Page 95 - Science at the nanoscale

RPS: PSP0007 - Science-at-Nanoscale
7:6
June 12, 2009
4.4. From Molecules to Supramolecules
by the Bragg’s law:
λ = 2d
(4.11)
sin θ
hkl
Here, d
is the spacing between the (hkl) planes that diffract the
hkl
radiation. This is the perpendicular distance between the parallel
planes and is given for the cubic crystals as:
a
d
= √
hkl
2
2
2
h + k + l
The XRD patterns of a powdered sample can be used to iden-
tify its crystalline phases and structural properties. An observed
shift in peak position indicates a change in d-spacing and hence
an internal strain in the crystals. An observed peak broaden-
ing is also frequently attributed to the finite size of the crystals.
The Debye-Scherrer equation relates peak width to the crystallite
size D:
Kλ
(4.13)
D =
W cos θ W
The peak width W is measured as the full width at half maximum
of a diffraction peak at θ W . K is the Scherrer constant of value
between 0.89 < K < 1 and is often taken as unity for common
crystals. The broadening of XRD peaks is illustrated in Fig. 4.25 for
cubic CdS nanocrystals prepared from solution. It is shown, for
the smallest CdS nanocrystals, that peak broadening has caused
the diffraction patterns between 40–50 degrees to merge.
4.4 FROM MOLECULES TO SUPRAMOLECULES (4.12) 85 ch04
We have discussed in Section 4.2 simple molecules such as H 2 ,
N 2 , CH 4 and HCl. These are relatively small gaseous molecules
with dimensions of a few angstroms (1 ˚ A = 0.1 nm). Common
molecules have sizes range from dozens of angstroms to several
tens of angstroms.
4.4.1 Macromolecules
It is interesting to note that Nature makes use of some small
molecular units as building blocks to form molecules of macro-
3
scopic sizes (1 micron = 10 nm) for specific functional purposes.