Negative Coefficient of Thermal Expansion

The volume expansivity of pure substances as given by Equation (2.20) is 

It is a parameter that is used to measure the volume expansivity of pure substances and is defined at constant pressure, P. In the field of materials science, the property of linear coefficient of thermal expansion is an important consideration in materials selection and design of products. This property is used to account for the change in volume when the temperature of the material is changed. The linear coefficient of thermal expansion is defined as 

For isotropic materials, P = 3a. Instruments such as dilatometers and x-ray diffraction (XRD) can be used to measure the thermal expansion coefQdent. Typical values of volume expansivity for selected isotropic materials at room tanperature are provided in Table 2.5. 

Volume Expansivity of Selected Materials at Room Temperature 

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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. 

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. 

Considering the thermal expansion process for pure substances in general and materials with negative coefficient of thermal expansion in particular, the process is not isobaric. Pressure was shown to be related to the square of the velocity of the molecules (Section 2.1.1). 

The process of measurement of volume expansivity cannot be isobaric in practice. When materials expand, the root mean square velocity of the molecules increases. For the materials with negative coefficient of thermal expansion when materials expand, the root mean square velocity of molecules is expected to decrease. In either case, forcing such a process as isobaric is not a good representation of theory with experiments. Such processes can even be reversible or isentropic. Experiments can be conducted in a careful manner and the energy needed supplied or energy released removed, as the case may be, in a reversible manner. Hence, it is proposed to define volume expansivity at constant entropy. This can keep the quantity per se from violating the laws of thermodynamics. 

Dimensional stability Is an Important attribute of space materials. High-performance carbon fibers possess a small, negative coefficient of thermal expansion at all temperatures below 375°C. That property, combined with their high modulus, permits a composites engineer to design a near-zerc thermal expansion material by combining carbon fibers with one of a variety of matrices. 

This is possible because carbon fibres have a negative coefficient of thermal expansion in fibre direction. The coefficient in the transversal direction is positive. This is due to the electrons in the basal planes of the graphite, which are highly mobile, similar to those in a metallic bond. 

An unusual feature observed in the Dhd phase of this compound is worth mentioning. The hexagonal lattice exhibits a negative coefficient of thermal expansion (Figure 7). This has been attributed to the... 

Figure 7. The intercolumn separation d in the columnar phases of HHTT plotted versus temperature, showing the negative coefficient of thermal expansion. ( ) Heating mode (O) cooling mode. (From Fontes et al. [18], reproduced by permission of the American Physical Society).

Like many oriented structures, LCP rods have very small or even negative coefficients of thermal expansion, which reduce stresses caused by temperature variations. Other favourable properties are their good chemical resistance and almost zero water uptake. 

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