Hexagonal diamond structure

Figure 4.2 Quasi-hexagonal dislocation loop lying on the (111) glide plane of the diamond crystal structure. The <110> Burgers vector is indicated. A segment, displaced by one atomic plane, with a pair of kinks, is shown a the right-hand screw orientation of the loop. As the kinks move apart along the screw dislocation, more of it moves to the right.

When the atomic size ratio is near 1.2 some dense (i.e., close-packed) structures become possible in which tetrahedral sub-groups of one kind of atom share their vertices, sides or faces to from a network. This network contains holes into which the other kind of atoms are put. These are known as Laves phases. They have three kinds of symmetry cubic (related to diamond), hexagonal (related to wurtzite), and orthorhombic (a mixture of the other two). The prototype compounds are MgCu2, MgZn2, and MgNi2, respectively. Only the simplest cubic one will be discussed further here. See Laves (1956) or Raynor (1949) for more details. 

In order to have around each atom in this hexagonal structure four exactly equidistant neighbouring atoms, the axial ratio should have the ideal value (8/3 that is 1.633. The experimental values range from 1.59 to 1.66. This practical constancy of the axial ratio, in contrast with what is observed for other families of isostructural compounds such as those of the NiAs type, may be attributed to a sort of rigidity of the tetrahedral (sp3) chemical bonds. As for the atomic positional parameters, the ideal value of one of the parameters (being the other one fixed at zero by conventionally shifting the origin of the cell) is z = 3/8 = 0.3750. The C diamond, sphalerite- and wurtzite-type structures are well-known examples of the normal tetrahedral structures (see 3.9.2.2). 

Several superstructures and defect superstructures based on sphalerite and on wurtzite have been described. The tI16-FeCuS2 (chalcopyrite) type structure (tetragonal, a = 525 pm, c = 1032 pm, c/a = 1.966), for instance, is a superstructure of sphalerite in which the two metals adopt ordered positions. The superstructure cell corresponds to two sphalerite cells stacked in the c direction. The cfla ratio is nearly 1. The oP16-BeSiN2 type structure is another example which similarly corresponds to the wurtzite-type structure. The degenerate structures of sphalerite and wurtzite (when, for instance, both Zn and S are replaced by C) correspond to the previously described cF8-diamond-type structure and, respectively, to the hP4-hexagonal diamond or lonsdaleite, which is very rare compared with the cubic, more common, gem diamond. The unit cell dimensions of lonsdaleite (prepared at 13 GPa and 1000°C) are a = 252 pm, c = 412 pm, c/a = 1.635 (compare with ZnS wurtzite). 

In hexagonal diamond (wurtzite structure) the wrinkled sheets are stacked in an ABABAB sequence, as shown in the Figure 7. Looking down on the stack from above, hexagonal holes can be seen formed by the six-membered carbon rings. The crystal has hexagonal symmetry about this axis, hence the name hexagonal diamond, or wurtzitic carbon. 

Boron nitride (BN) can normally be prepared from the reaction of boric acid and urea or melamine. For example, the pyrolysis of MB can yield hexagonal BN. It is commonly referred to as white graphite because of its platy hexagonal structure similar to graphite. Under high pressure and at 1600°C, the hexagonal BN is converted to cubic BN, which has a diamond-like structure. 

Abbreviations b.c. body-centered cubic f.c. face-centered cubic hex. hexagonal di. diamond other structures... 

Structural data are available (Table 30) for a range of binary, ternary and quaternary sulfides of manganese, almost invariably Mn", and these set the scene for the structures to be expected in the compounds with the more discrete polyhedra.319 Indeed, the structural pattern is established in the simple binary compound MnS. Whereas, the stable modification of this (a-MnS) is green and has the cubic rock salt structure with [MnS6] octahedra, the well-known flesh-coloured precipitates of the qualitative analysis system are metastable / - and y-modifications, which have [MnS4] tetrahedra with respectively the zinc blende or diamond (cubic) and wurtzite (hexagonal) structures. And so, in the rest of the known solids, there are almost equal numbers of four-coordinate tetrahedra and six-coordinate octahedra with no other polyhedra having been detected. 

Ice at 0°C has a hexagonal structure. At temperatures below about --80 C a cubic, diamond-type structure can be obtained. Shallcross and Carp>enter found that H2O vapor condensed at very low temperatures sometimes forms amorphous solid and sometimes a mixture of the cubic and hexagonal forms (1835). Ice prepared or annealed above — 80°C takes the hexagonal form and remains in this crystal form even though the solid is recooled to — 196°C. There are other crystal structures which become stable at high pressures. 

Fig. 8.2 LEED pattern after annealing at 873 K. (a) At a beam energy of 37 eV, (b) of 90 eV, and (c) of 98 eV. (d) Schematic representation of the LEED pattern in panel c, showing the presence of three different hexagonal structures of different unit ceU size, one being rotated from the Pd(lll) underlayer (filled circles) by 3° (diamonds), another by 6° (open circles). Reprinted with permission from [19]. Copyright (2008) Elsevier...

The carbon atoms are covalently bonded through sp bonds forming tetrahedral cells (Fig. 2). A rare form of diamond, hexagonal diamond, called lonsdaleite is also possible (Fig. 3). Essentially, the difference in the structures is the type of hybridization, sp or sp, or the ratio of sp and sp bonds and the structure type. 

All forms of carbon seem to possess a graphite structure with the exception of the diamond (p. 59). So-called amorphous carbon consists of small sheets of hexagonal structure and the smaller the sheets the more widely do they tend to lie apart. A variation in the properties of carbon with its fineness of division is thus to be expected. 

A second type of diamond (hexagonal lattice or isodiamond) having a crystal structure similar to wurtzite is less common and slightly more energy-rich owing to its eclipsed bonds (boat-shaped 6-membered rings) as in iceane. 

Crystal structure zinc blende diamond hexagonal hexagonal... 

Because fonnation of cubic boron carbonitride is of great fundamental interest with respect to superhard materials much additional effort is needed to succeed in the preferential synthesis of the cubic B-C-N phase. As follows from the above results the most promising way would be synthesis under nonequilibrium conditions such as flash-heating at static pressures or shock-wave compression [140]. Successful synthesis of cubic BC2.5N solid solution in 18% yield by shock-compression of hexagonal BC2.5N has been reported [143]. The material obtained was a single cubic BC2.5N phase with a diamond-like structure and crystals between 5 and 20 nm in size. 

---