Theoretical scientists recently applied topological mathematics and machine learning to determine a hidden link between nanoscale structures and thermal conductivity in amorphous silicon, a glassy material form without repeating crystalline order.
As indicated in a Phys.org report, amorphous solids like obsidian, glass, plastics, and wax don't have long-range repeating or crystalline construction to the molecules or atoms they are made of.
Additionally, this counters crystalline solids like salt, most rocks, and metals. As they lack long-range order in their construction, the amorphous solids' conductivity can be far lower than crystalline solids made of the same material.
Nonetheless, there can still be some medium-range order on the scale of nanometers. This medium-range order needs to impact the propagation and diffusion of atomic vibrations, which can carry heat.
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Luminescent microphotography of amorphous silicon dioxide (SiO2). UV microscopy, fluorescing screen, magnification 200X.
Amorphous Silicon
Essentially, the heat transport in disordered materials is of special interest to physicists because of its essentiality in industrial applications.
Silicon's amorphous form is used in many applications in the modern world, from solar cells to image sensors.
For this reason, scientists have intensively examined the structural signature of the medium-range order in amorphous silicon and the manner it relates to thermal conductivity.
According to Emi Minamitani, the corresponding author of the study, published in the Journal of Chemical Physics, for better regulation over applications that use amorphous silicon, regulating its thermal properties is high on the wish list of the engineers.
Minamitani, a theoretical molecular scientist with the Institute for Molecular Science in Okazaki, Japan, also said that extracting the nano-scale structural characteristics in amorphous, including medium-range order, is vital.
Topology Used
Regrettably, scientists have struggled in carrying out the said tasks as it is challenging to identify the essential nano-scale features of disordered systems using traditional approaches.
In investigations, the existence of medium-range order has been physically identified using fluctuation electron microscopy, involving statistical analysis of spreading from nano-scale volumes of a disordered material.
At the theoretical level, it has been discussed by evaluating the dihedral angles' distribution or use of ring statistics. The latter mentioned attempts to understand the structural traits from the atoms' connectivity.
This, in turn, is drawing on the field of mathematics called "topology," which examines properties of an object that are not changing or are "invariant," even when the object is constantly stretched and deformed minus being broken.
Topological Invariance
Focusing on this topological invariance is useful for delivering a qualitative description, like the tendency of the physical properties when it comes to randomness.
Nevertheless, it is demanding to identify the atomic structure that corresponds to a medium-range order, not to mention "predict its physical properties only from simple topological invariants," a similar Tabbed News report said.
The scientists pivoted to an approach known as persistent homology, a type of topological data assessment.
Related information about topology is shown on 3Blue1Brown's YouTube video below:
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