Expansion with increasing temperature

The EXAFS study of Ni in hydrothermal bromide-containing solutions by Wallen et al. (1998) shows a slight Ni-0 bond length expansion with increasing temperature, which contrasts with the EXAFS results for the other ions examined in hydrothermal solutions to date. The situation for NiBr solutions is complicated, however, by the formation of bromidonickel(II) complexes and increased hydrolysis with increasing temperature, so it is difficult to separate these effects from ion-solvent interactions on changes in Ni-0 distance and first-shell coordination number. 

BagGajsSiso- Qiu et al. synthesized BagGaisSiso via a stoichiometric route and characterized its structure [20]. The lattice parameter showed smooth expansion with increasing temperature. And the refinement of site mixed occupancies showed that Ga prefers to occupy the 6c site. 

For the optimization of SMP-based stents, their deployment process after insertion can be simulated. Previous simulations of braided stents based on shape memory polyurethanes showed gradual expansion with increasing temperature up to physiological temperature, so that abrupt overpressures to the arteries are avoided during the process (Hyun Kim et a/., 2010). 

Density reduction and liquid expansion with increasing temperature and pressure require only 85 % filling. 

One may expect that with increasing temperature the thermal expansion in the crystalline regions will lead to an enlargement of the chain cross-section in the crystalline phase which in turn will induce a decrease in the cohesion energy of the crystals thus causing a gradually lower resistance to plastic deformation. In order to minimize the effect of the surface layer, the influence of temperature on microhardness has been investigated in PE crystallized at 260 °C under a pressure of 5 Kbar 28). The decrease of MH with temperature for the above chain extended PE material is depicted in Fig. 11. The hardness decrease follows an exponential law... 

Paper [16] reported unusual behaviour of the widths of rotational components of the P-R doublet of HC1 dissolved in SFg. They decreased with increasing temperature. The widths of spectral lines, obtained with (7.73), really must decrease with increasing temperature, because tc decreases due to intensification of thermal motion, and V[ due to thermal expansion. 

It is not the purpose of chemistry, but rather of statistical thermodynamics, to formulate a theory of the structure of water. Such a theory should be able to calculate the properties of water, especially with regard to their dependence on temperature. So far, no theory has been formulated whose equations do not contain adjustable parameters (up to eight in some theories). These include continuum and mixture theories. The continuum theory is based on the concept of a continuous change of the parameters of the water molecule with temperature. Recently, however, theories based on a model of a mixture have become more popular. It is assumed that liquid water is a mixture of structurally different species with various densities. With increasing temperature, there is a decrease in the number of low-density species, compensated by the usual thermal expansion of liquids, leading to the formation of the well-known maximum on the temperature dependence of the density of water (0.999973 g cm-3 at 3.98°C). 

With increasing temperature the contrast [151,152] is, in general, increasing, because the thermal expansion coefficient of the soft (amorphous) phase is generally higher than that of the hard (crystalline) phase. 

Table 9-3 lists thermal expansion coefficients for a number of substances. Water behaves in an unusual fashion. The thermal expansion coefficient decreases with increasing temperature up to about 4°C, after which the thermal expansion coefficient increases with temperature. Coefficients for water are readily determined from the steam tables. 

The heat capacity models described so far were all based on a harmonic oscillator approximation. This implies that the volume of the simple crystals considered does not vary with temperature and Cy m is derived as a function of temperature for a crystal having a fixed volume. Anharmonic lattice vibrations give rise to a finite isobaric thermal expansivity. These vibrations contribute both directly and indirectly to the total heat capacity directly since the anharmonic vibrations themselves contribute, and indirectly since the volume of a real crystal increases with increasing temperature, changing all frequencies. The constant volume heat capacity derived from experimental heat capacity data is different from that for a fixed volume. The difference in heat capacity at constant volume for a crystal that is allowed to relax at each temperature and the heat capacity at constant volume for a crystal where the volume is fixed to correspond to that at the Debye temperature represents a considerable part of Cp m - Cv m. This is shown for Mo and W [6] in Figure 8.15. 

The thermal expansion of a crystal with increasing temperature is generally described by a second-order polynomial in T of type... 

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