Rare thermal expansion coefficients

Keywords rare-earth compound, hydride, magnetization, magnetic ordering temperature, magnetostriction, thermal expansion coefficient... 

Cordierite. This material possesses a rare combination of properties, i.e., relatively high strength and hardness, low thermal expansion coefficient, high heat conductivity and plasticity it conserves mechanical strength under thermal shocks. Therefore, its application areas are varied. 

This section covers some other heterometallic rare earth oxides, including Al, Ti, Zr, Sn, Mo, W, Mn, Fe, Co, Ni, and Cu complex oxides, while certain well-known oxysalts, Y-Ba-Cu-O, for example, will not be specifically discussed. For these heterometallic compounds, due to their relatively complex compositions, it is usually difficult to obtain phase-pure products, especially when some dopant ions are added. At elevated temperatures, some of these oxides undergo phase transitions, which may significantly change their physical and chemical properties such as thermal expansion coefficient and ionic conductivity. And for fhose oxides with variable metal valencies, different nonstoichiometric compositions may also result in distinct functionalities in magnetism and catalysis. 

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. 

From Table 29 and Figure 52A, it is evident that the linear thermal expansion coefficients for orthorhombic rare earth aluminates in the temperature range of 300-1200 K lie within the limits a = (8.9-11.3) x 10 = (3.8-7.S) x 10 ... 

Senyshyn et al. (2005b) calculated the above-mentioned properties and determined the thermal expansion coefficient of rare earth gallates using a semi-classical approach. Ideal (X-ray) density, Griineisen parameter, isohoric heat capacity Cy, bulk and shear moduli, and thermal expansion coefficient were calculated for RGaOa (R = La-Gd) at 300 K are listed in Table 47. 

TABLE 48 Thermal expansion coefficients of rare earth gallates (K )... 

FIGURE 83 Components of the thermal expansion tensor (A) and volumetric thermal expansion coefficient (B) versus rare earth cation radius in rare earth gallates. The dashed lines are guides for the eye. 

The rare earth-doped oxynitride glasses demonstrated higher densities and thermal expansion coefficients, but a substantially lower hardness, compared to the a- and P-Si3N4 single crystals. 

Equilibrium thermodynamics controls the PVT behavior of any system and its thermal expansion coefficient, compressibility, bulk modulus, hardness, etc. The thermodynamic pressure, which can be defined as a partial derivative of the Helmholtz free energy (see Eq. 2.5), for multicomponent systems, comprises of two interaction parameters, e.g., (e )(v ) k = 2,4. These values can as easily be determined from dilatometric measurements as from the phase diagram (Jain et al. 1982). With the advance of other methods, dUatometry has been largely neglected It is still being used to characterize the compressibility of neat resins, but rarely nowadays to study the behavior of polymeric blends (Plochocki 1982, 1983, 1986 Zoller 1989 Steller and Zuchowska 1990 Zoller and Walsh 1995). 

Up to now we have discussed the influence of the crystal field eflect on (due to phonon resonance scattering by the rare earth ions) and the heat capacity (Schottky effect). It is known that the crystal field can significantly influence the behaviour of the elastic constants (Luthi et al. 1973), the thermal expansion coefficient (Ott and Liithi 1976), the magnetostriction and thermoemf (Sierro et al. 1975), the electrical conductivity (Liithi et al. 1973, Friederich and Fert 1974, Andersen et al. 1974) and the electron part of the thermal conductivity (Smirnov and Tamarchenko 1977, Wong 1978, Matz et al. 1982, Muller et al. 1982). 

FIGURE 27 (A) d electron number versus linear expansion coefficient transition metals (White, 1979). (B) Linear thermal expansion coefficient a (closed circles) and bulk modulus (solid line) Bo of the rare earth elements (Benedict and Holzapfel, 1993 Spedding et al., 1961). 

In this section, we discuss thermal expansion coefficients of rare earth compounds that exhibit HF behavior, intermetallic compounds with magnetic order, and other compoimds that exhibit valence fluctuations. In all of the examples, the temperature dependence of the thermal expansion is influenced significantly by applying pressure. 

Leucite powders (KAISi206) have been extensively used in dental applications to reduce the mismatch between the linear thermal expansion coefficient (TEC) of porcelain and metal reinforcement, thus enhancing the mechanical strength. However, they have been rarely used as bulk material because they exhibit a phase transition with different TEC values. ... 

The temperature dependence of the lattice constants a and c and the thermal expansion coefficients of hexagonal ZnO have been determined by the capacitive method [138]. The thermal expansion coefficients measured between 4 and 800 Rare shown in Figure 1.25. Reeber [30] has employed X-ray powder diffraction methods instead to measure the temperature dependence of the lattice parameters of ZnO in the range of 4.2-296 K. The results are shown in Figure 1.26. When analyzing the dependence of the lattice parameters on temperature, fourth-order polynomials... 

Thermosetting-encapsulation compounds, based on epoxy resins (qv) or, in some niche appHcations, organosiHcon polymers, are widely used to encase electronic devices. Polyurethanes, polyimides, and polyesters are used to encase modules and hybrids intended for use under low temperature, low humidity conditions. Modified polyimides have the advantages of thermal and moisture stabiHty, low coefficients of thermal expansion, and high material purity. Thermoplastics are rarely used for PEMs, because they are low in purity, requHe unacceptably high temperature and pressure processing conditions. 

Liquids and solids are in the condensed state in which chemical substances are very dense and hardly undergo any volume change with changing pressure in the range of ordinary pressures. Let us now consider a condensed system of a pure substance. The coefficient of thermal expansion a and the compressibility (rare defined in terms of the molar volume v by the following two equations, respectively ... 

The thermal expansion curves of the individual Si02 modifications are plotted in Fig. 2, which also illustrates the discontinuous change in the specimen size occurring at the inversion temperature. The high-temperature quartz exhibits a quite rare anomaly, namely a negative coefficient of expansion in all crystallographic directions. On its expansion curve, tridymite likewise exhibits a peak followed by contraction. 

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