Entropy stabilized compounds

The binary systems we have discussed so far have mainly included phases that are solid or liquid solutions of the two components or end members constituting the binary system. Intermediate phases, which generally have a chemical composition corresponding to stoichiometric combinations of the end members of the system, are evidently formed in a large number of real systems. Intermediate phases are in most cases formed due to an enthalpic stabilization with respect to the end members. Here the chemical and physical properties of the components are different, and the new intermediate phases are formed due to the more optimal conditions for bonding found for some specific ratios of the components. The stability of a ternary compound like BaCC>3 from the binary ones (BaO and CC>2(g)) may for example be interpreted in terms of factors related to electron transfer between the two binary oxides see Chapter 7. Entropy-stabilized intermediate phases are also frequently reported, although they are far less common than enthalpy-stabilized phases. Entropy-stabilized phases are only stable above a certain temperature,... 

DilP recently discussed the merits and limitations of models that assume thermodynamic additivity and independence (of energy types, of neighbor interactions, of conformational freedom, of monomer contact pairing frequencies, etc.). He states that biological molecules may achieve stability in the face of thermal uncertainty, as polymers do, by compounding many small interactions this summing can stump modelers because application of the additivity principle leads to accumulated error. Entropies and free energy may not be additive to describe weak interactions that are ensembles of states. He concludes that additivity principles appear to be few and limited in scope in biochemistry. 

Condensation theory is based on thermodynamic equilibrium. More than a century s worth of experiments have yielded thermodynamic data (entropy and enthalpy of formation, plus heat capacity) for elements and compounds. Equations of state describing the stabilities of different compounds under various conditions can be calculated from these data, as briefly described in Box 7.1. Because liquids are not normally stable at the low pressures appropriate for space, the compounds in condensation calculations are generally solid minerals, but liquids can exist at higher pressures (achievable if areas of the nebula with enhanced dust concentrations relative to gas were vaporized). 

Kx for copper (II)-diamine complex is 10.36 and 9.45 for 1,2-ethanediamine and 1,3-propanediamine, respectively (-2)]. The large difference in the stabilities of the two copper (II)-diamine complexes is attributed to an unfavorable entropy effect associated with an increase in the size of the metal-chelate ring (2). Extrapolating to the / -ketoimine derivatives, it seems reasonable to expect that the stability of bisacetylacetonetrimethylenediiminocopper(II) would be less than that of the ethylenediamine analog and to suspect that the former compound is less stable than bis-(4-iminopentane-2-ono) copper (II). That this is reasonable is... 

Although the energy of this compound is higher than that of FeO, it is stabilized at higher temperature because it has a greater entropy, the Fe2 ions being partially replaced by Fe3 ions and gaps. The formula for the entropy would be... 

Compounds with variable composition are not really stable at low temperature. Even at room temperature the entropy is insufficient for stabilization. At room temperature, however, the speed of the reaction, in which the two pure oxides are formed, e.g. 

In Section 24 it was shown that, under favorable conditions, two oxides of the same metal, in different states of valency, may form solid solutions which have been described as compounds with variable composition. The stabilizing factor in this case is the increase in entropy, due to the random distribution of the two positive ions these systems, strictly speaking, are stable only at elevated temperature. The conditions may be such that two oxides form a real compound, because this process is connected with a decrease in energy. The compounds formed in this way have a stoichiometric composition, with two kinds of positive ions in fixed positions, so arranged that the energy of the system is minimal. A good example of a compound of this type is Fe304. 

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