Cryo-Crystallography: Diffraction at Low Temperature and More - Advanced X-Ray Crystallography - page 58

associated with other useful information like, for example, heat capacity and heat
exchange measurements (available from DSC experiments) or spectroscopic signals.
The nature and the mechanisms of phase transitions in solids are still matters of
discussion among crystallographers, as nicely summarized in a recent review [ 20 ].
The reader is referred to textbooks for a comprehensive overview of this long term
debate [ 98 - 100 ]. Here, we summarize the qualitative nature of the main changes
that are possible in a solid to solid phase transition.
4.3.1 Symmetry
The symmetry of the crystal system could change during a phase transition, because
of a transformation of the lattice into a super-lattice or sub-lattice, a change in the
space group type, or both. 4 A change of symmetry (in R 3 space) is a sufficient
condition to assess occurrence of phase transformation, but it is not a necessary
condition. It is not rare, however, to observe iso-symmetric phase transitions, i.e.,
transformations where the space group type and the lattice type remain unchanged,
but two different structures are in equilibrium at the critical point. As a consequence
the sole determination of the space group may not be sufficient to detect a phase
transition, unless the thermal expansivity is calculated (which usually requires
measures over a wide temperature range). A discontinuity of the cell volume
[hence of the molar volume, V ( T )] or a discontinuity of the expansivity [first
derivative of V ( T )] would reveal a phase transition. For the second-order type of
transition (see below) it is necessary that a group-subgroup relationship is
maintained between the space groups of the two phases [ 94 , 95 ].
4.3.2 Molecular Structure
Changes of molecular structure as a function of temperature could reveal a phase
transition. However, caution should be applied because molecular geometries can
change together with crystal shrinking or expansion without implying formation of
a new phase [ 101 ]. So what kind of structural changes are compatible with a phase
transformation? If a crystallographic symmetry element appears/disappears through
the phase transition, then the space group type would change and the phase
transition is evident. Iso-symmetric phase transitions are instead caused by a
4 It is important here to talk about space group type , not just space group . In fact, the space group
is determined by the combination of lattice and symmetry operators. When crystallographers
report a given space group , in reality they refer to a space group type (i.e., the coincidence of
symmetry operations with those cataloged in the International Tables of crystallography, regard-
less the actual lattice dimensions). This distinction is particularly important when discussing phase
diagrams and in particular it is fundamental to appreciate the exact meaning of iso-symmetric
phase transition.