Solid solutions, defect interstitial

Heterovalent replacement in the cation sublattice leads to an increase in the number of anion defects, for example vacancies <-> M " " + Vp) in Ri xMxF3 x solid solutions or interstitial ions <-> R + Fj) in Mi xRxF2+x solids solutions. Of course, this replacement greatly increases the conductivity of doped phases and will be discussed in detail hereinafter. 

Extrinsic Defects Extrinsic defects occur when an impurity atom or ion is incorporated into the lattice either by substitution onto the normal lattice site or by insertion into interstitial positions. Where the impurity is aliovalent with the host sublattice, a compensating charge must be found within the lattice to pre-serve elec-troneutality. For example, inclusion of Ca in the NaCl crystal lattice results in the creation of an equal number of cation vacancies. These defects therefore alter the composition of the solid. In many systems the concentration of the dopant ion can vary enormously and can be used to tailor specific properties. These systems are termed solid solutions and are discussed in more detail in Section 25.1.2. 

The doped semiconductor materials can often be considered as well-characterized, diluted solid solutions. Here, the solutes are referred to as point defects, for instance, oxygen vacancies in TiC - phase, denoted as Vq, or boron atoms in silicon, substituting Si at Si sites, Bj etc. See also -> defects in solids, -+ Kroger-Vink notation of defects. The atoms present at interstitial positions are also point defects. Under stable (or metastable) thermodynamic equilibrium in a diluted state, - chemical potentials of point defects can be defined as follows ... 

In order to decide whether the nonstoichiometric phases contain interstitial anions, or vacant cation sites, we compared the pycnometric density with the calculated density for each type of defect. The experimental values agree with the last type of defects, and these solid solutions are represented using Rees s notation by... 

The defective structure in nanocrystalline ceria based catalysts proved to have strong effect on the OSC. Mamontov et al. (2000) reported the neutron diffraction studies of the atomic structures of nanocrystalline powder of ceria and ceria-zirconia solid solution. They found that the concentration of vacancy-interstitial oxygen defects has a direct correlation with the OSC. This effect is stronger than the correlation of surface area with OSC. Zirconia reduces ceria and preserves oxygen defects to retard the degradation of ceria-zirconia in OSC. Yan et al. observed the strong correlation between OSC and the lattice strain in nanosized ceria-zirconia, which could be measured via XRD (Si et al., 2004 Figure 11). 

Empirical calculations carried out for cations show that vacancy compensation is clearly the preferred route, at least for large dopant cations (radius >0.8A). Formation of interstitials is also ruled out by measurements of true density and comparison with calculated values . For the smaller cations (i.e. Al ), some compensation via dopant interstitial may occur. The reactions described in Eq. 2.18 and 2.21 (for a divalent cation) therefore summarise the main route to defect formation in solid solutions of the type Ce. jMj02,o.5x and Ce, xMx02.x respectively. 

Point (microscopic) defects in contrast from the macroscopic are compatible with the atomic distances between the neighboring atoms. The initial cause of appearance of the point defects in the first place is the local energy fluctuations, owing to the temperature fluctuations. Point defects can be divided into Frenkel defects and Schottky defects, and these often occur in ionic crystals. The former are due to misplacement of ions and vacancies. Charges are balanced in the whole crystal despite the presence of interstitial or extra ions and vacancies. If an atom leaves its site in the lattice (thereby creating a vacancy) and then moves to the surface of the crystal, it becomes a Schottky defect. On the other hand, an atom that vacates its position in the lattice and transfers to an interstitial position in the crystal is known as a Frenkel defect. The formation of a Frenkel defect therefore produces two defects within the lattice—a vacancy and the interstitial defect—while the formation of a Schottky defect leaves only one defect within the lattice, that is, a vacancy. Aside from the formation of Schottky and Frenkel defects, there is a third mechanism by which an intrinsic point defect may be formed, that is, the movement of a surface atom into an interstitial site. Considering the electroneutrality condition for the stoichiometric solid solution, the ratio of mole parts of the anion and cation vacancies is simply defined by the valence of atoms (ions). Therefore, for solid solution M X, the ratio of the anion vacancies is equal to mJn. 

We consider solid solutions here because we can think of them as being formed by distributing a large number of point defects in a host crystal. As always, we must balance charge and be sure that the size of the impurity (guest) ion is appropriate to fit into the available site. If the impurity ions are incorporated in regular crystal sites the resulting phase is a substitutional solid solution. In an interstitial solid solution the impurity atoms occupy interstices in the crystal structure. The rules for substitutional solid solutions (the Hume-Rothery rules) can be summarized as follows. Note that the last two requirements are really very closely tied to the first two. 

For instance, if MgO is used to dope AI2O3, because the ionic radii of Mg " and Al with coordination number of six are very close, the Mg ions can enter the lattice of AI2O3 to form solid solution as substitutional defects. AI2O3 has the corundum structure, in which one-third of the octahedral sites formed by the close-packed O ions are vacant, so that it is also highly possible for the Mg ions to sit on the interstitial sites. The defects with lower energy are more favorable. In AI2O3, the cation sites and anion sites have a number ratio of 2 3. If substitutional defects are formed, every two Mg atoms on cation sites will replace two A1 sites and two O sites are involved. In this case, the third O site should be a vacancy for site conservation. Therefore, on the basis of mass and site balance, the defect reaction is given by ... 

In solid solutions or alloys the atoms on the lattice sites are replaced by the atoms of the dissolved species, the solute. Apart from these substitutional solutions, interstitial solutions can also occur if the atoms or ions of the solute are small and can be accommodated in the interstices of the host lattice. The solubilities vary. The phase diagrams of spinel, lithium aluminum silicate (LAS), Ta/C, and Ti/N show to what extent dissolution is possible. Apart from having the dopants in the lattice, these alloys often have other defects that are the result of a difference in charge between the ions being replaced in the lattice and those replacing them. 

Undoubtedly the rare earth metals, with the continuous change of size within the series, offer a highly promising field of study for these new, partly interstitial solid solutions. Examples of the variety of defect structures that can be obtained are the Y(Cu) and the Gd(Cu, Fe) systems. In the former, splat quenching (Giessen et al., 1971) yielded a purely interstitial solid solution in the latter, (Ray, et al., 1972) the solutes were in the form of bi-substitutionals i.e. associated solute pair at one lattice site. 

The electrical resistivity is the summation of two contributions the contribution of the lattice or the thermal resistivity, i.e., the thermal scattering of conduction electrons due to atomic vibrations of the material crystal lattice (i.e., phonons), and the residual resistivity, which comes from the scattering of electrons by crystal lattice defects (e.g., vacancies, dislocations, and voids), solid solutes, and chemical impurities (i.e., interstitials). Therefore, the overall resistivity can be described by the Matthiessen s equation as follows ... 

The majority of Ni atoms were neutral and formed interstitial solid solutions. The electrically-active Ni atoms were located on Si lattice sites and amounted to 0.1% of the total Ni content. The total concentration of Ni was independent of the nature and concentration of defects. The Ni atoms diffused via a mainly interstitial mechanism. M.K.Bakhadyrkhanov, S.Zainabidinov, A.Khamidov Fizikai Tekhnika Poluprovodnikov, 1980,14[2], 412-3 (abstract only given)... 

Solid state ionic conductivity is observed when ions and hence defects are free to move through the soUd. In order to do this, ions must have sites available for occupation, i.e., vacancies and these must be cormected by suitable conduction pathways. Site vacancies may be present due to intrinsic defects such as Schottky or Frenkel defects, or may be extrinsic through solid solution formation (see Section VII). The conduction pathways may be interstitial, i.e., solely involve ions in interstitial sites, or may involve an interstitialcy mechanism where framework ions are also involved. In both cases ions of one sublattice will approach... 

Another type of point defect is the incorporation of an impurity atom. Impurity atoms may replace host atoms in the regular crystal structure, in which case they are called substitutional defects, or they may occupy an interstitial site as interstitial impurities. Impurities are often purposely introduced in a lattice to strengthen it (solid solution hardening) or to otherwise alter its properties, e.g., doping a semiconductor to tailor the number and sign of charge carriers. However, as seen later, it is virtually impossible to completely eliminate unwanted impurity atoms. 

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