Structure types diamond

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...). 

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. 

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. 

This section presents a brief overview of a few other compounds that have not been described in previous sections. Because it can function as a nonmetal, silicon forms sihcides with several metals. These materials are often considered as alloys in which the metal and silicon atoms surround each other in a pattern that may lead to unusual stoichiometry. Examples of this type are Mo3Si and TiSi2. In some sihcides, the Si-Si distance is about 235 pm, a distance that is quite close to the value of 234 pm found in the diamond-type structure of elemental silicon. This indicates that the structure contains Si22-, and CaSi2 is a compound of this type. This compound is analogous to calcium carbide, CaC2 (actually an acetylide that contains C22- ions (see Chapter 10)). 

An attempt was made in this paper to sketch the behavior of elemental semiconductors (with the diamond-type structure) and of the IH-V compounds (with the zinc blende strut ture) in aqueous solutions. These covalent materials, in contrast to metals, exhibit properties which sharply reflect their crystalline structure. Although they have already contributed heavily to the understanding of surfaces in general, semiconductors with their extremely high purity, crystalline perfection, and well-defined surfaces are the most promising of materials for surface studies in liquid and in gaseous ambients. 

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. 

Zinc blende (sphalerite, ZnS) has a diamond-type structure. The space group is F43m for a cubic unit cell with a = 5.42 A. The structure is illustrated in Figure 14.20. Parallel to the (100) face of zinc blende... 

The degree of differential etching at defects depends on the orientation of the crystal. In general, for diamond-type structures such as silicon it is much easier to reveal dislocations on the 111 planes than on other planes. Some etchants, such as Sirtl etch, reveal sharply the defects on (111) planes but are not satisfactory for (100) planes. 

Silicon is a shiny, blue-gray, high-melting, brittle metalloid. It looks like a metal, but it is chemically more like a nonmetal. It is second only to oxygen in abundance in the earth s crust, about 87% of which is composed of silica (Si02) and its derivatives, the silicate minerals. The crust is 26% Si, compared with 49.5% O. Silicon does not occur free in nature. Pure silicon crystallizes with a diamond-type structure, but the Si atoms are less closely packed than C atoms. Its density is 2.4 g/cm compared with 3.51 g/cm for diamond. 

Subsequently, a peak in the RSL spectra, similar to the one observed by Krishnan, was not found in some crystals, such as silicon and germanium, which have the same type of structure as diamond and have even stronger anharmonicity than diamond. This encouraged Tubino and Birman (33) to improve the accuracy of the calculations of the structure of the phonon bands in crystals with a diamond-type structure. It was shown as a result of comprehensive investigations that the dispersion curve of the above-mentioned optical phonon in diamond has its highest maximum not at k = 0, but at k 0. The result of these calculations indicates that the peak experimentally observed in the RSL spectra of diamond falls within the region of the two-phonon continuum. It cannot correspond to a biphonon and is most likely related to features of the density of two-particle (dissociated) states. 

Values for C, Si, Ge and Sn refer to diamond-type structures and thus refer to 4-coordination the value for Pb also applies to a 4-coordinate centre. Values are for 6-coordination. 

The effect was investigated of the nature and energy of the interatomic interaction on the structure and physical properties of crystals. Factors were studied which determine the thermodynamic properties and their temperature dependences. The effect of various parameters on the form of the frequency spectmm of phonons was investigated, taking, as an example, crystals with a diamond-type structure. The problem was also studied of the determination of the elastic constants as derivatives of the crystal energy in terms of the distribution functions of the electron density, represented by various approximations. 

We will consider the change in the phonon spectrum of a crystal with a diamond-type structure, whose ionic mass (isotopic effect) and lattice constant change, but whose elastic constants remain the same. We will give the calculated phonon spectra of a crystal with a dia-mond-lype structure, with different atomic masses. The calculation scheme was similar to that in [15]. 

Fig. 5. Phonon spectra of crystals with a diamond-type structure, plotted for mj = mg. (a) and m2 = 0.43 mg. (b) is in relative units.

Elemental silicon has a diamond-type structure. Crystalline silicon is a gray metallic-looking solid that melts at 1410 °C. The element is a semiconductor, as we saw in Chapters 7 and 12, and is used to make solar cells and transistors for computer chips. To be used as a semiconductor, it must be extremely pure, possessing less than 10 (1 ppb) impurities. One method of purification is to treat the element with CI2 to form SiCl4, a volatile liquid that is purified by fractional distillation and then converted back to elemental silicon by reduction with H2 ... 

Sip4 A semiconductor at 298 K with a diamond-type structure... 

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