Lattice carbon allotropes

Buckminsterfullerene is an allotrope of carbon in which the carbon atoms form spheres of 60 atoms each (see Section 14.16). In the pure compound the spheres pack in a cubic close-packed array, (a) The length of a side of the face-centered cubic cell formed by buckminsterfullerene is 142 pm. Use this information to calculate the radius of the buckminsterfullerene molecule treated as a hard sphere, (b) The compound K3C60 is a superconductor at low temperatures. In this compound the K+ ions lie in holes in the C60 face-centered cubic lattice. Considering the radius of the K+ ion and assuming that the radius of Q,0 is the same as for the Cft0 molecule, predict in what type of holes the K ions lie (tetrahedral, octahedral, or both) and indicate what percentage of those holes are filled. 

The limitations of the simple Zintl-Klemm concept can be illustrated by differences in the two [MT1] intermetallics (M = Na [79] and Cs [80]). Complete electron transfer from M to T1 leads to [ M TI, where the Tl anion with four valence electrons is isoelectronic with a neutral group 14 atom and four bonds and needed to attain the octet configuration. Hence, the Tl- anion should form structures similar to allotropes of carbon or heavier group 14 elements. Indeed, [NaTl] has a stuffed diamond structure [79] with internal Na and an anionic (Tl-) lattice similar to diamond. However, the Tl- anions in [CsTl] form tetragonally compressed octahedra [80] unlike any structures of the allotropes of carbon or its heavier congeners. 

Carbon nanotubes (CNTs) constitute a nanostructured carbon material that consists of rolled up layers of sp2 hybridized carbon atoms forming a honeycomb lattice. After diamond, graphite and fullerenes, the one-dimensional tubular structure of CNTs is considered the 4th allotrope of carbon (graphene is the 5th). 

Pure iron is a fairly soft silver/white ductile and malleable moderately dense (7.87 gcm ) metal melting at 1,535 °C. It exists in three allotropic forms body-centered cubic (alpha), face-centered cubic (gamma), and a high temperature body-centered cubic (delta). The average value for the lattice constant at 20 °C is 2.86638(19)A. The physical properties of iron markedly depend on the presence of low levels of carbon or silicon. The magnetic properties are sensitive to the presence of low levels of these elements, and at room temperature pure iron is ferromagnetic, but above the Curie point (768 °C), it is paramagnetic. 

The fee unit cell can be thought of as having holes in which other atoms or ions can be placed. For example, the Na + ions occupy octahedral holes in the fee CF lattice (connecting the six CF ions surrounding a Na+ by lines defines an octahedron). The fee lattice also has tetrahedral holes if we divide the unit cell into 8 smaller cubes, the centers of these little cubes are surrounded by 4 lattice points which define a tetrahedron. The diamond allotropic form of carbon has a fee structure with C atoms in 4 of these tetrahedral sites each C atom is surrounded by (covalently bound to) 4 other C s. 

Table 3.2 compares unit cell dimensions for the various allotropes and Fe-C alloys. Since the dopant species are entrained within individual unit cells, the volume of each unit cell will increase concomitantly with the concentration of carbon. Although the 5-Fe lattice is isomorphous with ferrite, the difference in volume between these allotropes corresponds to different concentrations of carbon in each solid solution. That is, 5-Fe contains an order of magnitude greater concentration of carbon than ferrite. Since a greater number of interstitial sites may be occupied by fee unit cells relative to bcc, austenite may contain an even greater concentration of C in the lattice, up to 2.1 wt%. It must be noted that the trend of increasing volume with dopant concentration is not only exhibited by the Fe-C system, but is also followed by all other interstitial alloys that we will examine later. 

Cohen and coworkers 113] used the pseudopotential localized-orbital approach and found that this allotropic carbon structure is a low-compressibility metal because of the nearly perfect lattice match with the diamond (100) surface, they preposed that it may be possible to grow this structure epitaxially on the diamond OOO) surface. 

Are different allotropes of the same element, e.g., graphite (carbon atoms arranged in hexagonal sheets with each atom bonded to three other atoms in the plane of a given sheet) and diamond (carbon atoms arranged in a tetrahedral lattice with each atom bonded to four other atoms). 

Other recently discovered allotropes include a nanofoam—z web of light magnetic carbon clusters, lonsdaleite—a sort of disfigured hexagonal diamond lattice, and an aggregated diamond nanorod. 

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