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Multipolar Models for Anisotropic Vacancy Interactions in MXenes.

Steven R Goldy1, Garritt J Tucker2, Cristian V Ciobanu3

  • 1Department of Mechanical Engineering, Colorado School of Mines, Golden, Colorado 80401, United States.

ACS Applied Materials & Interfaces
|November 21, 2025
PubMed
Summary
This summary is machine-generated.

Atomic-scale vacancies in two-dimensional (2D) MXenes exhibit complex interactions, with short-range oscillations and long-range power-law behaviors. Understanding these defect interactions is crucial for tuning MXene properties for electronic and catalytic applications.

Keywords:
2D elasticityMXenesanisotropymultipolar modelsvacancy interactions

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Surface Science

Background:

  • Atomic-scale defects, such as vacancies, are inherent in two-dimensional (2D) MXene synthesis.
  • These defects influence the electronic, catalytic, and sensing properties of MXenes.
  • Understanding defect interactions and their spatial distribution is key to controlling material properties.

Purpose of the Study:

  • Investigate the interaction energy between vacancies in Ti$_{m+1}$C$_m$ MXenes.
  • Analyze the anisotropic dependence of these interactions on intervacancy separation.
  • Develop a model to describe the long-range interactions of vacancies in 2D materials.

Main Methods:

  • Employ molecular statics calculations utilizing bond-order interatomic potentials.
  • Extract strain-mediated interaction energies between vacancies.
  • Model vacancy interactions using multipole expansions (force dipoles and tripoles).

Main Results:

  • Observed attraction-repulsion oscillations at short vacancy separations.
  • Established a long-range interaction model for vacancies as superposed in-plane force tripoles and out-of-plane force dipoles.
  • Demonstrated that long-range interactions follow a combination of 1/r^2 and 1/r^4 power laws, distinct from elastic semi-infinite media.

Conclusions:

  • The derived two-multipole model accurately describes vacancy interactions in MXenes.
  • This model's principles may extend to other defects or adatoms on various 2D materials.
  • The identified attractive interaction between nearest-neighbor Ti vacancies explains their observed clustering in MXenes.