Stability and Strength of Atomically Thin Borophene from First Principles Calculations (1608.05877v1)

Abstract: A new two-dimensional (2D) material, borophene (2D boron sheet), has been grown successfully recently on single crystal Ag substrates by two parallel experiments [Mannix \textit{et al., Science}, 2015, \textbf{350}, 1513] [Feng \textit{et al., Nature Chemistry}, 2016, \textbf{advance online publication}]. Three main structures have been proposed ($\beta_{12}$, $\chi_3$ and striped borophene). However, the stability of three structures is still in debate. Using first principles calculations, we examine the dynamical, thermodynamical and mechanical stability of $\beta_{12}$, $\chi_3$ and striped borophene. Free-standing $\beta_{12}$ and $\chi_3$ borophene is dynamically, thermodynamically, and mechanically stable, while striped borophene is dynamically and thermodynamically unstable due to high stiffness along $a$ direction. The origin of high stiffness and high instability in striped borophene along $a$ direction can both be attributed to strong directional bonding. This work provides a benchmark for examining the relative stability of different structures of borophene.

Stability and Strength of Atomically Thin Borophene: A First Principles Analysis

Atomically thin borophene, a novel two-dimensional (2D) boron sheet material, has been the subject of extensive research following its successful synthesis on single crystal Ag(111) substrates. This paper presents a thorough analysis of the stability and mechanical properties of three prominent borophene structures — namely, $\beta_{12}$, $\chi_3$, and striped borophene — using first principles calculations. The findings highlight the distinct differences in the stability and mechanical attributes of these structures, as well as their potential implications for various applications in electronics and materials science.

Characterization of Borophene Structures

The paper initiates with an examination of the geometric and electronic structures of the borophene variants. Both $\beta_{12}$ and $\chi_3$ borophene are depicted as planar configurations with periodic voids, offering insights into their inherent structural properties. In contrast, striped borophene exhibits a buckled pattern with anisotropic corrugation, primarily due to the absence of vacancies in its structure. The differences in structure inform both the physical behavior and stability of each borophene type.

Stability Analysis

A multidimensional approach is applied to assess the stability of the borophene structures, encompassing dynamical, thermodynamical, and mechanical aspects. The $\beta_{12}$ and $\chi_3$ borophene structures are confirmed to be dynamically, thermodynamically, and mechanically stable. Interestingly, the striped borophene structure reveals dynamical instability, particularly phonon instability along the $\Gamma$-X direction. The high stiffness characteristic of striped borophene, while advantageous for mechanical robustness, contributes to its thermodynamically unstable nature by elevating the Helmholtz free energy due to increased vibrational frequencies.

Mechanical Properties and Bonding Characteristics

The investigation of mechanical properties through elastic constants and 2D Young's modulus uncovers significant insights about the structural rigidity of borophene. Striped borophene demonstrates notable stiffness along the $a$ direction, rivaling that of graphene, but simultaneously showcases negative Poisson's ratios indicative of its unique structural dynamics. The paper correlates these mechanical characteristics with the bonding features revealed by electron localization functions and projected density of states analysis. It is the enhanced directional bonding in striped borophene that accounts for both its strength and instability under tension.

Implications and Future Directions

The potential applications of borophene, particularly in fields requiring high-strength materials, are influenced by its mechanical properties and stability. The demonstrated stability of $\beta_{12}$ and $\chi_3$ variants suggests their suitability for experimental realization and integration into electronic devices. Conversely, the instability of striped borophene warrants further exploration, as modifications in its electronic and structural properties might extend its applicability.

Future research directions include exploring the electronic characteristics and optimizing the synthesis conditions to enhance the stability of striped borophene. The interplay between vacancy distributions and borophene stability presents an intriguing avenue for paper, potentially unlocking greater structural control and material properties tailored for specific applications.

In summary, this paper provides a comprehensive foundation for understanding the diverse properties and stability challenges of borophene, contributing significantly to the theoretical groundwork required for advancing its practical applications in next-generation materials science.