Metastable structures

Fernandez A 1991 Functional metastable structures in RNA replication Physica A 176 499-513... 

Which spatial arrangement of atoms results in a stable or metastable structure depends decisively on the distribution of their electrons. 

In addition, silicon adopts a number of metastable structures that can be obtained, depending on pressure, by rapid release of the pressure from Si-II, Si-XII is formed, and from this Si-III upon heating, Si-III transforms to the hexagonal diamond structure (Si-IV). Si-III has a peculiar structure with a distorted tetrahedral coordination of its atoms. The atoms are arranged to interconnected right- and left-handed helices (Fig. 12.7). The structure being cubic, the helices run in the directions a, b as well as c. Si-VIII and Si-IX... 

Initiation of growth may also proceed by formation of metastable structures when nucleation is inhibited. Multiply twinned structures have been observed for a number of metals. Their presence indicates an icosohedral or decahedral precursor cluster which has decomposed to a multiply twinned crystal at a critical size [117, 118], Another example of metastable intermediate structures was reported by Dietterle et al. 

It is clearly desirable to see if the total curve can be de-convoluted into parts that can be identified with a specific physical property so that trends can be established for the many cases where data for metastable structures are not experimentally accessible. In principle, the TC lattice stability of an element in a specified crystal structure 0 relative to the standard state a can be comprehensively expressed as follows (Kaufman and Bernstein 1970) ... 

With the exception of a few allotropic elements, the necessary input parameters to Eqs (6.1) or (6.2) are not available to establish the lattice stabilities of metastable structures. Therefore an alternative solution has to be found in order to achieve the desired goal. This has evolved into a standard format where the reference or ground state Gibbs energy is expressed in the form of genera] polynomials which reproduce assessed experimental Cp data as closely as possible. An example of such a standard formula is given below (Dinsdale 1991) ... 

Figure 6.4. (a) Variation of the entropy of fusion with melting point for different crystal structures (from Saunders el at. 1988) and (b) schematic illustration of the possibility of a change in value and sign for the entropy of transformation if the metastable structure has a low melting point (from Miodownik 1992). 

The increasing availability of electron energy calculations for lattice stabilities has produced alternative values for enthalpy differences between allotropes at 0 K which do not rely on the various TC assumptions and extrapolations. Such calculations can also provide values for other properties such as the Debye temperature for metastable structures, and this in turn may allow the development of more physically appropriate non-linear models to describe low-temperature Gibbs energy curves. 

By contrast, electron energy calculations have the inherent capability of yielding accurate values for many metastable structures at 0 K but have little or no capability of predicting the temperature dependence of the Gibbs energy, especially in cases where mechanical instabilities are involved. 

C. Stampfl and A. J. Freeman, Stable and Metastable Structures of the Multiphase Tantalum Nitride System, Phys. Rev. B 71 (2005), 024111. 

In another example, the high temperature reaction of calcium and strontium sub-nitrides with molybdenum foil has also recently been claimed to produce novel molybdenum ternary nitride oxides which contain isolated [MoN4] tetrahedra in an ordered sub-lattice of and anions. High temperature-high pressure syntheses are also yielding novel metastable structures, such as the spinel analogues mentioned previously. There is therefore an ever-increasing base of nitrides and oxynitrides with diverse structures and potential catalytic interest. 

One form of a photochrome is usually "metastable with respect to the other form, i.e., the metastable structure spontaneously reverts to the stable structure with little or no energy of activation. Therefore, it may be assumed that additional energy is pumped into the system by increasing the ratio of metastable to stable components. An accurate knowledge of this factor of energy storage is, in fact, a measure of the useful energy extracted from the visible or ultraviolet radiation. 

In recent years a number of so-called complex phases, such as the bicontinuous gyroid and perforated layer structures, have been identified. The former has been established as an equilibrium structure, whereas the latter seem to be metastable structures observed during transformations to and from the gyroid structure. 

Fig. 5.17 SAXS patterns for PEQwPBO.w showing (a) the ordered melt structure (T = 90 °C) (b) a metastable structure at T = 42 °C (c) the equilibrium once-folded structure grown at T - 50°C by a self-seeding process (Ryan et al. 1997). Numbers indicate the order of reflection from a lamellar structure and the arrow indicates the position of the peak in the ordered melt. The calculated repeat lengths for possible molecular conformations are indicated.

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