P 08 ISSRNS 2012: Abstracts / Synchrotron Radiation in Natural Science Vol. 11, No 1 – 2 (2012)
COMPTON PROFILE OF Mg SINGLE CRYSTAL:
HIGH RESOLUTION EXPERIMENT AND THEORY
M. Brancewicz1∗, A. Andrejczuk1, E. ˙Zukowski1, L. Dobrzy´nski2, Y. Sakurai3, and M. Itou3
1Faculty of Physics, University of Bialystok, ul. Lipowa 41, 15–424 Bialystok, Poland
2National Centre for Nuclear Research, ul. Andrzeja Soltana 7, 05–400 Otwock-Swierk, Poland
3Japan Synchrotron Radiation Research Institute, Mikazuki, Sayo, Hyogo 679–5198, Japan Keywords: synchrotron radiation, Compton scattering, inelastic scattering, Compton profile, Mg
∗e-mail : brancew@alpha.uwb.edu.pl
Compton scattering is a very powerful method for investigating the electronic structure in con- densed matter physics. The spectrum of inelasti- cally scattered monoenergetic photons in a target is related through Doppler effect to momentum den- sity distribution ρ(p), which is directly connected with the electron wave function in reciprocal space χ(p) and hence with Fourier transform of the wave function in real space ψ(r):
ρ(p) =| χ(p) |2=|
Z
ψ(r)eiprd3r |2
Thus the Compton scattering technique is the most direct test of solid state theories, where electron wave functions are calculated from the first prin- ciples.
The final result of single Compton scattering ex- periment is the Compton profile J (pz) (CP), which is a one-dimensional projection (double integral) of the electron momentum density ρ(p) onto the scat- tering vector direction (usually chosen as z axis):
J (pz) = Z +∞
−∞
Z +∞
−∞
ρ(p)dpxdpy
To test theoretical calculations, one usually shows differences between CPs measured in two directions (CPs anisotropies) [1, 2]. This approach has many advantages because some systematic errors in ex- perimental data can be cancelled and sharp features connected with the anisotropy of electron momen- tum density are emphasized.
The directional Compton profiles of Mg single crystal have been measured along [100], [110], [001]
and [310] directions using high resolution Comp- ton spectrometer at SPring-8 (beamline BL08W) [3]. Preliminary results of this experiment were published in [1]. Apart from standard data anal- ysis procedures taking into account a number of energy dependent corrections applied to the raw data, final results were prepared with the use of some modified algorithms. The experimental data
were compared with the Korringa-Kohn-Rostoker (KKR) semi-relativistic calculations and previous medium resolution Compton profile measurements [2]. Medium and high resolution CPs anisotropies show good agreement with theoretical KKR calcu- lations, except the low momentum region where the agreement is worse, suggesting a need for revision of theoretical calculations.
It was observed later that the experimental CPs anisotropies of Mg agree slightly better with the old CP calculations performed with the use of APW theory [4]. It can be simply explained by almost free character of the valence electrons in Mg. In KKR theory electron wave functions outside the muffin- tin spheres are described by the linear combination of spherical harmonics. In the APW theory this is realized by the superposition of the plane waves (like in the case of free electrons).
The new theoretical band structure calculations for hexagonal Mg should take into account sug- gested almost free character of valence electrons and describe their behavior as a linear combination of plane wave like functions.
References
[1] M. Brancewicz, A. Andrejczuk, Y. Sakurai, M. Itou, L. Dobrzy´nski, E. ˙Zukowski, S. Kaprzyk, “Electron momentum density of hexagonal magnesium studied by high-resolution Compton scattering,” Rad. Phys.
Chem. 78 (2009) 137 – 139.
[2] M. Brancewicz, H. Reniewicz, A. Andrejczuk, L. Do- brzy´nski, E. ˙Zukowski, and S. Kaprzyk, “Electron momentum density of hexagonal magnesium studied by Compton scattering,” Solid State Phenom. 112 (2006) 123 – 132.
[3] Y. Sakurai, M. Itou, “A Cauchois-type X-ray spec- trometer for momentum density studies on heavy- element materials,” J. Phys. Chem. Solids 65 (2004) 2061 – 2064.
[4] S. Wakoh, “Momentum density distribution in mag- nesium for Compton scattering and positron annihi- lation,” J. Phys. Soc. Jpn. 50 (1981) 490 – 497.
88
