## 3 Materials and Methods
### Non-Linear Ultrasonic Measurements  
In this study, two piezoelectric lead zirconate titanate (PZT) patches were used as the transmitter and the receiver, respectively. The model of the PZT was PSN-33 with a size of \(\phi\) 8 mm \(\times\) 0.48 mm, which was provided by the Haiying company. Table 2 shows the parameters of PZT. Where \(d_{33}\) is piezoelectric strain constant, \(C\) is capacitance, \(\tan\delta\) is dielectric dissipation factor, \(ft\) is resonance frequency, \(Zr\) is impedance. As shown in Figure 1, the PZTs were arranged on two opposite sides of the specimen. Epoxy resin was used to bond PZT to the center of the specimen surface. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Category** & **CI** & **CII** \\ \hline Cement (P.O 42.5) (kg/m\({}^{3}\)) & 415 & 368 \\ Fine aggregate (kg/m\({}^{3}\)) & 609 & 619 \\ Coarse aggregate (kg/m\({}^{3}\)) & 1181 & 1250 \\ Water (kg/m\({}^{3}\)) & 195 & 195 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mixture proportions of the concrete specimen. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Model** & \(\mathbf{d_{33}}\) (**pC\(\cdot\) N\({}^{-1}\)**) & \(\mathbf{C}\) (pF) & \(\mathbf{tan}\) \(\delta\) (\%) & \(\mathbf{ft}\) (MHz) & \(\mathbf{Zr}\) (\(\Omega\)) \\ \hline PSN-33 & 377 & 1167 & 1.77 & 4.03 & 5.45 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The parameters of PZT. Using the device illustrated in Figure 2, measurements of ultrasonic longitudinal parameters were taken. A sine pulse signal with 5 cycles and a frequency of 75 kHz was generated by the signal generator (SDG 5162) at a repetition rate of 3 ms and a peak-to-peak voltage of 8 Vp-p. Then, the voltage of the signal was increased to 56 V using a wideband power amplifier (KROHN-HITE 7602M) and transmitted to the PZT transducer. At the other end of the specimen, another PZT received the signal. In addition, a channel was set up to monitor the output of the sync signal. An oscilloscope (Agilent InfiniiVision DSOX 3014A) acquired the received time-domain signal averaging 256 times with a sample length of 16,000 at a sample rate of 625 MSA/s. The acquired signal was transmitted to the computer for filtering, windowing, and fast Fourier transforms (FFT). Figure 3a shows the received time-domain signal (the blue marked area is the Hann window width) in carbonated concrete. It should be noted that the boundary reflected waves arrived at approximately 38 us (the 4 th cycle) and then interfered with the directly propagating wave. In order to avoid contributions from these reflected waves, the first 2 cycles of the signal were used for FFT. It was experimentally shown that the reflected waves did not affect the first 2 cycles for the concrete specimens in this paper. The frequency spectrum for the windowed signal after FFT is shown in Figure 3b. In addition, CI was used to carry out the test at excitation frequencies of 50 kHz, 75 kHz, and 100 kHz to investigate the relationship between the ultrasonic excitation frequency and the non-linear parameters of concrete carbonation. The amplifier was connected to the oscilloscope to test the linearity of the amplified signal, as illustrated in Figure 4. The linearity of ultrasonic signals transmitted and received by PZT was also tested in the air. There was a distance of 100 mm between the PZTs, and the center of the two PZTs was in a straight line. Figure 5 shows the received time-domain signal and the spectrum for the test in Figure 4a. The fundamental amplitude can be seen in the figure, while the second-harmonic amplitude is not easy to be observed. Whereas the configuration had a minor non-linearity in which the fundamental amplitude is 385 times  
Figure 1: Placement of PZT. Figure 2: Detection device for the non-linearity parameter of ultrasonic longitudinal waves. with low excitation frequency due to the length of ultrasonic propagation in this paper being 100 mm.