Volume 10 - Materials Characterization Part 10 ppt

I I, I I
I.
I s I s I s I s
I s I s
(Eq 1)
s I
I I
π θ λ
i s
(Eq 2)
f
rG r si s
(Eq 3)
r r
r
s
s s
s
s s
s
s s s
s,
si s
s. s
Ann. Phys.,
Z. Phys.,
X-ray Diffraction,
X-ray Diffraction,
s
I

s,
s
θ
I
s s
s
I
I
I
I s W
n
s a
n
b
n
ds
e
(Eq 4)
W
n
d e
a
n
b
n
c
n
i s
si s N
ij

f
i
f
j
s
sr
ij
/r
ij
f
(Eq 5)
r
ij
i j N
ij
l
ij
s
l
ij
s
rG r s
rG r
(Eq 6)
(Eq 7)
(Eq 8)
(Eq 9)
(Eq 10)
r
ij

l
ij
N
ij
a
n
b
n
c
n
K
uc sd;
A
I
(Eq 11)
p q u v
w
a, b, A I K, r
ij
l
ij
and N
ij
si s si s
si s I r
ij
l
ij
K, A,
I

Table 1 Initial and final short-distance parameters for the silica glass refinement
Material Cycle
r
ij
,
l
ij

0.03
0.06
0.10
0.10
0.10
si s
s I
uc uc
NT NT NT
NT NT
j f
j
if
j
i f
i
f
j
f
i
F
j

f
i
f
j
A
ij
IP
IP
ij k,m
s
sr
k,m
sr
k,m
(Eq 12)
k,m i j.
I s i s
I s
I s A
ij
IP
ij
(Eq 13)
N N A
ij
N N N
IP
ij
Acta Cryst.,
J. Appl. Cryst.,

Advances In X-ray Analyses,
r r w
i
w
j
f
i
f
j
r r
ij
r
ij
l
ij
f
(Eq 14)
i
j
i j
r,R
(Eq 15)
r,R r R
(Eq 16)
t.
(Eq 17)
F rG r rG r dr
(Eq 18)
J. Appl. Cryst.,
t

r r G r
Table 2 Correlation coefficients comparing the silica glass radial distribution function with those for various
bonding topologies defined in the text
Range,
1412 atom model Tridymite Cristobalite


0.26
0.28
0.10
1.00
0.46
0.44
-0.17
0.00
-0.32
0.31
0.33
0.76
18-20 0.75 0.40 0.70 0.72
r
s
s
I
I s
π ρ π ρ
a a
b b b b
b a.

rG r r
F
F rG r rG r dr
rG r dr
(Eq 19)
Table 3 Comparison of the correlation functions F(calc,exp) and F'(calc,exp) for carbon with five models
b-ribbon bent Layer bent Layer b-ribbon
a
Range Å
(a) (b) (a) (b) (a) (b) (a) (b) (a)

0.85

0.88

F
F
b
J. Non-Cryst. Solids,
Carbon,
Ann. Phys.,
Z. Phys.,
X-ray Diffraction,
X-ray Diffraction,
Phys. Rev.,
J. Non-Cryst. Solids,
Acta Cryst.,
J. Appl. Cryst.,

Advances In X-ray Analyses,
J. Appl. Cryst.,
J. Non-Cryst. Solids,
Carbon,
General Uses
•
•
Examples of Applications
•
•
•
•
•
Samples
• Form:
• Size:
Limitations
•
•
Estimated Analysis Time
•
Capabilities of Related Techniques
• Scanning electron microscopy:
• Transmission electron microscopy:
• X-ray diffraction:
Small-Angle Scattering of X-rays,
Small-Angle X-ray Scattering,
X-rays in Theory and Experiment,
X-ray Diffraction Procedures,
Newer Methods of Polymer Characterization,

Direct Analysis of Diffraction by Matter,
J. Appl. Crystallogr.,
J. Appl. Crystallogr.,
J. Appl. Crystallogr.,
Mater. Sci. Eng.,
x, y
λ λ
Small-Angle Scattering of X-rays,
Newer Methods of Polymer Characterization,
Acta Crystallogr.,
J. Coll. Int. Sci.,
Macromolecules,
r
i
r
i
i
R i
(Eq 1)
k E R, S S
S
k k k ik
E h
(Eq 2)
C k R t
(Eq 3)
r
i
r
j

i
k
r
k
r
(Eq 4)
I h C
i j
iks r dr
i
dr
j
(Eq 5)
r
(Eq 6)
(Eq 7)
r r
(Eq 8)
a
(Eq 9)
a I h
r
R,
r.
(Eq 10)
(Eq 11)
h,
(Eq 12)
h
Small-Angle Scattering of X-rays,

X-rays in Theory and Experiment,
J. Math. Phys.,
J. Appl. Phys.,
Kolloid. Zh.,
Acta Metall.,
x x
T
I I d
(Eq 13)
d
I I I d
(Eq 14)
I I
h