Hole formation, energy

Fig. 6. The hole formation energy 2ajk), the barrier to internal rotation (/de/fi) and the glass transition temperature vs. compoafdon for NaPOjijCa(PO, counterion copolymers (2 /ft) and (Aelk) calculated from the Gibbs-DiMarzio theory at 10% intervals. T, points experimental...

Kg. 7. The hole formation energy vs. tanier to internal rotation 1 both calculated from Gibbs-DiMarzio theory. Organic Polymers O polyphosphates... 

The hole model discussed above is different from the hole model proposed by Ramachandrarao et al. (1977) and also used by Hirata (1979). In the latter model the hole formation energy is estimated from experimental data on the changes in specific heat and thermal expansion at the glass transition. Also in this hole model a linear relationship is found between the hole formation energy and the glass transition temperature, although the model lends itself less easily for making predictions. 

T Aa is seen to be a function of V only, and since, according to quite well established observations of Simha and Boyer this product is a constant for all polymers (10), eqn. (1) implies an iso-free volume glass transition state. In fact, using the empirical Simha-Boyer constant of 0.113 for T Aa, it is found that V = 0.025 at T, identical with the free volume estimated from tne WLF equation (11). The hole formation energy, E, in the Gibbs-DiMarzio treatment is a function of T alone and is directly proportional to the latter, as is seen in eqn. (2). 

While zinc interstitials are possible, the formation energy for these defects is higher than that of oxygen vacancies. As in the case of NiO, continuing theoretical studies are needed to clarify the location of holes and electrons in these phases. 

Fig. 3-11. Energy for decomposing ionization of compound AB to form gaseous ions A(giD) and via electron-hole pair formation and via cation-anion vacancy pair formation r = reaction coordinate of decomposing ionization e, s semiconductor band gap . vmb) = cation-anion vacancy pair formation energy (Va- Vb-) Lab = decomposing ionization energy of compound AB.

The decomposing ionization will take place preferentially by way ofthe electron-hole pair formation, if the formation energy of the electron-hole pair, e, is smaller than the formation energy of the cation-emion vacancy pair, Hv(ab>, and vice versa. In general, compound semiconductors, in which the band gap is small (e,< Jfv(AB>), will prefer the formation of electron-hole pairs whereas, compound insulators such as sodium chloride, in which the band gap is great (e(>Hv(AB>), will prefer the formation of cation-anion vacancy pairs [Fumi-Tosi, 1964]. 

All PV cells depend upon the absorption of light, the subsequent formation and spatial separation of electrons and holes, and the collection of the electrons and holes at different energies (called electrical potential). The efficiency of electron and hole formation, separation, and collection determines the photocurrent, whereas the energy difference between the electrons and the holes in their final state before leaving the cell determines the photovoltage. 

Hirai and Eiring20 established that the value Aa 7g is dependent on the energy of hole formation eh in accordance with the equation ... 

Some very interesting ideas concerning the relationship between free-volume formation and the energy of one mole of hole formation were developed in detail by Kanig42. Kanig introduced some improvements to the definition of free-volume, On the basis of Frenkel s ideas43 he divided the free-volume into two parts, one of which is determined only by the thermal vibrations of atoms in the lattice of a real crystal while the other is connected with inherent free-volume, i.e. voids and holes. It is the latter that makes possible the exchange of particles, i.e. the very existence of the liquid state. He introduced some new definitions of fractions of free-volume ... 

Here oth is the fraction of thermal expansion connected with changes in hole concentration (free-volume expansion), ), is the energy of hole formation, r=M/p0 Vn Na, where NA is the Avogadro number,M molecular weight, p0 the density of a liquid without holes at absolute zero, and Vn the hole volume. For polymeric systems r is very small, and then ahTis the function of E IRTalone. The value Of, is identified with experimentally observed changes in the thermal expansion coefficients A a at Tg, i.e. 

In Pd the 4 p width is considerably larger than the shift which means that during the formation of the tidal wave, the energy loss ( friction") is dominant and a maximum relaxation shift is not very probable. However, this does of course not violate the picture of a 4p hole as a stable excitation in the sense that the total width is still much smaller than the core-hole binding energy. However, in order to observe the Weisskopf-Wigner limit of exponential decay one may have to go back to the elements around 42Mo. 

New stars form from clouds of dust and gas when the clouds are able to cool. One of the reasons the contracting clouds can cool is that they contain carbon monoxide and oxygen that radiate away energy. Therefore the presence of carbon and oxygen facilitate star formation, black hole formation, and life formation.25 We are parasites—intelligent tapeworms feeding off the processes that produce black holes. If black holes create new Universes, we owe our lives not only to the warm suns but also to their blackened corpses. 

The explanation of the heat of transport is given by the hindrance energy Qh and the gap formation energy Qg for a particle [i, ii]. The gap formation energy is the energy necessary to form a hole to insert a particle i in a determined place on the other hand, the hindrance energy is the energy necessary for the entrance of the particle into the hole formed. The heat of transport is a function of both contributions. 

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