## 3 Results and Discussion
first order mode, the optimal normalized layer thickness was 0.2023 and 0.2691, and the highest normalized mass sensitivity was 2.5052 and 1.8261, which is approximately 2.5 times and 1.8 times of that of a fused quartz/ST-quartz structure device, respectively [4]. Clearly, for a given piezoelectric substrate, the device with a smaller elastic constant \(c_{44}\) of the CFEC waveguide has a higher normalized mass sensitivity. Figure 4a,b show the normalized mass sensitivity \(\left|S_{m}^{f}\right|\lambda\) for the first order mode for the CFEC/Mn:0.24 PIN-0.46 PMN-0.30 PT structure device with the CFs in the guiding layer along the \(x\)-axis and \(y\)-axis, respectively, at different temperatures. The peak values of normalized mass sensitivity from Figure 4 are listed in Table 2, which indicate that the highest normalized mass sensitivity \(\left(\left|S_{m}^{f}\right|\lambda\right)_{\max}\) decreases with temperature for a fixed fibers orientation. Meanwhile, the optimum design \(\left(h/\lambda\right)_{\text{opt}}\) exhibits a gradual increasing tendency, while the phase velocities (\(v_{\text{opt}}\)) of the Love waves for the first order mode at the optimums exhibit a decreasing trend, and the elastic constants \(c_{44}^{E}\) and \(c_{66}^{E}\) of the substrate also show a decline. By comparing Figure 4a,b, for a given temperature in the range of 25-55 \({}^{\circ}\)C, the device with the CFs in the CFEC waveguide layer along the \(x\)-axis has the highest normalized mass sensitivity. Further, the optimal normalized layer thickness \(\left(h/\lambda\right)_{\text{opt}}\) of the waveguide with the fibers along the \(x\)-axis is less than that of the fibers along the \(y\)-axis, which implies lower acoustic loss for a fixed wavelength. Figure 4: Normalized mass sensitivity for the sensor operating in first order mode with CFEC/Mn:0.24 PIN-0.46 PMN-0.30 PT configuration in the range of 25–55\({}^{\circ}\)C. (**a**) CFs along the \(x\)-axis. (**b**) CFs along the \(y\)-axis. The peak values in Figure 4 are the simulation data of the highest normalized mass sensitivity \(\left(\left|S_{m}^{f}\middle|\lambda\right)_{\max}\) and the optimum design \(\left(h/\lambda\right)_{\mathrm{opt}}\) at different temperatures. Figure 5 shows the fitted data, and the fitting equations for the two cases with the CFs in the CFEC waveguide along the \(x\)-axis and \(y\)-axis are as follows:  
\[\left(\left|S_{m}^{f}\middle|\lambda\right)_{\max}\right.=\ 2.54859\ -\ 0.00102T\ -\ 2.55238\ \times 10^{-5}T^{2}\left(10^{-3}\mathrm{m}^{3}/ \mathrm{kg}\right) \tag{9}\]  
\[\left(h/\lambda\right)_{\mathrm{opt}}\ =\ 0.19734\ +\ 1.74524\ \times\ 10^{-4}T+\ 8.09524\ \times 10^{-7}T^{2} \tag{10}\]  
\[\left(\left|S_{m}^{f}\middle|\lambda\right)_{\max}\right.=\ 1.85722\ -\ 7.11431\ \times 10^{-4}T-\ 1.90938\ \times 10^{-5}T^{2}\left(10^{-3}\mathrm{m}^{3}/ \mathrm{kg}\right) \tag{11}\]  
\[\left(h/\lambda\right)_{\mathrm{opt}}\ =\ 0.25978\ +\ 4.18431\ \times\ 10^{-4}T-\ 2.27476\ \times\ 10^{-6}T^{2} \tag{12}\]  
where Equations (9) and (10) describe the case that the CFs are parallel to the \(x\)-axis, and Equations (11) and (12) describe the case that the CFs are parallel to the \(y\)-axis. From Figure 5 and Table 2, it was found that the changing trend of the highest normalized mass sensitivity \(\left(\left|S_{m}^{f}\middle|\lambda\right)_{\max}\right.\) is considerably dependent on the variation in elastic constants \(c_{44}^{E}\) and \(c_{66}^{E}\) of the Mn:0.24 PIN-0.46 PMN-0.30 PT single crystal with temperature. Although the optimal design \(\left(h/\lambda\right)_{\mathrm{opt}}\) exhibited a slight increasing trend, it was almost invariant from 25 \({}^{\circ}\)C to 55 \({}^{\circ}\)C for a fixed CFs orientation.