Mechanisms Underlying Hardness Numbers
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R10.11.1/T6.11.1
Mechanisms Underlying Hardness Numbers John J. Gilman Materials Science and Engineering University of California at Los Angeles Los Angeles, CA 90095
ABSTRACT Relationships of indentation hardness numbers to to other physical properties are demonstrated. They differ depending on the type of chemical bonding; metals, alloys ionic, covalent, and metal-metalloid. The properties are: shear modulus; ionic charge; band-gap density; polarizability; and formation energy, respectively. In each case the rationale is provided. The concept of a “bonding Modulus” is introduced. It is concluded that the conventional wisdom that hardness is a purely empirical prop erty does not hold. Phase transformations and indentation hard ness are co nnected broad ly.
INTRODUCTION A purpose of this paper is to show that hardness is not a chaotic empirical property. Instead, hardness is determined by the energy densities of chemical bonding. That is, by bond moduli. These are not universal parameters, but vary depending on the type of bonding. They are closely related to chemical hardness. Two standard methods are used for measuring the hardnesses of structural materials. One is indentation, and the other is scratching. They both depend on the type of chemical bonding in the material: alloy, covalent, ionic, metallic, metal-metalloid, or dispersion. The inelastic deformation during indentation, or scratching, involves either: the motion of glide dislocations; or a phase transformation (twinning is taken to be a monomolecular phase transformation); or both. The atomic forces that determine hardness are electrodynamic just as they are for the elastic stiffnesses. The strongest forces are of the electron exchange type, but weaker photon exchange forces are sometimes important. They act at the atomic scale of dimensions so quantum mechanics is required to understand hardness properly. Continuum mechanics can provide an operational description of hardness measurements, but not an understanding of what underlies the numbers. This paper describes mostly quantitative theories based on chemical behavior, including the quantity known as “chemical hardness” which is the second derivative of the chemical energy per unit volume taken with respect to a change in the number density of valence electrons. It has been found empirically that the chemical hardness and the physical hardness are proportional to one another. Thus, an understanding of mechanical hardness helps in developing an understanding of chemical stability and reactivity. Predominantly Vickers Hardness Numbers are discussed. That is, numbers derived from indentations made by square diamond pyramids with apex angles of about 135°. The friction coefficients between such indenters and specimens are large. Therefore, the stresses in the specimens consist of two parts: shear and hydrostatic compression. The shear strains can be expected to cause dislocation activity (and twinning), while the compression will tend to cause phase transformations. Since both of these cause electron e
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