Total-reflection High-energy Positron Diffraction Research Articles

A fast and efficient computation method for reflective diffraction simulations

We present a new computation method for simulating reflection high-energy electron diffraction and the total-reflection high-energy positron diffraction experiments. The two experiments are used commonly for the structural analysis of material surface. The present paper improves the conventional numerical method, the multi-slice method, for faster computation, since the present method avoids the matrix-eigenvalue solver for the computation of matrix exponentials and can adopt higher-order ordinary differential equation solvers. Moreover, we propose a high-performance implementation based on multi-thread parallelization and cache-reusable subroutines. In our tests, this new method performs up to 2,000 times faster than the conventional method without compromising accuracy.

A two-stage data-analysis method for total-reflection high-energy positron diffraction (TRHEPD)

A two-stage data-analysis method for total-reflection high-energy positron diffraction (TRHEPD)

Data-analysis software framework 2DMAT and its application to experimental measurements for two-dimensional material structures

An open-source data-analysis framework 2DMAT has been developed for experimental measurements of two-dimensional material structures. 2DMAT offers five analysis methods: (i) Nelder-Mead optimization, (ii) grid search, (iii) Bayesian optimization, (iv) replica exchange Monte Carlo method, and (v) population-annealing Monte Carlo method. Methods (ii) through (v) are implemented by parallel computation, which is efficient not only for personal computers but also for supercomputers. The current version of 2DMAT is applicable to total-reflection high-energy positron diffraction (TRHEPD), surface X-ray diffraction (SXRD), and low-energy electron diffraction (LEED) experiments by installing corresponding forward problem solvers that generate diffraction intensity data from a given dataset of the atomic positions. The analysis methods are general and can be applied also to other experiments and problems. Program summaryProgram Title: 2DMATCPC Library link to program files:https://doi.org/10.17632/c2t3vzbx9f.1Developer's repository link:https://www.pasums.issp.u-tokyo.ac.jp/2dmat/Code Ocean capsule:https://codeocean.com/capsule/7260490Licensing provisions: GNU General Public License v3.0Programming language: Python 3External routines/libraries: Numpy, Scipy, Tomli, mpy4pyNature of problem: Analysis of experimental measurement data.Solution method: Optimization, grid-based global search, Monte Carlo method.

Structure of χ3-Borophene Studied by Total-Reflection High-Energy Positron Diffraction (TRHEPD).

We have investigated the structure of χ3-borophene on Ag(111), a monolayer material of boron atoms, via total-reflection high-energy positron diffraction (TRHEPD). By comparing the experimental rocking-curves with ones for several structures calculated by using dynamical diffraction theory, we confirmed that the χ3-borophene layer has a flat structure. The distance from the topmost layer of the metal crystal is 2.4 Å, which is consistent with results reported by X-ray standing wave-excited X-ray photoelectron spectroscopy. We also demonstrated that the in-plane structure of χ3-borophene is compatible with the theoretical predictions. These structural properties indicate that χ3-borophene belongs to a group of epitaxial monolayer sheets, such as graphene, which have weak interactions with the substrates.

Sim-trhepd-rheed – Open-source simulator of total-reflection high-energy positron diffraction (TRHEPD) and reflection high-energy electron diffraction (RHEED)

The present paper reports sim-trhepd-rheed (STR), an open-source simulator of total-reflection high-energy positron diffraction (TRHEPD) and reflection high-energy electron diffraction (RHEED) experiments which are used for atom-scale surface structure determination of a material. Diffraction data obtained by these experiments are analyzed by comparison with numerical simulations. The STR simulator is used for the analysis of experimental diffraction data by simulating the rocking curve from a given trial surface structure by solving the partial differential equation of the dynamical quantum diffraction theory for positron or electron wavefunctions. Using the obtained surface structure, electronic structure, and other physical quantities can be evaluated through first-principles calculations. For this purpose, a utility software was also developed in order to realize a first principles calculation with the Quantum ESPRESSO suite. Program summaryProgram title: sim-trhepd-rheedCPC Library link to program files:https://doi.org/10.17632/89vpfvp84k.1Developer's repository link:https://github.com/sim-trhepd-rheed/sim-trhepd-rheed/Code Ocean capsule:https://codeocean.com/capsule/2323181Licensing provisions: GNU General Public License v3.0Programming language: Fortran 90, Python 3External routines/libraries: BLAS library, LAPACK libraryNature of problem: Partial differential equation in dynamical quantum diffraction theory.Solution method: Numerical solution by the multi-slice method for the partial differential equation.

Data-driven sensitivity analysis in surface structure determination using total-reflection high-energy positron diffraction (TRHEPD)

The present article proposes a data analysis method for experimentally-derived measurements, which consists of an auto-optimization procedure and a sensitivity analysis. The method was applied to the results of a total-reflection high-energy positron diffraction (TRHEPD) experiment, a novel technique of determining surface structures or the position of the atoms near the material surface. This method solves numerically the partial differential equation in the fully-dynamical quantum diffraction theory with many trial surface structures. In the sensitivity analysis, we focused on the experimental uncertainties and the variation over individual fitting parameters, which was analyzed by solving the eigenvalue problem of the variance-covariance matrix. A modern massively parallel supercomputer was used to complete the analysis within a moderate computational time. The sensitivity analysis provides a basis for the choice of variables in the data analysis for practical reliability. The effectiveness of the present analysis method was demonstrated in the structure determination of a Si4O5N3 / 6H-SiC(0001)-(3×3) R30∘ surface. Furthermore, this analysis method is applicable to many experiments other than TRHEPD.

Development of Data-Analysis Software for Total-Reflection High-Energy Positron Diffraction (TRHEPD)

The present paper reports on the recent activity of the data analysis software development for total-reflection high-energy positron diffraction (TRHEPD), a novel experimental technique for surface structure determination. Experiments using TRHEPD are being conducted intensively at the Slow Positron Facility, Institute of Materials Structure Science, High Energy Accelerator Research Organization, revealing surface structure of interest. The data analysis software provides a solution to the inverse problem in which the atomic positions of a surface structure are determined from the experimental diffraction data (rocking curve). The forward problem is solved by the numerical solution of the partial differential equation in the quantum scattering problem. A technical demonstration with a test problem was carried out to confirm the software functioned as expected. Since the analysis method has a general mathematical foundation, it is also applicable to other experiments, such as X-ray or electron diffraction experiments.

Structure of superconducting Ca-intercalated bilayer Graphene/SiC studied using total-reflection high-energy positron diffraction

We have investigated the atomic structure of superconducting Ca-intercalated bilayer graphene on a SiC(0001) substrate using total-reflection high-energy positron diffraction. By comparing the experimental rocking-curves with ones calculated for various structural models using a full-dynamical theory, we have found that Ca atoms are intercalated in the graphene-buffer interlayer, rather than between the two graphene layers. From transport measurements, the superconducting transition was observed to be at Tc_onset = 4K for this structure. This study is the first to clearly identify the relation between the atomic arrangement and superconductivity in Ca-intercalated bilayer graphene.

Asymmetrically optimized structure in a high-Tc single unit-cell FeSe superconductor

We report asymmetric Se heights in a single unit-cell (UC) FeSe on SrTiO3(0 0 1) substrate with the highest superconducting transition temperature (Tc) among the Fe-based superconductors revealed by total-reflection high-energy positron diffraction measurements. Among various iron-based superconductors, this single UC FeSe on the SrTiO3(0 0 1) has been the best material to achieve the highest-Tc above 50 K. We found the asymmetric Se heights of 1.44 ± 0.03 and 1.33 ± 0.03 Å from the single Fe layer by the intensity analysis based on dynamical diffraction theory. The average Se height results in 1.39 ± 0.04 Å, corresponding to the optimum value for Fe-based superconductors. In addition, the average of bond angles of Se–Fe–Se, 107.2 ± 1.1 and 111.5 ± 1.2° becomes 109.3 ± 1.6°, which is close to the optimum value of 109.5° for a regular tetrahedron. Thus, this single UC FeSe is found to have asymmetrically optimized structure. Based on our first-principles calculations, the asymmetry does not change the bandwidth whereas it splits the electron bands at the M point only at the bottom. These calculations suggest that at low electron doping, the structural asymmetry is expected to lead to exotic properties of non-centrosymmetric superconductivity, whereas after a certain amount of electron doping, average anion height plays an important role for high-Tc.

Research progress at the Slow Positron Facility in the Institute of Materials Structure Science, KEK

Recent results at the Slow Positron Facility (SPF), Institute of Materials Structure Science (IMSS), KEK are reported. Studies using the total-reflection high-energy positron diffraction (TRHEPD) station revealed the structures of rutile-TiO2(110) (1×2), graphene on Cu (111) and Co (0001), and germanene on Al (111). First observations of the shape resonance in the Ps− photodetachment process were made using the positronium negative ion (Ps−) station. Experiments using the positronium time-of-flight (Ps-TOF) station showed significant enhancement of the Ps formation efficiency and the energy loss in the Ps formation-emission process. A pulse-stretching section has been implemented, which stretches the positron pulse width from 1.2 μs up to almost 20 ms.

Asymmetric structure of germanene on an Al(111) surface studied by total-reflection high-energy positron diffraction

The structure of germanene on an Al(111) surface has been experimentally investigated using the total-reflection high-energy positron diffraction (TRHEPD) method. The observed spot intensities are asymmetric, revealing no mirror symmetry in the atomic coordinates of germenene with respect to the 〈110〉 direction. Quantitative TRHEPD rocking curve analysis, based on dynamical diffraction theory, has revealed that the germanene layer has a 3 × 3 structure with asymmetrical buckling due to the protrusion of one of the Ge atoms in the unit cell, which is unlike the structural model proposed in previous studies. The magnitude of the buckling was found to be 0.94 Å, and the spacing between the germanene and the Al(111) substrate to be 2.51 Å. The new structure proposed in the present investigations, though different from that reported in studies before, does not contradict the other characteristics which were found experimentally in the previous studies.

Spacing between graphene and metal substrates studied with total-reflection high-energy positron diffraction

The spacing between graphene and metal substrates has been investigated using total-reflection high-energy positron diffraction (TRHEPD). The rocking curve analysis performed, based on the dynamical diffraction theory, shows that the spacing between the graphene layer and a substrate of Cu(111) and that between graphene and a Co(0001) substrate are 3.34 Å and 2.06 Å, respectively. The former is close to the interlayer spacing in graphite, suggesting a weak interaction with the substrate material, whereas the latter value experimentally verifies that, in the case of graphene on Co(0001), there is a strong interaction with the substrate.

全反射高速陽電子回折法（TRHEPD）による最表面構造解析

Total-reflection high-energy positron diffraction (TRHEPD) is a surface-sensitive tool owing to the total reflection of positrons. Since the sign of the crystal potential energy for positrons is positive, opposite to that for electrons, the positron beam at a grazing incidence is totally reflected at a crystal surface. The penetration depth of the positron beam in the total reflection region is estimated to be about a few Å, which corresponds to the thickness of 1-2 atomic layers. Thus, the positron beam in the total reflection region sees only the topmost surface layer of the crystal. Slightly over the critical angle for the total reflection, the positon beam also sees the underlying surface layer. Adjusting the glancing angle of the incident positron beam, the diffraction intensity selectively contains information about the topmost and the underlying surface layers without any effect from the bulk. Therefore, the TRHEPD is very useful for structure determinations of crystal surface and two-dimensional atomic sheet adsorbed on the substrate. In this paper, we will show the surface-sensitivity of the TRHEPD. Shown is also the recent result of silicene, two-dimensional atomic sheet of silicon, using the TRHEPD.

Structure determination of the rutile-TiO2(110)-(1 × 2) surface using total-reflection high-energy positron diffraction (TRHEPD).

The exact structure of the rutile-TiO2(110)-(1 × 2) surface, which had been under debate over the past 30 years, was investigated using the newly developed technique of total-reflection high-energy positron diffraction (TRHEPD), which is a positron counterpart of reflection high-energy electron diffraction (RHEED). The rocking-curves for the 00-spot obtained from the experimental diffraction patterns were compared to the curves for various models calculated with a full-dynamical theory. It was found that the rocking-curves matched those for a surface consisting of a Ti2O3 configuration, originally suggested by Onishi and Iwasawa [H. Onishi and Y. Iwasawa, Surf. Sci., 1994, 313, L783], but with a further modification of atomic positions close to the ones proposed by Wang et al. [Q. Wang, A. R. Oganov, Q. Zhu and X. F. Zhou, Phys. Rev. Lett., 2014, 113, 266101]. This result demonstrates that TRHEPD can distinguish between the existence and absence of the oxygen atoms on the topmost surface, and between the Ti atoms residing in positions at the interstitial-vertical sites and those at interstitial-horizontal sites.

全反射高速陽電子回折によるCo(0001)基板上のグラフェンへの金属原子インターカレーションの研究

全反射高速陽電子回折によるCo(0001)基板上のグラフェンへの金属原子インターカレーションの研究

23pAE-8 全反射高速陽電子回折法による金属表面上のグラフェンの構造解析 : 基板依存性

23pAE-8 全反射高速陽電子回折法による金属表面上のグラフェンの構造解析 : 基板依存性

Development of the Reflection High-Energy Electron Diffraction in Japan and Evolution to the Total Reflection High-Energy Positron Diffraction(One Hundred Years of X-ray and Particle Diffraction)

Development of the Reflection High-Energy Electron Diffraction in Japan and Evolution to the Total Reflection High-Energy Positron Diffraction(One Hundred Years of X-ray and Particle Diffraction)

Structure determination of two-dimensional atomic sheet of silicene using TRHEPD

This study reports determination of the atomic coordinates of a two-dimensional atomic sheet, silicene, by using total reflection high-energy positron diffraction (TRHEPD) [1]. TRHEPD method, formerly called as RHEPD, is a surface-sensitive tool owing to the total reflection of positrons. Since the sign of the potential energy for positrons in crystals is positive, opposite to that for the electrons, the positron beam at a grazing incidence are totally reflected at a crystal surface. The penetration depth of the positron beam in the total reflection region is estimated to be approximately a few Å, which corresponds to the thickness of 1-2 atomic layers. Thus, the positron beam selectively sees the topmost surface layer and hence the TRHEPD method is very useful for structure determinations of crystal surface and two-dimensional atomic sheet on the substrate. Silicene is a two-dimensional atomic sheet of silicon. Since the silicene has an intriguing property such as a Dirac cone like a graphene, it attracts increasing attention as a candidate for future devices. Recently, the synthesis of silicene on a Ag(111) surface was successfully performed [2]. Although the atomic coordinates of the silicene in this system was theoretically calculated, they were not confirmed experimentally. It is very important to experimentally determine the magnitude of the buckling in silicene and the spacing between the bottom of the silicene and the substrate because the dispersion of the Dirac cone is closely related to these structure parameters. We thus investigated the atomic positions of the silicene on the Ag(111) surface using the TRHEPD [3]. From the rocking curve analysis based on the dynamical diffraction theory of positrons (see figure), the existence of the buckling (0.83 Å) in silicene was verified experimentally. Moreover, the spacing between the silicene and the substrate was determined as 2.17 Å. The structural difference with the graphene will be also discussed.

Surface sensitivity of total reflection high-energy positron diffraction

"Reflection high-energy positron diffraction (RHEPD) is the positron counterpart of reflection high-energy electron diffraction (RHEED). RHEPD was proposed in 1992 [1], and first demonstrated in 1998 [2]. Unlike the case of the electron, the potential energy of the positron inside a crystal is positive, and hence positrons incident on a crystal surface with a glancing angle smaller than a certain critical angle are totally reflected. This feature makes the positrons a tool extremely sensitive to the topmost layer of the crystal surface. Recent development of a brightness-enhanced intense positron beam at KEK [K. Wada, et al., J. Phys.: Conf. Ser. 443, 012082 (2013)] has made it possible to obtain clear RHEPD patterns. We rename the technique with a refined beam as ""total reflection high-energy positron diffraction (TRHEPD)"". Here we demonstrate that the TRHEPD pattern from the Si(111)-7x7 DAS surface taken with a glancing angle smaller than the critical angle for the total reflection is essentially determined only by the atoms exposed on the surface (adatoms and the atoms in the first surface layer) [3]. The technical details of the positron beam preparation [M. Maekawa, et al., to be published in Eur. Phys. J. D (2014)], results on the Pt/Ge(001) nano-wire surface[I. Mochizuki, et al., Phys. Rev. B 85, 245438 (2012)], TiO2(110)-1x2 surface, and silicene on Ag(111) surface [Y. Fukaya, et al., Phys. Rev. B 88 205413 (2013)] are also presented in this conference. "

A total reflection high-energy positron diffraction station at the KEK-SPF

A high-intensity mono-energetic positron beam generated by using a linear electron accelerator (linac) provides total reflection high-energy positron diffraction (TRHEPD) researches at Slow Positron Facility (SPF), KEK [1,2]. A pulsed 50-Hz electron beam generated with a dedicated linac (operated at 55 MeV, 0.6 kW) is injected on a Ta converter and causes fast positron-electron pair creation through bremsstrahlung. The positrons showering down on 25 μm-thick W foils, are moderated to thermal energy, and a fraction spontaneously comes out of the foils with an energy of 3 eV owing to the negative work function. The positron converter/moderator assembly is held at an electrostatic voltage of 15 kV for TRHEPD experiment. The emitted positrons are consequently accelerated to 15 keV as they enter the grounded beam-line and are guided by the magnetic field of about 0.015 T to the TRHEPD station. For diffraction experiments, positrons transported by the magnetic field have to be first released into a nonmagnetic region. Since the released positron beam has a large diameter, a brightness-enhancement unit is effectively used to achieve a small-diameter and highly-parallel beam with a sufficient flux. The linac-based positron beam gives about 60 times intensified diffraction pattern from a Si(111)-7x7 reconstructed surface compared to a previous result with a Na-22-based positron beam [3]. An improved signal-to-noise ratio in the obtained pattern due to the intensified beam allowed an observation of clear fractional-order spots in the higher Laue-zones, which had not been observed previously. The much intensified beam with the present system allows adjustment of the sample orientation without accumulating the positron signals. With the brightness enhanced beam, several remarkable results have been obtained efficiently by users of this facility. (Everybody is invited to use KEK Slow Positron Facility through approval of his/her research proposal.)