Quasicrystals, strange solids that blur the line between crystals and glass, have puzzled scientists for decades. Unlike ordinary crystals, the atomic arrangement of quasicrystals never repeats but remains highly ordered. Now, for the first time, researchers have used quantum mechanical simulations to reveal why these materials exist: They are intrinsically stable, rather than briefly cooling rapidly. This breakthrough solved a 40-year-old scientific mystery and opened the door to the development of engineered materials with unique, breakthrough properties.
Quasicrystals: a strange state between crystals and glass
University of Michigan research suggests that an exotic and rare form of matter somewhere between a crystal and glass may actually be the most stable structure in certain combinations of atoms.
The conclusion stems from the first quantum mechanical simulations of quasicrystals, a type of solid that was once thought to be impossible. Like crystals, quasicrystals have atoms arranged in a lattice, but their patterns never repeat like traditional crystals. New simulation methods show that quasicrystals, like crystals, are inherently stable, despite their similarities to disordered materials such as glass, which typically form when molten matter cools too quickly.
A single grain of scandium-zinc quasicrystal has 12 pentagonal crystal faces. Image source: Yamada et al. (2016). IUCrJ
Why do quasicrystals exist?
"If we want to design materials with desired properties, we need to know how to arrange atoms into specific structures," said Wenhao Sun, an early career assistant professor in Dow's Department of Materials Science and Engineering and corresponding author of the paper published today in Nature Physics. "Quisicrystals force us to rethink how and why certain materials form. Before our studies, scientists didn't know why they existed."
The discovery first shocked the scientific community in 1984 when Israeli researcher Daniel Shechtman observed quasicrystals while studying aluminum and manganese alloys. He discovered that some atoms formed an icosahedral structure, similar to a cluster of 20-sided dice with connected faces. This structure gives the quasicrystal a five-fold symmetry - meaning it looks exactly the same from five different angles - which was once thought to be impossible in solid matter.
To calculate the stability of solids whose atoms do not repeat in sequence, the researchers simulated quasicrystal spoons randomly sampled from a larger bulk. Because particles have well-defined boundaries, the energy within each nanoparticle can be calculated using quantum mechanics. By repeating the calculations over a range of scoop sizes, the researchers can extrapolate the energy calculations to bulk quasicrystals. Image credit: Woohyeon Baek, University of Michigan Solar Research Group
From controversy to Nobel Prize
Scientists at the time believed that atoms in a crystal could only be arranged in a sequence that repeated in each direction, but five-fold symmetry ruled out this pattern. Shechtman initially faced intense scrutiny for proposing such an improbable hypothesis, but other labs have since synthesized quasicrystals and discovered them in meteorites from billions of years ago.
Shechtman eventually won the 2011 Nobel Prize in Chemistry for this discovery, but scientists still cannot answer fundamental questions about the formation of quasicrystals. The obstacle is that density functional theory, a quantum mechanical method used to calculate the stability of crystals, relies on infinitely repeating patterns in a sequence, which quasicrystals lack.
"The first step in understanding a material is knowing what makes it stable, but it's hard to tell how quasicrystals are stable," said Woohyeon Baek, a doctoral student in materials science and engineering at the University of Michigan and first author of the study.
The atoms in any given material are usually arranged into crystals so that chemical bonds achieve the lowest possible energy. Scientists call this structure an enthalpy-stable crystal. But other materials are formed because they have high entropy, which means their atoms can be arranged or vibrated in many different ways.
University of Michigan research team. Each researcher was armed with a geometric model that couldn't fit into a traditional crystal. Pictured, from left to right: Vikram Gavini, professor of mechanical engineering and materials science and engineering; Sambit Das, research associate in mechanical engineering; Woohyeon Baek, doctoral student in materials science and engineering; Wenhao Sun, early career assistant professor of materials science and engineering at Dow; and Shibo Tan, doctoral student in materials science and engineering. Image credit: Marcin Szczepanski, Michigan College of Engineering
Quasicrystals: order without repetition
Glass is an example of an entropically stable solid. It forms when molten silica cools rapidly and the atoms instantly freeze into a patternless form. But if the cooling rate is slowed, or a base is added to the heated silica, the atoms arrange themselves into quartz crystals—the optimal, lowest-energy state at room temperature. Quasicrystals are a puzzling intermediate between glass and crystals. They have locally ordered arrangements of atoms like crystals, but like glasses, they do not form long-range repeating patterns.
To determine whether quasicrystals have enthalpy- or entropy-stable properties, the researchers' approach was to scoop out smaller nanoparticles from larger blocks of simulated quasicrystals. The researchers then calculated the total energy of each nanoparticle. Since particles have well-defined boundaries, this does not require an infinite sequence.
Revealing the secret power of quasicrystals
Because the energy in a nanoparticle is related to its volume and surface area, by repeating the calculations for nanoparticles of increasing size, the researchers can infer the total energy within the larger quasicrystal. Using this approach, the researchers discovered that two well-studied quasicrystals possess enthalpy-stabilizing properties. One is a scandium-zinc alloy and the other is a ytterbium-cadmium alloy.
The most accurate estimate of the energy of a quasicrystal requires the largest possible particles, but scaling up nanoparticles is difficult with standard algorithms. For nanoparticles with only a few hundred atoms, doubling the number of atoms increases the calculation time eightfold. But researchers have also found ways around the computational bottleneck.
Accelerating the future of materials research
"In traditional algorithms, each computer processor needs to communicate with each other, but our algorithm is 100 times faster because only adjacent processors communicate, and we effectively leverage GPU acceleration in supercomputers," said study co-author Vikram Gavini, a professor of mechanical engineering and materials science and engineering at the University of Michigan.
"We can now simulate glass and amorphous materials, interfaces between different crystals, and crystal defects that could enable quantum computing bits."
Compiled from /scitechdaily