Thermal expansion coefficient

Almost all reported thermal expansion coefficients for glasses have been obtained using some variation of a push-rod dilatometer. In its simplest 

Most dilatometers used in studies of glasses are constructed from vitreous silica. Since the average linear thermal expansion coefficient of vitreous silica is only about 0.55 ppm over typical temperature ranges covered in these measurements, the correction factor for the apparatus expansion is quite small. Furthermore, since virtually all glasses have glass transformation temperatures less than that of vitreous silica, the upper use temperature of = 1000 °C imposed by the viscosity of this material is rarely of concern. 

A more sensitive and accurate dilatometer can be constructed by use of two push-rods in an arrangement which measures the difference between the expansions of the sample and a reference standard. This design is particularly useful for studies of glasses to be used for sealing to another material, since the two materials to be joined can be used in the sample and reference positions and the difference between their expansions can be determined directly. 

The most accurate thermal expansion measurements are obtained using interferometry. These instruments are capable of detecting changes in dimension of as little as 20 nm, using visible light. While not used widely for routine measurements, NIST expansion standards are calibrated using these techniques. Readers interested in these methods should consult a thermal analysis text for details. 

In a crystal, displacements of atomic nuclei from equilibrium occur under the joint influence of the intramolecular and intermolecular force fields. X-ray structure analysis encodes this thermal motion information in the so-called anisotropic atomic displacement parameters (ADPs), a refinement of the simple isotropic Debye-Waller treatment (equation 5.33), whereby the isotropic parameter B is substituted by six parameters that describe a libration ellipsoid for each atom. When these ellipsoids are plotted [5], a nice representation of atomic and molecular motion is obtained at a glance (Fig. 11.3), and a collective examination sometimes suggests the characteristics of rigid-body molecular motion in the crystal, like rotation in the molecular plane for flat molecules. Lattice vibrations can be simulated by the static simulation methods of harmonic lattice dynamics described in Section 6.3, and, from them, ADPs can also be estimated [6]. 

Nuclear motion drags along the electronic cloud, so that as temperature rises, molecular envelopes oscillate more and more. If the intermolecular potential were perfectly harmonic, the overall volume effect would be nil, because the compressions and expansions would average out but the potential is much steeper on the compression side (Fig. 4.4), so expansion is hindered less than contraction and molecules effectively occupy more and more space as mobility increases. So thermal expansion is very strictly dependent on the shape of the potential curve, that is on the strength and anisotropy of the intermolecular potential, in a typical structure-property relationship. The simple equation that defines the isobaric thermal expansion coefficient a is 

X anthracene o anthraquinone A benzoic acid o dinitrobenzene chlorobenzoquinone o difluorobiphenyl 

Compound P, crystal P, liquid Compound P, crystal P, liqnid 

Thermal expansion coefficients can be easily estimated by running molecular dynamics or Monte Carlo simulations, yielding molar volumes as a function of temperature, a complete equation of state for the considwed material (as was shown in Fig. 9.6 notice there the significant difference in steepness between the curve for the solid and that for the liquid). Note however that for f) 2 x 10 the total expansion of an organic material from zero-K crystal to its melting point is as low as 5-6%, so highly refined or ad hoc potentials may be required for accurate results (ref. [22], Chapter 9). 

The lattice parameters of semiconductors depend on temperature and are quantified by thermal expansion coefficients, which are denoted as Aa/a or and Ac/c or a for 

Also shown is the thermal expansion coefficient of polyc stalline ZnO. (After Ref [139].) 

As alluded to earlier, ZnO is widely used in thin-film form deposited on normative substrates. Therefore, the material quality, actually properties in general, of the ZnO films depends on the properties of the substrates used. Especially, the lattice parameters and thermal expansion coefficients of these substrates are extremely important since reduction of strain and dislocation density in ZnO thin films is the main objective, and substrates with parameters similar to those of ZnO are favorable in this context. Thermal expansion coefficients of various substrates used for thin-film ZnO growth are given in Table 2.3. 

Sesquiselenides have lower a than the monoselenides, probably due to the more covalent bond character in M2S03 and higher harmonic lattice vibrations  

The tabulated data are mean values determined in a quartz dilatometer at 300 to 800 K, Lashkarev et al. [1], Dudnik et al. [2], also see Lashkarev, Paderno [6]. 

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Glass has a very low thermal expansion coefficient the materials joined with glass have to be similar in expansion or must be duetile, while staying vacuum tight. Even with best-matched materials skilled craftsmanship is asked for the joining process. 

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. 

Metal Crystal 22° C stmeture 1000° c Melting point, °C Density, g/cm Thermal expansion coefficient at RT, ioV°c Thermal conductivity at RT, W/(m-K)" Young s modulus, GPa "... 

Low Expansion Alloys. Binary Fe—Ni alloys as well as several alloys of the type Fe—Ni—X, where X = Cr or Co, are utilized for their low thermal expansion coefficients over a limited temperature range. Other elements also may be added to provide altered mechanical or physical properties. Common trade names include Invar (64%Fe—36%Ni), F.linvar (52%Fe—36%Ni—12%Cr) and super Invar (63%Fe—32%Ni—5%Co). These alloys, which have many commercial appHcations, are typically used at low (25—500°C) temperatures. Exceptions are automotive pistons and components of gas turbines. These alloys are useful to about 650°C while retaining low coefficients of thermal expansion. Alloys 903, 907, and 909, based on 42%Fe—38%Ni—13%Co and having varying amounts of niobium, titanium, and aluminum, are examples of such alloys (2). 

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%. 

Because of the high functional values that polyimides can provide, a small-scale custom synthesis by users or toU producers is often economically viable despite high cost, especially for aerospace and microelectronic appHcations. For the majority of iudustrial appHcations, the yellow color generally associated with polyimides is quite acceptable. However, transparency or low absorbance is an essential requirement iu some appHcations such as multilayer thermal iusulation blankets for satellites and protective coatings for solar cells and other space components (93). For iutedayer dielectric appHcations iu semiconductor devices, polyimides having low and controlled thermal expansion coefficients are required to match those of substrate materials such as metals, ceramics, and semiconductors usediu those devices (94). 

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. 

Cordierite [12182-53-5] Mg Al Si O g, is a ceramic made from talc (25%), kaolin (65%), and Al O (10%). It has the lowest thermal expansion coefficient of any commercial ceramic and thus tremendous thermal shock resistance. It has traditionally been used for kiln furniture and mote recently for automotive exhaust catalyst substrates. In the latter, the cordierite taw materials ate mixed as a wet paste, extmded into the honeycomb shape, then dried and fired. The finished part is coated with transition-metal catalysts in a separate process. 

A summary of physical and chemical constants for beryUium is compUed ia Table 1 (3—7). One of the more important characteristics of beryUium is its pronounced anisotropy resulting from the close-packed hexagonal crystal stmcture. This factor must be considered for any property that is known or suspected to be stmcture sensitive. As an example, the thermal expansion coefficient at 273 K of siagle-crystal beryUium was measured (8) as 10.6 x 10 paraUel to the i -axis and 7.7 x 10 paraUel to the i -axis. The actual expansion of polycrystalline metal then becomes a function of the degree of preferred orientation present and the direction of measurement ia wrought beryUium. 

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