Thermal linear coefficient

Table 1.8 Thermal linear coefficient of expansion for anisotropic crystals [100-102]...

This table lists values of /3, the cubical coefficient of thermal expansion, taken from Essentials of Quantitative Analysis, by Benedetti-Pichler, and from various other sources. The value of /3 represents the relative increases in volume for a change in temperature of 1°C at temperatures in the vicinity of 25°C, and is equal to 3 a, where a is the linear coefficient of thermal expansion. Data are given for the types of glass from which volumetic apparatus is most commonly made, and also for some other materials which have been or may be used in the fabrication of apparatus employed in analytical work. 

Thermal Properties. Many commercial glass-ceramics have capitalized on thek superior thermal properties, particularly low or zero thermal expansion coupled with high thermal stabiUty and thermal shock resistance properties that are not readily achievable in glasses or ceramics. Linear thermal expansion coefficients ranging from —60 to 200 x 10 j° C can be obtained. Near-zero expansion materials are used in apphcations such as telescope mirror blanks, cookware, and stove cooktops, while high expansion frits are used for sealing metals. 

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%. 

Material CAS Registry Number Formula Mp, °C Tme specific gravity, g/cm Mean J/(kg-K)" specific heat Temp range, °C Thermal conductivity, W/(m-K) 500° 1000° C C Linear thermal expansion coefficient peTC X 10 from 20-1000°C... 

The Rheometric Scientific RDA II dynamic analy2er is designed for characteri2ation of polymer melts and soHds in the form of rectangular bars. It makes computer-controUed measurements of dynamic shear viscosity, elastic modulus, loss modulus, tan 5, and linear thermal expansion coefficient over a temperature range of ambient to 600°C (—150°C optional) at frequencies 10 -500 rad/s. It is particularly useful for the characteri2ation of materials that experience considerable changes in properties because of thermal transitions or chemical reactions. 

Data for thermal movement of various bitumens and felts and for composite membranes have been given (1). These describe the development of a thermal shock factor based on strength factors and the linear thermal expansion coefficient. Tensile and flexural fatigue tests on roofing membranes were taken at 21 and 18°C, and performance criteria were recommended. A study of four types of fluid-appHed roofing membranes under cycHc conditions showed that they could not withstand movements of <1.0 mm over joiats. The limitations of present test methods for new roofing materials, such as prefabricated polymeric and elastomeric sheets and Hquid-appHed membranes, have also been described (1). For evaluation, both laboratory and field work are needed. 

Automated soldering operations can subject the mol ding to considerable heating, and adequate heat deflection characteristics ate an important property of the plastics that ate used. Flame retardants (qv) also ate often incorporated as additives. When service is to be in a humid environment, it is important that plastics having low moisture absorbance be used. Mol ding precision and dimensional stabiUty, which requites low linear coefficients of thermal expansion and high modulus values, ate key parameters in high density fine-pitch interconnect devices. 

E = Young s modulus a = linear coefficient of thermal expansion. 

Table 27. Linear thermal expansion coefficient, a, of sodium chloride...

Plastics can also be combined with other materials such as aluminum, steel, and wood to provide specific properties. Examples include PVC/wood window frames and plastic/ aluminum-foil packaging material. All combinations require that certain aspects of compatibility such as processing temperature and linear coefficient of thermal expansion or contraction exist. 

We assume that the thermal expansion coefficient of the composite (c) is given by the linear-mixture equation ... 

An additional check is the almost coincidence of the linear thermal expansion coefficients of the composite in the glassy region. Theory yields acl = 48.20 x 10-6 °C whereas experiment gives ac, = 48.00x 10 6 °C 1. This coincidence does not hold beyond glass transition. Indeed it was found that ot = 122.90 x 10-6 °C, whereas the experiment gave a 2 = 158 x 10"6 °C 1. 

If a volume expansion is required, then mccisurements in three simultaneous dimensions are needed, a result experimentally difficult to achieve, to say the least. Even a slab of a single crystal does not completely solve the problem since thermal expansion in three dimensions is needed for the volume thermal expansion coefficient. The crystal has three (3) crystallographic axes and may have three (3) linear coefficients of expansion. Only if the crystal is cubic does one have the case where all three values of ol are equal. 

Joule appears to have assumed dL/dT)p,f/L to be zero for/=0. Given above in parentheses in column three is the value of the linear thermal expansion coefficient on the basis of which initial values in parentheses in other columns replace those given by Joule (see table on p. 106 of Ref. 4). 

For an isotropic material, the linear coefficient of thermal expansion a at constant pressure is ... 

As in the case of and cv, ap does not differ significantly from av at low temperatures. For anisotropic solids, there are two or three (depending on the symmetry of the crystal) principal linear coefficients. For isotropic solids, the volumetric thermal expansion is j8 = 3a. 

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...

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

---