Constant, hardness

Analysis of Table II shows discrepancies in the hardness and stress behavior of a-C(N) H films. Although all the works reported a clear stress reduction upon nitrogen incorporation, the hardness sometimes is quoted as almost constant, or on the other hand clearly decreasing. In addition to the possible effect of different deposition methods and conditions, it can be easily seen that the differences in hardness testing methods are the major source for discrepancies. Constant hardness behavior is only reported with the use microindentation methods, like Vickers and Knoop microhardness. On the other hand, the use of low-load nanoindentation methods always led to a nitrogen-induced decrease in hardness. This is basically the consequence of two factors. The first one is the higher penetration... 

There have been several extensions of this analysis to incorporate the effect of time-dependent rate constants (hardly appropriate when there are so few reactants present) and an initial skewed Gaussian distribution for the hydrated electron which give an initial zero density at the origin... 

For rough estimates, the collisional cross section may be assumed to be velocity-independent, Qn(vn) = Qo = constant (hard-sphere approximation), so that the mean time between collisions becomes... 

Thus, standard tests account for much of the testing done in industry and are used to ensure product specifications. These tests measure stress-strain relationships, flex life, tensile strength, abrasion resistance, moisture retention, dielectric constant, hardness, thermal conductivity, etc. New tests are continually being developed and submitted to ASTM, and after adequate verification through "round robin" testing are finally accepted as standard tests. 

How fast do IMR actually proceed in comparison with ki and k, respectively The above discussion infers lhat ki and kc represent upper limits for rate constants of actual IMR. Indeed, experimentally measured rate constants hardly ever exceed these values, and in cases where substantially higher values have been reported in the literature, careful reexamination has shown that the reactions proceed with rate constants k ions with a substantial dipole moment, as will be shown below. 

The system is subject to two types of energies, one type of which is constant. Each bead of A or B has a constant hard core, such that no site on the lattice may be occupied by more than one bead. There is also a variable pairwise interaction applied when X and Y are nonbonded nearest neighbors. These interactions are assigned reduced energies... 

Therefore, the average of all entries can serve as an estimate for the entire family of reactions. This average rate constant hardly changes with temperature, so that we can use a value of 1.3E14cm /(molsec) for all temperatures. The rate constant for the reverse reaction (the C-H fission) is not constant but depends via IQq on the C-H bond strength. 

Kakiuchi and Endo studied the influence of the nature of the solvent on the pyridine-catalyzed reaction of benzoic acid with l,2-epoxy-3-phenoxypropane. The reaction is first order for acid, epoxide, and catalyst it was carried out in toluene-nitrobenzene and in toluene-dioxane mixtures as well as in different pure solvents. The dielectric constant was measured before the reaction started and after the reaction stopped it was noted that this constant hardly changes during the course of the reaction. A linear relationship between log q and D was dbserved in toluene-nitrobenzene, but not in dioxane-nitrobenzene according to the authors, this could be due to a specific solvating effect of dioxane. 

Figure 9.7 shows the hardness and modulus distributions of the MoDTC/ZDDP and ZDDP tribofilms, carburized steel disc, and fused silica as a function of the contact depth [1]. Since the fused silica as the standard sample for tip-shape calibration retained constant hardness and modulus values in a contact depth range from 5 nm, the hardness and modulus of the tribofilms were examined at contact depths greater than 5 nm. It was found that both kinds of tribofilms had the same hardness and modulus distributions relative to the contact depth. When the contact depth was greater than 30-40 nm, the mechanical properties were constant, with hardness staying at the fused silica level of 10 GPa and the modulus at the carburized disc level of 215 GPa. However, when the contact depth was reduced from 30 nm to 5 nm near the film surface, film hardness decreased from the fused silica level of 10 GPa to 6 GPa, and the modulus decreased from the carburized steel level of 215 GPa to 150 GPa. 

Another way to achieve the strongly time-dependent hardness range, preceding the achievement of the constant time independent minimum value of hardness predicted by equation (4.18), is to make hardness tests at elevated temperatures. As the test temperature increases above where T is the melting point of the sample, the hardness rapidly decreases and becomes time dependent until a temperature is reached where the dislocation mobility becomes high, the yield strength becomes very low, and hardness approaches the constant, time-independent value. It may not be easy with some ceramics to achieve the constant hardness zone because elevated temperature may permit diffusional creep, when once again the hardness will become obviously time dependent, and hardness values lower than that predicted by equation (4.18) will be achieved. 

One last matter deserves a few comments. Cracking appears to affect Vickers and Knoop indentations in different ways as illustrated in Figure 10. Extensive cracking underneath Vickers indentations seem to cause the ISE to have a transition point to a constant hardness plateau as described by Quinn and Quinn. The effect is most pronounced for very brittle ceramics. On the other hand, the present study shows that cracking around Knoop indentations causes the ISE trend to shift to lower hardness values, but only in some materials. A possible explanation for the differences may be made with reference to the schematics in Figure 10. 

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