arXiv subjects

Zbigniew Kozioł

Publications and source records attributed to Zbigniew Kozioł.

5 recordsLinked to original sources

arXiv2025

Dynamic breaking of axial symmetry of acoustic waves in crystals as the origin of nonlinear elasticity and chaos: Analytical model and MD simulations

A Chain of Springs and Masses (CSM) model is used in the interpretation of molecular dynamics (MD) simulations of movement of atoms in orientated FCC crystals. A force of dynamic origin is found that is perpendicular to the direction of the external shear pressure. It is proportional to the square of the applied pressure; It causes breaking of axial symmetry for propagation of transverse acoustic waves. It leads to a non-linear elastic response of crystals and to chaotic patterns in the motion of atoms. We provide an analytical derivation of an effective atomistic 3D potential for interaction between crystallographic layers. The potential is found to possess a component that has an anharmonic threefold axial symmetry around one direction. It reduces to the H{é}non-Heinen potential in a 2D cross-section, leading to mathematically rich, complex dynamic features. Results of simulation predict displacements of atoms that are inconsistent with the static theory of elasticity that may have been overlooked in experiments.

cond-mat.mtrl-sci↗

arXiv2025

Stretched-exponential stress dynamics in chain of springs and masses model of crystals: analytical results and MD simulations

The model of a chain of springs and masses (CSM), originating from the works of Schrödinger (1914), and Pater (1974), is found suitable as an analytical description of the dynamics of layers in orientated FCC crystals. An analytical extension of that model has been developed for the case of linear-in-time ramp pressure applied to a sample surface. Examples are provided of molecular dynamics (MD) simulations, confirming the usefulness of the model in the description of dynamic effects on steel 310S under pressure. Qualitatively the same results have been obtained by us for several other medium-entropy alloys CoNiCr (with EAM and MEAM inter-atomic potentials), and CoNiV (with MEAM potential). For studies of dynamic stability on large sizes of samples and for long times, the proposed earlier table-style harmonic interlayer potential has been used. The results of MD simulations suggest that the dynamics of the CSM model of perfectly ordered matter is described by stretched-exponential time functions, and it is characterised by simple scaling relations in time and size of the sample.

cond-mat.mes-hall↗

arXiv2024

Dynamics of stress propagation in anharmonic crystals: MD simulations

Anharmonic inter-atomic potential x to power of n, n>1, has been used in molecular dynamics (MD) simulations of stress dynamics of FCC oriented crystal. The model of the chain of masses and springs is found as a convenient and accurate description of simulation results, with masses representing the crystallographic planes. The dynamics of oscillations of two planes is found analytically to be given by Euler beta functions, and its scaling with non-linearity parameter and amplitude of oscillations, or applied shear pressure is discussed on examples of time dependencies of displacements, velocities, and forces acting on masses (planes). The dynamics of stress penetration from the surface of the sample with multiply-planes (an anharmonic crystal) towards its interior is confirmed to be given exactly as a series of Bessel functions, when n=2 (Schrodinger and Pater solutions). When n<>2 the stress dynamics (wave propagation) in bulk material remains qualitatively of the same nature as in the linear case. In particular, results suggest that the quasi-linear relationship between frequency and wave number is preserved. Speed of the transverse sound component, dependent on sound wave amplitude, is found to be a strongly decreasing function of n. The results are useful in the analysis of any MD simulations under pressure, as they help to understand the dynamics of pressure retarded effects, as well help design the proper methodology of performing MD simulations, such as studies of dynamics of dislocations.

cond-mat.mes-hall↗

arXiv2022

Size effects in stress penetration and dynamics of dislocations: Fe-Ni-Cr steel

Movement of edge (line) dislocations in FCC steel 310S is shown to depend on the size on nanoscale structures, based on modeling withing molecular dynamics (MD). The effect is attributed to time (and size) dependencies of pressure propagation into the medium interior. The observation is crucial in interpreting any MD studies of pressure effects since these are governed by time-dependent internal virial stresses. In particular velocity of dislocations scales well with value of local internal shear component of virial stress $S_{xy}$ and not with external shear pressure. Dynamics of stress penetration is described well within the model of damped harmonic oscillator, where characteristic oscillation frequency depends on number of crystallographic layers in direction along the wave propagation while the speed of stress propagation is the speed of sound. The minimal stress required for dislocation movement (Peierls stress) is determined to be 0.75 GPa. Pressure and temperature effects on dislocation movement are systematically investigated.

cond-mat.mtrl-sci↗

arXiv2020

Number of equidistant neighbors on honeycomb lattice

A convenient scheme is presented for calculating potential energy of van der Waals interacting bilayer graphene and other similar 2D compounds. It is based on the notion of the existence of two types of local symmetry of carbon atoms ordering, a 3- and 6-fold one. Potential energy of an atom is expressed as a sum of contributions from rings of equidistant atoms on neighboring layer. Methods are described to compute the radius of rings of equidistant atoms and number of atoms they contain. Exact positions of atoms are found as well, allowing to apply the introduced method in modelling of anisotropic potentials and to be used when twisting between layers is present.

cond-mat.mes-hall↗