Crystal structure stability

Zircon, complete solid-solution behavior is observed, and a plot of the unit cell volume against x shows that Vdgard s Law is followed. When the end members are not is structural, a systematic change in the solubility range in both structures is found as A is varied, and the data have been systematized in terms of a simple, potentially predictive, structure-field map. The pervasive polymorphism of these ABO4 compounds, involving both reconstructive and displacive transformations and metastable structures produced by different sample preparation methods, indicates that the crystal structural stability of substituted compounds needs to be carefully evaluated as a function of temperature to assess the structural integrity of waste-form materials. 

Binary addition elements, having in general Face-Centered-Cubic (FCC) crystal structures, stabilize the a-hydride phase against the P-hydride phase transition, reducing the problem of embrittlement, and also increase hydrogen permeability above that of pure palladium (see Table 14.2). 

The mean value of the bz is responsible for the fall (undercooling) or rise (overheating) of the of a surface and a nanosolid. The bz is also responsible for other thermally activated behavior such as phase transition, catalytic reactivity, crystal structural stability, alloy formation (segregation and diffusion), and stability of electrically charged particles (Coulomb explosion), as well as the crystal growth and atomic diffusion, atomic gliding displacement that determine the ductility of nanosolids. 

The induction energy is inlierently non-additive. In fact, the non-additivity is displayed elegantly in a distributed polarizability approach [28]. Non-additive induction energies have been found to stabilize what appear to be highly improbable crystal structures of the alkalme earth halides [57]. 

Only the bisected conformation aligns the cyclopropyl C—C orbitals for effective overlap. Crystal structure determinations on two cyclopropylmethyl cabons with additional stabilizing substituents, C and D, have confirmed file preference for the bisected geometry. The crystal structures of C and D are shown in Fig. 5.8. 

X-r crystal structure determinations have been completed on two salts containing bicyclo[2.2.1]heptyl cations (Fig. 5.12). Both are more stable than the 2-norbomyl cation itself 18 is tertiary whereas 19 contains a stabilizing methoxy group. The crystal structure of 18 shows an extremely long (1.74 A) C—C bond between C-1 and C-6. The C(1)—C(2) bond is shortened to 1.44 A. The distance between C-2 and C-6 is shortened from 2.5 A in norbomane to 2.09 AThese structural changes can be depicted as a partially bridged structure. 

The syn isomer can achieve a conjugated system with angles of up to 35° between adjacent p orbitals. The anti isomer is much more twisted. An X-ray crystal structure of the syn isomer shows C—C bond lengths between 1.368 and 1.418 A for the conjugated system (Fig. 9.3). ° The spectroscopic properties of the syn isomer are consistent with considering it to be a delocalized annulene. B3LYP calculations indicate that both the syn and anti structures are stabilized by delocalization, the syn (17.6kcal/mol) more so than the anti (8.1 kcal). ... 

The crystal structure of the potassium salt of 1,3,5,7-tetramethylcyclootatetraene dianion has been determined by X-ray dififaction. ° The eight-membered ring is planar, with aromatic C—C bond lengths of about 1.41 A without significant alternation. The spectroscopic and structural studies lead to the conclusion that the cyclooctatetraene dianion is a stabilized delocalized structure. 

The materials shown and described above were generally prepared from the nucleophilic phenoxide or alkoxide and the appropriate bromide. The syntheses of a variety of such compounds were detailed in a report which appeared in 1977. In the same report, complex stability and complexation kinetics are reported. Other, detailed studies, of a similar nature have recently appeared" . Vogtle and his collaborators have also demonstrated that solid complexes can be formed even from simple polyethylene glycol ethers . Crystal structures of such species are also available... 

P Fluonnation always strongly stabilizes carbamons both by induction and by negative (anionic) hyperconjugaQon, 7 The latter "no-bond resonance has been controversial, but its importance is now well established both theoretically [133, 134] and expenmentally [67] The X-ray crystal structures of salts 8 [fi5] and 9 [136] provide cogent evidence for negative hyperconjugation... 

The binary oxides and hydroxides of Ga, In and T1 have been much less extensively studied. The Ga system is somewhat similar to the Al system and a diagram summarizing the transformations in the systems is in Fig. 7.13. In general the a- and y-series have the same structure as their Al counterparts. )3-Ga203 is the most stable crystalline modification (mp 1740°) it has a unique crystal structure with the oxide ions in distorted ccp and Ga " in distorted tetrahedral and octahedral sites. The structure appears to owe its stability to these distortions and, because of the lower coordination of half the Ga ", the density is 10% less than for the a-(corundum-type) form. This preference of Ga "... 

Although Fc304 is an inverse spinel it will be recalled that Mn304 (pp. 1048-9) is normal. This contrast can be explained on the basis of crystal field stabilization. Manganese(II) and Fe" are both d ions and, when high-spin, have zero CFSE whether octahedral or tetrahedral. On the other hand, Mn" is a d and Fe" a d ion, both of which have greater CFSEs in the octahedral rather than the tetrahedral case. The preference of Mn" for the octahedral sites therefore favours the spinel structure, whereas the preference of Fe" for these octahedral sites favours the inverse structure. 

Generally the name of a compound should correspond to the most stable tautomer (76AHCS1, p. 5). This is often problematic when several tautomers have similar stabilities, but is a simple and reasonable rule whose violation could lead to naming phenol as cyclohexadienone. Different types of tautomerism use different types of nomenclature. For instance, in the case of annular tautomers both are named, e.g., 4(5)-methylimidazole, while for functional tautomerism, usually the name of an individual tautomer is used because to name all would be cumbersome. In the case of crystal structures, the name should reflect the tautomer actually found therefore, 3-nitropyrazole should be named as such (97JPOC637) and not as 3(5)-nitropyrazole. 

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