The detection of the inelastic scattering of gamma rays at crystal diffraction maxima using the Mössbauer effect

THE PREDICTION OF SPOT POSITIONSit leaves the sphere of reflexion. Fig. 5 shows the geometry; the arc AA' is the track of a reciprocal-lattice point rotated about R, and RA=r, and RR=RM= MA, the radius of the circle which the spehre of reflexion cuts in the n-layer net. Then cos r/= [r2/{2 x (RR)2}] -1.Thus, a reflexion generated at A will appear in the top half of the record with z-coordinate = zt, corresponding to ~0; and, after the crystal has been rotated by 2 × t/, the reflexion at A' will appear on the lower half of the film with z coordinate = Zl, corresponding to (~0 + 2 x t/); or, zl = z~ + r/.A program written in FORTRAN IV for an ICL 1905 computer to perform the operations analysed above is available from the author. Measurement and theoretical estimate of the anharmonic non-quadratic contribution to the DebyeWaller factor for NaC1 are reported. For the experiment the M6ssbauer ),-ray diffraction technique was used to find the elastic diffracted intensity separated from the thermal diffuse scattering. The theoretical treatment makes use of the asymptotic form of the displacement correlation functions to give simple explicit expressions for the non-quadratic term. The role of the relevant lattice dynamical parameters is discussed. The deviation from the Gaussian form of the Debye-Waller factor is shown to be large enough to be observed, and the possibility of estimating the third-order anharmonic coupling constant from such a measurement is indicated.

Section: Experimental Methodsmentioning

confidence: 99%

Section: F(kt)=(etku)rmentioning

confidence: 99%

Anharmonic non-Gaussian contribution to the Debye–Waller factor for NaCl

Butt¹,

Solt²

1971

“…Several computer programs (Stevens, 1974;Helmholdt & Vos, 1977;Kurittu & Merisalo, 1977) are available which allow the calculation of integrated TDS intensities from the elastic constants taking into account the anisotropy of the elasticity. Experimentally the extraordinary high energy resolution of the M6ss-bauer effect can be used to separate elastically and inelastically scattered radiation from crystals not containing M6ssbauer isotopes (O'Connor & Butt, 1963;Albanese, Ghezzi, Merlini & Pace, 1972;Albanese & Deriu, 1979) offering the possibility to test these theoretical calculations if special care is taken for the intensity measurements. In addition, the temperature factor B can be determined either directly from the elastically scattered intensities or with some assumptions concerning the TDS from the inelastically scattered intensities.…”

Section: Introductionmentioning

confidence: 99%

Investigation of a silicon single crystal by means of the diffraction of Mössbauer radiation

Kreč¹,

Steiner²

1984

Diffraction experiments with resonant y-radiation were performed on a single crystal of silicon at room temperature. The high energy resolution of the M6ss-bauer effect was used to separate elastically and inelastically scattered radiation. A special experimental setup is described, which in addition allows the determination of the total thermal diffuse scattered intensity. Inelastically scattered radiation was observed in the whole investigated angular range. In the vicinity of Bragg reflections the ratio of the integrated intensities of inelastically to elastically scattered radiation was in very good agreement with the results of calculations using different computer programs based on first-order thermal diffuse scattering theory for a wide range of chosen scan lengths. The measured ratios of the elastically scattered radiation of different Bragg reflections were used to determine the temperature factor B.

“…The experiments were performed by the M6ssbauer ),-ray diffraction technique (O'Connor & Butt, 1963) which allows measurement of the strictly elastic component of the diffraction intensity.…”

Section: I(kt)~-lf(kt)[ Zmentioning

confidence: 99%

“…To determine the strictly elastic part of the peak intensity, the M6ssbauer ),-ray diffraction technique (O'Connor & Butt, 1963;Butt & O'Connor, 1967) seems to be extremely well adapted, since inelastic contributions are not present even in the rough data. Some details of the M/Sssbauer diffraction set-up used for obtaining the present data were given in the previous paper (Butt & Solt, 1971) and here only the results for KC1 are discussed.…”

Section: D(t)=[~~¢mentioning

confidence: 99%

Anharmonic non-Gaussian contribution to the Debye–Waller factor. II. KCl

Solt¹,

Butt²,

O'Connor³

1973

M6ssbauer ~'-ray diffraction data obtained by the technique of O'Connor & Butt [Phys. Lett. (1963), 7, 233-235] are analysed to deduce the anharmonic fourth-order term in the Debye-Waller factor for KCI and to estimate the third-order anharmonic coupling constant in this way. The theoretical treatment assumes that the displacement correlation function can be approximated by its large-distance asymptotic value. For the anharmonic coupling parameter (O m an estimate of -6.2 x 1013 erg cm -3 is found, which differs by a factor of about 6 from that given previously by Leibfried & Ludwig.