Chemical and Physical Hardness of Solids
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CHEMICAL AND PHYSICAL HARDNESS OF SOLIDS John J. Gilman Materials Science and Engineering University of California at Los Angeles Los Angeles, CA 90095
ABSTRACT The conc ept of chem ical hard ness was originally de velop ed as a mea sure of the stability of molecules. Its relationship to physica l hardn ess and to solids is demonstrated here. Also, it is shown that shear moduli, and polarizabilitites, as well as band gaps are related to chemical hardness. Finally, evidence is presented that indentation hardness numbers are better measures of critical phase transition compressions than “pressure-cell” data.
INTRODUCTION A measure of the stabilities of molecules (atoms) is chem ical hard ness (Pearson. 1997). T his is an energy scalar, and therefore inad equate for a com plete d escription of so lids, unless it is modified. One reason is that isotrop ic solids have two types of stability: size and shape. The elastic bulk modulus measures the size stability, while the elastic shear modulus measures the shape stability. The less symmetric solids require the full set of elastic tensor coefficients to describe their stab ilities. The formal definition of the electronic chemical hardness is that it is the derivative of the electronic chemical potential with respect to the numbe r of valence electrons. The elec tronic chemical po tential itself is the ch ange in total energy of a molecule with a change of the number of valence electrons. Since the elastic moduli depend on valenc e electron densities, it might be expected that they wo uld also depend on chemical hard ness densities (energy / volum e). This is indeed the case. A physica l hardn ess can b e defined that is prop ortional (and sometimes equa l) to the ch emical hard ness. D ata that verify this are presented. 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 Mo h scratch hardness) are proportional to the chem ical hardness density. One implication of these findings is that chemical hardness should be related to the band gaps of covalent crystals, since it is related to the LUM O-H OM O ga ps of m olecu les. Data indica te that this is indeed the case . Another implication is that the chemical potential of a solid is, in general, a second order tensor that is related to the deformation tensors (strains) through the fou rth order tenso r of elastic coefficients. The theo ry of chemical and physical hardness is useful because it unifies understanding o f various prop erties; and it connects the behaviors o f molecules with those of liquids and solids. Stability is som etimes associated with the bulk modulus alone, b ut th
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