Coefficient linear thermal expansion

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. 

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. 

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

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. 

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). 

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...

Examining the mean polyhedral linear thermal expansion coefficients of a large number of crystalline compounds, Hazen and Prewitt (1977) formulated two important generalizations ... 

With increasing T and constant P, olivines expand their octahedral sites Ml and M2, whereas the tetrahedral group [8104] remains virtually unaffected. Table 5.9 lists linear thermal expansion coefficients for Ml-O and M2-0 polyhedra in some olivine compounds, according to Lager and Meagher (1978). These values are generally higher than those obtained by the method of Hazen and Prewitt (1977) (see eq. 1.93 and section 1.14.2). In particular, thermal expansion is anom-... 

A study was made of the effects of processing conditions and of blowing and nucleating agents and external lubricants on the apparent density, mechanical properties, linear thermal expansion coefficient and surface roughness of extruded cellular MDPE. Based on the results, recommendations were formulated for the properties of cellular MDPE pipes for the protection of light conducting cables. 16 refs. (Translation of Polimery, Tworzywa Wielkoczasteczkowe, No. 10, 1996, p.580). 

For materials that are isotropic, that is, have the same properties in all directions, it can be shown that ay = 3ai. A material that has different properties in different directions is said to be anisotropic. Thus, a linear expansion coefficient, if no direction of measurement is explicitly stated, implies an isotropic material. Conversely, a volume thermal expansion coefficient implies an anisotropic material, and one should exercise caution when deriving linear thermal expansion coefficients from volume-based measurements. 

Equations (6) and (7) express these relationships. are the elastic compliance constants OC are the linear thermal expansion coefficients 4 and d jj,are the direct and converse piezoelectric strain coefficients, respectively Pk are the pyroelectric coefficients and X are the dielectric susceptibility constants. The superscript a on Pk, Pk, and %ki indicates that these quantities are defined under the conditions of constant stress. If is taken to be the independent variable, then O and are the dependent quantities ... 

Finally, making use the equation of state of Eq. (28) one can demonstrate that the linear thermal expansion coefficient depends on the deformation as follows (for isoenergetic chains)26 211... 

The linear thermal expansion coefficient p calculated from these measurements are in excellent agreement with literature data obtained by the conventional method. For example, the values of P calculated from the thermal effects Q during stretching of PS and PET films agree well with conventional dilatometric results, i.e. for PS PQ = 6.8xKT5 -1, PdU = 7.0x 10-5 K 1 for PET PQ = 5.4x 10 5 K-1, Pdu = 5 0 x 10"5 K 1. The characteristic heat to work ratio q depends hyper-bolically on strain which is also in an excellent agreement with prediction following from the thermomechanical analysis (see Fig. 1). 

Fig. 15. Hypothetical dependence of the linear thermal expansion coefficient 3 on the degree of orientation 7). 1 — crystallizable stretched rubber, 2, 3 — crystalline drawn polymers, 4 — p n...

Fig. 16. Dependence of the linear thermal expansion coefficient of HDPE on the degree of drawing at different temperatures170,1711...

Linear thermal expansion coefficient Shear rate... 

Aj3th is the jump of the linear thermal expansion coefficient at the glass transition temperature. As Fig. 1 lb shows, da is proportional to the rate (1 — a) of the flowing units, that is to the molecular arrangements, which can form some confer-... 

Figure 2.18 Linear thermal expansion coefficient vs. temperature for si and sll hydrates, and ice Ih (Hester et al. 2007).

The linear thermal expansion coefficient shows the greatest increase in temperature for bituminous coals. The values for the linear thermal expansion coefficient are less than 33 x 10-6 C 1 in the 30 to 330°C (86 to 626°F) range (van Krevelen, 1961). For anthracite, the linear thermal expansion coefficient changes very little with temperature and is accompanied by a pronounced anisotropy effect. The values for the linear thermal expansion coefficient are about twice as high for coal perpendicular to the bedding plane than for coal parallel to the bedding plane (van Krevelen, 1961). 

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