| Crystal materials are a kind of special solid materials in which different energy forms, for examples, electrical/optical/acoustic/thermal/magnetic, can interact and transform to each other due to their unique physical characteristics. Therefore, crystal materials are the substaintial base of laser, optical-electric and microelectronics technologies. The variety of functions, as well as their good stability made crystal materials been widely used in nowaday society. Such as for civil and military applications, scientific research and industrial developments, people's daily life and the economic development, crystal have become the indispensable, vital and key materials. As the developments of science and technologies, crystal materials with higher quality are needed. Thereby, research of new crystal materials has become a focused subject currently.Recently, under the guide of the second order Jahn-Teller (SOJT) effect, a novel kind of compounds including both d0 transition metal cations and lone-pair electrons cations have attracted people's huge attention. In such kind of compounds, the coordination polyhedra are easily distored due to the SOJT effect, which induces the ions off-center, thus makes the compounds with noncentrosymmetric structures. If the vectors generated by the structure distortion can not be completely offset, the crystals will show the external macro-asymmetry which indicates the emergence of third-order tensor physical properties. It has been reported that many of these compounds exhibit piezoelectric/ferroelectric/strong power second harmonic generation (SHG) efficiency. BaTeMo2O9 is one of these compounds, since it includes both the d0 transition metal Mo cations and the Te cation with lone-pair electrons. Especially, Mo is the transition metal which can impose the biggest distortion on the coordination polyhedra, therefore BaTeMo2O9 is an extremely potential functional crystal material. It has already been reported that the powders of BaTeMo2O9 has relatively large power second-harmonic generation efficiencies. Howerve, up to date the researches on BaTeMo2O9 are still limited in the crystal structure and the basic physical properties of polycrystalline powers, while the primary physical properties of BaTeMo2O9 single crystals haven't been reported yet. Our group has successfully prepared the first high-quality and large size (30 x 23 x 18 mm3) of BaTeMo2O9 single crystal in the world. In this thesis, based on the growth of high-quality and large size of BaTeMo2O9 crystal, the piezoelectric/dielectric/elastic/electro-optic/pyroelectric properties have been studied in detail, moreover, a piezoelectric resonator has also been designed and evaluated. According to the analysis of this low symmetrical crystal, we have defined the scope of low symmetrical crystals from third-order tensor. The main contents are as follows:1. The definition, characters, classification, development and current status of crystals are introduced and summarized. Under the guidance of the SOJT effect, BaTeMo2O9 has been selected as the object of study. A simple introduction of BaTeMo2O9, as well as the significance of reseaches on BaTeMo2O9 single crystal has been elucidated.2. Structure analysis and the crystal growth of BaTeMo2O9The crystal structure of BaTeMo2O9 has been analyzed. The octahedral and tetrahedral structures in the crystal structure, as well as the bond length and angles, have been studied. The results indicated that BaTeMo2O9 is not only a potential nonlinear optical crystal, but also a multifunction crystal. Based on the well-developed flux system and the crystal growth parameters obtained in our group, we have successfully grown high-quality and large size BaTeMo2O9 single crystal by using the orientational seed method, which is the material basis for our sequent research.3. Dielectric, piezoelectric and elastic properties on BaTeMo2O9 crystalBy analyzing the crystal symmetry of BaTeMo2O9 crystal, the piezoelectric coordinate system has been established according to IEEE standard. The appropriate samples for determining the dielectric/piezoelectric/elastic properties have been designed by using coordinate rotation method. The dielectric, piezoelectric and elastic properties have been studied by resonance method and transmission method in detail at room temperature. The temperature dependence and frequency dependence of the elastic constants, dielectric constants and dielectric loss diversification have also been studied. From the sight of crystal structure, we have explained the origin of good piezoelectric properties. Compared with the commonly used piezoelectric crystals, a comprehensive evaluation has been given to BaTeMo2O9 crystal.4. The electro-optic properties on BaTeMo2O9 crystalThe electro-optic coordinate system has been established. Appropriate samples for the determination of electro-optic properties have been designed. The electro-optic coefficients have been determined by interference method, while the inverse piezoelectric effect has been eliminated so as to achieve the reliable results. The refractive index ellipsoid of BaTeMo2O9 crystal under electric field has been obtained and analyzed by using dielectric isolation tensor as the parameters. By comparing with the requirements of electro-optic crystals, a comprehensive evaluation has been given to BaTeMo2O9 crystal.5. Pyroelectric properties of BaTeMo2O9 crystalThe pyroelectric coefficients are obtained by using charge integral method at the temperature range from 30℃to 260℃. We have explained the variation rule of pyroelectric coefficient by analyzing the influences of temperature on the resistivity and spontaneous polarization. The parameters related to the pyroelectric properties have been analyzed and compared with common pyroelectric crystals. Finally a comprehensive evaluation of BaTeMo2O9 crystal was given.6. Design and characterization of piezoelectric devices based on BaTeMo2O9 crystalThe low symmetry of monoclinic system BaTeMo2O9 crystal induces lots of difficulties in designing of the devices, since as the reduction of the symmetry, forms of piezoelectric and elastic coefficients matrix become complex, which may affect the available coefficients, and thus interfere the signals of the devices. We have successfully cleared out the negative affections and designed valuable practical devices by using coordinate rotation method. The parameters such as resonant frequency, electromechanical coupling coefficients, mechanical quality factor, frequency drift and temperature drift of the resonator have also been determined and evaluated. This research is a significant grope for the real application of low symmetrical crystals, and opens up a new application field for low symmetrical crystals.7. Research on tensorsFor crystals with low symmetry, there are less symmetric elements, and it is not possible to obtain the physical parameters in different quadrants by the extrapolation method. By analyzing the third-order tensors for the piezoelectric, electro-optic and second-order nonlinear optical properties, as well as the fourth-order tensor for the elastic properties of BaTeMo2O9 crystal, we have discussed the sign changing of the tensor components in different quadrant, as well as the influences of such sign changing on the performance of the devices and the virtual values calculations. This work will significantly promote the application of BaTeMo2O9 crystal. Finaly, by comparing the tensors of BaTeMo2O9 with those of crystals with higher symemetry (orthorhombic), we have defined the scope of low symmetrical crystal according tothe third-order tensor.
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