Substitutional atom solution

When a pure metal A is alloyed with a small amount of element B, the result is ideally a homogeneous random mixture of the two atomic species A and B, which is known as a solid solution of in 4. The solute B atoms may take up either interstitial or substitutional positions with respect to the solvent atoms A, as illustrated in Figs. 20.37a and b, respectively. Interstitial solid solutions are only formed with solute atoms that are much smaller than the solvent atoms, as is obvious from Fig. 20.37a for the purpose of this section only three interstitial solid solutions are of importance, i.e. Fc-C, Fe-N and Fe-H. On the other hand, the solid solutions formed between two metals, as for example in Cu-Ag and Cu-Ni alloys, are always substitutional (Fig. 20.376). Occasionally, substitutional solid solutions are formed in which the... 

There are a number of differences between interstitial and substitutional solid solutions, one of the most important of which is the mechanism by which diffusion occurs. In substitutional solid solutions diffusion occurs by the vacancy mechanism already discussed. Since the vacancy concentration and the frequency of vacancy jumps are very low at ambient temperatures, diffusion in substitutional solid solutions is usually negligible at room temperature and only becomes appreciable at temperatures above about 0.5T where is the melting point of the solvent metal (K). In interstitial solid solutions, however, diffusion of the solute atoms occurs by jumps between adjacent interstitial positions. This is a much lower energy process which does not involve vacancies and it therefore occurs at much lower temperatures. Thus hydrogen is mobile in steel at room temperature, while carbon diffuses quite rapidly in steel at temperatures above about 370 K. 

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. 

In interstitial compounds, however, the nonmetal is conveniently regarded as neutral atoms inserted into the interstices of the expanded lattice of the elemental metal. Obviously, this is an oversimplification, as the electrons of the nonmetal atoms must interact with the modified valence and conduction bands of the metal host, but this crude picture is adequate for our purposes. On this basis, Hagg made the empirical observation that insertion is possible when the atomic radius of the nonmetal is not greater than 0.59 times the atomic radius of the host metal—there is no simple geometrical justification for this, however, as the metal lattice is concomitantly expanded by an unknown amount. These interstitial compounds are sometimes called Hagg compounds.9,10 They are, in effect, interstitial solid solutions of the nonmetal in the metal (as distinct from substitutional solid solutions, in which actual lattice atoms are replaced, as in the case of gold-copper and other alloys Section 4.3). 

This type of constraint will be absent in amorphous materials because any of the Nc components can be added (or removed) anywhere in the material without exchanging with any other components. The dNi will also be independent for interstitial solutes in crystalline materials that lie in the interstices between larger substitutional atoms, as, for example, carbon atoms in body-centered cubic (b.c.c.) Fe, as illustrated in Fig. 8.8. In such a system, carbon atoms can be added or removed independently in a dilute solution. 

Solution. Substitutional atoms of type 1 may diffuse more rapidly than atoms of type 2 if they diffuse independently by the interstitialcy mechanism in Fig. 8.4. To sustain the unequal fluxes, interstitial-atom defects can be created at climbing dislocations acting... 

The alloys just considered are substitutional solid solutions. Interstitial solid solutions are alloys with small atoms, for example, H, C, N, and O, in the interstitial sites, usually O and T sites. Some alloys have random distribution (disordered) if the melt is quenched but become ordered if heated and annealed or if cooled slowly. An example is the 1 1 alloy CuAu. The disordered structure is ccp, and the ordered structure is also ccp, except alternate layers parallel to a cell face contain Cu or Au. 

As the amount of Fe is increased, the (111) peak shifts to smaller d-spacings, reflecting a contraction of the lattice. The (111) peak positions in Fig. 11.5 show a continuous shift from pure Pt to pure Fe. The Pt-Fe XRD patterns are consistent with a single-phase, substitutional solid solution (disordered alloy) over the entire compositional range. In contrast, Fig. 11.6 clearly displays diffraction from inter-metallic compounds of lower symmetry. Post-deposition annealing has resulted in an ordering of the Pt and Fe atoms, the effect of which is the crystallization of an ordered metal alloy of lower symmetry than 100% Pt. In essence, the applied vacuum deposition method is ideally suited for the preparation of multi-component,... 

In the framework of the A-potential model, combined with the frozen-cage approximation, the problem is solved simply. Namely, HF wavefunctions and energies of the encaged atom, solutions of the extended to encaged atoms Hartree-Fock equations (2), must be substituted into corresponding formulae for the photoionization of an nl subshell of the free atom, Equations (18)-(26), thereby turning them into formulae for the encaged atom (to be marked with superscript " A") rrni(o>) —> a A(co), Pni(fi>) Yni o>) - and 8ni((o) - 8 A(co). This accounts... 

In Chapter 8, the simple case of totally immiscible solids, exhibiting a minimum melting eutectic, was discussed. There are a variety of other behaviors that can be demonstrated in solid-liquid equilibria. For example, a solid solution may be formed. In a solid solution, the arrangement of atoms shows some degree of randomness on the molecular level. This occurs in a substitutional solid solution, where the components are very similar and can substitute for each other in the solid lattice. Although the lattice is regular, which atoms in the lattice are substituted is random. (If the substitution were periodic, the system would be a compound.) Copper and nickel illustrate this behavior and form a substitutional solid solution at all concentrations. Another type of solid solution is an interstitial... 

The Kirkendall effect arises from the different values of the self-diffusion coefficients of the components of a substitutional solid solution, determined by Matano s method. Matano s interface is defined by the condition that as much of the diffusing atoms have migrated away from the one side as have entered the other. If DA = DB, its position coincides with the initial interface between phases A and B. If I)A f DB, it displaces into the side of a faster diffusant (see Fig. 1.22c). Note that KirkendalFs discovery only relates to disordered phases. It was indeed a discovery since at that time most reseachers considered the relation l)A = DB to hold for any solid solution of substitutional type. KirkendalFs experiments showed that in fact this is not always the case. 

Peculiarity of the fullerene molecule formation also reveals itself in a fullerite crystal structure. Cubic crystal lattices of fullerites and hydrofullerites behave like those of different metals and alloys. Fullerene molecules are distributed in the lattice sites while atoms of elements are distributed in the octa- and tetrahedral interstitial sites forming the interstitial solid solutions. Fullerene molecules substitute each other in the sites of lattice and form the substitution solid solutions. Forming exo- and endocompounds, fullerene molecules that are in the lattice sites can change considerably the properties of crystal, whereas its crystalline structure remain unchanged. 

For the present applications it is relevant to ask how accurate is the intersection of the Ewald sphere with the reciprocal lattice point. Each of these points represents a (series of parallel) lattice planes defined by atom positions in the unit cell. The thermal motion of the atoms expands the ideal plane into a slab. Elements of disorder such as microstrain, chemical impurities in lattice positions (substitution, solid solutions), and interstitial atoms producing "chemical microstrain" also expand the lattice planes effectively into lattice slabs of locally varying thickness. 

The tuning of electron counts is one of the strategies of the solid state chemists. Elements can be substituted, atoms intercalated, nonstoichiometries enhanced. Oxidation and reduction, in solid state chemistry as in ordinary molecular solution chemistry, are about as characteristic (but experimentally not always trivial) chemical activities as one can conceive. The conclusions we reached for the Pt-Pt chain were simple, easily anticipated. Other cases are guaranteed to be more complicated. The COOP curves allow one, at a glance, to reach conclusions about the local effects on bond length (will bonds be weaker, stronger) upon oxidation or reduction. 

With alloys and substitutional solid solutions, it is possible that a mixture of atoms (of similar size, valence, etc.) may reside at a general or special position and all its equivalent coordinates. The fraction of atoms of one type residing at that position is given by the site occupancy, or site occupation factor. The sum of the site occupation factors for that site must equal unity. The distribution of two or more types of atoms over a single site is completely random. Where two atoms are distributed over all the equivalent coordinates of different sites with similar local coordination environments (but not identical site symmetry), electronic, or other, effects can result in partial site preferences. That is, there can be a nonstatistical distribution over the two sites. 

NDIS techniques have been used for many years in the study of aqueous electrolyte solutions. Difrfaction measurements for two liquids which differ only in the isotopic composition of one of the components reduce the total number of correlations observed in the data from N(N+1)I2 in the pure liquid to N (corresponding to correlations to the substituted atom) in the first order diffnence function. By careful analysis of the first order difference function details of the geometric arrangement of molecules around the substituted atom can be established. The supplementary technique of QENS allows a more detailed knowledge of the exchange times of the water in the hydration shells of these ions to be established. 

The structure of alloys— When two or more metals are melted together in suitable proportions a homogeneous solution often results. On cooling, the homogeneous solid is termed a solid solution, since as in a liquid solution, the atoms are distributed in a random fashion. If the structure of the solid solution is identical with that of one of the components (the solvent) the solution is termed a primary or a solid solution. Primary solid solutions are of two types interstitial solid solutions, in which the atoms of the dissolved substance are situated in the holes between the atoms of the solvent and substitution solid solutions in which the solute atoms have taken the place of solvent atoms in the lattice of the latter. 

In a substitution solid solution two possibilities arise the distribution of the atoms may be entirely random throughout the lattice, or at particular ratios of the constituent atoms an ordered arrangement may exist in the crystal. Such a solid solution is termed a superlattice. 

Impurity atoms ( 3.7). The presence of substitutional atoms can lead to modified chemical centers on the surface. The replacement of Mg ions by Ni ions, as in MgO-NiO solid solutions, introduces transition metal atoms in a MgO matrix and can alter the local properties of the material. Even more effective is the replacement of a divalent Mg cation by a monovalent dopant like Li. In order to compensate the charge, some O anions at the surface become O, a paramagnetic species. 

This method of isomorphous replacement (Figure 8.27), together with anomalous dispersion data collection (see Chapter 14) is, to date, the principal method that has been successful for phase determination of macromolecules.Unfortunately, it is common to find that, although a heavy-atom solution has been soaked into a protein crystal, no regular (ordered) substitution has occurred, and solutions of other heavy-atom compounds must be tried. 

In a substitutional solid solution AA there is random arrangement of A and A atoms in equivalent positions in the crystal structure. If on suitable heat treatment... 

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. 

Still another type of structure worth noting is that of ordered solid solutions. As described above, a typical substitutional solid solution has solute atoms distributed more or less at random on the lattice points of the solvent.f On the other hand, there are solutions in which this is true only at elevated temperatures when cooled to lower temperatures, the solute atoms take up an orderly, periodic... 

---