1. 0.0 0.1 0.2 0.3 0.4 0.5 0.6
10
3
10
4
10
5
10
6
10
7
Intensity(arb.units)
q (Å
-1
)
Experiment
Fit
Probing Inhomogeneity of Glasses by
Small-angle X-ray Scattering
Sundararajan, Mayur; Chen, Gang Department of Physics and Astronomy, Ohio University, Athens, Ohio, USA
Abstract
Background
Small-angle X-ray Scattering (SAXS) is an effective technique for studying
heterogeneous glasses, especially those with nanostructures. In this poster,
we show a few examples of application of SAXS to the study of
heterogeneous glasses such as two-phase glasses, glass ceramics, nanoporous
glasses and ion-diffusion-induced heterogeneous glasses. A tabletop SAXS
system was employed and structural information such as shape and size
distribution of the inhomogeneous features is obtained. The results are used
to explain interesting phenomena in glass and glass-related materials.
Experimental
Data & Analysis
Conclusion References &Acknowledgement
2θ
λ = 2dSinθ
Sample
X-rays
Transmitted X-rays
Beam Stop
Detector
Small Angle
0 – 5o
Large Structure
1nm – 100nm
• Size and Form
• Inhomogeneous
structure
• Degree of crystallinity
• Crystal size
• Crystal distortion
Colloids
Nanocomposite
SiO2 ceramic Crystallization Proteins
Real Space Reciprocal Space
Electron Density Scattering Amplitude
Scattering IntensityAuto Correlation
Function
Fourier Transform
Inverse
Fourier Transform
Squaring
Autocorrelation
q or 2θ
ScatteringIntensityI(q)
Interparticle
Size of
Particle
Form of particle
Surface
structure
Inter-atomic
structure
Larger Structures Smaller Structures
Two Phase System:
Phase 1: ρ1, Volume fraction φ , Phase2: ρ2 , Volume fraction 1 - φ
𝑨 𝒒 =
𝑽
∆𝝆 𝐞𝐱𝐩 𝒊𝒒𝒓 𝒅𝒓 + 𝝆 𝟐 𝜹(𝒒)
𝑰 𝒒 = 𝟒𝝅𝝋(𝟏 − 𝝋)(∆𝝆) 𝟐
𝟎
∞
𝜸 𝟎(𝒓)
𝐬𝐢𝐧(𝒒𝒓)
𝒒𝒓
𝒓 𝟐
𝒅𝒓
Scattered X-ray Intensity:
𝑰 𝒒 =
(∆𝝆) 𝟐
𝑽 𝒑𝒂𝒓𝒕𝒊𝒄𝒍𝒆
𝟐
𝑽
𝟑
𝒔𝒊𝒏𝒒𝑹 − 𝒒𝑹𝒄𝒐𝒔𝒒𝑹
𝒒𝑹 𝟐
𝟐
Spherical Particle – Size distribution
Glass ceramic nanoparticle on thin film
2θ
Incident X-ray
ki
Sample
ki
ks q = ks - ki
𝒒 =
𝟒𝝅 𝑺𝒊𝒏 𝜽
𝝀
I 𝒒 =
𝑨 𝒒 𝑨∗(𝒒)
𝑽
𝑨 𝒒 =
𝑽
𝝆 𝒓 𝐞𝐱𝐩 −𝒊𝒒𝒓 𝒅𝒓Amplitude of scattered X-ray
Scattering Intensity per Volume
= 𝑭 𝒒 . 𝑺(𝒒)
0.01 0.1 1
100
1000
10000
100000
Intensity
Q[A-1
]
Relative Pressure (p/p°)
0.000.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00
QuantityAdsorbed(cm³/gSTP)
100100
150
200
250
300
350
400
450
IsothermLinearPlot
MCM41_500C-Adsorption
MCM41_500C-Desorption
Gas Adsorption
QuantityAdsorbed
Relative Pressure
Isotherm
Pore Width (Å)
2020 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
dV/dlog(w)PoreVolume(cm³/g·Å)
00
1
2
3
4
5
6
BJH Desorption dV/dlog(w) Pore Volume
User-Defined : Standard
BJH Desorption dV/dlog(w) Pore Volume
Pore Width(Å)
dV/dlog(w)PoreVolume(cm^3/g.Å)
Pore Size Distribution
3.2
nm
0 50 100 150 200 250 300 350
0.0
0.5
1.0
1.5
2.0
(r)
(r)"
r (Å)
(r)(arb.units)
-5
0
5
10
(r)"(arb.units)
r (Å)
d10
60°
Inter-pore
distance
Pore wall
Pore
2D hexagonal
3.3nm
Intensity(arb.units)
q(nm-1
)
SAXS WAXS
Log(Intensity(arb.Units)
Glass ceramic in the powder form
SAXS data
Data Fitting – Particle size Distribution
Nanoporous glass
SAXSData Fitting – Particle size DistributionSAXS data
62SiO2 – 13AlO1.5 – 25YbO1.5 synthesized by Rui Almeida, Instituto Superior Tecnico, Portugal
SiO2-LaF3 syntesised by Alicia Duran, Instituto de Ceramica y Vidrio, Spain
Structure Analysis by Small-Angle X-Ray and Neutron Scattering by L.A. Feigin, D.I. Svergun 335 pages
ISBN 1475766246
Small Angle X-Ray Scattering by Otto Glatter ISBN-10: 0122862805
NSF DMR – 1507670; NSF DMR - 0906825
Colloid:http://www.tedpella.com/gold_html/nanoxact-gold.htm; Crystal-Amorphous: http://eurjmin.geoscienceworld.org/cgi/content/abstract/23/6/937?etoc
Silica Ceramic:Nature Chemistry 3, 349–358 (2011) doi:10.1038/nchem.1031; Size Distribution:http://cheiron2011.spring8.or.jp/text/lec/14_Y.Amemiya_2011.pdf
62SiO2 – 13AlO1.5 – 25YbO1.5 deposited on Muscovite SiO2-LaF3 MCM-41
• SAXS is a versatile technique which has been shown to characterize size,
shape and inhomogeneity in glass, glass ceramic, porous glasses.
• SAXS results here have been compared with other characterization
techniques such as TEM and Gas-sorption Method.
Conversion of 2D – 1D data
0.01 0.1 1
102
103
104
105
Intensity(arb.units)
q(A-1
)
SiO2
-LaF3
-As Made
0.01 0.1 1
103
104
Intensity(arb.units)
q(A-1
)
SiO2
-LaF3
-620C-40Hr
TEM images
As Made Annealed
Sample Raw data Raw dataSample Raw data Raw data
Pore Size
SAXSess
X-ray film reader
X-ray film
Sample