Solution atomization

Tlere, y Is the friction coefficien t of the solven t. In units of ps, and Rj is th e random force im parted to th e solute atom s by the solvent. The friction coefficien t is related to the diffusion constant D oflh e solven l by Em stem T relation y = k jT/m D. Th e ran doin force is calculated as a ratulom number, taken from a Gaussian distribn-... 

Th eri water mo Iccu les are elim in ated if an y of th c Lh rce atom s arc closer to a solute atom than the contact distance you specify. 

Here, y is the friction coefficient of the solvent, in units of ps and Rj is the random force imparted to the solute atoms by the solvent. The friction coefficient is related to the diffusion constant D of the solvent by Einstein s relation y = kgT/mD. The random force is calculated as a random number, taken from a Gaussian distribu-... 

Prior to solvation, the solute is oriented according to its inertial axes such that the box size needed to accommodate it is minimized (minimizing the number of water molecules). The principal inertial axis is oriented along the viewer s Z axis, for example. Then water molecules are eliminated if any of the three atoms are closer to a solute atom than the contact distance you specify. 

Both sohd-solution hardening and precipitation hardening can be accounted for by internal strains generated by inserting either solute atoms or particles in an elastic matrix (11). The degree of elastic misfit, 5, produced by the difference, Ai , between the lattice parameter, of the pure matrix and a, the lattice parameter of the solute atom is given by... 

Effect of Thermal History. Many of the impurities present in commercial copper are in concentrations above the soHd solubihty at low (eg, 300°C) temperatures. Other impurities oxidize in oxygen-bearing copper to form stable oxides at lower temperatures. Hence, because the recrystallization kinetics are influenced primarily by solute atoms in the crystal lattice, the recrystallization temperature is extremely dependent on the thermal treatment prior to cold deformation. 

When there is a large difference between ys(A) and ys(B) in the equation above, there must be signihcant deparmres from dre assumption of random mixing of the solvent atoms around tire solute. In this case tire quasi-chemical approach may be used as a next level of approximation. This assumes that the co-ordination shell of the solute atoms is hlled following a weighting factor for each of tire solute species, such that... 

In liquid metal solutions Z is normally of the order of 10, and so this equation gives values of Ks(a+B) which are close to that predicted by the random solution equation. But if it is assumed that the solute atom, for example oxygen, has a significantly lower co-ordination number of metallic atoms than is found in the bulk of die alloy, dieii Z in the ratio of the activity coefficients of die solutes in the quasi-chemical equation above must be correspondingly decreased to the appropriate value. For example, Jacobs and Alcock (1972) showed that much of the experimental data for oxygen solutions in biiiaty liquid metal alloys could be accounted for by the assumption that die oxygen atom is four co-ordinated in diese solutions. 

As we saw in Chapter 10, the stress required to make a crystalline material deform plastically is that needed to make the dislocations in it move. Their movement is resisted by (a) the intrinsic lattice resistance and (b) the obstructing effect of obstacles (e.g. dissolved solute atoms, precipitates formed with undissolved solute atoms, or other dislocations). Diffusion of atoms can unlock dislocations from obstacles in their path, and the movement of these unlocked dislocations under the applied stress is what leads to dislocation creep. 

When other elements dissolve in a metal to form a solid solution they make the metal harder. The solute atoms differ in size, stiffness and charge from the solvent atoms. Because of this the randomly distributed solute atoms interact with dislocations and make it harder for them to move. The theory of solution hardening is rather complicated, but it predicts the following result for the yield strength... 

It is shown that solute atoms differing in size from those of the solvent (carbon, in fact) can relieve hydrostatic stresses in a crystal and will thus migrate to the regions where they can relieve the most stress. As a result they will cluster round dislocations forming atmospheres similar to the ionic atmospheres of the Debye- Huckel theory ofeleeti oly tes. The conditions of formation and properties of these atmospheres are examined and the theory is applied to problems of precipitation, creep and the yield point."... 

Fig. 5 illustrates a peculiar kinetic phenomenon which occurs when an initially disordered alloy is first annealed at temperature T corresponding to area b in Fig. 1 and then quenched to the final temperature T into the spinodal instability area d antiphase boundaries "replicate , generating approximately periodic patterns. This phenomenon reflects the presence of critical, fastest growing concentration waves under the spinodal instability (the Calm waves ). Lowering of the temperature to T < T results in lowering of the minority concentration minimum ("c-well ) within APB, while the expelled solute atoms build the c-bank adjacent to the well . Due to the... 

If, therefore, the solute atoms can be prevented from entering the boundary film from the solid the process will be halted. A method for doing this... 

In metals, the distance between the individual atoms in the lattice is of the order of 0-4 nm and only atoms of very small size are able to penetrate interstitially. This takes place, for instance, in the diffusion of hydrogen into iron, and of carbon into austenite, etc. This type of interstitial diffusion is usually rapid, since the inward movement of the solute atoms is relatively unhampered. 

Interstitial diffusion is rarely possible when two metals interdiffuse, since their atomic radii are usually of the same order. Several mechanisms have been proposed, but it is now generally accepted that interdiffusion is due to the motion of vacant sites within the lattice, solvent and solute atoms moving as the vacant sites migrate. The diffusion process is thus dependent upon the state of imperfection of the solvent metal and the alloy being formed. 

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. 

Just as the saturated solubility of sugar in water is limited, so the solid solubility of element B in metal A may also be limited, or may even be so low as to be negligible, as for example with lead in iron or carbon in aluminium. There is extensive interstitial solid solubility only when the solvent metal is a transition element and when the diameter of the solute atoms is < 0 6 of the diameter of the solvent atom. The Hume-Rothery rules state that there is extensive substitutional solid solubility of B in >1 only if ... 

The writer45 60 has criticized the elasticity theory model on the basis that this partial character renders the theory unverifiable by experiment, unless this model is correlated with another model that may be postulated to represent the negative portion of the AH, a correlation which has never been achieved. Another criticism has been the inconsistency of the model when it is applied to the case of solute atom smaller than the solvent atom, as opposed to... 

Vo is given in A electron charge units, r is the closest distance (in A) between the grid points to the indicated solute atom. 

Finds the smallest distance between the solute and the grid points. Checks if the given grid point is within the van der waals distance from I any of the solute atoms. 

I Calculates the potential from the solvent I dipoles at the sites of the solute atoms. 

In the previous chapter we considered a rather simple solvent model, treating each solvent molecule as a Langevin-type dipole. Although this model represents the key solvent effects, it is important to examine more realistic models that include explicitly all the solvent atoms. In principle, we should adopt a model where both the solvent and the solute atoms are treated quantum mechanically. Such a model, however, is entirely impractical for studying large molecules in solution. Furthermore, we are interested here in the effect of the solvent on the solute potential surface and not in quantum mechanical effects of the pure solvent. Fortunately, the contributions to the Born-Oppenheimer potential surface that describe the solvent-solvent and solute-solvent interactions can be approximated by some type of analytical potential functions (rather than by the actual solution of the Schrodinger equation for the entire solute-solvent system). For example, the simplest way to describe the potential surface of a collection of water molecules is to represent it as a sum of two-body interactions (the interac-... 

Apparently the rigorous all-atom FEP approach reflects a rather simple physics The solvent polarization responds linearly to the development of charges on the solute atoms (Ref. 1). This is why the simple LD model gives similar results to those obtained by the FEP approach (see Ref. 10). 

Now knowing how to evaluate solvation-free energies, we are ready to explore the effect of the solvent on the potential surface of the reacting solute atoms. Adapting the EVB approach we can describe the reaction by including the solute-solvent interaction in the diagonal elements of the solute Hamiltonian, using... 

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