side@hacettepe.edu.tr
IAEA Regional Training Course , 8-12 November 2010
Nano structured
materials
Multilayer Films,
Polycrystalline,
Nanocomposites,
Patterned structures,
Bulk structures,
Liquid crystals,
Biological samples,
Fractals,
Gels,
and etc.
“When scientists have learned how to control the arrangment
of matter at a very small scale, they will see materials take an
enormously richer variety of properties”
Richard Feynman (1959)
1013 photon/s/mm2
High flux, more intensed x-rays
108 photon/s/mm2
Widely used flux, conventional x-rays
Different formed aggregats can be investigated
Diluted -I
Lamellar
Densed -I
The other densed systems
Diluted -II
Densed -II
03.01 -20.07 2009
SWAXS (Small and Wide Angle X-Ray Scattering) Analizleri
-k
q
k’
I (Scattering intensity)
I (Scattering intensity)
2ө
k
q, X-ray scattering vector
q= k´-k
|q|=2 k sin
q= 4 sin / 
q (Å-1)
q (Å-1)
A(q)
= Ae  (r) exp(-iq.r) dr
=  [A(q)/Ae] exp(iq.r) dq
Scattered wave amplitude
Radial electron density
I(q)= |A(q)|2
= Ae2 |  (r) exp(-iq.r) dr |2
=  P(r) exp(-iq.r) dr
Scattered wave intensity
Reciprocal space
(r)
Fourier T.
P(r)
Fourier T.
=  (u+r) (u) du
=  I(q) exp(iq.r) dq
Distance distribution function
Real space
The followed process to determine structures is used
Measuring data
Determining of structural
parameters R, M, V etc.
In addition to SAXS technique
other techniques are:
SANS
scattering)
XAFS
Defining model structure in real
space and for this purpose using
other collaborative techniques
Construction of the model in q
space and fitting of the
experimental and theoretical results
( Small angle neutron
(X-ray Absorption
Fine structure),
XRD
(X-ray Diff.) and
Microscopy techniques.
More sensitive and recordable
structural results can be
obtained by this combination .
1. region
2. region
3. region
I
Experimental curve
I(q) = N [F(q)]2 S(q)
q
P
Particle Form Factor P(q)= F(q) 2
F(q)= 3V (1-2) [ sin(qR) – qR cos(qR) ] / (qR)3
S
I(q) = N [P(q)]
q
Diluted identical
I(q) = N1 [P1(q)]+ N2 [P2(q)]
Solution Structure Factor
Dilute two type particles
It defines the relatonship between
the positions of the particles
I(q) = N  g(R) [P(q)] dR
Dilute polydisperse
q
WAXS
sample: lactose powder
sample-detector distance: 29.5 cm
active length of detector ~ 5 cm
1024 pixels
50 µm/pixel
2~18°
4.8 Å
Calibration of the q-scale (WAXS)
with p-Br-BA powder:
2~26°
3.2Å
SAXS
Calibration of the qscale (SAXS)
with Ag-behenate
powder:
Lamellar d-spacing:
d = 58.38 Å
center of incident
primary beam
2665 Å
800 Å
Primary beam
(attenuated)
FWHM ~ 350 µm
sample: Lupolen
sample-detector distance: 28 cm
active length of detector ~ 5 cm
1024 pixels
50 µm/pixel
2~8°
11Å
Diluted systems-I
Protein or polymer solutions, etc.
First determined structural information
- Radius of gyration,
- Mass, volume and shape
Guinier
region
I
ln I
I(q) =I(0) exp(-R2q2/3)
1/R
.
q(nm-1)
Guinier line
tan  = -R2/3
q2
Spherical nano crystals embeded SiO2
Nanocrystals
glass
Nanocrystals
Noncrystallized
aggregations
Before cystallization
R<R0
R=R0
Different electron densities
After the cryst.
R<R0
Radius of gyration
____________
R= (a2+b2+c2)/5
Elipsoid
a,b,c
R2 =
 r 2 (r) d3r

 (r) d3r
elipsoid axes
Guinier law
(q0)
____
R=  (3/5) r = 0.77 r
Sphere
r, radius
I(q)q4
Porod law (q)
lim I(q)
q4 =
constant
Porod region
lim I(q)= 2 (1-2)2 S / q4
S, surface area
q (Å-1)
Kratky plots
I.q2 (nm) -2
Invariant
Q
Q = V <2>
 Fluctuation in the electron
densities
V Total volume causing the
scattering
Sample: Amorph and crystalline
regions in the structure
Two phase polymers
Q = V (k-a)2 ak
k , a electron densities of the phases
q (nm) -1
Kratky plots with Porod law
a , k volume fractions of the phases
Lamellar Structures
I
The positions of
Bragg peaks for
h = 1, 2, 3 give
the lamellar
distance (1/d)
q
If we look through the perpendicular direction of the lamelar structure,
we may define crystallographic order in SAXS range. In this case, by
using scattering intensity ratios and peak positions, some scattering
rules ( for hexagonal, cubic etc.) controlled and compaired to obtain
the real phases.
80
80
60
60
60
40
40
40
20
20
20
0
0 .0
I(q )
80
I( q )
I(q )
Some ordered cubic morphologies
0 .1
0 .2
0 .3
0 .4
0 .5
0
0 .0
P-surface
0 .2
0 .3
0 .4
0 .5
0
0 .0
Pn3
m
D-surface
0 .1
0 .2
0 .3
0 .4
0 .5
q
q
q
Im3m
0 .1
Ia3d
G-surface
Figures, H. Amenitsch,
SR School-ICTP
Hegzagonal struct.
Lamellar fluid
?
I.
III.
II.
lam
hex
According to the observed q ratios
(1) Periodic structure：
1 : 2 : 3 : 4…;
(2) Cubic：
1: 2 : 3 : 4 : 5 …. ;
(3) Hegzagonal
1: 3 : 4 : 7 : 9 : 12
PS-b-PEO Co-polymer phase transition
Photonic crystals
Interplanar distance is increasing with
increasing temperature
Blue
Heating
Light blue
Spin-cap (rotating capillary)
300 s / Frame
Sample rotation enhances
signal-noise ratio
SAXS
300 s / Frame
45 °
WAXS
SWAXS scanning of phase transitions
20°
www.hecus.at
23
ln I(q)
ln I(q)
0.05
0.10
0.15
0.05
q (Å-1)
ln I(q)
ln I(q)
0.10
0.15
q (Å-1)
Guinier
Slope
Porod
0.05
0.10
0.15
q (Å-1)
-2.50
-2.00
-1.50
-1.00
ln q
Shape reconstruction
A serial research on pH and temperature dependent-water soluble diblock copolymers
[2-(dietilamino) etil metakrilat]-b-[2-(dimetilamino) etil metakrilat] (DEAn-b-DMAm)
Hydrophillic(repulsion)
DEAn-b-DMAm diblock copoylmers are
stable (n/m=1/2) in misellar forms at 23C
ve pH=7,7. size distributions are narrow
and forms are spherical.
For
T=22,0-25,5C,
pH=7,6-8,0
and
n/m=0,25-0,73 values, misel numbers per
unit volume, misel sizes, shell thickness,
core radius and densities have been
determined by SAXS analysis.
Hydrophobic (attraction)
shell
core
t = thicknes of the shell
t
Rc = core radius
Rs = t + Rc
Rc
ρc
ρc = core electron density
ρs
ρç
Rs
ρs = shell electtron density
ρç = solution electron density
pH controls charge level and if the misel size
increase s, electrostatic repulsion becomes
effective.
Volume hight and base area
of the cone were determined
beside of packing parameter
Cubic structures occured by DNA and peptid connected spherical gold
nanoparticles
13 nm
Y9,Y10
Y11, ……, Y20
Y9,Y10
liquid paraffin, non-ionic
surfactants (Brij 72 and Brij 721P)
and/or pure water
H3
Formulation
Liquid Parafin
(%w/w)
Brij 721 P/ Brij 72
(3/1) (%w/w)
H2O (%)
A3
H3
L2
F1
70
6
40
30
30
31
10
70
63
50
AFM View
TEM View
[D.I. Svergun, Biophysics J.
1999, 76, 2879-2886]
Ferroelectric thin films, P.C.
Mclntyre Res. Group,
Stanford
Nonhomogen dielect.
(sculptured) thinfilm, STF,
A. Lakhtakia, Penn State
Photovoltaics, H. Kurz, Inst. of
Semiconductor Elect.
Germany
SrGa2S4:Ce thin-film, K.
Tanaka, NHK Lab. Japan
Multilayered Al-Si Porous
thin films, C. Orilall ,
Cornel Univ.
Ultra-thin solid oxide fuel cell,
F.B. Prinz ,RPL Stanford
Engineering
n+ Ga As
Sample I (7)
20 mol%
400 Å
65 Å
400 Å
21 mol%
55 Å
24
55
24
45
27
400 Å
n Ga As
400 Å
Sample II (8)
i Al Ga As
n+ Ga As
45
30
40
33
GaAs , a= 5.65 Å,
AlGaAs, a= 5.66 Å,
35
 = 5.32 g/cm3
 = 3,76 g/cm3
dac
da
dc
k is decay constant (interfacial area) for a
two phase system.
It depends on the total inner surface (S) and
the mean-square electron density fluctuations
Q
invariant
It has the
dimention of a
resprocal volume
Volume fractions
Total irradiated
volume
d(Å)Sample I (7)
d(Å) Sample II (8)
330.00
202.70
184.73
116.40
136.59
80.24
104.70
61.00
82.67
70.59
60.41
52.79
49.87
42.16
37.40
30.35
Mean sizes of the planar aggregations in the content of the sample I and
II are 198.09 and 121.67 Å , respectively.
R( Å)
Sample I
R( Å)
Sample II
5.32
30.77
56.41
79.48
100.02
125.64
184.63
217.94
258.97
317.95
371.80
425.64
453.85
6.44
35.42
62.79
83.72
122.36
161.10
194.81
223.79
262.43
281.75
Summary
Analysis of total scattering gives
valuable insight in the structureproperties relationship
High resolution instruments open the
door to medium-range order
investigations
Usage of collaborative techniques
always preferable to reach more
detailed knowledge.
GISAXS
0.2- 0.6 ⁰
2. BP
Düzgün
yönelmiş
tabakalar
LS
1. BP
İzotropik
lipozom
SB
+ PB
f
W- tarama
i
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42
SAXS ile algılanan nano-oluşumlar (1-100 nm)
WAXS ile algılanan nano-oluşum iç yapıları ( 1-10 Å)
Lc : correlation
Lc
distances
SAXS ile elde edilen bilgiler:
*Kesikli çizgilerle gösterilen elektron yoğunluk
farklarının yüksek olduğu nano oluşumların
şekli/şekilleri
* Nano-oluşumların ortalama büyüklükleri
*Nano-oluşumlar arası ortalama uzaklık ve uzaklık
dağılımları
*Birim hacimdeki nano-oluşum sayıları v.b. bilgiler.
Plaka formu için yapısal
bilgiler
İkili uzaklık dağılımları
Polimer içine
dağılarak
bulundukları
genel malzeme
ortamının
elektron
yoğunluğunu
artıran
moleküler
saçaklanmalar
Bütün verinin GNOM programı ile arıtılması
F o lie :S A X S 6 .d o c
F o u r ie r T r a n s fo r m a tio n o f P a r tic le S c a tte r in g C u r v e

I h   4  

0
p r
sin ( h r )
dr
hr
I(h )
h
p (r )
r
p (r )...P a ir -D is ta n c e D is tr ib u tio n F u n c tio n w ith in th e P a r tic le