Allotropic phase transition

Since the vibrational spectra of sulfur allotropes are characteristic for their molecular and crystalline structure, vibrational spectroscopy has become a valuable tool in structural studies besides X-ray diffraction techniques. In particular, Raman spectroscopy on sulfur samples at high pressures is much easier to perform than IR spectroscopical studies due to technical demands (e.g., throughput of the IR beam, spectral range in the far-infrared). On the other hand, application of laser radiation for exciting the Raman spectrum may cause photo-induced structural changes. High-pressure phase transitions and structures of elemental sulfur at high pressures were already discussed in [1]. 

The Nobel prize in Chemistry for the year 1996 was awarded for the discovery of the fullerenes, the third allotropic form of carbon, with Cgo and C70 as the two most prominent representatives. While the fullerenes of course are the epitome of carbon-rich molecular compounds, it is an irony that their synthesis is more of a physical phase transition, taking place under drastic conditions [1]. 

Metallic tin has many allotropic forms rhombic white tin (also called /3-tin) is stable at temperatures above 13 °C, whereas the stable form at lower temperatures is cubic grey tin (also called a-tin). A transition such as tin(white) tin ey) is called a solid-state phase transition. 

There has been much controversy over the structure of jS-sulfur, and the question of whether it is a true allotrope. It has been suggested that it constitutes merely a thermally distorted lattice expansion of orthorhombic sulfur. Furthermore, phase transition, at 101°C, has been described by various authors (S2), but it has been shown that this eJffect was due to traces of water in the lattice (65). However, recently a true anomaly in the heat capacity has been found (7i) at —75°C. 

Above 95°C, rhombic sulfur is less stable than monoclinic sulfur (mp 119°C), an allotrope in which the cyclic S8 molecules pack differently in the crystal. The phase transition from rhombic to monoclinic sulfur is very slow, however, and rhombic sulfur simply melts at 113°C when heated at an ordinary rate. 

This shows that the main phases at 450 °C and 500 °C are pure anatase, but the calcinations temperature higher Aan 500 °C, die rutile phase begined to appear and major phase of rutile appeared on the calcinations temperature at 750 °C. The increase of firing temperature above 500 °C results in the phase transition from anatase to rutile. This is already reported in previous literature [3, 5]. The anatase phase is die more photocatalytically active allotropic form of Ti02. 

In the work reported in this chapter, oriented pyrolytic graphite was shock-loaded at pressures up to 15 GPa perpendicular or parallel to the basal plane of the graphite. The phase transitions of graphite to other carbon allotropes will be discussed using nanostructural data obtained by high-resolution electron microscopy (HREM). 

Consider a material that undergoes a first order phase transition such as fusion, vaporization, allotropic transformation, and the like. In each case two phases remain in equilibrium at a fixed temperature while heat flows in or out of the system during the transition. The theoretical background for characterizing this process will be provided in Chapter 2. 

This table gives the phase transition temperatures for the elements that can exist in two or more crystalline forms (allotropes). The crystal phases are labeled by Greek letters in the most common conventions, although some variation is found. All data refer to normal atmospheric pressure. 

Elemental antimony under normal conditions has a structure of A7 and at 8.5-12 GPa transforms into a modification with a complex atomic lattice (Sb-II) [20], which at 28 GPa converts to a bcc structure. The heavier analogue Bi has the same phase transitions as Sb, at generally lower pressures Bi-I (A7 structure) transforms at 2.5 GPa to a strongly distorted sc structure (Bi-II). Already at 2.8 GPa there occurs a structural reorganization into the Bi-III phase, which has an incommensurate crystal structure with Nc 9. This arrangement is very similar to that found for high-pressure allotropes of As and Sb. Upon further compression, up to P > 8 GPa, bismuth transforms to a bcc solid [20]. 

Solid nitrogen exhibits two allotropes with a phase transition occurring at 36.15 K (-237 C). 

We also recall here that the reference state of the Gibbs energies of formation was not always stated by the authors in their experimental results. It was thus impossible for the reviewers to define the reference state when a phase transition (allotropic transformation or melting) of one component occurred in the investigated temperature range. 

A phase transition occurs when a pure component changes from one phase to another. Table 6.1 lists the different types of phase transitions, most of which should already be familiar to you. There are also phase transitions between different solid forms of a chemical component, which is a characteristic called polymorphism. For example, elemental carbon exists as graphite or diamond, and the conditions for phase transitions between the two forms are well known. Solid H2O can actually exist as at least six structurally different solids, depending on the temperature and pressure. We say that water has at least six polymorphs. (In application to elements, we use the word allotrope instead of polymorph. Graphite and diamond are two allotropes of the element carbon.) In mineral form, calcium carbonate exists either as aragonite or calcite, depending on the crystalline form of the solid. 

The underlying issue (as to whether ozone and oxygen are or are not allotropes or polymorphs) seems to be the question how to situate various physico-chemical (phase) transitions relative to chemical transformations on the one hand and physical transitions on the other. 

Figure 5.3 shows the phase diagram of tin, and clearly shows the transition from tin(white) to tin(grey). Unfortunately, the tin allotropes have very different densities p, so p(tm, grey) = 5.8 gem-3 but p(tm, white) = 7.3 g cm-3. The difference in p during the transition from white to grey tin causes such an unbearable mechanical stress that the metal often cracks and turns to dust - a phenomenon sometimes called tin disease or tin pest . 

In the case of the graphite-to-diamond transformation, thermodynamic results predict that graphite is the stable allotrope at a fixed temperature at all pressures below the transition pressure and that diamond is the stable aUotrope at all pressures above the transition pressure. But diamond is not converted to graphite at low pressures for kinetic reasons. Similarly, at conditions at which diamond is the thermodynamically stable phase, diamond can be obtained from graphite only in a narrow temperature range just below the transition temperature, and then only with a catalyst or at a pressure sufficiently high that the transition temperature is about 2000 K. 

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