Phase rule apparent violation

Sometimes when a mineral becomes supersaturated, there is no logical aqueous species in the basis with which to swap the mineral. Such a situation occurs when no species appear in the reaction to form the mineral. Wolery (1979) and Reed (1982) refer to such a situation as an apparent violation of the phase rule, because adding the mineral to the basis would produce more phases in the system than there are components. 

Virtually everything that exists or happens in real space has a corresponding property or effect in diffraction space, and vice versa. The correspondences are established through the Fourier transform, which, as we have seen, operates symmetrically in both directions, getting us from real space into reciprocal space and back again. It may occasionally appear that this rule is violated, but in fact it is not. For example, the chirality of molecules and the handedness of their arrangement in real space would seem to be lost in reciprocal space as a consequence of Friedel s law and the addition of a center of symmetry to reciprocal space. If, however, we could record phases of reflections in reciprocal space, we would see that in fact chirality is preserved in phase differences between otherwise equivalent reflections. The phases of Fhu, for example, are 0, but the phase of F-h-k-i are —0. Fortunately the apparent loss of chiral information is usually not a serious problem in the X-ray analysis of proteins, as it can usually be recovered at some point by consideration of real space stereochemistry. 

Abstract The Gibbs phase rule relating the number of degrees of freedom / of a system to the number of components c and the number of coexisting phases p is a central, universally used relation, expressed by what is probably the simplest formula in the natural sciences,/ = c — p + 2. Research into the behavior of small systems, notably atomic clusters, has shown in recent years that the phase rule is not as all-encompassing as is often assumed. Small systems can show coexistence of two or more phases in thermodynamic equilibrium over bands of temperature and pressure (with no other forces acting on them). The basis of this apparent violation of the phase rule, seeming almost like violation of a scientific law, is in reality entirely understandable, consistent with the laws of thermodynamics, and even allows one to estimate the upper size limit of any particular system for which such apparent violation could be observed. 

Observability of Coexistence in Apparent Violation of the Phase Rule. 226... 

The history of the phase rule is the subject of a review written for its centenary [4] that history need not concern our discussion here because it reviews the applications and the controversies over the derivation of the rule. Here, we concern ourselves with the deviations and apparent violations of the phase rule, a topic essentially untouched until computer simulations of small systems suggested that the phase rule might, after all, not be so universal. 

The relative importance of different eclipsed conformations in substituted propenes can be controlled stereoelectronically by variations in the donor and acceptor properties of aUyUc C-X bonds and the alkene (Figure 6.31). For example, the difference between the two conformations of aUyl fluoride is small (the -0.2-0.8 kcal/mol gas phase preference for the conformation with the C-F eclipsed bond). This is an apparent violation of the main stereoelectronic rule (the best acceptor, p, is orthogonal to the best donor in this... 

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