Debye temperature, Mossbauer studies

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.

AEq = 0.37 for the LS (1A1) state (relative to natural ion at 298 K). Debye-Waller factors were determined for the two states. The values -lnf(sT2) and -lnfi A,) follow the Debye model between 175 and 250 K with 0D (ST2) = 126 K and between 105 and 225 K with 0D (J Aj) = 150 K, respectively. Deviations encountered outside these regions were considered as evidence for the formation of cooperative domains as suggested by Sorai and Seki34,87T The difference between the Debye temperatures 0d(5T2) and 0d( Ai) may well be understood in terms of more rigidity in the lattice of the 2A state as compared to that of the ST2 state. A study of the magnetic hyper-fine interaction at 4.2K yielded VZZ( A1) < O. VZZ(5T2) > O, however, was concluded from the spin reversal of the texture-induced asymmetry of the Mossbauer line intensities. 

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]. 

The Mossbauer spectra of Dy2(glu)3 2H2O at temperatures from 77 to 265 K are given in Fig. 6.3. Figure 6.4 shows the temperature dependence of the areas of this compiex. The lattice dynamics study is visualized where the natural logarithm of the normalized area is plotted versus temperature for the glu complex the slope is found to be —0.00530 (61) K . The Debye temperature Oo is estimated from the equation for the high-temperature approximation ... 

As mentioned before, the first study of f(T) was carried out by Mossbauer (1958), and since then many systems have been studied. Mossbauer s results were theoretically analysed by Visscher (1960). The effective absorption cross-section for Ir as a function of temperature is shown in Figure 6.1, while in Figure 6.2 the temperature dependence of the Debye-Waller factor of tin metal is shown. Serious corrections to the Debye model are needed to fit the experimental observations. One correction is due to the expansion of the crystal, which causes the Debye temperature, to be temperature dependent. The other correction is due to the anharmonicity of the nuclear motion (Boyle, Bunbury, Edwards Hall, 1961). 

In several cases Mossbauer studies have revealed a recoil-free fraction with a very flat temperature dependence, which is significantly different from the predictions of either the Einstein or Debye models. Such results were mainly obtained with the Mossbauer probe atom bound within a volume large relative to the atomic size of the probe. They were analysed within a square well potential model, which yields a temperature-independent recoil-free fraction, since in a square well is bound for all states and is dictated by the width of the well, in contrast to the increasing width of the harmonic potential (Nussbaum, 1966). 

Mossbauer studies of glassy nematic [4-6], cholesteric [7, 8] and smectic [9-12] liquid crystals allow the determination of characteristic Debye temperatures, order parameters, intramolecular and lattice contributions to the nuclear vibrational anisotropy, and molecular orientation [13] in the liquid crystal states. For example, Bekeshev et al. have shown from In/ versus temperature data at very low temperatures that MBBA [A -(/7-methoxybenzylidene)-/7-bu-tylaniline] and some liquid-crystalline di-substituted derivatives of ferrocene have weak intermolecular bonds that result in the appearance of additional degrees of free-... 

S = 0.24 (FBA) at 110 K. Measurements of /versus temperature were made and Debye temperatures found to be 23 K lower in the SmB glass than the erystalline phase of the material. A small anisotropy in the vibrational modes of the SmB phase was also reported from angular Mossbauer measurements. Most of the published work has used Fe, though the Mossbauer effect of tin bearing solute molecules has also been studied [22]. 

Studies of molecular mobility in various microregions of polymeric liquid crystals were made by Kosova et al. [25]. Estimates of characteristic Debye temperatures and mean square vibrational amplitudes of the label molecules ferrocene (F) and ferrocene aldehyde (FA) were used to determine the rigidity of regions in both the vitreous and liquid crystal phases of poly l-[2-(4 -cyano-4-biphenyloxy)undecyloxycarbonyl]ethylene (CBO-II-PM). Mossbauer spectra obtained in these studies are shown in Fig. 1. 

Further Mossbauer effect studies (304 — 12 K) and magnetic susceptibility measurements (301 - 1K) on the neutral complex [Fe(papt)2 ] have been performed recently 1S9 The magnetic data are shown in Fig. 34. The values of - In f(s T2) and - In f(J Aj) have been found to follow the high-temperature approximation of the Debye model above 105 K and 140 K, respectively, if anharmonic corrections have been introduced. No simple model is available at present, which would be capable to account for the complete temperature dependence of the Debye-Waller factors in this crossover system. 

Two of the more direct techniques used in the study of lattice dynamics of crystals have been the scattering of neutrons and of x-rays from crystals. In addition, the phonon vibrational spectrum can be inferred from careful analysis of measurements of specific heat and elastic constants. In studies of Bragg reflection of x-rays (which involves no loss of energy to the lattice), it was found that temperature has a strong influence on the intensity of the reflected lines. The intensity of the scattered x-rays as a function of temperature can be expressed by I (T) = IQ e"2Tr(r) where 2W(T) is called the Debye-Waller factor. Similarly in the Mossbauer effect, gamma rays are emitted or absorbed without loss of energy and without change in the quantum state of the lattice by... 

Independent of whether or not a well-defined crossover temperature can be observed in NS data above Tg, it has been well known for a considerable time that on heating a glass from low temperatures a strong decrease of the Debye-Waller factor, respectively Mossbauer-Lamb factor, is observed close to Tg [360,361], and more recent studies have confirmed this observation [147,148,233]. Thus, in addition to contributions from harmonic dynamics, an anomalously strong delocalization of the molecules sets in around Tg due to some very fast precursor of the a-process and increases the mean square displacement. Regarding the free volume as probed by positron annihilation lifetime spectroscopy (PALS), for example, qualitatively similar results were reported [362-364]. 

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