Meta stable structure

With the constraint of the same chemical formula, there can exist a number of (meta)stable structures, the phenomena known in crystallography as polymorphism. The global minimum of the ideal cost function might not be the only important minimum of interest. Under the same physical conditions more than one polymorph may exist in the same crystalline sample. Mathematically this happens to be when the local minima and the global minimum are of a similar value. One can either search for the most stable structure under given conditions or try to identify all important polymorphs. Incidently, a-quartz has two equally valid global minima where the structures are mirror images of each other (enantiomers). 

So far the emphasis has been on solving the crystal structure from the knowledge of the unit cell and ionic content. The motivation for this work is to provide an automated procedure to help determine or solve the crystal structure of new compounds that are synthesised in a powder form. Of course the methods developed can generate other structural topologies and perhaps a new, yet to be synthesised, crystal structure. However, the task has been to solve a particular structure and so one might extract more information from the experimental data to aid the prediction process (e.g. use of symmetry elements). Thus, the number of unwanted possible (meta)stable structures, or polymorphs, that could be generated may be reduced. In this section, the emphasis is on finding all the important polymorphs for a particular chemical formula. 

The next step in the prediction of metastable compounds consists in the exploration of this energy landscape. For T = 0 K, it is very clear what constitutes a (meta)stable structure It is the one, and only one, configuration that is associated Avith a local minimum of the energy hypersurface. Thus, for T = 0 K our task is to determine all local minima of the energy landscape. In contrast, for T > 0 K, equili-... 

Figure 36 Different (meta-)stable structures and transition states for the formaldehyde molecule, COH2. Reproduced with permission of American Chemical Society from 138...

There are various morphologies of latex particles available these include core-shell and other complex morphologies within the latex particles, and also hollow latex particles. The traditional route to hollow latex particles is the production of core-shell latexes whore the inno core of the latex particles can be removed in a post-polymerization process [8]. These hoUow latex particles have a varied of uses in surface coatings, controlled release tedmologies and as opacifiers. Recently a new approach to the production of hollow latex particles has been developed [9]. In tiiis approach a surfactant structure is stabilized by the polymerization of a vinyl monomer via free radicals in the walls of the vesicles. A vesicle, which is usually a meta-stable structure is converted into a hollow latex particle . This process, while not strictly an emulsion polymerization, has been optimized by use of emulsion polymerization procedures [10]. In the future it is possible that many other unique surfactant structures may be maintained by the in situ introduction of polymer. 

The structures shown for ions, such as in Equations 7 and 8, are entirely speculative since the mass spectrum gives only relative abundance of the various m/e-groups formed. Chemical reasoning, meta-stable-ion peaks, peak shifts in the deuterated analogs, and published mass spectra of similar compounds are the bases for the proposed modes of fragmentation and for the postulated structures.)... 

In the case of lithium orthoniobate, Li3Nb04, no meta-stable phase was found that had a rock-salt crystal structure with disordered cation distribution [268]. Nevertheless, solid solutions Li2+xTii-4xNb3x03, where 0 < x < 0.22, have a monoclinic structure at low temperatures and undergo transformation to a disordered NaCl type structure at high temperatures [274]. 

From Fig. 4.49(d) and the last row of Table 4.32 one can see that the quadruply hyperbonded [PtFg]2- dianion is indeed a (meta)stable local equilibrium species, formally of 20e count at the metal atom. Owing to highly unfavorable anion-anion repulsion, the binding of F to [PtF ]- is endothermic, but this species is nevertheless atrue local equilibrium structure (Rptp = 2.04 A, all positive frequencies) of Oh... 

Another important outcome of these CVD experiments is the possibility to synthesize meta-stable phases as transparent films, like HAIO. The subsequent local treatment with different energy beams allows the structural patterning of the meta-stable layers to create chemical landscapes, which have the characteristics to consist of physically and chemically different regions of the surface (A1 AI2O3 parts in a HAIO matrix). These patterns can in principal be reduced to nanometer scales, opening a large field of applications. 

Note that y phase does not exist as a stable phase at the present temperature and pressure. In other words, if y phase is seen in the structure, then the system is not in die equilibrium, but a meta-stable, non-equilibrium state. However, if the thermodynamic state of the system is changed (e.g., different temperature or pressure), y phase may exist as a stable phase in a certain composition range ... 

TCP, Ca3(PC>4)2, exists in two crystal forms, viz. a-TCP and p-TCP. Both forms can only be prepared by calcination at high temperature (>800 °C).70 a-TCP is meta stable at room temperature and is more soluble than p-TCP in water. The crystal structure of a-TCP shows that there are 16 inequivalent phosphorus sites.110 Its 31P MAS spectrum contains only 14 peaks, where the chemical shifts range from —3 to 5 ppm.111 Although there are only three crystallographically inequivalent phosphorus sites for (3-TCP,112,113 there are as many as 16 resolved peaks in the 31P MAS spectrum because of the presence of some calcium vacancies.114 The 31P chemical shifts of (S-TCP are in the same range as reported for a-TCP, but the overall patterns of their 31P MAS spectra are quite different. In addition, it has also been found that even a minor substitution of Ca2+ by Na+, Mg21 or Zn2+ ions will perturb the 31P MAS spectrum, revealing the substantial effect of the counter ions near the phosphorus sites.114,115... 

In addition to a library computer search for matching spectra, the usual procedure for interpretation of a mass spectrum involves (1) identification of the molecular ion peak and, if possible, determination of the elemental composition of the molecule based on the observed mass number (m/z) for the molecular ion, (2) establishment of the fragmentation patterns of the molecular ion, and finally (3) reduction of the number of possible structures for the compound, based on the interrelationships of the observed fragmentation patterns. The absence of meta-stable ions mass spectra obtained by GC-MS analysis makes (2) very difficult to achieve. 

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