international materials institute for
TRANSCRIPT
June 2005 International Materials Institute for
NEW FUNCTIONALITY IN GLASSES Glass Tutorial
Glass structure by infrared reflectance spectroscopy E.I. Kamitsos
Theoretical and Physical Chemistry InstituteNational Hellenic Research Foundation, Athens, Greece
Glass Tutorial Series: prepared for and produced by theInternational Material Institute for New Functionality in Glass
An NSF sponsored program – material herein not for sale Available at www.lehigh.edu/imi
Outline of presentation
1. Basic principles of vibrational spectroscopy • Comparison of infrared / Raman: common characteristics & differences
in mechanism and selection rules
2. Sampling methods in infrared spectroscopy• Advantages of infrared reflectance spectroscopy
3. Methods of analysis of infrared reflectance spectra • Fitting of reflectivity using classical dispersion theory • Kramers-Kronig (K-K) transformation• Comparison of K-K and reflectivity fitting results
4. Examples of IR reflectance spectroscopy in glass structural studies • Single alkali & alkaline earth borate glasses:
structure of glass network & metal ions sites
• Dependence of Na-borate glass structure on depth from the glass surface.
Basic principles of vibrational spectroscopy
Electronic, vibrational, rotational transitions
Vibrationaltransition
(in infrared)
Electronictransition
(in optical or uv)
Infrared & Raman spectroscopy in materials scienceCommon characteristics: • Probe structure and bonding through molecular vibrations• Can probe both crystalline and amorphous phases (no long-range order required)• Widely used in materials science
Infrared & Raman spectroscopy: differences in mechanism & selection rules
INFRARED
∆Ε=hνvib
Infrared:• Resonance phenomenon: Ε=hν0=∆Ε=hνvib
• Selection rules (harmonic oscillator): ⇒ ∆n=±1, n: quantum number⇒ (∂µ/∂x)0 ≠ 0, µ: dipole moment
Infrared & Raman spectroscopy: differences in mechanism & selection rules, cont.
RAMAN
inelastic anti-Stokes Raman
<<0.01%
elasticRayleigh>>99.99%
inelasticStokes Raman
<<0.01%
νο νονο-νvibνο νο νο+νvib
∆Ε=hνvib ∆Ε=hνvib ∆Ε=hνvib
Raman:
• Scattering phenomenon: Ε=hν0 >> ∆Ε=hνvib
• Selection rules (harmonic oscillator): ⇒ ∆n=±1, n: quantum number⇒ (∂α/∂x)0 ≠ 0, α: polarizability (µind=αE)
Sampling methods for measuring infrared spectra
I 0 I I 0 Iθ iθ r
Transmission Specular Reflection
I R
θ
n 2
n 2
n 1
I
θ
n 2
R
n 1
ATR – multiple reflectionAttenuated Total Reflectance (ATR) – single reflection
Sampling methods for measuring infrared spectra , cont.
R
M E T A L
Iθ RI θ
M E T A L
M E T A L
Reflection-Absorption Spectroscopy (RAS) – single reflection
RAS – multiple reflection
H E
A T
S U P P O
R T
E
K
M I C R O P H O N E
I R
Emission Spectroscopy
Diffuse Reflectance Spectroscopy
PhotoacousticSpectroscopy
Advantages of infrared reflectance spectroscopy
• True band shapes: - no band distortion and hydrolysis effects associated with the use of alkali halide salts as matrix materials in traditional transmission measurements,
-no saturation effects and background interference patterns encountered in transmission measurements on films.
• Use the same samples for data acquisition in a broad frequency range covering both the mid- and far-infrared (ca. 20 – 5000 cm-1).
• Combined with the use of modern Fourier-transform spectrometers and the availability of software, infrared reflectance leads to the quantitative determination of the frequency-dependent optical and dielectric properties of materials.
⇒ Infrared reflectance spectroscopy is a powerful tool in materials science.
)(]1)([)(]1)([)( 22
22
ννννν
knknR
+++−
=
ANALYSIS OF REFLECTIVITY SPECTRA
R(ν): measured reflectivity
n(ν): refractive index
k(ν): exctinction coefficient
(ν)=n(ν)+ik(ν) complex refractive index
Analysis methods:• Reflectance curve fitting • Kramers-Kronig transformation
n~
REFLECTANCE CURVE FITTING
Use a model for the dielectric function, , to fit the reflectivity spectrum. . Classical dispersion theory:)(~)()()(~ νενikνnνn =+≡
)(~ νε
~( ) ' ( ) ' ' ( )ε ν ε ν ε ν εν
ν ν νΓ= + = +
− −∞ ∑ii
j j
j jj
∆ε 2
2 2
Lorentzian oscillators:νj = resonance frequency; Γj = bandwidth; ∆εj = dielectric strength ε∞ = high frequency dielectric constant
ε ν ν ν εν ν ν
ν ν ν' ( ) ( ) ( )
( )( )
= − = +−
− +∞ ∑n k j j j
j jj
2 22 2 2
2 2 2 2 2
∆ε
Γ
ε ν ν νν ν
ν ν ν' ' ( ) ( ) ( )
( )= =
− +∑22
2 2 2 2 2n k j j j
j jj
∆ε Γ
Γ
Example of Reflectance Curve Fitting
)](''),('[)(])([)(])([)( νενεf
νkνnνkνnνR =
+++−
= 22
22
11
The adjustable parameters (νj, Γj, ∆εj, ε∞) are determined by best fitting the calculated R(ν) spectrum to the experimental reflectivity spectrum.
0 500 1000 15000,0
0,1
0,2
0,3
0,0
0,1
0,2
fit exp
x=0.5
REF
LEC
TAN
CE
WAVENUMBERS (cm-1)
x=0.4
xCuI-(1-x)Cu2MoO4
fit
0 250 500 750 10000
1
2
3
4
5
0 250 500 750 10000
4
8
12
0 250 500 750 10000,0
0,2
0,4
0,6
0,8
0 250 500 750 10001,01,52,0
2,53,03,5
ε"
WAVENUMBERS (cm-1)
ε'
WAVENUMBERS (cm-1)
kn0.5CuI-0.5Cu2MoO4
Dispersion parameters obtained by fitting the reflectivity data of xCuI-(1-x)Cu2MoO4 glasses
0.4CuI-0.6Cu2MoO4 0.5CuI-0.5Cu2MoO4
j νj(cm-1)
Γj(cm-1)
∆εj νj(cm-1)
Γj(cm-1)
∆εj
1 58.0 110.0 3.422 62.8 110.0 6.2542 113.8 115.0 1.029 110.0 112.1 1.6623 175.0 50.0 0.025 180.0 50.0 0.0434 301.0 90.0 0.109 310.0 113.7 0.4305 390.0 144.6 0.161 399.4 145.2 0.3946 490.0 100.0 0.048 501.9 91.2 0.1677 579.2 79.9 0.034 570.3 88.3 0.1928 670.0 70.0 0.010 684.4 58.2 0.0779 782.5 104.8 0.441 779.0 110.7 0.50010 881.5 30.3 0.011 875.1 40.0 0.027
ε∞=3.4 ε∞=4.4
KRAMERS-KRONIG TRANSFORMATION
Measured quantity: Reflectivity, R(ν)=Ir(ν)/Ii(ν)
Ir(ν) = Intensity of the reflected beam
Ii(ν) = Intensity of the incident beam
ρ(ν)=r(ν) exp[iθ(ν)]
ρ(ν) = complex reflectivity coefficient
r(ν) = amplitude = [R(ν)]1/2
θ(ν) = phase difference between reflected and incidence beam
θ ννπ
ν νν ν
ν( )ln ( ) ln ( )
=−−
∞
∫22 2
0
Pr r
di
ii
Kramers-Kronig (K-K) transformation: measure R(ν) ⇒ calculate θ(ν)
⇒ Optical response functions for normal incidence (Fresnel relations):
⇒ Dielectric functions:
⇒ Absorption coefficient:
nr
r r( )
( )( ) ( ) cos ( )
νν
ν ν θ ν=
−+ −
11 2
2
2
kr
r r( )
( ) sin ( )( ) ( ) cos ( )
νν θ ν
ν ν θ ν=
+ −2
1 22
′ = −ε ν ν ν( ) ( ) ( )n k2 2
′′ =ε ν ν ν( ) ( ) ( )2 n k
α ν πν ν( ) ( )= 4 k
⇒ Optical conductivity: σ(ν) = (2πcε0)νε′′(ν)
Kramers-Kronig transformation, cont.
Optical (n, k) and dielectric (ε′, ε′′) properties of the 0.5CuI-0.5Cu2MoO4 glass obtained by K-K analysis and fitting of reflectivity spectra
0.5CuI-0.5Cu2MoO4
0 500 1000 15000,0
0,1
0,2
0,3
REF
LEC
TAN
CE
WAVENUMBERS (cm-1)
0.5CuI-0.5Cu2MoO4
0 250 500 750 10000
1
2
3
4
5
0 250 500 750 10000
4
8
12
0 250 500 750 10000,0
0,2
0,4
0,6
0,8
0 250 500 750 10001,01,52,02,53,03,5
ε'' K-K fit
WAVENUMBERS (cm-1)
ε' K-K fit
WAVENUMBERS (cm-1)
k K-K fitn K-K
fit
K-K
fit
Infrared absorption spectra of alkali diborate glasses obtained by K-K analysis of the reflectance spectra
0 200 400 600 800 10001200140016000
2
4
6
8
10
12
14
16
18
M+-Site vibr.
Network def.
BO3 str.BO4 str.
M2O.2B2O3
Li
NaKRbCs
Abs
orpt
ion
Coe
ffici
ent (
103 c
m-1)
Wavenumbers (cm-1)
Mid-Infrared (above ca. 500 cm-1)
⇒ Vibrations of Short Range Order (SRO) borate network units
Far-Infrared (below ca. 500 cm-1)
⇒ Metal ion–site (M-O) vibrations
Normalized infrared intensity A4 versus the fraction of four-fold coordinated boron atoms, N4, determined from NMR
3,05 3,10 3,15 3,20 3,25 3,30600
650
700
750
800
0,28 0,30 0,32 0,34 0,36 0,38 0,4050
55
60
65
70
75
80
CsRb
K Na
Li
(b)
T g (K)
Nb
M2O.2B
2O
3
(a)
CsRb
KNa
Li
A 4 (10
6 cm
/mol
)
N4
A4= <A4> Vmol
<A4> = integrated intensityof the 800-1200 cm-1 region
Vmol = glass molar volume
Glass transition temperature, Tg, versus number of bridging B-O
bonds per boron atom, Nb.
Nb=2.5+2N4
Infrared absorption spectra of alkaline earth borate glasses obtained by K-K analysis of the reflectance spectra
0 200 400 600 800 1000 1200 1400 1600
MgCaSr
Ba
x=0.45
Wavenumbers (cm-1)
CaSr
Ba
xMO-(1-x)B2O3
x=0.33In
frare
d A
bsor
ptio
n Mid-Infrared:
⇒ SRO structure depends on both MO content and type
Fraction of four-fold coordinated boron atoms, N4, in alkaline earth borate glasses obtained from analysis of the infrared spectra
0,0 0,1 0,2 0,3 0,4 0,5 0,60,0
0,2
0,4
0,6
N4=Ar/(α+Ar)
xMO-(1-x)B2O
3
Ba Sr Ca Mg
N4=x/(1-x)
N4
xMO
N4 = Ar/(α+Ar)
Ar = <A4>/<A3>
<A4> = integrated intensityof the 800-1150 cm-1 region
<A3> = integrated intensityof the 1150-1550 cm-1 region
α =relative absorption coefficient of borate
tetrahedral units (α=1.3)
Comparison of N4 values of alkaline earth borate glasses obtained from IR, NMR, neutron diffraction (ND) and molecular dynamics (MD) studies
0,0
0,2
0,4
0,6
Ba IR NMR ND MD
N4=x/(1-x)
0,0
0,2
0,4NMR: Bray &Moon et al. Sr
0,0
0,2
0,4ND, MD: Fukunaga & Umesaki et al.
N4
N4
N4
Ca
N4
0,0 0,1 0,2 0,3 0,4 0,5 0,60,0
0,2
0,4Mg
xMO-(1-x)B2O3
xMO
Proper analysis of infrared reflectance
spectra can lead to the quantitative determination
of the short-range order borate structure
Far-Infrared absorption spectra of alkali triborate glasses, M2O-3B2O3, resulted from K-K analysis of the reflectance spectra
0 100 200 300 400 500 600
0 100 200 3000 100 200
L
H
Li
LH
Wavenumbers (cm-1)
Na
L
H
K
Infra
red
Abs
orpt
ion
(arb
.uni
ts)
L
H
Rb
L
H
Cs
Far-Infrared absorption spectra of alkaline earth borate glasses resulted from K-K analysis of the reflectance spectra
0 200 400 600
0 150 300 450
H
L
Mg
0 150 300 450
H
L
Wavenumbers (cm-1)
Ca
H
L
Sr
Infra
red
Abs
orpt
ion
(arb
. uni
ts)
0 150 300 450
Ba
H
L
0.45MO-0.55B2O3
Meta-ion site vibration frequencies, νM-O, versus the square root of the inverse metal ion mass, Mc
-1/2
M2O-3B2O3 (M=Li–Cs) & 0.45MO-0.55B2O3 (M=Mg-Ba)
0,1 0,2 0,3 0,40
100
200
300
400 H
BaSr
Ca
Mg
CsRb
KNa
Li
(a)
ν M-O
(H)
(cm
-1)
0,1 0,2 0,3 0,40
100
200
300
L
(b)Cs
RbK
Na
Li
BaSr
Ca
Mg
ν M-O
(L) (
cm-1)
MC-1/2 (au)-1/2
νΜ-Ο = (1/2πc) [fM-O / µΜ-Ο]1/2
fM-O & µΜ-Ο: the force constant
and reduced mass of the
metal ion – site vibration
µΜ-Ο ≈ΜC
Meta-ion site vibration frequencies, νM-O, versus qCMC-1/2
where qC and MC are the charge and mass of metal ion
M2O-3B2O3 (M=Li–Cs) 0.45MO-0.55B2O3 (M=Mg-Ba)
Far-IR spectra:•presence of two type of sites where M-O vibrations give rise to bands H & L
MD simulations on Li-borate glasses:
•H band: M-O vibrations in nb-type sites (non-bridging & bridging oxygen atoms)
•L band: M-O vibrations in b-type sites (bridging oxygen atoms)
0,0 0,1 0,2 0,3 0,40
100
200
300
400
MgLi
Ca
SrNa
KBa
RbCs
L
H
ν M-O
(cm
-1)
qCMC-1/2
fM-O ∝ qC2
νΜ-Ο∝ qC ΜC-1/2
Dependence of Na-borate glass structure on depth from the glass surface
0 500 1000 1500 2000 25000,00
0,05
0,10
0,15
0,20
0.3Na2O-0.7B2O3
0µm 40µm 110µm 180µm 1300µm
Ref
lect
ance
Wavenumbers (cm-1)
⇒ Glass disks were prepared by quenching from the melt, with diameter: 15mm, thickness: 2mm
⇒ Controlled removal of glass layers by grinding & polishing the same specimen on an automatic polishing machine
⇒ Recording infrared reflectance spectra at various depths from the original glass surface
Infrared absorption spectra calculated from the reflectance spectra measured at different depths from the surface of the 0.3Na2O-0.7B2O3 glass
0 500 1000 15000,00
0,25
0,50
0,75
1,00
BO3
BO4
A3A4
0.3Na2O-0.7B2O3
0µm 40µm 110µm 180µm 1300µm
Extin
ctio
n C
oeffi
cien
t
Wavenumbers (cm-1)
BØ3BØ2O-
BØ4-
0
500
1000 0.3Na2O-0.7B2O3
d= 0µm
H
L
Abso
rptio
n C
oeffi
cien
t (cm
-1)
0 100 200 300 4000
500
1000
1500 d= 1300µm
H
L
Wavenumbers (cm-1)
0.3Na2O-0.7B2O3 Glass: Na Ion – Site Vibrations
Deconvolution of far infrared absorption spectra into Gaussian component bands
0 400 800 12000,28
0,32
0,36
A L/(A H
+AL)
d (µm)
L-component band (b-type) of the Na-O (site) vibration gains relative intensity up to ca. 200 µm
0.3Na2O-0.7B2O3 glass: Short-Range Order (SRO) Borate Structure
0 400 800 12000,47
0,48
0,49
0,50
d (µm)A 4/(
A 3+A 4)
Borate SRO structure: • Tetrahedral units: BØ4
- (intensity A4, mole fraction X4)• Trigonal units: BØ3 & BØ2O- (intensity A3, mole fractions X3 & X2)
mass balance: X4+X3+X2=1⇒ X3= [BØ3]=0.57
charge balance: X4+X2=0.3/0.7=0.43
BØ2O- ⇒ BØ4-
Cooling rate gradient from the surface to the core of the glass sample
0.3Na2O-0.7B2O3 Glass: Mid-IR & Far-IR correlations
Mid-Infrared: Short-Range Order (SRO) Borate Structure Far-Infrared: Na Ion – Site Vibrations
0 400 800 12000,28
0,32
0,36
A L/(A H
+AL)
d (µm)
0 400 800 12000,47
0,48
0,49
0,50
d (µm)
A 4/(A 3+
A 4)
BØ2O- ⇒ BØ4- nb-type ⇒ b-type
Na-O sites
Infrared reflectance spectroscopy facilitates the simultaneous study of the SRO borate structures (mid-IR) and their effect on the relative population of
the network sites hosting metal ions (far-IR)