Investigation of Nanomechanical Properties of β-Si3N4 Thin Layers in

Letter pubs.acs.org/JPCL

Investigation of Nanomechanical Properties of β‑Si3N4 Thin Layers in a Prismatic Plane under Tension: A Molecular Dynamics Study Xuefeng Lu,* Peiqing La, Xin Guo, Yupeng Wei, Xueli Nan, and Ling He State Key Laboratory of Gansu Advanced Non-ferrous Metal Materials, Lanzhou University of Technology, Lanzhou 730050, China ABSTRACT: We report molecular dynamics simulations of the nanomechanical properties and fracture mechanisms of β-Si3N4 thin layers in a prismatic plane under uniaxial tension. It is found that the thin layers in the y loading direction display a linear stress−strain relationship at ε < 0.021, and afterward, the stress increases nonlinearly with the strain until fracture occurs. However, for the z direction, the linear response is located at ε < 0.051. The calculated fracture stresses and strains of the thin layers increase with strain rates both in both directions. The thin layers exhibit the higher Young’s modulus of 0.345 TPa in the z direction, higher than that in the y direction. The origins of crack derive from N2c‑1−Si and N6h‑1−Si bonds for the y and z loading directions, respectively.

SECTION: Physical Processes in Nanomaterials and Nanostructures

A

thin layers in the basal plane under uniaxial tension were studied. It was concluded that the thin layers first display a nonlinear stress−strain relationship at ε < 0.06 and then a linear response at 0.06 < ε < 0.09, and finally the stresses increase nonlinearly with the strains until fracture occurs.9 In this Letter, we will not only construct models of β-Si3N4 thin layers in a prismatic plane but also perform objective molecular dynamics simulations on the tension stress, strain, and failure mechanisms. We perform a theoretical tensile experiment on β-Si3N4 thin layers in a prismatic plane, illustrated in Figures 1 and 2. It can be see in Figure 1a that the primitive hexagonal unit cell contains two Si3N4 formula units (14 atoms as indicated by 6 brown atoms of Si and 8 purple atoms of N). The basic unit of the prismatic plane in Figure 1b consists of three brown atoms of Si and four purple atoms of N, as displayed in the black dashed frame in Figure 1c. The simulation bonding configuration of β-Si3N4 thin layers in the prismatic plane is demonstrated in Figure 2. The model is close to square with a thickness of 1.521 nm and side length of about 7.607 nm. Zigzag and armchair structures are oriented along the y and z directions, respectively. Figure 3a and b illustrates the calculated stress−strain data for the thin layers in the prismatic plane subjected to uniaxial tension in the y and z directions, respectively, at different strain rates. Pay attention that the strain is defined as the elongated percentage of the entire thin layer model in the loading direction. The fracture stress is determined as the peak stress, and the corresponding strain is the fracture strain. One can see from Figure 3 that the thin layers subjected to uniaxial tension

s the pace of scientific studies progresses to smaller and smaller length scales, predominant and fascinating mechanical properties of nanomaterials recently represented by nanomechanical experiments allow them to stand out from their bulk counterparts.1,2 Simultaneously, mechanical control of nanomaterials and nanosystems is emerging as a fascinating means for exploring the unique properties and potential applications of nanoscale materials.3,4 The insight and fabrication of stimuli-responsive materials are concerned predominantly because they provide a mechanism for designing nanoscale devices and for enhancing the performance of devices. Motivated by the subject, extensive research studies have been conducted to reveal the physical properties of nanosized β-Si3N4. However, there are two particularly challenging problems; experimentally obtaining the nanowire characteristics and mechanical responses is difficult and theoretically well constructed single-crystal β-Si3N4 models are lacking, and these challenges hamper the achievements of the appreciated structure−property relationship. Recently, considerable efforts have been paid to take into insight their microscopic properties using ab initio and molecular dynamics (MD) methods. Vashishta investigated dynamic fracture in nanophase Si3N4 using 106-atom molecular dynamics simulations and showed that intercluster regions are amorphous and that they deflect cracks and give rise to local crack branching.5 Ching reported a model of Y-doped intergranular glassy film in silicon nitride ceramics by large-scale ab initio modeling and concluded that this microstructure has a complex nonlinear deformation under stress and that Y doping significantly enhances the mechanical properties.6 In previous study, we constructed the models of β-Si3N4 nanowires and investigated the tension, compression, and bending behaviors.7,8 Then, the mechanical properties and failure mechanisms of the β-Si3N4 © XXXX American Chemical Society

Received: April 15, 2013 Accepted: May 17, 2013

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Figure 1. The bonding configuration of β-Si3N4: (a) the primitive hexagonal unit cell; (b)the basic unit of the prismatic plane; and (c) a thin layer in the prismatic plane. Si: brown atoms; N: purple atoms.

of 50%, shown in Table 1, are parallel to the y direction. However, only a small number of bonds for the N6h‑1−Si ones (4), with a percentage of 16.67%, are parallel to the z direction. As the tensile load is employed in the y direction, those bonds parallel to the loading direction will suffer stress and deformation helpful for bond lengthening, which causes the bond elongation and fracture. In contrast to the y direction, when the tensile load acts on the z direction, only a few bonds locate at the loading direction; therefore, it has not such a significant effect on the bond elongation. This difference in the bond configuration distribution leads to anisotropic fracture properties. The Young’s moduli of the thin layers can be calculated from the stress−strain data in Figure 3 by employing Hooke’ law σ = Eε for the y direction at ε < 0.021 and for the z direction at ε < 0.051, where the structures are fully in accordance with the linear deformation and the law is appropriate for the determination of the Young’s modulus, which are shown in Table 1. Similar to the trend of fracture stresses, the thin layers exhibit the higher Young’s modulus of 0.345 TPa in the z direction, higher than that in the y direction. The results are in agreement with the theoretical values10,11 and experimental results.12,13 For experimental results reported by the nanoindentation technique, a strong anisotropy is observed owing to a coarse-grained polycrystalline sample, composed of whiskers up to 15 μm in diameter and 100 μm in length, that is employed. For the conventional methods reported by Lee, the c-axes lie in the hot-pressing plane, and there is a random

Figure 2. The simulation bonding configuration of β-Si3N4 thin layers in prismatic plane. Si: light gray atoms; N: blue atoms.

in the y direction display a linear stress−strain relationship at ε < 0.021, and afterward, the stress increases nonlinearly with the strain until fracture occurs. However, for the z direction, the linear response is located at ε < 0.051, which is probably due to the differences of the configuration change and internal defects in the course of loading at the end of the elastic phase. The calculated fracture stresses and strains of the thin layers increase with strain rates both in the y (zigzag) and z (armchair) directions. It can be seen from Table 1 that the fracture stresses and strains of the thin layers in the z direction are higher than those in the y direction. The direction-dependent properties can be explained as follows. Figure 2 indicates that some bonds, including N6h‑2−Si ones (1) and N2c‑1−Si ones (2 and 3), although being not in the same plane, which have a percentage

Figure 3. Stress−strain curves of β-Si3N4 thin layers in a prismatic plane with different strain rates under tensile loading in the (a) y (zigzag) and (b) z (armchair) directions. 1879

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Table 1. Fracture Stresses, Strain, and Young’s Moduli of the β-Si3N4 thin layers stress (GPa)

percentage of bonding parallel to the loading direction (%)

strain

Young’s modulus (TPa)

strain rates

y

z

y

z

y(1, 2, 3)

z(4)

the rest(5, 6)

y

z

× × × ×

8.69 8.78 8.92 9.06

18.21 18.44 18.67 18.95

0.044 0.045 0.046 0.046

0.062 0.063 0.064 0.065

50 50 50 50

16.67 16.67 16.67 16.67

33.33 33.33 33.33 33.33

0.333 0.333 0.333 0.333

0.345 0.345 0.345 0.345

1.3 2.6 3.9 4.2

109 109 109 109

Figure 4. The β-Si3N4 thin layers with a strain rate of 5.2 × 109 s−1 under tensile loading. (a) Snapshot at a strain of 0.001 in the y direction; the atoms are colored by their coordination numbers; (b,c) morphologies at stains of 0.041 and 0.047 before and after fracture for y direction loading; the colors of the atoms follow the calculated values of the potential energy, with the same below; (d,e) configurations at strains of 0.001 and 0.053 in the z direction; (f) fractured morphology at a fracture strain of 0.066 for the z direction loading.

fracture strain. In contrast, in terms of the z loading direction, N6h‑1−Si bonds in a puckered plane are more susceptible to external force and thus responsible for the initial fracture, as shown in Figure 4e. Thus, N2c‑1−Si and N6h‑1−Si bonds weaken the fracture properties under tension and break first in the y and z loading directions, respectively, and become the origins of the cracks, as illustrated in Figure 4. Then, the cracks extend to all directions upon further loading, resulting in the thin layers to destroy finally. In conclusion, we report the results of the nanomechanical properties and fracture mechanisms of β-Si3N4 thin layers in a prismatic plane under uniaxial tension using molecular dynamics simulations. It is found that the thin layers in the y loading direction display a linear stress−strain relationship at ε < 0.021, and afterward, the stress increases nonlinearly with the strain until fracture occurs. However, for the z direction, the linear response is located at ε < 0.051, which is probably due to the differences of configuration change and internal defects in the course of loading at the end of the elastic phase. The fracture stresses and strains increase with strain rates in both directions. The origins of cracks derive from N2c‑1−Si and N6h‑1−Si bonds for the y and z loading directions, respectively. The present work brings insights for better understanding of the nanomechanical properties and failure mechanisms of the β-Si3N4 thin layers.

orientation of the whiskers. Therefore, the small difference in Young’s moduli can be obtained by averaging over all orientations in the plane, which is related to the single-crystal elastic constants with low anisotropies. With regards to the thin layers researched here, the Young’s moduli in the y and z directions are quite close, demonstrating the Young’s modulus’s low anisotropy. After having studied the stress changes of β-Si3N4 thin layers in a prismatic plane under tension, we now go inside of the nanospace and investigate its internal structural evolution, as well as potential energy distributions. With the purpose of exploring the fracture mechanism and giving readers clearer pictures, in Figure 4, we present snapshots of the thin layers with a strain rate of 5.2 × 109 s−1 in the y and z directions. When the thin layers are subjected to the z-axial direction tension, the thin layers in the loading external force direction show higher fracture stresses than that in the y direction, as indicated by the corresponding potential energy distribution in Figure 4b and e. For the y loading direction, because N2c‑1−Si bonds are in a puckered planar geometry and easily withstand external force compared to N6h−Si bonds in the course of tension, the fracture of N2c‑1−Si bonds occurs first in the external force direction upon further deformation. This can be verified from the corresponding fractured morphology in Figure 4b. The partial magnification view evidently demonstrates that the initial bond fractures occur in the N2c‑1−Si bonds (as indicated by two red dotted lines) of the thin layers close to the 1880

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Letter

Mechanical Properties for α- and β-Si3N4. J. Chem. Phys. 1992, 97, 5048−5062. (11) Ching, W. Y.; Xu, Y. N.; Julian, D. G.; Manfred, R. Ab-Initio Total Energy Calculation of α- and β-Silicon Nitride and the Derivation of Effective Pair Potentials with Application to Lattice Dynamics. J. Am. Ceram. Soc. 1998, 81, 3189−3196. (12) Jack, C. H.; Ellen, Y. S.; George, M. P.; Paul, F. B.; Kathleen, B. A. Elastic Anisotropy of β-Silicon Nitride Whiskers. J. Am. Ceram. Soc. 1998, 81, 2661−2669. (13) Farnjeng, L.; Keith, J. B. Texture and Anisotropy in Silicon Nitride. J. Am. Ceram. Soc. 1992, 75, 1748−1755. (14) Li, J. Atomeye: An Efficient Atomistic Configuration Viewer. Modell. Simul. Mater. Sci. Eng. 2003, 11, 173−178. (15) Tersoff, J. Empirical Interatomic Potential for Silicon with Improved Elastic Properties. Phys. Rev. B 1988, 38, 9902−9905. (16) Tersoff, J. Modeling Solid-State Chemistry: Interatomic Potential for Multicomponent Systems. Phys. Rev. B 1989, 39, 5566−5568. (17) Vikas, T.; Gan, M. Temperature Dependent Nanomechanics of Si−C−N Nanocomposites with an Account of Particle Clustering and Grain Boundaries. Int. J. Hydrogen Energy 2011, 36, 4605−4616. (18) Katsuyuki, M.; Yuji, I. Molecular Dynamics Study of Atomic Structure and Diffusion Behavior in Amorphous Silicon Nitride Containing Boron. J. Am. Ceram. Soc. 2001, 84, 2213−2219.

COMPUTATIONAL METHODS Molecular dynamics simulations are performed employing the LAMMPS program package. The visualization program Atomeye is employed for the MD simulation.14 In view of empirical potential models available for covalent systems, the interatomic potential used in the calculation is the effective one proposed by Tersoff,15,16 which has been successfully used to study the mechanical properties of carbide and nitrides.17,18 Prior to loading, the primitive thin layers model, containing 7280 atoms, is fully relaxed to an equilibrium minimum energy in terms of the steepest descent algorithm in order to obtain a stable configuration and then thermally equilibrated to 300 K for 200 ps using a Nosé−Hoover thermostat ensemble with a time step of 0.5 fs. Uniaxial tensile tests are performed along the y and z directions accompanying periodic boundary conditions to remove the edge influences. Similar elongation steps are repeated until the thin layers are fully fractured and wellseparated.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: 86-0931-2973563. Fax: 86-0931-2973561. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work was supported by The National Natural Science Foundation of China (51164022), The Natural Science Foundation of Gansu Province-B class (2011GS04157), Gansu Provincial Department of Construction Project (1201ZTC042), and The Natural Science Foundation of Gansu Province (1014RJZA027).

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REFERENCES

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dx.doi.org/10.1021/jz4007977 | J. Phys. Chem. Lett. 2013, 4, 1878−1881