Advanced Solid State Physics

This effect is often observed in insulators with different phases in them and these different phases have different dielectric c ...

14.4.2 Example: Tin A popular example for structural phase transitions is tin (Chemical symbol: Sn). This element has two forms: ...

Figure 130: Dispersion relations forα-tin andβ-tin Figure 131: Density of states ofα-tin andβ-tin ...

14.4.3 Example: Iron Fig. 132 shows the phase diagram of iron with the specific heat in dependence of the temperature and the cr ...

In fig. 134 we can see the spontaneous polarization of barium titanate as a function of temperature. The phase transition from t ...

like the Curie-Weiss law: χ= 1 T−TC (255) The fact that susceptibility and dielectric constant are related, causes the peak in t ...

14.4.5 Pyroelectricity Pyroelectricity is strongly related to ferroelectricity in the way that in both cases, one needs a materi ...

(a) (b) Figure 136: a) Pyroelectric constant ofPbTiO 3 ; b) Dielectric constant ofPbTiO 3 Figure 137: Graphical description for ...

PbTiO 3 ,KNbO 3 andLiNbO 3. Fig. 138 shows the phase diagram of PZT. The area labeledPCmeans in there the crystal is paraelec- t ...

14.5 Landau Theory of Phase Transitions Landau took a look at phase transitions and realized that each of these transitions is a ...

The free energy as a function ofmis plotted in fig. 139. One can see, that the curvature of the free energy at the critical temp ...

For ferroelectricity, one gets the same dependence of the order parameterP on the temperature (fig. 141) and also the supercondu ...

These results are quite interesting, as one can see that the entropy changes slope at the phase transition (fig. 143) and the sp ...

14.5.2 First Order Phase Transitions First order phase transitions are very complicated to deal with, because the order paramete ...

Figure 146: The polarization ofBaTiO 3 as a function of temperature ...

15 Summary: Silicon Silicon is the second most common element in the earth’s crust (in the form of rocks, sand, glass, etc...) a ...

Figure 148: First Brillouin zone of silicon Figure 149: Phonon dispersion relation of silicon frequency is determined by the sho ...

Figure 150: Vibration of atoms with the shortest wavelength Figure 151: Phonon density of states of silicon however is, that the ...

Figure 152: Electron dispersion relation of diamond Figure 153: Electron dispersion relation of silicon ...

Figure 154: Electron dispersion relation of germanium Figure 155: Electron dispersion relation of tin ...