Polymorphism and Allotropy

Some metals, as well as nonmetals, may have more than one crystal structure, a polymorphism phenomenon known as polymorphism. When found in elemental solids, the condi- 

Another common metal that experiences an al-lotropic change is tin. White (or p) tin, having a body-centered tetragonal crystal structure at room temperature, transforms, at 13.2°C (55.8°F), to gray 

The rate at which this change takes place is extremely slow however, the lower the temperature (below 13.2°C) the faster the rate. Accompanying this white-to-gray-tin transformation is an increase in volmne (27%), and, accordingly, a decrease in density (from 7.30 g/cm to 5.77 g/cm ). Conseqnently, this volmne expansion results in the disintegration of the white tin metal into a coarse powder of the gray allotrope. For normal subambient temperatures, there is no need to worry about this disintegration process for tin products because of the very slow rate at which the transformation occurs. 

This white-to-gray tin transition produced some rather dramatic results in 1850 in Russia. The winter that year was particularly cold, and record low temperatures persisted for extended periods of time. The uniforms of some Russian soldiers had tin buttons, many of which crumbled because of these extreme cold conditions, as did also many of the tin church organ pipes. This problem came to be known as the tin disease. 

Specimen of white tin (left). Another specimen disintegrated upon transforming to gray tin (right) after it was cooled to and held at a temperature below 13.2°C for an extended period of time. 

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As well, the real behavior in the liquid and solid phase has an influence on the SLE behavior. In some cases one or more solid compounds are formed. At the same time miscibility gaps can appear. Furthermore, many substances occur in more than one crystalline form. This phenomenon is called polymorphism for compounds and allotropy in the case of elements. If the transition curve lies within the region of stable states the phenomenon is called enantiotropy. In the metastable region it is called monotropy. 

When an element can exist in more than one physical form in the same state it is said to exhibit allotropy (or polymorphism). Each of the different physical forms is called an allotrope. Allotropy is actually quite a common feature of the elements the Periodic Table (p. 136). Some examples of elements which show allotropy are sulfur, tin, iron and carbon. 

Polymorphism is the existence of more than one crystalline form of the same chemical substance. If there are only two forms, the phenomenon is dimorphism if the materials are elements, it is allotropy if the forms differ by solvent of crystallization, they are called pseudopolymorphs. Different polymorphs have different relative stabilities, but these may be varied by changing temperature, pressure, and other conditions. 

Univariant Systems.—Equilibrium between liquid and vapour. Vaporisation curve. Upper limit of vaporisation curve. Theorems of van t Hoff and of Le Chatelier. The Clausius-Clapeyron equation. Presence of complex molecules. Equilibrium between solid and vapour. Sublimation curve. Equilibrium between solid and liquid. Curve of fusion. Equilibrium between solid, liquid, and vapour. The triple point. Complexity of the solid state. Theory of allotropy. Bivariant systems. Changes at the triple point. Polymorphism. Triple point Sj—Sg— V. Transition point. Transition curve. Enantiotropy and monotropy. Enantiotropy combined with monotropy. Suspended transformation. Metastable equilibria. Pressure-temperature relations between stable and metastable forms. Velocity of transformation of metastable systems. Metastability in metals produced by mechanical stress. Law of successive reactions. 

The allotropy was discussed above, in the crystal structure section, 3.2. The polymorphic forms and the various transformation temperatures of the lanthanide metals are summarized in fig. 4. The behavior of scandium and yttrium are similar to those of the middle-heavy lanthanides having a room-temperature hep phase and a high-temperature bcc form. 

The difference and the similarity between allotropy and polymorphism can be illustrated by considering sulfur. The rhombic and monoclinic crystalline forms both consist of puckered Ss rings, and these two modifications can interconvert by heating and cooling. It is tempting to call this relationship crystal allotropy, but the correct term is polymorphism because both structures involve the same compound (i.e., atomic connectivity). When heated to above 160 °C, the Ss rings open by means of a free radical reaction to form polymeric chains. In contrast to crystal allotropy, the relationship between the polymeric chains and the Sg rings can be termed chemical allotropy. However, since polymorphism is the preferred term for crystal allotropy, chemical allotropy can be shortened to allotropy. 

Allotropy is one form of polymorphism, but polymorphism also covers noncrystalline forms. Each polymorphic form of a substance is stable within a range of physical conditions (temperature, pressure) and will transform to another polymorphic form at a fixed transition temperature. 

The principal business of this chapter is to establish the thermodynamic relations obeyed by two or more phases that are at equilibrium with each other. A phase is a portion of a system (or an entire system) inside which intensive properties do not change abruptly as a function of position. The principal kinds of phases are solids, liquids, and gases, although plasmas (ionized gases), liquid crystals, and glasses are sometimes considered to be separate types of phases. Solid and liquid phases are called condensed phases and a gas phase is often called a vapor phase. Several elements such as carbon exhibit solid-phase allotropy. That is, there is more than one kind of solid phase of the element. For example, diamond and graphite are both solid carbon, but have different crystal structures and different physical properties. With compounds, this phenomenon is called polymorphism instead of allotropy. Most pure substances have only one liquid phase, but helium exhibits allotropy in the liquid phase. 

Si3N4 (silicon nitride) is also produced synthetically. It exhibits allotropy. The lower-temperature a form and the higher-temperature P form are the two polymorphic forms of Si3N4. When the a form transforms to the P form, the crystals are elongated. The following routes are used for the production of silicon nitride ... 

Polymorphism is the ability of a solid material to exist in more than one form or crystal lattice structure and can potentially be found in any crystalline material, including polymers and metals, and is related to allotropy, which refers to packing variations in elemental sohds. (For example, both graphite and diamond are aUotropes of carbon.) Together with polymorphism, the complete morphology of a material is described by other variables, such as crystal habit, amorphous fraction or crystallographic defects. 

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