Phase observation of crystal structure factor by using rocking curves

Abstract

According to the resonant X-ray dynamical theory of diffraction, the crystal structure factor for a crystal with centre of symmetry is given by }] ) {arg( exp[ ) 1 ( 2 / 1 2 θ + ⋅ + = + = hr hr hi hr h F i k F iF F F . Here hr F and hi F are the crystal structure factor due to the real and imaginary parts of the atomic scattering factor. For the crystal, arg(Fhr) is either 0 or π, )}] arg( ) cos{arg( [ tan 1 hr hi F F k − ⋅ = − θ and | | / | | hr hi F F k = . In the two-beam approximation, the crystal structure factor must satisfy the condition: θ 2 2 2 ) ( i hi hr h h e F F F F = + − . This condition is expressed as a point on the unit circumference in Fig.1 [1]. If the phase difference φ Δ between interference fringes in the diffracted and transmitted rocking curves is measured, the angle of θ 2 can be determined. The diffraction experiments of GaAs 200 in Laue case were carried out at BL-15C of KEK-PF. The X-rays from synchrotron radiation were monochromated by a Si 111 double-crystal monochromator and by an asymmetric GaAs 200 monochromator. The energy resolution was ±0.5eV. X-rays with σ-polarization were used. The sample thickness was 45μm and the EPD value of the sample was less than 500cm. Fig. 2 shows the diffracted ( h I ) and transmitted intensities ( t I ) measured by changing the incident X-ray energy ω as (a) 10360.5 eV, (b) 10501.0eV, (c) 11403.0 eV, (d) 11805.0eV and (e) 11861.5 eV [2]. The phase difference φ Δ is π (anti-phase) in Fig.2 (a), 0 (inphase) in (c) and π − in (d). If the origin of the coordinate is chosen at a Ga site, arg(Fhi) is 0, because ω is changed between Ga-K and As-K edges in this experiment. At point B in Fig.1, as the measured φ Δ is -0.4π from Fig. 2 (b), θ 2 is -0.41π and arg(Fhr) is determined to be π. This result is reasonable, as Ga f f ) ' ( 0 + AS f f ) ' ( 0 + near As K-edge. It is noted that the measurement of θ 2 is quite useful for the phase determination of the structure factor. Reference [1] Negishi, R., et al., J. Synchrotron Rad., 11,266-271(2004). [2] Negishi, R., et al., J. Phys. Soc. Jpn., 77, 23709_1-3(2008),. Fig.1 A unit circle representing scattering conditions. arg(Fhi) is 0.