This journal is c the Owner Societies 2013 Phys. Chem. Chem. Phys., 2013, 15, 6175--6178 6175

Cite this: Phys. Chem.Chem.Phys.,2013,15, 6175

Investigation of the nanomechanical propertiesof b-Si3N4 nanowires under three-point bendingvia molecular dynamics simulation

Xuefeng Lu,a Hongjie Wang,*a Meng Chen,a Lei Fan,a Chao Wanga and Shuhai Jiab

The nanowire with an aspect ratio of 3 : 1 possesses a higher

bending stress of 15.85 GPa. It can be observed that the initial

Si–Si bond and N atom defects with a coordination number of 2,

subsequently evolving to 0 and 1, with Si evolving from 5 to 6

and 7, are mainly responsible for the final fracture.

The unique and fascinating mechanical properties of nanowiresand nanopillars, exhibited by conducting nanomechanicalexperiments, are making them stand out from their bulkcounterparts,1–4 which has recently stimulated a great deal ofresearch focused on the fabrication and mechanical propertiesof b-Si3N4 nanowires in many experimental and theoreticalinvestigations.5–7 Simultaneously, the mechanical control ofnanomaterials and nanosystems is emerging as a fascinatingmeans for exploring the unique properties and potential appli-cations of nanoscale materials.8–10 However, two particularlychallenging problems have deprived progress from being madeexperimentally. Obtaining the nanowires’ characteristics andmechanical responses is difficult due to the limits of theexperimental technique, and theoretically, the absence of awell constructed single crystal b-Si3N4 model by moleculardynamics (MD) simulation hinders the achievements of theappreciated structure–property relationship. Recently, consid-erable efforts have been devoted to exploring the mechanicalproperties of nanoscale silicon nitride by simulation,11,12 forinstance, Ching13 reported a theoretical tensile experiment on anew intergranular glassy film model with prismatic planesusing an ab initio method and concluded that the pre-peakresponse is nonlinear and the failure considerably abrupt.Shigenobu14 investigated the shear deformation properties ofb-Si3N4 single crystals using the classical MD method and theresults showed that shear deformation does not occur in any ofthe experimentally predicted slip systems. In previous work,

using MD simulation, we constructed models of b-Si3N4 nano-wires and thin layers in a basal plane, and then investigatedtheir mechanical responses.15,16 Despite experiments exploringthe mechanical properties of b-Si3N4 nanowires subjected touniaxial stress and shear deformation being conducted, resultsof their bending behavior are lacking. To study the mechanicalproperties of b-Si3N4 nanowires systematically, we performedobjective molecular dynamics simulations on the bendingresponses and failure mechanisms.

In this letter, we report the results of three-point bendingtests on b-Si3N4 [001] oriented nanowires using MD simulationsand demonstrate the mechanical response process. The repre-sentative structure of the internal model is displayed in Fig. 1.

b-Si3N4, classified as hexagonal, contains two formula unitsand can be built as a stacking of the idealized Si–N layer in anABAB sequence. Si atoms bonded with four N atoms are atthe center of a slightly irregular tetrahedron. The simulatednanowires consist of perfect b-Si3N4 crystals aligned along the[001] direction, which has periodic boundary conditions. Theother two directions, perpendicular to the nanowires’ axis, havefree boundary conditions. All of the nanowire models areapproaching cuboids with a cross section of 9.26 nm2 andlengths of 9.02, 15.14 and 21.25 nm, respectively. The softwarepackage LAMMPS17 and visualization program Atomeye18 areemployed. From the empirical potential models available forcovalent systems, the interatomic potential employed herein all simulations is the effective potential proposed byTersoff,19,20 which has been parameterized and used success-fully to investigate the mechanical properties of carbides andnitrides.21,22 Prior to loading, the nanowires are fully relaxed toan equilibrium minimum energy using the steepest descentalgorithm in order to obtain stable configurations, and thenthermally equilibrated to 300 Kfor 150 ps using a Nose–Hooverthermostat ensemble with a time step of 0.5 fs. A bending loadis applied to the middle of the nanowires along the y directionwith a loading velocity of 0.02 nm ps�1. The radius of thesimulated indenter is 1.5 nm. Both ends, with a length ofabout 2 nm in the nanowires, are fixed along the y direction.

a State Key Laboratory for Mechanical Behavior of Materials, School of Materials

Science and Engineering, Xi’an Jiaotong University, Xi’an, 710049, China.

E-mail: hjwang@mail.xjtu.edu.cn; Fax: +86 029-82667981; Tel: +86 029-82667942b School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

Received 26th January 2013,Accepted 26th February 2013

DOI: 10.1039/c3cp50372k

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After each loading step, the simulated nanowires were relaxedfor 100 time steps to reach a steady state, and the set conditionsensured a constant bending moment in the middle part of thenanowires. The simulated loading steps were repeated until thenanowires were fully ruptured and well separated.

We plot in Fig. 2 the displacement evolution of stress for theb-Si3N4 nanowires subjected to bending. It can be observed thattheir stress increases with displacement lengthening afterthe indenter contacts the nanowires in the bending regions,and suddenly decreases when fracturing of the nanowires isinitiated, as the dotted lines point to. Two regions that arequasi-elastic and nonlinear were identified for the three curves.The boundary of the two regimes is located at the momentwhen the initial fracture of the nanowires takes place, atdisplacements of 4.10, 4.29, and 4.34 nm. The nanowire withan aspect ratio of 3 : 1 possesses the highest bending stress of15.85 GPa and a slope regime much larger than the other two.The other nanowires have aspect ratios of 5 : 1 and 7 : 1,respectively. Beyond the peaks in each of the three curves, thestress drops rapidly, but not to zero as would be expected fromthe fracture mechanics of brittle materials. Even at displace-ments of 4.20, 4.72, and 5.12 nm, respectively, where thenanowire models are fully fractured, there still remains sizablestresses of roughly 1/3–1/2 of the maximum values. It is alsoobserved that the stress at displacements greater than 4.31,4.82, and 5.31 nm actually increase slightly when the nanowires

are already broken. This is most likely due to the extremely slowconvergence in the relaxation process, which requires far moresteps when the vacuum region is created after the fractureof nanowires.

After having studied the stress changes of nanowires underbending, we now go inside the nano-space and investigate itsinternal structural evolution, as well as local configuration.With the purpose of exploring the fracture mechanism andgiving readers clearer pictures, in Fig. 3 we present snapshots ofthe three-point bending process of a nanowire with an aspectratio of 7 : 1. Since the rupture occurred mainly in the inter-mediate section of the nanowire, the region of breaking wasmagnified for observing the mechanical responses and localbonding patterns. Simultaneously, defective atoms wereidentified and displayed in terms of coordination numbers.We chose fourteen representative points in the stress curve, asindicated in Fig. 2. Points 1–6 are classified as the bendingstage, where the nanowire displays a quasi-linear stress–displacement relationship before the initial fracture. The initia-tion of the fracture takes place in point 6, followed by thefracture failure process in points 7–14. Snapshots on the left ofFig. 3 show that the nanowire, subjected to indentation,gradually bends as displacement increases. The initial fracturehappens at two end portions displayed in the red square. In theintermediate position, at a displacement of 4.34 nm, whichaccompanies the depth of the indenter, a fracture located in thecentral portion of the lower surface occurs and spreads, causingthe nanowire to finally rupture. From the corresponding defectsnapshots, as shown on the right in Fig. 3, located in themiddle part of the upper surface, one can see the initial Si–Sibond defects and the N atom defects with the coordinationnumber of 2 at a displacement of 3.64 nm. The number ofdefects increases progressively with time, reaching a number ofabout a dozen at 4.34 nm along the direction of the indenta-tion, where the initial fracture occurs. With the evolution of theinternal defects configuration, it is worth noting that in thecentral part of the lower surface, except for the above defects,N and Si atoms defect with the coordination numbers of 0 and1 and 6 and 7, respectively. The total number of all of the defectscomes to several dozen at a displacement of 5.74 nm, which ismainly responsible for the final fracture of the nanowire.

To understand the influences of loading velocity on themechanical response relative to the displacement investigatedhere, the simulation was carried out at different indentationvelocities (0.03, 0.04, 0.05 and 0.06 nm ps�1) for the nanowire

Fig. 1 The internal model of the simulated b-Si3N4 nanowire. (a) Network of bonds; (b) network of atoms; (c) network of bonds and atoms. Si: gray atoms;N: blue atoms.

Fig. 2 The displacement evolution of stress for the simulated b-Si3N4 nanowireswith different aspect ratios at a load velocity of 0.02 nm ps�1.

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with an aspect ratio of 7 : 1. How the stress changes withdisplacements with different velocities, as well as defect

configurations located in the middle part of the nanowire, areillustrated in Fig. 4 as the peak positions of the stress curves.

Fig. 3 Snapshots of the simulated b-Si3N4 [001] oriented nanowire with an aspect ratio of 7 : 1 at a load velocity of 0.02 nm ps�1 during the three-point bending process atseveral displacements: (1) 3.64, (2) 3.76, (3) 3.90, (4) 4.04, (5) 4.20, (6) 4.34, (7) 4.52, (8) 4.72, (9) 4.86, (10) 4.92, (11) 4.98, (12) 5.08, (13) 5.30, and (14) 5.74 nm. The color ofthe atoms in the fourteen pictures on the left is in accordance with calculated potential energy values, while the atoms on the right, only displayed in terms of defectiveatoms located in the intermediate section of the nanowire, are colored by their coordination numbers, which are 0, 1, 2, 5, 6 and 7 for the six atoms in the upper right corner.

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We can see that the bending stress is interrelated tothe indentation velocity. When the velocity is 0.03 nm ps�1,the maximum bending stress is about 12.7 GPa, while when thevelocity is 0.06 nm ps�1 it increases to 13.7 GPa. Simulta-neously, the position of the appearance of the maximumbending stress shifts to the left, which is caused by theindentation velocity, similar to that reported by Fang.23 Corres-ponding peak defect snapshots show that the number of Si–Sibond defects decreases from 14 to 10 as the velocity increases to0.06 nm ps�1. This is possibly related to the appearance of animpact deformation tendency caused by a higher indentationvelocity, resulting in the differences in defect bonding struc-tures in the four cases. The study performed here opens awindow into the detail of nanowires under three-points ofbending on the molecular level and provides a deep insightinto the understanding of the mechanical responses of perfectb-Si3N4 crystals.

In conclusion, we have investigated the bending propertiesand failure mechanisms of b-Si3N4 nanowires with differentaspect ratios under three-point bending via a moleculardynamics simulation. The bending stresses increase withdisplacement lengthening after the indenter contacts the nano-wires, i.e. in the bending regions, and suddenly decrease whenthe initial fracture of the nanowires is initiated. Two regionsthat are quasi-elastic and nonlinear were identified forthe three curves. The nanowire with an aspect ratio of 3 : 1possesses the highest bending stress of 15.85 GPa and a sloperegime much larger than the other two. The other nanowireshave aspect ratios of 5 : 1 and 7 : 1. The initial Si–Si bond defectsand N atom defects with the coordination number of 2, locatedin the middle part of the upper surface, can be observed at adisplacement of 3.64 nm. With the evolution of the internaldefects configuration, in the central part of the lower surface,except for the above defects, Si and N atoms defects with thecoordination numbers of 0 and 1 and 6 and 7, respectively, canalso be observed. The total number of all of the defects comes

to several dozen at a displacement of 5.74 nm, which is mainlyresponsible for the final fracture of the nanowire.

Acknowledgements

The work was supported by The National Natural ScienceFoundation of China (51272206, U1233116).

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Fig. 4 Displacement evolution of stress for simulated b-Si3N4 nanowires with anaspect ratio of 7 : 1 at different indentation velocities.

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