Stabilization, lattice

The calculated barrier to dissociation of the [S3N2] dication into [SN]" and [S2N] in the gas phase is 10.9 kcal mof . However, lattice-stabilization effects allow the isolation of [MEg] salts (M = As, Sb) of this six r-electron system in the solid state from the cycloaddition of [SN] and [S2N] cations in SO2 (Eq. 5.11)."° The S-S and S-N bond distances in the planar, monomeric dication are shorter than those in the... 

Melting. Loss of crystallinity of a solid reactant through melting, or eutectic formation, or dissolution in a product often results in an enhanced rate of decomposition as a consequence of the relaxation of the bonding forces responsible for lattice stabilization. The appearance of a... 

It should be remembered that the CALPHAD approach is based on the hypothesis that, for all the phases and structures existing across the complete alloy system, entire Gibbs energy vs. composition curves may be constructed even by extrapolation into regions where they are unstable or metastable. A particular case concerns the pure component elements for which the relative Gibbs energy for the different crystal structures (the so-called lattice stabilities) must also be established and defined as a function of temperature (and pressure). 

Lattice stabilities of Ca, Sr andYb disilicides have been reported by Brutti etal. (2006). Structural stabilities of six different prototype lattices have been investigated and discussed. 

Chapter 6 therefore deals in detail with this issue, including the latest attempts to obtain a resolution for a long-standing controversy between the values obtained by thermochemical and first-principle routes for so-called lattice stabilities . This chapter also examines (i) the role of the pressure variable on lattice stability, (ii) the prediction of the values of interaction coefficients for solid phases, (iii) the relative stability of compounds of the same stoichiometry but different crystal structures and (iv) the relative merits of empirical and first-principles routes. 

Not surprisingly, Kaufman found the Battelle meeting discouraging. The values of lattice stabilities proposed by Brewer (1967) were substantially different to those proposed on thermodynamic grounds, but there was at least the possibility of a dialogue on this issue, and so Kaufman (1966a) wrote, in a letter to Brewer, that... 

The discussion between Hume-Rotheiy and Kaufman also dealt with the apparent conflict between different sets of competing lattice stabilities. It was particularly worrying to him that Brewer (1967) and Engel (1964) proposed values based on spectroscopic data that could differ by almost an order of magnitude in some instances. To an outsider, these were simply alternatives which had equal validity. 

Lattice-stability values obtained by electron energy calculations also differed from those obtained by thermochemical routes, but at that time such calculations were still at a relatively rudimentary stage and it was assumed that the two sets of values would eventually be related. However, there is no doubt that lack of agreement in such a fundamental area played a part in delaying a more general acceptance of the CALPHAD methodology. 

This ensures that thermochemical (TC) lattice stabilities are firmly anchored to the available experimental evidence. Although the liquid phase might be considered a common denominator, this raises many problems because the structure of liquids is difficult to define it is certainly not as constant as popularly imagined. It is therefore best to anchor the framework for lattice stabilities in the solid state. 

It is clearly desirable to see if the total curve can be de-convoluted into parts that can be identified with a specific physical property so that trends can be established for the many cases where data for metastable structures are not experimentally accessible. In principle, the TC lattice stability of an element in a specified crystal structure 0 relative to the standard state a can be comprehensively expressed as follows (Kaufman and Bernstein 1970) ... 

With the exception of a few allotropic elements, the necessary input parameters to Eqs (6.1) or (6.2) are not available to establish the lattice stabilities of metastable structures. Therefore an alternative solution has to be found in order to achieve the desired goal. This has evolved into a standard format where the reference or ground state Gibbs energy is expressed in the form of genera] polynomials which reproduce assessed experimental Cp data as closely as possible. An example of such a standard formula is given below (Dinsdale 1991) ... 

The excess term should allow the total Gibbs energy to be fitted to match that of Eq. (6.3) while at the same time incorporating a return to the inclusion of f 6) and f i) in the lattice stabilities. With the increased potential for calculating metastable Debye temperatures and electronic specific heats from first principles (Haglund et al. 1993), a further step forward would be to also replace Eq. (6.5) by some function of Eq. (6.8). 

It was therefore appropriate that the first attempt to produce lattice stabilities for non-allotropic elements dealt with Cu, Ag and Zn (Kaufman 1959b). It is also significant that, because of the unfamiliarity of the lattice stability concept, this paper did not appear as a mainstream publication although the work on Ti and Zr (Kaufman 1959a) was published virtually at the same time. It was also realised that Ae reliability of metastable melting points derived by extrapolation were best... 

Determination of transformation enthalpies in binary systems. Just as consistent values of for elements can be obtained by back-extrapolation from binary systems, so it is possible to obtain values of by extrapolating the enthalpy of mixing vs composition in an alloy system where the phase has a reasonable range of existence. The archetypal use of this technique was the derivation of the lattice stability of f.c.c. Cr from the measured thermodynamic properties of the Ni-based f c.c. solid solution (7) in the Ni-Cr system (Kaufman 1972). If it is assumed that the f.c.c. phase is a regular solution, the following expression can be obtained ... 

Plotting Oq xct vs then leads to a straight line with an intercept equal to the Gibbs energy difference between the f.c.c. and b.c.c. forms of Cr, at the temperature where measurements were made (Fig. 6.5), while the slope of the line yields the associated regular solution interaction parameter. The lattice stability and the interaction parameter are conjugate quantities and, therefore, if a different magnitude... 

However, on the basis of calculations of lattice stabilities from spectroscopic data. Brewer (1967, 1979) has consistently maintained that interaction coefficients can change drastically with composition, and that extrapolated lattice stabilities obtained with simple models should therefore be considered as only effective values. While this may indeed be true when mechanical instability occurs, many of the assumptions which underlie Brewer s methodology are questionable. A core principle of the spectroscopic approach is the derivation of promotion energies which require the definition of both ground and excited levels. Assumptions concerning the relevant excited state have always been strongly coloured by adherence to the empirical views of Engel (1964) and Brewer (1967). By definition, the choice... 

Although this method is essentially restricted to a particular sub-set of lattice stabilities, it nevertheless provides an additional experimental input, especially in cases where it is not possible to access the metastable phase by other methods. It is therefore disappointing that there are no experimental values of the SEE available for Ru or Os, which could provide confirmation of G p obtained by other methods. High SEE values have, however, been both observed and predicted for Rh and Ir, which is indirect confirmation for a larger variation of g " p with (/-shell filling than proposed by Kaufinan and Bernstein (1970). 

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