Crystal allotropy

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 in the solid state can also arise because of differences in crystal structure. For example, solid iron has a body-centered cubic structure (recall Figure 9.16, page 246) at room temperature. This changes to a face-centered structure upon heating to 910°C. 

A number of chemical elements, mainly oxygen and carbon but also others, such as tin, phosphorus, and sulfur, occur naturally in more than one form. The various forms differ from one another in their physical properties and also, less frequently, in some of their chemical properties. The characteristic of some elements to exist in two or more modifications is known as allotropy, and the different modifications of each element are known as its allotropes. The phenomenon of allotropy is generally attributed to dissimilarities in the way the component atoms bond to each other in each allotrope either variation in the number of atoms bonded to form a molecule, as in the allotropes oxygen and ozone, or to differences in the crystal structure of solids such as graphite and diamond, the allotropes of carbon. 

The allotropy of carbon is due to variations in the crystal structure of the element. There are three allotropes of carbon graphite, diamond, and... 

Another element that exhibits allotropy because of variations in the crystal structure is tin. The common allotrope is tin metal, also known as a alpha) tin, which is stable at ambient temperatures. The other allotrope, which generally occurs as a gray powder and is known as p beta) tin, but also as tin pest, is formed only at very low temperatures when tin cools down to temperatures below -18°C, the ordinary allotrope, a tin, is converted to p tin, and the transformation is irreversible under ordinary temperatures. Tin objects exposed to temperatures below -18°C in very cold regions of the world, for example, are generally severely damaged when part of the tin converts to tin pest. In extreme cases, when exposure to low temperatures extends for long periods of time, the allotropic conversion may result in the transformation of tin objects into heaps of gray p-tin powder. 

A table of crystal structures for the elements can be found in Table 1.11 (excluding the Lanthanide and Actinide series). Some elements can have multiple crystal structures, depending on temperature and pressure. This phenomenon is called allotropy and is very common in elemental metals (see Table 1.12). It is not unusual for close-packed crystals to transform from one stacking sequence to the other, simply through a shift in one of the layers of atoms. Other common allotropes include carbon (graphite at ambient conditions, diamond at high pressures and temperature), pure iron (BCC at room temperature, FCC at 912°C and back to BCC at 1394°C), and titanium (HCP to BCC at 882°C). 

Nucleation and Growth (Round 1). Phase transformations, such as the solidification of a solid from a liquid phase, or the transformation of one solid crystal form to another (remember allotropy ), are important for many industrial processes. We have investigated the thermodynamics that lead to phase stability and the establishment of equilibrium between phases in Chapter 2, but we now turn our attention toward determining what factors influence the rate at which transformations occur. In this section, we will simply look at the phase transformation kinetics from an overall rate standpoint. In Section 3.2.1, we will look at the fundamental principles involved in creating ordered, solid particles from a disordered, solid phase, termed crystallization or devitrification. 

Elemental sulfur exhibits complicated allotropy, that is, it exists in many modifications.4 The stable, prismatic crystal form at room temperature, a-S or orthorhombic sulfur, is built up of stacks of Ss rings (Section 3.4). If heated quickly, it melts at 112.8 °C. If it is heated slowly, however, it changes to needlelike crystals of /3-S or monoclinic sulfur, which is the stable form above 95.5 °C and which melts at 119 °C. Both 0-S and the yellow mobile melt (below 160 °C) are composed exclusively of Ss rings. Solids containing S7, Sg, S10, S12, and other rings are known, but all slowly revert to Sg below 160 °C. 

Sulphur, selenium and tellurium exhibit allotropy, and in certain of their crystalline forms the elements are isomorphous. As would be expected from the increased positive character of tellurium, the allotropy of this element is less well defined. In the liquid condition the elements arc miscible with one another and yield mixed crystals the ternary system, S— Sc—Tc, exhibits neither the formation of compounds nor ternary eutectics, but contains two zones of complete miscibility in which there exist mixed crystals of selenium and tellurium with sulphur, and of sulphur and tellurium with selenium.2... 

A review of the alleged allotropes of phosphorus reduces their number to four, namely, the a- and/3-forms of yellow phosphorus, red or violet phosphorus, and black phosphorus. Most of the work of various investigators has been directed towards elucidating the nature of red phosphorus, and of the transformation of yellow to red phosphorus and conversely. Red phosphorus was formerly considered to be amorphous, and it was often called amorphous phosphorus. The term amorphous, however, here referred more to the general appearance of the powder rather than to its minute structure. J. W. Retgers 5 showed that the particles of ordinary red phosphorus are rhombohedral crystals, which are well developed in those of W. Hittorf s violet phosphorus. All four varieties are therefore crystalline. J. W. Terwen has reviewed this subject in a general way and M. Copisarow discussed the theory of allotropy,... 

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. 

Between 98 and 122° -sulphur is stable. Its monoclinic crystals also contain 8-membered rings. The two modifications (with a range of stability and a definite transition temperature) are the best-known example of enantio-tropic allotropy ... 

Allotropy.—Dimorphism apart, a few substances are known to exist in more than one solid form. These varieties of the same substance exhibit different physical properties, while their chemical qualities are the same in kind. Such modifications are said to be allotropic. One or more allotropic modifications of a substance are usually crystalline, the other or others amorphous or vitreous. Sulfur, for example, exists not only in two dimor-j)hous varieties of crystals, but also in a third,. allotropic form, in which it is flexible, amorphous, and transparent. Carbon exists in three allotropic forms two crystalline, the diamond and graphite the third amorphous. 

Introduction.—The possibility of allotropy in vanadium metal at sub-ambient temperatures has been investigated by measuring the electrical resistivity in the [110] direction of a single crystal, the elastic constants, and by. Y-ray diffraction studies. The results were consistent with no allotropy. The information available on vanadium chemistry has been indexed and the organometallic chemistry of this element reported during 1971 has been reviewed. Dicyclopentadienylpentacarbonyldivanadium has been shown... 

Sulfur exhibits allotropy and its structure in all phases is quite complex. The common crystalline modification, rhombic sulfur, is in equilibrium with a triclinic modification above 96°C. Both have structures based on Sg-rings but the crystals are quite different. If molten sulfur is poured into water a dark red plastic form is obtained in a semielastic form. The structure appears to be a helical chain of S atoms. Selenium and tellurium both have a gray metal-like modification but sulfur does not have this form. 

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. 

Several elements exist in the form of two or more different substances. This phenomenon is called allotropy. Allotropic fonns may differ from each other in chemical bonding, molecular composition, or crystal structure. Only differences in bonding or molecular composition (primary allotropy) will be considered here. 

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 when a specific material can have more than one crystal structure. Allotropy is polymorphism for elemental solids. 

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