Physical hardness defined

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. 

Hard wired. A preprocessor that is capable of performing only certain defined tasks and no others without major physical modification. 

It has been shown that the anisotropy depends on the orientation of the diagonals of indentation relative to the axial direction 14). At least two well defined hardness values for draw ratios A. > 8 emerge. One value (maximum) can be derived from the indentation diagonal parallel to the fibre axis. The second one (minimum) is deduced from the diagonal perpendicular to it. The former value is, in fact, not a physical measure of hardness but responds to an instant elastic recovery of the fibrous network in the draw direction. The latter value defines the plastic component of the oriented material. 

As mentioned in [Section 24.1], and as already demonstrated in Equation 24.39, the Fukui functions as well as the chemical hardness of an isolated system can be properly defined without invoking any change in its electron number. We define a new Fukui function called polarization Fukui function, which very much resembles the original formulation of the Fukui function but with a different physical interpretation. Because of space limitation, only a brief presentation is given here. More details will appear in a forthcoming work [33]. One assumes a potential variation <5wext(r), which induces a deformation of the density 8p(r). A normalized polarization Fukui function is defined by... 

This last model of the hardness is modified and given in Equation 6. The hardness H is according to (21) a function of several physical properties. Cg is the constant defined in Equation 7, Z is the largest common valency of the atoms, f is the force constant per unit charge and represents the interatomic distance. 

In this contribution, we would like to show how such an approach allowed us to synthesize both soft and very hard molecule-based magnets. This contribution is organized as follows first, we define briefly the field of molecular magnetism, then we indicate the successive steps which led us to three-dimensional molecule-based magnets with fully interlocked structures. We describe these original structures in detail. Finally, we focus on the physical properties of these objects, with special emphasis on the huge coercivity of one of the compounds, which confers a memory effect on this compound. 

The resulting equilibrium concentrations of these point defects (vacancies and interstitials) are the consequence of a compromise between the ordering interaction energy and the entropy contribution of disorder (point defects, in this case). To be sure, the importance of Frenkel s basic work for the further development of solid state kinetics can hardly be overstated. From here on one knew that, in a crystal, the concentration of irregular structure elements (in thermal equilibrium) is a function of state. Therefore the conductivity of an ionic crystal, for example, which is caused by mobile, point defects, is a well defined physical property. However, contributions to the conductivity due to dislocations, grain boundaries, and other non-equilibrium defects can sometimes be quite significant. 

Just as energy is hard to define in everyday terms and comes in many forms, so too with work. In physics, work (w) is defined as the force (F) that produces the movement of an object times the distance moved (d) ... 

---