Negative coefficient of expansion

The thermal expansion curves of the individual Si02 modifications are plotted in Fig. 2, which also illustrates the discontinuous change in the specimen size occurring at the inversion temperature. The high-temperature quartz exhibits a quite rare anomaly, namely a negative coefficient of expansion in all crystallographic directions. On its expansion curve, tridymite likewise exhibits a peak followed by contraction. 

Some investigators report novel polymer composite materials that possess a negative coefficient of expansion. This means that the volume expansivity is negative. Can 8 be negative for such materials, as predicted in Equation (4.7). 

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. 

Composite material with a negative coefficient of thermal expansion. 

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. 

TdSand Fare positive. Therefore, the change in length d/ must be negative entropy-elastic bodies have a negative thermal coefficient of expansion. The total differential of the change in length of an entropy-elastic body is... 

According to Equation (11-20), the thermal coefficient of expansion 7 = (I ll)(dl IdT) of an entropy-elastic body is negative. The denominator (dlldF)r in Equation (11-22) corresponds to the increase in length when the stress is increased and is positive, so that (dF/dT)i must be positive in Equation (11-22). When an entropy-elastic body is heated, the stress increases. 

Most satellites and spacecraft have large antennas made of carbon/epoxy composites to achieve dimensional stability. Carbon fibers have a negative coefficient of thermal expansion (CTE) and epoxies yield composites which have no thermal expansion or contraction within the temperature range corresponding to the space environment. As a result, both the shape of the antenna surface and Its precise alignment are properly maintained. 

The lASAP radionuclide release model also assumes that because the Pb-Bi mixture has a negative coefficient of thermal expansivity, the volume of Pb-Bi has not decreased and remains in close contact with the SNF and SS structures, preventing water from seeping through any gaps and coming... 

The expansion of the areas of application for carbon fibers is stimulated by their attractive properties, not found in other materials, such as strength, electrical conductivity, stability on exposure to reactive media, low density, low-to-negative coefficient of thermal expansion, and resistance to shock heating. The most representative applications of carbon fibers and element carbon fibers are as sorption materials, electrostatic discharge materials, catalysts, and reinforcement materials in composites. 

Pu is a typically silver-white appearing metal which has a number of peculiar physical properties. The metal undergoes a total of five allotrppic modifications below the melting point, two of which have negative coefficients of thermal expansion. Table IV-1 summarizes the more important physical properties. 

Because of its slightly negative coefficient of thermal expansion in the longitudinal directions, composites made with polyaramid fibers exhibit excellent dimensional stability. One special application area is in high-performance electronic circuit boards requiring low x-y axis thermal expansion. 

Up to 200 C, the polyimide-based C/C composites have negative coefficients of thermal expansion parallel to the fibre axis (a = -1 10 °C . This expansion characteristic, generally typical of high-performance carbon fibres, is due to the carbon matrix, which has a partially preferred orientation structure and an expansion behaviour similar to C fibres. A proof of the preferred orientation can be seen in the fact that the coefficient of thermal expansion at room temperature is more negative for composites with higher final heat-treatment temperatures. Between the temperatures of 400 and 1400°C, the thermal expansion is linear, with a = 2 10 C-. ... 

For substances with a negative coefficient of thermal expansion under the proposed definition of isentropic volume, expansivity, P, does not violate the laws of thermodynamics quid pro quo. 

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