Substitutional solutions

Fig. 7.7. Solid-solution structures. In interstitial solutions small atoms fit into the spaces between large atoms. In substitutional solutions similarly sized atoms replace one another. If A-A, A-B and B-B bonds hove the some strength then this replacement is random. But unequal bond strengths con give clustering or ordering.

Another subsidiary field of study was the effect of high concentrations of a diffusing solute, such as interstitial carbon in iron, in slowing diffusivity (in the case of carbon in fee austenite) because of mutual repulsion of neighbouring dissolved carbon atoms. By extension, high carbon concentrations can affect the mobility of substitutional solutes (Babu and Bhadeshia 1995). These last two phenomena, quenched-in vacancies and concentration effects, show how a parepisteme can carry smaller parepistemes on its back. 

Equation 12-5 gives an onset temperature that eorresponds to a time-to-maximum rate t. (min) using a sueeessive substitution solution proeedure. An initial guess of T = 350 K for the right side of Equation 12-5 will give a solution value of on the left side of Equation 12-5 within 1% or on an absolute basis 3°C. Con-vergenee is reaehed within several sueeessive substitution iterations. 

The description of electronic distribution and molecular structure requires quantum mechanics, for which there is no substitute. Solution of the time-independent Schrodinger equation, Hip = Eip, is a prerequisite for the description of the electronic distribution within a molecule or ion. In modern computational chemistry, there are numerous approaches that lend themselves to a reasonable description of ionic liquids. An outline of these approaches is given in Scheme 4.2-1 [1] ... 

Changes in the atomic correlations are enabled by atomic jumps between neighbouring lattice sites. In metals and their substitutional solutions point defects are responsible for these diffusion processes. Ordering kinetics can therefore yield information about properties of the point defects which are involved in the ordering process. 

Fig. 20.37 (a) Interstitial solid solution, (b) random substitutional solution and (c) an ordered substitutional solid solution forming a superlattice... 

On the other hand, if Fig. 24b is compared with Fig. 23a, it will be seen that here each solute particle occupies a position that in the pure solvent would be occupied by a solvent particle. Such a solution, which can be formed by one-for-one substitution, is called a substitutional solution."1 This kind of solution will not be formed if the forces of attraction between adjacent solute and solvent particles are weak, while the forces of attraction between adjacent solvent particles are strong. For, if we look at Fig. 24b, we see that each solute particle prevents three solvent particles from coming together under their mutual attraction—that is to say, it prevents them from falling to a state of much lower potential energy. We can be certain that, when neon or argon is dissolved in water, the solute particles will not tend to take up such positions, which are suitable only for a solute particle which attracts an adjacent solvent particle with a force at least as great as the force of attraction between two adjacent solvent particles. 

First, lithium introduced into NiO (61, 62) acts as an acceptor (forms a substitutional solution), and, as shown by Schwab and Block, it may also function as a donor (form an interstitial solution). Indeed, as shown by Bielanski and Deren (64), with increasing concentration of lithium added the manner of its inclusion is changed (the substitutional solution at low concentrations is changed at high concentrations to the interstitial solution). ... 

Especially concerning substances involved in pubhc scandals , decisions to substitute are then taken underpressure , in which the enviromnent and health-related quality of substitution solutions remains to a large extent open and mere shifts of risks are probable. 

Two types of impurities should be distinguished namely, acceptor and donor impurities which play the part of traps (i.e., localization centers) for the free electrons and the free holes, respectively. It should be especially stressed that foreign particles dissolved in the crystal may act as acceptors or donors depending not only on their nature, but also on whether they enter the lattice (interstitially or substitutionally). For example, the interstitial Li atoms in the NiO lattice are donors, but the same Li atoms when replacing the Ni atoms act as acceptors. In the case of a substitutional solution, the foreign atoms of a given type may be either acceptors or donors depending on the lattice in which they are dissolved. For example, Ga atoms are donors in the ZnO lattice and acceptors in the Ge lattice. Thus, if the adsorbed particles are, say, acceptors, the same particles when dissolved in the volume of the crystal may act as donors, and vice versa. 

Equation (5.21) assumes ternary interactions are small in comparison to those which arise from the binary terms. This may not always be the case and where evidence for higher-order interactions is evident these can be taken into account by a further term of the type Gijit = x< xj Xk Lijk, where Lijk is an excess ternary interaction parameter. There is little evidence for the need for interaction terms of any higher order than this and prediction of the thermodynamic properties of substitutional solution phases in multi-component alloys is usually based on an assessment of binary and ternary terms. Various other polynomial expressions for the excess term have been considered, see for example the reviews by Ansara (1979) and Hillert (1980). All are, however, based on predicting the properties of... 

In the dissociative mechanism, a substitutional solute atom enters an interstitial site, leaving a vacancy, V, behind according to the reaction... 

An accurate determination of f can be obtained by considering all contributing vacancy trajectories to determine (cos ) by use of Eq. 8.29 [13]. For f.c.c., the accurate value of f is found to be 0.78 thus, correlations affect the diffusivity value by about 22% in Eq. 7.52.7 Correlations can have a considerably larger effect on the diffusivity for substitutional solute atoms by the vacancy mechanism. 

Diffusion of Solute Atoms by Vacancy Mechanism in Close-Packed Structure. Diffusion of substitutional solutes in dilute solution by the vacancy mechanism is more complex than self-diffusion because the vacancies may interact with the solute atoms and no longer be randomly distributed. If the vacancies are attracted to the solute atoms, any resulting association will strongly affect the solute-atom diffusivity. 

Ernest Kirkendall s doctoral thesis on the interdififiision between copper and brass disproved the almost universally accepted concept that diffusion in substitutional solutions occurs by interchange of atoms and led to the conclusion that diffusion was the result of vacancy migration. His results were so startling to the leading metallurgists of the day that publication of his work was held up by reviewers who doubted his results. 

The most important adverse effect results from the antigenicity of dextrans, which may lead to an anaphylactoid reaction. Dextran antibodies can be intercepted without an immune response by injection of small dextran molecules (MW 1000), thus obviating any incompatibility reaction to subsequent infusion of the dextran plasma substitute solution. 

What is a substitutional solution What is an ordered sublattice phase ... 

Note that at this point we selected the function g arbitrarily, because we did not specify the shape of the source-generated pulse. To determine the function gi, we should substitute solution (13.68) into equation (13.64) ... 

The liquid Si-based solution, here abbreviated as 1 , is described using a simple polynomial expression based on a substitutional solution with random mixing. The same model is employed for the diamond-structured Si-rich solid phase, denoted as s. The Gibbs energies of the liquid and solid Si-based phases are given by the following equation ... 

Concerning the curve forms it is seen that for the 0.05 mole % VO sample there is a hyperfine splitting indicative of a substitutional solution of N in rutile (22,26). It is quite clear that on increasing the content from 0.05 to 0.5 mole %, the ESR spec-... 

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