Hardness ambiguity

Hardness is a somewhat ambiguous property. A dictionary definition is that it is a property of something that is not easily penetrated, spread, or scratched. These behaviors involve very different physical mechanisms. The first relates to elastic stiffness, the second to plastic deformation, and the third to fracturing. But, for many substances, the mechanisms of these are closely related because they all involve the strength of chemical bonding (cohesion). Thus discussion of the mechanism for one case may provide some understanding of all three. 

These qualitative explanations, whether they be hard-soft or ionic-covalent or Class A-Class B, all suffer from the arbitrary way in which they can be employed. All Lewis acid-base type interactions are composed of some electrostatic and some covalent properties, i.e., hardness and softness are not mutually exclusive properties. Predictions are straightforward when dealing with the extremes, but with other more ambiguous systems, one can be very arbitrary in explaining results and the predictive value is impaired. What is needed is a quantitative assessment of the essential factors which can contribute to donor strength and acceptor strength. Proper combination of these parameters should produce the enthalpy of adduct formation. Until this can be accomplished, one could even question the often made assumption that the strength of the donor-acceptor interaction is a function of the individual properties of a donor or acceptor. 

One of the drawbacks of sequential optimization methods is that optimizing two or more criteria at the same time is hard, if not impossible. If the two or more criteria are combined in one overall criterion, which is advocated sometimes, then ambiguous results are obtained. This is shown in Chapter 4. There are ways to overcome this ambiguity to some extent [21]. Another drawback of a sequential procedure is that it gives not much information on the dependence of the criterion on the design variables. In the context of robustness this is a very serious drawback. This is one of the reasons why the use of sequential optimization methods is not present in this book. 

Many of the chemical and physical properties of mineral fillers are important in their application in thermoplastics. These include purity, specific gravity, hardness, electrical, thermal and optical properties, surface area, particle shape and size. The determination and importance of many of these has been covered in several reviews [65,66]. Only a brief coverage is given here for the less ambiguous properties such as specific gravity, hardness and standard thermal and optical properties, with most attention being concentrated on properties such as size and shape which have been found to give particular problems in measurement and interpretation. 

Many of the standard principles of managerial control are of course relevant to a project. Milestones and targets by which you can judge whether or not project objectives are satisfactorily on the road to attainment need to be set. Reports on progress need to be called for. But any attempt at a mechanistic approach to control would be quite inappropriate for ambiguous, uncertain tasks in a dynamic context, when it is hard to specify in advance which elements to control and how to do so . (Boddy and Buchanan, 1992). 

We should also briefly discuss the reliability of PC threshold measurements for determining ,. The problem here is that for each temperature the spectroscopic data (Atheoretical expression, such as that found in Eq. (45). Above T = 0, when phonons are involved, there is no well-accepted theory of the photon capture cross section to use for data fitting. In fact, even at T = 0, the theoretical situation is ambiguous because the exact form of the impurity potential is not known. Thus, unless the PC threshold data are very steep, the energies derived from them may be hard to determine with great accuracy. 

An attempt has been made to analyse whether the electrophilicity index is a reliable descriptor of the kinetic behaviour. Relative experimental rates of Friedel-Crafts benzylation, acetylation, and benzoylation reactions were found to correlate well with the corresponding calculated electrophilicity values. In the case of chlorination of various substituted ethylenes and nitration of toluene and chlorobenzene, the correlation was generally poor but somewhat better in the case of the experimental and the calculated activation energies for selected Markovnikov and anti-Markovnikov addition reactions. Reaction electrophilicity, local electrophilicity, and activation hardness were used together to provide a transparent picture of reaction rates and also the orientation of aromatic electrophilic substitution reactions. Ambiguity in the definition of the electrophilicity was highlighted.15... 

Responses should be relevant to the questions being asked, as well as being fairly easy to obtain. They should provide both necessary and sufficient answers to the questions being posed. An ambiguous response is a poorly designed one, from which it is often hard to salvage meaning, especially after the fact and after the deadline for decision. 

To illustrate descriptive analysis, I will draw from both the wine and beer industry. Oregon State University s Sensory Science Laboratory, located in the Department of Food Science and Technology, is heavily involved in wine and beer research. The principle problems and solutions in the sensory analysis of wine and beer should be transferable to other products. Common wine descriptors, such as soft, hard, fat, are ambiguous. What do soft or hard mean when referring to wine The goal of descriptive analysis is to use precise terms, even referring to specific chemical entities when possible. In the wine industry, objective sensory analysis must overcome the historical romance of wine. 

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