Topological mathematics and machine learning have been used by theoretical scientists to determine a hidden relationship between thermal conductivity and nano-scale structures in amorphous silicon. It is an attractive form of material with no repetitive crystalline order.
A study explaining their method appeared in Journal of Chemical Physics on June 23third2022.
Amorphous solids, such as glass, wax, plastics and obsidian, have no long-range repeats or crystalline structures for the atoms or molecules from which they are made. It differs from most crystalline solids such as metals, salts and rocks. Since they move less than an order of magnitude longer in their structure, the thermal conductivity of amorphous solids can be significantly lower than that of crystalline solids made from the same material.
But there may still be availability of some medium-range order at the nanometer scale. This medium-range order should affect the propagation and propagation of atomic vibrations, which carry heat. The heat transport caused by disordered materials is of unique interest to physicists as a result of its importance in industrial applications.
The amorphous form of silicon has been used in the present world in a vast range of applications, ranging from solar cells to image sensors. For this reason, scientists have intensively investigated the structural signature of medium-range order in amorphous silicon and how it relates to thermal conductivity.
Controlling its thermal properties is high on engineers’ wish list, for better control over applications that use amorphous silicon., Extracting nano-scale structural features in amorphous including medium-range order is an important key,
Amy Minamitani, study correspondent and theoretical molecular scientist, Institute of Molecular Sciences, National Institute of Natural Sciences
Obviously, this task has proved challenging for researchers because of the difficulty of using conventional methods to identify key nano-scale features of disordered systems.
In experiments, the existence of medium-range order has been detected in a physical way with the help of fluctuating electron microscopy. It involves statistical analysis of scattering from nano-scale volumes of disordered material.
As far as the theoretical level is concerned, it is discussed by taking into account the distribution of dihedral angles (the angle between two sectioning planes between sets of atoms) or by using so-called “ring statistics”. The latter tries to understand structural features from the association of atoms.
It is based on a field of mathematics called topology, which deals with the analysis of properties of an object that do not change – or are known as “immutable” – even when the object is continuously deformed and deformed. (like figures written on rubber sheet).
Focusing on this topological invariance appears to be beneficial for providing qualitative details, such as the tendency of physical properties to be related to randomness. But it is difficult to identify an atomic structure equivalent to the middle-order order and to predict its physical properties derived only from simple topological invariants.
Therefore, scientists turned to an evolved method known as persistent homology—a type of topological data analysis. Consistent homology has been used elsewhere to investigate complex structures ranging from proteins to amorphous solids.
The advantage of this technique lies in the detection of topological features in complex structures at different spatial scales. This is important because there are semi-repetitive structures at many scales in the medium-range order. With this characteristic, it is possible to extract middle-order order that is otherwise hidden beneath what appears to be randomness.
Computational models of amorphous silicon were constructed by scientists with the help of classical molecular dynamics, in which the temperature of silicon was raised above the melting point and slowly cooled (quenched) to room temperature. Changes in structural characteristics were introduced by changing the cooling rate.
In addition, the firm diagram, which is a two-dimensional view of firm homology, was calculated for each model. The scientists focused on diagrams that showed the structural features of amorphous silicon.
Therefore, he created numerical representations, known as “descriptors”, that could be used in machine learning. The scientist found that the consecutive diagram satisfies the creation of a good descriptor for use in the machine learning process, which in turn helps to obtain accurate predictions about thermal conductivity.
By additionally examining stable homology data and machine-learning models, the scientists demonstrated a previously hidden connection between medium-order order in amorphous silicon and its thermal conductivity.
At present, the study should set the stage for an opportunity to regulate the physical characteristics of amorphous silicon and other amorphous solids through the topology of their nanostructures.
Minamitani, E., and others, (2022) Topological descriptor of thermal conductivity in amorphous Si. Journal of Chemical Physics, doi.org/10.1063/5.0093441.