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Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
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Updated: Jun 11, 2025

Fabricating van der Waals Heterostructures with Precise Rotational Alignment
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Auxeticity Tuning by Nanolayer Inclusion Ordering in Hard Sphere Crystals.

Jakub W Narojczyk1, Krzysztof W Wojciechowski1,2, Jerzy Smardzewski3

  • 1Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland.

Materials (Basel, Switzerland)
|September 28, 2024
PubMed
Summary

Altering nanolayer inclusion order in hard sphere crystals significantly impacts elastic and auxetic properties. This study demonstrates precise tuning of auxeticity by controlling layer arrangement, offering new material design possibilities.

Keywords:
Monte Carlo simulationsauxeticshard spheres inclusionsnanolayersnegative Poisson’s ratio

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Computational Materials Science

Background:

  • Tailoring material elastic properties through structural modification is complex and often unpredictable.
  • Previous research indicates molecular-level structural changes can yield desirable elastic properties.
  • Nanolayer inclusions in crystalline structures present a potential avenue for property tuning.

Purpose of the Study:

  • To investigate the effect of nanolayer inclusion ordering in hard sphere crystals on elastic properties.
  • To specifically analyze the impact on auxetic properties in different crystallographic directions.
  • To determine if layer ordering can be used to predictably tune auxetic behavior.

Main Methods:

  • Utilized Monte Carlo simulations in the isothermal-isobaric (NpT) ensemble for two sets of hard sphere crystal models (6x6x6 unit cells).
  • Introduced nanolayer inclusions of spheres with different diameters, oriented orthogonally to the [001] direction.
  • Employed the Parinello-Rahman approach to calculate elastic constants and evaluate auxetic properties.

Main Results:

  • Introducing nanolayer inclusions altered the crystal symmetry from cubic to tetragonal.
  • Significant changes in elastic properties were observed due to both neighboring and separated layer ordering.
  • Nanolayer ordering enabled tuning of auxetic properties along the [110][11¯0] and [101][1¯01] directions.

Conclusions:

  • The arrangement of nanolayer inclusions (neighboring vs. separated) critically influences auxeticity.
  • Separated layers enhanced auxeticity in one direction ([101][1¯01]) while diminishing it in another ([110][11¯0]).
  • Neighboring layers maintained auxetic properties in both directions, offering independent control regardless of inclusion size.