Specific heat jump

Fig. 5. Typical DSC-traces for the specific-heat jumps at the glass transition regions of iron-epoxy particulates, or E-glass fiber-epoxy composites and the mode of evaluation of ACp s...

Fig. 14. The variation of the specific heat jumps at glass-transition temperatures of elacc-epoxy composites, versus the fiber volume content, uf. The values for the factor X and the mesophase, (uj and matrix, (nm) volume fractions, versus uf, as derived from the values of the respective AC, s are also plotted...

In all cases, the specific heat jump was recorded, which corresponds to the glass transition of phases polymers. It was noted that displacement... 

ACm specific heat jump at the magnetic transition AS entropy gain... 

The CeCuj orders antiferromagnetically at = 3.8 K, showing a structure in the specific heat jump at 4 K. This double transition is also seen in thermal expansion and in magnetic susceptibility measurements at 3.6 and 3.8 K, respectively. The entropy associated with both transitions is approximately Rln2 and 7lt = 50 mJ K /Ceatom (Willis et al. 1987). The temperature dependence of C at T second-order transition, furthermore, the cusp observed at and the strong anomaly in the thermal expansion suggest such a... 

The sample dependence of the specific-heat jump as illustrated in fig. 71 for UPtj points to the importance of lattice imperfections [i.e., impurities in the... 

As is displayed by table 4, the specific-heat jump ratios of CeCu2Si2 and UPtj do not seem to be considerably enhanced over the conventional BCS value, i.e., they are even smaller for most samples. In contrast, UBejj (Ott et al. 1983) shows an enhanced value of AC/yr = 2.4 (fig. 73). This is comparable to the value for Pb and has, likewise, been ascribed to strong-coupling effects (cf. Scalapino 1969). 

Fig. 86. Pair breaking by non-magnetic dopants in CCi. M Cu, 25 M= La (T), Y( ) (Ahlheim et al. 1990). (a) Concentration dependence of transition temperature, T, plotted against x. Lines are guides to the eye. (b) Reduced specific heat jump,...

At the multicritical points associated with the partial reentrances of the metal, the specific heat jump displays a discontinuity, from a low value on the low field side, to a large value on the high field one (arrows on Fig. 2). This oscillatory behavior has been tentatively explained within the quantized nesting model, but only a qualitative description has been achieved, due to the quoted limitation of the weak coupling limit. 

Fig. 2. Oscillatory behavior of the normalized specific heat jump at the metal-FTSDW transition, plotted as a function of the magnetic field.

In all cases, the specific heat jump was recorded, which corresponds to the glass transition of phases pol5miers. It was noted displacement values of glass transition temperature of phase PIB to higher temperatures with increasing content of PHB (fi-om 68°C for pure PIB to 64°C for the composition with 60% by weight of the PHB). For PHB phase displacement of values of glass transition temperature is shown in Fig. 4.4. 

Fig. 9. Calculated specific heat for various superconducting order parameters in comparison to experimental results for URu2Si2 (Hasselbach et al., 1993). The specific heat jump ACsiTc) agrees best for ( , 1) or B a state.

Fig. 22. Left panel Linear speeifie heat eoeffieient of CeCoIn5 vs temperature, for zero field anomalous nFl behaviour is observed. AC Tc)jyTc 5 is strongly enhaneed over the isotropie BCS value 1.43. Inset shows corresponding entropies. Right panel 7/ 2 curve from specific heat data. At 7q 1.1 K the transition changes from second to first order. Lower inset shows entropy gain as function of T starting fi-om 0.13 K, for increasing field (right to left 8.6 T-11.4 T) a step is evolving. Upper inset shows specific heat jump at the transition line Tfflo to the Fulde-Ferrell-Larkin-Ovchinnikov state (Bianchi et al., 2003).

Fig. 64. Left panel Electronic specific heat ACjT vs. temperature (Vollmer et al., 2003). Solid line is an entropy conserving construction leading to SC transitions at T =1.85 K and T 2 = 1-75. Total specific heat jump ACsc/E Tc- i- Right panel Corresponding jumps in the volume thermal expansion at Tj-i 2 (Oeschler et al., 2003,...

In matrix-impurity systems in which the matrix is a superconductor and Tg is sufficiently low compared to the critical temperature of the pure host, the temperature dependent scattering of conduction electrons by impurity spins may even lead to the striking phenomenon of re-entrant superconductivity (where alloys within a certain impurity concentration range exhibit a transition to the superconducting state at a critical temperature Tg, which is followed by a return to the normal state at a second lower critical temperature as well as pronounced deviations of the specific heat jump from the BCS law of corresponding states. 

In addition to the remarkable re-entrant behavior of the TjTe vs n curve, the depression of the specific heat jump AC at as a function of Tc (Armbriister et al., 1974 Luengo et al., 1972 Bader et al., 1975) also displays some interesting features which are shown in fig. 11.10. Here, it can be seen that the curve of reduced specific heat jump AClACo vs reduced transition temperature shows a pronounced downward deviation from both the BCS law of corresponding states and, as well, the AG theory. It is worth noting that recent specific heat measurements (Bader et al., 1975) on a re-entrant (LaCejAh specimen (0.64 at.% Ce) to temperatures lower than indicate that the tran-... 

Fig. 11.10. Reduced specific heat jump ACldC vs. reduced transition temperature TJT for the (LaCe)AI, system. The solid triangles, circles and squares represent data from Luengo et al. (1972), ArmbrOster et al. (1974), and Bader et al. (1975), respectively. The dashed line represents the BCS law of corresponding states, the dot-dashed line indicates the AG result, and the solid line is a smooth curve drawn through the data [after Maple (1976)].

However, the most remarkable results of the measurements of McCallum et al. (1975a) were the large, positive deviations of the reduced specific heat jump ACIACo from the predictions of the BCS theory as shown in fig. 11.12. This was the first time such a positive deviation has been observed for any superconductor. It is most important to point out that all of the above phenomena in (I Pr)Sn3 can be adequately described by the theories of Fulde and coworkers... 

Fig. 11.12. Reduced specific heat jump ACIACq vs reduced transition temperature TJT for (LaPr)Sn, alloys (solid circles and solid squares McCallum et al., 197Sa) and (LaSmjSn alloys (open circles DeLong et al., 1976). The solid line is derived from numerical calculations based on the theory of Keller and Fulde (1973) for crystal field-split lanthanide impurities in a superconductor. The BCS law of corresponding states behavior (dashed curve) and the AG behavior (dot-dashed curve) are shown for comparison. The negative deviations of the ACIACn vs TJT data from the AG curve are consistent with Kondo behavior (see fig. 11.10) for (I Sm)Sn3 alloys.

Lipatov (22) analyzed specific heat data for an array of filled polymer composites. He characterized the interactions due to the existence of the interphase region surrounding filler particles as a function of filler content. Because the magnitude of the specific heat jump at the glass transition temperature decreases with increase in filler content, this is indicative of exclusion of a certain portion of macromolecules in the polymer matrix to participating in the cooperative process of glass transition. 

The ratio of molecules in the immobilized layer of molecules in the region of the glass fiber surface, compared with the remaining polymer matrix, has an empirical relationship with the corresponding specific heat jump attributed to the unfilled polymer resin ... 

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