Defect enthalpy

Because a defect entropy (Ai j), a defect enthalpy and a defect vol-... 

If we assume, at first approximation, that AHs does not change with T, it is obvious that the increase in defect concentration with T is simply exponential. Table 4.4, for instance, hsts Schottky defect concentrations calculated in this way at various T by Lasaga (1981c) for NaCl and MgO, assuming defect enthalpies of 2.20 and 4.34 eV, respectively. 

It is apparent, from the above short survey, that kinetic studies have been restricted to the decomposition of a relatively few coordination compounds and some are largely qualitative or semi-quantitative in character. Estimations of thermal stabilities, or sometimes the relative stabilities within sequences of related salts, are often made for consideration within a wider context of the structures and/or properties of coordination compounds. However, it cannot be expected that the uncritical acceptance of such parameters as the decomposition temperature, the activation energy, and/or the reaction enthalpy will necessarily give information of fundamental significance. There is always uncertainty in the reliability of kinetic information obtained from non-isothermal measurements. Concepts derived from studies of homogeneous reactions of coordination compounds have often been transferred, sometimes without examination of possible implications, to the interpretation of heterogeneous behaviour. Important characteristic features of heterogeneous rate processes, such as the influence of defects and other types of imperfection, have not been accorded sufficient attention. 

Equation 3.6.10. given above shows that intrinsic defect concentrations will increase with increasing temperature and that they will be low for high Enthalpy of defect formation. This arises because the entropy effect is a positive exponential while the enthalpy effect is a negative exponential. Consider the following examples of various types of compounds and the natural defects which may occur (depending upon how the compounds were originally formed) ... 

The following gives the standard Enthalpy and Entropy of these defect reactions, according to Kroeger (1965) ... 

The number of defects is maximal in the amorphous and liquid states. The phase diagram in Figure 5 shows the volume-temperature relationships of the liquid, the crystalline form, and the glass (vitreous state or amorphous form) [14], The energy-temperature and enthalpy-temperature relationships are qualitatively similar. 

Similar relationships hold if the Gibbs energy of formation per defect, Agy and the enthalpy of formation per defect, Afij, is used and R is replaced by k, the Boltzmann constant ... 

The Gibbs energy, AGs, is often replaced by the enthalpy of Schottky defect formation, AHs, as in previous sections, to give... 

Some values for the enthalpy of formation of Schottky defects in alkali halides of formula MX that adopt the sodium chloride structure are given in Table 2.1. The experimental determination of these values (obtained mostly from diffusion or ionic conductivity data (Chapters 5 and 6) is not easy, and there is a large scatter of values in the literature. The most reliable data are for the easily purified alkali halides. Currently, values for defect formation energies are more often obtained from calculations (Section 2.10). 

TABLE 2.1 Formation Enthalpy of Schottky Defects in Some Alkali Halide Compounds of Formula MX"... 

TABLE 2.2 Formation Enthalpy of Frenkel Defects in Some Compounds of Formula MX and MX2... 

Some experimental values for the formation enthalpy of Frenkel defects are given in Table 2.2. As with Schottky defects, it is not easy to determine these values experimentally and there is a large scatter in the values found in the literature. (Calculated values of the defect formation energies for AgCl and AgBr, which differ a little from those in Table 2.2, can be found in Fig. 2.5.)... 

If we apply this formula to defects in a crystal, and again assume that the defects are oppositely charged, so that they attract each other, the energy term will be roughly equivalent to the enthalpy of formation of a defect pair, AHp. The closest separation of the defects will normally be equivalent to the spacing between two adjacent lattice sites. 

The enthalpy of formation of Frenkel defects (kJ mol-1) is AgCl, 140, AgBr, 109, Agl, 58. The compound with the greatest number of Ag+ interstitials is ... 

Pure potassium bromide, KBr, which adopts the sodium chloride structure, has the fraction of empty cation sites due to Schottky defects, ncv/Nc, equal to 9.159xl0-21 at 20°C. (a) Estimate the enthalpy of formation of a Schottky defect, Ahs. (b) Calculate the number of anion vacancies per cubic meter of KBr at 730°C (just below the melting point of KBr). The unit cell of KBr is cubic with edge length a = 0.6600 nm and contains four formula units of KBr. 

The favored defect type in strontium fluoride, which adopts the fluorite structure, are Frenkel defects on the anion sublattice. The enthalpy of formation of an anion Frenkel defect is estimated to be 167.88 kJ mol-1. Calculate the number of F- interstitials and vacancies due to anion Frenkel defects per cubic meter in SrF2 at 1000°C. The unit cell is cubic, with a cell edge of 0.57996 nm and contains four formula units of SrF2. It is reasonable to assume that the number of suitable interstitial sites is half that of the number of anion sites. 

The following table gives the values of the fraction of Schottky defects, S/N, in a crystal of NaBr, with the sodium chloride structure, as a function of temperature. Estimate the formation enthalpy of the defects. 

However, the activation energy, Ea, will consist of two terms, one representing the enthalpy of migration, AHm, and the other enthalpy of defect formation AH ol. 

As defect clusters tend to disassociate at high temperatures, the aggregation enthalpy, Af/agg, would tend to zero at high temperatures. The high-temperature activation energy would then simply correspond to the migration enethalpy ... 

To obtain a solid with a high conductivity, it is clearly important that a large concentration, c, of mobile ions is present in the crystal [Eq. (6.1)]. This entails that a large number of empty sites are available, so that an ion jump is always possible. In addition, a low enthalpy of migration is required, which is to say that there is a low-energy barrier between sites and ions do not have to squeeze through bottlenecks. Hence the structure should ideally have open channels and a high population of vacancy defects. 

The enthalpy change involved, AHs, is not explicitly calculated. It is assumed that the enthalpy to form one defect, Ahs, is constant over the temperature range of interest, so that the total enthalpy change, AHs, is given by... 

Here A vac. S and A vacH are the molar entropy and enthalpy of formation of the defects. Using a pure metal like aluminium as an example, the fractional number of defects, heat capacity and enthalpy due to defect formation close to the fusion temperature are 5-10-4, 0.3 J K-1 mol-1 and 30 J mol-1 [30],... 

Heat capacities at high temperatures, T > 1000 K, are most accurately determined by drop calorimetry [23, 24], Here a sample is heated to a known temperature and is then dropped into a receiving calorimeter, which is usually operated around room temperature. The calorimeter measures the heat evolved in cooling the sample to the calorimeter temperature. The main sources of error relate to temperature measurement and the attainment of equilibrium in the furnace, to evaluation of heat losses during drop, to the measurements of the heat release in the calorimeter, and to the reproducibility of the initial and final states of the sample. This type of calorimeter is in principle unsurpassed for enthalpy increment determinations of substances with negligible intrinsic or extrinsic defect concentrations... 

---