Solid solutions, defect substitutional

Fig. 11. The Si3N4-Si02-Al203-AlN-Be0-Be3N2 system. A wide solid solution range was observed in this system. The single-phase /8—Si 3N4 solid solution region is restricted to the metal-to-nonmetal ratio of 3 4 plane. This indicates that the solid-solution is substitutional and no lattice defects exist in the structure [23].

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 ... 

The model of oxidation will depend on the nature of the main defects in each oxides and their relative layout. We choose two oxides with anion vacancies. BO layer being above the AO one, this implies that B ions are a little soluble in AO to be able to cross through this layer. We assume a solid solution of substitution and we suppose that B diffusion coefficient through AO is very high, which means that B concentration in AO has the same value at each point. 

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. 

It is important that the copper is in the monovalent state and incorporated into the silver hahde crystals as an impurity. Because the Cu+ has the same valence as the Ag+, some Cu+ will replace Ag+ in the AgX crystal, to form a dilute solid solution Cu Agi- X (Fig. 2.6d). The defects in this material are substitutional CuAg point defects and cation Frenkel defects. These crystallites are precipitated in the complete absence of light, after which a finished glass blank will look clear because the silver hahde grains are so small that they do not scatter light. 

Many alloys are substitutional solid solutions, well-studied examples being copper-gold and copper-nickel. In both of these examples, the alloy has the same crystal structure as both parent phases, and the metal atoms simply substitute at random over the available metal atom sites (Fig. 4.4a). The species considered to be the defect is clearly dependent upon which atoms are in the minority. 

The Mossbauer effect, although not a substitute for other analytical methods such as x-ray diffraction, can be used to obtain several kinds of structural information about solids. In favorable cases, it is possible to obtain rather detailed information about the electronic configuration of atoms and the local symmetry of their sites by measuring the isomer shift and quadrupole splitting. If more than one valence state of a given atom is present, a semiquantitative determination of the amount of each kind is possible. In solid solutions, the amount of local or long range order can be estimated, and in certain defect structures the relation between the active atoms and the defects can be studied. 

The second type of impurity, substitution of a lattice atom with an impurity atom, allows us to enter the world of alloys and intermetallics. Let us diverge slightly for a moment to discuss how control of substitutional impurities can lead to some useful materials, and then we will conclude our description of point defects. An alloy, by definition, is a metallic solid or liquid formed from an intimate combination of two or more elements. By intimate combination, we mean either a liquid or solid solution. In the instance where the solid is crystalline, some of the impurity atoms, usually defined as the minority constituent, occupy sites in the lattice that would normally be occupied by the majority constituent. Alloys need not be crystalline, however. If a liquid alloy is quenched rapidly enough, an amorphous metal can result. The solid material is still an alloy, since the elements are in intimate combination, but there is no crystalline order and hence no substitutional impurities. To aid in our description of substitutional impurities, we will limit the current description to crystalline alloys, but keep in mind that amorphous alloys exist as well. 

One of the exceptions was the discovery of high ionic conductivity in appropriately doped FaGa03.128 129 As in the other oxide ion conductors, its ionic conductivity depends on both the dopant level as well as on the nature of the dopant. A major difference to ceria and zirconia is the presence of two cations that can be substituted the detailed defect chemistry of such solid solutions is far from being fully understood. Co-doping of Sr on A sites and Mg on B-sites leads to an ionic conductivity of ca. 0.12—0.17 S cm 1 at 800°C,130-133 which is similar to doped ceria but considerably exceeds the value of YSZ (ca. 0.03 S cm 1 at 800°C80 81). The activation energy also varies with composition and can be as low as ca. 0.6 eV.130 131 At about 600-700°C, the... 

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 ... 

The existence of coloured specimens of normally colourless minerals, such as sodium chloride and alumina, has been known for centuries. Some sodium chloride crystals appear yellow due to the selective absorption of blue light, and sapphires/rubies are coloured forms of a-alumi-na. The coloured forms of these minerals are due to defects. In sodium chloride, excess sodium can lead to additional mobile electrons which can be trapped on vacant anion sites, giving the solid a yellow hue. In the gemstones, the colour is generated by substitution of a few of the aluminium cations by other trivalent cations, such as chromium, in a solid solution. 

What is found by experiment is that, as a general rule, at substitutional concentrations close to the maximum in the conductivity isotherms, there is a minimum in the activation energy. In an early (but very comprehensive) study of ceria solid solutions with the trivalent rare earths, Faber etal. [IS] showed that the depth of the minimum, and the concentration at which it occurs, depends upon the identity of the rare earth cation (Figure 9.1). The minima have been ascribed [19] to competitive defect interactions. Initially, the effect is a weakening ofthe association energy of the dimers caused by an electrostatic interaction between the cluster and the unassociated substitutionals having an opposite effective charge in the lattice note, however, that... 

Apart from the point defects, there are impurity defects in ionic crystals due to some impurities in raw materials. The impact of impurity segregation on ionic conductivity of the solid electrolytes will be considered in detail in section 1.4 of this chapter. The vacancies, developed in the solid solutions during the substitution of the main ion (M in the solid solution M(Mi)02 x) by the ion substituent (Mj) of the different valence, have special meaning for solid electrolytes among impurity defects. In this case, the vacancies must appear from one of the solid-state sublattices... 

The dimensionally stable anode in this system is composed of an electrically conductive substrate of titanium, having a coating of a defect solid solution containing mixed crystals of precious metal oxides. These substitutional solid solutions are both electrically conductive, electrocatalytic, and dimensionally stable. Within the aforementioned solid-solution host structures the valve metals include titanium, tantalum, niobium, and... 

In a substitutional solid solution, the solute ion directly substitutes for the host ion nearest to it in electronegativity, which implies, as noted in Chap. 6, that cations will substitute for cations and anions for anions. Needless to say, the rules for defect incorporation reactions (see Chap. 6) have to be satisfied at all times. For instance, the incorporation reaction of NiO in MgO would be written as... 

A substitutional solid solution is a mixture of two similar elements in which one atom substitutes on the sites of the other atoms in the structure. In the copper-nickel system, both parent phases adopt the same crystal stmcture. When both atom types are present, they occupy random positions in the crystal to form a substitutional solid solution (Figure 3.14a). Near to pure copper it is possible to say that the nickel atoms form substitutional impurity defects, and near to pure nickel it is possible to say that copper forms substitutional impurity defects. Substitutional alloys generally have lower thermal... 

The ruby laser, invented in 1960, was the first device to put the ideas just described into practice. Rubies are crystals of alumina (aluminium oxide, corundum, AI2O3), containing about 0.5 % chromium ions, Cr +, in place of aluminium ions, Al " ". Ruby is a dilute solid solution, and the Cr " " ions form substitutional defects. The laser action involves only the Cr " " ions and is due to the transition of electrons from the ground state to higher energy levels among the 3d orbitals. 

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. 

Doping Zr02 with Ca is a special example of a Zr02 solid solution. We can incorporate -15% CaO in the structure to form Ca-stabilized cubic zirconia (CSZ). (CZ is the general abbreviation for cubic zirconia.) The special feature here is that the cubic (fluorite structure) phase is not stable at room temperature unless the Zr02 is heavily doped. However, we write the point defect equations as if it were always stable. The Ca " cation substitutes for the Zr" cation as shown in Figure 11.5. Since the charges are different, we must compensate with other point defects. 

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