Chemistry Reference
In-Depth Information
to switch between a paramagnetic high spin state (HS) and a diamagnetic low-spin
ground state (LS) [
109
]. This does not necessarily imply a change of crystal
symmetry, but it clearly modifies the molecular geometry, hence the packing.
Phase transitions are not only characterized by atomic or molecular structural
changes - they can also be characterized by significant modifications in the
microstructure and domains and at a much larger size scale. One notable example
has been recently reported by Glazer et al. [
110
] using linear birefringence
measurements in LiTaO
3
and LiTa
x
Nb
1
x
O
3
crystals at high temperature.
In this chapter combinations of low/high temperature and pressure have not been
discussed. However it might be clear that this would offer even further possibilities
to expand the knowledge on the phase diagram of a given species. At the same time,
further accuracy could be obtained from high pressure experiments if atomic
displacements are significantly reduced. Most of these applications can be exploited
in the future with the continuous improvements of high pressure techniques and
scientific research in this area (see [
114
] for more details).
4.4 Thermodynamics from Multi-Temperature Diffraction
As has become clear in previous sections, atomic thermal parameters refined from
X-ray or neutron diffraction data contain information on the thermodynamics of a
crystal, because they depend on the atom dynamics. However, as diffracted
intensities (in kinematic approximation) provide magnitudes of structure factors,
but not their phases, so atomic displacement parameters provide the mean
amplitudes of atomic motion but not the “phase” of atomic displacement (i.e., the
relative motion of atoms).
5
This means that vibrational frequencies are not directly
available from a model where
U
ij
parameters are refined. However, Burgi
demonstrated [
111
] that such information is in fact available from sets of
U
ij
s
refined on the same molecular crystals at different temperatures.
Using a rigid body approximation, i.e., assuming that molecules move in crystals
without correlation between external (low frequency) and internal (high frequency)
modes, Cruickshank demonstrated in 1956 how the atomic displacements (at just
one temperature) could be used together with infra-red spectroscopy to obtain
information on the entropy of crystalline naphthalene [
112
]. A partial rigid body
approximation could also be applied to some functional groups in a molecule,
having much lower rotational barriers (for example methyl,
tert
-butyl groups
attached to some rigid aromatic skeleton).
B
urgi generalized the model, assuming a temperature independent high frequency
term accounting for displacements due to the internal modes. By means of multi-
€
5
This problem is sometimes referred to as the
second phase problem
in crystallography.
