Contraction, thermal

The thermal expansion of a material depends on the overall balance between all of the interatomic and intermolecular forces present. In some cases, this can produce materials that contract as the temperature increases. 

There are also materials known in which all axes contract as the temperature rises, including cubic ZrW20g and a silica polymorph with the faujasite stmcture. 

In the families of cordierite, yS-eucryptite, /3-cordierite and NZP, a mechanism similar to that giving rise to auxetic (negative Poisson s ratio) materials seems to occur (Section 10.3.2). The stmcture is built from inflexible layers, similar to those found in clay minerals (see Sub-section 

There are an increasing number of perovskite phases known that show a contraction as the temperature increases, at least over a certain temperature range. This effect is usually known, somewhat circuitously, as negative thermal expansion (NTE). Thermal contraction is not the result of a single mechanism. Here two examples are given. 

Doping the A-sites of PbTiOj with La causes the transition temperature from tetragonal to cubic to fall, and the thermal contraction to diminish steadily, so that at an approximate composition of Pb La TiOj, ceramic samples show a mean thermal expansion coefficient of a=-0.11 x 10 K from room temperature to 130°C. Above this temperature the cubic polymorph has a thermal expansion coefficient of approximately the same value as the undoped material, of 3.82x 10 K , indicating that the substituent influences the distortion of the low-temperature phase rather than other factors. A-site substitution with even modest amounts of Cd has the opposite effect, as a=-2.40x 10 K for ceramic Pb g Cd gTiOj. 

Lanthanoid manganites, such as LaMnOj, NdMnOj and GdMnOj, are of potential value in solid oxide fuel cell cathodes. However, many of these phase show thermal contraction because of the diminishing Jahn-Teller distortion of the Mtf cations as the temperature is increased. Such effects tend to rule out these materials for real cell applications, although A- and B-site substitution, as demonstrated for PbTiOj earlier, can ameliorate the problem. 

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The formation volume factor for water (B, reservoir volume per stock tank volume), is close to unity (typically between 1.00 and 1.07 rb/stb, depending on amount of dissolved gas, and reservoir conditions), and is greater than unity due to the thermal contraction and evolution of gas from reservoir to stock tank conditions. 

Although the continuous casting of steel appears deceptively simple in principle, many difficulties are inherent to the process. When molten steel comes into contact with a water-cooled mold, a thin soHd skin forms on the wall (Eig. 10). However, because of the physical characteristics of steel, and because thermal contraction causes the skin to separate from the mold wall shortly after solidification, the rate of heat abstraction from the casting is low enough that molten steel persists within the interior of the section for some distance below the bottom of the mold. The thickness of the skin increases because the action of the water sprays as the casting moves downward and, eventually, the whole section solidifies. 

The results of a specific case study are shown in Fig. 26-49. This depicts the change in inbreathing volume flow rate as a function of time. The middle curve describes the case when the tank is filled with dry air that is, no condensation occurs. When the air is saturated with water vapor at 55°C (131°F) and condensation occurs, the top curve is obtainea. The bottom line represents the volume flow rate brought about by thermal contraction alone, not including the amount condensed. Because of the heat of condensation released, this fraction is less than the volume flow rate without condensation, but this effect is more than compensated for by the additional volume flow rate due to condensation. 

Because oxides are usually quite brittle at the temperatures encountered on a turbine blade surface, they can crack, especially when the temperature of the blade changes and differential thermal contraction and expansion stresses are set up between alloy and oxide. These can act as ideal nucleation centres for thermal fatigue cracks and, because oxide layers in nickel alloys are stuck well to the underlying alloy (they would be useless if they were not), the crack can spread into the alloy itself (Fig. 22.3). The properties of the oxide film are thus very important in affecting the fatigue properties of the whole component. 

Thermal contraction of piping must be allowed for, based on the lowest possible service temperature. 

Underpressure (vacuum) Withdrawals exceed inflow Thermal contraction Open outlet Pressure control system failure Low pressure... 

Therefore, before a final wall structure can be selected, it is necessary to conduct a combined strain analysis in both the longitudinal and hoop directions. This analysis will consider thermal contraction strains, the internal pressure, and the pipe s ability to bridge soft spots in the trench s bedding. In order to do this we must know more about the inherent properties of the material we are dealing with that is a structure made up of successive layers of continuous filament-wound fiberglass strands embedded within a plastic matrix. We must know the modulus of the material in the longitudinal direction and the... 

In a sealing situation, leakage past the elastomer, outside and around its surface, usually due to imperfections in the housing this applies especially in a dynamic arrangement if the sealing stress diminishes due to relaxation, wear, and/or thermal contraction... 

Figure 5. Logarithm of the retractive force at 49% strain (lower curve) and sample temperature (upper curve) plotted against logarithm of time reduced to 263 K. Cross-links are introduced at log t/aT is 3 in the glassy state where the spike on the force curve is due to thermal contraction upon cooling below the glass transition temperature. Equilibrium force at 263 K after cross-linking is feQ. (Reproduced, with permission, from Ref. 27. Copyright 1981, Journal of Chemical Physics.)...

The subsequent thermal processes201 give rise to diffusion of the polycarbonate substrate into the dye layer, decomposition of the dye, and mechanical deformation of the film due to thermal contraction. Each of these processes can contribute to a reduction in the optical path length of the low-intensity readout beam. The optics within the detector are designed such that phase differences due to the optical path length differences cause the light intensity falling on the detector to be reduced when the beam passes over a recorded mark .196... 

Different structural materials have different thermal contraction coefficients, meaning that accommodations should be made for their different dimensions at cryogenic temperatures. If not, problems associated with safety (e.g., leaks) may arise. Generally, the contraction of most metals from room temperature (300 K) to a temperature close to the liquefaction temperature of hydrogen (20 K) is <1%, whereas the contraction for most common structural plastics is from 1% to 2.5% [23]. 

Data of linear thermal contraction coefficients are reported in ref. [34,79,80] and in Table 3.3. 

The low-temperature thermal conductivity of different materials may differ by many orders of magnitude (see Fig. 3.16). Moreover, the thermal conductivity of a single material, as we have seen, may heavily change because of impurities or defects (see Section 11.4). In cryogenic applications, the choice of a material obviously depends not only on its thermal conductivity but also on other characteristics of the material, such as the specific heat, the thermal contraction and the electrical and mechanical properties [1], For a good thermal conductivity, Cu, Ag and A1 (above IK) are the best metals. Anyway, they all are quite soft especially if annealed. In case of high-purity aluminium [2] and copper (see Section 11.4.3), the thermal conductivities are k 10 T [W/cm K] and k T [W/cm K], respectively. 

For this measurement, the sample was a Te02 optical quality crystal of 2 x 2 x 3 cm3, corresponding to a mass of 75.493 g. It was sustained by four pure tin cylinders, which kept the crystal blocked inside a copper frame, as shown in Fig. 12.5. The length of the cylinders was chosen to compensate the thermal contraction of the crystal, down to the lowest reached temperatures. 

The uncertainty of the expansion data was evaluated to be less than 5%. The relative thermal expansion AL/L versus T is shown in Fig. 13.3. Curves for other materials are also reported for the sake of comparison. Torlon shows a linear thermal expansion lower than most polymers. As Stycast 2850FT, Torlon thermal contraction closely matches that of some common metals (i.e. aluminium [53] and brass [54]). Smoothed values for the thermal expansion of Torlon relative to 4.2K are reported in Table 13.1. The data... 

S. Pattanayak, S. Kanagaraj Thermal contraction of FRPs and its measurements at cryogenic temperature. Proceedings of Beijing International Cryogenic Conference, p. 185 (2000)... 

The radial (compressive) stress, qo, is caused by the matrix shrinkage and differential thermal contraction of the constituents upon cooling from the processing temperature. It should be noted that q a, z) is compressive (i.e. negative) when the fiber has a lower Poisson ratio than the matrix (vf < Vm) as is the normal case for most fiber composites. It follows that q (a,z) acts in synergy with the compressive radial stress, 0, as opposed to the case of the fiber pull-out test where the two radial stresses counterbalance, to be demonstrated in Section 4.3. Combining Eqs. (4.11), (4.12), (4,18) and (4.29), and for the boundary conditions at the debonded region... 

Another important mechanical property of a coating layer is the coefficient of thermal expansion (CTE). Residual stresses generated due to the differential thermal contraction between the composite constituents are extremely detrimental to the... 

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