## 3 Experiments
### Absolute Nonlinearity Parameter Measurement  
The piezoelectric method was carried out at room temperature to measure the absolute ultrasonic nonlinearity parameter [13], which involved two steps: calibration and nonlinear measurement. The calibration process converts a measured electrical current into acoustic displacement. Calibration was conducted using the pulse-echo method, as shown in Figure 2a, to obtain the calibration function that converts the electrical output signal of the receiving transducer into the displacement amplitude [12,13]. Calibration was carried out for the 0.25-in 10-MHz PZT transducer used as the receiver during the nonlinear measurements. A couplant was applied between the material and transducer. An ultrasonic pulser-receiver (Panamertrics, PR5072, New York, NY, USA) was used to transmit a broadband ultrasonic wave into the specimen. The incident ultrasonic wave propagated through the specimen. The propagating ultrasonic wave was reflected from the back wall and received by the 10-MHz PZT transducer. During calibration, the input current, \(\mathrm{I^{\prime}}_{in}\), and voltage, \(\mathrm{V^{\prime}}_{in}\), from the pulser to the transducer were detected, and the output current, \(\mathrm{I^{\prime}}_{out}\), and voltage, \(\mathrm{V^{\prime}}_{out}\), which were echo signals from the back wall, were measured using a current probe (Lecroy, CP030, Milpitas, NY, USA) and a voltage probe (Tektronix, P2220, Beaverton, OR, USA). The signal was acquired by an oscilloscope (Lecroy, Wavesurfer452, Chestnut Ridge, NY, USA). The acquired voltage and current signals were Fourier-transformed using fast Fourier transform (FFT) after applying a Hanning window. To compensate for the energy loss occurring because of windowing, the frequency spectrum is multiplied by a scaling factor [12,22]. From the final spectrum, we calculated the calibration function, \(\mathrm{H}(\omega)\), as follows [13]:  
\[\mathrm{H}(\omega)=\sqrt{\frac{\left|\mathrm{I^{\prime}}_{in}(\omega)\left( \frac{\mathrm{V^{\prime}}_{out}(\omega)}{\mathrm{I^{\prime}}_{out}(\omega)} \right)+\mathrm{V^{\prime}}_{in}(\omega)\right|}{2\omega^{2}\rho\mathrm{u} \left|\mathrm{I^{\prime}}_{out}(\omega)\right|}}, \tag{3}\]  
where \(\omega\) is the frequency of the propagating ultrasonic wave, \(\rho\) is the density of the material, \(\upsilon\) is the longitudinal velocity of the propagating ultrasonic wave, and a is the area of the receiving transducer. Figure 2b shows the \(\mathrm{H}(\omega)\) values, which converts a measured electrical current into the acoustic displacement, obtained through calibration; \(\mathrm{H}(\omega)\) increases slightly as the surface roughness increases owing to scattering of the propagating ultrasonic wave. \(\mathrm{H}(\omega)\) values at interesting frequencies (5 and 10 MHz) are listed in Table 1.  
Figure 1: Experimental procedures for (**a**) both rough surfaces; (**b**) one rough surface and one smooth surface. After calibration, the nonlinear measurements were carried out using the through-transmission technique, as shown in Figure 3a. A 0.25-in 5-MHz PZT transducer was used as the transmitter and a 10-MHz PZT transducer was used as the receiver to sensitively receive the second-order harmonic frequency components. The nonlinear measurement process measures the second-order harmonic components in the electrical output signals after the ultrasonic wave passes through the material. A tone-burst signal with 20 cycles was generated using a high-power ultrasonic pulser (RTIEC, RAM 5000, Warwick, RI, USA) to drive the transmitting transducer. This high-power signal passes through a 7-MHz low pass filter before driving the transmitting transducer to suppress the second-order frequency component generated within the pulser. During the nonlinear measurement, the contact pressure was maintained at 0.45 MPa using pneumatic equipment to maintain the contact condition of the receiving transducer with that existing during calibration [23].