spectroscopy studies of metal raman...
TRANSCRIPT
Raman and Infrared Spectroscopy Studies of Metal Hydrides
Herschel
Raman
Fourier
Materials Sci ence & Technolog y
/E
0B
EjB
BE
jdiv
EPED r
00
HMHB r
00
Fundamentals: The Maxwell equations
Et
Et
jt
Ht
E
2
2
0002
2
22
2
111,1 rr
cn
cEtc
E
EE
rn
nn
ir
2, 222
1
21
0j
22
22
11.,.
,,,
nnRge
ATR
Apatura iris : blue in perp reflection / brown in
side reflection
© Wikipedia
Papilio blumeipigments are green
Brilliant colours of butterflies
Microstructure of butterfly wings/scales
Haruna Tada et al. Optics Express 5, (1999) 87 / wikipedia
Haruna Tada et al. Optics Express 5, (1999) 87
Victoria’s secrets revealed
Structure sensitive properties appear if
~ l
infra red spectroscopy: > 1 m
corresponds to energies below 1 eV
which is the energy range of molecular vibrations
l
I0 I0
= c
detector
Transmission of light through a medium (Lambert-Beer)
leIIT 0 we are interested in the frequency
dependence of ()
=> “transmission spectrum”
UV-VIS spectroscopy: eVsIR-/Raman-Spectroscopy: 1 meV…1 eV
8
Schrödinger equation starts from interactions…and gives energies
iiieffeffeffeffeffeff EpAAppBp
21
22
21
2
212
21
44
Photon-matter interactions
Chem. interaction
magnetic interaction
Darwin-term
Dipole interactionSpin-orbit-coupling
Landau-term
Chem. enthalpy: 0.1...10 eV
Exchange interaction: 0.1...5 eV Magn. anisotropy: 1...1000 µeV
Phonons: 1...100 meV
UV IR RF400 nm 800 nm 1000’000 nm
3 eV 1.5 eV 1.2 meV
mfexx
dtxdmxxfF
xxfV
ti
00
2
2
0
202
1
xx0
V
Molecular vibrations
f m
xx0
V
Real potential
causes anharmonicity
021 )( nE
Quantum mechanics
9.01111
HBHB mmm
fmB mH
Reduced mass
imeqEtx
eqEfxxmxmti
ti
20
0
0
q-
xq+
222220
2
2
222220
220
2
1
220
1/
mq
mq
imqEP
qxP
IR-absorption by a dipole
lII /ln 0
2
if more than one oscillator is involvedN0
clII
0ln
in a fixed volume this is better described by a concentration and
extinction coefficient
0
1000 1250 1500 1750 2000 2250 2500 27500.0
0.2
0.4
0.6
abso
rptio
n (1
)
frequency (1/cm)
16
13
17
14
18
8
IR-spectrum of gaseous decomposition product: B2H6
cl
physical quantity may be compared to references,
e.g., http://webbook.nist.gov/chemistry/
Decomposition by combined FTIR and gravimetric measurements
TGmm
dtd
0
fl
Mcm
IImm
dtd
ref
ref
IR
0
0
0
/log
Quantitative analysis of gaseous decomposition products of complex hydrides (except H2 etc.)
Reaction mechanisms by labeling experiments
A. Borgschulte, et al.J. Phys. Chem. C, 2011, 115 (34), 17220-17226.
Decomposition of LiZn2(BH4)5 into diborane (and H2)
20 30 40 50 60 70 80 901E-6
1E-5
1E-4
1E-3
0.01
tota
l rat
e d/
dt m
/m0 (1
/min
)
Time (min)
1E-6
1E-5
1E-4
1E-3
0.01
IR d
/dt m
/m0 B
2H6 (1
/min
)
50 60 70 80 90 100Temperature (°C)
Li(Zn2BH4)5
2B2H6 + 2H2 + LiBH4
m(H2) = 2
m(B2H6) = 27.6
Why is there no signal from hydrogen?
(HT) = +0.01
(B) = +0.16
(HB) = -0.13
Is there another spectroscopy, which sees H2?
ttxx
tP
ttxx
P
t
xxx
qPEP
tPtEE
kk
ind
kk
ind
kk
000
00
00
00
coscoscos
coscos
cos
;/
coscos
coscoscoscos 21
Classical derivation of the Raman effect
0
monochromator
detector analyzer
objective
focus lens
polarizer
sam
ple
Raman Spectroscopy = Inelastic Photon Spectroscopy
energy
StokesAnti-Stokes
062
0
24
2
2
2
10
,
Ixx
I
tPt
I
kk
L
Laser line
ttxx
tP kk
ind 000 coscoscos
Hertz’ dipole:
Photons in Photons out
Anti-StokesPhonon annihilation
StokesPhonon generation
Raman effect explained by Quantum mechanics
ener
gy
0'0' '0'
'0'
Phonons are bosons
kTNN
II
kT
N
Stokes
anti 0
0
0
00
exp1
1exp
1
T. R. Hart, R. L. Aggarwal, B. Lax, PRB 1, 638 (1970)
Raman spectra of gaseous H2 and D2
100 200 300 400 500 600 700 800 900 1000 2900 3000 31000
200
400
600
H2: ~4143
S0(4)S0(3)
S0(2)
S0(1)S0(0)
S0(3)S0(2)
S0(0)
S0(1)
Inte
nsity
(CC
D o
utpu
t)
Raman shift (cm-1)
D2
H2
Q1(0,...4)
rotations vibrations
IR spectra of H2 on different oxide surfaces
Mg2+O2- Mg2+O2- Mg2+O2-
H- - H+ H- - H++ H2
C. Lamberti, A. Zecchina, E. Groppo and S. Bordiga, Chem. Soc. Rev., 2010, 39, 4951–5001
H2 on
~ interaction
low pressure
high pressure
MgO
http://symmetry.otterbein.edu/index.html
Some basics in group theory: Point groups
C4v E 2C4 (z) C2 2v 2d
A1 1 1 1 1 1 z x2+y2, z2 z3, z(x2+y2)
A2 1 1 1 -1 -1 Rz - -
B1 1 -1 1 1 -1 - x2-y2 z(x2-y2)
B2 1 -1 1 -1 1 - xy xyz
E 2 0 -2 0 0 (x, y) (Rx, Ry) (xz, yz) (xz2, yz2) (xy2, x2y) (x3, y3)
Point groupClasses of symmetry operations
Symmetry or Mulliken
labels, each corresponding to a different irreducible
representation Characters (of the IRs of the group)
Basis functions having the same symmetry as the irreducible
representations (IR)
linear functionstranslations along specified axisR, rotation about specified axis
quadratic functions
cubic functions
Totally symmetric
representation of the group
Symmetries of the s, p, d, and f orbitals can be found here (by their labels). Ex: the dxy orbital shares the
same symmetry as the B2 IR.The s orbital always belongs to the totally symmetric representation (the first listed IR of any point group).
Some basics in group theory: character tables
At the end of a symmetry analysis (often implemented in electronic structure calculations), one obtains a list of the irreducible r.s (all possible vibrations+translations):
e.g.: B2H6 tot = 4Ag + 3B1g + 3B2g + 2B3g + Au + 4B1u + 3B2u + 4B3u = 24
Generally their names indicate the result of the application of a symmetry operator: A symmetric with respect to the main axis of symmetry B antisymmetric with respect to the main axis of symmetry ‘ symmetric with respect to a plane of symmetry ‘’ antisymmetric with respect to a plane of symmetry g symmetric with respect to the center of symmetry (from German gerade) u antisymmetric with respect of the center of symmetry (from German ungerade) E doubly degenerate with respect to the main axis T triply degenerate with respect to the main axis G fourfold degenerate with respect to the main axis H fivefold degenerate with respect to the main axis 1,2,3 (as subscripts) symmetric or antisymmetric with respect to a rotation axis (Cn)
or a rotation-reflection axis (Sn) or, if the other symbols are not sufficient to specify different species
Some basics in group theory
R
RRi
Rhi Ca 1The number of the irreducible r. is calculated from the character tables
IR: dipole moment P changes during vibration Raman: polarizability changes during vibration
Selection rules
dxPM '*'
A vibration which is symmetric with regard to the center of symmetry is forbidden in the infrared spectrum, whereas a vibration which is antisymmetric
to the center of symmetry is forbidden in the Raman spectrum.
mutual exclusion rule
0'*0
'
dxPMif P were a constant,
P is to be replaced by the dipole moment operator
iiiiii zqyqxqPP ˆ
Transitions are allowed, when we know the symmetries of p(n’)*, p(n), and the operators P, i.e., if the direct product
P̂'
contains the totally irreducible representation of the point group, the IR transition is active.
Symmetry analysis of gaseous diborane
(HT) = +0.01
(B) = +0.16
(HB) = -0.13
IR- and Raman spectroscopy on gaseous diborane
1000 1500 2000 25000.0
0.2
0.4
0.6
0.8
1.0
Ram
an in
tens
ity, I
R-T
rans
mis
sion
(arb
. u.)
frequency (cm-1)
4
1418
17
16, 8
1, 11
3
2H2
H2
H2, N2, O2… R B2H6, NH3, AlH3… IR, R gaseous borohydrides (e.g. Ti(BH4)3,…) IR (R) H2O, CO2, CO, CH4, VOCs … IR, R also many liquids
and solids?
Gases possibly relevant in H-M systems by IR/Raman
http://www.chem.ox.ac.uk/icl/heyes/structure_of_solids/lecture1/lec1.html
Some Basic Definitions
LATTICE = An infinite array of points in space, in which each
point has identical surroundings to all others.
CRYSTAL STRUCTURE = The periodic arrangement of atoms
in the crystal.It can be described by
associating with each lattice point a group of atoms called
the MOTIF (BASIS)
Reminder: Crystallography
Reminder: Bravais lattice
The combination of the 14 Bravais lattices with all possible symmetry operations gives 230 space groups
Notations: Herrmann – Mauguin: quartz : P3112 Schönfliess: D3
3
Reminder: Space groups
alternative: Electronic structure calculations
Important property is d/a
)/2()( akk
Largest wavelength => infinity (k=0), smallest => a (k=/a), because
k-vector = 2d/a
Can be understood as a wave with wave length a
kidadi eeadd /2)()(
k-space and electronic structure
k = -1 0 1 2 3 4 52D Brillouin zone
3D-BZ
Brillouin zones
Band structure: Bloch functions
airRr /2exp)()( 0
Schrödinger equation
ÜberlappAtom hHH
Tight-binding electronic bandstructure
k = 0
k = /a
k = 0
k = 0 k = /a
E(k)
E0
Example s-orbitals
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’
kkmax
TALA
TO
LO
DISPERSION of a LINEAR CHAIN with TWO ATOMS
LO: = 2C(1/M + 1/m)
TO: = 2C’(1/M + 1/m)
LA = TA
TO
TO: = 2C’(1/m)
TA: = 2C’(1/M)
TA2
k
Phonon band structure of PdD
J. M. Rowe, et al. Phys. Rev. Lett. 33, 1297 (1974)
)(k
kN )(
BZ of %1.02.0
2002.08.0
maxmax
410
kk
nmak
nmkmm
n
i
i
Conservation of momentum
inphotphonousphot kkk ,,
Conservation of energy
inphotphonoutphot ,, (Raman-shift)
Conservative Laws in Raman Scattering
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)
2nd ~20
A simple metal hydride: Raman spectra of YH2
Space group Fm-3m (no 225, isostructural to CaF2)Y on site 4a transl. modes F1uH on site 8c transl. modes F1u + F2g
Acoustic modes: F1uOptical modes: F1u + F2g :1 Raman band at 1142 cm-1 (D: 802cm-1), and the IR?
A.-M. Carsteanu, et al., Phys. Rev. B 69, 134102 (2004).
Y
H
Pure yttrium YH2 is still a metal=> No IR- signal
YH3 is an insulatorStrong IR-signal
And the infra-red signal of YH2?
YH0
YH2
YH3
Huiberts et al. Nature (1996)
Remhof and BorgschulteChemPhysChem (2008)
M. Rode, Dissertation TU Braunschweig 2004
Ref
lect
ion
(%)
frequency (cm-1)
no effective dipole moment in an electron jelly, however, the polarizibility can change!
YH2 Fm-3m F2gYH2+ I4/mmm 3A1g+ 3B1g + B2g + 5EgYH3 P63mmc A1g + E1g + 2E2gYH3 P63 11A + 11E1 + 12E2
Less simple metal hydrides: YHx>2
A.-M. Carsteanu, et al., Phys. Rev. B 69, 134102 (2004).
centrosymmetric P63mmcnon-centrosymmetric P63
Application of the mutual exclusion rule
H. Kierey, et al., Phys. Rev. B 63, 134109 (2001).
T. R. Hart, R. L. Aggarwal, B. Lax, PRB 1, 638 (1970) A. Racu, J. Schoenes, PRL 96, 017401 (2006)
Broadening of Raman lines
Weak broadening due to life time of the phonon (Bosons):
Strong broadening: new physics, here:thermally excited electrons from a donor state couple with the phonon, and reduce the life time of the phonon:
1
212
kTe
h
kTE
NNNh
D
C
D
D
exp411
YH3
Si
T. R. Hart, R. L. Aggarwal, B. Lax, PRB 1, 638 (1970)A. Racu, et al., J. Phys. Chem. A 2008, 112, 9716;$H. Hagemann et al., Phase Transitions 82 (2009) 344
Shift of Raman lines
hardening
due to anharmonicity (e.g. Morse potential),
reversed shift indicates special effects (e.g. PT)1
21
xeh
LiBH4Si
BH4-
Li+
Structure of LiBH4
J-Ph. Soulié, G. Renaudin, R. Černý, and K. Yvon, J. AlloysCompd. 346, 200 (2002).F. Buchter et al., Phys. Rev. B 78, 094302 (2008),M. Hartman, et al. J. Solid State Chem. 180, 1298 (2007).
Structure of NaAlH4
Lauher et. al., Acta Crystallographic, B35, 1979K. J. Gross, et al., J. Alloys Compd. 297, 270 (2000).
Structure of complex hydrides
Na+
AlH4-
46
Structure factor :
Structure information
Charge density mapping of LiBD4
LiBD4 is an ionic crystal:Li+ (B-D4)-
F. Buchter et al. Phys. Rev. B, (2011)
z = 2.14 => Li0.86+
z = 9.86 => BD40.86-
+-
47
Vibrational SpectroscopyCompley hydrides
Raman light scattering
Infrared spectroscopy
Inelasticneutron scattering
LiBD4
LiBH4
HT-LiBH4
S. Gomes, H. Hagemann, K. Yvon, JalCom 346 (2002) 206–210A. Borgschulte, et al., Faraday Discuss. 2011, 151, 213.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
frequ
ency
(1/a
mu1/
2 )
momentum (Ka)
0
//0exp////0
0///exp/0//2
2
2
2
2
nCFnmnnCF
mCFBnmBm
mmmmCFmCF
LCFLCFLCF
MCCMCikaMCMCMCCMC
MCMCCMCikaMCMCMC
0
0
0
2
2
2
n
n
B
n
B
nm
B
m
m
m
m
m
MC
MC
MCC
MC
MC
MC
02exp1
exp12
2
2
H
CF
H
CF
L
CF
L
CF
MCika
MC
ikaMC
MC
The linear chain complex
02exp1
exp12
2
2
H
CF
H
CF
L
CF
L
CF
MCika
MC
ikaMC
MC
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
coupled system uncoupled system
frequ
ency
(1/a
mu1/
2 )
momentum (Ka)
0
0
0
2
2
2
n
n
B
n
B
nm
B
m
m
m
m
m
MC
MC
MCC
MC
MC
MC
ML MH ak
Two solutions
molecular vibrations
lattice vibrations
0 1 2 30.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
1.0 0.5 0.0
2 4 6 8 10
2a=2cCF/mheavy
2o => 2cCF/mlight
2sym=cB/mH
2asym=cB/mred
coupled system uncoupled system
frequ
ency
(1/a
mu1/
2 )
momentum (Ka)
decreasing cCF =>
increasing cB =>
crystal fieldparameter (arb. u.)
molecular bonding strength (arb.u.)
constCm
CB
L
CF for
molecule free from deviation
,
Phonon band structure of the linear chain complex
1600 1650 1700 1750 1800 2200 2300 2400 2500 2600
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
NaBD4
192h114h
90h18h
3h1h
1612
1641
1712
Inte
nsity
(arb
.uni
ts)
Raman shift (cm-1)
1677
0h, NaBH4
600h
100 bar D2
250°C
1618HD-exchange in NaBH4
B-D stretching
+
1600 1650 1700 1750 1800 1850
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
NaBD4
192h
114h90h
18h
3h
1h
Inte
nsity
(arb
.uni
ts)
Raman shift (cm-1)
0h, NaBH4
600h
100 bar D2
250°C
NaBD4
1612
16401677
1712
R. Gremaud,, J. Phys. Chem. C, 2011, 115, 2489O. Redlich, Z. Phys. Chem. B 28, 371 (1935)W. R. Angus et al., J. Chem. Soc. II, 971 (1936)
Raman shift (cm-1)
HD-exchange in NaBH4
shift ~30 cm-1/H
4
3
4431
3431
BD
BHD
H
D
mm
mm
NaBDNaBHD
02.1
41
31 NaBD
NaBHD
H
D
1550 1600 1650 1700 1750 18000
5
10
0
5
10
15
20
5
10
15
20
20
40
60
40
80
120
Raman shift [cm-1]
x = 0.14
1(D)1(D2)1(D3)
x = 0.45
1(D4)
x = 0.72
Inte
nsity
[kct
s]
x = 0.87
3'
4"4
3"3
x = 1
1
LiBD4
LiB(H1-xDx)4
H-D partial exchangein LiBH4 measured by Raman:D-stretching region
R. Gremaud, et al., Phys. Rev. B, 2009, 80, 100301;
Isotopomers in LiBH4 follow binomial distribution
;...16;14;1)1(),( 22314 xxxxxxxkn
xnp knk
Evidence for single H transport in LiBH4.
R. Gremaud, et al., Phys. Rev. B, 2009, 80, 100301; A. Borgschulte et al., Phys. Chem. Chem. Phys., 2010, 12, 5061
Molecular unit is distorted by crystal field The symmetry of all lattice vibrations can be obtained starting from the
crystal structure data many modes Molecules and molecular ions have vibrational spectra which do not change
very much from solution to solid
Site group analysis Define I.R. of vibrations for the isolated molecule Transform I.R. of the high symmetry case to those of the site group of the
molecule in the crystal Expand the I.R. to those of the point group of the crystal
Crystals containing molecules or molecular ions
Internal Vibrations of the BH4- Ion (here Ca(BH4)2)
Free ion
Ion in the crystal D2hTd C2
A1 A Ag+Au+B2g+B2u
E 2A 2* (Ag+Au+B2g+B2u )
T2 A+2B Ag+Au+B2g+B2u + 2* (B1g+B1u+B3g+B3u )
T2 A+2B Ag+Au+B2g+B2u + 2* (B1g+B1u+B3g+B3u)
Site group analysis
T2 E
V. D’Anna et al. / Journal of Alloys and Compounds 580 (2013) S122–S124
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.
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.
IR/Raman: Daniel C. Harris and Michael D. Bertolucci , Symmetry and
Spectroscopy: An Introduction to Vibrational and Electronic Spectroscopy, Dover Books on Chemistry
B. Schrader (ed.), Infrared and Raman Spectroscopy, Methods and Applications, VCH, Weinheim 1995.
Literature
reminder of the basics of group theory, crystallography
selection rules Raman/IR studies on gaseous hydrogen
compounds Raman/IR studies on metal hydrides Raman/IR studies on complex metal hydrides
Summary
Hans Hagemann, University Geneve Timmy Ramirez-Cuesta, Oak Ridge National
Laboratory (formerly: ISIS)
Acknowledgements
2050 2100 2150 2200 22500.00
0.02
0.04
0.06
0.08
A
bsor
banc
e (1
)
frequency (cm-1)
CO rotational IR transitions
61
Teller-Redlich rule: for isotope exchange in molecules
1 2 3 1 2
1 2 3 1 2
' '' ' ' ' ''' '
yx ztf yx z
f x y z
IIm m IMm m M I I I
For LiBH4/LiBD4:
O. Redlich, Z. Phys. Chem. B 28, 371 (1935)W. R. Angus et al., J. Chem. Soc. II, 971 (1936);
4
4
23 4 4
3 4 4
( ) (1.33)( )
BHD
H BD
mLiBH mm mLiBD
1 4 2 4
1 4 2 4
( ) ( ) 1.41( ) ( )
H
D
LiBH LiBH mLiBD LiBD m
0.0
0.1
0.2
0 500 1000 1500 2000
0.0
0.5
1.0
0.0
0.5
1.0
Ram
an In
t. [a
.u.]
IR
Abs
orba
nce
Nor
m. R
aman
Int.
Nor
m. I
R A
bsor
banc
e
wavenumber [cm-1]
Infrared Raman
Ab initio calculations of Raman and infrared intensities
Experiment
DFT CASTEP calculationT. Ramirez-Cuesta, ISIS, UK
B-D bending
B-D stretching
1
sym
met
ric
3
Ant
i-sym
m.
LiBD4
63
0
0
1
/331
NN
N
r
r