Phases, stability

The direction (but not the rate) of a phase transformation can be determined from the equilibrium thermodynamic properties of the phases involved. For this purpose, the most important thermodynamic parameter is the Gibbs energy (or Gibbs free energy) of the phases. The Gibbs energy, G (units J moP ), of a pure material is dehned by the equation  

A reaction at constant pressure will take place spontaneously (should the kinetics allow) if the Gibbs energy of the system decreases because of 

Gibbs energy change = (total Gibbs energy of products) 

The Gibbs energy of formation of a compound, AGf, is used in these calculations. The Gibbs energy change for a reaction is therefore given by  

Because the Gibbs energy varies with temperature, the free energy values have to be adjusted accordingly. This is especially true for reactions involving solids, as these are carried out at high temperatures. 

Chemical Thermodynamics of Materials by Svein St0len and Tor Grande 2004 John Wiley Sons, Ltd ISBN 0 471 492320 2 

However, at some specific pressure the high-density polymorph becomes mechanically unstable. This low-pressure limit is seldom observed, since it often corresponds to negative pressures. When the mechanical stability limit is reached the phase becomes unstable with regard to density fluctuations, and it will either crystallize to the low-pressure polymorph or transform to an amorphous phase with lower density. 

Phases may also become unstable with regard to compositional fluctuations, and the effect of compositional fluctuations on the stability of a solution is considered in Section 5.2. This is a theme of considerable practical interest that is closely connected to spinodal decomposition, a diffusion-free decomposition not hindered by activation energy. 

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Several alternative attempts have been made to quantify Lewis-acid Lewis-base interaction. In view of the HSAB theory, the applicability of a scale which describes Lewis acidity with only one parameter will be unavoidably restricted to a narrow range of struchirally related Lewis bases. The use of more than one parameter results in relationships with a more general validity ". However, a quantitative prediction of the gas-phase stabilities of Lewis-acid Lewis-base complexes is still difficult. Hence the interpretation, not to mention the prediction, of solvent effects on Lewis-add Lewis-base interactions remains largely speculative. 

Pure metallic cobalt has a soHd-state transition from cph (lower temperatures) to fee (higher temperatures) at approximately 417°C. However, when certain elements such as Ni, Mn, or Ti are added, the fee phase is stabilized. On the other hand, adding Cr, Mo, Si, or W stabilizes the cph phase. Upon fcc-phase stabilization, the energy of crystallographic stacking faults, ie, single-unit cph inclusions that impede mechanical sHp within the fee matrix, is high. 

The design of this alloy was unique in that it utilized phase stability and other predictive techniques to balance the levels of critical elements (Cr, Mo, Co, Al, Wand Ta), thereby maintaining the hot corrosion resistance of IN-738 at higher strength levels without compromising phase stability. Most... 

Staeking faults and sometimes proper polytypism are found in many inorganic compounds - to pick out just a few, zinc sulphide, zinc oxide, beryllium oxide. Interest in these faults arises from the present-day focus on electron theory of phase stability, and on eomputer simulation of lattice faults of all kinds investigators are attempting to relate staeking-fault concentration on various measurable character-isties of the compounds in question, such as ionicity , and thereby to cast light on the eleetronic strueture and phase stability of the two rival structures that give rise to the faults. 

Australia, is the doyen of materials scientists who study the elastic and plastic properties of minerals under hydrostatic pressure and also phase stability under large shear stresses (Paterson 1973). J.-P. Poirier, in Paris, a professor of geophysics, was trained as a metallurgist one of his special skills is the use of analogue materials to help understand the behaviour of inaccessible high-pressure polymorphs, e.g., CaTi03 perovskite to stand in for (Mg, FelSiOi in the earth s mantle (Poirier 1988, Besson el al. 1996). 

Stocks, G.M. and Gonis, A. (eds.) (1989) Alloy Phase Stability (Kluwer Academic Publishers, Dordrecht). 

There is an excellent correlation between these data and the gas-phase data, in terms both of the stability order and the energy differences between carbocations. A plot of the gas-phase hydride affinity versus the ionization enthalpy gives a line of slope 1.63 with a correlation coefficient of 0.973. This result is in agreement with the expectation that the gas-phase stability would be somewhat more sensitive to structure than the solution-phase stability. The energy gap between tertiary and secondary ions is about 17kcal/mol in the gas phase and about 9.5 kcal/mole in the SO2CIF solution. 

CRYSTAL STRUCTURE AND PHASE STABILITY IN Fei Co FROM AB INITIO THEORY... 

In summary, we have demonstrated the possibility of calculating the phase stability of a magnetic random alloy from first principles by means of LMTO-CPA theory. Our calculated phase diagram is in good agreement with experiment and shows a transition from the partially ordered a phase to an hep random alloy at 85% Co concentration. 

AB INITIO STUDY OF PHASE STABILITY AND EQUATION OF STATE OF TITANIUM DIOXIDE... 

AUGMENTED SPACE RECURSION APPROACH FOR ALLOY PHASE STABILITY... 

One of the major ingredient for the understanding of alloy phase stability is the configurational energy. Models have been proposed to represent the configurational energies in terms of effective multisite interactions, in particular effective pair interactions (EPls). 

For the phase stability analysis we follow the method given by Kanamori and Kakehashi of geometrical inequalities and compute the antiphase boundary energy defined by... 

Our results demonstrate that the augmented space recursion and the orbital peeling method in conjunction with the LMTO formalism, constitute a viable and computationally feasible approach to the calculation of phase stability in binary substitutionally disordered alloys. ... 

F. Ducastelle. Order and Phase Stability in Alloys, edited by F. R. de Boer and D. G. Pettifor, Cohesion and Structure Vol 3, North-Holland, Amsterdam, (1991). 

To further discuss the underlying mechanisms that forces the phase stabilities we also did calculations where the alloying effects were treated within the so-called virtual crystal approximation (VGA) where the real alloy constituents are replaced by an atom with an average (noninteger) atomic number. 

A. I. Abrikosov, P. James, O. Eriksson, P. Soderlind, A. V. Ruban, H. L. Skriver, and B. Johansson, Magnetically induced crystal structure and phase stability in FecCoi c, Phys. Rev. B (to be published). 

T. Mohri, Structural and Phase Stability of Alloys, ed. J. L. Moran-Lopez et al.. Plenum Press, New York (1992), 87-101. 

T. Mohri, Interatomic Potential and Phase Stability, Springer Series in Solid-State Sciences 114, ed. by K. Terakura and H. Akai, Springer-Verlag, (1993), 168-177. 

F. Ducastelle, Order and Phase Stability (North Holland, Amsterdam, 1991). 

G. Foumet, Order-disorder phenomena in solid solutions, in. Phase Stability in Metals and Alloys", P S. 

M. Sluiter, P.E.A. Turchi, F.I. Pinski and G.M. Stocks, A first-principles study of phase stability in Ni-Al... 

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