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1
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84989503836
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The chemistry of the solid state has been put on a firm scientific footing by the publications of Wagner, Schottky[2], and Frenkel [3]. Most of the basic relationships underlying the subject are reviewed in the monographs by Schmalzried [4]. Schmalzried and Navrotsky[5], Hauffe[6], Kröger[7], and Rickert[8], and in special review articles such as that by Lidiard[9]. More recent developments are described in other publications. For example in those cited in references [10–13].
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20
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84989525323
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The analogy with water is even more complete if one considers defects in covalently bonded materials such as Si, Ge, SiC, N, C, or GaAs.
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24
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84989563849
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3 + 3HCl.
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25
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84989586250
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The structural elements notation is an exact relative notation only with regard to charge, not with regard to material.
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30
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84989525336
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(b) The defect‐defect interaction can be expressed in terms of activity coefficients. This corresponds to another free enthalpy contribution in Figure 4 that can lead to a second minimum at high defect concentrations. Under certain conditions, this minimum becomes the absolute minimum. Then a transition from a low defective state into a highly disordered (superionic) state occurs (if the totally molten state is not more favorable).
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33
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84989594706
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Strictly speaking in the case of charged species, the electrochemical potential should be used to describe the equilibrium condition, as in Figure 5. However, the average electrical potential terms cancel out in cases where the reaction equations relate to (approximately) the same position. (k = 1 in Fig. 5.)
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36
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84989598134
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See for example ref. [8].
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37
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0 is small.
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40
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2/3, where Ĉ is the equilibrium fraction of point defects whose free enthalpy of formation would be g def0.
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41
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36149008975
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In contrast to this, the surface areas of phases are determined by the limited mass. However, here too the equilibrium morphology, as specified by the Wulff conditions, is usually not estblished, see for example
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(1951)
Phys. Rev.
, vol.82
, pp. 87
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Herring, C.1
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42
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84989525505
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The electrical neutrality condition is a consequence of electrostatics for the special case of the interior of an extended homogeneous body (in general Poisson's equation applies, see Section 3.2).
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45
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Chlorine partial pressures of more than 1 bar increase the total hydrostatic pressure, whereas lower pressures can be obtained with a total pressure of 1 bar by using mixtures such as chlorine plus argon.
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47
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84989511954
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0 is negligible, and only the (small) migration energy is significant. At lower temperatures this modification is unstable and it becomes converted to the “normal” β phase.
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48
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The usual dopant levels of around 10% are well above the regime of low defect concentrations, and interactions between the defects play an important role [9].
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49
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2O).
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54
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84989511944
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An alternative possibility in principle would be Sn ions in the interstitial lattice, but this is refuted by density measurements, and is also inconsistent with the observed slopes of the isotherms. The Schottky equilibrium only becomes important at very high temperatures.
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55
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The occupation of singly charged oxygen vacancies by oxygen would also explain the slope of 1/4 at lower temperatures, but would result in a critical isotherm of a completely different shape [43].
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56
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84989583136
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For kinetic reasons the main electron sourec or sink at low temperatures is no longer the interaction with the gas phase, but is instead the transfer of electrons to or from the vacant sites, as in Equation (50). However, the gas phase still has an effect on the boundary regions, as discussed later (Section 3.2.3).
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57
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7 for the reference composition leads to an inconsistency, since a lower oxygen content would then correspond to vacancies (V 0••, V 0•, V 0×), which would be compensated by conduction electrons. This would then lead (assuming comparable mobilities) to n‐type conduction, rather than the p‐type conduction that is observed (n and p mobilities are comparable).
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69
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•⇌h 2••.
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76
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84989570669
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Columbia University, New York, personal communication.
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Nowick, A.S.1
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83
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0 is constant), and b as a consequence of Equation (21) the distance from the Fermi level gives the corresponding charge carrier concentration.
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88
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A simplified treatment is given in [70], but this does not properly take into account the spatial structure of the double layer.
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96
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In cases where blocking by boundary layers occurs, its effects can often be determined separately by impedance spectroscopy or time‐resolved direct current measurements.
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111
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Analogous electronic phenomena are treated thoroughly in publications on semiconductor junctions, see for example [87].
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114
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Segregation of ions at grain boundaries plays an important role in sintering behavior. However, the literature is inconclusive on this point, see for example ref. [89].
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122
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84989577310
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see also ref. [85]. The functional relationship can only be expressed in implicit form, as explained in these publications.
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