Entropy stabilisation

This result indicates that Th-brannerite is entropy-stabilised and may be stable at high temperature only. 

Thus the results indicate that both the thorium and the cerium titanates are entropy stabilised compounds and are probably stable at high temperature only, while ura-niirm titanate is presumably stable at ambient conditions. 

In conclusion, lipid vesicles that are fully equilibrated (freeze-thaw procedure) may be stabilised by both translational as well as undulational entropy. 

This law is particularly useful as it allows the total entropy of a substance to be obtained if sufficiently low-temperature enthalpy or heat-capacity measurements are available. However, questions remain as to its validity when considering metastable crystalline forms and the law, as stated, would not apply to defect-stabilised structures and amorphous phases. 

The position of Ti and Zr is again important in this context. While the b.c.c. phase in these elements has long been known to indicate mechanical instability at 0 K, detailed calculations for Ti (Petty 1991) and Zr (Ho and Harmon 1990) show tiiat it is stabilised at high temperatures by additional entropy contributions arising from low values of the elastic constants (soft modes) in specific crystal directions. This concept had already been raised in a qualitative way by Zener (1967), but the... 

Depending on the data available, Eqs (6.17)-(6.23) reproduce experimental pressure effects with considerable accuracy in many cases. In particular, Eq. (6.18) can be used to confirm entropy data derived using more conventional techniques and can also provide data for metastable allotropes. Ti again provides a leading example, as pressure experiments revealed that the u -phase, previously only detected as a metastable product on quenching certain Ti alloys, could be stabilised under pressure (Fig. 6.14). Extrapolation of the P/w transus line yields the metastable allotropic transformation temperature at which the / -phase would transform to w in the absence of the a-phase, while die slope of the transus lines can be used to extract a value for the relevant entropy via Eq. (6.18). 

Merenyi R, Janousek Z, Viehe HG (1986) Studies on the captodative effect. Entropy/enthalpy compensation as solvent effect in radical forming reactions. A relative radical stabilisation scale. In Viehe HG (ed) Substituent effects in radical chemistry. Reidel, Dordrecht, pp 301-324 Merga G, Schuchmann H-P, Rao BSM, von Sonntag C (1996) The oxidation of benzyl radicals by Fe(CN)63. J Chem Soc Perkin Trans 2 551-556... 

Figure 1. The calcite-aragonite phase boundary in P/T space is curved, due to the temperature-dependence of the entropy of calcite. The entropic stabilisation of calcite at high-T arises from the order-disorder phase transition from orientationally ordered R3c calcite at low temperatures to the orientationally disordered R3c stmcture, stable above 1260 K. Figure after Redfern etal. (1989a).

Entropic, volume restriction or elastic interaction, G p This results from the loss in configurational entropy of the chains on significant overlap. Entropy loss is unfavourable and, therefore, G j is always positive. A combination of G,. with G gives the total energy of interaction Gj (theory of steric stabilisation). 

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