Machine learning algorithm reveals long-theorized glass phase in crystal

X-ray technology and machine learning converge to shed light on the nature of complex materials.

A dish made of crystal and a dish made of glass might look similar from the outside, but internally, their structures differ significantly. Crystals consist of perfectly ordered, repeating patterns of atoms, while glasses display a more disordered, fluid-like structure.

For decades, scientists have been puzzled by glasses — how they form, what they are and why they behave the way they do. Glasses exist right at the intersection of liquid and solid, which makes their nature elusive to traditional ways of classifying and understanding material behavior.

Even more perplexing and elusive is a phase of matter called a Bragg glass. It displays both the ordered properties of crystals and the disordered nature of glasses at the same time. Scientists at the U.S. Department of Energy’s (DOE) Argonne National Laboratory, along with collaborators at Cornell University and Stanford University, have recently found experimental evidence of a Bragg glass phase present in a material.

The team discerned the subtle features of a Bragg glass within large volumes of X-ray scattering data using a new machine learning data analysis tool, X-ray temperature clustering, developed at Cornell.

Their result contributes to a larger effort in modern materials science to investigate the nature of glasses, whose mysterious structures give rise to useful material properties for applications in electronics, aerospace engineering, architecture, medicine, nuclear waste management and much more. The study also demonstrates the potential of machine learning algorithms as powerful tools for discovery in the era of big data.

“We can collect massive amounts of X-ray data in short periods of time, and analyzing the data manually can make it impossible to see the forest for the trees,” said Ray Osborn, a senior physicist in Argonne’s Materials Science division and an author on the study. ​“With the combination of cutting-edge X-ray and computational technology, we were able to uncover a signature that is unique to the Bragg glass phase.”

The atomic structures of all crystals — including diamonds, table salt and even snowflakes — display what scientists call long-range order, where a certain pattern of atoms is repeated in three dimensions across the material. In this study, the researchers searched for the Bragg glass state in a crystal based on ErTe₃, which has a particular long-range order to its structure that scientists refer to as a charge density wave (CDW).

“With the combination of cutting-edge X-ray and computational technology, we were able to uncover a signature that is unique to the Bragg glass phase.” — Senior Physicist Ray Osborn

About thirty years ago, it was theorized that CDW materials could host Bragg glass states if a little bit of chaos is introduced to their otherwise ordered structures. When creating the samples used in this experiment, Stanford University scientists randomly distributed palladium atoms into the ErTe₃ crystals to impose this type of disorder.

Scientists at Argonne’s Advanced Photon Source (APS), a DOE Office of Science user facility, used the 6-ID-D beamline to perform X-ray scattering on the samples, measuring hundreds of gigabytes of 3D structural data for each crystal.

In X-ray scattering experiments, when a pattern in a sample’s structure repeats, scientists see what’s called a Bragg peak in the data. ​“The term Bragg glass is almost an oxymoron. ​‘Bragg’ refers to the sharp Bragg peaks you see with perfect crystals, which indicate long-range order. And in a glass, you see broader, more diffuse features that indicate local patterns,” said Matthew Krogstad, an assistant physicist at the APS and author on the study. ​“But in a Bragg glass, you see each type of feature simultaneously.”

The team took X-ray scattering measurements of the samples at temperatures ranging from 30 K to 300 K, recording how their structures changed. After the fact, the machine learning analysis conducted at Cornell confirmed that at a certain transition temperature, the samples froze into a state that maintained a significant amount of long-range order, while also displaying the local features that characterize a Bragg glass.

“You can think of a regular crystal as a perfect pattern of squares side by side,” said Krogstad. ​“When you introduce random palladium atoms, the pattern changes a bit because of the randomness, but it’s not completely disrupted, either. The structure can accommodate a little randomness.”

The discovery answers a long-held question of whether a disordered CDW sample will lose its crystalline order and break up into little patches when cooled, or become Bragg glass. Insight into the structure and behavior of Bragg glasses has the potential to inform the design of useful materials down the line.

A paper on the study, ​“Bragg glass signatures in Pd_xErTe₃ with X-ray diffraction temperature clustering,” was published in Nature Physics. This work was supported by DOE’s Office of Basic Energy Sciences, Division of Materials Sciences and Engineering. In addition to Krogstad and Osborn, authors include Krishnanand Mallayya, Joshua Straquadine, Maja D. Bachmann, Anisha G. Singh, Stephan Rosenkranz, Ian R. Fisher and Eun-Ah Kim.

About the Advanced Photon Source

The U. S. Department of Energy Office of Science’s Advanced Photon Source (APS) at Argonne National Laboratory is one of the world’s most productive X-ray light source facilities. The APS provides high-brightness X-ray beams to a diverse community of researchers in materials science, chemistry, condensed matter physics, the life and environmental sciences, and applied research. These X-rays are ideally suited for explorations of materials and biological structures; elemental distribution; chemical, magnetic, electronic states; and a wide range of technologically important engineering systems from batteries to fuel injector sprays, all of which are the foundations of our nation’s economic, technological, and physical well-being. Each year, more than 5,000 researchers use the APS to produce over 2,000 publications detailing impactful discoveries, and solve more vital biological protein structures than users of any other X-ray light source research facility. APS scientists and engineers innovate technology that is at the heart of advancing accelerator and light-source operations. This includes the insertion devices that produce extreme-brightness X-rays prized by researchers, lenses that focus the X-rays down to a few nanometers, instrumentation that maximizes the way the X-rays interact with samples being studied, and software that gathers and manages the massive quantity of data resulting from discovery research at the APS.

This research used resources of the Advanced Photon Source, a U.S. DOE Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357.

Argonne National Laboratory seeks solutions to pressing national problems in science and technology. The nation’s first national laboratory, Argonne conducts leading-edge basic and applied scientific research in virtually every scientific discipline. Argonne researchers work closely with researchers from hundreds of companies, universities, and federal, state and municipal agencies to help them solve their specific problems, advance America’s scientific leadership and prepare the nation for a better future. With employees from more than 60 nations, Argonne is managed by UChicago Argonne, LLC for the U.S. Department of Energy’s Office of Science.

The U.S. Department of Energy’s Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of the most pressing challenges of our time. For more information, visit https://​ener​gy​.gov/​s​c​ience.