Hardening of fcc hard-sphere crystals by introducing nanochannels: Auxetic aspects

Jakub W. Narojczyk, Konstantin V. Tretiakov, Jerzy Smardzewski, and Krzysztof W. Wojciechowski

Phys. Rev. E 108, 045003 – Published 16 October 2023

Abstract

Tailoring the materials for a given task by modifying their elastic properties is attractive to material scientists. However, recent studies of purely geometrical atomic models with structural modifications showed that designing a particular change to achieve the desired elastic properties is complex. This work concerns the impact of nanochannel inclusions in fcc hard sphere crystal on its elastic properties, especially auxetic ones. The models containing six nanochannel arrays of spheres of another diameter, oriented along the [110]-direction and its symmetric equivalents, have been studied by Monte Carlo simulations in the isothermal-isobaric $(N p T)$ ensemble using the Parinello-Rahman approach. The inclusions have been designed such that they do not affect the cubic symmetry of the crystal. The elastic properties of three different models containing inclusions of various sizes are investigated under four thermodynamic conditions. We find that six nanochannels filled with hard spheres of larger diameter increase system stiffness compared with the fcc crystal without nanoinclusions. The current finding contrasts the recently reported results [J.W. Narojczyk et al. Phys. Status Solidi B 259, 2200464 (2022)], where the fcc hard sphere crystal with four nanochannels shows reduced stiffness compared to the system without nanoinclusions. Moreover, the six nanochannel models preserve auxetic properties in contrast to the fcc hard sphere crystal with four nanochannel arrays, which loses auxeticity.

Received 31 July 2023
Accepted 19 September 2023

DOI:https://doi.org/10.1103/PhysRevE.108.045003

Physics Subject Headings (PhySH)

Elasticity

Monte Carlo methods

Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Jakub W. Narojczyk ^1,*, Konstantin V. Tretiakov ^1,2, Jerzy Smardzewski ³, and Krzysztof W. Wojciechowski ^1,2,†

¹Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland
²Uniwersytet Kaliski im. Prezydenta Stanisława Wojciechowskiego, Wydział Politechniczny, Katedra Informatyki, Nowy Świat 4, 62-800 Kalisz, Poland
³Department of Furniture Design, Faculty of Forestry and Wood Technology, Poznan University of Life Sciences, Wojska Polskiego 28, 60-637 Poznań, Poland

^*narojczyk@ifmpan.poznan.pl
^†kww@ifmpan.poznan.pl

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 108, Iss. 4 — October 2023

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
The structures of studied systems with inclusions in the form of nanochannels in the [110]-direction and its symmetric equivalents. (a) The investigated structure with eight supercells where red cylinders schematically represent nanochannels. (b) Supercell structures: the hard spheres forming crystals (green points) are artificially scaled down to show the topology of inclusions; the colored spheres belong to the nanochannels. (c) The radius $r_{c}$ is shown on the cross section of the channel, together with spheres lying on the axis of the nanochannel (blue), in the first coordination zone (red), and the second coordination zone (yellow).
Reuse & Permissions
Figure 2
The diagonal box matrix components $h_{i i}$ (top row) plotted with respect to $σ^{'} / σ$ . Ratios of the diagonal and off-diagonal $h$ components (bottom row). The data for corresponding pressure values have been indicated with colors. Data for different inclusion sizes have been organized in three columns for C0 (left), C1 (center), and C2 (right). This convention for colors and column arrangement is kept throughout the paper.
Reuse & Permissions
Figure 3
The components $B_{i j}^{*} = B_{i j} β σ^{3}$ of elastic constant matrix $B$ , plotted with respect to $σ^{'} / σ$ . The rows show results for different pressures. The columns show results for systems C0, C1, and C2, which are additionally described by graphical inserts.
Reuse & Permissions
Figure 4
(a) The Poisson's ratio in main crystallographic directions. Results for systems C0, C1, and C2 (indicated at the top of the figure) are presented in columns. Open symbols represent the results obtained for systems consisting of $N = 864$ particles. Full small symbols describe results for system $N = 6912$ spheres. (b) The absolute value of the minimum negative Poisson's ratio and the maximum value of the Poisson's ratio in all crystallographic directions plotted in spherical coordinates for $p^{*} = 50$ .
Reuse & Permissions
Figure 5
The elastic constants of system C1 with six nanochannels (in the [110]-direction and equivalent ones) and system C1 with four nanochannels (in the [111]-direction and equivalent ones) at $p^{*} = 50$ . Open circles represent the results obtained in this work. Results of MC simulations are described in open squares from Ref. [62].
Reuse & Permissions
Figure 6
The Poisson's ratio in the $[110] [1 \bar{1} 0]$ -direction of system C1 with six nanochannels (in the [110]-direction and equivalent ones) and system C1 with four nanochannels (in the [111]-direction and equivalent ones) at $p^{*} = 50$ . Open circles represent the results obtained in this work. Results of MC simulations are described in open squares from Ref. [62]. The inserts represent the minimum positive Poisson's ratio (yellow) and the absolute value of the minimum negative Poisson's ratio (blue) in all crystallographic directions for $σ^{'} / σ = 1.0$ and $σ^{'} / σ = 1.055$ .
Reuse & Permissions

Physical Review E

covering statistical, nonlinear, biological, and soft matter physics