Debye anomalies

He did not observe an anomaly indicated by M. Jona at room temp., but there is a definite increase near the point of liquefaction. The results can be represented by P. Debye s expression (e—1)d2 =0i0007682,- -1-74, where v denotes the sp. vol. of 1 c.o. of an ideal gas at n.p. 9. C. Manneback also studied the dielectric capacity... 

Low-temperature adiabatic heat capacity (Cp) measurements then were carried out on microcrystalline BABI to look for evidence of ordering below 2K 190 The expected anomaly was somewhat broad but readily seen in the right-hand chart of Fig. 25, with a maximum at 2 K the shape was consistent with expectations for a low-dimensional antiferromagnet. After subtraction of molecular lattice contributions by a Debye-type extrapolation from the higher... 

Many origins have been proposed for the T line, ranging from subtle structural distortions to electronic distortions like a charge density wave. Among the structural distortions, Walstedt et al. originally proposed that T could be surrounded by misoriented C60 or be a neighbor of an octahedral site where the alkali atom would be displaced (the Debye-Waller factor for O sites presents some anomalies). SEDOR double-resonance experiments put some very strict con-... 

Flere (1 - f) and (1 - S) are the losses brought about by the corresponding process and gfastj/3 (t -> oo) = 0 (see Fig. 6). The factor / can be regarded as a generalized non-ergodicity parameter and, hence, it is expected to show a similar anomaly as the Debye-Waller factor /g (see Fig. 5). Such decomposition of the correlation function is useful in spin-lattice relaxation studies, as will be discussed in Section 3.2.4. 

A recent specific-heat measurement is shown in Fig. 2.31 for -(ET)2l3 [198]. At Tc = 3.4 K (3.5 K with magnetization measurements at the same crystal) a clear anomaly in C/T vs T can be seen. The height of the jump at Tc is AC sa 103 mJ/molK. In a small field applied perpendicular to the ET planes the anomaly of C becomes smaller and much broader. In an overcritical magnetic field of Bx = 0-5 T (not shown here) the normal-state specific heat was measured. Besides the usual linear electronic and cubic Debye specific heat a hyperfine contribution at low temperatures and an appreciable T phononic term had to be taken into account. Therefore, below 5K C was fitted by... 

The plot shows a distribution closely around a slope of unity indicated by the solid line in Figure 2 except for the alcohols and nitrobenzene. Such anomaly in alcohols is also reported for other chemical processes and time-dependent fluorescence stokes shifts and is attributed to their non-Debye multiple relaxation behavior " the shorter relaxation components, which are assigned to local motions such as the OH group reorientation, contribute the friction for the barrier crossing rather than the slower main relaxation component, which corresponds to the longitudinal dielectric relaxation time, tl, when one regards the solvent as a Debye dielectric medium. If one takes account of the multiple relaxation of the alcohols, the theoretical ket (or v,i) values inaease and approach to the trend of the other solvents. (See open circles in Figure 2.)... 

The heat capacities of sintered specimens of LaN and NdN were measured from 1.2°K. to 45°K. by Veyssie, et al. 185). LaN shows a slight anomaly attributed to magnetic impurities NdN has a peak at 27.6 zh 0.1°K. corresponding to a (ferromagnetic) Curie transition. Debye 0 values are 300° and — 360 °K., respectively, but the data do not cover an adequate range to permit evaluation of the thermodynamic properties. 

Anderson (1 ) measured the heat capacity of V20g(cr) in the range 57-287 K. The data indicated an anomaly in the region 165-182 K. These heat capacity data are Joined smoothly at 298 K with the high temperature heat capacity values as derived from the enthalpy measurements of 0>ok (JJ.). The adopted C values are based on these two studies (1, 13 ). Using the combination of Debye and Einstein functions as suggested by Anderson (12), we calculate S (50 K) 0.783 cal K mol and H (50 0) 0.0284 kcal mol. There is considerable scatter in the data of Cook (13) the deviations from the adopted values range from -0.8 to 0.6% except for the data point at 369.1 K which is -1.4% low ( 25 cal K mol ),... 

Low temperature heat capacities have been measured by Cristescu and Simon 76) from 13 to 210 K., and by Weertman, Burk, and Goldman (545) from 50 to 200 K. Since the latter workers have not substantiated the anomaly reported by the former workers, we have adopted the values of the latter group and have extrapolated them to absolute zero with a Debye function. From this information, we calculate the entropy at 298 K. to be 10.91 e. u. and the enthalpy at 298 K. to be 1448 cal./gram atom. We have estimated the heat capacity of the solid above 298 K. and of the liquid. A transition point has been reported by Duwez 91) and by Fast 110). The melting point has been reported by Adenstedt (5), Litton (575), and Zwikker 352). Considerable disagreement is evidenced by these values. There is probably a transition in the vicinit> of the melting point, but in view of the uncertainty existing, we have elected to minimize the necessary... 

Although Si02 is a typical inorganic glass, it is also atypical in many ways. Several properties of vitreous silica are known to vary anomalously at low temperatures. Anomaly in the low temperature specific heat is the most notable and well investigated. This is reflected in serious disagreement between Debye temperatures calculated from thermal and acoustic measurements. (thermal) and(elastic) are respectively given by (Anderson and Dienes, 1960),... 

The work of Debye and Erich Hiickel (1896-1880), published in 1923, led to a theory of ionic solutions that explained a number of anomalies concerning conductivities of electrolytic solutions. In 1926, Lars Onsager (1903-76) added the treatment of Brownian motion toward understanding the transport properties of ions in melts, aqueous, and... 

However, contrary to CeBCu this mode softening in Cei La Bei3 for 0.8 is also observed for all other symmetry modes with respect to the average behavior of the reference materials. The phonon softening in Cej La, Be,3 for 0.1 X 0.8, independent of the mode symmetry is also reflected by the behavior of the Debye temperature 0 (Besnus et a. 1983), which is displayed at the bottom of fig. 35. No temperature dependent phonon anomaly has been observed for the optical phonons of CeBcij, contrary to the anomalous softening of the bulk modulus upon cooling down below 350 K (Lenz et al. 1984). 

Elastic anomalies in actinide-based heavy-fermion systems are most pronounced for UPt3. The temperature dependences of two representative elastic modes are shown in flg. 36 (Yoshizawa et al. 1985). Unlike the case of UPdj, CF effects as a possible source do not seem very likely. The phonon dispersions of UBOjj, as measured by neutron scattering (Robinson et al. 1986), do not show strong anomalies. The elastic constant Cj2, however, is negative at low temperatures, similar to some IV compounds. Remarkably, UBejj possesses a low Debye... 

Changes of the lattice parameters 4.1. Anomalies of the Debye-Waller factor ... 

Indications for local structure anomalies emerge from the value of the Debye-Waller factors (B) resulting from the average structure refinements. A good example in the case of the HTc superconductors is the chain oxygen deformation. 

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