vii
CONTENTS
CHAPTER
1
TITLE
PAGE
TITLE
i
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENT
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
xii
LIST OF FIGURES
xiii
LIST OF SYMBOLS
xvi
LIST OF APPENDICES
xix
INTRODUCTION
1.1
Research Background
3
1.2
Research Problem
5
1.3
Research Objective
6
1.4
Scope of Studies
6
1.5
Organization of Thesis
7
viii
2
LITERATURE REVIEW
3
THEORY
8
3.1
Introduction
13
3.2
Fundamental Aspect Of Small Angle Scattering
15
3.2.1
15
Scattering Vector
3.2.2 Scattering Length, Scattering Length
Density and Contrast Term
3.2.2.1 Scattering Length
18
3.2.2.2 Scattering Length Density
19
3.2.2.3 Contrast Term
19
3.2.3 Scattering Cross section
3.2.3.1 Microscopic Cross Section
20
3.2.3.2 Macroscopic Cross Section
21
3.2.3.3 Differential Scattering Cross Section
22
3.2.4 Separation of Coherent and Incoherent Parts
24
of Neutron Scattering
3.2.5 The Measured Intensity and Scattering
25
Cross Section
3.3
3.4
3.5
3.2.6 Intraparticle scattering: Form factor P(Q)
28
3.2.7 Interparticle scattering: Structure factor S(Q)
29
Sample Description
3.3.1
What is Aerogels?
31
3.3.2
Synthesis of Silica Aerogels
33
3.3.3 Silica Aerogels Application
34
Determination of Fractal Dimension
35
3.4.1
Mass Fractal Dimension
37
3.4.2
Surface Fractal
38
Determination of Particle Size
40
ix
4
METHODOLOGY
4.1
Introduction
42
4.2
Synthesis of Silica Aerogels from Rice Husk Ash
42
4.3
Experiment Preparation
4.4
4.3.1 Sample Cell and Sample Thickness
45
4.3.2
46
Required Q-Range
SANS Instrument Component at MINT
47
4.4.1
Course Collimator
50
4.4.2
Biological Shielding
50
4.4.3
Beam Filter
50
4.4.4
Monochromator
51
4.4.5
Neutron Monitor
52
4.4.6
Collimator
53
4.4.7
Post Sample Flight Path
54
4.4.8
Two Dimensional Position Sensitive
54
Detector (PSD)
4.4.9 Data Acquisition System
56
4.5
SANS Instrument at BATAN
57
4.6
Data Acquisition
4.7
4.6.1
Configuration of SANS Instrument
59
4.6.2
Measurements
59
4.6.3
Counting Times
61
4.6.4
SANS Data Acquisition Program
62
Data Reduction
4.7.1
Data Reduction Protocol
66
4.7.2
Data Reduction Program
68
4.7.2.1 CENTER
70
4.7.2.2 EFFI
71
4.7.2.3 IQ1D
72
x
5
RESULTS AND DISCUSSION
5.1
Introduction
75
5.2
SANS Instrument Alignment at MINT
76
5.3
SANS Facility at BATAN
83
5.4
Determination of Fractal Dimension
85
5.4.1 SANS Result at MINT
85
5.4.2 SANS Result at BATAN
5.4.4.1 Silica Aerogels and Titanium
88
Containing Silica Aerogels
5.4.4.2 pH Varying Silica Aerogels
5.5
90
Determination of Particle Size
95
5.5.1 SANS Result at MINT
95
5.5.2 SANS Result at BATAN
5.5.2.1 Silica Aerogels and Titanium
97
Containing Silica Aerogels
5.5.2.2 pH Varying Silica Aerogels
6
99
SUMMARY AND CONCLUSION
6.1
Alignment of SANS Instrument at MINT
103
6.2
SANS Data Reduction Program Development
103
6.3
Determination of Fractal Dimension and
104
Particle Size of Silica Aerogels and
Titanium Containing Silica Aerogels
(MINT & BATAN)
6.4
Determination of Fractal Dimension and
105
Particle Size of Silica Aerogels with Different
Acid Concentration (BATAN)
6.5
Conclusion and Suggestions
105
xi
REFERENCE
107
APPENDIX A
119
APPENDIX B
140
APPENDIX C
143
APPENDIX D
154
APPENDIX E
155
APPENDIX F
169
APPENDIX G
170
APPENDIX H
172
xii
LIST OF TABLES
TABLE NO.
1.1
TITLE
The properties of the interaction of X-Rays and neutrons
PAGE
2
with matters.
4.1
Physical properties of Maerogel.
44
4.2
Specification of the 8m SANS Instrument at MINT
56
4.3
Instrument parametre of SANS facility at BATAN
57
5.1
Sample to detector distance and resultant Q range
83
5.2
Fractal dimension of silica aerogels and
85
titanium containing silica aerogels (MINT).
5.3
Fractal dimension of silica aerogels and
88
titanium containing silica aerogels (BATAN)
5.4
Fractal dimension of silica aerogels with different
91
acid concentration
5.5
Guinier analysis of silica aerogels and
95
titanium containing silica aerogels
5.6
Guinier analysis of silica aerogels and
97
titanium containing silica aerogels (particle radius)
5.7
Guinier analysis of silica aerogels and
97
titanium containing silica aerogels (cluster radius)
5.8
Guinier analysis of silica aerogels (particle radius)
99
with different acid concentration
5.9
Guinier analysis of silica aerogels (cluster radius)
with different acid concentration
100
xiii
LIST OF FIGURES
FIGURE NO.
TITLE
PAGE
3.1
Neutron scattering experimental setup
14
3.2
Schematic drawing of small angle neutron
15
scattering experiment
3.3
A scattering event
16
3.4
Scattering geometry
16
3.5
A parallel neutron beam incident normally on a thin target
20
3.6
Physical situation of detector placed in the outgoing beam
22
to detect the product
3.7
Silica Matrix in aerogels
32
3.8
Illustration for two dimensional mass fractal
38
4.1
Schematic procedure of preparing silica aerogels from
43
rice husk ash
4.2
Schematic procedure of preparing titanium containing
44
silica aerogels
4.3
Selection of sample thickness for maximum
46
scattered intensity
4.4
Cutaway view of TRIGA reactor
48
4.5
General layout of SANS instrument at MINT
49
4.6
The shutter, beryllium filter and monochromator assembly
52
4.7
Experimental setup from collimator to post sample
53
flight tube
4.8
Arrangement of post sample flight tube and
55
position sensitive detector
4.9
SANS Instrument Setup at BATAN
58
xiv
4.10
Input control and scale display screen
63
4.11
Data acquisition program flow chart
64
4.12
FORTRAN data reduction program flowchart
73
5.1
Output screen of the data acquisition system for the
77
SANS instrument before instrument alignment was
carried out
5.2
Dos Prompt of program used to control the motor
78
of rotating table and goniometre
5.3
Output screen of the data acquisition system for the
79
SANS instrument after instrument alignment was carried out
5.4
Graph of intensity I(Q) versus scattering vector Q
81
for SiO2 (1996)
5.5
Graph of intensity I(Q) versus scattering vector Q
81
for SiO2 (2004)
5.6
Double logarithmic plot of intensity I(Q) versus
82
scattering vector Q for SiO2 (1996)
5.7
Double logarithmic plot of intensity I(Q) versus
82
scattering vector Q for SiO2 (2004)
5.8
Scattering pattern recorded by position-sensitive
83
detector with sample to detector distance of 13 m
5.9
Scattering pattern recorded by position-sensitive
84
detector with sample to detector distance of 4 m
5.10
Scattering pattern recorded by position-sensitive
84
detector with sample to detector distance of 1.5 m
5.11
Double logarithmic plot of Intensity I(Q) versus
87
scattering vector, Q for silica aerogels (MINT)
5.12
Double logarithmic plot of Intensity I(Q) versus
scattering vector, Q for titanium containing
silica aerogels (MINT)
88
xv
5.13
Double logarithmic plot of intensity I(Q) versus
89
scattering vector, Q for silica aerogels (BATAN)
5.14
Double logarithmic plot of intensity I(Q) versus
89
scattering vector, Q for titanium containing
silica aerogels (BATAN)
5.15
Double logarithmic plot of intensity I(Q) versus
93
scattering vector, Q for silica aerogels 1N
5.16
Double logarithmic plot of intensity I(Q) versus
93
scattering vector, Q for silica aerogels 1.25N
5.17
Double logarithmic plot of intensity I(Q) versus
94
scattering vector, Q for silica aerogels 1.5N
5.18
Double logarithmic plot of intensity I(Q) versus
94
scattering vector, Q for silica aerogels 1.75N
5.19
Guinier plot for silica aerogels (MINT)
96
5.20
Guinier plot for titanium containing silica aerogels (MINT) 96
5.21
Guinier plot for silica aerogels (BATAN)
98
5.22
Guinier plot for titanium containing silica aerogels
98
(BATAN)
5.23
Guinier plot for silica aerogels 1N
101
5.24
Guinier plot for silica aerogels 1.25N
101
5.25
Guinier plot for silica aerogels 1.5N
102
5.26
Guinier plot for silica aerogels 1.75N
102
xvi
LIST OF SYMBOLS
A
-
area
b
-
barns
b
-
scattering length
bc
-
coherent part of scattering length
bic
-
incoherent part of scattering length
bi
-
scattering length of ith atom
bo
-
average scattering length
d
-
sample thickness
dc
-
correlation length / average chord
D
-
fractal dimension
Db
-
bulk density of scattering body
Dm
-
mass fractal dimension
Ds
-
surface fractal dimension
Ei
-
incident energy
Es
-
final energy
F(r)
-
autocorrelation function
F(Q)
-
form factor of single particle
g(r)
-
pair correlation function
I
-
beam intensity
I(Q)
-
scattering intensity
I(T)
-
scattering intensity, in function of scattering angle
J1
-
first order spherical Bessel function
ki
-
incident wave vector
ks
-
scattered wave vector
M(r)
-
distribution of mass
xvii
Mw
-
molecular weight
n
-
number of particle
ni
-
reflecting index
N
-
number density of target nuclei
P(Q) -
form factor
P(r)
-
Patterson function
Q
-
scattering vector / momentum transfer
r
-
average radius
r
-
position of nucleus
Rc
-
cluster radius
Rg
-
radius of gyration
Rp
-
particle radius
S
-
surface area
S(Q)
-
structure factor
t
-
counting time
Ts
-
sample transmission
z
-
atomic number
Å
-
Angstrom
nm
-
nanometre
Pm
-
micrometer
mm
-
milimetre
cm
-
centimetre
m
-
metre
0
C
-
centigrade degree
keV
-
kilo electron volt
Ȉ
-
macroscopic cross section
6t
-
total cross section per unit sample volume
6c
-
coherent cross section per unit sample volume
6i
-
incoherent cross section per unit sample volume
6a
-
absorption cross section per unit sample volume
xviii
V
-
scattering cross section
ıs
-
standard deviation
vo
-
incident wave frequency
v
-
scattered wave frequency
T
-
scattering angle
O
-
wavelength
Oi
-
incident wavelength
Os
-
final wavelength
U
-
scattering length density
(¨U)2 -
contrast term
Um
-
scattering length density of surrounding medium
Up
-
scattering length density of sample
ȡ(r)
-
density of subvolume
I
-
neutron flux
:
-
solid angle
H
-
detector efficiency
M
-
tilting angle
ǻx
-
thickness
dV/d: -
differential cross section
xix
LIST OF APPENDICES
APPENDIX
TITLE
PAGE
A
SANS Data Acquisition System Program
119
B
CENTER Program
140
C
EFFI Program
143
D
EFFI.DAT
154
E
IQ1D Program
155
F
IQ
1D.DAT
G
Example Output File
170
H
Publications
172
169