Chia-Hung Chu

Measuring interface strains at the atomic resolution in depth using x-ray Bragg-surface diffraction

A generic x-ray diffraction method, using three-wave Bragg-surface diffraction, is developed to measure strains at the interface of molecular beam epitaxial Au∕GaAs(001), where grazing-incidence diffraction cannot be applied due to the difference in refractive index between Au and GaAs. Changes in diffraction images of the surface reflection (1−13) of GaAs(006)∕(1−13) three-wave Bragg-surface diffraction and the (−1−13) of GaAs(006)∕(−1−13) at different azimuth and Bragg angles give the depth penetration of 2A resolution and variations of lattice constant, −49%, −27%, and 2%, along the surface normal [001] and in-plane directions [−1−10] and [1−10] within the depths of 18, 72, and 72A, respectively.

Diffraction-Enhanced Beam-Focusing for X-rays in Curved Multi-Plate Crystal Cavity

Unusual x-ray focusing effect is reported for parabolic curved multi-plate x-ray crystal cavities of silicon consisting of compound refractive lenses (CRL). The transmitted beam of the (12 4 0) back reflection near 14.4388 keV from these monolithic silicon crystal devices exhibits extraordinary focusing enhancement, such that the focal length is reduced by as much as 18% for 2-beam and 56% for 24-beam diffraction from the curved crystal cavity. This effect is attributed to the presence of the involved Bragg diffractions, in which the wavevector of the transmitted beam is bent further when traversing several curved crystal surfaces.

Inclined-incidence hard-X-ray resonator with ultrahigh efficiency and resolution.

We report a high-efficiency hard-X-ray resonator with inclined-incidence geometry. A beam incident at 36.87° with respect to [3 1 0] excites Bragg back diffraction along (12 4 0) at 14.4388 keV for resonance in a Si-based resonator to produce intense resonance fringes. The experimental results showed the visibility enhanced by nearly 30 times compared with normal incidence. Also numerical calculations of the inclined-incidence resonator demonstrate ultrahigh efficiency and extremely narrow resolving power (sub-meV) with low background. This geometry surpasses the intrinsic limits of normal-incidence crystal-based resonators and enables ultrahigh-resolution X-ray optics for X-ray diffraction, spectroscopy, and imaging applications.

Focusing X-Rays with Curved Multiplate Crystal Cavity

An overview is given of the study on X-ray focusing using the Fabry-Perot type multi-plate silicon crystal cavities consisting of compound refractive lenses. Silicon (12 4 0) is used as the back reflection for cavity resonance at the photon energy of 14.4388 keV. Measurements of focal length of the transmitted beam through the crystal cavities show enhanced focusing effect due to the presence of back diffraction. Also, an incident beam with ultrahigh energy resolution can improve the focusing owing to the wider acceptance angle of the back diffraction. Considerations based on the excitation of dispersion surface within the framework of X-ray dynamical diffraction theory are also presented to reveal the origin of this enhanced focusing.

Revisiting La0.5Sr1.5MnO4 lattice distortion and charge ordering with multi-beam resonant diffraction

Sinusoidal wave type distortions of La0.5Sr1.5MnO4 in the low-temperature orthorhombic phase were observed using multi-beam resonant X-ray diffraction (MRXD) with (7/4 7/4 0) fractional primary diffraction. Two four-beam diffractions with opposite asymmetry were measured at 6.5545 keV and compared with the curves simulated by the dynamical X-ray diffraction theory. This approach provides the possibility of resolving the distortion modes which are perpendicular to the momentum transfer by a single azimuthal scan. The paper also demonstrates the sensitivity of MRXD profiles versus incident X-ray energy in the vicinity of the Mn K edge to the charge disproportion between the two manganese sites, reconfirming the small charge disproportion feature.

Study La0.5Sr1.5MnO4 with Multi-Beam X-ray Diffraction

We have used resonant multi-beam diffraction with the primary reflections G=(h/2 h/2 0) and G=(h/4 h/4 0) (h is an odd number) to investigate the charge ordering and Jahn-Teller distortion, respectively, in La0.5Sr1.5MnO4 low temperature phase. While the Renninger scans with G=(h/2 h/2 0) shows several Aulfhellung-type four-beam diffraction, most of the multi-beam diffraction with G=(h/4 h/4 0) has an Umweganregung-type nature. A detailed study of multi-beam diffraction anomalous fine structure (M-DAFS) of (0 0 0)/(3/2 3/2 0)/(1 -1 0)/(5/2 1/2 0) OUT diffraction is carried out. Its triplet invariant phase approach 180° when the x-ray energy is tuned away from manganese K-edge, and approach 90° when the x-ray energy is tuned on manganese K-edge. In other words, its multi-beam diffraction profile shows strong asymmetry when (3/2 3/2 0) diffraction intensity is dominated by Jahn-Teller distortion, and becomes more symmetric when charge ordering dominated. This characteristic can be successfully simulated by tensor form dynamical x-ray diffraction theory accompanied with FDMNES software [1] calculations.

An algorithm for calculating diffraction profiles of 2θ scans for multiple diffraction from crystals and thin films

An algorithm is developed based on the dynamical theory of X-ray diffraction for calculating the profiles of the diffracted beam, i.e. the diagrams of the intensity distribution versus 2θ when a crystal is fixed at an angle of its maximum diffracted intensity. Similar to Fraunhofer (far-field) diffraction for a single-slit case, in the proposed algorithm the diffracted beam from one atomic layer excited by X-rays is described by the composition of (N + 1) coherent point oscillators in the crystal. The amplitude and the initial phase of the electric field for each oscillator can be calculated based on the dynamical theory with given boundary conditions. This algorithm not only gives diffraction profiles but also provides the contribution of the excitation of modes when extremely asymmetric diffraction is involved in the diffraction process. Examples such as extremely asymmetric two-beam surface diffraction and three-beam surface diffraction are presented and discussed in detail.

The study of wide-angle incidence X-ray nano-wires using crystal asymmetric surface diffraction

Wide-angle incident x-ray Si-wires are devised by using crystal asymmetric surface diffraction. The Si (113) is chosen as an asymmetric surface diffraction for the photon energy 8.8785 keV according to the Si crystal orientation and diffraction geometry. The asymmetric surface diffracted beam propagates alone [110] if the incident beam is parallel to [110]. 2θ-scan (vertical) shows two diffraction peaks; one is the Si(113) Bragg diffraction, and the other is its surface specular reflection. The position of the specular reflection does not vary with photon energy in the range from E=9.05 keV to E=8.75 keV. The positions of these two peaks in vertical (2θ-scan) and horizontal (betascan) direction also depend on azimuth angle around [001], which is the angle between [110] and the incident-beam direction. The behavior of the diffracted beams in the vertical direction is governed by the photon energy and azimuth angle. In addition, interference patterns of specular reflection in the vertical direction are detected. The oscillatory intensity is related to the azimuth angle and extinction length, which we believe is a dynamical diffraction effect. The experimental results are in good agreement with the theoretical calculations using the dynamical theory of x-ray diffraction. In conclusion, we have studied the wide-angle incidence x-ray Si-wires using crystal asymmetric surface diffraction. This idea can be applied to design a new type wide-angle incidence xray optics using crystal surface diffraction.