Hole, heat capacity number

Although the lattice heat capacity in a metal is much larger than its electronic contribution, the Fermi velocity of electrons (typically 106 m/s) is much larger than the speed of sound (about 103 m/s). Due to the higher energy carrier speed, the electronic contribution to the thermal conductivity turns out to be more dominant than the lattice contribution. For a semiconductor, however, the velocity is not the Fermi velocity but equal to the thermal velocity of the electrons or holes in the conduction or valence bands, respectively. This can be approximated as v /3kBT/m, where m is the effective electron mass in the conduction band or hole mass in the valence band. This is on the order of 105 m/s at room temperature. In addition, the number density of conduction band electrons in a semiconductor is much less than... 

The model is linked easily to the heat capacity of the liquid, as seen in the upper box of Fig. 6.5. The Cp arises mainly from vibrations, Cp(vib), and a contribution from the holes, Cp(h). In Cp(h) one finds the energy needed to change conformational isomers to accommodate the hole, as well as the potential energy required to create the extra volume of the holes that permits the large-amplitude molecular motion. Below Tg, Cp(h) is zero, as shown in the second box, because the hole-equiUbrium is arrested. Above Tg, it contributes the hole energy, Cij, multiplied with the change in equiUbrium number of holes with temperature 3N /9T at constant pressure. The equations can be... 

Figure 6.6 shows schematically with curve 1 how on slow cooling a system deviates at Tg from equilibrium of V, H, and S (heavy line, compare also to Fig. 4.128). The indicated Active temperature points to the equilibrium liquid with the identical number of holes as are frozen in the glass. The derivative quantities, heat capacity and expansivity, are shown in the lower curve of Fig. 6.6. Following the slow cooling with fast heating, curve 1 cannot be followed in the glass-transition...

The next step after evaluation of the change of hole numbers with time (and temperature) is to calculate the heat capacities obtained from the reversing signal. 

The simplest model to represent the glass transition is based on the hole theory which was developed by Frenkel and Eyring some 60 years ago and is described in more detail in Sect. 6.1.3 (see also Sect. 4.4.6). The equilibrium number of holes at T is N and each contributes an energy e, to the enthalpy. As given on Fig. 6.5, the hole contribution to the vibrational heat capacity Cp and its kinetics is represented by ... 

Below this glass transition r on of about 30 width to about 10 K, the heat capacity of the glass is often quite similar to the heat capacity of the crystalline polymer. The drop in hra,t capacity in goii from the liquid to the glass can be evaluated by insertion of the equilibrium hole number [Eq. (21)] into equation (27) [Wunderlich (19 )]. Table III.6 contains an up to date list of SJ and VJ fm polyn rs of known ACp. 

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