Anisotropy of the recoilless fraction

Mössbauer Spectroscopy Division, Pedagogical University, Cracow, Poland

Basic principles of the Rayleigh scattering of the Mössbauer radiation (RSMR) in the energy domain are shown in Fig. 1.

Fig. 1. Basic setup for RSMR experiments.

A well collimated beam from the very high intensity Mössbauer source (super-source) falls under Bragg conditions on the single crystal free of the resonant atoms, and after being scattered by the Rayleigh mechanism goes to the detector through the movable resonant absorber. The above method has been mastered by Mullen et al. [1] applying 46.5-keV line of 183W. 183Ta in metallic tantalum is used as a source, while the absorber is made of metallic tungsten. Sources of the 70 Ci activity could be prepared by neutron irradiation of tantalum. A facility to work with the above sources was set by the Purdue University and Missouri University Research Reactor (MURR).

Measurements of the Mössbauer line intensity for various Bragg reflections and at various temperatures allow to get recoilless fraction for each atom within the unit cell of the scattering crystal as a function of the wave-vector transfer to the lattice. Such measurements were performed for alkali halides by Shepard et al. [2].

A general theory of the recoilless fraction allows for the anisotropy in a cubic environment in quartic (and higher even) terms of the wave-vector transfer [3]. Hence, the data obtained for NaCl [2] have been analyzed in terms of the above theory. One has to realize, that NaCl structure belongs to the highest cubic symmetry group Fm3m. A unit cell of the sodium chloride is shown in Fig. 2.

Fig. 2. Chemical unit cell of the sodium chloride.

We discovered a significant anisotropy of the recoilless fraction for both Na and Cl [4]. Spatial "thermal" distribution functions around the equilibrium positions have been reconstructed at various temperatures for Na and Cl [4]. Fig. 3 shows such a distribution function plotted vs. scaled departure from the equilibrium position for two distinct directions. A departure from the Gaussian shape responsible for the anisotropy is shown as well. More details could be found in [5] or down-loaded here as NACL.DOC.

Fig. 3. "Thermal" distributions around equilibrium position for two directions in a crystal. Lower diagram shows corresponding departures of the distributions from the Gaussian shape.

One can conclude that the anisotropy of the thermal atomic motion in cubic systems HAS BEEN DISCOVERED [4]. Atoms of Na and Cl move more freely in the main axes directions than along the diagonal of the unit cell in the case of NaCl. Hence, the well known fact that NaCl crystals like to grow as cubes has found a simple explanation at the basic atomic level.

[1]W.B.Yelon, G.Schupp, M.L.Crow, C.Holmes, and J.G.Mullen, Nucl. Instrum. Methods Phys. Res. B 14, 341 (1986)
[2]C.K.Shepard, J.G.Mullen, and G.Schupp, Phys. Rev. B 57, 889 (1998)
[3]K.Ruebenbauer, U.D.Wdowik, and M.Kwater, Physica B 229, 49 (1996)
[4]K.Ruebenbauer and U.D.Wdowik, Phys. Rev. B 61, 11416 (2000) - see PRB www page
[5]K.Ruebenbauer and U.D.Wdowik, Mol. Phys. Reports 30, 137 (2000)

November 2000. Please send comments to Krzysztof Ruebenbauer. Back to Mössbauer Spectroscopy Division home page.
Background: aerial view of the Nazca Desert, Peru; 600 m altitude above the desert floor (photo: A. Ruebenbauer).