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Mossbauer Debye-Waller factor

The Bragg scattering of X-rays by a periodic lattice in contrast to a Mossbauer transition is a collective event which is short in time as compared to the typical lattice vibration frequencies. Therefore, the mean-square displacement (x ) in the Debye-Waller factor is obtained from the average over the ensemble, whereas (r4) in the Lamb-Mossbauer factor describes a time average. The results are equivalent. [Pg.14]

An important accessory in many applications of Mossbauer spectroscopy is a cryostat for low temperature and temperature-dependent measurements. This may be necessary to keep samples frozen or to overcome small Debye-Waller factors of the absorbers at room temperature in the case of an isotope with high y-energy. Paramagnetic samples are measured at liquid-helium temperatures to slow down... [Pg.41]

Mossbauer nuclei per square centimetre, the Debye-Waller factor/a of the absorber material, and the resonance cross-section Gq of the Mossbauer isotope. For a multiline spectrum, the result must be split into separate values for each line, which are obtained by weighting t with the relative transition probability of each line. [Pg.46]

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. 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.
Mossbauer spectroscopy with started only in 1965, when Harris et al. [322] measured the Mossbauer absorption spectra of the 99 keV transition of Pt in platinum metal as a function of temperature (between 20 and 100 K) and of absorber thickness and derived the temperature dependence of the Debye-Waller factor. [Pg.339]

Housley RM, Hess F (1966) Analysis of Debye-Waller-factor and Mossbauer-thermal-shift measurements. 1. General theory. Phys Rev 146 517-526... [Pg.99]

Single crystals of Te are highly anisotropic and occur as either right-hand or left-hand crystals. It would be interesting to use the Te Mossbauer effect to measure the anisotropic Debye-Waller factor in such crystals. [Pg.157]

From variable-temperature 57Fe Mossbauer spectra Konig and Ritter82) determined the Debye-Waller factors f over the temperature range of 298-4.2 K in III (on polymorph one with 0.9 B.M. at 77 K). Whereas the magnetic moment and other physical properties show an abrupt change with temperature near Tc ( 213 K), they found a continuous change of -Inf. [Pg.102]

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. [Pg.113]

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. [Pg.157]

A pronounced hysteresis of ATC = 9.5 K has been observed (Tc = 181.86 K for rising and Tc = 172.33 K for falling temperature). The authors attempted to describe the results with the thermodynamic model for spin transitions of Slichter and Drickamer 91 Different diffraction patterns were recorded above and below Tc, where only one spin isomer was present (see Fig. 39). This provides evidence that a crystallographic phase change accompanies the abrupt spin phase transition in this compound. The temperature dependence of the peak profiles was found to follow that of the HS fraction as derived from the Mossbauer spectra, which shows that the crystallographic phase change is directly associated with the interconversion of the two spin phases. The Debye-Waller factors were evaluated for the two spin phases they showed at Tc a discontinuity of Af 35% on going from the HS to the LS phase. The shape of the transition curve near Tc and Tc itself, were somewhat different in three independently prepared samples. [Pg.166]

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... [Pg.138]

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]. [Pg.216]

This is often written as / = e . The factor W is sometimes loosely called the Debye-Waller factor though it might be better in this context to call it the Lamb-Mossbauer factor. [Pg.11]

The Debye-Waller factor was originally derived during the development of Bragg X-ray scattering theory. The difference between the two effects is that X-ray scattering is fast when compared with the characteristic time for lattice vibrations whereas the mean lifetime of a Mossbauer nucleus is long when compared with the lattice time. [Pg.11]

The probability of the recoilless emission or absorption is given by the recoilless fraction f, meaning the fraction of all y rays of the Mossbauer transition that are emitted (fs) or absorbed (A) without recoil-energy loss. This is also commonly referred to as the Mossbauer fraction, Debye-Waller factor, Mossbauer-Lamb factor or, simply, the /-factor. [Pg.1388]

The Mossbauer spectra of powdered samples of the clathrate are shown in Fig. 1. The statistics of the spectra is very poor at high temperature due to a low Debye-Waller factor (the absorption is 0.4 % at 320 K) and a relaxation phenomenon(absorption becomes broad in the region of the releixation time of 120 ns. The accumulated counts are more than a million counts above 250 K. The low temperature spectra of this clathrate are quite normal The efg for ferrocene derivatives is known to be essentially of molecular origin and the QS values do not... [Pg.800]

Debye model for solids leads to the following expression for Lamb-Mossbauer factor (called Debye-Waller factor / in Atomic Physics)... [Pg.186]

Here the Debye temperature Or, = fttUE/ke is the measure of the strength of the bonds between Mossbauer atoms of the lattice. The Debye-Waller factor / increases with (a) decreasing Sr, i.e., decreasing y-photon energy Sy, (b) decreasing temperature and (c) increasing Debye temperature. [Pg.186]

The existence of conformational substates can also be seen in many other experiments, particularly through the determination of the Debye-Waller factor in X-ray diffraction [8, 9, 13,14] and through the Mossbauer-Lamb factor in the Mossbauer effect [15-17]. [Pg.146]

The recoil-free fraction in Mossbauer spectroscopy is equivalent to the fraction of X-ray scattering processes without lattice excitation this fraction of elastic processes in X-ray and neutron diffraction is described by the Debye-Waller factor ... [Pg.564]

The evaluation of a Mossbauer spectrum implies the determination of the physical parameters, the isomer shift, Debye-Waller factor, and electric and magnetic hyperfine fields. When flue-... [Pg.573]

The fundamentals of SSS are based on the theory of impurity centers in a crystal. The optical spectrum of an organic molecule embedded in a matrix is defined by electron-vibrational interaction with intramolecular vibrations (vibronic coupling) and interaction with vibrations of the solvent (electron-phonon coupling). Each vibronic band consists of a narrow zero-phonon line (ZPL) and a relatively broad phonon wing (PW). ZPL corresponds to a molecular transition with no change in the number of phonons in the matrix (an optical analogy of the resonance -line in the Mossbauer effect). PW is determined by a transition which is accompanied by creation or annihilation of matrix phonons. The relative distribution of the integrated intensity of a band between ZPL and PW is characterized by the Debye-Waller factor ... [Pg.749]

Where k is the wavevector of the gamma ray and is the mean-square displacement of the Mossbauer nucleus in the direction of the gamma ray. The exponent 2W s the Debye-Waller factor, which is also relevant to X-ray and neutron scattering line intensities. Thus a measurement of the recoil-free fraction at a particular temperature /(T) yields the value of at this temperature, which can be compared with theoretical calculations of... [Pg.222]

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). [Pg.224]

L. Wiehl, Structures of hexakis(l-propyltetrazole)iron(II) bis(tetrafluoroborate), [Ee(CHN4C3H7)6](BE4)2, hexakis(l-methyltetrazole)iron(II) bis(tetrafluoroborate), [Ee(CHN4CH3)6](BE4)2, and the analogous perchlorates. Their relation to spin crossover behaviour and comparison of Debye-Waller factors from stracture determination and Mossbauer spectroscopy. Acta Cryst. B 49, 289-303 (1993)... [Pg.80]

If the Mossbauer atom is bound in a solid, the recoil energy may be taken up by the matrix via excitation of lattice vibrations. The recoil energy is then reduced by a factor given by the atom and the solid mass ratio. If the phonon energy is low enough, there will be a finite probability, f, that the emission (absorption) will take place with no creation or annihilation of phonon in the lattice, that is, with no recoil energy loss, and this is the Mossbauer effect. The / factor (recoil-free fraction, Debye-Waller factor, Lamb-Mossbauer factor) is given by... [Pg.477]


See other pages where Mossbauer Debye-Waller factor is mentioned: [Pg.14]    [Pg.46]    [Pg.83]    [Pg.201]    [Pg.43]    [Pg.116]    [Pg.156]    [Pg.156]    [Pg.358]    [Pg.246]    [Pg.121]    [Pg.32]    [Pg.150]    [Pg.160]    [Pg.195]    [Pg.11]    [Pg.564]    [Pg.200]    [Pg.131]    [Pg.180]    [Pg.215]   
See also in sourсe #XX -- [ Pg.195 ]




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