Allotropes defined

Carbon nanotubes (CNTs) as well as fullerenes are splendid gift brought to the Earth from the red giant carbon stars in the long-distant universe through the spectroscopy. Moreover, those belong to new carbon allotropes of the mesoscopic scale with well-defined structures. In particular, CNTs are considered to be the materials appropriate to realise intriguing characteristics related to the mesoscopic system based on their size and physicochemical properties. 

The state of research on the two classes of acetylenic compounds described in this article, the cyclo[ ]carbons and tetraethynylethene derivatives, differs drastically. The synthesis of bulk quantities of a cyclocarbon remains a fascinating challenge in view of the expected instability of these compounds. These compounds would represent a fourth allotropic form of carbon, in addition to diamond, graphite, and the fullerenes. The full spectral characterization of macroscopic quantities of cyclo-C should provide a unique experimental calibration for the power of theoretical predictions dealing with the electronic and structural properties of conjugated n-chromophores of substantial size and number of heavy atoms. We believe that access to bulk cyclocarbon quantities will eventually be accomplished by controlled thermal or photochemical cycloreversion reactions of structurally defined, stable precursor molecules similar to those described in this review. 

The heat of transformation is defined as the change in enthalpy that results when one mole of a substance undergoes a specific change of state such as melting, evaporation, or allotropic modification. 

Allotropes are defined as different forms of the same element in the same physical state. Two examples of allotropes are ... 

In Section II, the structures of fourteen well-defined allotropes have been described. About forty other allotropes have been reported, but for these structural data are incomplete or contradictory. The reason for this varies. Some allotropes, such as r-sulfur that forms only in 2 out of 5000 experiments (29), are hard to prepare or are unstable. Others, such as w-sulfur are easy to prepare and reasonably stable, but X-ray data are contradictory and have led to much confusion and controversy. 

In addition to the melting point of the P phase and the a/P allotropic transfonnation temperature in Fig. 6.1(b), there is a fluther intersection between the Gibbs energy of a and liquid phases. This corresponds to the metastable melting point of the a phase. A linear model will then dictate that the entropy of melting for a is defined by the entropies of melting and transformation at the two other critical points (Ardell 1963),... 

The fee unit cell can be thought of as having holes in which other atoms or ions can be placed. For example, the Na + ions occupy octahedral holes in the fee CF lattice (connecting the six CF ions surrounding a Na+ by lines defines an octahedron). The fee lattice also has tetrahedral holes if we divide the unit cell into 8 smaller cubes, the centers of these little cubes are surrounded by 4 lattice points which define a tetrahedron. The diamond allotropic form of carbon has a fee structure with C atoms in 4 of these tetrahedral sites each C atom is surrounded by (covalently bound to) 4 other C s. 

It is defined as that temperature at which one allotropic form of a substance is converted into another allotropic form of the same substance. The point where this change occurs is called the transition point. 

Based on the extension by the repetition of three kinds of C-C bonds to infinite molecules, we may define carbon families, consisting of diamond, graphite, fullerenes, and carbynes [1], In each family, the structure shows characteristic diversities representative structures are listed in Figure 2.2. The detailed diversity in structure will be explained in the following sections for each family. Most structures in each family are thermodynamically metastable, and the family is represented by the allotrope name. In Figure 2.2, some possibilities to accept foreign species are also illustrated. 

The two allotropcs of carbon with particularly well defined properties are hexagonal graphite, as thermodynamically stable modification at ambient conditions, and its high-pressure, high-temperature allotrope. cubic diamond. Although both wcll-cryslalliscd forms with only very rarely be encountered in catalytic systems, it is important to recall some details about their prop-... 

Key terms are defined in the Glossary, allotrope (5.1) electron sharing (5.5) nonoctet structure (5.5)... 

Allotropic modifications of an element bear the name of the atom from which they are derived, together with a descriptor to specify the modification. Common descriptors are Greek letters (a, (3, y, etc.), colours and, where appropriate, mineral names (e.g. graphite and diamond for the well known forms of carbon). Such names should be regarded as provisional, to be used only until structures have been established, after which a rational system based on molecular formula (see Section IR-3.4.3) or crystal structure (see Section IR-3.4.4) is recommended. Common names will continue to be used for amorphous modifications of an element and for those which are mixtures of closely related structures in their commonly occurring forms (such as graphite) or have an ill-defined disordered structure (such as red phosphoms) (see Section IR-3.4.5). 

An allotrope of a chemical element is defined as a solid phase (of the pure element) which differs by its crystal structure and therefore by its X-ray diffraction pattern from the other allotropes of that element. This definition can be extended to microcrystalline and amorphous phases which may be characterized either by their diffraction pattern or by suitable molecular spectra. 

In the following, we present a summary of the structures of the three solid allotropes of polymeric sulfur at STP conditions which have been studied so far. Doubtful forms, not verified up to now, will be omitted here. Although several authors are claiming crystalhne structures in the case of certain polymeric allotropes it seems hkely that in these solids regions with well defined ordered structures and regions with amorphous structures co-exist. This has clearly been shown by more or less sharp diffraction patterns in X-ray studies of different samples depending on the method of preparation. 

The Saturated Solution.—From what has been said above, it will be seen that the condition of saturation of a solution can be defined only with respect to a certain solid phase if no solid is present, the system is undefined, for it then consists of only two phases, and is therefore bivariant. Under such circumstances not only can there be at one given temperature solutions of different concentration, all containing less of one of the components than when that component is present in the solid form, but there can also exist solutions containing more of that component than corresponds to the equilibrium when the solid is present. In the former case the solutions are unsaturated, in the latter case they are supersaturated with respect to a certain solid phase in themselves, the solutions are stable, and are neither unsaturated nor supersaturated. Further, if the solid substance can exist in different allotropic modifications, the particular form of the substance which is in equilibrium with the solution must be known, in order that the statement of the solubility may be definite for each... 

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