Hardness increment

A straightforward estimate of the maximum hardness increment can be made in terms of the strain associated with mixing Br and Cl ions. The fractional difference in the interionic distances in KC1 vs. KBr is about five percent (Pauling, 1960). The elastic constants of the pure crystals are similar, and average values are Cu = 37.5 GPa, C12 = 6 GPa, and C44 = 5.6 GPa. On the glide plane (110) the appropriate shear constant is C = (Cu - C12)/2 = 15.8 GPa. The increment in hardness shown in Figure 9.5 is 14 GPa. This corresponds to a shear flow stress of about 2.3 GPa. which is about 17 percent of the shear modulus, or about C l2n. 

As mentioned above alkali halide crystals are strongly hardened by small additions of divalent impurities. Data are available for 12 cases, the host crystals NaCl, NaBr, KC1, and KBr with additions of Ca2+, Sr2+, and Ba2+ (Chin, et al., 1973). It was found that the hardness increases depend only on the concentrations of the additions and not on the divalent specie (Ca, Sr, or Ba). However, a dependence on the valence (1, 2, or 3) is observed. It was also found that hardness increment is proportional to the square root of the concentration, (C1/2). 

Fig. 5.13. Construction to derive the additive hardness increment equation in generating a three-constituent solid solution.

Since linear variation of hardness is not always the case, equation (5.7) is approximate. But Glazov and Vigdorovich consider that the production of many very complex solid solution systems does require some method if only rough, for hardness analysis of such systems. They formulate the additivity principle for multicomponent systems as follows the numerical increase in hardness of multi-component solid solutions equals the sum of hardness increments in bi-component solutions... 

Similar relations were obtained in tests of three-component systems. It should be noted that analysis of hardness variation with composition is possible only in the case of additive hardness increment as a function of concentration. For low concentrations of admixtures, usually below 5%... 

Assuming tentatively zero interaction in hardness increment between individual constitutents, and the existence of a linear hardness-composition relation in a two-component system, we obtain... 

The hardness of the electron beam irradiated specimens increased from that of crack-healed specimens without electron beam irradiation in the vicinity of the sur ce. The dq>th influenced by electron beam irradiation was found to be about 2 pm. Irradiation of0.432 MGy caused a 38 % hardness increment to surface of the crack-healed specimens. A similar irradiation effect was achieved in non crack-healed specimen. The hardness in the vicinity of the surface varied with electron beam irradiation dose and the optimized conditions of electron beam irradiation to crack-healed and non crack-healed specimens were determined to be 0.432 MGy and 0.216 MGy, respectively. 

But the two curves still do not exactly match, as Fig. 8.7 shows. The reason is a displacement of (for example) u = l f2 in tension and compression gives different strains) it represents a drawing out of the tensile specimen from 1q to 1.5 1q, but a squashing down of the compressive specimen from /q to 0.5/q. The material of the compressive specimen has thus undergone much more plastic deformation than the material in the tensile specimen, and can hardly be expected to be in the same state, or to show the same resistance to plastic deformation. The two conditions can be compared properly by taking small strain increments... 

Theisen C, Johann C, Deacon MP, Harding SE (2000) Refractive Increment Data Book for Polymer and Biomolecnlar Scientists. Nottingham University Press, Nottingham, UK... 

Another way to think about this is in terms of shallow and deep innovation. Shallow innovation focuses on incremental changes to existing products and services. Shallow innovation can be quick to deliver and relatively low risk. The benefits may not be great, but they are easy to obtain. Deep innovation takes a hard look at the real user needs. It uses a thorough understanding of the way in which a product or service is used, and the benefits it delivers, to produce new concepts that can transform a market. 

An alternative to the measurement of the dimensions of the indentation by means of a microscope is the direct reading method, of which the Rockwell method is an example. The Rockwell hardness is based on indentation into the sample under the action of two consecutively applied loads - a minor load (initial) and a standardised major load (final). In order to eliminate zero error and possible surface effects due to roughness or scale, the initial or minor load is first applied and produce an initial indentation. The Rockwell hardness is based on the increment in the indentation depth produced by the major load over that produced by the minor load. Rockwell hardness scales are divided into a number of groups, each one of these corresponding to a specified penetrator and a specified value of the major load. The different combinations are designated by different subscripts used to express the Rockwell hardness number. Thus, when the test is performed with 150 kg load and a diamond cone indentor, the resulting hardness number is called the Rockwell C (Rc) hardness. If the applied load is 100 kg and the indentor used is a 1.58 mm diameter hardened steel ball, a Rockwell B (RB) hardness number is obtained. The facts that the dial has several scales and that different indentation tools can be filled, enable Rockwell machine to be used equally well for hard and soft materials and for small and thin specimens. Rockwell hardness number is dimensionless. The test is easy to carry out and rapidly accomplished. As a result it is used widely in industrial applications, particularly in quality situations. 

Centralized electrification requires massive amounts of capital [10]. The dispersed nature of houses and low potential demand create little incentive for power companies to provide access to rural areas. In addition, extending the grid may be unrealistic due to transmission line costs or hard terrain [5]. Thus, in rural areas, off-grid and mini-grid solutions make the most sense. Such systems can consist of a single home or several small homes and businesses. The systems can be incremental and scalable and applied to many different conditions and environments [10]. Off-grid and mini-grid options for renewable electricity include solar, wind, clean biomass, and micro-hydro. These options for renewable power will be discussed in more detail below. 

The loops around the precipitates act as stress concentrators. They exert shearing stresses in addition to the applied stress on the particles. When enough of them have accumulated, the precipitates will be plastically sheared as the loops disappear one by one. This is the basis of a theory of precipitation hardening in an aluminum-copper alloy by Fisher, Hart, and Pry (1953). The precipitate in this case is CuA12, and the precipitates cause an increment of hardening added to the hardness of the solid-solution (Al-Cu) matrix. Quantitative agreement with experimental measurements is fair. 

Figure 9.9 Effect of mixing Ca and Sr fluorides on hardness. The increment of hardness at 50% SrF2 is about 58kg/mm2. Data from (Chemevskaya, 1966).

The idea of using the linear phase increments to achieve frequency-shifted excitation can be adopted almost to any pulses, such as hard (amplitude fixed) pulses, shaped pulses, and even adiabatic inversion pulses. Unlike any other pulses, the adiabatic pulses have already used non-linear phase increments for tilting the effective RF field slowly compared with the Larmor frequency of the spins in the rotating frame in order to fulfill the adiabatic condition. 

The error in (a) is stated to compare favourably with calibration from benzene, since the absolute value of R90 is hardly known to this accuracy. In (b) the concentration of DNA was measured spectrophotometrically via the molar phosphorous extinction coefficient of 6415 (with a standard deviation of 2%). The low error in (c) arises from low levels of dust achieved as well as the integration over a period of 10 secs of the readings on a digital output. The specific refractive index increment used in (d) was an experimental one from the literature. In point of fact the assess-... 

Different surfactants are usually characterised by the solubility behaviour of their hydrophilic and hydrophobic molecule fraction in polar solvents, expressed by the HLB-value (hydrophilic-lipophilic-balance) of the surfactant. The HLB-value of a specific surfactant is often listed by the producer or can be easily calculated from listed increments [67]. If the water in a microemulsion contains electrolytes, the solubility of the surfactant in the water changes. It can be increased or decreased, depending on the kind of electrolyte [68,69]. The effect of electrolytes is explained by the HSAB principle (hard-soft-acid-base). For example, salts of hard acids and hard bases reduce the solubility of the surfactant in water. The solubility is increased by salts of soft acids and hard bases or by salts of hard acids and soft bases. Correspondingly, the solubility of the surfactant in water is increased by sodium alkyl sulfonates and decreased by sodium chloride or sodium sulfate. In the meantime, the physical interactions of the surfactant molecules and other components in microemulsions is well understood and the HSAB-principle was verified. The salts in water mainly influence the curvature of the surfactant film in a microemulsion. The curvature of the surfactant film can be expressed, analogous to the HLB-value, by the packing parameter Sp. The packing parameter is the ratio between the hydrophilic and lipophilic surfactant molecule part [70] ... 

Further, ions are not hard, billiard ball like spheres. Since the wave functions that describe the electronic distribution in an atom or ion do not suddenly drop to zero amplitude at some particular radius, we must consider the surfaces of our supposedly spherical ions to be somewhat fuzzy. A more subtle complication is that the apparent radius of an ion increases (typically by some 6 pm for each increment) whenever the coordination number increases. Shannon10 has compiled a comprehensive set of ionic radii that take this into account. Selected Shannon-type ionic radii are given in Appendix F these are based on a radius for O2- of 140 pm for six coordination, which is close to the traditionally accepted value, whereas Shannon takes the reference value as 126 pm on the grounds that it gives more realistic ionic sizes. For most purposes, this distinction does not mat-... 

At room temperature, the storage modulus is increased about fivefold in OMMT-filled vulcanizates. The increment of this value in CR-OLDH is much smaller, whereas unmodified clays give hardly any change at room temperature. 

A1203. On the other hand, from a comparison of Hv for pure binder and wheel binder, it follows that the increment in binder hardness was 500 (+77.6%), and therefore the A1203 diffusion from grain into the binder was of the order of 20% enrichment compared with the initial composition of the binder. In turn, for a 4.2% increase of A1203 content in the binder (Fig. 4.5.13) the depth of a hole made by the blower decreases by... 

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