Mdssbauer nucleus

For a three- or fourfold axis of symmetry passing through the Mdssbauer nucleus as the center of symmetry, one can show that the FFG is symmetric, that is, = Vyy and therefore, r/ = 0. In a system with two mutually perpendicular axes of threefold or higher-symmetry, the EFG must be zero. 

For ionic compounds, crystal field theory is generally regarded a sufficiently good model for qualitative estimates. Covalency is neglected in this approach, only metal d-orbitals are considered which can be populated with zero, one or two electrons. To evaluate (Vzz)vai 4t the Mdssbauer nucleus, one may simply take the expectation value of the expression — e(3cos 0 — for every electron in a valence orbital i/, of the Mdssbauer atom and sum up,... 

Since in general the nuclear g factors are different for ground and excited states of a Mdssbauer nucleus, the spin state must be quoted when giving numerical values for A in energy (which, however, is usually not necessary for NMR spectroscopy or other ground-state techniques). Thus, for a comparison of A values obtained from Mdssbauer and NMR or ENDOR spectra, usually the ground state is considered. 

First, the sample must be isotopically enriched with Fe or other Mdssbauer nucleus of interest. Small molecule... 

The thermal shift 6j of the Mdssbauer spectrum is the sum of a contribution due to the second-order Doppler effect (6sod) and a possible contribution due to an intrinsic dependence of the isomer shift (8j) on temperature. The second-order Doppler shift is proportional to the mean square velocity of the Mdssbauer nucleus. For the purpose of a comparison with thermodynamic data, the SOD shift may be described in terms of the Debye approximation,6... 

The inadequacy of the Debye approximation in describing the details of the frequency distribution function in a real solid is well known. This results in noticeable disparities between Debye temperatures derived from the results of different experimental techniques used to elucidate this parameter on the same solid, or over different temperature ranges. Substantial discrepancies may be expected in solids containing two (or more) different atoms in the unit cell. This has been demonstrated by the Debye-Waller factors recorded for the two different Mdssbauer nuclei in the case of Snl4,7 or when the Debye-Waller factor has been compared with the thermal shift results for the same Mdssbauer nucleus in the iron cyanides.8 The possible contribution due to an intrinsic thermal change of the isomer shift may be obscured by an improper assignment of an effective Debye temperature. 

The electron density centered at M is the only central contributor at the nuclear position M, as in this case the nucleus coincides with the field point P, which is excluded from the integrals. For transition metal atoms, the central contributions are the largest contributors to the properties at the nuclear position, which can be compared directly with results from other experimental methods. The electric field gradient at the nucleus, for instance, can be measured very accurately for certain nuclei with nuclear quadrupole resonance and/or Mdssbauer spectroscopic methods, while the electrostatic potential at the nucleus is related to the inner-shell ionization energies of atoms, which are accessible by photoelectron and X-ray spectroscopic methods. 

Fig. 5.4 In order to cover all possible transitions in the absorbing nucleus, the energy of the source radiation is modulated by using the Doppler effect. For 57Fe the required velocities fall in the range between — 1 and +1 cm s-1. In Mdssbauer emission spectroscopy, the sample under investigation is the source, and a single line absorber is used to scan the emission spectrum.

Sample purity is a key concern. The NRVS experiment is a bulk technique sampling all Fe nuclei, and impurities that also contain the probe nucleus may confound quantitative data interpretation. Impurities may be introduced during sample preparation or may result from sample instability during measurement. Because of this, care must be taken to ensure purity and reproducibility as judged by Mossbauer (see Mdssbauer Spectroscopy), single-crystal X-ray diffraction, electronic absorption spectroscopy (see Electronic Spectroscopy), Raman spectroscopy or other qnalitative techniqnes. 

In the same way. the Au MOssbauer spectrum of CsAu is very similar lo that of CslC 222) Au (Chapter 12). indicaling that the. Au anion is present in both (Fig. IX.V).- Since the Mdssbauer effeci is a nuclear one. it is very sensiiive to electron density ji the nucleus. ind ihercri>re to both suomic chaigc and chnnKicr. ... 

The sTjTe Mdssbauer parameters for the tin-, germanium-, and antimony-capped clathrochelate compounds (Tables 22-24) are typical low-spin iron(II) complexes. The increase in the ligand field strength (a "macrocyclic" effect), causes the increase in s-electron density on the iron nucleus, is less pronounced for these compounds than for their boron-capped analogs experimental ISs are only slightly lower than those calculated from a PIS concept. 

In this chapter we are concerned with nuclear properties and reactions involving the nucleus. When they occur naturally, such transformations of the nucleus lead to it being radioactive transformations may also be brought about artihcially and the energy released in nuclear fission reactions is harnessed in the nuclear fuels industry. The techniques of nuclear magnetic resonance (NMR) and Mdssbauer spectroscopies owe their existence to properties of particular nuclei. 

Equation (1.10) indicates that the probability of zero-phonon emission decreases exponentially with the square of the y-ray energy. This places an upper limit on the usable values of Ey, and the highest transition energy for which a measurable Mdssbauer effect has been reported is 155 keV for Os. Equation 1.10 also shows that/increases exponentially with decrease in which in turn depends on the firmness of binding and on the temperature. The displacement of the nucleus must be small compared to the wavelength X of the y-ray. This is why the Mossbauer effect is not detectable in gases and non-viscous liquids. Clearly, however, a study of the temperature dependence of the recoil-free fraction affords a valuable means of studying the lattice dynamics of crystals. 

Measurement of the energy of a y-ray emitted (or absorbed) in a recoilless event registers information only about the immediate chemical environment of the emitting (or absorbing) nucleus. Mdssbauer experiments are performed by comparison of a source and an absorber, and it is usual to utihse a source without hyperfine effects as a reference standard for a series of absorber experiments. This is not the only option available, however. If we use a reference absorber, it is possible to study hyperfine effects in the source. These are produced by the chemical environment in which the excited-state Fe nucleus finds itself when it is generated in the source matrix. The total concentration of the Co parent atoms is very small indeed, and each atom can therefore be considered as an isolated impurity in the source matrix. 

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