Theoretical Studies On Dielectric Properties Of ReCa₄O（BO₃）₃ Crystals

Rare-earth calcium oxyborates ReCa4O(BO3)3(abbreviated as ReCOB,Re represents a rare earth ion)is a new type of piezoelectric crystal materials which has excellent electrical,optical,and thermodynamic properties,It found to be promising for ultrahigh temperature sensing applications.Dielectric properties is one of the important electrical properties of ReCOB and comprehensively reflects the storage and loss of electrostatic energy by the medium.The dielectric properties of ReCOB can be adjusted by means of component regulation,which can modulate their electroelastic properties and be used to optimize the best crystal cutting type for sensor design.Therefore,exploring the dielectric properties of ReCOB is of great significance to promote their high temperature application on electrical sensor devices.It has been reported that the dielectric properties of ReCOB crystals can be modulated by changing the Re3+ ions.The relative dielectric permittivity ε22T/ε0 was found to increase with increasing the radius of the Re3+ ion,and this was deemed to be associated with Re3+ ion-induced lattice distortion and disorder in the distribution of Re3+ and Ca2+ ions in the lattice.However,the relationship between the relative dielectric component and the radius of rare earth cation is not a perfect linear increase,the ε22T/ε0 of LaCOB was found to exhibit an abnormal decrease.The inflection point indicates that the rare earth cation radius is not the only factor that determines the dielectric properties of ReCOB crystals.The unknown regulatory factors have made it difficult to optimize the dielectric properties of ReCOB crystals.Microscopically,the dielectric permittivity is related to the polarization and the movement of free charge.Increasing the Re3+ ion radius could induce larger lattice distortion of the ReO6 octahedron,resulting in greater polarization and higher dielectric permittivity of ReCOB crystals.At the same time,the polarization is also influenced by the orbital hybridizations of Re3+ and its neighboring O atoms.The electronic configurations of the Re3+ ions,and the relationship between the electronic distribution of Re d or f orbitals and the spatial configuration of ReO6 octahedron,can thus be regarded as potentially important factors that can influence the dielectric permittivity of ReCOB.In addition,disorder structures such as antisite and vacancy defects could further increase the polarization of ReCOB crystals.Intrinsic defects could trap electrons or holes,and turn into charged defects,forming a potential well at the defect site.It will block the movement of free carriers in the crystal by electro-acoustic coupling interactions,and ultimately affecting the dielectric properties of ReCOB.In conclusion,the factors which affect the dielectric permittivity of ReCOB are quite complicated and microscopic.Considering that experimental characterizations are limited to detecting the microstructure,electronic structure and phonon properties of ReCOB,it is of great importance to use theoretical methods to explore the influence of microscopic lattice distortions,electronic structures,and lattice vibrations on the dielectric properties of ReCOB crystals However,relevant theoretical work is quite scarce as the ReCOB are quaternary crystals and their components are complicated,and the difficulty in accurately describing the electronic configurations of rare earth ions.In this thesis,we select YCOB,PrCOB and LaCOB as representative to explore the key factors affecting macroscopic dielectric properties of ReCOB and its microscopic mechanism,and find the origin of the abnormal drop in the dielectric component 82r2/6:o of LaCOB.It is conducive to regulate the dielectric properties of ReCOB crystals through component design,so as to get new high temperature piezoelectric materials which have better performanceBased on the first-principle calculations,we carry out systematic research on the dielectric properties of ReCOB(Re=Y,Pr,La,hereinafter referred to as ReCOB)crystals.We analyze the crystals structures and get the optical band gaps of ReCOB The geometric and electronic structures of these three crystals have been calculated using different functionals.By comparing with the experimental results,the most suitable functional for calculating the ground state properties of ReCOB crystals has thus been obtained.On this basis,the frequency-dependent dielectric functions and the static dielectric permittivity of ReCOB are studied.We also explore the existence form of intrinsic defects in crystals and how they affect the static dielectric permittivity of crystals microscopically.The main research contents and results are as follow:In chapter one,we mainly introduce the research background and significance of this work.We firstly introduce the research progress of ReCOB crystals,and the structure as well as dielectric properties of ReCOB crystals are presented in a general way.Finally,the significance and research ideas of this thesis are clarifiedIn chapter two,we introduce the basic principle of density functional theory and density functional perturbation theory.The approximate functional of exchange correlation and the calculation process of self-consistent field is also introduced.On this basis,the VASP software package used in the thesis is introducedIn chapter three,we get crystal structure parameters of ReCOB by experiments,and obtain the band gaps by absorption spectrum.Based on the density functional theory,we study the structures and electronic properties of ReCOB using GGA-PBE,HSE06 and GGA+U.Compared with experiments,we evaluate the accuracy and rationality of different exchange correlation functionals and correction methods for describing the crystal structures and electronic properties of which include rare earth ions.Research have shown that the GGA-PBE is the most suitable functional for describing the crystal structure,while the GGA+U for describing the electronic properties.As to GGA+U,we test a series of Ueff values to fit the experimental band gap.For YCOB and LaCOB,it is found that only if applying Ueff to the O-2p and Y-4d/La-5d states at the same time,the obtained band gap could be consistent with the experimental value.However,for PrCOB,we could get the reasonable band gap only applying Ueff to the Pr 4f states.By further evaluating the electronic structure such as the density of states,we choose GGA+U to calculate the electronic structures and dielectric properties of ReCOB.In chapter four,we study the frequency-dependent dielectric functions and the static dielectric permittivity of ReCOB(Re=Y,Pr,La).Research have shown that PrCOB has a larger dielectric loss than YCOB and LaCOB in the high frequency range,which is consistent with the phenomenon observed in the experiments.It indicates that more energy is consumed during the electronic transition in PrCOB,thus it is not suitable for application in light-emitting devices.As the frequency approaches zero,the static dielectric permittivity of ReCOB is the result of the electronic polarization and ionic displacement polarization,while the contribution of ionic polarization to the dielectric response is larger than that of the electronic polarization.It is seen that the electronic contributions are isotropic for YCOB,PrCOB,and LaCOB,and the exact values for the three crystals are almost the same.The phonon contributions are anisotropic,with the values of εPh.22 distinctly larger than the other components.It is the main reason for the difference in dielectric permittivity of different crystals.By estimating the local polarization of LaO6 and PrO6 octahedra,it is found that the decrease in the dielectric component ε22 of LaCOB relative to PrCOB is attributed to the displacement of 04 atoms in LaO6 octahedron is smaller than that of PrO6,resulting in a smaller ionic polarization.It ultimately leads to a lower dielectric component ε22 of LaCOB.Finally,by comparing the calculated static dielectric permittivity with experimental values,we speculate that intrinsic defects are also one of the important factors affecting the dielectric properties of ReCOBIn chapter five,we study the effect of intrinsic antisite defects on the dielectric properties of ReCOB and its micro-mechanism.Through structural analysis we find that there are CaY/La,Y/LaCa1 and Y/Laca2 three types intrinsic defects in YCOB and LaCOB.But PrCOB contains almost no intrinsic defects.The calculation results of defect formation energies further show that Cay and Yca2 are the main intrinsic defects in YCOB.The formation energies of three types of defects for PrCOB are too high to form.The defects Laca1 and Laca2 are the main intrinsic defects in LaCOB.Research have shown that the intrinsic defects do play an important role in the dielectric properties of ReCOB.Taking the defects Cay and Yca2 into consideration make the dielectric constants of YCOB significantly improved,and they are more identical to the experimental values.For PrCOB,the dielectric constants deviate from the experimental value after taking intrinsic defects into consideration.In contrast,the calculated dielectric constants of pristine PrCOB are more consistent with experiments,which further proves that the PrCOB crystals we have grown are defect-free.In LaCOB.the charged defects Laca1+ and Laca2+ play an important role in improving the dielectric component E22 of LaCOB and the calculated results are very close to the experimental values.Further research have shown that the La atom at the defect site generates a large vibration amplitude in the y direction,and has a strong interaction with the neighboring O atoms,which results in a strong ionic polarization in the y direction.This eventually leads to an increase in the dielectric component ε22In chapter six,the main conclusions and innovations of this thesis are summarized,and we also put forward the next research plan.