## 3 Results and Discussion  
Using the dispersion Equation (1), and the material parameters of the CFEC and Mn:0.24 PIN-0.46 PMN-0.30 PT piezoelectric single crystal, the dispersion curves of the Love mode surface acoustic waves for the CFs in the CFEC guiding layer along the \(x\)- and \(y\)-axes at 25 \({}^{\circ}\)C are shown in Figure 2a,b, respectively. All the dispersion curves in Figure 2 have the initial SH wave speed of 2809.9 m/s in the Mn:0.24 PIN-0.46 PMN-0.30 PT ternary single crystal substrate, and each high-order Love mode has a low-frequency cut-off at this velocity. The velocities of Love waves asymptotically reach the SH wave speed of 1916 m/s in the waveguide with an increase in \(h/\lambda\). By comparing Figure 2a,b, it is clear that the CFs orientation of the CFEC waveguide influence the propagation characteristics of the Love waves. The change in elastic constants \(c_{44}\) and \(c_{55}\) in Table 1 is the immediate cause of the variation of dispersion curves with different orientations of CFs. Different propagation characteristics of the Love waves will result in different performances of the devices with the CFs in the CFEC guiding layer parallel to the \(x\)-axis and \(y\)-axis. In the introduction, it is mentioned that the elastic property of CFEC is almost invariable in the range of 25-55 \({}^{\circ}\)C [27]. In fact, the change of elastic constants of CFEC with temperature is much smaller than that of Mn:0.24 PIN-0.46 PMN-0.30 PT ternary single crystal in the range of 25-55 \({}^{\circ}\)C. Therefore, we assume that the elastic constants of CFEC are constant in the range of 25-55 \({}^{\circ}\)C. At temperatures 30, 35, 40, 45, 50, and 55 \({}^{\circ}\)C, we obtained dispersion relations similar to those in Figure 2. (see Appendix A) However, note that the SH mode wave speed in the substrate decreases with temperature (2761.1 m/s at 55 \({}^{\circ}\)C), while the low-frequency cut-offs of higher-order Love modes exhibit an increasing trend for a fixed CFs orientation. Figure 3a,b show the relationship of normalized mass sensitivity \(\left|S_{m}^{f}\right|\lambda\) against the normalized layer thickness \(h/\lambda\) for the CFEC/Mn:0.24 PIN-0.46 PMN-0.30 PT structure device with the CFs in the CFEC waveguide parallel to the \(x\)- and \(y\)-axes at 25 \({}^{\circ}\)C. The order correspondence between Figures 2a and 3a is the same as that between Figures 2b and 3b. Both the highest normalized mass sensitivity \(\left(\left|S_{m}^{f}\right|\lambda\right)_{\max}\) and optimal normalized layer thickness \(\left(h/\lambda\right)_{\mathrm{opt}}\) are observed in the first order mode as shown in Figure 3. For each order mode, the normalized mass sensitivity increases rapidly to the maximum value and then decreases slowly, approaching zero, with the normalized layer thickness \(h/\lambda\). By comparing Figure 3a,b, for the same order modes, we can see that the devices with the CFs in the guiding layer along the \(x\)-axis (the propagation direction of the Love wave) have higher  
Figure 2: Dispersion relation of Love waves at 25 \({}^{\circ}\)C. (**a**) CFs in CFEC waveguide along the \(x\)-axis. (**b**) CFs in CFEC waveguide along the \(y\)-axis. normalized mass sensitivity at the maximum values. A Love wave sensor is expected to have the high mass sensitivity in practical applications. For a fixed wavelength and fiber orientation, the optimal waveguide thickness \(h\) of the first order mode is much less than that of higher-order modes. For a feasible sensor design, the greater the waveguide thickness \(h\), the higher the acoustic loss [16]. In addition, the first order mode has the highest electromechanical coupling factor [4]. Hence, the device has an optimal performance in the first order mode. As shown in Figure 3a,b, employing  
Figure 3: Normalized mass sensitivity against normalized layer thickness for the CFEC/Mn-doped 0.24 PIN-0.46 PMN-0.30 PT structure sensor at 25 \({}^{\circ}\)C. (**a**) CFs in CFEC along the \(x\)-axis. (**b**) CFs in CFEC along the \(y\)-axis.