/M))1/2
TA
28
monochromator
detector analyzer
objective
focus lens
polarizer
sam
ple
Raman Spectroscopy = Inelastic Photon Spectroscopy
Photons in Photons out
Anti-StokesPhonon annihilation
StokesPhonon generation
energy
Laser line
StokesAnti-Stokes
062
0
24 10 Ik
dkdI L
−≈∝αω
29
kkmax
ω
TA
LA
TO
LO
BZ of %1.02.0
2002.08.0
maxmax
410
=⇒≈=
==⇒=⋅≈=
kk
nmak
nmkmm
n
i
i
ππ
πλπµµλλ
Conservation of momentum→→→
=± iphons kkk
Conservation of energy
inphotphonoutphot ,, ωωω hhh =±(Raman-shift)
Conservative Laws in Raman Scattering
30
Phonon dispersion of Si and Raman spectrum
M. T. Yin and Marvin L. Cohen, Phys. Rev. B 25, 4317 - 4320 (1982)
40 35 30 25 20 15 10
Si (001)
Raman shift (THz)
Inte
nsity
(log
. uni
ts)
ω2nd ~2ω0
31
Raman Intensity
nn
ijn kk
R ⋅∂
∂=
0
α Means: we will see a Raman line, if the vibration changes the polarizability of the molecule.
Example [AlH4]-
Bending mode
stretching mode
symmetric
Anti symmetric
Porto and Scott, Phys. Rev. 157, 716 (1967)
Infra-red active => climate change!
Raman active
Example CO2
C+ O-O-
32
400 600 800 1000 1200 1400 1600 1800 2000
νlib2
νlib1
ν2, ν
4ν
3ν1 75°C
250°C
250°C
225°C200°C
175°C150°C125°C100°C75°C50°C
no
rmal
ized
inte
nsity
(1)
Raman shift (1/cm)
Temperature resolved Raman spectroscopy on NaAlH4
Melting at 180°C
Al-H stretching modesAl-H bending modesLibrational modes
Na+ [AlH4]-
A. Borgschulte, submitted (2007); Majzoub, McCarty, and Ozolins, Phys. Rev. B 71, 024118 (2005)
33
250 500 750 1000 1250 1500 1750 20000.00
0.25
0.50
0.75
1.00
inte
nsity
(1)
Raman shift (1/cm)
Calculations:A. Ramirez-Cuesta (2008)
Partial exchange of H by D: (AlH4-xDx)- ?
NaA
lH4
NaA
lH4-x D
x
mfπω 2=2tra
ns
400 600 800 1000 1200 1400 1600 1800
DoVS AlD4- Unit
DoVS AlH1D3- Unit
DoVS AlH2D2- Unit
DoVS AlH3D1- Unit
DoVS AlH4- Unit
Den
sity
of V
ibra
tiona
l Sta
tes
(DoV
S)/
AU
ω/cm-1
Ref.: A. Borgschulte et al., PCCP (2008)
34
Optical Spectroscopy on Hydrides I
-
+
UV-VIS spectroscopy
Optical and electronic properties (band gap etc.)
EG
Data: R. Gremaud et al. VU Amsterdam
Ref.: A. B. K
unz and D. J. M
ickish,P
hys. Rev. B (1975)
30 40 50 60 70 80 90 100
-70 -60 -50 -40 -30 -20 -10 0
inte
nsity
(cou
nts)
kinetic energy (eV)
Pt 4
f 5/2
Pt 4
f 7/2
Pt 5
p
Cr 3
p
valence bondhν = 120 eV
binding energy (eV)
Photoemissionspectroscopy
Structural and electronic properties of the surface (composition, atomic arrangement, band structure etc.)
35
Optical Spectroscopy on Hydrides II
d
Spatially resolved optical spectroscopy (visible, Raman)
Vibrational properties, structure transformations
Ref.: A. Borgschulte et al., J. Phys. Chem A (2008)
-
+
Ref.: A. Borgschulte et al., PCCP (2008)
AlH
3=>
A
l + 3
/2 H
2
2NaH
+ N
aAlH
4=>
N
a 3Al
H6
Vibrational spectroscopy (infra-red, Raman)
Morphology, surface properties, diffusion coefficients, reaction mechanisms
Bending modes
librationalmodes
Stretchingmodes
400 600 800 1000 1200 1400 1600 1800 2000
νlib2νlib1
ν2, ν
4ν3
ν1 75°C
250°C
250°C
225°C200°C
175°C150°C125°C100°C75°C50°C
norm
aliz
ed in
tens
ity (1
)
Raman shift (1/cm)
Solid
Liquid
Na+[AlH4]-
36
Fundamentals:C. Kittel, Introduction to Solid State Physics, Wiley & Sons Inc., NY, 1986.P. W. Atkins, Physical Chemistry, Oxford University Press, 1986.H. Kuzmany, Solid State Spectroscopy, Springer Verlag, Berlin 1998.
Photoemission:S. Hüfner, Photoelectron Spectroscopy: Principles and Applications, Springer Verlag, Berlin 2003.D. Briggs and M. P. Seahm, Practical surface analysis, Vol. 1: Auger and x-ray photoelectron spectroscopy, Wiley, Chichester, 1990.
Optics:Max Born, Emil Wolf, A.B. Bhatia, and P.C. Clemmow, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, Cambridge University Press, 1999. B. Schrader (ed.), Infrared and Raman Spectroscopy, Methods and Applications, VCH, Weinheim 1995.
Literature