# Effective Mechanical Properties and Thickness Determination of Boron Nitride Nanosheets Using Molecular Dynamics Simulation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Computational Model

## 3. Results and Discussion

#### 3.1. Validation of the Simulation Model

^{2}which is comparable with the ab initio prediction of 271 J/m

^{2}[35] and MD prediction of 267 J/m

^{2}[29]. Hence, the above confirmation study validates the accuracy of the simulation model adopted in the study.

#### 3.2. Effect of Geometry and Tensile Loading Direction

#### 3.3. Effect of the Concentration and Position of Vacancy Defect

#### 3.4. Effect of Temperature and Vacancy Defects

## 4. Determination of Thickness and the Young’s Modulus of BNNS

_{a}is the strain energy of the BNNS structure under axial loading, A is the surface area of the BNNS, a

_{j}(j = 0,1,2,3,…) is the coefficient of the fitted polynomial of W

_{a}in terms of strain, and ε derived from the strain energy-strain plot.

_{b}is the energy of the BNNS structure during bending process to form a BNNT, b

_{j}(j = 0,1,2,3,…) is the coefficient of the fitted polynomial of W

_{b}in terms of curvature, and κ is derived from the energy-curvature plot.

^{2}and 1.785 eV, respectively. These values are in good agreement with the K and D values computed from various numerical approaches, as illustrated in Table 1. From Figure 7, the correct thickness of BNNS is determined by the intersection of the K and D curves, while also satisfying the Vodenitcharova-Zhang necessary criterion [40]. Hence, the correct effective thickness of BNNS is h ≈ 0.106 nm and the Young’s modulus ≈ 2.75 TPa.

- (1)
- (2)
- For a thickness of 3.4 Å, the Young’s modulus of the BNNS reported by computational studies is lower than that of graphene, and should be valid regardless of any thickness considered. As the computed modulus of BNNS (2.75 TPa) is lower than the correct modulus of graphene, which is reported to be 3.4–3.5 TPa [41,55], the above findings can be validated.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Simulation of BNNS under tensile loading. The atoms enclosed inside the black rectangle at either ends of BNNS is subjected to tensile loading. The loading direction is indicated by the arrows. Atoms depicted in ochre are boron and atoms depicted in blue are nitrogen.

**Figure 4.**Tensile loading stages of single-layer BNNS at 300 K at (

**a**) ɛ = 0.0; (

**b**) ɛ = 0.12; and (

**c**) ɛ = 0.25.

**Figure 5.**Tensile loading characteristics of single layer BNNS with vacancy defects along the axial and transverse directions at 300 K.

**Figure 8.**Determination of the correct thickness and Young’s modulus of BNNS from the intersection of axial stiffness and bending stiffness curves on the E-h coordinate plane.

Experimental Method | Young’s Modulus (TPa) |
---|---|

Nanoindentation measurement of few layer BNNS exfoliated from single crystal BN [1]. | 0.865 ± 0.073 |

IXS of BNNS crystal synthesized from Ba-B-N catalyst system under high temperature and pressure [11]. | 0.811 |

Nanoindentation measurement on defective BNNS synthesized by CVD from bulk BN crystal [12]. | 0.334 ± 0.024 |

AFM measurement on high quality BNNS synthesized from borazine precursor using CVD process [13]. | 1.16 ± 0.1 |

Thermal assisted vibration of cantilevered BNNT observed using TEM [14]. | 1.22 ± 0.24 |

Electric-field-induced technique to apply sinusoidal signal which induces vibration in BNNT [15]. | 0.505–1.031 |

Technique | Temperature (K) | Young’s Modulus (TPa) | Axial Stiffness (TPa nm) | Bending Stiffness (eV) |
---|---|---|---|---|

Tersoff potential [16] | 300 | 0.930 | NA | NA |

Tersoff potential [17] | NA | 0.730–0.890 | 0.248–0.292 | NA |

Tersoff potential [18] | 0–2000 | 0.398–0.720 | NA | NA |

DFT calculation [19] | NA | NA | 0.293–0.311 | NA |

Mechanics model [20] | 0 | NA | 0.332 | NA |

Tersoff potential [21] | 300 | 0.800–0.850 | 0.264–0.280 | NA |

DFT calculation [22] | NA | 0.760–1.055 | NA | 0.95 |

DFT-QHA model [23] | 0–1000 | NA | 0.278–0.283 | NA |

T-B potential [24] | 300 | 0.881 | NA | NA |

Continuum model [25] | NA | 0.900–1.000 | NA | NA |

Tight binding [26] | NA | NA | 0.284–0.310 | NA |

MM-DFT model [27] | NA | 0.83 | 0.282 | 1.74 |

DFT calculation [28] | NA | 0.700–0.830 | NA | NA |

Tersoff potential [29] | 0 | NA | 0.267 | NA |

Tersoff-like model [30] | 300 | NA | NA | 1.5–1.7 |

Atomistic-FEM [31] | NA | NA | 0.240–0.315 | NA |

DMH technique [32] | NA | NA | 0.267 | NA |

Tersoff potential [33] | NA | 0.295–0.695 | NA | 0.22–0.56 |

MM model [34] | NA | NA | 0.260–0.269 | NA |

Ab initio [35] | NA | NA | 0.271 | 1.29 |

DFT calculation [36] | NA | NA | 0.279 | NA |

Modified T-B [37] | NA | 0.982–1.113 | NA | NA |

Tersoff potential [38] | 300 | 0.716 | NA | NA |

Tersoff potential [39] | 0 | 0.749–0.770 | 0.248–0.258 | NA |

Factors | Tensile Strength of BNNS |
---|---|

Temperature | Decreases |

Defect concentration | Decreases |

Geometry | Unknown |

Defect position | Unknown |

Defects and Temperature | Unknown |

Loading direction | Superior in zigzag direction |

Aspect Ratio (L/W) | BNNS Dimensions (L × W) | Total Number of Atoms |
---|---|---|

1.0 | 62.38 Å × 60.27 Å | 1408 |

2.0 | 89.11 Å × 42.63 Å | 1420 |

3.0 | 104.39 Å × 33.81 Å | 1328 |

4.0 | 120.94 Å × 29.40 Å | 1344 |

Aspect Ratio (L/W) | BNNS Dimensions (L × W) | Total Number of Atoms |
---|---|---|

1.0 | 62.48 Å × 61.11 Å | 1450 |

2.0 | 86.73 Å × 43.28 Å | 1400 |

3.0 | 104.37 Å × 33.10 Å | 1344 |

4.0 | 119.81 Å × 30.55 Å | 1374 |

**Table 6.**Percentage reduction of the maximum tensile force of BNNS with defects when temperature is increased from 300 to 900 K.

Number of Defects | Reduction of Maximum Tensile Force (%) |
---|---|

0 | 14.25 |

2 | 13.83 |

4 | 11.97 |

6 | 10.16 |

Armchair BNNS | Zigzag BNNS | ||
---|---|---|---|

Aspect Ratio | Mechanical Strength (GPa) | Aspect Ratio | Mechanical Strength (GPa) |

1.0 | 254.31 | 1.0 | 302.75 |

2.0 | 266.82 | 2.0 | 318.51 |

3.0 | 259.33 | 3.0 | 317.70 |

4.0 | 266.21 | 4.0 | 306.67 |

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**MDPI and ACS Style**

Vijayaraghavan, V.; Zhang, L.
Effective Mechanical Properties and Thickness Determination of Boron Nitride Nanosheets Using Molecular Dynamics Simulation. *Nanomaterials* **2018**, *8*, 546.
https://doi.org/10.3390/nano8070546

**AMA Style**

Vijayaraghavan V, Zhang L.
Effective Mechanical Properties and Thickness Determination of Boron Nitride Nanosheets Using Molecular Dynamics Simulation. *Nanomaterials*. 2018; 8(7):546.
https://doi.org/10.3390/nano8070546

**Chicago/Turabian Style**

Vijayaraghavan, Venkatesh, and Liangchi Zhang.
2018. "Effective Mechanical Properties and Thickness Determination of Boron Nitride Nanosheets Using Molecular Dynamics Simulation" *Nanomaterials* 8, no. 7: 546.
https://doi.org/10.3390/nano8070546