Hardness defined

The hardness, defined as the resistance to plastic deformation, of microporous silicon decreases with porosity p from the bulk silicon value of about 11.5 GaP to values around 4 GaP for porosities in the order of 75% following a (1-p)2/3 dependence. For porosities above 75% a further decrease in hardness is observed. The hardness of PS formed on highly doped p-type substrates is found to be somewhat less than that observed for low doped substrates, which may be caused by the more columnar structure of meso PS [Du5]. 

E. Winkler, F. Grashof, H. Hertz,8 etc., have studied the stresses which are set up when two elastic isotropic bodies are in contact over a portion of their surface, when the surfaces of contact are perfectly smooth, and when the press, exerted between the surfaces is normal to the plane of contact. H. Hertz showed that there is a definite point in such a surface representing the hardness defined as the strength of a body relative to the kind of deformation which corresponds to contact with a circular surface of press. and that the hardness of a body may be measured by the normal press, per unit area which must act at the centre of a circular surface of press, in order that in some point of the body the stress may first reach the limit consistent with perfect elasticity. If H be the hardness of a body in contact with another body of a greater hardness than H, then for a circular surface of pressure of diameter d press. p radius of curvature of the line p and the modulus of penetration E,... 

Some investigators believe that the best course to follow in scratch hardness determination is to find the tangential force acting on the surface of material under test required to obtain a scratch of width b. In this case, hardness is expressed as the ratio of that force to the scratch cross-section or a magnitude proportional to it, or else as a quotient of the work necessary to produce the scratch and its volume. Proponents of this method (Yushkin, 1971) consider that scratch hardness tests in the present form play only a marginal role. Unlike Shreyner (1949), who contended that the results obtained under these methods are less accurate than those for mineral-bymineral scratch after Mohs, they accept that these tests have certain usefulness, but only of a complementary nature. The differences of opinion arise from the different approach to the question of accuracy of the method of determination itself, since as can readily be proved, a strict relationship exists between hardness defined as the ratio of load P to square of... 

The electronic chemical hardness, defined in eqn (23), gives a measure of the chemical reactivity of a given compound. Also the chemical potential,... 

It should be noted that the definition of local hardness has inherent ambiguity in it [87], The local hardness defined above requires a variation of p(7 ), keeping v(7 ) constant, which seems to be ambiguous because v(7 ) and p(7 ) are interdependent as has been proven by Hohenberg and Kohn [88]. 

It is interesting to analyze the long range behavior of the generalized local hardness defined by Eq. (20). Because of the exponential decay of the electronic density, one can show that far away from the nuclei, the dominant term comes from the coulombic contribution to the hardness kernel [28], that is... 

Expectancies that feed the flux come from all kind of human and non-human network-actors. They have no determined origin. As Egyptian mosquitoes, hardly definable targets that forge links and arouse chain reactions (Gallon 2006), injunction as a flux does not structure society but crosses it, transmitting what it brings. 

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