## 4 Conclusions  
In this article, the Love mode acoustic dispersion relation, normalized mass sensitivity, optimum normalized waveguide layer thickness, and TCF were calculated for the CFEC/Mn:0.24 PIN-0.46 PMN-0.30 PT structure sensor. For a given piezoelectric substrate, the smaller the elastic constant \(c_{44}\) of the guiding layer, the higher normalized mass sensitivity of device. For a fixed waveguide layer, the highest normalized mass sensitivity \(\left(\left|S_{m}^{f}\right|\lambda\right)_{\max}\) decreases with temperature, which is considerably dependent on the change in the elastic constants \(c_{44}^{E}\) and \(c_{66}^{E}\) of Mn:0.24 PIN-0.46 PMN-0.30 PT ternary single crystal substrate. The optimal design \(\left(\hbar/\lambda\right)_{\text{opt}}\) is approximately invariant for the CFEC waveguide with a fixed CFs orientation in the range of 25-55 \({}^{\circ}\)C. For the CFs in the CFEC waveguide along the propagation direction of Love wave, the sensor has a relatively small TCF of \(-\)10.92 ppm/\({}^{\circ}\)C at \(\hbar\)/\(\lambda\) = 0.4001, where the normalized mass sensitivity \(\left|S_{m}^{f}\right|\lambda\) is approximately 1.5 times that of a typical fused quartz/ST-quartz configuration device. It may provide some beneficial changes, including low density and acoustic loss, and good thermal stability by varying the content of the CFs in CFEC waveguide, which can improve device performance. Although the Mn:PIN-PMN-PT ternary single crystal has high electromechanical coupling and good temperature stability, the elastic constants \(c_{44}^{E}\) and \(c_{66}^{E}\) of Mn:0.24 PIN-0.46 PMN-0.30 PT slightly decrease with temperature. Thus, it is important to find a substrate material that has large electromechanical coupling coefficients and elastic constants \(c_{44}^{E}\) and \(c_{66}^{E}\). Besides waveguide and substrate, the operating frequency is also a key parameter [47; 48]. When the frequency increases, the wave attenuation in substrate is stronger. If the thickness of substrate is lower than the penetration depth of the Love wave, loss of energy occurs [47]. The piezoelectric substrate of sensor be considered to be a semi-infinite medium in this work. In this paper we present a new waveguide/substrate system of Love wave device that has potential to maintain a high mass sensitivity with a relatively small temperature coefficients of frequency. In addition, this work provides a new idea to improve the polymer waveguide. For example, the unidirectional CFs may be added into PMMA to reduce the acoustic loss of PMMA. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**TCF** & & \(\left|S_{m}^{f}\right|\lambda\) (\(\text{10-3m}^{3}\)/kg) & & \\ \cline{2-5} **(ppm/\({}^{\circ}\)C)** & **25 \({}^{\circ}\)C** & **35 \({}^{\circ}\)C** & **45 \({}^{\circ}\)C** & **55 \({}^{\circ}\)C** & \\ \hline \(-\)126.62 & 2.5043 & 2.4801 & 2.4415 & 2.4006 & 0.2002 \\ \(-\)76.33 & 2.4336 & 2.4216 & 2.4025 & 2.3825 & 0.2251 \\ \(-\)50.59 & 2.2834 & 2.2765 & 2.2650 & 2.2547 & 0.2502 \\ \(-\)36.09 & 2.1241 & 2.1200 & 2.1133 & 2.1063 & 0.2750 \\ \(-\)26.93 & 1.9778 & 1.9748 & 1.9703 & 1.9655 & 0.3002 \\ \(-\)20.83 & 1.8437 & 1.8414 & 1.8381 & 1.8345 & 0.3250 \\ \(-\)16.45 & 1.7240 & 1.7221 & 1.7198 & 1.7172 & 0.3501 \\ \(-\)13.30 & 1.6190 & 1.6177 & 1.6158 & 1.6136 & 0.3750 \\ \(-\)10.92 & 1.5228 & 1.5215 & 1.5199 & 1.5183 & 0.4001 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: TCF and normalized mass sensitivity \(\left|S_{m}^{f}\right|\lambda\) for a sensor operating in the first order mode with the CFs in CFEC waveguide along the \(x\)-axis. **Author Contributions:** Methodology, N.H. and E.S. ; Software, R.Z. and N.H.; Validation, B.Y., J.L. and T.L. ; writing--original draft preparation, N.H. and W.C.; Writing--review and editing, N.H., L.H. and E.S. ; Funding acquisition, N.H. All authors have read and agreed to the published version of the manuscript.