1

Optics and spectroscopyon (complex) hydrides

Andreas Borgschulte andreas.borgschulte@empa.ch

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

3

Photons in =>

electrons out

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

7

k = -1 0 1 2 3 4 52D Brillouin zone

3D-BZ

Brillouin zones

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).

12

Photons in =>

Photons out

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

21

Hydrogen induces changes of the

electronic properties

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).

25

Hydrogen vibrates

Vibrational Spectroscopy

RAMAN

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