Biomedical Engineering Reference
In-Depth Information
3000
CS+MPI
2000
MPI
GA
1000
HAP
0
10
20
30
40
50
60
2
θ
°
2.6
Phases in polymers and the identifi cation of inorganic phases by XRD.
X-ray diffraction data of calcifi c deposits of implanted ostrich pericardium.
Patterns from borohydride-treated samples, labeled GA (glutaraldehyde),
MPI (metaperiodate) and CS (chondroitin sulfate) +MPI, and that of
reference hydroxyapatite (HAP) are also shown in the fi gure. (Source:
Reprinted with permission from Ref. 5. Copyright 1973. Elsevier B.V.)
arrangements.
6-8
PDF, denoted by
g
(
r
), gives the probability of fi nding two
atoms separated by a distance
r
.
g
(
r
) is widely used in describing the struc-
ture of materials with small molecules because it emphasizes the structures
at smaller length scales (e.g. interatomic distances between bonded atoms).
In polymeric materials, a related function, structure function,
S
(
Q
), is often
used;
S
(
Q
) is the numerical Fourier transform of
g
(
r
).
S
(
Q
) is preferred
for describing structures in polymeric materials because it emphasizes the
structures at larger distances (e.g. between polymer chains). The relations
between
g
(
r
),
S
(
Q
), and the measured coherent scattered intensity,
I
coh
(
Q
),
are given by:
π
1
∫
()
⎣
()
⎦
(
QR
)
1
1
i
dQ
QS
Q
=+
g
r
2
2
πρ
2
r
o
[2.12]
2
∑
coh
()
()
I
Q
cf
Q
−
i
f
i
()
S
Q
1
+
=
2
∑
()
cf
Q
c
i
f
i
where
c
i
and
f
i
are the atomic concentration and X-ray atomic form factor,
respectively, for the atomic species of type
i
.
