Physicists at the University of Bristol have created a series of mazes inspired by the Knight’s movements on a chessboard. These labyrinthine designs could potentially be used to address global challenges, such as enhancing carbon capture and streamlining fertilizer production processes.
Knight’s Tour Inspires Hamiltonian Cycles in Quasicrystals
Lead author Dr. Felix Flicker and his team constructed an infinite number of increasingly larger Hamiltonian cycles within irregular structures known as quasicrystals. A Hamiltonian cycle is a loop through a map that visits all stopping points only once, similar to a Knight’s tour on a chessboard.
Quasicrystals differ from regular crystals in their atomic arrangement. While crystal atoms repeat at regular intervals, quasicrystal atoms do not. Instead, they can be described mathematically as slices through crystals that exist in six dimensions.
Hamiltonian Cycles Form Complex Mazes with Practical Applications
The group’s Hamiltonian cycles visit every atom on certain quasicrystal surfaces precisely once, resulting in paths that form complex mazes. These paths have the property of allowing an atomically sharp pencil to draw straight lines connecting all neighboring atoms without lifting or crossing the line.
This finding has applications in scanning tunneling microscopy, where an atomically sharp microscope tip is used to image individual atoms. The Hamiltonian cycles provide the fastest possible routes for the microscope to follow, potentially reducing the time required to produce images.
Quasicrystals as Adsorbers for Carbon Capture and Storage
The research results demonstrate that quasicrystals can be efficient adsorbers, a process in which molecules stick to surfaces. Here are some key points about quasicrystals as adsorbers:
- Flexible molecules can pack efficiently by lying along the atomic mazes of quasicrystals
- Quasicrystals’ irregular atomic arrangement and brittleness allow them to break into tiny grains with maximum surface area
- These properties make quasicrystals potentially effective for adsorption applications such as carbon capture and storage
Co-author Shobhna Singh highlighted the significance of these findings in relation to the potential use of quasicrystals for adsorption applications.
Potential for Catalysis and Fertilizer Production
Efficient adsorption suggests that quasicrystals could be candidates for catalysts, which increase industrial efficiency by lowering the energy of chemical reactions. Adsorption is a key step in the Haber catalysis process used to produce ammonia fertilizer.
The research by Dr. Flicker and his team has opened up possibilities for utilizing the properties of quasicrystals in addressing challenges from carbon capture to industrial process optimization.
