In ferroelectric liquid crystals, phase transitions can be induced by an electric field. The current constant method allows these transition to be quickly localized and thus the(E, T) phase diagram of the studied pr...In ferroelectric liquid crystals, phase transitions can be induced by an electric field. The current constant method allows these transition to be quickly localized and thus the(E, T) phase diagram of the studied product can be obtained.In this work, we make a slight modification to the measurement principles based on this method. This modification allows the characteristic parameters of ferroelectric liquid crystal to be quantitatively measured. The use of a current square signal highlights a phenomenon of ferroelectric hysteresis with remnant polarization at null field, which points out an effect of memory in this compound.展开更多
From the sound velocity measured using the Brillouin scattering technique, the elastic, piezoelectric, and dielectric constants of a high-quality monodomain tetragonal Rh:BaTiO3 single crystal are determined at room ...From the sound velocity measured using the Brillouin scattering technique, the elastic, piezoelectric, and dielectric constants of a high-quality monodomain tetragonal Rh:BaTiO3 single crystal are determined at room temperature. The elastic constants are in fairly good agreement with those of the BaTiO3 single crystal, measured previously by Brillouin scattering and the low-frequency equivalent circuit methods. However, their electromeehanical properties are significantly different. Based on the sound propagation equations and these results, the directional dependence of the compressional modulus and the shear modulus of Rh:BaTiO3 in the (010) plane is investigated. Some properties of sound propagation and electromechanical coupling in the crystal are discussed.展开更多
Surface cell Madelung constant is firstly defined for calculating the surface free energy of nanosized crystal grains, which explains the physical performance of small crystals and may be greatly beneficial to the ana...Surface cell Madelung constant is firstly defined for calculating the surface free energy of nanosized crystal grains, which explains the physical performance of small crystals and may be greatly beneficial to the analysis of surface states and the study of the dynamics of crystal nucleation and growth. A new approximative expression of the surface energy and relevant thermodynamic data are used in this calculation. New formula and computing method for calculating the Madelung constant α of any complex crystals are proposed, and the surface free energies and surface electrostatic energies of nanosized crystal grains and the Madelung constant of some complex crystals are theoretically calculated in this paper. The surface free energy of nanosized-crystal-grain TiO2 and the surface electrostatic energy(absolute value) of nanosized-crystal-grain α-Al2O3 are found to be the biggest among all the crystal grains including those of other species.展开更多
The characteristics of photonic forbidden bands, transmission gain and absorption of one-dimensional (ID) dual-periodical photonic crystals (PC) with a complex dielectric layer were studied by using the optical tr...The characteristics of photonic forbidden bands, transmission gain and absorption of one-dimensional (ID) dual-periodical photonic crystals (PC) with a complex dielectric layer were studied by using the optical transfer matrix (TM) method. The results show that the photonic band gap (PBG) of this structure is enlarged and many transmission resonance peaks appear in PBG. Large transmission gain for transmission peaks is obtained if the imaginary part of dielectric constant is negative. With the increase of the absolute value of the imaginary part, the transmission gain increases firstly and the transmittance gain gets to an apex. The imaginary parts of dielectric constant corresponding to transmission gain apex are different according to wavelength. However, the transmission ratio of resonance peaks is less than 1 if the imagi- nary part of dielectric constant is positive. The properties might be used to design multi-narrow-channel band filters and optical amplification devices synchronously.展开更多
Surface cell Madelung constant is firstly defined in calculating surface free energy of nanosized crystal grains, which explains the physical performance of small crystals and may be great benefit to make surface anal...Surface cell Madelung constant is firstly defined in calculating surface free energy of nanosized crystal grains, which explains the physical performance of small crystals and may be great benefit to make surface analysis and study dynamics of crystal nucleus growth. A new approximative expression of surface energy and relevant thermodynamic data was used in this calculation. A new formula and computing method for calculating the Madelung constant a of any complex crystals is proposed, and surface free energies and surface electrostatic energies of nanosized crystal grains as well as Madelung constant of some complex crystals are theoretically calculated in this paper. The surface free energy of nanosized crystal grain TiO2 and surface electrostatic energy(absolute value) of nanosized crystal grain α-A12O3 are found to be the biggest among other crystal grains.展开更多
Euler’s rotation theorem and tensor rotation technique are applied to develop a generalized mathematical model for determining photoelastic constants in arbitrary orientation of cubic crystal system. Two times rotati...Euler’s rotation theorem and tensor rotation technique are applied to develop a generalized mathematical model for determining photoelastic constants in arbitrary orientation of cubic crystal system. Two times rotations are utilized in the model relating to crystallographic coordinates with Cartesian coordinates. The symmetry of photoelastic constants is found to have strong dependence with rotation angle. Using the model, one can determine photoelastic constants in any orientation by selecting appropriate rotation angle. The outcome of this study helps to characterize spatial variation of residual strain in crystalline as well as polycrystalline materials having cubic structure using the experimental technique known as scanning infrared polariscope.展开更多
The propagation characteristics of flexural waves in periodic grid structures designed with the idea of phononic crystals are investigated by combining the Bloch theorem with the finite element method. This combined a...The propagation characteristics of flexural waves in periodic grid structures designed with the idea of phononic crystals are investigated by combining the Bloch theorem with the finite element method. This combined analysis yields phase constant surfaces, which predict the location and the extension of band gaps, as well as the directions and the regions of wave propagation at assigned frequencies. The predictions are validated by computation and experimental analysis of the harmonic responses of a finite structure with 11 × 11 unit cells. The flexural wave is localized at the point of excitation in band gaps, while the directional behaviour occurs at particular frequencies in pass bands. These studies provide guidelines to designing periodic structures for vibration attenuation.展开更多
Two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , are proposed and studied numerically. The band gaps structures of the photonic c...Two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , are proposed and studied numerically. The band gaps structures of the photonic crystals for TE and TM waves are different from the two-dimensional conventional photonic crystals. Some absolute band gaps and semiDirac points are found. When the medium column radius and the function form of the dielectric constant are modulated, the numbers, width, and position of band gaps are changed, and the semi-Dirac point can either occur or disappear. Therefore,the special band gaps structures and semi-Dirac points can be achieved through the modulation on the two-dimensional function photonic crystals. The results will provide a new design method of optical devices based on the two-dimensional function photonic crystals.展开更多
Perovskite [(Ba0.6Sr0.4)TiO3]-[2SiO2-B2O3]-[K2O]-La2O3 glass was prepared by conventional melt quench method. The differential thermal analysis (DTA) was performed on glass sample in the temperature range from 100℃ t...Perovskite [(Ba0.6Sr0.4)TiO3]-[2SiO2-B2O3]-[K2O]-La2O3 glass was prepared by conventional melt quench method. The differential thermal analysis (DTA) was performed on glass sample in the temperature range from 100℃ to 1000℃ by different heating rate to study the crystallization kinematics. The kinetic parameters characterizing the crystallization have been determined using an Arrhenius model. Glass samples were subjected to appropriate heat treatment schedules for their suitable crystallization. X-ray diffraction analysis (XRD) of glass and glass ceramic samples were done to check the amorphous state and crystalline nature. XRD of glass ceramic sample shows the major perovskite phase of BaTiO3 (BT) along with the formation of secondary phases Ba2TiSi2O8 (BTS) and Ba2Ti2B2O9 (BTB). Scanning electron microscopy (SEM) is also studied to see the morphology of the grains of major and secondary phase formation in BST glass ceramic samples. La2O3 is played an important role to increase the nucleation of the crystallites in the glassy matrix. The addition of La22O3 results in development of well interconnected crystallites formed as major phase of BST. In this paper, we are reporting the crystallization behavior of BST borosilicate glass system and high temperature dielectric characteristics of their glass ceramics.展开更多
Na2O-PbO-Nb2O5-SiO2 glass-ceramic were synthesized by melt-quench process. The crystallization processing of the dielectric phases were carried out at temperature range from 750 to 900 ℃. The effects of Na2O content ...Na2O-PbO-Nb2O5-SiO2 glass-ceramic were synthesized by melt-quench process. The crystallization processing of the dielectric phases were carried out at temperature range from 750 to 900 ℃. The effects of Na2O content on crystallization and dielectric properties of Na2O-PbO-Nb2O5-SiO2 glass-ceramic were investigated by means of differential thermal analysis(DTA), X-ray diffraction (XRD) and dielectric constant measurements. The results show that Pb2Nb2O7, NaNbO3 and PbNb2O6 are the crystallization phases which would be formed from the Na2O-PbO-Nb2O5-SiO2 glass at the temperature range from 750 to 900 ℃. For a definite Na2O content, the dielectric constant increases with crystallization temperature. The initial crystallization temperature of NaNbO3 phase decreases with the increase of Na2O content, leading to the increase of dielectric constant of the glass-ceramic. Formation of PbNb2O6 phase at 850 and 900 ℃ would greatly increase the dielectric constant of Na2O-PbO-Nb2O5-SiO2 glass-ceramics, but the increase of Na2O content will inhibit the crystallization of PbNb2O6 phase.展开更多
In this work we study the behaviour of the dielectric constant of BaTiO3 single crystals doped with Cu and Fe for different ion percentages, particularly, the influence of these heterovalent substitutions on the ferro...In this work we study the behaviour of the dielectric constant of BaTiO3 single crystals doped with Cu and Fe for different ion percentages, particularly, the influence of these heterovalent substitutions on the ferroelectric-paraelectric phase transition whose temperature is found at Tc=120 °C for pure samples. The dielectric constant ε in terms of temperature shows that the Curie temperature decreases when the quantity of impurities increases and presents a broadening and flattering of the maxi-mum of ε(T) within higher values, with the transition becoming more and more diffuse. It is interesting to have a material with very high permittivity (high-k) because of its capacity to store an important quantity of electric charges. The ε anisotropy and the Curie-Weiss law are also verified with a good ratio between the slopes of ε-1(T) from both sides of the transition, leading to a Curie constant:C=13×104 K for BaTiO3:1.6%Fe in the polar phase. BaTiO3 is a displacive ferroelectric going through a first-order phase transition. The substitutions have an effect on the dynamics of the perovskite lattice. They induce charges transfer to Ti and a diminution of elastic forces in BaTiO3. Then we discuss the fact that the maximum of permittivity does not depend on the phase transition but on the nature of the material.展开更多
Single crystals of Glycine Zinc Chloride (GZC) were grown from aqueous solution by slow evaporation technique. Single crystal X-ray diffraction analysis reveals that the crystal belongs to orthorhombic system with the...Single crystals of Glycine Zinc Chloride (GZC) were grown from aqueous solution by slow evaporation technique. Single crystal X-ray diffraction analysis reveals that the crystal belongs to orthorhombic system with the space group Pna21.The optical transmission study reveals the transparency of the crystal in the entire visible region and the cut off wavelength has been found to be 230 nm. The optical band gap is found to be 3.40eV. The transmittance of GZC crystal has been used to calculate the refractive index (n), the extinction coefficient (K) and the real er and imaginary ei components of the dielectric constant. Mechanical studies were carried out on the as grown crystal. Dielectric constant and dielectric loss measurements were carried out at different temperatures and frequencies. Photoconductivity measurements carried out on the grown crystal reveal the negative photoconducting nature.展开更多
Crystallization of enzymes in presence of impurities is important for clarifying the role of enzymes in natural world. Although it is proposed that impurities inhibit nucleation of enzyme crystallization, details are ...Crystallization of enzymes in presence of impurities is important for clarifying the role of enzymes in natural world. Although it is proposed that impurities inhibit nucleation of enzyme crystallization, details are unclear. In this study, crystallization of cellobiohydrolase from Aspergillus niger was investigated by dynamic and time-resolved static light scattering using cellobiose as an impurity. We aimed to clarify how cellobiose inhibits cellobiohydrolase crystallization and to crystallize cellobiohydrolase in concentrated cellobiose without using seeds. The contribution of attractive forces to total intermolecular interactions of cellobiohydrolase monomers increased with the molar ratio of cellobiose/cellobiohydrolase (R(cb/ce)). Association dynamics of cellobiohydrolase using lithium sulfate, however, showed that the initial aggregation rate decreased with an increase in R(cb/ce). Because binding sites of cellobioses to cellobiohydrolase molecules differed from those for the growth of protein crystals, the binding of cellobioses would increase the chemical potential of the cellobiohydrolase monomers, which gradually reduced supersaturation for growth as the aggregate size increased. This result was in contrast with the conventional idea that cellobiose inhibits the nucleation of cellobiohydrolase crystals. Gentle agitation of cellobiose-containing cellobiohydrolase solutions during sitting-drop vapor-diffusion growth resulted in the growth of cellobiohydrolase single crystals for all R(cb/ce) conditions without using seeds.展开更多
The definitions of the third-order elastic,piezoelectric,and dielectric constants and the properties of the associated tensors are discussed.Based on the energy conservation and coordinate transformation,the relations...The definitions of the third-order elastic,piezoelectric,and dielectric constants and the properties of the associated tensors are discussed.Based on the energy conservation and coordinate transformation,the relations among the third-order constants are obtained.Furthermore,the relations among the third-order elastic,piezoelectric,and dielectric constants of the seven crystal systems and isotropic materials are listed in detail.These third-order constants relations play an important role in solving nonlinear problems of elastic and piezoelectric materials.It is further found that all third-order piezoelectric constants are 0 for 15 kinds of point groups,while all third-order dielectric constants are 0 for 16 kinds of point groups as well as isotropic material.The reason is that some of the point groups are centrally symmetric,and the other point groups are high symmetry.These results provide the foundation to measure these constants,to choose material,and to research nonlinear problems.Moreover,these results are helpful not only for the study of nonlinear elastic and piezoelectric problems,but also for the research on flexoelectric effects and size effects.展开更多
文摘In ferroelectric liquid crystals, phase transitions can be induced by an electric field. The current constant method allows these transition to be quickly localized and thus the(E, T) phase diagram of the studied product can be obtained.In this work, we make a slight modification to the measurement principles based on this method. This modification allows the characteristic parameters of ferroelectric liquid crystal to be quantitatively measured. The use of a current square signal highlights a phenomenon of ferroelectric hysteresis with remnant polarization at null field, which points out an effect of memory in this compound.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10874236 and 60808010)
文摘From the sound velocity measured using the Brillouin scattering technique, the elastic, piezoelectric, and dielectric constants of a high-quality monodomain tetragonal Rh:BaTiO3 single crystal are determined at room temperature. The elastic constants are in fairly good agreement with those of the BaTiO3 single crystal, measured previously by Brillouin scattering and the low-frequency equivalent circuit methods. However, their electromeehanical properties are significantly different. Based on the sound propagation equations and these results, the directional dependence of the compressional modulus and the shear modulus of Rh:BaTiO3 in the (010) plane is investigated. Some properties of sound propagation and electromechanical coupling in the crystal are discussed.
文摘Surface cell Madelung constant is firstly defined for calculating the surface free energy of nanosized crystal grains, which explains the physical performance of small crystals and may be greatly beneficial to the analysis of surface states and the study of the dynamics of crystal nucleation and growth. A new approximative expression of the surface energy and relevant thermodynamic data are used in this calculation. New formula and computing method for calculating the Madelung constant α of any complex crystals are proposed, and the surface free energies and surface electrostatic energies of nanosized crystal grains and the Madelung constant of some complex crystals are theoretically calculated in this paper. The surface free energy of nanosized-crystal-grain TiO2 and the surface electrostatic energy(absolute value) of nanosized-crystal-grain α-Al2O3 are found to be the biggest among all the crystal grains including those of other species.
基金supported by the Natural Science Foundation of China (Nos. 50061001 and 50661001)the Science Foundation of Guangxi Province,China(Nos. 0991026,0832029 and 0639004)
文摘The characteristics of photonic forbidden bands, transmission gain and absorption of one-dimensional (ID) dual-periodical photonic crystals (PC) with a complex dielectric layer were studied by using the optical transfer matrix (TM) method. The results show that the photonic band gap (PBG) of this structure is enlarged and many transmission resonance peaks appear in PBG. Large transmission gain for transmission peaks is obtained if the imaginary part of dielectric constant is negative. With the increase of the absolute value of the imaginary part, the transmission gain increases firstly and the transmittance gain gets to an apex. The imaginary parts of dielectric constant corresponding to transmission gain apex are different according to wavelength. However, the transmission ratio of resonance peaks is less than 1 if the imagi- nary part of dielectric constant is positive. The properties might be used to design multi-narrow-channel band filters and optical amplification devices synchronously.
文摘Surface cell Madelung constant is firstly defined in calculating surface free energy of nanosized crystal grains, which explains the physical performance of small crystals and may be great benefit to make surface analysis and study dynamics of crystal nucleus growth. A new approximative expression of surface energy and relevant thermodynamic data was used in this calculation. A new formula and computing method for calculating the Madelung constant a of any complex crystals is proposed, and surface free energies and surface electrostatic energies of nanosized crystal grains as well as Madelung constant of some complex crystals are theoretically calculated in this paper. The surface free energy of nanosized crystal grain TiO2 and surface electrostatic energy(absolute value) of nanosized crystal grain α-A12O3 are found to be the biggest among other crystal grains.
文摘Euler’s rotation theorem and tensor rotation technique are applied to develop a generalized mathematical model for determining photoelastic constants in arbitrary orientation of cubic crystal system. Two times rotations are utilized in the model relating to crystallographic coordinates with Cartesian coordinates. The symmetry of photoelastic constants is found to have strong dependence with rotation angle. Using the model, one can determine photoelastic constants in any orientation by selecting appropriate rotation angle. The outcome of this study helps to characterize spatial variation of residual strain in crystalline as well as polycrystalline materials having cubic structure using the experimental technique known as scanning infrared polariscope.
基金Project supported by the National Natural Science Foundation of China (Grant No 50875255)
文摘The propagation characteristics of flexural waves in periodic grid structures designed with the idea of phononic crystals are investigated by combining the Bloch theorem with the finite element method. This combined analysis yields phase constant surfaces, which predict the location and the extension of band gaps, as well as the directions and the regions of wave propagation at assigned frequencies. The predictions are validated by computation and experimental analysis of the harmonic responses of a finite structure with 11 × 11 unit cells. The flexural wave is localized at the point of excitation in band gaps, while the directional behaviour occurs at particular frequencies in pass bands. These studies provide guidelines to designing periodic structures for vibration attenuation.
基金Project supported by the National Natural Science Foundations of China(Grant No.61275047)the Research Project of Chinese Ministry of Education(Grant No.213009A)the Scientific and Technological Development Foundation of Jilin Province,China(Grant No.20130101031JC)
文摘Two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , are proposed and studied numerically. The band gaps structures of the photonic crystals for TE and TM waves are different from the two-dimensional conventional photonic crystals. Some absolute band gaps and semiDirac points are found. When the medium column radius and the function form of the dielectric constant are modulated, the numbers, width, and position of band gaps are changed, and the semi-Dirac point can either occur or disappear. Therefore,the special band gaps structures and semi-Dirac points can be achieved through the modulation on the two-dimensional function photonic crystals. The results will provide a new design method of optical devices based on the two-dimensional function photonic crystals.
文摘Perovskite [(Ba0.6Sr0.4)TiO3]-[2SiO2-B2O3]-[K2O]-La2O3 glass was prepared by conventional melt quench method. The differential thermal analysis (DTA) was performed on glass sample in the temperature range from 100℃ to 1000℃ by different heating rate to study the crystallization kinematics. The kinetic parameters characterizing the crystallization have been determined using an Arrhenius model. Glass samples were subjected to appropriate heat treatment schedules for their suitable crystallization. X-ray diffraction analysis (XRD) of glass and glass ceramic samples were done to check the amorphous state and crystalline nature. XRD of glass ceramic sample shows the major perovskite phase of BaTiO3 (BT) along with the formation of secondary phases Ba2TiSi2O8 (BTS) and Ba2Ti2B2O9 (BTB). Scanning electron microscopy (SEM) is also studied to see the morphology of the grains of major and secondary phase formation in BST glass ceramic samples. La2O3 is played an important role to increase the nucleation of the crystallites in the glassy matrix. The addition of La22O3 results in development of well interconnected crystallites formed as major phase of BST. In this paper, we are reporting the crystallization behavior of BST borosilicate glass system and high temperature dielectric characteristics of their glass ceramics.
文摘Na2O-PbO-Nb2O5-SiO2 glass-ceramic were synthesized by melt-quench process. The crystallization processing of the dielectric phases were carried out at temperature range from 750 to 900 ℃. The effects of Na2O content on crystallization and dielectric properties of Na2O-PbO-Nb2O5-SiO2 glass-ceramic were investigated by means of differential thermal analysis(DTA), X-ray diffraction (XRD) and dielectric constant measurements. The results show that Pb2Nb2O7, NaNbO3 and PbNb2O6 are the crystallization phases which would be formed from the Na2O-PbO-Nb2O5-SiO2 glass at the temperature range from 750 to 900 ℃. For a definite Na2O content, the dielectric constant increases with crystallization temperature. The initial crystallization temperature of NaNbO3 phase decreases with the increase of Na2O content, leading to the increase of dielectric constant of the glass-ceramic. Formation of PbNb2O6 phase at 850 and 900 ℃ would greatly increase the dielectric constant of Na2O-PbO-Nb2O5-SiO2 glass-ceramics, but the increase of Na2O content will inhibit the crystallization of PbNb2O6 phase.
文摘In this work we study the behaviour of the dielectric constant of BaTiO3 single crystals doped with Cu and Fe for different ion percentages, particularly, the influence of these heterovalent substitutions on the ferroelectric-paraelectric phase transition whose temperature is found at Tc=120 °C for pure samples. The dielectric constant ε in terms of temperature shows that the Curie temperature decreases when the quantity of impurities increases and presents a broadening and flattering of the maxi-mum of ε(T) within higher values, with the transition becoming more and more diffuse. It is interesting to have a material with very high permittivity (high-k) because of its capacity to store an important quantity of electric charges. The ε anisotropy and the Curie-Weiss law are also verified with a good ratio between the slopes of ε-1(T) from both sides of the transition, leading to a Curie constant:C=13×104 K for BaTiO3:1.6%Fe in the polar phase. BaTiO3 is a displacive ferroelectric going through a first-order phase transition. The substitutions have an effect on the dynamics of the perovskite lattice. They induce charges transfer to Ti and a diminution of elastic forces in BaTiO3. Then we discuss the fact that the maximum of permittivity does not depend on the phase transition but on the nature of the material.
文摘Single crystals of Glycine Zinc Chloride (GZC) were grown from aqueous solution by slow evaporation technique. Single crystal X-ray diffraction analysis reveals that the crystal belongs to orthorhombic system with the space group Pna21.The optical transmission study reveals the transparency of the crystal in the entire visible region and the cut off wavelength has been found to be 230 nm. The optical band gap is found to be 3.40eV. The transmittance of GZC crystal has been used to calculate the refractive index (n), the extinction coefficient (K) and the real er and imaginary ei components of the dielectric constant. Mechanical studies were carried out on the as grown crystal. Dielectric constant and dielectric loss measurements were carried out at different temperatures and frequencies. Photoconductivity measurements carried out on the grown crystal reveal the negative photoconducting nature.
基金ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (No.20473108, No.10672173, and No.10432060) and the "Chuang-xin Project" of the Chinese Academy of Sciences.
文摘Crystallization of enzymes in presence of impurities is important for clarifying the role of enzymes in natural world. Although it is proposed that impurities inhibit nucleation of enzyme crystallization, details are unclear. In this study, crystallization of cellobiohydrolase from Aspergillus niger was investigated by dynamic and time-resolved static light scattering using cellobiose as an impurity. We aimed to clarify how cellobiose inhibits cellobiohydrolase crystallization and to crystallize cellobiohydrolase in concentrated cellobiose without using seeds. The contribution of attractive forces to total intermolecular interactions of cellobiohydrolase monomers increased with the molar ratio of cellobiose/cellobiohydrolase (R(cb/ce)). Association dynamics of cellobiohydrolase using lithium sulfate, however, showed that the initial aggregation rate decreased with an increase in R(cb/ce). Because binding sites of cellobioses to cellobiohydrolase molecules differed from those for the growth of protein crystals, the binding of cellobioses would increase the chemical potential of the cellobiohydrolase monomers, which gradually reduced supersaturation for growth as the aggregate size increased. This result was in contrast with the conventional idea that cellobiose inhibits the nucleation of cellobiohydrolase crystals. Gentle agitation of cellobiose-containing cellobiohydrolase solutions during sitting-drop vapor-diffusion growth resulted in the growth of cellobiohydrolase single crystals for all R(cb/ce) conditions without using seeds.
基金Project supported by the National Natural Science Foundation of China(Nos.11872186 and11272126)the Fundamental Research Funds for the Central Universities(No.HUST:2016JCTD114)
文摘The definitions of the third-order elastic,piezoelectric,and dielectric constants and the properties of the associated tensors are discussed.Based on the energy conservation and coordinate transformation,the relations among the third-order constants are obtained.Furthermore,the relations among the third-order elastic,piezoelectric,and dielectric constants of the seven crystal systems and isotropic materials are listed in detail.These third-order constants relations play an important role in solving nonlinear problems of elastic and piezoelectric materials.It is further found that all third-order piezoelectric constants are 0 for 15 kinds of point groups,while all third-order dielectric constants are 0 for 16 kinds of point groups as well as isotropic material.The reason is that some of the point groups are centrally symmetric,and the other point groups are high symmetry.These results provide the foundation to measure these constants,to choose material,and to research nonlinear problems.Moreover,these results are helpful not only for the study of nonlinear elastic and piezoelectric problems,but also for the research on flexoelectric effects and size effects.