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Page 6 of 12 Zhang et al. Microstructures 2023;3:2023010 https://dx.doi.org/10.20517/microstructures.2022.39

where E is the elastic modulus of the indenter (1140 GPa for diamond), v and v are the Poisson’s ratios of
I
s
I
the sample and the indenter. The Poisson’s ratio of diamond is 0.07 and that of CIPS-IPS is close to zero.
The E of CIPS-IPS is calculated to be around 22.20 ± 0.48 GPa.
s
A critical issue is that we do not know whether the nanoindentation position is CIPS or IPS. To further
correlate it with the corresponding regions, we characterize the same regions with the aid of CR-AFM,
Lateral Force Microscopy (LFM), and PFM. Figure 2B-D show resonance frequency, friction force and
phase images, respectively. The corresponding complete PFM amplitude and deflection images are shown
in Supplementary Figure 2. The frequency and friction force images corresponding to the CIPS phase and
IPS show a labyrinth-like distribution which can also be seen from the frequency statistics curve in
Supplementary Figure 3. In addition, the CIPS phase resonance frequency is larger, and the corresponding
friction force is smaller. This phenomenon can be understood as follows: the higher the resonance
frequency, the higher the Young’s modulus, which is simply the harder. When measuring the lateral force
under the same pressure, the friction force of the harder material is smaller if ignoring other interface
factors, which is consistent with our experimental observation. Note that the direction of polarization has
little effect on the magnitude of the modulus and the magnitude of the frictional force. In addition, we also
ruled out the influence of topography fluctuation itself on the friction measurement; the magnitude of the
friction is still continuous, even if in the two regions of the fault [Supplementary Figure 4].

In order to quantify the magnitude of elastic modulus of different phases of CIPS-IPS, a reference material
of highly oriented pyrolytic graphite (HOPG) with a modulus of 15 GPa was used for calibration, given
[40]
the difficulty in accurately determining the tip radius and contact area. Typical first and second-order
contact resonance frequency (CRF) spectra are shown in Figure 2E, from which the higher CRF of CIPS
reflects its higher modulus. The relative tip position γ was determined as 0.92 from the intersection of curves
for the first and second modes of HOPG [Figure 2H]. Then, the mappings of the first-order CRF were also
carried out in HOPG and CIPS-IPS, as shown in Figure 2F and G. By fitting the resonance frequency-
frequency distribution curves of Figure 2F and G inset, the mean value and deviation of the resonance
frequency were obtained. In order to more accurately determine the value of elastic modulus, single-point
measurements of the contact resonance frequency were performed on the basis of the modulus mapping
image, and the results are shown in Supplementary Table 3.

The process of the contact resonance model to quantify Young’s modulus is as follows:

When the cantilever vibrates freely in the air, according to the cantilever flexural vibration governing
equation and boundary conditions, the characteristic equation can be obtained:

The first two roots of Equation (3) are [x L, x L,] = [1.8751,4.6941] [41,42] . When the cantilever tip is in
0
0
1
2
contact with the sample, the normalized contact stiffness k /k can be expressed as the nth order flexural
*
lever
[41]
contact resonance and the relative tip position γ as :