A method for screening strontium potassium niobate ceramics with high spontaneous polarization

Abstract

This invention discloses a method for screening potassium strontium niobate ceramics with high spontaneous polarization intensity, by considering the KSN under high-temperature sintering K + and Sr 2+ And a small amount of Nb 5+ It is easily volatile, and at the same time, it generates oxygen vacancies, introducing oxygen vacancies and A-site cations (K). + and Sr 2+ ) vacancy and B-site cation (Nb1) 5+ and Nb2 5+ Based on the first-principles calculation approach, oxygen vacancies and A-site cation vacancies (K) are calculated. + Empty space, Sr 2+ (vacancy) and oxygen vacancy, B-site cation vacancy (Nb 5+ The spontaneous polarization intensity of potassium strontium niobate with vacancies and oxygen vacancies was investigated to screen out potassium strontium niobate ceramics with high spontaneous polarization intensity. Theoretical calculations were performed using first-principles methods to theoretically screen out potassium strontium niobate material components with high spontaneous polarization intensity, enabling on-demand design, shortening the research and development cycle, providing theoretical guidance for actual experiments, and saving experimental time and costs.

Description

Technical Field

[0001] This invention belongs to the field of oxide ceramics technology, specifically relating to a method for screening potassium strontium niobate ceramics with high spontaneous polarization intensity. Background Technology

[0002] Ferroelectric materials are materials that exhibit spontaneous polarization within a certain temperature range, varying with an external electric field. Within ferroelectric materials, the shift in the centers of positive and negative charges generates electric dipole moments, resulting in spontaneous polarization within the crystal. Polarization intensity is a crucial physical quantity for evaluating their ferroelectric properties; their macroscopic electrical properties, such as dielectric constant and conductivity, are related to the spontaneous polarization intensity at the unit cell scale. Due to their unique dielectric, piezoelectric, pyroelectric, and ferroelectric properties, as well as their excellent electro-optic, acousto-optic, photorefractive, and nonlinear optical effects, ferroelectric materials play a vital role in the fabrication and research of novel components such as ferroelectric memories, pyroelectric infrared detectors, and dielectric phase shifters.

[0003] Lead-free ferroelectric ceramics not only possess satisfactory performance characteristics but also lack lead and other substances that may harm the ecological environment, humans, and organisms, thus demonstrating promising development prospects. In particular, lead-free ferroelectric ceramics with a tungsten bronze structure have attracted increasing attention, among which potassium strontium niobate crystals (KSr2Nb5O3) with a tetragonal tungsten bronze structure have received growing attention. 15 Surface acoustic wave (SAW) materials, or KSNs for short, possess significant optical birefringence, strong spontaneous polarization, and high electro-optic coefficients, making them promising for applications in optoelectronics, ferroelectrics, and dielectrics. They can be used to manufacture electronic components such as SAW filters, oscillators, temperature compensators, and photocatalysts. Since the spontaneous polarization of most displacement ferroelectrics is due to the distortion of the oxygen octahedron, with the central atom deviating from its centrosymmetric position and increasing the dipole moment, the influence of intrinsic and extrinsic defects on the material's electrical properties is also manifested through microscopic polarization intensity. Therefore, the central atom of the octahedron plays a crucial role in the polarization of ferroelectrics. For KSNs with a tungsten bronze structure, studying the influence of the oxygen octahedron central atom on polarization is essential. One feasible method to improve the ferroelectric properties is to introduce suitable cation vacancies to form defect dipoles with oxygen vacancies, increasing the induced dipole moment and spontaneous polarization intensity, thereby improving the dielectric constant and ultimately enhancing the spontaneous polarization intensity.

[0004] In DOI: 10.1016 / j.physb.2021.413038, Qian Chen et al. published "Spontaneous electric polarization of high-valance-ion-doped lead-free ferroelectric KSr2Nb5O". 15The paper, titled "First-principles calculations," investigates the high-valent cation La using first-principles calculations. 3+ ,Bi 3+ ,Y 3+ Ti 4+ ,Ta 5+ and W 6+ KSr2Nb5O doped 15 The spontaneous polarization intensity of KSr2Nb5O is shown in the study results. 15 The polarization intensity was improved. However, this paper only studied the effect of cation doping substitution on the spontaneous polarization intensity of KSN from a theoretical perspective. In actual experiments, KSN under high-temperature sintering K + and Sr 2+ And a small amount of Nb 5+ It is easily volatile, and the generation of oxygen vacancies is also present, so the model established in this paper cannot better reflect the actual situation. Furthermore, the cross-correlation pseudopotential used in the calculation process of this paper to optimize the unit cell structure is LDA(CA-PZ), and the optimized KSN unit cell volume is... The cell volume of KSN in the PDF card The difference is significant. Since the gap between the optimized cell structure and the actual cell volume has a great impact on the stability and performance of the material system, it is essential to select a more appropriate pseudopotential to obtain a crystal structure that better matches the actual structure.

[0005] In DOI: 10.1002 / pssb.202100488, Qian Chen et al. published "Effect of intrinsic Nb 5+ vacancy on dielectric and polarization behaviors of KSr2Nb5O 15 The paper, titled "First-principles investigation," investigates Nb using first-principles calculations. 5+ The influence of vacancies on the spontaneous polarization behavior of KSNs was investigated. However, the cell model established in this paper is based solely on theoretical research, and its application to studying the influence of vacancy defects on the spontaneous polarization intensity of KSNs in actual experimental processes is still lacking. Furthermore, the cell volume optimized using the cross-correlated pseudopotential LDA (CA-PZ) differs significantly from that in the PDF card, indicating a need to select a more suitable pseudopotential for further optimization of the cell structure.

[0006] The macroscopic polarization intensity of KSN bulk materials can be obtained by testing the hysteresis loop, but the spontaneous polarization intensity at the unit cell scale is difficult to measure experimentally and needs to be obtained by calculation using first-principles methods to further understand the intrinsic relationship between intrinsic and non-intrinsic defects, microscopic polarization intensity and macroscopic polarization intensity. Summary of the Invention

[0007] To overcome the shortcomings of the prior art, the present invention aims to provide a method for screening potassium strontium niobate ceramics with high spontaneous polarization intensity, by considering the KSN under high-temperature sintering K + and Sr 2+ And a small amount of Nb 5+ It is easily volatile, and at the same time, it generates oxygen vacancies, introducing oxygen vacancies and A-site cations (K). + and Sr 2+ ) vacancy and B-site cation (Nb1) 5+ and Nb2 5+ Based on the first-principles calculation approach, oxygen vacancies and A-site cation vacancies (K) are calculated. + Empty space, Sr 2+ (vacancy) and oxygen vacancy, B-site cation vacancy (Nb 5+ The spontaneous polarization intensity of potassium strontium niobate with vacancies and oxygen vacancies was used to screen out potassium strontium niobate ceramics with high spontaneous polarization intensity.

[0008] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0009] A method for screening potassium strontium niobate with high spontaneous polarization intensity includes the following steps:

[0010] Step 1, construct KSr2Nb5O 15 The cell structure model is denoted as KSN, and its cell structure is ordered.

[0011] Step 2, based on the ordered KSr2Nb5O in Step 1 15 The cell structure of KSr2Nb5O was constructed with oxygen vacancies, A-site cation vacancies and oxygen vacancies, and B-site cation vacancies and oxygen vacancies. 15 The unit cell structure models are denoted as KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O, and KSN-Nb2&O, respectively.

[0012] Step 3: Use VASPKIT software to perform convergence tests on the KSN obtained in Step 1 and the KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O and KSN-Nb2&O obtained in Step 2 respectively, and determine the calculation parameters when the system reaches convergence.

[0013] Step 4: Based on the calculation parameters when the system reaches convergence in Step 3, the KSN obtained in Step 1 and the KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O and KSN-Nb2&O unit cell structures obtained in Step 2 are optimized using CASTEP software to achieve the lowest energy of the system and obtain the most stable unit cell structure.

[0014] Step 5: Use CASTEP software to calculate the optical frequency dielectric constants of the most stable KSN, KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O and KSN-Nb2&O unit cell structures in Step 4, respectively.

[0015] Step 6: Based on the Clausius-Mosotti equation, calculate the ionic polarizability of the most stable KSN, KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O and KSN-Nb2&O unit cell structures in Step 4, respectively.

[0016] Step 7: Calculate the spontaneous polarization intensity range of the KSN unit cell structure based on the ionic polarizability of the KSN unit cell structure obtained in Step 6.

[0017] Step 8: Based on the spontaneous polarization intensity range of KSN obtained in Step 7, calculate the built-in electric field range, and then, based on the relationship between spontaneous polarization intensity and built-in electric field, obtain the spontaneous polarization intensity of the most stable KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O and KSN-Nb2&O unit cell structures in Step 4.

[0018] Step 9: Based on the spontaneous polarization intensity range of the KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O and KSN-Nb2&O cell structures obtained in Step 8, select potassium strontium niobate ceramics with high spontaneous polarization intensity.

[0019] In step 2, KSr2Nb5O is constructed with oxygen vacancies, A-site cation vacancies and oxygen vacancies, and B-site cation vacancies and oxygen vacancies. 15 The process of modeling the unit cell structure is as follows:

[0020] Delete KSr2Nb5O 15 One O atom in the unit cell structure corresponds to a vacancy concentration of 2.17 atom%, yielding K2Sr4Nb. 10 O 29 The unit cell structure is denoted as KSN-O;

[0021] Delete KSr2Nb5O 15A K atom and an O atom in the unit cell structure correspond to a vacancy concentration of 4.35 atom%, yielding KSr4Nb. 10 O 29 The unit cell structure is denoted as KSN-K&O;

[0022] Delete KSr2Nb5O 15 A single Sr atom and one O atom in the unit cell structure correspond to a vacancy concentration of 4.35 atom%, yielding K2Sr3Nb. 10 O 29 The unit cell structure is denoted as KSN-Sr&O;

[0023] Delete KSr2Nb5O 15 The vacancy concentration of Nb and O atoms at the Nb1 positions in the unit cell structure is 4.35 atom%, yielding K2Sr4Nb9O. 29 The unit cell structure is denoted as KSN-Nb1&O;

[0024] Delete KSr2Nb5O 15 The Nb and O atoms located at the Nb2 positions in the unit cell structure have a vacancy concentration of 4.35 atom%, yielding K2Sr4Nb9O. 29 The cell structure of it is denoted as KSN-Nb2&O.

[0025] 3. The method for screening potassium strontium niobate with high spontaneous polarization intensity according to claim 1, characterized in that, in step 3, the KSN obtained in step 1 and the KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O and KSN-Nb2&O obtained in step 2 are subjected to convergence tests using the PBE pseudopotential library in VASPKIT software, and the cutoff energy is determined to be 750 eV, the k-point is 6×6×6, and the energy convergence criterion is 4.0×10⁻⁶. -5 eV, the convergence criterion for force is that a single atom is less than... The maximum displacement is

[0026] The process of calculating ion polarizability based on the Clausius-Mosotti equation in step 6 is as follows:

[0027] The Clausius-Mosotti equation is expressed as follows:

[0028]

[0029] Where, ε r ε represents the relative permittivity, and ε0 represents the vacuum permittivity, 8.85 × 10⁻⁶. -12 F / m, α represents ionic polarizability, and n0 represents the number of polarized particles per unit volume of dielectric.

[0030] If we replace the volume with molar volume M / ρ, then we have:

[0031]

[0032] Where N0 represents Avogadro's constant, with units of mol. -1 M represents the molar mass of the dielectric, and ρ represents the density;

[0033] because

[0034] Where V is the unit cell volume;

[0035] Substituting formula (3) into the transformation of formula (2): get:

[0036]

[0037] At optical frequencies, the relative permittivity ε of the dielectric is... r The usable optical frequency dielectric constant ε ∞ In this case, equation (1) can be expressed as:

[0038]

[0039] The optical frequency dielectric constant ε at the optical frequency is calculated based on the first-principles calculation in step 5. ∞ The product of the number of polarized particles n0 and the ionic polarizability α per unit volume of the material is calculated using formula (5); and the number of polarized particles n0 per unit volume is obtained from formula (4), and then the ionic polarizability α is obtained.

[0040] The process of calculating the spontaneous polarization intensity range of the KSN unit cell structure in step 7 is as follows:

[0041] Step 7.1: Calculate the dipole moment of KSN using both experimental methods and first-principles calculations, i.e.:

[0042] Method 1: Calculate the dipole moment of KSN according to the experimental method:

[0043] The Curie temperature T of KSN obtained according to experimental methods c To obtain Nb in KSN 5+ The offset Δz is then used to obtain the dipole moment of KSN;

[0044] The displacement Δz of the cation deflection charge center in the displacement-type ferroelectric cell is related to the Curie temperature T. c The relationship is as follows:

[0045] T C =2×10 4(Δz) 2 (6)

[0046] Among them, T c This indicates the Curie temperature, measured in Kelvin (K).

[0047] The relationship between the displacement Δz of the cation shift charge center in the displacement ferroelectric cell and the dipole moment of KSN is as follows:

[0048] μ KSN =nqΔz (7)

[0049] Where, μ KSN The value represents the dipole moment of KSN, in C·m; n represents the number of atoms; q represents the unit charge, 1.6 × 10⁻⁶. -19 C;

[0050] Method 2: Calculate the dipole moment of KSN based on first-principles calculations:

[0051] The most stable KSN unit cell structure obtained in step 4 is input into VASP software to obtain the distance l between the average positive and negative charges. The dipole moment of KSN is calculated according to first-principles calculations, and the expression is as follows:

[0052] μ KSN =nql (8)

[0053] Where, μ KSN The dipole moment of KSN is represented by C·m; n represents the number of atoms; l represents the average distance between positive and negative charges; q represents the unit charge, 1.6 × 10⁻⁶. -19 C;

[0054] Step 7.2: Calculate the spontaneous polarization intensity range of KSN based on the dipole moment of KSN obtained in Step 7.1;

[0055] The two expressions for the spontaneous polarization intensity are as follows:

[0056]

[0057] Where μ represents the dipole moment and V represents the unit cell volume;

[0058] P=n0μ=n0αE e (10)

[0059] Where n0 represents the number of polarized particles per unit volume of the dielectric; μ represents the dipole moment; α represents the ionic polarizability; E e Indicates a built-in electric field;

[0060] Substitute the dipole moment of KSN obtained from the experimental method and first principle calculation in step 7.1 into equations (9) and (10) respectively to obtain the spontaneous polarization intensity range of KSN.

[0061] The chemical composition of the potassium strontium niobate ceramic with high spontaneous polarization intensity selected in step 9 is: K2Sr4Nb 10 O 29 KSr4Nb 10 O 29 and K2Sr4Nb9O 29 .

[0062] Compared with existing technologies, the beneficial effects achieved by this invention are as follows:

[0063] 1. This invention introduces oxygen vacancies and A-site cations (K... + and Sr 2+ ) vacancy and B-site cation (Nb1) 5+ and Nb2 5 + The vacancy structure introduces a greater degree of lattice distortion, resulting in a larger distance from the center of the Nb-O octahedron and thus a greater spontaneous polarization intensity. Simultaneously, based on first-principles calculations, the spontaneous polarization intensity of potassium strontium niobate ceramics with oxygen vacancies, A-site cation vacancies and oxygen vacancies, and B-site cation vacancies and oxygen vacancies was determined. The potassium strontium niobate material composition with higher spontaneous polarization intensity was selected, i.e., the spontaneous polarization intensity of potassium strontium niobate materials satisfies KSN-Nb1&O>KSN-O>KSN-K&O>KSN-Nb2&O>KSN-Sr&O.

[0064] 2. In the prior art, when using VASP to calculate the dipole moment of an insulator system containing doped and vacant structures, the system tends to default to treating it as a conductor, causing the calculation results to deviate from reality. However, the results of this invention, through the dipole moment and spontaneous polarization intensity range of a defect-free KSN, confirm the dipole moment and spontaneous polarization intensity range of a defective system, which conforms to reality and can obtain more accurate results of spontaneous polarization intensity.

[0065] 3. Compared with the LDA pseudopotential library used in the prior art, the present invention uses the electronic structure information of the corresponding atoms in the PBE pseudopotential library in the process of determining the calculation parameters when the system reaches convergence in step 3. This is more suitable for the structure of unit cell with defects, the calculation results of spontaneous polarization intensity are more accurate, and the whole process is characterized by simple calculation, easy operation and short research and development cycle.

[0066] In summary, this invention constructs oxygen vacancy and A-site cations (K... + ,Sr 2+ ) vacancy and oxygen vacancy and B-site cation (Nb1)5+ and Nb2 5+ The unit cell structure of potassium strontium niobate (KSN) with vacancies and oxygen vacancies was investigated. Its optical frequency dielectric properties were calculated using first-principles calculations. Then, its ionic polarizability was obtained using the Clausius-Mosotti equation. The dipole moment and spontaneous polarization intensity of KSN were calculated from its ionic polarizability to determine the spontaneous polarization intensity with defects. Finally, the KSN-Nb1&O material composition with the highest spontaneous polarization intensity was selected, reaching 56.39 μC / cm. 2 The spontaneous polarization intensity of pure KSN is 34.45 μC / cm. 2 It is 1.637 times that of KSN single crystals, and also higher than the spontaneous polarization intensity (25 μC / cm) reported in the literature for KSN single crystals. 2 The invention employs first-principles calculations to theoretically screen out potassium strontium niobate material components with high spontaneous polarization intensity, enabling on-demand design, shortening the R&D cycle, providing theoretical guidance for actual experiments, and saving experimental time and costs. Attached Figure Description

[0067] Figure 1 This is a cell structure diagram of the present invention, wherein, Figure 1 (a) is KSN, Figure 1 (b) is KSN-O. Figure 1 (c) is KSN-K&O. Figure 1 (d) is KSN-Sr&O. Figure 1 (e) is KSN-Nb1&O. Figure 1 (f) is KSN-Nb2&O.

[0068] Figure 2 The optical frequency dielectric constants of KSN, KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O and KSN-Nb2&O of the present invention are defined as follows.

[0069] Figure 3 The ionic polarizability of KSN, KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O and KSN-Nb2&O of the present invention.

[0070] Figure 4 The spontaneous polarization intensities of KSN, KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O and KSN-Nb2&O of the present invention are given. Detailed Implementation

[0071] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0072] A method for screening potassium strontium niobate with high spontaneous polarization intensity involves calculating the spontaneous polarization intensity of potassium strontium niobate containing oxygen vacancies, A-site cation vacancies and oxygen vacancies, and B-site cation vacancies and oxygen vacancies, thereby screening out potassium strontium niobate ceramics with high spontaneous polarization intensity. The chemical composition of the potassium strontium niobate with high spontaneous polarization intensity is: K₂Sr₄Nb. 10 O 29 KSr4Nb 10 O 29 and K2Sr4Nb9O 29 The specific process is as follows:

[0073] Step 1, construct KSr2Nb5O 15 The cell structure model is denoted as KSN, and its cell structure is ordered. The specific process is as follows:

[0074] First, a perfect KSN cell structure model is established. The KSN cell structure model (Code 95741) is exported from the ICSD database and ordered. Then, the Sr cells located in the pentagonal interstices are ordered. 2+ and K + Use Sr for all 2+ Instead, Sr, located in the four directions 2+ Use K + Instead, satisfy KSr2Nb5O 15 The stoichiometry is used to achieve the desired effect on KSr2Nb5O. 15 Ordering of the unit cell structure;

[0075] Step 2, based on the ordered KSr2Nb5O in Step 1 15 The cell structure of KSr2Nb5O was constructed with oxygen vacancies, A-site cation vacancies and oxygen vacancies, and B-site cation vacancies and oxygen vacancies. 15 The cell structure model, the specific process is as follows:

[0076] like Figure 1 As shown, delete KSr2Nb5O 15 One O atom in the unit cell structure corresponds to a vacancy concentration of 2.17 atom%, yielding K2Sr4Nb. 10 O 29 The unit cell structure is denoted as KSN-O;

[0077] Delete KSr2Nb5O 15 A K atom and an O atom in the unit cell structure correspond to a vacancy concentration of 4.35 atom%, yielding KSr4Nb. 10 O 29 The unit cell structure is denoted as KSN-K&O;

[0078] Delete KSr2Nb5O 15A single Sr atom and one O atom in the unit cell structure correspond to a vacancy concentration of 4.35 atom%, yielding K2Sr3Nb. 10 O 29 The unit cell structure is denoted as KSN-Sr&O;

[0079] Since the number of atoms surrounding the two types of Nb and their distances from surrounding atoms are different, the spontaneous polarization intensity of B-site cation vacancies and O-site vacancies needs to be considered separately; KSr2Nb5O is deleted. 15 The vacancy concentration of Nb and O atoms at the Nb1 positions in the unit cell structure is 4.35 atom%, yielding K2Sr4Nb9O. 29 The unit cell structure is denoted as KSN-Nb1&O;

[0080] Delete KSr2Nb5O 15 The Nb and O atoms located at the Nb2 positions in the unit cell structure have a vacancy concentration of 4.35 atom%, yielding K2Sr4Nb9O. 29 The unit cell structure is denoted as KSN-Nb2&O;

[0081] Step 3: Use VASPKIT software to perform convergence tests on the KSN obtained in Step 1 and the KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O, and KSN-Nb2&O obtained in Step 2, respectively, to determine the computational parameters at which the system reaches convergence; the specific process is as follows:

[0082] The convergence of KSN obtained in step 1 and KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O, and KSN-Nb2&O obtained in step 2 was tested using the PBE pseudopotential library in VASPKIT software. The cutoff energy was determined to be 750 eV, the k-point to be 6 × 6 × 6, and the energy convergence criterion to be 4.0 × 10⁻⁶. -5 eV, the convergence criterion for force is that a single atom is less than... The maximum displacement is We choose PBE functional theory under the generalized gradient approximation (GGA) to explain the interaction between electrons, and call on the electronic structure information of the corresponding atoms in the PBE pseudopotential library. PBE functional theory has high accuracy in describing electron correlation, can predict the physical properties of materials such as lattice constants, and can be widely applied to a variety of material systems, including metals, semiconductors, insulators and superconductors. At the same time, the computational cost is relatively low, which is suitable for the defective unit cell system structure.

[0083] Step 4: Based on the calculation parameters when the system reaches convergence in Step 3, the KSN obtained in Step 1 and the KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O and KSN-Nb2&O unit structures obtained in Step 2 are optimized using CASTEP software to achieve the lowest energy of the system and obtain the most stable unit structure; the optimized unit cell volumes are shown in Table 1.

[0084] Step 5: Use CASTEP software to calculate the optical frequency dielectric constants of the most stable KSN, KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O, and KSN-Nb2&O unit cell structures from Step 4, respectively; the specific process is as follows:

[0085] The optical frequency dielectric constant ε of the most stable KSN, KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O, and KSN-Nb2&O unit cell structures in step 4 was calculated using CASTEP software. ∞ In the CASTEP software's Calculation window, select the Optical properties option and perform the calculation; after the calculation is complete, the optical frequency dielectric constant ε will be obtained in the results window. ∞ As shown in Table 1;

[0086] Step 6: Based on the Clausius-Mosotti equation, calculate the ionic polarizability of the most stable KSN, KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O and KSN-Nb2&O unit cell structures in Step 4, respectively.

[0087] The Clausius-Mosotti equation is expressed as follows:

[0088]

[0089] Where, ε r ε represents the relative permittivity, and ε0 represents the vacuum permittivity, 8.85 × 10⁻⁶. -12 F / m, α represents ionic polarizability, and n0 represents the number of polarized particles per unit volume of dielectric.

[0090] If we replace the volume with molar volume M / ρ, then we have:

[0091]

[0092] Where N0 represents Avogadro's constant, with units of mol. -1 M represents the molar mass of the dielectric, and ρ represents the density;

[0093]

[0094] Where V represents the unit cell volume;

[0095] Substituting formula (3) into the transformation of formula (2): get:

[0096]

[0097] At optical frequencies, the relative permittivity ε of the dielectric is... r The usable optical frequency dielectric constant ε ∞ In this case, equation (1) can be expressed as:

[0098]

[0099] The optical frequency dielectric constant ε at the optical frequency is calculated based on the first-principles calculation in step 5. ∞ The product of the number of polarized particles n0 and the ionic polarizability α per unit volume of the material is calculated using formula (5); and the number of polarized particles n0 per unit volume is obtained by formula (4), and then the ionic polarizability α is obtained, as shown in Table 1.

[0100] Table 1. Ionic polarizability α of KSN, KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O and KSN-Nb2&O

[0101]

[0102] Step 7: Calculate the spontaneous polarization intensity range of the KSN unit cell structure based on the ionic polarizability of the KSN unit cell structure obtained in Step 6.

[0103] Step 7.1: Calculate the dipole moment of KSN using both experimental methods and first-principles calculations, i.e.:

[0104] Method 1: Calculate the dipole moment of KSN according to the experimental method:

[0105] Previous studies (Zhang Liangying. Dielectric Physics [M]. Xi'an Jiaotong University Press, 1991.) have shown that the displacement Δz of the cation shifting charge center in a displacement ferroelectric cell is related to the Curie temperature T. c The relationship is as follows:

[0106] T C =2×10 4 (Δz) 2 (6)

[0107] Among them, T c Indicates Curie temperature T c The unit is K;

[0108] The spontaneous polarization of KSN originates from Nb5+ The ions are offset along the

[001] direction from the center of the oxygen octahedron. The Curie temperature of KSN is 150℃, i.e., 423K. Substituting into the above equation (6), we obtain the Nb in KSN. 5+ The offset Δz is Therefore, the dipole moment of KSN is:

[0109] μ KSN =nqΔz=10×5×1.6×10 -19 ×0.1454×10 -10 =11.632×10 -29 (7)

[0110] Where, μ KSN The value represents the dipole moment of KSN, in C·m; n represents the number of atoms; q represents the unit charge, 1.6 × 10⁻⁶. -19 C;

[0111] Method 2: Calculate the dipole moment of KSN based on first-principles calculations:

[0112] The most stable KSN unit cell structure obtained in step 4 is input into the VASP software to obtain the distance l between the average positive and negative charges. The dipole moment of KSN is calculated according to first principles, and the expression is as follows:

[0113] μ KSN =nql=10×1.309×10 -10 ×1.6×10 -19 =20.951×10 -29 (8)

[0114] Where, μ KSN The dipole moment of KSN is represented by C·m; n represents the number of atoms; l represents the average distance between positive and negative charges; q represents the unit charge, 1.6 × 10⁻⁶. -19 C;

[0115] Step 7.2: Calculate the spontaneous polarization intensity range of KSN based on the dipole moment of KSN obtained in Step 7.1;

[0116] Spontaneous polarization intensity is defined as the vector sum of the molecular electric dipole moments per unit volume, reflecting the degree of polarization of the dielectric, and can be expressed by equation (9):

[0117]

[0118] Where μ represents the dipole moment and V represents the unit cell volume;

[0119] The spontaneous polarization intensity can also be expressed by equation (10):

[0120] P=n0μ=n0αEe (10)

[0121] Where n0 represents the number of polarized particles per unit volume of the dielectric; μ represents the dipole moment; α represents the ionic polarizability; E e Indicates a built-in electric field;

[0122] According to KSN's standard card PDF#34-0123, The unit cell volume can be obtained Substituting the dipole moment of the KSN obtained experimentally in step 7.1 into equation (9), we obtain the spontaneous polarization intensity of the KSN as 19.07 μC / cm. 2 Substituting the dipole moment of the KSN obtained experimentally in step 7.1 into equation (10), we obtain the spontaneous polarization intensity of the KSN as 19.12 μC / cm. 2 ;

[0123] The unit cell volume of KSN calculated using first-principles calculations in step 4 is: Substituting the dipole moment of KSN calculated using first-principles calculations in step 7.1 into equation (9), we obtain the spontaneous polarization intensity of KSN as 34.45 μC / cm. 2 Substituting the dipole moment of KSN obtained from the first-principles calculation in step 7.1 directly into equation (10), we obtain the spontaneous polarization intensity of KSN as 34.44 μC / m. 2 ;

[0124] Therefore, the spontaneous polarization intensity of KSN ranges from 19.07 to 34.45 μC / cm. 2 As shown in Table 2;

[0125] Step 8: Based on the spontaneous polarization intensity range of KSN obtained in Step 7, calculate the built-in electric field range, and then, based on the relationship between spontaneous polarization intensity and built-in electric field, obtain the spontaneous polarization intensity of the most stable KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O and KSN-Nb2&O unit cell structures in Step 4.

[0126] Substituting the values ​​of the product of the number of polarized particles n0 and the ionic polarizability α per unit volume of the material in Table 1 into (10), the relationship between the spontaneous polarization intensity and the built-in electric field of KSN, KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O and KSN-Nb2&O can be obtained as follows:

[0127] P KSN =13.979×10 -12 E e (11)

[0128] P KSN-O=19.805×10 -12 E e (12)

[0129] P KSN-K&O =19.110×10 -12 E e (13)

[0130] P KSN-Sr&O =12.664×10 -12 E e (14)

[0131] P KSN-Nb1&O =22.881×10 -12 E e (15)

[0132] P KSN-Nb2&O =16.245×10 -12 E e (16)

[0133] The unit of spontaneous polarization intensity P is .

[0134] Substituting the spontaneous polarization intensity range of KSN obtained in step 7.2 into equation (11), we obtain the built-in electric field E. e The range is 13.642-24.644 MV / mm; the built-in electric field E obtained in step 8... e Substituting the ranges into equations (12)-(16), the spontaneous polarization intensity ranges of KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O, and KSN-Nb2&O are obtained, as shown in Table 2. min P represents the minimum value of spontaneous polarization intensity. max ΔP represents the maximum value of spontaneous polarization intensity, and ΔP represents the change in spontaneous polarization intensity.

[0135] Step 9: Based on the spontaneous polarization intensity range of the KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O and KSN-Nb2&O cell structures obtained in Step 8, select potassium strontium niobate ceramics with high spontaneous polarization intensity.

[0136] The spontaneous polarization intensity of KSN single crystal reported in the literature (RRNeurgaonkar, WKCory, JROliver, et al. Growth and optical properties of ferroelectric tungsten bronze crystals[J]. Ferroelectrics.1993,142:167-188.) is 25 μC / cm. 2 For example, substituting into equation (10), we obtain the built-in electric field E. e The value is 17.88 (MV / mm); the built-in electric field E e Substituting into equations (11)-(15), the spontaneous polarization intensities of KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O and KSN-Nb2&O are obtained, as shown in Table 2. The calculated spontaneous polarization intensities are all within the range of spontaneous polarization intensities obtained by the screening method of this invention, which shows the rationality of this method.

[0137] Table 2. Spontaneous polarization intensities (μC / cm) of KSN, KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O, and KSN-Nb2&O 2 )

[0138]

[0139] Figure 1 The unit cell structure diagram of this invention shows that when establishing the KSN-O structure with oxygen vacancies, one O atom is deleted; when establishing the K... + When KSN-K&O with both vacancies and oxygen vacancies coexist, one K atom and one O atom are deleted; to establish Sr 2+ When KSN-Sr&O has both vacancies and oxygen vacancies, one Sr atom and one O atom are deleted; to establish Nb1 5+ When KSN-Nb1&O has both vacancies and oxygen vacancies, delete one Nb atom and one O atom at the Nb1 position; to establish Nb2... 5+ In KSN-Nb1&O where vacancies and oxygen vacancies coexist, one Nb atom and one O atom located at the Nb1 position are deleted.

[0140] Figure 2 The optical frequency dielectric constants of KSN, KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O, and KSN-Nb2&O in this invention; the optical frequency dielectric constants ε of other structures with vacancies except KSN-Sr&O. ∞ Both are improved compared to KSN, mainly due to Sr 2+Vacancies and oxygen vacancies carry the same but opposite charges, and their interaction partially cancels each other out, thus reducing the optical frequency dielectric constant. Figure 2 It can be seen that KSN-Nb1&O has the highest optical frequency dielectric constant at 19.070, which is 4.4 times that of KSN (4.336). The optical frequency dielectric constants of KSN-O, KSN-K&O, and KSN-Nb2&O are 9.809, 8.750, and 5.729, respectively.

[0141] Figure 3 The ionic polarizability of KSN, KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O, and KSN-Nb2&O in this invention is shown. When vacancies are present, the ionic polarizability of all materials except KSN-Sr&O is improved. Among them, KSN-Nb1&O has the highest ionic polarizability, which is 1.638 times that of KSN. The order is KSN-O > KSN-K&O > KSN-Nb2&O > KSN-Sr&O. It can be seen that the presence of vacancies can effectively improve the ionic polarizability of KSN, especially KSN-Nb1&O.

[0142] Figure 4 The spontaneous polarization intensity of KSN, KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O, and KSN-Nb2&O in this invention is represented by the maximum value P within the spontaneous polarization intensity range. max For example, the blue area represents the built-in electric field E. e Within a certain range, the spontaneous polarization intensity of each material was measured; except for KSN-Sr&O, the spontaneous polarization intensity of other vacancy systems was enhanced; among them, KSN-Nb1&O exhibited the highest spontaneous polarization intensity, at 56.39 μC / cm. 2 , is the KSN spontaneous polarization intensity (34.45 μC / cm). 2 The value is 1.637 times that of KSN-O; followed by the spontaneous polarization intensity of KSN-O at 48.81 μC / cm. 2 The spontaneous polarization intensity of KSN-K&O is 47.09 μC / cm. 2 The spontaneous polarization intensity of KSN-Nb2&O is 40.03 μC / cm. 2 Therefore, the presence of vacancies can effectively increase the spontaneous polarization intensity of KSN, especially the Nb at the Nb1 position. 5+ The spontaneous polarization intensity is highest when vacancies and oxygen vacancies coexist.

Claims

1. A method for screening potassium strontium niobate with high spontaneous polarization intensity, characterized in that, Includes the following steps: Step 1, construct KSr2Nb5O 15 The cell structure model is denoted as KSN, and its cell structure is ordered. Step 2, based on the ordered KSr2Nb5O in Step 1 15 The cell structure of KSr2Nb5O was constructed with oxygen vacancies, A-site cation vacancies and oxygen vacancies, and B-site cation vacancies and oxygen vacancies. 15 The unit cell structure models are denoted as KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O, and KSN-Nb2&O, respectively. Step 3: Use VASPKIT software to perform convergence tests on the KSN obtained in Step 1 and the KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O and KSN-Nb2&O obtained in Step 2 respectively, and determine the calculation parameters when the system reaches convergence. Convergence tests were performed on the KSN obtained in step 1 and the KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O, and KSN-Nb2&O obtained in step 2 using the PBE pseudopotential library in VASPKIT software. The cutoff energy was determined to be 750 eV, the k-point to be 6 × 6 × 6, and the energy convergence criterion to be 4.0 × 10⁻⁶. -5 eV, the convergence criterion for force is that a single atom is less than... The maximum displacement is Step 4: Based on the calculation parameters when the system reaches convergence in Step 3, the KSN obtained in Step 1 and the KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O and KSN-Nb2&O unit cell structures obtained in Step 2 are optimized using CASTEP software to achieve the lowest energy of the system and obtain the most stable unit cell structure. Step 5: Use CASTEP software to calculate the optical frequency dielectric constants of the most stable KSN, KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O and KSN-Nb2&O unit cell structures in Step 4, respectively. Step 6: Based on the Clausius-Mosotti equation, calculate the ionic polarizability of the most stable KSN, KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O, and KSN-Nb2&O unit cell structures from Step 4. The process for calculating the ionic polarizability based on the Clausius-Mosotti equation is as follows: The Clausius-Mosotti equation is expressed as follows: Where, ε r ε represents the relative permittivity, and ε0 represents the vacuum permittivity, 8.85 × 10⁻⁶. -12 F / m, α represents ionic polarizability, and n0 represents the number of polarized particles per unit volume of dielectric. If we replace the volume with molar volume M / ρ, then we have: Where N0 represents Avogadro's constant, with units of mol. -1 M represents the molar mass of the dielectric, and ρ represents the density; Where V is the unit cell volume; Substituting formula (3) into the transformation of formula (2): get: At optical frequencies, the relative permittivity ε of the dielectric is... r The usable optical frequency dielectric constant ε ∞ In this case, equation (1) can be expressed as: The optical frequency dielectric constant ε at the optical frequency is calculated based on the first-principles calculation in step 5. ∞ The product of the number of polarized particles n0 and the ionic polarizability α per unit volume of the material is calculated using formula (5); and the number of polarized particles n0 per unit volume is obtained from formula (4), and then the ionic polarizability α is obtained. Step 7: Calculate the spontaneous polarization intensity range of the KSN unit cell structure based on the ionic polarizability of the KSN unit cell structure obtained in Step 6. Step 8: Based on the spontaneous polarization intensity range of KSN obtained in Step 7, calculate the built-in electric field range, and then, based on the relationship between spontaneous polarization intensity and built-in electric field, obtain the spontaneous polarization intensity of the most stable KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O and KSN-Nb2&O unit cell structures in Step 4. Step 9: Based on the spontaneous polarization intensity range of the KSN-O, KSN-K&O, KSN-Sr&O, KSN-Nb1&O and KSN-Nb2&O cell structures obtained in Step 8, select potassium strontium niobate ceramics with high spontaneous polarization intensity.

2. The method for screening potassium strontium niobate with high spontaneous polarization intensity according to claim 1, characterized in that, In step 2, KSr2Nb5O is constructed with oxygen vacancies, A-site cation vacancies and oxygen vacancies, and B-site cation vacancies and oxygen vacancies. 15 The process of modeling the unit cell structure is as follows: Delete KSr2Nb5O 15 One O atom in the unit cell structure corresponds to a vacancy concentration of 2.17 atom%, yielding K2Sr4Nb. 10 O 29 The unit cell structure is denoted as KSN-O; Delete KSr2Nb5O 15 A K atom and an O atom in the unit cell structure correspond to a vacancy concentration of 4.35 atom%, yielding KSr4Nb. 10 O 29 The unit cell structure is denoted as KSN-K&O; Delete KSr2Nb5O 15 A single Sr atom and one O atom in the unit cell structure correspond to a vacancy concentration of 4.35 atom%, yielding K2Sr3Nb. 10 O 29 The unit cell structure is denoted as KSN-Sr&O; Delete KSr2Nb5O 15 The vacancy concentration of Nb and O atoms at the Nb1 positions in the unit cell structure is 4.35 atom%, yielding K2Sr4Nb9O. 29 The unit cell structure is denoted as KSN-Nb1&O; Delete KSr2Nb5O 15 The Nb and O atoms located at the Nb2 positions in the unit cell structure have a vacancy concentration of 4.35 atom%, yielding K2Sr4Nb9O. 29 The cell structure of it is denoted as KSN-Nb2&O.

3. The method for screening potassium strontium niobate with high spontaneous polarization intensity according to claim 1, characterized in that, The process of calculating the spontaneous polarization intensity range of the KSN unit cell structure in step 7 is as follows: Step 7.1: Calculate the dipole moment of KSN using both experimental methods and first-principles calculations, i.e.: Method 1: Calculate the dipole moment of KSN according to the experimental method: The Curie temperature T of KSN obtained according to experimental methods c To obtain Nb in KSN 5+ The offset Δz is then used to obtain the dipole moment of KSN; The displacement Δz of the cation deflection charge center in a displacement ferroelectric cell is related to the Curie temperature T. c The relationship is as follows: T C =2×10 4 (Δz) 2 (6) Among them, T c This indicates the Curie temperature, measured in Kelvin (K). The relationship between the displacement Δz of the cation shift charge center in the displacement ferroelectric cell and the dipole moment of KSN is as follows: m KSN =nqΔz (7) Where, μ KSN The value represents the dipole moment of KSN, in C·m; n represents the number of atoms; q represents the unit charge, 1.6 × 10⁻⁶. - 19 C; Method 2: Calculate the dipole moment of KSN based on first-principles calculations: The most stable KSN unit cell structure obtained in step 4 is input into VASP software to obtain the distance l between the average positive and negative charges. The dipole moment of KSN is calculated according to first-principles calculations, and the expression is as follows: μ KSN =ngl (8) Where, μ KSN The dipole moment of KSN is represented by C·m; n represents the number of atoms; l represents the average distance between positive and negative charges; q represents the unit charge, 1.6 × 10⁻⁶. -19 C; Step 7.2: Calculate the spontaneous polarization intensity range of KSN based on the dipole moment of KSN obtained in Step 7.1; The two expressions for the spontaneous polarization intensity are as follows: Where μ represents the dipole moment and V represents the unit cell volume; P=n0μ=n0αE e (10) Where n0 represents the number of polarized particles per unit volume of the dielectric; μ represents the dipole moment; α represents the ionic polarizability; E e Indicates a built-in electric field; Substitute the dipole moment of KSN obtained from the experimental method and first principle calculation in step 7.1 into equations (9) and (10) respectively to obtain the spontaneous polarization intensity range of KSN.

4. The method for screening potassium strontium niobate with high spontaneous polarization intensity according to claim 1, characterized in that, The chemical composition of the potassium strontium niobate ceramic with high spontaneous polarization intensity selected in step 9 is: K2Sr4Nb 10 O 29 KSr4Nb 10 O 29 and K2Sr4Nb9O 29 .

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