**Appendix A.**

#### *Appendix A.1. Nanoindentation Test*

A load of 0.78 mN was applied on the sample for the nanoindentation test with a Berkovich indenter and a typical loading and unloading curve is shown in Figure A1. The unloading curve was fitted by

$$P\_{\boldsymbol{\mu}} = a(\boldsymbol{h} - \boldsymbol{h}\_f)^m,\tag{A1}$$

where *a*, *h* and *hf* are the fitting parameters, which were fitted using MATLAB in the present study. Then, the contact stiffness was established as

$$S = \frac{dP\_{\rm u}}{dh}|\_{\rm h} = h\_{\rm max} = ma(h\_{\rm max} - h\_f)^{m-1} \,\tag{A2}$$

where *h*max is the maximum indentation depth.

The elastic modulus and hardness were calculated by the Oliver–Pharr method and were expressed as

$$\frac{1}{E\_r} = \frac{1 - v^2}{E} + \frac{1 - v\_i^2}{E\_i},\tag{A3}$$

where *Ei* and *vi* are the elastic modulus (1140 GPa) and Poisson's ratio (0.07), respectively, of the indenter, and *E* and *v* are the elastic modulus and Poisson's ratio, respectively, of the test material. The modulus *Er* was expressed as

$$E\_{\mathcal{I}} = \frac{\sqrt{\pi}}{2} \cdot \frac{S}{\sqrt{A}},\tag{A4}$$

where *S* is the contact stiffness and *A* is the projected contact area. The projected contact area A was calculated by

$$A = \mathbb{C}\_1 \mathfrak{h}\_{\varepsilon}^2 + \mathbb{C}\_2 \mathfrak{h}\_{\varepsilon} + \mathbb{C}\_3 \mathfrak{h}\_{\varepsilon}^{1/2},\tag{A5}$$

where *C*1 = 23.97, *C*2 = 391.7, and *C*3 = 2018.2, which were calibrated by the test machine. The contact depth *hc* was estimated by

$$h\_{\mathfrak{c}} = h\_{\text{max}} - \varepsilon \frac{P\_{\mathfrak{u}}}{S} \, \tag{A6}$$

where *ε* is a constant, which is related to the geometry of the indenter. For a Berkovich indenter, *ε* = 0.75.

**Figure A1.** The loading and unloading curve from the nanoindentation test.

For all the material points tested, the ratio of final indentation depth *hf* to the maximum indentation depth *h*max (*hf* /*h*max) was ∼0.83, which indicated that slight pile-up may have occurred under nanoindentation. As a result, the measured elastic modulus and hardness may be slightly overestimated. As reported by Moharrami and Bull [33], for the indentation depth obtained in the present study, the maximum overestimation for the elastic modulus was 8%.

#### *Appendix A.2. Vickers Hardness Test*

A maximum load of *F* = 1000 mN was applied for the Vickers hardness test with the maximum indentation depth of ∼4.6 μm. The loading and unloading time were both 20 s and the dwell time was 10 s. For the Vickers hardness test, a diamond indenter with the tip angle of 136◦ was employed and the averaged diagonal length d (μm) of the contact area was measured to calculate the Vickers hardness HV by

$$\text{HV} = \frac{0.1891F}{d^2} \times 10^3. \tag{A7}$$
