Covalent crystals hardness

However, It has been found that in many cases, simple models of the properties of atomic aggregates (monocrystals, poly crystals, and glasses) can account quantitatively for hardnesses. These models need not contain disposable parameters, but they must be tailored to take into account particular types of chemical bonding. That is, metals differ from covalent crystals which differ from ionic crystals which differ from molecular crystals, including polymers. Elaborate numerical computations are not necessary. 

A measure of shear strength is the shear modulus. For covalent crystals this correlates quite well with hardness (Gilman, 1973). It also correlates with the hardnesses of metals (Pugh, 1954), as well as with ionic crystals (Chin, 1975). Chin has pointed out that the proportionality number (VHN/C44) depends on the bonding type. This parameter has become known as the Chin-Gilman parameter. 

Inelastic shearing of atoms relative to one another is the mechanism that determines hardness. The shearing is localized at dislocation lines and at kinks along these lines. The kinks are very sharp in covalent crystals where they encompass only individual chemical bonds. On the other hand, in metal crystals they are often very extended. In metallic glasses they are localized in configurations that have a variety of shapes. In ionic crystals the kinks are localized in order to minimize the electrostatic energy. 

The differences just outlined cannot be explained by means of a classical mechanical model. However, they can be explained by considering chemical bonding. In particular, hardness depends in covalent crystals on the fact that the valence (bonding) electrons are highly localized as shown by electron-diffraction studies which can provide maps of electron densities (bonds). 

For covalent crystals temperature has little effect on hardness (except for the relatively small effect of decreasing the elastic shear stiffness) until the Debye temperature is reached (Gilman, 1995). Then the hardness begins to decrease exponentially (Figure 5.14). Since the Debye temperature is related to the shear stiffness (Ledbetter, 1982) this softening temperature is proportional to C44 (Feltham and Banerjee, 1992). 

In the high temperature regime for covalent crystals where the hardness drops rapidly, its values are affected by impurities (dopants). Both hardening and softening occur depending on whether the dopant is is a donor, or an accepter... 

The concept of chemical hardness was originally developed as a measure of the stability of molecules. Its relationship to physical hardness and to solids is discussed here. Also, it is pointed out that shear moduli and polarizabilitites, as well as band gaps in covalent crystals, are related to it. 

Physical hardness can be defined to be proportional, and sometimes equal, to the chemical hardness (Parr and Yang, 1989). The relationship between the two types of hardness depends on the type of chemical bonding. For simple metals, where the bonding is nonlocal, the bulk modulus is proportional to the chemical hardness density. The same is true for non-local ionic bonding. However, for covalent crystals, where the bonding is local, the bulk moduli may be less appropriate measures of stability than the octahedral shear moduli. In this case, it is also found that the indentation hardness—and therefore the Mohs scratch hardness—are monotonic functions of the chemical hardness density. 

One implication of these findings is that chemical hardness is related to the band gaps of covalent crystals, consistent with its being related to the LUMO-HOMO gaps of molecules. Data indicate that this is indeed the case. Another... 

In relatively recent years, it has been found that that indentations made in covalent crystals at temperatures below their Debye temperatures often result from crystal structure changes, as well as from plastic deformation via dislocation activity. Thus, indentation hardness numbers may provide better critical parameters for structural stability than pressure cell studies because indentation involves a combination of shear and hydrostatic compression and a phase transformation involves both of these quantities. 

The principal intention of the present book is to connect mechanical hardness numbers with the physics of chemical bonds in simple, but definite (quantitative) ways. This has not been done very effectively in the past because the atomic processes involved had not been fully identified. In some cases, where the atomic structures are complex, this is still true, but the author believes that the simpler prototype cases are now understood. However, the mechanisms change from one type of chemical bonding to another. Therefore, metals, covalent crystals, ionic crystals, and molecular crystals must be considered separately. There is no universal chemical mechanism that determines mechanical hardness. 

Extended covalent array Atoms Mainly covalent Strong hard crystals of high m.t. insulators Diamond, silica... 

Since the vek computation was only rough, as Fersman himself admitted, the hardness values calculated from the formulae (3.3) and (3.4) were not sufficiently accurate and failed to consider all crystallochemical factors. Next, Sobolev in 1946 established a relationship between hardness and coordination number, attempting to extend the applications of Goldschmidt s formula to complex minerals, including silicate minerals. It was discovered by that time that crystal hardness with both ionic and covalent bonds, depends on ... 

Covalent crystals are held together by strong, highly directional bonds usually described by the valence bond hybrid orbital method. Each atom is part of a large extended single molecule that is the crystal itself. Because of the nature of their bonds, covalent crystals have very high melting points and are hard and brittle. 

Each constituent atom of a covalent crystal is linked to its neighbours through directed covalent bonds. The crystal structure is determined by the spatial dispositions of these bonds. Because primary valence forces are involved, such solids are hard and have high melting points, e.g. diamond, silicon carbide, etc. Relatively few entirely covalent solids have been studied at elevated temperatures and it is, therefore, premature to comment on their decomposition characteristics. 

Another covalent crystal is quartz (Si02). The arrangement of silicon atoms in quartz is similar to that of carbon in diamond, but in quartz there is an oxygen atom between each pair of Si atoms. Since Si and O have different electronegativities, the Si—O bond is polar. Nevertheless, Si02 is similar to diamond in many respects, such as hardness and high melting point (1610°C). 

Diamond (r.d. 332) occurs naturally and can be produced synthetically. It is extremely hard and has highly refractive crystals. The hardness of diamond results from the covalent crystal structure, in which each carbon atom is ilnloed by covalent bonds to four others situated at the comers of a tetrahedron. The C-C bond length is 0.154 mn and the bond angle is 109.5°. 

Covalent crystals are sometimes called macromolecular or giant-molecular crystals. They are hard high-melting substances. Examples are diamond and boron nitride. 

Crystalline solid electrolytes have been subdivided into soft ionic crystals such as P-Pbp2 and hard covalent crystals such as P-alumina. The conduction mechanism can be pictured as involving a liquid-like charge carrier array moving in the vibrating potential energy profile set up by the immobile counterions. 

Here, Hhp = (Hq + kd ) and Hqc = (Cd ) represent dislocation-related dislocation hardening based on the H-P effect and bandgap-related hardening based on the quantum confinement effect, as indicated above, following Tse s [34] calculations. Ho is the single-crystal hardness and k is a material constant. C is a material-specific parameter equal to zero for metals and equal to 211Ny exp (1.191fi) for covalent materials, where Ne is the valence electron density and fj is the Philips ionicity of the chemical bond. 

Solvent extraction of metals embodies all aspects of coordination chemistry rates, equilibria, stereochemistry, crystal field theory, covalent bonding, hard-soft acid-base theory, hydrogen bonding, steric hindrance, enthalpy and entropy. All of these basic principles can link together to produce pure metals on an industrial scale from dilute aqueous solutions — a remarkable achievement of elegant coordination chemistry. To achieve this result it is only necessary to form within the aqueous medium a neutral species containing the metal to be extracted. 

Fig. 30.5 lonicity (fj), bandgap, and bond length dependence of the reduced hardness of covalent crystals, Hy/Ei N (reprinted with permission from [35])... 

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