Thermal negative coefficients

Thermal Expansion. Coefficients of linear thermal expansion and linear expansion during transformation are listed in Table 7. The expansion coefficient of a-plutonium is exceptionally high for a metal, whereas those of 5- and 5 -plutonium are negative. The net linear increase in heating a polycrystalline rod of plutonium from room temperature to just below the melting point is 5.5%. 

Note Negative average error indicates that the correlation is conservative. The thermal diffusion coefficients of the reactor vendors proprietary grid geometries are not considered in this comparison. 

The thermal expansion coefficients of PVCL and a copolymer in water, tfpol> were determined by PPC as a function of temperature (Fig. 23) [180]. The plots can be divided into four temperature ranges. Below the transition temperature, 10 < T < 30 °C, g i for PVCL remains constant, while in the case of PVCL-g-34, apoi has a negative slope. In both cases, apoi undergoes a sharp... 

The thermal expansion coefficient of bulk silicon is positive at RT (2.6 x 1CT6 K-1), but becomes negative below 120 K. The thermal expansion coefficient of micro PS for heating from 290 to 870 K is found to be negative (-4.3x 10 6 KT1), which can be ascribed to hydrogen desorption and oxidation of the inner surface [Di7]. For meso PS the thermal expansion coefficient was found to increase with porosity in the temperature regime between 90 K and 300 K, from 0.4xl0-6 K 1 to... 

Figure 13.14 The PPC traces of the thermal expansion coefficient a (deg-1) as a function of temperature for chymotrypsinogen and RNase A. The data show that both native (low-temperature region) proteins exhibit a strong negative temperature coefficient as well as a large positive curvature. (Permission to use the figure granted by MicroCal, LLC.)...

Some zeolites such as AIPO4-5 (API) have a negative coefficient of thermal expansion over certain temperature ranges [230, 231]. For a zeolite formed into a pellet, one method to verify the presence of a negative coefficient of thermal expansion is by thermal mechanical analysis (TMA). For just the zeolite, powder X-ray diffraction at various temperatures can be used. Such an analysis can be of importance for identifying pellet strength or vessel containment issues. 

The state of polarization, and hence the electrical properties, responds to changes in temperature in several ways. Within the Bom-Oppenheimer approximation, the motion of electrons and atoms can be decoupled, and the atomic motions in the crystalline solid treated as thermally activated vibrations. These atomic vibrations give rise to the thermal expansion of the lattice itself, which can be measured independendy. The electronic motions are assumed to be rapidly equilibrated in the state defined by the temperature and electric field. At lower temperatures, the quantization of vibrational states can be significant, as manifested in such properties as thermal expansion and heat capacity. In polymer crystals quantum mechanical effects can be important even at room temperature. For example, the magnitude of the negative axial thermal expansion coefficient in polyethylene is a direct result of the quantum mechanical nature of the heat capacity at room temperature." At still higher temperatures, near a phase transition, e.g., the assumption of stricdy vibrational dynamics of atoms is no... 

Negative thermal expansion coefficients along the chain axes have been observed experimentally on many crystalline polymer lattices7,16 -18). Hence, the thermal contraction along the chain axis seems to be a general phenomenon in crystalline polymers. As a result of this conclusion, we are immediately faced with the question... 

A surprising disappearance of the thermomechanical inversion of heat at elevated temperatures has been observed by Kilian 9,88). At 90 °C, the thermomechanical inversion in SBR and NR is found to disappeare in spite of the constant value of the thermal expansion coefficient. This means that the temperature dependence of elastic force should be negative from the initial deformations, which is in contradiction with experiment. This very unusual phenomenon was supposed to be closely related to rotational freedom which will continuously be activated above some characteristic temperature 9,88). 

Dilatometric studies have demonstrated the negative thermal expansivity for many oriented crystalline polymers 64,170 176). The results of these experimental studies may be summarized as follows. Cold-drawing of PE below Tm 172) and solid-state extrusion under elevated pressure 170 1711 lead to a monotonous decrease of the positive thermal expansion coefficient with increasing draw ratio. At a certain degree of orientation, dependent on temperature, PM becomes negative with Pi < Pell (Fig. 16). This is the second way of reaching negative expansivity applied, e.g. to POM (w = 63 % Tdr = 423 K) 173>. 

Composite material with a negative coefficient of thermal expansion. 

The possibility of negative thermal-expansion coefficient (TEC) values along a direction of strong coupling in layered or chain structures (the so-called membrane effect") was suggested for the first time by Lifshitz [4] for strongly anisotropic compounds. In the phonon spectra of such compounds... 

The general effect of most fillers is to reduce the coefficient of thermal expansion of the cured epoxy resin in proportion to the degree of filler loading. Certain fillers, such as zirconium silicate and carbon fiber, have a negative coefficient of thermal expansion. These are very effective in lowering the expansion rate of the epoxy, especially at elevated temperatures. 

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