A Universal Representation of the States of Chemical Matter Including Metastable Configurations in Phase Diagrams

Abstract

Encoding equilibrium states of matter in the format of phase diagrams is among the basic and at the same time most fruitful concepts in solid-state and materials chemistry. The appealing stringency of these concepts is related to the fact that any equilibrium state of matter, as characterized by its phase content (defined by the phases present, their compositions, and concentrations) and the respective activities of the components, is unambiguously determined by fixing the set of independent variables of state, p (or V), T, x iÀ1 for a system constituted of i components. In many fields of science and technology, analyzing chemical processes in terms of phase diagrams and equilibrium thermodynamics has proven an invaluable tool. [1][2][3] In spite of the impressive success of such an approach in specific areas, it fails seriously in addressing the full "real" materials world, since most of the matter around us stays trapped in metastable, in many cases quite persistent, states. Even at demanding thermal conditions, for example, prevailing in gas or steam turbines, many of the materials employed are not in equilibrium. Quite generally, it is easy to show that metastable materials are of substantial relevance: durable diamond is metastable at ambient conditions, glasses constitute an economically significant class of matter, and (metastable) amorphous ceramics can outperform thermodynamically stable crystalline ones with respect to the overall set of properties relevant for high-temperature applications. [4,5] As a consequence, a holistic consideration of a given chemical system, for example, for the purpose of synthesis planning, needs to include both the equilibrium and the metastable states. [6,7] Thus it would be highly desirable to address metastable states of matter in a similarly rational way as thermodynamically stable ones and to put both on a comparable footing. Regarding the most popular presentation of equilibrium phase diagrams that are obtained by projecting the lowest parts of the Gibbs energy surfaces of the competing thermodynamically stable phases onto the space spanned by the variables (p, T, x i ), such an objective would imply to perform an analogous procedure for metastable matter. After identifying all chemical compounds and phases that are capable of existence, one would determine their free energies as a function of the thermodynamic boundary conditions, and directly derive graphical representations (analogous to equilibrium phase diagrams) from this information. Noteworthy, such a procedure requires to involve the temperaturedependent lifetime of the metastable state under consideration as a further parameter.In the past, it has been shown that known features of equilibrium phase diagrams can be extra-and interpolated, as well as checked for consistency, by the well-known CAL-PHAD approach.[8] Furthermore, for a known configuration, its internal energy can be calculated, and, by considering the respective thermal excitations, the free energy can be derived,where G el and G magn refer to the...

Ruthenium(V) Oxides from Low‐Temperature Hydrothermal Synthesis

“…As with many multi‐element oxides, synthesis is dominated by the use of high temperature (>1200 °C), and this means that usually only the most thermodynamically stable compounds are isolated 10. Thus potentially large numbers of metastable oxide phases remain undiscovered, particularly for the 4d and 5d transition elements whose chemistry is less explored than the first‐row elements, and for which the use of mild reaction conditions may allow access to 11. 12 A range of complex ruthenium oxides containing Ca, Sr, or Ba have been reported and are of interest for their diverse and unusual magnetic and electronic properties.…”

From Ergodicity to Extended Phase Diagrams

“…A more complete answer has been proposed, [1] and comes in the form of an extended phase diagram that includes the notion of lifetimes for metastable phases. And why include metastable structures?…”

“…As the state of the chemical matter will depend upon the external conditions of temperature and pressure, a partial answer would be given by the standard phase diagram drawn for thermodynamically stable phases. A more complete answer has been proposed, [1] and comes in the form of an extended phase diagram that includes the notion of lifetimes for metastable phases. This novel approach is applied to an example system: Li 1Àx Na x Br.…”

Vom Konzept lokaler Ergodizität hin zu erweiterten Phasendiagrammen

“…Eine vollständigere Anwort wurde nun in Form eines erweiterten Phasendiagramms vorgeschlagen, [1] das die Begrifflichkeit der Lebensdauer metastabiler Phasen mit einschließt. Und warum sollte man metastabile Strukturen mit einbeziehen?…”

“…Da der Zustand der chemischen Materie von den äußeren Bedingungen der Temperatur und des Drucks abhängen wird, kann das für thermodynamisch stabile Phasen gezeichnete Phasendiagramm eine partielle Antwort geben. Eine vollständigere Anwort wurde nun in Form eines erweiterten Phasendiagramms vorgeschlagen, [1] das die Begrifflichkeit der Lebensdauer metastabiler Phasen mit einschließt. Der neuartige Ansatz wurde auf das Beispielsystem Li 1Àx Na x Br angewendet.…”