Allotropic solids

Three-Phase Transformations in Binary Systems. Although this chapter focuses on the equilibrium between phases in binary component systems, we have already seen that in the case of a entectic point, phase transformations that occur over minute temperature fluctuations can be represented on phase diagrams as well. These transformations are known as three-phase transformations, becanse they involve three distinct phases that coexist at the transformation temperature. Then-characteristic shapes as they occnr in binary component phase diagrams are summarized in Table 2.3. Here, the Greek letters a, f), y, and so on, designate solid phases, and L designates the liquid phase. Subscripts differentiate between immiscible phases of different compositions. For example, Lj and Ljj are immiscible liquids, and a and a are allotropic solid phases (different crystal structures). 

Several comments need to be made concerning the state of aggregation of the substances. For gases, the standard state is the ideal gas at a pressure of 1 bar this definition is consistent with the standard state developed in Chapter 7. When a substance may exist in two allotropic solid states, one state must be chosen as the standard state for example, graphite is usually chosen as the standard form of carbon, rather than diamond. If the chemical reaction takes place in a solution, there is no added complication when the standard state of the components of the solution can be taken as the pure components, because the change of enthalpy on the formation of a compound in its standard state is identical whether we are concerned with the pure... 

A renowned laboratory reports quadmple-point coordinates of 10.2 Mbar and 297.25 K (24.1°C) for four-pltase equilibrium of allotropic solid forms of the exotic chemical 6-miasmone. Evaluate tire claim. 

Detailed calorimetric data have been reported for M2Cli0 and AMC16 (A = Rb, Cs).417 Enthalpy contents and molar heat capacities were measured as functions of temperature. The ionic compounds underwent allotropic solid-solid transformations. 

Applications of the Foregoing Principles to the Transformation of Allotropic Solids. 

These allotropic solids can be classified into three major categories (i) the sp structures which include graphite, the graphitic materials, amorphous carbon, and other carbon materials (all reviewed in Ch. 3), (ii) the sp structures which include diamond and lonsdaleite (a form detected in meteorites), reviewed in Ch. 11, and (iii) he Fullerenes (see Ch. 15). 

Many substances exist in two or more solid allotropic fomis. At 0 K, the themiodynamically stable fomi is of course the one of lowest energy, but in many cases it is possible to make themiodynamic measurements on another (metastable) fomi down to very low temperatures. Using the measured entropy of transition at equilibrium, the measured heat capacities of both fomis and equation (A2.1.73) to extrapolate to 0 K, one can obtain the entropy of transition at 0 K. Within experimental... 

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. 

Phosphorus exists in four or more allotropic forms white (or yellow), red, and black (or violet). Ordinary phosphorus is a waxy white solid when pure it is colorless and transparent. White phosphorus has two modifications alpha and beta with a transition temperature at -3.8oC. 

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. 

A has three solid allotropic forms with change temperatures of 800°C and 1150°C and melts at 1980°C. These form solid solutions a, P and /containing B, a being the low-temperature one. 

Phosphorus exists as white and red phosphorus. The former allotrope may be preserved in the dark at low temperatures but otherwise reverts to the more stable red form. The white form is a waxy, translucent, crystalline, highly-toxic solid subliming at room temperature and inflaming in air at 35°C, so it is handled under water. The red form is a reddish violet crystalline solid which vaporizes if heated at atmospheric pressure and condenses to give white phosphorus. The red form ignites in air at 260°C. Both are insoluble in water, and white phosphorus can be stored beneath it. Phosphorus forms a host of compounds such as phosphine, tri- and penta-halides, tri-, tetra- and penta-oxides, oxyacids including hypophosphorous, orthophosphorous and orthophosphoric acids. 

Solid polycflt nwsulfur comes in many forms it is present in rubbery S, plastic (x)S, lamina S, fibrous (j4r,ip polymeric (/c) and insoluble (cu)S, supersublimation S, white S and the commercial product Crystex. All these are metaslable mixtures of allotropes containing more or less... 

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. 

Solid allotropes may differ from one another in their bonding patterns (recall Figure 9.11, page 241). White tin, the stable form of solid tin at 25°C, shows metallic bonding... 

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 ... 

The substance indicated by the same symbol in two or more equations is in exactly the same state in the reactions represented by those equations. In particular, the different allotropic modifications of a solid element (e.g., charcoal, graphite, diamond or yellow and red phosphorus) have different heats of combustion, and the particular form used must be specified in every case. 

Abnormally low atomic heats were explained by Richarz on the assumption of a diminution of freedom of oscillation consequent on a closer approximation of the atoms, which may even give rise to the formation of complexes. This is in agreement with the small atomic volume of such elements, and with the increase of atomic heat with rise of temperature to a limiting value 6 4, and the effect of propinquity is seen in the fact that the molecular heat of a solid compound is usually slightly less than the sum of the atomic heats of the elements, and the increase of specific heat with the specific volume when an element exists in different allotropic forms. 

Solid carbon exists as graphite, diamond, and other phases such as the fullerenes, which have structures related to that of graphite. Graphite is the thermodynamically most stable of these allotropes under ordinary conditions. In this section, we see how the properties of the different allotropes of carbon are related to differences in bonding. 

We can understand the differences in properties between the carbon allotropes by comparing their structures. Graphite consists of planar sheets of sp2 hybridized carbon atoms in a hexagonal network (Fig. 14.29). Electrons are free to move from one carbon atom to another through a delocalized Tr-network formed by the overlap of unhybridized p-orbitals on each carbon atom. This network spreads across the entire plane. Because of the electron delocalization, graphite is a black, lustrous, electrically conducting solid indeed, graphite is used as an electrical conductor in industry and as electrodes in electrochemical cells and batteries. Its... 

Calcium is miscible with Sr in the liquid and in all the solid bcc, hep and fee allotropic forms (Fig. 1). Barium exhibits no hep or fee forms, however, so that solid solubility between the close-packed structures of Ca and Sr, and the bcc structure of Ba is restricted in the Ca-Ba and also in the Sr-Ba systems. A continuous series of solid solutions is only achieved in Ca-Ba and Sr-Ba for the high-T bcc modifications. In Ca-Ba, the solid solutions are separated by a narrow heterogeneous field between 32 and 36 mol% Ba in Sr-Ba this occurs between 24 and 30 mol% Ba (Fig. 1). 

Molecular Spectra of Sulfur Molecules and Solid Sulfur Allotropes... 

Abstract Molecular spectroscopy is one of the most important means to characterize the various species in solid, hquid and gaseous elemental sulfur. In this chapter the vibrational, UV-Vis and mass spectra of sulfur molecules with between 2 and 20 atoms are critically reviewed together with the spectra of liquid sulfur and of solid allotropes including polymeric and high-pressure phases. In particular, low temperature Raman spectroscopy is a suitable technique to identify single species in mixtures. In mass spectra cluster cations with up to 56 atoms have been observed but fragmentation processes cause serious difficulties. The UV-Vis spectra of S4 are reassigned. The modern XANES spectroscopy has just started to be applied to sulfur allotropes and other sulfur compounds. 

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