Diamond lattice constant

Another example of epitaxy is tin growdi on the (100) surfaces of InSb or CdTe a = 6.49 A) [14]. At room temperature, elemental tin is metallic and adopts a bet crystal structure ( white tin ) with a lattice constant of 5.83 A. However, upon deposition on either of the two above-mentioned surfaces, tin is transfonned into the diamond structure ( grey tin ) with a = 6.49 A and essentially no misfit at the interface. Furtliennore, since grey tin is a semiconductor, then a novel heterojunction material can be fabricated. It is evident that epitaxial growth can be exploited to synthesize materials with novel physical and chemical properties. 

The atomic weight of silicon is 28.086 (4.6638xlO-23 g per atom). Its density of 2.328 gem-3 corresponds to roughly 5 X1022 atoms cm-3. Silicon has the same crystal structure as diamond (face-centered cubic, fee) with a lattice constant of 0.543095 nm. 

Let us consider, for example, separation along the (111) plane in diamond. The lattice constant for diamond is a = 3.56 A (see Table 1.11), so the number of atoms per square centimeter on the (111) surface is... 

The parameter is obtained by relating the static dielectric constant to Eg and taking in such crystals to be proportional to a - where a is the lattice constant. Phillips parameters for a few crystals are listed in Table 1.4. Phillips has shown that all crystals with a/ below the critical value of0.785 possess the tetrahedral diamond (or wurtzite) structure when f > 0.785, six-fold coordination (rocksalt structure) is favoured. Pauling s ionicity scale also makes such structural predictions, but Phillips scale is more universal. Accordingly, MgS (f = 0.786) shows a borderline behaviour. Cohesive energies of tetrahedrally coordinated semiconductors have been calculated making use... 

The Fick s law diffusion coefficient of a permeating molecule is a measure of the frequency with which the molecule moves and the size of each movement. Therefore, the magnitude of the diffusion coefficient is governed by the restraining forces of the medium on the diffusing species. Isotopically labeled carbon in a diamond lattice has a very small diffusion coefficient. The carbon atoms of diamond move infrequently, and each movement is very small—only 1 to 2 A. On the other hand, isotopically labeled carbon dioxide in a gas has an extremely large diffusion coefficient. The gas molecules are in constant motion and each jump is of the order of 1000 A or more. Table 2.1 lists some representative values of diffusion coefficients in different media. 

Preparation for X-ray Analysis. Lattice constants are calculated from patterns obtained on powder samples with a Norelco diffractometer using monochromatic radiation (AMR-202 Focusing Monochromator) from a high-intensity copper source. The crystals are powdered with a diamond mortar and pestle, and the powder passed through a 74-/ sieve. Accurate lattice constants are calculated from the x-ray data. 

As can be seen, there are eight parameters in the Stillinger-Weber potential A,B,p, q, /r, Tc, Z, and a. These parameters are fitted to experimental data, such as lattice constants and cohesive energy, for the diamond stmcture. The angle is the angle centered on atom i. If djik is 1010.47°, cos 6jii = the angular function has a minimum of zero, which... 

Surratt, G. T., R. N. Euwema, and D. L. Wilhite (1973). Hartree-Fock lattice constant and bulk modulus of diamond. Phys. Rev. B8, 4019-25. 

Figure 2.1. Diamond structure. The dotted cube indicates a crystallographic unit cell containing two carbon atoms. The lattice constant of diamond is fl =. t.567A.

Cubic boron nitride (cBN) has a zinc blende-type crystal structure with a lattice constant of 3.615 A, which is very close to that of diamond (3.567 A). The difference is only about 1.3%. According to RHEED measurements with the electron beam parallel to the 111 layer of cBN, a growth of diamond by DC plasma CVD on cBN(lll) [150] using c = 0.5%CH4/H2, T = 900°C, and F=180Torr led to a result that a smooth (111) layer of diamond was epitaxially deposited in such a way that the [110] direction of diamond was parallel to that of cBN. Namely, D 111 //cBN(lll and D[110]//cBN[110]. In the RHEED pattern, however, extra spots were observed, which were presumably due to the twinnings of (111 diamond layers. In the Raman spectra, there were two lines due to cBN at 1054.5 and... 

As a standard procedure of substrate pretreatment for diamond deposition, (i) scratching the substrate surface with diamond powder or paste, or (ii) ultrasonic treatment of the substrate in diamond powder suspended in alcohol are widely used. By contrast, for diamond growth on cBN(Ill), no such pretreatment is necessary, partly because of the close match of lattice constants. 

Material Crystal structure Lattice constant (A) Difference from diamond (%) Melting point (°C) Thermal expansion coefficient (10- /K)... 

Silicon is a semiconductor with an intrinsic conductivity of 4.3 x 10" Q" cm and a band gap of I.I2eV at 300K. It has a diamond crystal structure characteristic of the elements with four covalently bonded atoms. As shown in Fig. 2.1, the lattice constant, a, is 5.43 A for the diamond lattice of silicon crystal structure. The distance between the nearest two neighbors is V3a/4, that is, 2.35 A, and the radius of the silicon atom is 1.18 A if a hard sphere model is used. Some physical parameters of silicon are listed in Table 2.1. 

FIGURE 2.1. The diamond-crystal lattice charactrized by four covalently bonded atoms. The lattice constant, a, is 0.543 nm for silicon. Nearest neighbors are spaced (V3a/4) units apart. Of the 18 atoms shown in the figure, only 8 belong to the volume a . Since the 8 corner atoms are each shared by 8 cubes, they contribute 1 atom the face atoms are each shared by 2 cubes and thus contribute 3 atoms, and there are 4 atoms inside the cube. The atomic density is therefore 8/a which corresponds to 5.00 x 10 cm . After W, Shockley. - ... 

Crystal structure Atoms per unit cell Lattice constant Diamond 8 5.43 A a... 

A tetragonal form of BN can be prepared by vapor deposition on BN-coated Ta or graphite substrates at 1200-1600°C. The composition is close to BsoNx.g the density is 2.46 g/cm, and the lattice constants are a = 864.6 pm and c = 512.7 pmk Shock loading of diamond/BN mixtures produced several phases, including a tetragonal phase with the composition B2sN. ... 

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