## 3 Results and Discussion
Figure 5: Fitted curves of the highest normalized mass sensitivity and optimum design of normalized layer thickness for the first order mode sensor with the CFEC/Mn:0.24 PIN-0.46 PMN-0.30 PT structure in the range of 25–55 \({}^{\circ}\)C.  
Figure 6 shows the relationship of TCF and \(h/\lambda\) for the two devices operating in the first order mode with the fibers in the guiding layer along the \(x\)-axis and \(y\)-axis. The TCF tends to zero with an increase in the normalized layer thickness \(h/\lambda\) for a given fiber orientation, as shown in Figure 3.0 For a given \(h/\lambda\), the [TCF] of the device with the CFs in the guiding layer along the \(x\)-axis is smaller than that of the CFs along the \(y\)-axis. Optimizing the thickness of the waveguide layer can improve the TCF [10]. Although a zero TCF can be achieved by increasing \(h/\lambda\), the normalized mass sensitivity is reduced, as shown in Figure 4a,b. The wavelength \(\lambda\) in the normalized layer thickness \(h/\lambda\) is the distance between adjacent interdigital electrodes of IDT. Generally, the wavelength \(\lambda\) is a fixed value (e.g., 24 \(\upmu\)m). In this case, increasing \(h/\lambda\) means increasing \(h\). It is reported that the acoustic loss increases with the increase of waveguide thickness \(h\)[16]. Therefore, we can't make \(h\) too large. In addition, see Figure 4a, to ensure that the device has a relatively high mass sensitivity, the normalized layer thickness can't be increased unboundedly. Based on these reasons, it is necessary to balance the TCF and normalized mass sensitivity when optimizing the normalized layer thickness. From Figure 4a,b, the curves at different temperatures reach their highest point and then gradually merge together with increasing \(h/\lambda\). Table 3 shows TCF and normalized mass sensitivity \(\left|S_{m}^{f}\right|\lambda\) for the CFs in CFEC waveguide along the \(x\)-axis. When TCF = \(-\)126.62 ppm/\({}^{\circ}\)C, normalized mass sensitivity \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Temperature**} & \multicolumn{2}{c}{\(\left(\left[S_{m}^{f}\right]\right)_{\text{max}}\)} & \(\left(h/\lambda\right)_{\text{opt}}\) & \(\boldsymbol{v_{\text{opt}}\) (m/s)} & \(\boldsymbol{c_{66}^{E}}\) & \(\boldsymbol{c_{44}^{E}}\) \\  & \multicolumn{2}{c}{\(\boldsymbol{10^{-3}m^{3}/kg}\)} & & & & \(\boldsymbol{(10^{10}\text{ N/m^{2}})^{\text{a}}\)} & \(\boldsymbol{(10^{10}\text{ N/m^{2}})^{\text{a}}\)} \\ \cline{2-7}  & \(x\)-axis & \(y\)-axis & \(x\)-axis & \(y\)-axis & \(x\)-axis & \(y\)-axis & \\ \hline
25 & 2.5052 & 1.8261 & 0.2023 & 0.2691 & 2518.6 & 2492.0 & 6.409 & 6.171 \\
30 & 2.4974 & 1.8204 & 0.2032 & 0.2701 & 2513.8 & 2488.2 & 6.390 & 6.137 \\
35 & 2.4830 & 1.8099 & 0.2044 & 0.2710 & 2507.9 & 2484.0 & 6.353 & 6.101 \\
40 & 2.4669 & 1.7981 & 0.2056 & 0.2731 & 2501.2 & 2476.5 & 6.312 & 6.063 \\
45 & 2.4500 & 1.7858 & 0.2069 & 0.2744 & 2494.5 & 2471.1 & 6.269 & 6.023 \\
50 & 2.4314 & 1.7722 & 0.2082 & 0.2752 & 2487.8 & 2467.1 & 6.222 & 5.982 \\
55 & 2.4174 & 1.7618 & 0.2093 & 0.2757 & 2482.1 & 2464.2 & 6.188 & 5.930 \\ \hline \hline \end{tabular} \({}^{\text{a}}\) Ref. [41].  
\end{table} 
Table 2: Optimum design parameters of normalized layer thickness \(\left(h/\lambda\right)_{\text{opt}}\) and corresponding highest normalized mass sensitivity \(\left(\left|S_{m}^{f}\right|\lambda\right)_{\text{max}}\) for a sensor operating in the first order mode with the unidirectional CFEC/Mn:0.24 PIN-0.46 PMN-0.30 PT structure at different temperatures. Figure 6: TCF for different normalized layer thicknesses of the devices in the system CFEC/Mn:0.24 PIN-0.46 PMN-0.30 PT. \(\left|S_{m}^{f}\right|\lambda\) varies from 2.5043 to 2.4006; however, when TCF = \(-\)10.92 ppm/\({}^{\circ}\)C, the \(\left|S_{m}^{f}\right|\lambda\) varies from 1.5228 to 1.5183 (the change is less than 0.3%) in the range of 25-55 \({}^{\circ}\)C. This means that the variation in normalized mass sensitivity with temperature can be ignored when a relatively high \(\hbar\)/\(\lambda\) is employed.