Parent lattice

Always specific crystallographic relationship between martensite and parent lattice. 

Fig. 8.8. Martensites are always coherent with the parent lattice. They grow os thin lenses on preferred planes and in preferred directions in order to cause the least distortion of the lattice. The crystallographic relationships shown here ore for pure iron.

The T- and perovskite borides resemble each other (CU3AU parent lattice) (see above). The boron environment in the latter is Oj, whereas most interstitial borides... 

In the two-stage process, the product is formed in the first stage in a conformation imposed by the parent lattice. As we have argued above, the environmental change involved in the subsequent phase transformation, solid 1 — solid 2, will be associated with some conformational change that indeed may be major. 

Fig. 20. The relationship between the bond lattice and the parent lattice (a) unexcited, (b) with two excitations and local collapse (from Ref. 7>)...

In Eq. (6.1) 1 is the unit operator, there is one state /> associated with each lattice site, and l and l A A = 1, 2, 3, 4) label a molecule and its nearest neighbors in the tetrahedral lattice. Weare and Alben show also that the theorem remains valid when small distortions away from tetrahedrality exist, hence it can be used to describe a random amorphous solid derived from a tetrahedral parent lattice. Basically, the density of states of the amorphous solid is a somewhat washed out version of that of the parent lattice. The general shape of the frequency spectrum is not much altered by the inclusion of a non zero bond-bending force constant provided the ratio of it to the bond stretching force constant is small relative to unity. 

Exchange interactions in heterodinuclear transition metal complexes have attracted the attention of many researchers in the last few years. Nickel(II)-copper(II) dimers are, in a sense, the simplest systems to be investigated and several complexes containing paramagnetic nickel(II) and copper(II) ions have been reported, as pure complexes2985-2987 or as impurities in a parent lattice.2959,2987"2991 Magnetic susceptibility or EPR spectroscopy has been used to... 

The classical theory of Hume-Rothery states that a difference in atomic diameters of solute and solvent atoms of more than 15% produces restricted solid solubility. The closest distance of approach of the atoms in the crystals of the element is taken as a measure of the atomic size. Substitution of a larger atom into a lattice requires a high amount of energy due to the concomitant disorganization of the parent lattice. However, the size factor becomes less important [221] when the difference in size is 8% or less. It is desirable (though not essential) that the size factor and the crystal structure of the elements producing a solid solution in all proportions be favourable. It is, however, apparent that if elements forming alloys did not possess the same crystal structure, a continuous series of solid solutions would be impossible. 

Some of the defect equilibria which we have deduced by this type of analysis were not surprising—a parent lattice may dissociate into interstitials and vacancies in conformity with appropriate equilibrium constants defects may associate, again consistent with an equilibrium constant or the lattice may dissolve excess atoms in simple solubility. (When we speak of a solvent or parent lattice we mean the crystallographic lattice, as it would be determined by x-ray analysis, stoichiometri-cally perfect, and free of vacancies or interstitials. We call the process of vacancy and interstitial formation lattice dissociation. Simple solution adds interstitials or fills voids in the parent lattice). 

For purposes of discussion the dissociation of A2B was chosen as the principal net reaction. In practice dissociation will always occur, but it may be masked by other reactions. At higher concentrations of Aa, the simple random solution of Aa in A2B might be the principal net reaction, the vacancy concentration having become insignificant. On the other hand, at high Aa concentrations the Aa might cluster to extend the parent lattice while creating a B-vacancy. 

Occasionally, however, the ions are deviants and associate preferentially with the nonelectrolyte solute, shunning the water (hydrophobic effects). In the rare instances where these deviants appear, there is a rapid departure of the nonelectrolyte from the parent lattice and the solubility of the former is enhanced rather than deaeased. The phenomenon is called salting in. 

Reactivity in the solid-state is always connected with specific motions which allow the necessary contact between the reacting groups. In most cases solid-state reactions proceed by diffusion of reactions to centers of reactivity or by nucleation of the product phase at certain centers of disorder. This leads to the total destruction of the parent lattice. If the product is able to crystallize it is highly probable that nucleation of the crystalline product phase at the surface of the parent lattice will lead to oriented growth under the influence of surface tension. In such topotactic reactions certain crystallographic directions of parent and daughter phases will coincide. Typical examples for this behaviour are the solid-state polymerizations of oxacyclic compounds such as trioxane, tetroxane or 3-propiolactone... 

Fig. 11.9 STM image following co-dose of SO and onto Cu(l 10)-p(2x l)-0. As indicated in the imet, the Cu atoms comprising the (1 x 1) parent lattice are seen to sit in-between bright features in the p(2xl) structure, suggesting that the species imaged by the STM in the p(2xl)-0 overlayer are the added Cu atoms (white arrows). These two images indicate that the CuSO moieties occupy fourfold hollow sites. A structural model accompanying the boxed area is shown. Reprinted with permission from [18]. Copyright 2003 Elsevier...

The nuclei form both at the surface and in the interior of the cry tal, but the theory developed by Mott (49) assumes that the defects are interstitial Ba - ions and that the nuclei grow at the surface of the grains only. As in the formation of the latent image in sensitized Ag halide grains, the assumption of pure Frenkel defects could only lead to the formulation of surface nucleation, but recent developments have led Mitchell to consider the role of Schottky defects (F-centres), which may forn internal aggregates ultimately bi caking away from the parent lattice as minute nuclei of the new metal phase. It is possible that a similar state of affairs exists in azides (36) unfortunately, nothing is known of the nature of... 

Substitutional solid solutions can have any composition within the range of miscibility of the metals concerned, and there is random arrangement of the atoms over the sites of the structure of the solvent metal. At particular ratios of the numbers of atoms superstructures may be formed, and an alloy with either of the two extreme structures, the ordered and disordered, but with the same composition in each case, can possess markedly different physical properties. Composition therefore does not completely specify such an alloy. Interstitial solid solutions also have compositions variable within certain ranges. The upper limit to the number of interstitial atoms is set by the number of holes of suitable size, but this limit is not necessarily reached, as we shall see later. When a symmetrical arrangement is possible for a particular ratio of interstitial to parent lattice atoms this is adopted. In intermediate cases the arrangement of the interstitial atoms is random. 

Types of Solid Solution. There are two types of metallic solid solution—substitutional solid solution and interstitial solid solution—and, so far, research has been mainly confined to the former type. A substitutional solid solution is characterised by the fact that it retains the lattice of the solvent metal and that atoms of the solute metal are able, usually to a limited extent, to replace those of the solvent without unduly distorting the parent lattice of the solvent. This naturally leads to the idea that one, at least, of the factors influencing solid solubility of this type is the relative sizes of the atoms of the two metals under consideration, although, as we shall see later, size-factor alone is incapable of explaining solid solubility variations. It might be mentioned here that it is usual to find that in substitutional solid solutions there is a random arrangement of atoms of the solute metal in the lattice of the solvent even at... 

The introduction of a dopant may result in a change in the oxidation state of metal sites in the parent lattice a weU-cited example is the doping of NiO with Li20 in the presence of air/02. When an Ni ion is replaced by Li, electrical neutrality is retained by the oxidation of another Ni " " to Ni + (Figure 27.1). 

Preservation of regular site ratio the ratio between the numbers of regular cation and anion sites must remain constant and equal to the ratio of the parent lattice.Thus if a normal lattice site of one constituent is created or destroyed, the corresponding number of normal sites of the other constituent must be simultaneously created or destroyed so as to preserve the site ratio of the compound. This requirement recognizes that one cannot create one type of lattice site without the other and indefinitely extend the crystal. For instance, for an MO oxide, if a number of cation lattice sites are created or destroyed, then an equal number of anion lattice sites have to be created or destroyed. Conversely, for an M2O oxide, the ratio must be maintained at 2 1, etc. 

The ceramic electrolyte is based on zirconia (Zr02) or ceria (Ce02), each of which is an electronic insulator but is conductive towards oxide ions (0 ) at high temperatures. This conductivity is achieved by doping the chosen oxide with ions of lower valency. For instance, when zirconia is doped with yttrium ions (Y ), oxide ion vacancies are formed in the parent lattice to compensate for the charge difference, i.e.,... 

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