Peifeng Lia,
Qingliang Liao*a,
Zengze Wanga,
Pei Lina,
zheng zhanga,
Xiaoqin Yana and
Yue Zhang*ab
aState Key Laboratory for Advanced Metals and Materials, School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, People’s Republic of China. E-mail: liao@ustb.edu.cn
bKey Laboratory of New Energy Materials and Technologies, University of Science and Technology Beijing, Beijing 100083, People’s Republic of China. E-mail: yuezhang@ustb.edu.cn
First published on 26th March 2015
During the investigation of mechanical properties of nanomaterials by atomic force microscope (AFM), a non-normal stress state with large scanning angles is a universal phenomenon. The mechanical service behaviors of ZnO nanowires (NWs) with diameters ranging from 177 to 386 nm under non-normal stress state were studied by AFM at a scanning rate of 14.8 μm s−1. We expanded the application scope of the threshold force equation determining the fracture threshold forces of ZnO NWs which was established in our previous work. The criterion equation for security service of ZnO NWs was established by the threshold force equation and force calibration equation. The criterion equation was used to predict the security service range of ZnO NWs successfully. The modulus and fracture strength of the ZnO NWs were also calculated through the fracture threshold force obtained from the threshold force equation. The results have important and meaningful consequences for security practical applications of ZnO NWs under non-normal stress state.
Nanodevices based on piezoelectric and electromechanical properties need the drive of continuous, periodic external forces or loads, and the efficiencies are related to the size and rate of external forces.10,11 So the mechanical service behaviors of piezoelectric nanomaterials are important for the practical applications of the corresponding devices. However, most researchers focus on the physical performances of nanodevices at present,12–18 while few researchers focus on mechanical service behaviors of nanomaterials and nanodevices. Considering that the mechanical properties of nanomaterials allow potential applications of nanostructures in nanodevices, it is important and essential to investigate the mechanical service behaviors of nanomaterials before designing, manufacturing, and operating corresponding nanodevices. Some damage and breakdown phenomena of ZnO NWs or NBs under a mechanical field have been reported in previous work.19–30 Ni and Boland et al.19–21 studied the mechanical properties of ZnO NBs and NWs using an atomic force microscope (AFM) nanoindentation or bending method, but it could not supply sufficient forces for breaking down the ZnO NBs or NWs with larger diameters; this was only possible using an expensive diamond tip. Zhu, Xu, and Agrawal et al.23–27 researched the mechanical properties of ZnO NWs adopting scanning electron microscope (SEM) or transmission electron microscope (TEM) tensile and compressive methods, but the equipment is expensive and the methods are not easy to operate. Any tiny vibrations, external forces or loads would greatly affect the mechanical properties or service behaviors of nanomaterials, while it can be negligible to the macroscopic materials. Bai, Wang, and Zhang et al.28–30 studied the fatigue properties of ZnO NBs and NWs by in situ TEM electromechanical resonance, which showed excellent fatigue properties. Although it provided cyclical dynamic loads, the method is less effective for studying the mechanical service behaviors of nanomaterials. Although mechanical service behaviors of ZnO NWs have been investigated in recent years, the mechanical service behaviors of ZnO NWs under non-normal stress state studied by AFM are rarely reported. Actually, in most instances, ZnO NWs as the structural units damaged or fractured in nanodevices under non-normal stress state are a commonly encountered mode that determines the stability and lifetime of the nanodevices.
In this paper, the mechanical service behaviors of ZnO NWs under non-normal stress state were studied by AFM at a scanning rate of 14.8 μm s−1. The scope of the force calibration equation determining the actual forces applied on the ZnO NWs established in our previous work was expanded. The criterion for security service of ZnO NWs was established by the threshold force equation and force calibration equation to predict the mechanical service behaviors of ZnO NWs under non-normal stress state. The modulus and fracture strength of the ZnO NWs were also calculated through the fracture force obtained from the threshold force equation.
Then, the mechanical service behaviors of ZnO NWs were studied by AFM (Bruker, Multimode III) in the scanning process with large scanning angles (the angles between the ZnO NW length direction and AFM tip moving direction) at a rate of 14.8 μm s−1. The experimental procedures were carried out as follows. Firstly, ZnO NWs were ultrasonicated in ethanol, and dispersed on insulating silicon distributed with trench arrays. Secondly, ZnO NWs were double-fixed by Pt lines at both ends on the trenches through focused ion beam (FIB) deposition. Finally, AFM three-point bending was used for applying forces to measure the modulus and threshold forces of the fixed ZnO NWs.
No. | D (nm) | Ff (nN) | Fth (nN) | θ (°) | μ2 | μ2![]() ![]() |
β | Fth-l (nN) |
---|---|---|---|---|---|---|---|---|
1 | 177 | 812.5 | 2219.7 | 84 | 2.5 | 2.49 | 2.68 | 2177.42 |
2 | 187 | 1062.5 | 2386.9 | 50 | 2.68 | 2.05 | 2.28 | 2140.88 |
3 | 193 | 937.5 | 2487.22 | 64 | 2.54 | 2.28 | 2.49 | 2336.53 |
4 | 219 | 1312.5 | 2921.94 | 51 | 2.66 | 2.07 | 2.3 | 3014.03 |
5 | 223 | 1437.5 | 2988.82 | 41 | 2.98 | 1.96 | 2.2 | 2882.25 |
6 | 254 | 1562.5 | 3507.14 | 40 | 3.04 | 1.95 | 2.2 | 3429.84 |
7 | 296 | 1687.5 | 4209.38 | 68 | 2.53 | 2.35 | 2.55 | 4303.29 |
8 | 301 | 1937.5 | 4292.98 | 42 | 2.93 | 1.96 | 2.2 | 4264.24 |
9 | 348 | 2062.5 | 5078.82 | 76 | 2.51 | 2.44 | 2.63 | 5100.86 |
10 | 386 | 2187.5 | 5714.18 | 76 | 2.51 | 2.44 | 2.63 | 5759.03 |
11 | 318 | 1937.5 | 4577.22 | 76 | 2.51 | 2.44 | 2.63 | 5095.63 |
12 | 403 | — | 5998.42 | 4 | 27.88 | 1.94 | 2.18 | — |
According to the threshold force eqn (3) (Fth = 16.72d–739.74, range of application: 67 nm ≤ d ≤ 201 nm. This equation describes the relationship between fracture threshold forces of ZnO NWs and their diameters when the scanning angle is smaller than 3°, and in this situation the external forces leading to the fracture of ZnO NWs can be seen as the fracture threshold forces; when the scanning angle is larger than 3°, the actual forces applied on the ZnO NWs should be calibrated by a calibration coefficient β by multiplying the external forces. A detailed introduction can be found in our previous article ref. 32) of fracture threshold forces Fth and diameters of ZnO NWs established in our previous work,32 the fracture threshold forces Fth can be also obtained and shown with red points in Fig. 2g and h.
In order to verify the extendability of the scope of the threshold force equation, the calibrated fracture threshold forces Fth-l (Fth-l can be calculated from the force calibration equation Fth-l = βFf, when the scanning angle is larger than 3°.32 β = [1 + (μ2sin
θ)2]1/2: calibration coefficient, μ2: lateral resistance friction coefficient, θ: scanning angle, the values measured are shown in Table 1.) are also calculated and shown with purple points in Fig. 2h.
It can be seen that the two sets of fracture threshold force values (calculated by threshold force equation and force calibration equation, respectively) have good coincidence and present a good linearity with diameters of the ZnO NWs which indicates that the threshold force equation can be applied to a wider size range. The calculated threshold force values are also shown in Table 1.
βF = Fr−l < Fth = 16.72d − 739.74 | (1) |
βF = Fr−l ≥ Fth = 16.72d − 739.74 | (2) |
Eqn (1) is the security criterion equation, and eqn (2) is the damage or fracture criterion equation. If the actual force Fr−l applied on the ZnO NW is smaller than the fracture threshold force Fth, the ZnO NW can work safely; while the actual force Fr−l applied on the ZnO NW is larger than the fracture threshold force Fth, the ZnO NW would fracture.
Then, the criterion equation was used to predict the security of two ZnO NWs with diameters of 318 nm and 403 nm under some certain forces F that are shown in Fig. 3, and the calculated values are shown in Table 1 of no.11 and 12. The fracture threshold force Fth of the 318 nm ZnO NW calculated by threshold force equation was 4577.22 nN. The experimental applied force F leading the ZnO NW breakdown was 1937.5 nN, and it can provide the actual force Fr−l of 5095.63 nN (2.63 × 1937.5). So the experimental data are in accordance with the damage or fracture criterion eqn (2) (Fig. 3a–c). For the 403 nm ZnO NW, the largest applied force F the AFM tip can provide was 2687.5 nN, and the largest actual force Fr−l was 5858.75 nN (2.18 × 2687.5). However, the calculated fracture threshold force Fth led the ZnO NW fracture was 5998.42 nN (16.72 × 403–739.74). Since the calculated results meet the security criterion equation, the ZnO NW would not fracture under the applied force (Fig. 3d–f). The experimental results are consistent with the criterion equation which further certify the credibility of the criterion equation. The security zone is shaded light blue below the experimental data in Fig. 2h.
![]() | (3) |
![]() | (4) |
![]() | (5) |
Fig. 4a shows the Young’s modulus (the data also include a part obtained in ref. 32) of the ZnO NWs. It can be seen that the Young’s modulus of ZnO NWs exponentially decreased with an increase of diameter. It is surprising that the Young’s modulus values of ZnO NWs with larger diameters are far below the values in ref. 20, which indicates that the ZnO NWs with larger diameters have more defects.
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Fig. 4 Relationship between (a) Young’s modulus, (b) fracture strength of ZnO NWs and diameters obtained in the experiments. |
The fracture strength (the data also include a part obtained in ref. 32) of the ZnO NW can be calculated using the following equation:35
![]() | (6) |
![]() | (7) |
The fracture strength curve of the ZnO NW is shown in Fig. 4b. It can be seen that the fracture strength of ZnO NWs also exponentially decreased with an increase of diameter. The fracture strength values are approaching the values of ZnO NWs in ref. 17 and the values of bulk ZnO especially when the diameters exceed 200 nm.36 The calculated results indicate that the defects would greatly reduce the Young’s modulus of ZnO NWs, but have few effects on the fracture strength.
In practical applications, the nanomaterials building for the devices is inevitably influenced by external conditions, such as slight vibration and noise which are negligible for macroscopic devices, so the results obtained in the scanning process under non-normal stress state are more valuable for designing, fabricating, and operating electromechanical and piezoelectric nanodevices.
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