Atomic-scale computer simulations allow us to study material properties that are inaccessible to traditional experimental methods. In his latest work, a scientist from the National Centre for Nuclear Research (NCBJ) has proposed a new model describing the propagation of sound in crystals, which reveals the existence of previously unknown dynamic effects and forces occurring in the crystal structure under the influence of an acoustic wave.

A method called molecular dynamics (MD) is often used to model the motion of atoms in materials. It involves numerically solving equations of motion for a system of atoms or molecules, taking into account the interactions between them, in order to reproduce the phenomena occurring in reality as accurately as possible. A huge advantage of molecular dynamics is the ability to describe the motion of individual atoms in arbitrarily short time intervals, often on the order of picoseconds (10^-12 seconds). This allows us to study effects occurring in materials that are very difficult or even impossible to reproduce by other means. However, in order to use this method effectively, it is necessary to have a very good understanding of the physical phenomena being studied. Computer simulations alone, although capable of modelling the motion of millions of atoms simultaneously, are computationally demanding, and the efficient analysis of the enormous amount of data they produce requires appropriate technical preparation.

Despite the continuous development of science and technology, there are still many fundamental phenomena that have not been precisely described and studied. One of them is the mechanics of bodies and the movement of atoms in crystals, for example, the phenomenon of sound propagation in crystalline structures. Although the basics of this issue were formulated as early as the 19th century, there is still no widely accepted description of it. Such a description could be used in certain studies commonly used in the field of materials science. An attempt to formulate a precise description of sound propagation in crystals was undertaken by Zbigniew Kozioł, PhD, from the Materials Research Laboratory of the National Centre for Nuclear Research (NCBJ). The result was a chain of springs and masses (CSM) model, which introduces an analytical description of stress penetration into the crystal structure. - The first considerations on a similar model date back to the early 20th century, to Erwin Schrödinger and a little-known work by Dutch professor de Pater, an expert in railway engineering. I was able to expand on this work and show how well the resulting analytical equations describe a whole range of simulations using molecular dynamics - says Zbigniew Kozioł, creator of the CSM model and author of a new paper published in the Journal of Physics Communications. 

The application of the model and careful analysis of data for FCC (face-centred cubic) crystals revealed the existence of unexpected oscillations in the crystal layers. The movements of the atomic system occur when the sound wave front reaches a given crystallographic layer. The material then experiences previously unknown forces acting perpendicular to the direction of the applied pressure. - The discovered force is dynamic in origin and proportional to the square of the pressure. In addition to the oscillations of the atoms, it also causes them to shift in directions perpendicular to the external force. The phenomenon is related to the difference in relative displacements between the layers on either side of each layer. These effects are not described by the commonly used static theory of stress in materials," explains Zbigniew Kozioł, PhD. Although the phenomenon is presented in a specific crystal configuration in the paper, it should also occur in other cases. This creates an opportunity for experimental research to confirm the existence of the effect under sufficiently high pressures.

Film przedstawia wnikanie fali naprężeń do materiału po przyłożeniu ciśnienia 1 GPa na jego powierzchni w chwili t=0. Parametry materiału odtwarzają własności stali. Do stworzenia wykorzystano dane z symulacji komputerowej.

The discovery of a new force was not the only surprise resulting from the research. One part of the analysis involved deriving analytical formulas approximating the potential energy between individual crystal layers, which allows for the derivation of equations of motion. As it turned out, if one of the force components is omitted, the resulting potential reduces to the Hénon-Heiles potential. - The potential obtained in the research is a three-dimensional extension of the potential proposed in the 1960s, which is a very simplified model of the motion of stars in the centre of the Milky Way. Its introduction sparked intense interest and the development of chaos theory - emphasises Zbigniew Kozioł.

The new work opens up new research opportunities not only in the field of computer simulations in crystal structures, but also points to previously unknown links with other fields of science. It may also contribute to increased interest in the application of non-obvious theories, such as chaos theory, in materials research. The work is also an example of how, even in fields that seem well understood and currently of little interest to theorists, fundamentally important observations can still be made using simple and inexpensive methods.

The full results of the research are available in the publication: Dynamic breaking of axial symmetry of acoustic waves in crystals as the origin of nonlinear elasticity and chaos: analytical model and MD simulations, Zbigniew Kozioł 2026, J. Phys. Commun. 10 015003, https://doi.org/10.1088/2399-6528/ae37c8