Allotropic elements

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) ... 

It was therefore appropriate that the first attempt to produce lattice stabilities for non-allotropic elements dealt with Cu, Ag and Zn (Kaufman 1959b). It is also significant that, because of the unfamiliarity of the lattice stability concept, this paper did not appear as a mainstream publication although the work on Ti and Zr (Kaufman 1959a) was published virtually at the same time. It was also realised that Ae reliability of metastable melting points derived by extrapolation were best... 

We don t normally think of elemental carbon as an organic compound. Historically, carbon was known to exist as three allotropes (elemental forms with different properties) amorphous carbon, diamond, and graphite. 

Cyclosulfanes (Elemental Sulfur Allotropes). Elemental sulfur displays a great propensity for catenation and polysnlfhr rings (cyclosulfanes) of various ring sizes (13-22) are known as allotropic forms of elemental sulfur. ... 

Elements along a rough diagonal from boron to polonium are intermediate in behavior, in some cases having both metallic and nonmetallic allotropes (elemental forms) these elements are designated as metalloids or semimetals. As described in Chapter 7, some elements, such as silicon and germanium, are capable of having their conductivity finely tuned by the addition of small amounts of impurities and are consequently of enormous importance in the manufacture of semiconductors in the computer industry. 

Allotropic elements have other ways of being arranged. 

Allotropes are different forms of the same element. Different bonding arrangements between atoms result in different structures with different chemical and physical properties. Allotropes occur only with certain elements, in Groups 13 through 16 in the Periodic Table. This distribution of allotropic elements is illustrated in Figure 1. 

Boron (B), the second hardest element, is the only allotropic element in Group 13. It is second only to carbon (C) in its ability to form element-element bonded networks. Thus, in addition to amorphous boron, several different allotropes of boron are known, of which three are well characterized. These are red crystalline a-rhombohedral boron, black crystalline /3-rhombohedral boron (the most thermodynamically stable allotrope), and black crystalline /3-tetragonal boron. All are polymeric and are based on various modes of condensation of the Bj2 icosahedron (Figure 2). 

Strategy To calculate the standard fi ee-energy change of a reaction, we look up the standard free energies of formation of reactants and products in Appendix 2 and apply Equation (18.12). Note that all the stoichiometric coefficients have no units so AG°xn is expressed in units of kJ/mol, and AGf for O2 is zero because it is the stable allotropic element at 1 atm and 25°C. 

Arsenic and antimony resemble phosphorus in having several allotropic modifications. Both have an unstable yellow allotrope. These allotropes can be obtained by rapid condensation of the vapours which presumably, like phosphorus vapour, contain AS4 and Sb4 molecules respectively. No such yellow allotrope is known for bismuth. The ordinary form of arsenic, stable at room temperature, is a grey metallic-looking brittle solid which has some power to conduct. Under ordinary conditions antimony and bismuth are silvery white and reddish white metallic elements respectively. 

In 1824 Berzelius, generally credited with the discovery, prepared amorphous silicon by the same general method and purified the product by removing the fluosilicates by repeated washings. Deville in 1854 first prepared crystalline silicon, the second allotropic form of the element. 

Sulfur is pale yellow, odorless, brittle solid, which is insoluble in water but soluble in carbon disulfide. In every state, whether gas, liquid or solid, elemental sulfur occurs in more than one allotropic form or modification these present a confusing multitude of forms whose relations are not yet fully understood. 

Ytterbium has a bright silvery luster, is soft, malleable, and quite ductile. While the element is fairly stable, it should be kept in closed containers to protect it from air and moisture. Ytterbium is readily attacked and dissolved by dilute and concentrated mineral acids and reacts slowly with water. Ytterbium has three allotropic forms with transformation points at -13oC and 795oC. The beta form is a room-temperature, face-centered, cubic modification, while the... 

AUotropes. Systematic names for gaseous and liquid modifications of elements are sometimes needed. Allotropic modifications of an element bear the name of the atom together with the descriptor to specify the modification. The following are a few common examples ... 

Upon solidification of molten sulfur, Stt rapidly changes into S]l, which is converted into SL, although at a much slower rate. The molecular stmcture of Stt is that of an octatomic sulfur chain (1,2). The symbol S]1 designates long, polymerized chains of elemental sulfur. SX is perhaps the most characteristic molecular form of sulfur, namely, that of a crown-shaped, octatomic sulfur ring designated in more recent Hterature as (3). The allotropes have different solubiUty in carbon disulfide. Stt and SX are soluble in carbon disulfide, whereas S]1 does not dissolve in this solvent. 

Despite many publications on carbynes, their existence has not been universally accepted and the literature has been characterised by conflicting claims and counter claims [e.g., 27-29]. This is particularly tme of meteoritic carbynes. An interesting account of die nature of elemental carbon in interstellar dust (including diamond, graphite and carbynes) was given by Pillinger [30]. Reitmeijer [31] has re-interpreted carbyne diffraction data and has concluded that carbynes could be stratified or mixed layer carbons with variable heteroelement content (H,0,N) rather than a pure carbon allotrope. 

Boron is unique among the elements in the structural complexity of its allotropic modifications this reflects the variety of ways in which boron seeks to solve the problem of having fewer electrons than atomic orbitals available for bonding. Elements in this situation usually adopt metallic bonding, but the small size and high ionization energies of B (p. 222) result in covalent rather than metallic bonding. The structural unit which dominates the various allotropes of B is the B 2 icosahedron (Fig. 6.1), and this also occurs in several metal boride structures and in certain boron hydride derivatives. Because of the fivefold rotation symmetry at the individual B atoms, the B)2 icosahedra pack rather inefficiently and there... 

In the solid state all three elements have typically metallic structures. Technetium and Re are isostructural with hep lattices, but there are 4 allotropes of Mn of which the o-fomi is the one stable at room temperature. This has a bcc structure in which, for reasons which are not clear, there are 4 distinct types of Mn atom. It is hard and brittle, and noticeably less refractory than its predecessors in the first transition series. 

The element phosphorus forms a variety of allotropic forms in the solid state. In the chemistry stockroom, you are likely to find red phosphorus and possibly white phosphorus (Figure B). As you can see, white phosphorus has the molecular formula P4, whereas red phosphorus might be represented as Px, where x is a very large number. The difference in properties between the two allotropes reflects the difference in their bonding patterns, molecular versus network covalent ... 

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