14.4.3 Example: Iron
Fig. 132 shows the phase diagram of iron with the specific heat in dependence of the temperature
and the crystal structure. The low temperature phase is bcc. At higher temperatures it changes
to a fcc structure, which is more tightly packed than the bcc structure. Normally, we expect the
opposite, because tight packed structures are often dependent to low temperatures. This effect can be
understood by considering the magnetic energy. At low temperatures the bcc phase is ferromagnetic,
whereas the fcc phase is antiferromagnetic. Therefore, to create steel, which is not magnetic, impurities
have to be added to the fcc phase at high temperatures to prevent the material of phase transitions
to magnetic phases.
If the free energy including the magnet component is calculated, it turns out that the bcc phase has a
lower energy than the fcc phase at low temperatures. In experiments it is always easy to measure the
specific heat capacity, because that’s just the energy you need to warm the material up. If we have a
look at fig. 132, we can see that there is a jump from one phase to the other phase, where the solid
line marks the stable phase. So the specific heat has a jump at the phase transition. When the fcc
phase is stabilized by impurities, it is possible to measure the specific heat of this phase down close to
zero degrees. What we see is a peak at about 15 K, which is called the Néel temperature. That’s the
temperature where an antiferromagnetic material becomes paramagnetic. The other big peak at about
1100 K coresponds to the Curie temperature, where a ferromagnet becomes a paramagnet. Because
of its form, such peaks are calledλ-points.
Remember that the two peaks correspond to electronic phase transitions, where the two jumps have
to do with the structural phase transitions.
Figure 132: Phase diagram of iron with the specific heat in dependence of the temperature14.4.4 Ferroelectricity
It turns out that interesting ferroelectric materials at room temperature are perovskits. The structure
of a perovskit is shown in fig. 133, where we use BaTiO 3 as an example. The high temperature phase is
cubic and there is no dipole moment. In the low temperature phase the positive charged ions (barium
and titanium) move with respect to the oxygen, which is negative charged. So the unit cell gets a
dipole moment and this effect is called ferroelectricity.