Diamond bulk modulus

Mechanical Properties. Measuremeat of the mechanical properties of diamoad is compHcated, and references should be consulted for the vahous qualifications (7,34). Table 1 compares the theoretical and experimental bulk modulus of diamond to that for cubic BN and for SiC (29) and compares the compressive strength of diamond to that for cemented WC, and the values for the modulus of elasticity E to those for cemented WC and cubic BN. 

Among the metals of the Periodic Table, osmium has the highest bulk modulus (412 GPa), and shear stiffness constants of C44 = 270GPa and C66 = 268 GPa. (Pantea et al., 2008).The corresponding values for diamond are B = 433 GPa and C44 (111) = 507 GPa. Although the bulk modulus of Os is about 95% that of diamond, the indentation hardness is only about 3% of diamond s hardness. In other words dislocations move readily in Os but not in diamond. 

Figure 2.15 Pressure-volume data for diamond, SiC>2-stishovite, MgSiC>3 and 8102-quartz based on third order Birch-Murnaghan equation of state descriptions. The isothermal bulk modulus at 1 bar and 298 K are given in the figure.

Graphite is much more compressible than diamond, and the variation of its bulk modulus with pressure must be taken into account. Berman assumes a linear relationship of B with p so that... 

These three-dimensional fullerenes show interesting mechanical and thermal properties, although there is poor agreement between results from different groups. Although a bulk modulus exceeding that of diamond has been reported [ 12,121-123], other experimental and theoretical [ 124] work indicate somewhat lower values. 

The amorphous phase appearing above 20 GPa at room temperature (see above) has also recently been studied by X-ray diffraction [135] and Raman scattering [132,133]. Serebryanaya et al. [135] identify the structure as a three-dimensionally polymerized Immm orthorhombic lattice, but find that compression above 40 GPa gives a truly amorphous structure. In contrast to the orthorhombic three-dimensional polymer structure discussed in the last section, the best fit here is found for (2+2) cycloaddition in two directions, with (3+3) cycloaddition in the third, and thus some relationship to the tetragonal phase. From the in situ X-ray data a bulk modulus of 530 GPa is deduced, about 20% higher than for diamond. Talyzin et al. [132, 133] find that this phase depolymerizes on decompression into linear polymer chains, unless the sample is heated to above 575 K under pressure. A strong interaction with the diamond substrate is also noted, such that only films with a thickness of several hundred nm are able to polymerize fully [ 132]. Hardness tests were also carried out on the polymerized films, which were found to be almost as hard as diamond and to show an extreme superelastic response with a 90% elastic recovery after indentation [133]. 

At very high pressures, above 12 GPa, and temperatures above 1000 K, a transparent,yellowish, ultra-hard material, believed to consist of the remnants of collapsed molecules, is formed. In several cases ultrasonic, scratch, and indentation studies have shown this material to have a bulk modulus and hardness far exceeding that of diamond [123,131,147], although these reports are by no means uncontested [124,148,149]. The material is extremely disordered and probably has a high fraction of sp2 coordinated bonds, but the structure is unknown. There are some similarities with amorphous carbon (ta-C),but differences in Raman spectra and mechanical properties show that the structures differ. The question of bond types is interesting, since sp2 bonds are known to be stronger than sp3 ones. The materials are semiconducting and have Debye temperatures near 1450 K, somewhat lower than that of diamond [150]. 

Nevertheless, some conclusions may be drawn from the set of results presented here. First, with the notable exception of InN, the group III nitrides form a family of hard and incompressible materials. Their elastic moduli and bulk modulus are of the same order of magnitude as those of diamond. In diamond, the elastic constants are [49] Cu = 1076 GPa, Cn = 125 GPa and Cm = 577 GPa, and therefore, B = (Cn + 2Ci2)/3 = 442 GPa. In order to make the comparison with the wurtzite structured compounds, we will use the average compressional modulus as Cp = (Cu + C33)/2 and the average shear modulus as Cs = (Cu + Ci3)/2. The result of this comparison is shown in TABLE 8. 

For a crystal having the symmetry of diamond or /.incblende (thus having cubic elasticity), there are three independent clastic constants, c, t 12, and C4.4. The bulk modulus that was discussed in Chapter 7 is B = (c, + 2c,2)/3. We can discuss the bulk modulus, and the combination c, — c,2, entirely in terms of rigid hybrids, and therefore the two elastic constants c, and c,2 do not require deviations from this simple picture. This will not be true for the strain, which is relevant to c 44, and this is a complication of some importance. 

Use Eq. (15-18) to estimate the bulk modulus of C, Si, and Gc in the diamond structure and compare with the experimental values from Table 7-1. Check the [Pg.358]

The incompressibility (bulk modulus) of a material is directly related to its valence electron density, in units of electrons A . For example, diamond, the hardest known... 

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. 

The volume—pressure relationship for e-Fe has been determined up to 300 GPa at room temperature (Figure 3 Mao et al., 1990). Determining the temperature dependence of the bulk modulus of iron is crucial for accurate comparison between the density of iron and that of the iimer core. Several in situ X-ray diffraction studies in the diamond-anvil cell (Huangeta/., 1987 Dubrovinsky eta/., 1998, 2000) and in the multi-anvil apparatus (Funamori et al., 1996 Uchida et al., 2001) have provided limited data on the thermal expansion of e-Fe at high pressures. The data of Dubrovinsky et al. 

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