Thermal expansion transformation temperature

Apart from characteristic material values such as the coefficient of linear thermal expansion, transformation temperature, and elastic properties, the cooling rate (Fig. 3.4-31) and the shape can also have a considerable... 

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%. 

For maximum temperatures below 800°F, suitable ferritic steels are usually good selections. Above 800°F their loss of strength must be considered carefully and balanced against their lower thermal expansion. It should be recognized that if they are heated through the ferrite to austenite transformation temperature their behavior will become more complex and the results probably adverse. 

Transition region or state in which an amorphous polymer changed from (or to) a viscous or rubbery condition to (or from) a hard and relatively brittle one. Transition occurs over a narrow temperature region similar to solidification of a glassy state. This transformation causes hardness, brittleness, thermal expansibility, specific heat and other properties to change dramatically. 

Consider a planar premixed flame front, such as that sketched in Figure 5.1.1. For the moment, we will be interested only in long length scales and we will treat the flame as an infinitely thin interface that transforms cold reactive gas, at temperature and density T p, into hot burnt gas at temperature and density T, A.-The flame front propagates at speed Sl into the xmbumt gas. We place ourselves in the reference frame of the front, so cold gas enters the front at speed = Su and because of thermal expansion, the hot gases leave the front at velocity 14 = Sl(Po/a)- The density ratio, Po/Pb, is roughly equal to the... 

Dilatometric methods. This can be a sensitive method and relies on the different phases taking part in the phase transformation having different coefficients of thermal expansion. The expansion/contraction of a sample is then measured by a dilatometer. Cahn et al. (1987) used dilatometry to examine the order-disorder transformation in a number of alloys in the Ni-Al-Fe system. Figure 4.9 shows an expansion vs temperature plot for a (Ni79.9Al2o.i)o.s7Feo.i3 alloy where a transition from an ordered LI2 compound (7 ) to a two-phase mixture of 7 and a Ni-rich f c.c. Al phase (7) occurs. The method was then used to determine the 7 /(7 + 7O phase boundary as a function of Fe content, at a constant Ni/Al ratio, and the results are shown in Fig. 4.10. The technique has been used on numerous other occasions,... 

When the free energies F of the two crystal structures are identical, the system is at a critical point. The identity of F does not imply identical fimctions (otherwise the two phases would be indistinguishable). Therefore, at the critical point first derivatives of F might differ and therefore enthalpy, volume, and entropy of the two phases would be different. These transformations are first-order phase transitions, according to Ehrenfest [105]. A discontinuous enthalpy imphes heat exchange at the transition temperature, which can easily be measured with DSC experiments. A discontinuous volume is evident under the microscope or, more precisely, with diffraction experiments on single crystals or powders. Some phase transitions are however characterized by continuous first derivatives of the free energy, whereas the second derivatives (specific heat, compressibility, or thermal expansivity, etc.) are discontinuous. These transformations are second-order transitions and are clearly softer. 

A second-order structural transformation in La uC at 233 5°C was reported (118) in a thermal expansion study. The LajCu04 product was prepared at high temperature (1100°C) by the solid-state reaction of the corresponding binary oxides. The material was found to decompose above 1200°C with the loss of oxygen. Samples of La uC, prepared at 1200°C, then maintained at 750°C in vacuum, yielded products having the general composition La2Cu04.x, or... 

Variable-temperature X-ray diffraction studies of crystalline substances are useful in the study of phase transitions, thermal expansion and thermal vibrational amplitudes of atoms in solids. Similarly, diffraction studies at high pressures are employed to examine pressure-induced phase transitions. Time-resolved X-ray diffraction studies (Clark Miller, 1990) will be of great value for examining reactions and other transformations. 

The approach to the critical point, from above or below, is accompanied by spectacular changes in optical, thermal, and mechanical properties. These include critical opalescence (a bright milky shimmering flash, as incident light refracts through intense density fluctuations) and infinite values of heat capacity, thermal expansion coefficient aP, isothermal compressibility /3r, and other properties. Truly, such a confused state of matter finds itself at a critical juncture as it transforms spontaneously from a uniform and isotropic form to a symmetry-broken (nonuniform and anisotropically separated) pair of distinct phases as (Tc, Pc) is approached from above. Similarly, as (Tc, Pc) is approached from below along the L + G coexistence line, the densities and other phase properties are forced to become identical, erasing what appears to be a fundamental physical distinction between liquid and gas at all lower temperatures and pressures. 

From the dynamic mechanical investigations we have derived a discontinuous jump of G and G" at the phase transformation isotropic to l.c. Additional information about the mechanical properties of the elastomers can be obtained by measurements of the retractive force of a strained sample. In Fig. 40 the retractive force divided by the cross-sectional area of the unstrained sample at the corresponding temperature, a° is measured at constant length of the sample as function of temperature. In the upper temperature range, T > T0 (Tc is indicated by the dashed line), the typical behavior of rubbers is observed, where the (nominal) stress depends linearly on temperature. Because of the small elongation of the sample, however, a decrease of ct° with increasing temperature is observed for X < 1.1. This indicates that the thermal expansion of the material predominates the retractive force due to entropy elasticity. Fork = 1.1 the nominal stress o° is independent on T, which is the so-called thermoelastic inversion point. In contrast to this normal behavior of the l.c. elastomer... 

Certain alloys of iron, nickel, and cobalt (Kovar, Fernico, etc.) have thermal expansion curves which nearly match those of borosilicate glasses, and a good bond may be formed between the two. Kovar is similar to carbon steel in its chemical properties. For example, it oxidizes when heated in air and is not wet by mercury. It may be machined, welded, copper brazed, and soft soldered. Silver solders should not be used with Kovar since they may cause embrittlement. At low temperatures Kovar undergoes a phase transformation, and the change in expansion coefficient below this temperature may be sufficient to cause failure of a glass-to-Kovar seal. The transformation temperature usually is below... 

The pressure inside the heated chamber may also vary as a result of the local density changes produced by thermal expansion or phase changes resulting from the heating. For example NaCl may expand, melt, and thereby increase the local pressure, while pyrophyllite, a layer-lattice-type aluminum silicate, may transform into a denser assembly of coesite and kyanite, thereby reducing the local pressure. It follows that experimental results in high-pressure, high-temperature work must be interpreted with care. 

The very large pressure coefficient of the susceptibility (Fig. 14a) and conductivity in the metallic regime (d In room temperature [6]) raises a serious problem for the comparison with theory, which usually computes constant-volume temperature dependences. Hence the temperature dependence at constant pressure that is observed in actual experiments must be transformed into constant-volume data since the change of volume (due to the thermal expansion) cannot be ignored between 300 and 50 K. No detailed determinations of the constant-volume resistivity have been performed so far. However, a crude estimate of the intrinsic temperature dependence can be performed using the thermal expansion and the pressure dependence of the a axis at various temperatures [59] (Fig. 14b). 

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