Vacancies formation enthalpy

Diffusion in NijAl has been studied by few investigators - in particular Chou and Chou (1985) and Hoshino et al. (1988) -and has been reviewed and discussed with respect to mechanisms and defects (Bakker, 1984 Wever et al., 1989 Stoloff, 1989). The constitutional defects are antistructure atoms on both sides of stoichiometry, i.e. Al on Ni sites and Ni on Al sites, and the concentration of constitutional, i.e. ather-mal, vacancies is very small. The vacancy content of 6 x 10 at the melting temperature and the vacancy formation enthalpy of 1.60 eV correspond to the respective values for Ni, i.e. the vacancy behavior of NijAI is similar to that of pure metals (Schaefer et al., 1992). The diffusion of Ni in NijAl is not very different from that in pure Ni and at high temperatures it is insensitive to deviations from stoichiometry. The diffusion of Al in NijAl is less well studied because a tracer is not readily available. Defects may interact with dissolved third elements which affects diffusion. In particular vacancies interact with B which is needed for ductilization , and this leads to a complex dependence of the Ni diffusion coefficient on the Al and B content of NijAl (Hoshino etal., 1988). Data for the diffusion of the third elements, Co, Cr, or Ti, in Nij Al are available (Minamino etal., 1992). 

The important parts of Eq. (4.76) are the exponential terms. The first exponential, which contains the entropies associated with potassium ion movement and vacancy formation, respectively, form the temperature-independent contributions to Do, as discussed in the previous section. The second exponential, which contains the enthalpies of the two processes and the temperature dependence, form the activation energy, Ea, and temperature dependence of Eq. (4.71). 

As noted in Sections 5.3-5.5, vacancies in the anion or cation array can exist in equilibrium with the vapor of the depleted element. If the enthalpy of formation of a vacancy in the anion array is markedly greater than that of one in the cation sublattice—for example, in ZnTe, where it is about 1 electron volt (1 eV = 96.5 kJ mol-1) higher—the heated solid will tend to develop an excess of anions and so will become a p-type semiconductor. The enthalpies of vacancy formation correlate with the anion-cation radius ratios thus, very large anions such as Te2- matched with relatively small cations such as Zn2+ favor doping with vapor of the anionic element for... 

Table 5.1. Formation enthalpies for vacancy formation in a few ionic crystals...

The situation is equivalent to the formation of H30+ ( proton interstitial ) and OH ( proton vacancy ) in water where the endothermic formation enthalpy of the water dissociation reaction is also compensated by the gain of configuration entropy [61]. In both cases, defect chemical reactions can be formulated the dissociation reaction in water... 

In recent years, there has been considerable effort to derive defect formation enthalpies of intrinsic defects in ZnO [108-110,113-117]. An example is shown in Fig. 1.13 [115]. Horizontal curves belong to neutral defects, curves with positive or negative slopes to charged donors or acceptors, respectively. The donor with the lowest formation enthalpy is the oxygen vacancy Vo, the acceptor with the lowest formation enthalpy the zinc vacancy Vzn-... 

A finitE number of point defects (e.g. vacancies, impurities) can be found in any crystalline material as the configirrational entropy term, TAS, for a low point defect concentration, outweighs the positive formation enthalpy in the free-energy expression, AG = AH — TAS. Thus, introduction of a small number of point defects into a perfect crystal gives rise to a free energy minimum, as illustrated in Figure 2.6a. Further increases in the point defect concentration, however, will raise the free energy of the system. Point defects in crystals are discussed in Sections 3.5.1 and 6.4.1. 

Thermal vacancies are formed readily because of a low formation enthalpy. 

The thermodynamic description relates the density of vacancies [V ] and of interstitials [Ag°] to the formation enthalpy ( Ag number of Ag atoms per volume)... 

The formation enthalpy of a vacancy is of the order of 50-150 kJ mol R is the gas constant and T the Kelvin temperature. Vacancies and interstitials can move through the lattice. The activation energy for this transport is approximately 20-30% smaller than the formation enthalpy of vacancies (Kanani ). 

The quotient of electrical conductivity a and thermal conductivity X is inversely proportional to the temperature. The ionic conductivity of solids depends on the lattice type and the type of the defects. The conductivity increases with temperature. This property is used to distinguish the ion conductor from the electron conductor. For vacancies and interstitials in the ion lattice, conductivity depends on the formation enthalpy for vacancy-interstitial pairs, Afo v. 

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