Debye temperature comparison

Table 7.8 Summary of results obtained for the four Os Mossbauer transitions studied. The absorber thickness d refers to the amount of the resonant isotope per unit area. The estimates of the effective absorber thickness t are based on Debye-Waller factors / for an assumed Debye temperature of 0 = 400 K. For comparison with the full experimental line widths at half maximum, Texp, we give the minimum observable width = 2 S/t as calculated from lifetime data.

When Wqi / Wq2 the magnetization recovery may appear close to singleexponential, but the time constant thereby obtained is misleading [50]. The measurement of 7) of quadrupolar nuclei under MAS conditions presents additional complications that have been discussed by comparison to static results in GaN [50]. The quadrupolar (two phonon Raman) relaxation mechanism is strongly temperature dependent, varying as T1 well below and T2 well above the Debye temperature [ 119]. It is also effective even in cases where the static NQCC is zero, as in an ideal ZB lattice, since displacements from equilibrium positions produce finite EFGs. 

Table 8.3 Comparison of Debye temperatures derived from heat capacity data and from elastic properties.

Where v/ and v/- are the longitudinal and transverse velocities. A comparison of the elastic Debye temperature and calorimetric Debye temperature gives a measure of the contribution of the acoustic modes to heat capacity. Since no optic modes are excited at low temperatures, the elastic and calorimetric Debye temperatures are expected to be comparable which in the case of vitreous silica is not obeyed (see chapter 12). 

It should be emphasized that although this success of the Debye model has made it a standard starting point for qualitative discussions of solid properties associated with lattice vibrations, it is only a qualitative model with little resemblance to real normal-mode spectra of solids. Figure 4.1 shows the numerically calculated density of modes of lead in comparison with the Debye model for this metal as obtained from the experimental speed of sound. Table 4.1 list the Debye temperature for a few selected solids. 

Comparison of the magnetic properties of Sc3In and ZrZn2. The parameters pTM and peff are the moments per transition metal atom deduced from magnetization and susceptibility measurements respectively y the electronic specific heat coefficient, 0n the Debye temperature, 0p the paramagnetic Weiss temperature, and AS the entropy change at Tc. The ratio qc/qs is the Rhodes-Wohlfarth ratio. 

The redox behaviour and Debye temperature of Fe-FER and Fe-MFI ferrisili-cates have been studied using Mossbauer spectroscopy. Analysis and comparison of the data obtained support the conclusions that the redox centres are due to (Fe-framework)-O-(Fe-extra-framework) pairs [35]. 

TABLE 2. Comparison of Heats of Formation (Hp, in kcal/g-atom), Average Heats of Atomization (Hg, in kcal/g-atom). Experimental Heats of Atomization (Hg, in kcal/fe-atom), Energy Gaps (Eg, at 300°K, in eV), Melting Points (M. P., in °C), Microhardness (mh, in kg/4nm ), Debye Temperatures (6, in °K at 80°K), Refractive Indices (n), and Average Principal Quantum Numbers (Q)... 

To look into this further, we show in Fig 4, in part (a), the behavior of the heat capacity of polypropylene, in units of J/K.(mol of -CH2-CH2(CH3)- repeat units) (35,36) in comparison with that of the molecular liquid 3-methyl pentane (37) (divided by 2 to have the same mass basis as the polymer repeat unit) (38). It is seen that the liquid heat capacity of the hexane isomer (x 0.S) falls not much above the natural extrapolation to lower temperatures of the heat capacity per repeat unit of the polymer. This implies that the main effect of polymerization, as far as the change in heat capacity at Tg is concerned, is to postpone the glass transition until a much higher vibrational heat capacity has been excited. This not only reduces the value of ACp but has a disproportionate effect on the ratio Cp,i/Cp,g at Tg. This happens despite a lower glassy heat capacity in the polymer than in the molecular liquid at the same temperature. The latter effect is a direct consequence of the lower Debye temperature (and lower vibrational anharmonicity) at a given temperature for in-chain interactions in the polymer than for intermolecular interactions in the same mass of molecules. 

During the start-up of Superphenix, an experiment related to the Doppler effect has been performed, on the CMP core, decreasing slowly the temperature from 400 to 180°C while maintaining isothermal conditions in the reactor. The increase in reactivity was compensated by control rod insertion. The contributions of the expansion reactivity coefficient (linear with respect to temperature) and of the Doppler effect (logarithmic with respect to temperature) have been separated. The model took into account the effective temperature, using the Debye temperature. The comparison of experiment and calculation, using the reference scheme is given in Table 7. 

The Debye temperature of La is anomalously low, as first noticed by Kasuya (1966). Table 10.1 shows the Debye temperatures and electronic specific heat coefficients for La, Lu, Y and Sc. The Debye temperature of d-hep La is 152 K in comparison to 205 K for Lu. Strictly speaking, the data cannot be compared so simply. The Debye temperature of La will increase under a pressure of 100 kbar, which should be applied in a Gedanken-experiment to correct for the lanthanide contraction. The corresponding volume compression is 24% (Syassen and Holzapfel, 1975). For an estimate of an upper bound we use the largest... 

In the continuing series of reports from the Ames Laboratory, Kai et al. (1989) discuss more extensive and refined heat-capacity studies on LaD , and LaH . (1.9electronic specific heat coefficients (mJ/molK ) are y = 0.81 + 0.01 for LaH2(D2) and 0.038 0.01 for LaH3(D3), with Debye temperatures of D = 348 + 2 and 381 + 2K, respectively. As in the work of Ito et al. (1982,1983), four sharp peaks are observed for LaDj 95, but at slightly different temperatures. Similar results were also quoted for samples at x = 2.65,2.75,2.80 and 2.90 where the cubic-to-tetragonal transition occurs, and all have a common peak at 250 K. These results and the lack of an observed cubic-to-tetragonal distortion for x = 2.53 correlate with the X-ray data in fig. 3. On the basis of the variation of the electronic specific heat coefficient with composition, special stabilities are proposed for compositions with X = 2.25,2.50 and 2.75. For x = 2.25, the proposal seems somewhat nebulous because of the broad /1-phase shown in fig. 4, but a positive relation is evident for the y and t] phases. Whether the 5 and e phases, near 2.62 and 2.66, respectively, should appear is, of course, a matter of conjecture. The authors present entropies of transition and provide an extensive discussion that includes comparisons of their experimental results with band-structure values. 

Fig. 3.15 Calorimetrically measured Debye temperature, Qq for Ti-Al alloys. Condition as-cast (O) ordered ( ) various other heat treatments (A). TTie Debye temperatures of several pure metals are inserted for comparison [ColSO, Col82 ].

The bond energy b(0) is available by dividing the atomic cohesive energy b(0) with bulk coordination Zb (=12) for elemental specimen. 0d and are the Debye temperature and melting point as input in calculations. AT(K) is the temperature range of testing. Scattered data for a specific substance and the deviation from the reference values show the sensitivity of the LBA-derived b(0) to the extrinsic factors such as surface contamination in comparison with the reference data... 

Figure 27.12 presents the T-BOLS reproduction of the size and temperature-dependent Raman shift of II-Vl semiconductors. Table 27.3 features information of the atomic cohesive energy (Fcoh). Debye temperature (0d), and reference frequencies (o(l) derived from the reproduction, with comparison of the documented 0D-... 

Fig.2.12. A comparison of the Einstein and Debye specific heat for longitudinal acoustic and optic branches of the linear NaCl crystal. 0 is either the Einstein or the Debye temperature depending on which curve is being examined. Both curves are normalized to approach the classical value 2Nkg. For T 0, the specific heat Cr(T) drops exponentially reflecting the difficulty in thermally exciting optical modes at low temperatures. Cq(T) is linear at low temperatures this is due to the thermal excitation of low frequency acoustic modes...

The sound attenuations, sound velocities, Debye temperatures, and figures of merit for several garnets are listed in table 29.31 (Oliver et al., 1969a). The data for other crystals are also indluded in table 29.31 for comparison. 

Figure 10.13 Comparison of the experimental Cr.m for diamond (circles), with the Einstein prediction with 6>e —1400 K (dashed line) and the Debye prediction with D = 1890 K (solid line). The experimental results below T — 300 K are closely spaced in temperature, and not all are shown in the figure.

In Figs. 66 and 68 the calculated absorption and loss spectra are depicted for ordinary water at the temperatures 22.2°C and 27°C and for heavy water at 27°C. The solid curves refer to the composite model, and the dashed curves refer to the experimental spectra [42, 51]. For comparison of our theory with experiment at low frequencies, in the case of H20 we use the empirical formula [17] comprising double Debye-double Lorentz frequency dependences. In the case of D20 we use empirical relationship [54] aided by approximate formulae given in Appendix 3 of Section V. The employed molecular constants were presented in previous sections, and the fitted/estimated parameters are given in Table XXIV. The parameters of the composite model are chosen so that the calculated absorption-peak frequencies ilb and vR come close to the... 

Electron spin resonance (ESR) studies of radical probe species also suggest complexity. Evans et al. [250] study the temperature dependence of IL viscosity and the diffusion of probe molecules in a series of dissimilar IL solvents. The results indicate that, at least over the temperature range studied, the activation energy for viscous flow of the liquid correlates well with the activation energies for both translational and rotational diffusion, indicative of Stoke-Einstein and Debye-Stokes-Einstein diffusion, respectively. Where exceptions to these trends are noted, they appear to be associated with structural inhomogeneity in the solvent. However, Strehmel and co-workers [251] take a different approach, and use ESR to study the behavior of spin probes in a homologous series of ILs. In these studies, comparisons of viscosity and probe dynamics across different (but structurally similar) ILs do not lead to a Stokes-Einstein correlation between viscosity and solute diffusion. Since the capacities for specific interactions are... 

The concentration dependence of the hole mobility of TPM-E doped PS was described by Magin et al. (1996). TPM-E is a moderately polar molecule with a dipole moment of 2.10 Debye. Figure 5 shows the temperature dependencies for 45% TPM-E. The results are similar to those reported for vapor-deposited TPM glasses and doped polymers described previously. The data in Fig. 5 yield n0 = 2.9 x 10-2 cm2/Vs and a = 0.111 eV. For purposes of comparison, Fig. 6 shows the zero-field data of Fig. 5 plotted versus T-l. From these results, it is clear that the temperature dependence cannot be described by an Arrhenius relationship over an extended range of temperatures. A further problem concerning the use of an Arrhenius relationship is the prefactor mobility. At 272 K, the data in Fig. 6 yields a prefactor mobility of 690 cm2/Vs, a value that is difficult to justify. For all concentrations, plots of ft versus (a/kT)2 were linear with slopes between... 

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