Diamond types

Depending on the levels of trace impurities occurring in their crystal lattice, diamonds are classified into two major types, that is, those bearing nitrogen as major impurity (Type I) and those without nitrogen (Type II). These two subgroups are further subdivided into Types la, Ib, Ila, and Ilb respectivelly. A brief description of these various types is presented in Table 12.18. 

Type la Type la diamonds with an occurrence of 98%, the are the most common type of 

Type Ib Type Ib diamonds are naturally scarce (ca. 0.1 %). They have a low nitrogen content (25-30 ppm at. N) which is dispersed substitionally. Usually, most synthetic diamonds tend to be of the Type lb, with up to 0.05 wt.% N as single atoms, often giving rise to a brilliant yellow color (e.g., canary diamonds). 

Type Ila Type Ila diamonds are relatively free of nitrogen imputity and they contain less than 10 ppm at. N. They are all colorless (e.g., the Cullinan and the Koh-i-Noor) and exhibit enhanced optical and thermal properties. 

Type lib Type lib diamonds are extremely rare. Due to minute amounts of boron impurities and with nitrogen below 0.1 ppm at. N they behave as a p-type semiconductors. They exhibits a blue color (e.g., the blue Hope diamond) due to the absorption band in the tail of the infrared absorption spectrum combined with the acceptor center. 

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Thus we have shown that when s and p orbitals are available and s—p quantization is broken an atom can form four (or fewer) equivalent bonds which are directed towards tetrahedron corners. To the approximation involved in these calculations the strength of a bond is independent of the nature of other bonds. This result gives us at once the justification for the tetrahedral carbon atom and other tetrahedral atoms, such as silicon, germanium, and tin in the diamond-type crystals of the elements and, in general, all atoms in tetrahedral structures. 

In constructing this table, the radii for G, Si, Ge, and Sn were taken as half the observed interatomic distances in diamond-type crystals of the elements. It was next... 

The diamond-type structure of a-tin is stable at ambient pressure only up to 13 °C above 13 °C it transforms to /J-lin (white tin). The transition a-Sn —> /J-Sn can also by achieved below 13 °C by exerting pressure. Silicon and germanium also adopt the structure of p-Sn at higher pressures. The transformation involves a considerable increase in density (for Sn +21%). The J3-Sn structure evolves from the a-Sn structure by a drastic compression... 

Cr3Si-type structure W + / AgMgAs-type structure F + F + F" CaTi03-type structure P + P + J Cu2Mg-type structure T + D. For a few element structures Cu type structure F W-type structure 7 a-Po-type structure P Mg-type structure E C-diamond-type structure D. 

Equiatomic tetrahedral structure types. (Carborundum structure types). To this group pertain the diamond-type structure, the wurtzite (h) and the sphalerite (c) types, and the large family of SiC polytypes (such as he, hcc, hccc, hcchc,. .. (hcc)5(hccc)(hcc)5hc. .. (hchcc)17(hcc)2,. .. (hcc)43hc...). 

Diamond type (space group Fd3m, N. 227) — 12 — sphalerite type (space group F43m, N. 216). 

A traditional example of a Zintl phase is represented by NaTl which may be considered as a prototype of the Zintl rules. The structure of this compound (face centred cubic, cF16, a = 747.3 pm) can be described (see also 7.4.2.2.) as resulting from two interpenetrating diamond type lattices corresponding to the arrangements of the Na and T1 atoms respectively (Zintl and Dullenkopf 1932). Each T1 atom therefore is coordinated to other four T1 at a distance a)3/4 = 747.3)3/4 = 323.6pm which is shorter than that observed in elemental thallium (d = 341-346 pm in aTl, hP2-Mg type, CN = 6 + 6) and d = 336pm in /3 Tl, (cI2-W type, CN = 8). 

The otherl4th group elements, Si, Ge and oSn have the diamond-type structure. The tI4- 3Sn structure (observed for Si and Ge under high pressure) can be considered a very much distorted diamond-type structure. Each Sn has four close neighbours, two more at a slightly larger and another four at a considerable larger distance. Fig. 7.13 shows the (3Sn unit cell. Lead, at ambient pressure, has a face-centred cubic cF4-Cu type structure. 

For carbon, the diamond-type structure is metastable at room conditions it is stable at high pressure. See the phase diagram of carbon shown in Fig. 5.37. 

Sphalerite and wurtzite structures general remarks. Compounds isostructural with the cubic cF8-ZnS sphalerite include AgSe, A1P, AlAs, AlSb, BAs, GaAs, InAs, BeS, BeSe, BeTe, BePo, CdS, CdSe, CdTe, CdPo, HgS, HgSe, HgTe, etc. The sphalerite structure can be described as a derivative structure of the diamond-type structure. Alternatively, we may describe the same structure as a derivative of the cubic close-packed structure (cF4-Cu type) in which a set of tetrahedral holes has been filled-in. This alternative description would be especially convenient when the atomic diameter ratio of the two species is close to 0.225 see the comments reported in 3.7.3.1. In a similar way the closely related hP4-ZnO... 

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). 

Dawson and coworkers pioneered the application of the OPP model to diamond-type structures (Dawson 1967, Dawson et al. 1967). In the diamond-type structure, common to diamond, silicon, and germanium, the atoms are located at 1/8, 1/8, 1/8, at the center-of-symmetry related position at —1/8, —1/8, —1/8, and repeated in a face-centered arrangement. The tetrahedral symmetry of the atomic sites greatly limits the allowed coefficients in the expansion of Eq. (2.39). With x, y, z expressed relative to the nuclear position, the potential is given by... 

The Structure Factor Formalism for the Diamond-Type Structures... 

As first shown by Dawson (1967), Eq. (11.3) can be generalized by inclusion of anharmonicity of the thermal motion, which becomes pronounced at higher temperatures. We express the anharmonic temperature factor of the diamond-type structure [Chapter 2, Eq. (2.45)] as 71(H) = TC(H) -f iX(H), in analogy with the description of the atomic scattering factors. Incorporation of the temperature... 

The appearance of reflections in the diffraction pattern due to anharmonicity of thermal motion is not limited to the diamond-type structures, and is observed, for example, for the A 15-type structure of the low-temperature superconductor V3Si (Borie 1981), and for zinc (Merisalo et al. 1978). It has been described as thermal excitation of reflections, though no excitation in the spectroscopic sense of the word is involved. 

We shall now discuss the method of crystal growth and the electronic properties of GaAs, a typical example of a III-V compound which is expected to become more useful than Si and Ge in the near future, concentrating on the relation between non-stoichiometry and physical properties. GaAs has a zinc blende type structure, which can be regarded as an interpenetration of two structures with face centred cubic lattices, as shown in Fig. 3.29. Disregarding the atomic species, the structure is the same as a diamond-type... 

C is equal to unity when each nodule has six first neighbors, by analogy with a simple cubic lattice29. Similarly Cis of the order of 0.87,1.09,1.12 when the geometric functionality is of the order of 4,8,12, respectively these values originate from calculations carried out on diamond-type, centered, and face-centered cubic lattices, which exhibit precisely these geometric functionalities (or coordination indices). In any case, Cis a constant for a given network, and its value is never very far from unity. 

ANTHRAXOL1TE. A coal-like metamorphosed bitumen, often closely associated with igneous rocks. Commonly associated with Herkimer Diamond type quartz crystals in dolomitic limestones in Herkimer and Montgomery counties in New York State. 

Silicon and germanium as elemental substances are found only in the diamond-type form. The reluctance of Si and Ge to enter into pre-p bonding prohibits a graphite-type structure as a plausible allotrope. These are rather more reactive than diamond the weaker Si-Si and Ge-Ge bonds make disruption of the lattice kinetically easier. Tin occurs in both a metallic form (white tin) and a covalent (diamond-type) form the latter is slightly more stable at low temperatures. Lead forms only a metallic elemental substance. 

On the other hand, in covalently bonded materials like carbon, silicon, and germanium, the formation of energy bands first involves the hybridization of the outer s- and p-orbitals to form four identical orbitals, ilnh, which form an angle of 109.5° with each other, that is, each C, Si, and Ge atom is tetrahedrally coordinated with the other C, Si, and Ge atom, respectively (Figure 1.16), resulting in a diamond-type structure. 

FIGURE 1.16 Tetrahedral bonding of atoms in a diamond-type structure of C, Si, and Ge crystals. 

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