Thermal contraction coefficient

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. 

Material Total thermal contraction coefficient 295 K to 77 K Crack resistance... 

The authors wish to thank D. Hunt for his measured data on 70 samples of various composite materials and also for his advice on performing the measurements. They thank A. P. Barone, of the LBL Assembly Shop, for preparing the samples for thermal contraction coefficient measurements. 

Table 9.4 Linear Thermal Contraction Coefficients for Screen Channel Liquid Acquisition Device Metals...

F. J. HOllerue, Seram Primary Loop Thermal Contraction Coefficients, HN-73167, Harch 29, 1962 (Confidential)... 

The thermal contraction coefficient from to room temperature of alkaline earth alu-... 

Solution. The apparent strain caused by a JT will have two components (l)that caused by the temperature coefficient of resistance, y, from Table 8.1 and (2) that caused by the difference in thermal contraction of the gauge, olq, and the thermal contraction coefficient of the substrate, a. ... 

This favors a sample s contraction V is the volume). This attractive force, which will be temperature dependent, is balanced by the regular temperature-independent elastic energy of the lattice Fsiast/V = K/2) 6V/V). Calculating the equilibrium volume from this balance allows us to estimate the thermal expansion coefficient a. More specifically, the simplest Hamiltonian describing two local resonances that interact off-diagonally is... 

Fig. 3.14. Relative linear thermal expansion coefficient of (1) Invar, (2) Pyrex, (3) W, (4) Ni, (5) Cuo.7Ni03, (6) stainless steel, (7) Cu, (8) brass, (9) Al, (10) Torlon, (11) soft solder, (12) Vespel SP-22, (13) Hg, (14) In, (15) Araldite, (16) Stycast 1266, (17) PMMA, (18) Nylon, (19) Teflon [60]. Some additional data are Ag between (8) and (9) Stycast 2850 GT slightly larger than (9). The integral contraction between 300 and 4K is 103AL/L = 11.5, 4.2, 6.3 and 5.7 for Stycast 1266, Stycast 2850 GT, Vespel SP-22 and solders...

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... 

Thermal Expansion. Thermal expansion is a measnre of the expansion or contraction of a solid when it is heated or cooled. In the most general case, the coefficient of thermal expansion, a, sometimes called the volnme thermal expansion coefficient, is defined as fhe change in volnme per nnit volnme, V, with temperature, T, at constant pressure, P ... 

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... 

Figure 5.11 shows the isotherms as a function of time. Again the curves expand and contract with increasing time. However, the isotherms are elliptical because the thermal conductivity coefficient is different along the oaxis and in the basal plane. 

The decomposition follows rapid nucleation and contracting sphere kinetics with an activation energy of 150 kJ, somewhat higher than the enthalpy of decomposition.43"45 Densities are given in Table 2.43, thermal expansion coefficient in Table 2.44, and thermodynamic data in Tables 2.45 to 2.47. From data in Table 2.47, it is apparent that MgC03 is unstable above 700 K, in agreement with quoted experimental studies. 

Residual stress resulting from thermal expansion or contraction is due to the differences in the thermal expansion coefficient between the adhesive and adherend and to temperature distribution in the joint due to differences in thermal conductivity. 

When an amorphous polymer is gradually cooled from above the glass transition temperature Tg its volume decreases (see Fig. 13.32) according to its thermal expansion coefficient aj. In the region around the Tg the volume decrease will lag behind, starting at temperature Tel because the rate of reorganisation process becomes too small. The polymer starts to vitrify and a temperature Tel will be reached where the reorganisation completely stops and where the vitrification process is completed. Decrease of volume is only the result of normal volume contraction with expansion coefficient ag. The relationship between both thermal expansion coefficients is... 

Temperature gradients. These gradients produce cracks in rocks as a result of expansion-contraction cycles. The degree of expansion-contraction is dependent on the individual thermal expansion coefficients. Interestingly, it is believed that ancient civilizations took advantage of the expansion-contraction cycle of water/ice to split rocks apart for decorative and construction purposes. 

Other types of damage may be produced through thermomechanical effects. For example, when being annealed at 450°C a CVD aluminum film on a Si substrate is subjected to compressive thermoelastic stresses owing to the considerable difference between the thermal expansion coefficients of aluminum (a = 23 x 10 °C 0 and the silicon substrate (a. = 3.5 x 10 °C 0-When cooling, the film may therefore contract by as much as 1%. Due to the combined action... 

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