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Glass Structure by
Synchrotron Techniques
Sabyasachi Sen
Dept. of Materials Science
University of California, Davis
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Glass Structure by Synchrotron Techniques
• Knowledge of structure is
important in glass science
and technology
in:
– Understanding and
controlling physical and
chemical properties
– Leads to optimization of
processing
• Practically all atomic-scale
structural characterization
techniques are based on
– Elastic scattering
(e.g. neutron scattering,
SAXS, WAXS, AXS)
– Spectroscopy (XAS, magnetic
resonance, Raman/IR,
UV/VIS, XPS, QENS, XPCS,
IXS etc.)
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How do synchrotrons work?
• A Synchrotron accelerates electrons using magnets and RF waves, into an orbit at almost the speed of light. When electrons are deflected through magnetic fields they emit extremely bright light, million times brighter than sunlight.
• Basic parts of synchrotron
– 1. Electron gun
– 2. LINAC
– 3.Booster Ring
– 4. Storage Ring
– 5. & 6. Beamline- End Station
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Why Synchrotron ?
Brilliance / Intensity
Up to 12 orders of magnitude
Brighter than laboratory source
45 synchrotron sources worldwide
11 in the USA
SPRING8 in Japan is the brightest
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Neutron Sources
• Reactor sources
Neutrons produced from fission of 235U. Moderated to thermal
energies (5 to 100 meV corresponding to wavelengths of 1 to 4 Å)
e.g. with D2O. These are continuous sources.
• Spallation sources
Proton acclerator and heavy metal target (e.g. W or U)
Higher energy neutrons, comes in pulses, wider range of incident
neutron energies
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Neutron vs. x-ray: properties
• Mass = 1.675x10-27
kg
• Charge = 0; spin = ½
• Has magnetic dipole
moment
• Wavelength can vary
over a wide range
(e.g. 1 to 30 Ǻ)
• Mass = 0
• Spin = 1
• Charge =0
• Magnetic Moment = 0
• High-energy x-ray (40
to 100 keV) provides
wavelength range of
0.125 to 0.3 Ǻ
Neutron Photon
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Neutron vs. x-ray: advantages &
disadvantages
= inter-atomic spacing
Penetrates bulk matter
Strong isotopic contrast
possible
Magnetic order can be probed
Low brilliance, needs large sample
Not suitable for some elements e.g. B (needs isotopic replacement)
= inter-atomic spacing
High brilliance. High resolution
Needs small sample
Weak scattering from light elements
No isotopic contrast
Radiation damage to samples
Neutron X-ray
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Scattering Techniques
X-ray and Neutron Scattering
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Theory of elastic x-ray (and
neutron) scattering
d
d
Prmc
e
d
d 2
0
22
2
2
2
cos1
= # of scattered photons into unit solid angle/ # of incident photons per unit time
Elastic (Thomson) scattering of photon by one electron:
r0 = 2.82 fm is the Thomson scattering length, P is the polarization factor.
Atom has many electrons in the form of an electron cloud around the nucleus.
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Theory of elastic scattering (contd.)
Atomic form factor or scattering factor f is the ratio ofamplitude of wave scattered by an atom to that by an electron
0
iQ.r(r)e)( drQf
FT of the spatial distribution of electron cloud, considered to
spherically symmetric.
A wave has a momentum p = ħk . Momentum transfer due to
scattering is Q = kf − ki.
** Neutrons are scattered by nuclei;
b= nuclear scattering cross section (Q-independent !)
atom singlefor 2
bd
d
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X-ray and Neutron scattering lengths
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Theory of elastic scattering (contd.)
For many atoms with spherical electron clouds centeredaround each atom : add up phases of the waveletsscattered from all the electron clouds (atoms) in thesample.
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Theory of elastic scattering (contd.)
Measured experimentally (plus inelastic/Compton
scattering)
Distinct scattering contains structural information !!
It is related to structure factor S(Q), the FT of the pair
distribution function g(r):
)()()(2
QIQfcelasticd
d
x
Self Distinct
)'()()()'.('
rredrdrVQSNN
rriQ
positional correlation of atoms
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Theory of elastic scattering (contd.)
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Theory of elastic scattering (contd.)
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Theory of elastic scattering (contd.)
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How to obtain G(r) from I(Q) ?
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How to obtain DFs from I(Q) ?
corrections
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Effect of cutoff on resolution
J. Non-Cryst. Sol 111 (1989) 123.
As4O6 molecule
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Physical meaning of RDF
First
Coordination shell
Second
Coordination shell
g(r)
1.0
0 2 3
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Types of Disorder
Ori
en
tati
on
al D
iso
rde
r
Translational Disorder
Plastic
Crystals
Perfect
Crystals
Dense
fluid
Liquids
Glasses
Quasicrystals
Defects
Nanoparticles
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Glass structure at various length scales
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Glass structure at various length scales
0 5 10 15
-1
0
1
Total
Intra-molecular
Inter-molecular
S(Q
)
Q (Å-1
)
‘First sharp diffraction peak’
Sine Fourier
Transformation
S(Q) T(r) = 4 r.g(r) 0 2 4 6 8
0
2
4
6
8
T(r
)
r (Å)
intra inter
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Intermediate-range order
A case study of molecular Ge-doped As-S glasses:
0
1
2
3
4
5
6
7
8
2 0
4 0
6 0
8 0
1 0 0
1 2 0
1 4 0
1 6 0
1 8 0
3 0 3 5 4 0 4 5 5 0 5 5 6 0 6 5 7 0
D a ta 1 3 :3 7 :5 0 P M 1 1 /1 3 /2 0 0 8
B
B C
Re
lativ
e I
nte
ns
ity
of 2
73
cm
-1 B
an
d
Tg (
°C
)
A to m % G e + A s (x + y )
S. Soyer-Uzun et al. , 2009, JPC-C
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Intermediate-range order-contd.
A case study of molecular Ge-doped As-S glasses:
S. Soyer-Uzun et al. , 2009, JPC-C
0
1
2
3
4
5
6
7
8
0 5 1 0 1 5 2 0
D a ta 1
B
C
D
E
F
G
H
SX
(Q
)
Q (Å-1
)
S =35
S=37.5
S = 40
S = 45
S = 57
S = 60.5
S = 65
1 .1
1 .1 2
1 .1 4
1 .1 6
1 .1 8
1 .2
1 .2 2
1 .2 4
1 .2 6
0 .4
0 .6
0 .8
1
1 .2
1 .4
3 0 3 5 4 0 4 5 5 0 5 5 6 0 6 5 7 0
D a ta 1
N e u tr o n
X - r a y
N e u tr o n
X - r a y
Po
sit
ion
of F
SD
P (
Å-1
)
FS
DP
In
te
ns
ity
A to m % G e + A s (x + y )
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Intermediate-range order-contd.
A case study of molecular Ge-doped As-S glasses:
S. Soyer-Uzun et al. , 2009, JPC-C
0 .1 8
0 .2
0 .2 2
0 .2 4
0 .2 6
0 .2 8
0 .3
0 .3 2
1 8
2 0
2 2
2 4
2 6
2 8
3 0
3 2
3 4
3 0 3 5 4 0 4 5 5 0 5 5 6 0 6 5 7 0
D a ta 1
N e u t r o n
X - r a y
N e u t r o n
X - r a y
FS
DP
Wid
th
(Å
-1)
2/
QF
SD
P (
Å)
A to m % G e + A s (x + y )
0 .5
0 .6
0 .7
0 .8
0 .9
1
1 .1
1 .2
1 .3
0 .4
0 .5
0 .6
0 .7
0 .8
0 .9
1
-2 0 2 4 6 8
D a ta 1 1 :5 0 :5 8 P M 9 /2 3 /2 0 0 8
N e u tro n X -ra y
Ne
utr
on
FS
DP
In
te
ns
ity X
-r
ay
FS
DP
In
te
ns
ity
R e la t iv e I n te n s i ty o f 2 7 3 c m-1
B a n d
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Partial Pair Distribution Functions: The Holy Grail
1)()()(
)(
11)( :Remember
,
2QSQfcQfc
Qfc
QS
For a material with n different types of atoms there are
n(n+1)/2 partial structure factors S (Q) and hence, that
many partial pair distribution functions g (r).
A complete structural description at the short-range
requires this information.
Need to vary the weighting factors of S (Q) in the above
equation: combined neutron & x-ray, isotope substitution for
neutron and anomalous x-ray scattering (AXS)
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Partial Structure Factors: vitreous GeO2
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Partial Pair Distribution Functions: vitreous SiO2
1)(
1)(
1)(
)()()(2)(
2
2
)(
)(
)(
2222
22
29
2
29
2
2222
29
QS
QS
QS
QfcQfQfccQfc
bcbbccbc
bcbbccbc
QI
QI
QI
OO
SiO
SiSi
OOOSiOSiSiSi
OOOSiOSiSiSi
OOOSiNatOSiSiNatSi
X
N
N
Nat
0 5 10 15
0
5
10
15
Experiment
Molecular Dynamics
SOO(Q)
SSiO(Q)
SSiSi(Q)
S
(Q)
Q (Å-1)
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Anomalous x-ray scattering (AXS)
Kramers-Krönig Dispersion Relation
Marked change in atomic form factor near absorption edge:
f’f”
E (keV) E (keV)
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Anomalous x-ray scattering (AXS): contd.
• Limited applicability but powerful technique
• Good for heavy elements
• Longer range than EXAFS
• Depends on very small differences between
S(Q) collected near and away from the
absorption edge: hence requires sufficient
statistics and careful data processing
• Absorption and fluorescence corrections are
critical
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AXS on Rb2O-GeO2 glasses
D.L. Price et al., PRB, 55, 11249 (1997)
Ge-Rb third neighbor
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Diffraction + Simulation (MD/RMC)
• Often a combined analysis
is the best way to obtain
structural information
• Most useful for multi-
component systems (will
discuss later)
• Use SRO as constraint and
investigate IRO
(will discuss later)
Grandinetti and coworkers
PRB, 70, 064202, 2004
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Small-Angle X-ray Scattering (SAXS)
• X-rays (and neutrons) are also scattered at very small angles (0.001 to 0.5 Å-1) from large scale (bigger than individual atoms- e.g. 1-100 nm) fluctuations in electron/nuclear density
• For glasses small-angle scattering originates typically from density and/or concentration fluctuations related or unrelated to phase separation
• For glass-ceramics the coexistence of glass and crystal with different densities is important
• Particle shape, size distribution, crystallinity
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SAXS-Fundamentals
)()()(2
1
2
21QSQnPVQ
d
dDifferential Scattering Cross-section =
)/(iiA
MbdN
V1 = scattering particle volume
n= concentration of particles
d= density of particles
bi,Mi = scattering length and atomic weights of elements in
the particle
NA = Avogadro’s number
1, 2 = scattering length density of particle and matrix
P(Q) = form factor (intra-particle atomic arrangement)
S(Q)= structure factor (inter-particle correlations)
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SAXS-Fundamentals: Contd.Guinier (low Q) region, single particle scattering
approximation holds
Rg= radius of gyration, related to overall particle dimension
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SAXS-Fundamentals: Contd.
Porod limit, large Q
Spherical particles:
I(Q) ~ Q-4
Rod-shaped particles:
I(Q) ~ Q-1
Disk-shaped particles:
I(Q) ~ Q-2
422)( QSQILim
vQ
1.g
RQ
Guinier
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Hierarchical structures-many length scales
Bimodal size distribution
G. Beaucage, J.Appl. Cryst., 28, 717, 1995
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SAXS Invariant
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SAXS Invariant: Contd.
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SAXS – Form Factor
I(Q) ~ P(Q), the form factor that represents interference
between radiation scattered by different parts of the same
scattering body/particle
Provides information on particle morphology or shape
P(Q) = |F(Q)|2
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Alkali silicate glasses- density and
concentration fluctuations
G.N. Greaves and S. Sen, Adv. Phys., 56, 1, 2007
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Alkali Percolation Network Dimensionality
G.N. Greaves and S. Sen, Adv. Phys., 56, 1, 2007
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Long range fluctuation near glass
transition: OTP
A. Patkowski et al., PRE, 61, 6909, 2000
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X-ray Absorption Spectroscopy
EXAFS & XANES
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X-ray Absorption Process
Beer’s Law: I = I0e- t is absorption coefficient
At most x-ray energies is a smooth function of x-ray energy E
3
4
AE
Z: density, Z : atomic number, A : atomic mass
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X-ray Photoelectric effect
When the incident x-ray energy is equal to or higher
than the binding energy of a core K,L or M electron
there is a sharp rise in absorption:
this is Absorption Edge
The absorption edge energy scales with Z as Z2
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X-ray Photoelectric effect: Contd.
A few fs later
X-ray photon is absorbed by a core-level electron which is excited to an unoccupied
state above the Fermi level, the core hole that is left behind gets filled up within
a few femtoseconds by a higher-lying electron emitting fluorescence or Auger electron
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Absorption coefficient above edge
2
Η)( fiEFermi’s Golden Rule
For a bare atom: NO EXAFS, smooth drop in (E) above absorption edge
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Effect of neighboring atoms
)(
)()()(
0
0
E
EEE
The ejected photoelectron is scattered by the neighboring atoms
This results in interference between outgoing and backscattered
waves.
(E) depends on density of final states at energy E-E0 that is
modulated by the interference at the absorbing atom: EXAFS
THE EXAFS FUNCTION
Usually represented in terms of
wavevector k
2
0)(2
EEmk
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The EXAFS Equation
)](2sin[)(
)(2
)(/2222
kkRkR
eekfNk
jj
j j
kRk
jj
jj
N = coordination number
= mean square variation in distance (Debye-Waller
factor)
R= inter-atomic distance
f(k), (k) are scattering properties of the neighboring
atoms
(k)= mean free path of photoelectron
Typically N, and R are fitted to the (k) data
f(k) , (k) and (k) are theoretically calculated
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EXAFS Data Reduction Steps
Experimentally (E) log(I0/I) or If/I0
Subtract a smooth pre-edge function to get rid of instrumental background
and absorption from other edges
Identify E0, energy of the maximum derivative of (E)
Normalize (E) to go from 0 to 1
Remove a smooth post-edge background function to approximate 0(E)
Isolate the EXAFS: (k)
Fourier Transform to get real space pair-correlation function
Fit k2 or k3 –weighted (k) data to the EXAFS equation to get coordination
environment
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EXAFS Data Reduction Steps - I
Fitting of backgrounds Isolation of XANES
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EXAFS Data Reduction Steps - II
Experiment
Simulation
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XANES: Applications
Although physically and theoretically XANES is not
well understood, it is used as a fingerprint technique
for determination of
1.Valence state
2.Phase identification
3.Coordination number/chemistry
4.Hybridization, band structure etc.
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Nature of intermediate-range order
in Ge-As sulfide glasses: A case
study employing a combination of
EXAFS, Neutron & x-ray scattering,
SANS, RMC
S. Soyer Uzun*, S. Sen*, C.E. Benmore** and B.G. Aitken†
*Dept. of Materials Science, University of California at Davis
** Argonne National Laboratory† Corning Incorporated
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Background and Motivation
• Complex glasses with wide
compositional range of glass
formation
• Technologically important: passive
and active photonic devices
• Model system for testing structure-
property models based on average
coordination numbers
0 .0 0 .2 0 .4 0 .6 0 .8 1 .0
0 .0
0 .2
0 .4
0 .6
0 .8
1 .0 0 .0
0 .2
0 .4
0 .6
0 .8
1 .0
G eA s
S
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Short-range order from Ge and As K-
edge EXAFS
2 4 6 8 10 12 14 16
Wavenumber k (angstrom-1
)
k3
(k
)
+57.1%
+6.1%
0.0%
-14.3%
-30.2%
-42.9%
-53.3%
-61.9%
-69.2%
Ge K-edge EXAFS
FT
0 2 4 6 8 10
Radial Distance (angstrom)
Fo
ur
ier
Tr
an
sfo
rm
(a
rb
. u
nit
s)
+57.1%
+6.1%
0.0%
-14.3%
-30.2%
-42.9%
-53.3%
-61.9%
-69.2%
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Short-range order from Ge and As K-
edge EXAFS
• Ge and As are always 4 and 3
coordinated
• As-As homopolar bonding takes up
initial S-deficiency
• Ge takes part in homopolar
bonding when all As is used up in As-
As bonding
Sen et al. PRB, 64, 104202 (2001);
JNCS, 293-295, 204 (2001).
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How to study IRO ?
• Compositional evolution of RDF in real
space
• Behavior of First Sharp Diffraction Peak
(FSDP) parameters
• Combine RMC simulation with diffraction to
build large-scale structural models
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Experimental Methods
• Sample synthesis
– Ge-As-S glasses with Ge=As and 33.3 S 70.0
– melting of constituent elements ( 99.9995% purity) in
evacuated (10-6 Torr) fused silica ampoule at 1200 K for
24 h, quenched in water, annealed at Tg
• Neutron and high-energy x-ray diffraction
– GLAD Diffractometer at IPNS
– Sector 11-IDC at Advanced Photon Source, ANL
(115.47 keV)
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Why combine neutron & x-ray?
• structural interpretation of RDF for multi-component
glasses becomes non-unique due to the convolution of a
large number of pair-correlation functions
• neutrons and X-rays often weigh pair-correlations
differently
• For example in stoichiometric and S-excess glasses the
first peak at 2.24 Å in RDF corresponds to Ge-S and As-S
correlations:
CN = NWAsSCAs(S) + NWGeSCGe(S)
CX = XWAsSCAs(S) + XWGeSCGe(S)
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Neutron and x-ray structure factors
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Neutron and x-ray RDFs
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Short-range atomic correlations
~2.2 Å : Ge-S and As-S nearest neighbors
~2.5 Å : Ge-Ge, As-As and Ge-As nearest neighbors
~3.4 Å : Ge/As – S – Ge/As next-nearest neighbors
~3.6 Å : S – S nearest neighbors
~3.8 Å : Ge/As – Ge/As – Ge/As next-nearest neighbors
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FSDP parameters: intensity & position
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FSDP parameters: intensity & position
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FSDP parameters: width
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Small-angle neutron scattering
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Nature of Intermediate-Range Order
FSDP intensity shows reversal around x= 25 where Ge starts
participating in Ge-Ge/As bonding
Metal-metal correlations in GeS2 and As2S3 networks-
Additional IRO from As-As correlations in As-rich clusters-
increase in coherence length
Strong density fluctuation from coexistence of heteropolar and
homopolar bonded regions: increasing SAS
For x>25: loss of GeS2 network, structure dominated by metal-
metal bonded network, decrease in SAS and coherence length
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Reverse Monte Carlo Simulation
1. 1700-1800 atom simulation (box size ~ 3.6
nm)
2. Initial configuration was setup using short-
range order constraints from EXAFS and
diffraction
3. X-ray and neutron S(Q) were fitted
simultaneously using the code RMCA(McGreevy and Pusztai; J. Phys.: Cond. Matter 13, R877-R913, 2001)
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Stoichiometric glass
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S-deficient glass
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Most S-deficient glass
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New Techniques
(with a lot of future potential
for glasses & liquids)
IXS & XPCS
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Inelastic x-ray scattering
• Involves energy loss of x-ray photon associated with bound-state electronic transitions of core-level electrons
• Especially useful for low-Z atoms (e.g. B, C, Li) where absorption techniques are not practical due to low energies of absorption
• Use monochromatic high-energy x-ray and look at energy loss spectrum (sort of like the difference between IR and Raman spectroscopy)
• Can be done in resonance to get element-specific and amplify the effect (RIXS)
• More conventional application is in studying fast dynamics (ps), sound velocity, elastic properties (x-ray Brillouin spectroscopy)
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Inelastic x-ray scattering
S.K. Lee et al. PRL, 2007
IXS of borate glasses: pressure effect
on B coordination
Dynamics in Al2O3 liquid
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X-ray photon correlation spectroscopy
• PCS probes slow dynamics (mHz to MHz) by analyzing temporal correlation among scattered photons
• Visible light PCS is an important technique for studying the long wavelength dynamics in glass-forming liquids.
• XPCS offers unprecedented opportunity in probing slow dynamics at very short wavelengths: x-ray speckle spectroscopy
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X-ray photon correlation spectroscopy
• XPCS study of suspended nanoparticles in a supercooled glass-forming liquid
• At T >> Tg the particles undergo Brownian motion; measurements closer to glass transition (T ~ 1.2 Tg) indicate hyperdiffusive behavior
Caronna, et al., PRL 100, 055702 (2008)
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Acknowledgments
National Science Foundation DMR grant
Contents of some slides from:
Chris Benmore
Neville Greaves
Matt Newville