The anomalous and ultra-low thermal expansion of cordierite results from the interplay between lattice vibrations and the elastic properties of the material. That is the conclusion of Martin Dove at China’s Sichuan University and Queen Mary University of London in the UK and Li Li at the Civil Aviation Flight University of China. They showed that the material’s unusual behaviour stems from direction-varying elastic forces in its lattice, which act to vary cordierite’s thermal expansion along different directions.
Cordierite is a naturally-occurring mineral that can also be synthesized. Thanks to its remarkable thermal properties, it is used in products ranging from pizza stones to catalytic converters. When heated to high temperatures, it undergoes ultra-low thermal expansion along two directions, and it shrinks a tiny amount along the third direction. This makes it incredibly useful as a material that can be heated and cooled without changing size or suffering damage.
Despite its widespread use, scientists lack a fundamental understanding of how cordierite’s anomalous thermal expansion arises from the properties of its crystal lattice. Normally, thermal expansion (positive or negative) is understood in terms of Grüneisen parameters. These describe how vibrational modes (phonons) in the lattice cause it to expand or contract along each axis as the temperature changes.
Negative Grüneisen parameters describe a lattice that shrinks when heated, and are seen as key to understanding thermal contraction of cordierite. However, the material’s thermal response is not isotropic (it only contracts only along one axis when heated at high temperatures) so understanding cordierite in terms of its Grüneisen parameters alone is difficult.
Advanced molecular dynamics
In their study, Dove and Li used advanced molecular dynamics simulations to accurately model the behaviour of atoms in the cordierite lattice. Their closely matched experimental observations of the material’s thermal expansion, providing them with key insights into why the material has a negative thermal expansion in just one direction.
“Our research demonstrates that the anomalous thermal expansion of cordierite originates from a surprising interplay between atomic vibrations and elasticity,” Dove explains. The elasticity is described in the form of an elastic compliance tensor, which predicts how a material will distort in response to a force applied along a specific direction.
At lower temperatures, lattice vibrations occur at lower frequencies. In this case, the simulations predicted negative thermal expansion in all directions – which is in line with observations of the material.
At higher temperatures, the lattice becomes dominated by high-frequency vibrations. In principle, this should result in positive thermal expansion in all three directions. Crucially, however, Dove and Li discovered that this expansion is cancelled out by the material’s elastic properties, as described by its elastic compliance tensor.
What is more, the unique arrangement of crystal lattice meant that this tensor varied depending on the direction of the applied force, creating an imbalance that amplifies differences between the material’s expansion along each axis.
Cancellation mechanism
“This cancellation mechanism explains why cordierite exhibits small positive expansion in two directions and small negative expansion in the third,” Dove explains. “Initially, I was sceptical of the results. The initial data suggested uniform expansion behaviour at both high and low temperatures, but the final results revealed a delicate balance of forces. It was a moment of scientific serendipity.”
Altogether, Dove and Li’s result clearly shows that cordierite’s anomalous behaviour cannot be understood by focusing solely on the Grüneisen parameters of its three axes. It is crucial to take its elastic compliance tensor into account.
In solving this long-standing mystery, the duo now hope their results could help researchers to better predict how cordierite’s thermal expansion will vary at different temperatures. In turn, they could help to extend the useful applications of the material even further.
“Anisotropic materials like cordierite hold immense potential for developing high-performance materials with unique thermal behaviours,” Dove says. “Our approach can rapidly predict these properties, significantly reducing the reliance on expensive and time-consuming experimental procedures.”
The research is described in Matter.
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