Hardness parameters, table

Water Quality Maintenance. In addition to controlling algae and microorganisms such as bacteria, proper swimming pool maintenance requires control of free and combined available chlorine, pH, alkalinity, hardness, and saturation index. Ranges for various swimming pool parameters (Table 2) are recommended by The National Spa and Pool Institute (14). 

The hardness parameters specified in Table 8.1 apply to glazed bodies whose hardness is usually 0.16-0.25 degrees on the Mohs scale lower than that of unglazed material. The 7-8 hardness interval for porcelain materials given by many authors is incorrect. It is specific to materials ranked under special ceramics of steatitic or mullite-corundum type (Tables 4.4.4, 5.6, 5.7). 

The carbides and nitrides of vanadium and titanium crystallize in the same face centered cubic (fee) system, and because of the closeness of their cell parameters (Table 15.1) form solid solutions. These ceramic materials exhibit interesting mechanical, thermal, chemical and conductive properties.1,2 Their high melting point, hardness and wide range of composition have therefore attracted considerable attention in the last decade. Moreover, their good abrasion resistance and low friction also make these ceramics attractive for protective coating applications.3-5 Chemical vapor deposition (CVD) is a commonly used technique for the production of such materials. In the conventional thermally activated process, a mixture of gases is used.6-9 In the case of TiC, TiN, VC and VN, this mixture is... 

Mono and difluorosilyl radicals exhibit similar properties with gradually changing parameters (Table 27). a H decreases rapidly from SiHF2 (89.9 G) to SiH3 (8 G), while theg factor hardly varies. All data so far obtained are consistent with pyramidal structures for mono and difluorosilyl radicals. 

Table 1.4 Empirical Hardness Parameters for Cationic Lewis Acids ...

Table 1.5 Empirical Hardness Parameters for Anionic Bases ...

Table I. Ionic refractions (Ro) and corresponding hardness indices, n, = (4k oKo ) compared to ionic radii (r,) and hardness parameters derived therefrom. r)2 = Htieori). After Ref. [14]...

The chemical approximation also explained the question of units for hardness, 1 V/e = 6.2418 X 10 F" , and opened a way to evaluation of atomic hardness from available chemical data of polarizability and atomic radii for free as well as for bonded atoms and ions t) = (47tCo) Rn - The versatile properties of hardness parameters derived from atomic refractions are shown in Table 2. Chemical approximation made possible the transformation of the... 

Table 7. Charge Transfer AlTmity calculated by various approaches for selected pairs of atoms in diatomic molecules. Absolute electronegativity and hardness parameters as in Ref. [4]...

Table 8. Hardness parameters for the ring carbons in mono-substituted benzenes (in volt/elcctron). Tin, is hardness of the molecule...

Table 9. Intcrearbon hardness parameters tIar in mono-substituted benzenes between the ipsocarbon (substituted) and three other ring carbons ortho-, meta- and para- to the substituent...

The standard bond lengths from Sutton, L.E. Tables of Interatomic Distances and ConAguration in Molecules and Ions, The Chemical Society, London 1958, were assumed, together with the experimental neutral atom electronegativity and hardness parameters [11]... 

To illustrate the method, the water molecule is taken as a case study. Given the geometry (Rqh = 0.9700 A and Rhh = 1.5288 A) and the hardness parameters (r ), it is possible to construct the hardness matrix as is shown in Table 3. After diagonalization the eigenvalues h and eigenvectors U e are obtained the softness matrix is obtained by inverting q. The softness kernels can also be calculated by using Eq. (22) and local softnesses are obtained via Eq. (7), (23) or (27). Table 3 also summarizes some results for the other sensitivity coefficients. 

Equation (35-9) describes the experimental data of a large number of systems quite well (Figure 35-11). Low values of the parameter, n, lead to high continuity factors that only vary slightly with the volume fraction of the hard phase (Table 35-6). High values of n, on the other hand, give continuity factors that decrease sharply with diminishing hard-phase volume fraction. 

Later on, Pearson tried to establish a quantitative scale of absolute hardness and softness.Absolute hardness is characterized by the value 17 and absolute electronegativity by the value %. The absolute hardness (rj) (is given by the expression r/ = (/ - A)/2, and the absolute softness (cr) by the expression (7 = 1/r/. Table 2.7.5. contains a selection of Pearson s absolute hardness parameters. 

The second important influence of the solvent on Lewis acid - Lewis base equilibria concerns the interactions with the Lewis base. Consequently the Lewis addity and, for hard Lewis bases, especially the hydrogen bond donor capacity of tire solvent are important parameters. The electron pair acceptor capacities, quantified by the acceptor number AN, together with the hydrogen bond donor addities. O, of some selected solvents are listed in Table 1.5. Water is among the solvents with the highest AN and, accordingly, interacts strongly witli Lewis bases. This seriously hampers die efficiency of Lewis-acid catalysis in water. 

In methacrylic ester polymers, the glass-transition temperature, is influenced primarily by the nature of the alcohol group as can be seen in Table 1. Below the the polymers are hard, brittle, and glass-like above the they are relatively soft, flexible, and mbbery. At even higher temperatures, depending on molecular weight, they flow and are tacky. Table 1 also contains typical values for the density, solubiHty parameter, and refractive index for various methacrylic homopolymers. 

Ha.rd Coa.1, The amount of coal in international commerce since ca 1945 necessitated an international system of coal classification and in 1956 the Coal Committee of the European Economic Community agreed on a system designated the International Classification of Hard Coal by Type (3). Volatile matter and gross calorific value on a moist, ash-free basis are among the parameters considered. Table 4 shows the various classes of the international system and gives the corresponding national names used for these coals. 

On the basis of the nucleophilicity parameters B, NBs, and fi (see Table 8-2) one expects less of the homolytic product in water than in methanol. This is, however, not the case. It has been known for many decades that a very complex mixture of products is formed in the decomposition of diazonium ions, including polymeric products, the so-called diazo tars. In alcohols this is quite different. The number of products exceeds three or four only in exceptional cases, diazo tars are hardly formed. For dediazoniation in weakly alkaline aqueous solutions, there has, to the best of our knowledge, been only one detailed study (Besse et al., 1981) on the products of decomposition of 4-chlorobenzenediazonium fluoroborate in aqueous HCOf/ CO]- buffers at pH 9.00-10.30. Depending on reaction conditions, up to ten compounds of low molecular mass were identified besides the diazo tar. 

These considerations, aiong with the fact that this parameter is hardly mentioned in any availabie table, have led several authors to research models that incorporate estimations of limits of inflammability. 

Ahrland et al. (1958) classified a number of Lewis acids as of (a) or (b) type based on the relative affinities for various ions of the ligand atoms. The sequence of stability of complexes is different for classes (a) and (b). With acceptor metal ions of class (a), the affinities of the halide ions lie in the sequence F > Cl > Br > I , whereas with class (b), the sequence is F < Cl" < Br < I . Pearson (1963, 1968) classified acids and bases as hard (class (a)), soft (class (b)) and borderline (Table 1.23). Class (a) acids prefer to link with hard bases, whereas class (b) acids prefer soft bases. Yamada and Tanaka (1975) proposed a softness parameter of metal ions, on the basis of the parameters En (electron donor constant) and H (basicity constant) given by Edwards (1954) (Table 1.24). The softness parameter a is given by a/ a - - P), where a and p are constants characteristic of metal ions. 

They indicated that the softness parameter may reasonably be considered as a quantitative measure of the softness of metal ions and is consistent with the HSAB principle by Pearson (1963, 1968). Wood et al. (1987) have shown experimentally that the relative solubilities of the metals in H20-NaCl-C02 solutions from 200°C to 350°C are consistent with the HSAB principle in chloride-poor solutions, the soft ions Au" " and Ag+ prefer to combine with the soft bisulfide ligand the borderline ions Fe +, Zn +, Pb +, Sb + and Bi- + prefer water, hydroxyl, carbonate or bicarbonate ligands, and the extremely hard Mo + bonds only to the hard anions OH and. Tables 1.23 and 1.24 show the classification of metals and ligands according to the HSAB principle of Ahrland et al. (1958), Pearson (1963, 1968) (Table 1.23) and softness parameter of Yamada and Tanaka (1975) (Table 1.24). Compari.son of Table 1.22 with Tables 1.23 and 1.24 makes it evident that the metals associated with the gold-silver deposits have a relatively soft character, whereas those associated with the base-metal deposits have a relatively hard (or borderline) character. For example, metals that tend to form hard acids (Mn +, Ga +, In- +, Fe +, Sn " ", MoO +, WO " ", CO2) and borderline acids (Fe +, Zn +, Pb +, Sb +) are enriched in the base-metal deposits, whereas metals that tend to form soft acids... 

For interpreting indentation behavior, a useful parameter is the ratio of the hardness number, H to the shear modulus. For cubic crystals the latter is the elastic constant, C44. This ratio was used by Gilman (1973) and was used more generally by Chin (1975) who showed that it varies systematically with the type of chemical bonding in crystals. It has become known as the Chin-Gilman parameter (H/C44). Some average values for the three main classes of cubic crystals are given in Table 2.1. 

The hardnesses of some perovskites are given in Table 11.1 (based on the data of Yamanaka et al., 2004). The table shows that these perovskites are moderately hard and the third column which lists their Chin-Gilman parameters indicates that they are predominately ionically bound. 

Plasma Synthesis The use of plasma methods has lead to a new range of materials having unique properties. An example is the family of amorphous elemental hydrides (eg cr-C H Of -Si H or-P H) which contain a variable proportion of H from almost zero to 50 atomic %. The carbon films, known variously as "hard carbon", "diamond-like carbon", " a-carbon" etc (9 ) - These layers are of considerable interest because of their optical and abrasion-resistant properties etc (Table I). The properties of these Gr-carbon films, can be tailored by modifying the plasma parameters. 

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