Understanding glass structure is challenging and puzzling due to the lack of translational periodicity.
The use of quantum beam diffraction using X-rays, neutrons, and electrons is essential to understand glass structure beyond the first neighbor distance. Progress has been made in recent years in interpreting reciprocal space data to understand the structure of glass at an extended length scale. Understanding diffraction data in both reciprocal and real space is challenging and hence this knowledge will be shared in this TC. The two important topics of the TC are “diffraction measurement” and “modelling of glass structure”. Where the latter is consistent with diffraction data and other structural information.

Online Tutorial of Quantum Beam PDF Analysis and Topological Analysis for Disordered Materials

By ICG TC29 (Quantum Beam Diffraction) and JSPS Hyper-ordered structures science

In order to register the tutorial which will be held between September 13 -17, 2021, you can click on the link and fill out the form.

Shinji Kohara (National Institute for Materials Science)

Anita Zeidler (Bath University)

Akihiko Hirata (Waseda University)

Naoto Kitamura (Tokyo University of Science)

Motoki Shiga (Gifu University)

Ippei Obayashi (Okayama University)

Ayako Nakata (National Institute for Materials Science)

Yohei Onodera (Kyoto University)

Koji Kimura (Nagoya Institute of Technology)

September13 -17, 2021

The structure of disordered materials is still not well understood because of insufficient experimental data. Indeed, diffraction patterns from disordered materials are very broad and can be described only in pairwise correlations because of the absence of translational symmetry. The advance of instrumentation and measurement protocols makes it feasible to use X-ray diffraction and neutron diffraction techniques to investigate the structure of disordered materials at synchrotron and neutron facilities. Moreover, a combination of diffraction experiments and advanced computer simulation techniques enables understanding of the structure of disordered materials at both the atomistic and electronic levels.

In this online tutorial, we provide seven lectures, (i) basis of diffraction and pair distribution function (PDF) analysis, (ii) synchrotron X-ray diffraction, (iii) neutron diffraction, (iv) electron diffraction, (v) DFT simulation, (vi) reverse Monte Carlo (RMC) modelling, and (vii) topological analysis. Moreover, we organize (i) RMC modelling, (ii) DFT simulation, and (iii) topological analysis.

We hope participants will get deep understanding of amorphous diffraction and glass structure.

Lectures

(i) General introduction to diffraction and pair distribution function (PDF) analysis
Anita Zeider
In the first part of this tutorial I will introduce the general basics of diffraction and how we can extract useful information from measured diffraction patterns. For simplicity, I will focus on neutron diffraction using single wavelength neutrons from a reactor source to describe how the data needs to be treated to obtain real space information on the system following a PDF analysis. I will also briefly comment on information in reciprocal space the is often overlooked in diffraction data analysis.

(ii) Synchrotron X-ray diffraction
Shinji Kohara
With the advent of the third-generation synchrotron sources and the development of light source techniques, the high-energy X-ray diffraction technique has become feasible, leading to new approaches for studying the structure of disordered materials in a quantitative manner. In this lecture, we introduce high-energy X-ray beamline and the dedicated diffractometer for glass, liquids and amorphous materials. Moreover, we address anomalous X-ray scattering technique, which provides us with element specific information beyond the first coordination distance.

(iii) Neutron diffraction

Yohei Onodera

In comparison with X-rays, neutrons are sensitive to light elements and hence complementary use of the neutron diffraction technique with the X-ray diffraction is powerful to study the structure of disordered materials. In this lecture, we give a talk on the neutron diffraction technique for disordered materials using a pulsed neutron source. Furthermore, we introduce the neutron diffraction with isotopic substitution, which allow us to obtain element specific structural information around an isotopically substituted atom on local and intermediate-range order.

(iv) Electron diffraction
Akihiko Hirata
Using advanced transmission electron microscopes, it becomes possible to acquire both global and local structural information of disordered materials by changing the beam size from micrometer to sub-nanometer scale. In this lecture, we introduce an electron pair-distribution-function (PDF) analysis with a global electron diffraction obtainable from the wide region larger than several nanometers, together with a direct observation technique for short- to medium-range order using a recently developed angstrom-beam electron diffraction. We also show a few examples of the complementary use of the high-energy X-ray diffraction and electron diffraction techniques.

(v) DFT simulation

Ayako Nakata

With recent development of computers and calculation methods, density functional theory (DFT) calculations have become a powerful tool to investigate atomic and electronic structures of not only crystalline materials but also nonperiodic systems such as biomaterials and amorphous systems.

In this lecture, the basic idea of DFT and what information are required to perform DFT calculations will be learnt. We also introduce our large-scale DFT calculation code CONQUEST and its recent applications for the systems containing several thousand atoms.

(vi) Reverse Monte Carlo (RMC) modelling
Naoto Kitamura

A Monte Carlo simulation using experimental data instead of an energy calculation, which is referred to as a reverse Monte Carlo (RMC) modelling, can be regarded as one of the most promising ways to construct atomic configurations of disordered materials. In this lecture, we explain fundamentals on a structure factor and a pair distribution function level, and then give a talk on an algorithm of RMC modelling using these data. We also introduce a few examples of structural modelling of disordered materials.

 (vii) Topological analysis
Ippei Obayashi and Motoki Shiga
Characterizing the geometric structures of data is one of the important issues in materials research. Topological data analysis (TDA) provides mathematical tools for quantifying the shape of data using

topology. Persistent homology (PH), one important tool of TDA, is useful for characterizing

disordered materials such as liquids and glasses. This lecture explains the theoretical basis of PH and its application to materials science, especially the analysis of amorphous materials.

Tutorials

(i) RMC modelling
Naoto Kitamura

This tutorial explains some features of recent RMC programs and demonstrates RMC modelling using diffraction data. The demonstration will use RMC_POT++ as the program for disordered materials (https://www.szfki.hu/~nphys/rmc++/opening.html). You will be able to perform the modelling with your own PCs, and learn methods to obtain bond distances, coordination numbers, and bond angles from the modelling result.

(ii) DFT simulation
Ayako Nakata
In this tutorial, we will perform DFT calculations of small systems using CONQUEST with the users’ own PCs. VirtualBox machine with the image “MateriApps LIVE!” will be used to perform the calculations. Although large-scale DFT calculations are possible only with cluster machines and supercomputers, we will learn the basic usage of the DFT program by testing some small systems through the tutorial.

(iii) Topological analysis
Ippei Obayashi and Motoki Shiga

This tutorial will demonstrate data analysis using PH. This demonstration will use python and HomCloud (https://homcloud.dev/index.en.html), data analysis software based on PH. We will use Google Colab (https://colab.research.google.com/) for the demonstration. Participants will be able to experience the contents on the browser if the participants have a Google account and know how to use Google Colab. Therefore, it is recommended that you prepare a Google account and Google Colab before attending this tutorial. The URL for the demo will be presented just before the tutorial.