Order of Hardness

One could, of course, attempt to use Equation (1.4) by taking one set of data to assign values of 5a, 5b, ta and ctr to a number of acids and bases, and then using another set of data to check them. Actually something similar to this has already been done by Drago and Wayland, with their well-known four-parameter equation.  

Here E a and Eq measure ionic bonding and Ca and Cb measure covalent bonding. This is appropriate, since in looking for the reasons underlying the HSAB effect, it is clear that hard-hard interactions are mainly ionic and soft-soft interactions are mainly covalent. But there are many other effects, such as repulsions due to the overlap of filled atomic orbitals on A and B. For this and other reasons, E and C may not be good measures of 5 and a. A disadvantage of Equation (1.5) is that different numbers are needed for different environments. 

Actually chemistry is usually not based on Reaction (1.1), but on the exchange reaction 

The following conclusion can then be drawn, provided A and A are acids of the same strength, or B and B are bases of the same strength  

Equation (1.7) is based on Equation (1.5) but does not require numbers for its 

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The strength of the complexation is a function of both the donor atom and the metal ion. The solvent medium is also an important factor because solvent molecules that are potential electron donors can compete for the Lewis acid. Qualitative predictions about the strength of donor-acceptor complexation can be made on the basis of the hard-soft-acid-base concept (see Section 1.2.3). The better matched the donor and acceptor, the stronger is the complexation. Scheme 4.3 gives an ordering of hardness and softness for some neutral and ionic Lewis acids and bases. 

Hardness and softness are determined by atomic size, and the order of hardness in each of these sets is consistent with the size trends among the species. 

The EA/CA ratio was proposed as a measure of hardness of the Lewis acid, and EB/CB as hardness of the Lewis base in aqueous solution (17). It now seems that the E/C ratio is not a measure of hardness in the sense in which Pearson (5,5a) defined hardness. Rather, the E/C ratio for a Lewis acid or base is a measure of the tendency to ionicity in the M-L bonds formed. The EAICA ratio should rather be called IA, and the EbICb ratio IB, the tendency to ionic bonding in forming the M-L bond. Acids and bases in Tables I and II are placed in order of increasing tendency towards ionicity in the M-L bond, according to the E/C ratios IA and 7b. A justification for this interpretation is that the order of IA values for metal ions in aqueous solution strongly resembles the order of hardness derived by Pearson (19) from enthalpies of complex forma-... 

If an external body is engulfed, it can enrich the star with the original interstellar medium abundances of 6Li, 7Li, 9Be and 10,11B (written here in increasing order of hardness to be destroyed by thermonuclear reactions). This mechanism is then supposed to produce stellar enrichment of these elements up to the maximum meteoritic value. Also, the engulfing star will suffer a rotational increase due to the gain of the planet momentum and a thermal expansion phenomenon due to the penetration of the body provoking mass loss phenomena (Siess Livio 1999). An extension to this scenario has been proposed by Denissenkov Weiss (2000) in order to explain supermeteoritic Li abundance values, via a combination of stellar rotation and activation of the 7Be mechanism at the base of the convective layer produced by the penetration of the external body. 

Table SAG Example of tool materials arranged in order of hardness... 

There is no single technique for measuring hardness which covers the range of hardness values available in plastics. Therefore, it is necessary to quote four different hardness scales. In decreasing order of hardness they are ... 

Mohs Hardness. A scale of scratch hardness based on a series of minerals in ascending order of hardness. The original scale, due to Mohs, in the early 19th century, is still used, with minor changes, but an extended scale takes account of the need for greater differentation between hard materials. See APPENDIX C. 

HSAB (Hard and Soft, Acids and Bases) principle was proposed by Pearson (1963, 1968). This is summarized as (1) hard acids are in an affinity with hard bases, (2) soft acids are in large volume and have small charge and their electronegativity is large, (3) hard acids react with hard acids to form ionic compounds, while (4) covalent compounds form by the reaction of soft acids with soft bases. Acids and bases are classified according to this principle (Table 1.6). For instance, the order of hardness is F > Cl > Br > I , Cu" > Ag" > Au". HS tends to combine with soft cations such as Au", Hg" and PF to form HS complexes. Base metal cations such as Zn ", Pb ", Cu", and Fe " tend to combine with relatively hard anions such as Cl to form chloro-complexes. 

Hardness is defined as the resistance of a material to deformation, particularly permanent deformation, indentation or scratching. Hardness is purely a relative term and should not be confused with wear and abrasion resistance of plastics. For example, polystyrene has a high hardness but a poor abrasion resistance. Many tests have been devised to measure hardness. However, Rockwell and Durometer hardness tests are commonly used. The Rockwell hardness test measures the net increase in depth impression as the load on an indentor is increased from a fixed minor load to a major load and then returned to a minor load. The hardness numbers derived are just numbers without units. Rockwell hardness numbers in increasing order of hardness are R, L, M, E and K scales. The higher the number in each scale, the harder is the material. The Durometer hardness test is based on the penetration of a specified indentor forced into... 

The difference in behavior due to having different secondary slip systems active in these two tetragonal silicides appears to be slight. First, WSi2 has a more obvious anisotropy factor, 37% on (100) second, there is a reversal in the order of hardness on (101) when [100] is the softest direction for VSi2 but hardest for MoSi2. 

J. F. Lutsko, Molecular Chaos, Pair Correlations and Shear-Induced Ordering of Hard Spheres, Phys. Rev. Lett. 77, 2225-2228 (1996). 

G. Lasher, Nematic Ordering of Hard Rods Derived from a Scaled Particle Treatment, J. Chem. Phys., Vol. 53, p. 4141 (1970). 

Lutsko, J. 1996. Molecular chaos, pair correlations, and shearinduced ordering of hard spheres. Phys. Rev. Lett. 77 2225. 

In ascending order of hardness and polymerization, we singled out three types of structures of crystalline superhard phases ... 

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