Mechanical properties and deformation mechanism of Al₂O₃ determined from in situ transmission electron microscopy compression

Figures 1(a)–(f) presents TEM images of Al₂O₃ pillar of radius of 75 nm under a dynamic compression and for an unloading process. The initial contact process between the nanopillar and diamond punch is shown in figure 1(a). Figure 1(b) displays the internal local elastic deformation of concentrated wave propagation along the longitudinal direction of pillar top at the compressive distance of 100 nm. It is important to note that these elastic deformations propagate along the pillared microstructure. As it is evident from figure 1(b) the sliding phenomenon of the pillared microstructure on the carbon needle due to a small contact area between pillar and carbon needle was realized. For example, when attached to 100 nm the amount of the nanopillar slip is 200 nm, as denoted in figure 1(b) by b'. Figure 1(c) shows the TEM image of the nanopillar at a maximum compressive displacement of 180 nm, while figure 1(d) presents the compressed pillar at the beginning of the unloading process at displacement of 170 nm. It is important to note that the Al₂O₃ pillar was allowed to relax its deformation. Figure 1(e) show the TEM image taken at the unloading displacement of 100 nm. As can be seen from figure 1(e), at the displacement of 100 nm the elastic recovery and stabilizing structure phenomena of the pillar was realized. The TEM image of pillar after a compressive loading is given in figure 1(f). We must emphasis here that the tested material exhibited almost no inner local plastic deformation at the compressive loads smaller than 300 µN.

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Figure 2 presents the TEM images of Al₂O₃ nanopillar of radius of 175 nm under a dynamic compression and for an unloading process. Figure 2(a) again shows the initial contact process between the pillar and diamond punch, whereas figure 2(b) displays the internal local elastic deformation of concentrated wave slowly propagating along the longitudinal direction of the pillar top at the compressive distance of 150 nm. The TEM image of pillar at a maximum compressive displacement of 180 nm given in figure 2(c) confirmed an existence of a sliding phenomenon of the nanopillar on carbon needle. Compressed pillar at beginning of the unloading process at displacement of 179 nm is shown in figure 2(d). Figure 2(e) presents TEM image taken at the unloading displacements of 28 nm. As visible from figure 2(e), during an unloading process the nanopillar was relaxed but due to a presence of the resulting internal stresses the small slip of 52 nm denoted by e' in figure 2(e) was observed.

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Figure 3 presents the normal force–displacement curve of Al₂O₃ pillars with radiuses of 75 and 175 nm under loading and unloading process during a dynamic compression. The maximum force occurs at load of 122.2 (160.6) µN for Al₂O₃ pillar with radius of 75 (175) nm, as denoted in figure 3 by a circle. Then after the maximum compressive load has been reached, the pillar was relaxed and retracted during the unloading process. The force–displacement curve reveals that the elastic deformation dominates the unloading process. We have found that the elastic energy increases with an increase of the nanopillar radius. For instance, the elastic energy of 75 nm and 175 nm thick Al₂O₃ nanopillars calculated based on the basis of cover area below the unloading curve are approximately 85.98  ×  10⁻¹² J and 102.89  ×  10⁻¹² J, respectively. Similarly, the strain energy are found to be 64.68  ×  10⁻¹² J for nanopillar of radius of 75 nm and 71.08  ×  10⁻¹² J for 175 nm thick pillar. Since the local contact deformations are caused by an increase of the interaction between defects during compression, therefore the contact stress induces the internal structural deformation, which contains the grain boundaries and dislocation defects.

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To begin we recall a known fact that the FIB ions impacted on the Al₂O₃ nanopillars surface cause not only the removal of material surface but also the formation of a damaged surface with thickness of up to several nanometers, i.e. they can form an amorphous surface layer [23, 24]. Importantly, thickness of the amorphous surface layer formed on Al₂O₃ nanopillars surface is roughly proportional to the primary energy of Ga ions. Figure 4 displays the stress–displacement curves of Al₂O₃ nanopillars with radii of 75 and 175 nm during the compressive loading. In this case stress is defined as the average force F (µN) per unit area A (nm²). It is a well-known fact that the elastic limit point and macroscopic yield point (MYP) are two key points of the stress–displacement curves. The elastic limit of force per unit area of the material can arise before the onset of permanent deformation [24].

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We must emphasis here that in present work the Young's modulus of Al₂O₃ nanopillars were determined from results of the in situ TEM compression experiments, which are in principle different from the nanoindentation. As a result, the Young's modulus of Al₂O₃ nanopillar was calculated using the Euler's buckling formula [25, 26]

$$\begin{eqnarray}&&{{P}_{\text{cr}}}=6E\pi /{{L}^{2}}\left(0.1r_{\text{L}}^{4}+0.5r_{\text{L}}^{3}{{r}_{0}}+r_{\text{L}}^{2}r_{0}^{2}+{{r}_{\text{L}}}r_{0}^{3}+0.5r_{0}^{4}\right),\end{eqnarray} \tag{ 1 }$$

where E is the Young's modulus, P_cr is the critical load, L is the effective length, i.e. in our case the nanopillar effective length is 5 µm, and r₀ and r_L are the diameters of pillar A and B, respectively; P_cr is critical load predicted by the Rayleigh–Ritz method as P_cr  =  6EI/L². Then accounting for equation (1) and results of the compressive test the desired value of Al₂O₃ nanopillars Young's modulus can be easily obtained, and it reads 347.5 GPa for radius of 75 nm and 54.8 GPa for 175 nm thick pillar. The following important conclusions can be made from the in situ TEM experiments: (i) the Young's modulus decreases with an increase of the nanopillar radius; and (ii) the size and tapering effects have dominant impact on deformation of the pillar.

Here, the mechanical properties of nanopillars are determined from the nanoindentation experiments. The representative load–displacement (P–h) curves of the Al₂O₃ structures during nanoindentation are presented in figure 5. The hardness and the Young's modulus of prepared samples were obtained by means of the well-known quasi-static indentation method [27, 28]. The contact area A was calculated from the contact depth h_c using a pre-calibrated shape function A  =  f(h_c) of Berkovich indenter, where h_c can be obtained from

$$\begin{eqnarray}&&{{h}_{\text{c}}}={{h}_{\max}}-\varepsilon \left({{P}_{\max}}/S\right),\end{eqnarray} \tag{ 2 }$$

where h_max is the maximum indenter penetration depth, ε is a constant, which for Berkovich indenter tip is 0.72, S is the contact stiffness during unloading and P_max is the maximum indentation load. The Young's modulus was estimated from the following expression [29, 30]

$$\begin{eqnarray}&&E=\left(1-{{\nu}^{2}}\right){{\left(\frac{1}{{{E}^{\ast}}}-\frac{1-\nu _{i}^{2}}{{{E}_{i}}}\right)}^{-1}},\end{eqnarray} \tag{ 3 }$$

where ν and E are the Poisson's ratio and the Young's modulus, respectively; and the indenter properties were E_i  =  1.14 TPa and ν_i  =  0.07. Then E^* is the effective Young's modulus given by

$$\begin{eqnarray}&&{{E}^{\ast}}=\frac{\sqrt{\pi}}{2}\frac{S}{\beta \sqrt{A}},\end{eqnarray} \tag{ 4 }$$

where S is tested sample stiffness obtained from the initial unloading slope by evaluating the maximum load and the maximum depth, i.e. S  =  dP/dh. Then the determined Young's modulus of the Al₂O₃ samples was ranging from 32.42 to 136.10 GPa. Similarly, the sample hardness was calculated from the known ratio of P_max to the projected contact area A, where P_max is the maximum indentation load of a prescribed sharp, i.e. Berkovich tip. The obtained hardness values of Al₂O₃ samples were ranging from 3.19 to 20.6 GPa.

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Besides it is also evident from figure 5 that the multiple displacement discontinuities, i.e. pop-in events, were occurred during loading in ranges of 1.5–2 mN. It is worth noting that these findings are in a good agreement with the already published results [5, 31].

An optical image of an indented Al₂O₃ substrate, where a square-pyramidal residual indentation remained after the Vickers test, is presented in figure 6. The Vicker hardness test is commonly used to evaluate the residual plastic behavior of solid substrates. The Vickers hardness function HV can be calculated from the load P divided by the residual surface area of indenter d in the following way

$$\begin{eqnarray}&&HV=1.8544P/{{d}^{2}},\end{eqnarray} \tag{ 5 }$$

where P is load (in kg) and d is the average length of two residual indentation diagonals (in mm). It has been found that the Vickers micro-hardness of Al₂O₃ samples is ranging from 14 to 20.21 GPa under a loading force of 0.25–1.96 N. For readers' convenience, a comparison of the here calculated and previously reported values of Al₂O₃ substrate hardness H and the Young's modulus E are summarized in the table 1. As can be seen from table 1 here presented results are in a good agreement with those determined in previous studies [31–34]. Our findings confirmed that the Al₂O₃ substrate has a very high compression strength, high mechanical strength and extraordinary high hardness. Before the measurement, the Al₂O₃ substrate need to do the cutting and paste. Therefore, after the measurement of nanoindentation, the measured hardness value between this paper and previous studies may not be in a very good agreement.

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Figure 7 displays a comparative micro-Raman spectrum of Al₂O₃ substrate for both no indentation and indentation tests, respectively. Results given in figure 7 revealed that the Raman spectral peak of Al₂O₃ substrate, which did not undergo the indentation test, is similar with the one obtained previously by Li et al [35]. However, after the indentation test the peak wavenumber of Raman spectra has a production peak at 577.3 (cm⁻¹), i.e. between 418.3 and 645.2 (cm⁻¹) peaks. It indicates that after the indentation test of Al₂O₃ substrate, not only the surface was deformed but also the internal structural characteristics were changed.

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Figure 8 displays the FIB micrographs of Al₂O₃ substrate after the Vickers punched substrate by a force of 1.96 N. As it was expected a square-pyramidal residual indentation remained after the Vickers test. Figure 8(b) presents a details of the impression that was marked first in order to obtain a cross-section right thought the middle of the indent. Afterwards a platinum layer with thickness of about 1 µm was deposited on the sample surface to minimize the damage caused by the ion beam.

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In this section, the HR-TEM images of the Al₂O₃ substrate after the Vickers hardness indent force of 1.96 N placed on the nickel grid right after cut embossing position by the FIB are given and the observed results are discussed in details. The HR-TEM image of Al₂O₃ substrate after Vickers indent, where the indent surface caused a dislocation slip line, is given in figure 9(a). This dislocation slip line was the difference in thickness direction through the film came in the TEM image of a typical form. The magnified dislocation loop shape marked by a red circle in figure 9(a) is presented in figure 9(b). As can be seen, the dislocation loop is evenly distributed alongside dislocation slip line. Consequently, it can be concluded that after the Vickers indentation of Al₂O₃ substrate the interior materials produced both: dislocation slip in a direction of 45° and the dislocation loop phenomenon.

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