Temperature-dependence of hardness

Lankford J., 1983, Comparative study of the temperature dependence of hardness and compressive strength in ceramics, J. Mater. Sci., 18, 1666. 

Figure 2.9 Temperature dependence of hardness of TiC, A1203, and TiN. The range of hardness of WC-Co alloys is also shown. (Ref. 14).

In the present section it will be shown that microhardness can conveniently detect the glass transition temperature Tg by following // as a function of temperature. We will illustrate the temperature dependence of hardness in case of two amorphous polymers - PMMA and poly(vinyl acetate) (PVAc) - and two semicrystalline... 

Figure 3. Temperature dependences of hardness (HV) for the ternary (Ti) + T +TiB and binary (Ti) +TiB eutectic alloys.

Polysiloxane added to tire tread rubber composition improves processing characteristics of rubber containing silica but also improves several characteristics of tire such as temperature dependency of hardness, grip on ice/snow, abrasion resistance, etc. Polysiloxane does not migrate from tire composition. ... 

A third indentation test parameter of fundamental importance is temperature. In several studies of the temperature dependence of hardness, an activated process becomes apparent from Arrhenius-type behavior. Calculation of the activation energies associated with thermal softening is characteristic of the activated processes governing plastic flow in crystals. " Thus, the role played by the crystal structure in determining micro- and low-load hardness values must be a major one since, apart from its effect on lattice energy, the actual arrangement of the ions in a ceramic crystal is important in determining the ease of plastic flow. This aspect of ceramic hardness and its potential applications is discussed in Chapter 3. 

Nis2] Mechanical tests Temperature dependence of hardness... 

J. H. Westbrook, The temperature dependence of hardness of some common oxides , Rev. Hautes Temper, et Refract. 3, 47-57 (1966). 

The long-wavelength IR spectra of trigonal prismatic technetium clusters and a number of unusual physico-chemical properties of the clusters with ferrieinium cations [108] support the latter assumption. The discovered properties of the clusters with ferrieinium cations may be accounted for by the formation of the conductivity bands and, probably, hard-fermion bands in these compounds by the 5s(5p)-AO s of technetium atoms and 4s(4p)-AO s of the iron atoms. The formation of these bands may be supported by the following facts the ESR spectra of these compounds with geft close to that of a free electron temperature independent conductivity and an unusual temperature dependence of the Mossbauer and X-ray photoelectron spectra [108]. 

Calculations of the capacitance of the mercury/aqueous electrolyte interface near the point of zero charge were performed103 with all hard-sphere diameters taken as 3 A. The results, for various electrolyte concentrations, agreed well with measured capacitances as shown in Table 3. They are a great improvement over what one gets104 when the metal is represented as ideal, i.e., a perfectly conducting hard wall. The temperature dependence of the compact-layer capacitance was also reproduced by these calculations. 

Figure 5.14 Normalized temperature dependence of the hardnesses of diamond, Si, and Ge. Note that the hardnesses divide by the low temperature hardnesses begin to decrease at the respective Debye temperatures (0).

J. H. Westbrook, Temperature Dependence of the Hardness of Secondary Phases Common in Turbine Bucket Alloys, Trans. TMS-AIME, 209,898 (1957). 

Debye phonon velocity) and lower in the case of very dissimilar materials. For example, the estimated Kapitza resistance is smaller by about an order of magnitude due to the great difference in the characteristics of helium and any solid. On the other hand, for a solid-solid interface, the estimated resistance is quite close (30%) to the value given by the mismatch model. The agreement with experimental data is not the best in many cases. This is probably due to many phenomena such as surface irregularities, presence of oxides and bulk disorder close to the surfaces. Since the physical condition of a contact is hardly reproducible, measurements give, in the best case, the temperature dependence of Rc. 

The natural van der Waals radii of Table 1.1 are generally found to be in good correspondence to empirical values. However, one can establish that the van der Waals surface of a bonded atom is generally somewhat ellipsoidal (rather than spherical), with major and minor axes respectively transverse and longitudinal to the bond direction. One can also evaluate the hardness (radial derivative of steric energy), charge dependence, and temperature dependence of van der Waals radii, thereby obtaining many quantitative refinements of empirical steric concepts. 

Softening as a result of micro-Brownian motion occurs in amorphous and crystalline polymers, even if they are crosslinked. However, there are characteristic differences in the temperature-dependence of mechanical properties like hardness, elastic modulus, or mechanic strength when different classes of polymers change into the molten state. In amorphous, non-crosslinked polymers, raise of temperature to values above results in a decrease of viscosity until the material starts to flow. Parallel to this softening the elastic modulus and the strength decrease (see Fig. 1.9). 

Figure 6.5 Temperature dependence of the characteristics of sodium k-carrageenan particles dissolved in an aqueous salt solution (0.1 M NaCl). The cooling rate is 1.5 °C min-1, (a) ( ) Weight-average molar weight, Mw, and (A) second virial coefficient, A2. (b) ( ) Specific optical rotation at 436 nm, and ( ) penetration parameter, y, defined as tlie ratio of the radius of the equivalent hard sphere to the radius of gyration of the dissolved particles (see equation (5.33) in chapter 5). See the text for explanations of different regions I, II, III and IV.

Fig. II. (a) Temperature dependence of the magnetization for 200-nm thick Ga, MnrAs with x =0.053. The magnetic field is applied perpendicular to the sample surface (hard axis). The inset shows the temperature dependence of the remanent magnetization (0 T) and the magnetization at 1 T in a field parallel to the film surface, (b) Temperature dependence of the saturation magnetization determined from the data shown in (a) by using ArTott plots (closed circles). Open circles show inverse magnetic susceptibility and the Curie-Weiss fit is depicted by the solid straight line (Ohno and Matsukura 2001).

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