A static optical refractive index quantitative prediction method and prediction model based on crystal structure

Abstract

This invention provides a method and model for quantitative prediction of static optical refractive index based on crystal structure. The model includes: 1. obtaining the crystal structure of the sample material, and deriving the intrinsic physical parameters and key parameters of the sample material based on the crystal structure as input data for the model; 2. calculating the crystallographic prior parameter (effective valence electron number γ). μ Chemical bond ratio coefficient F μ 4. Combining intrinsic physical quantities, key parameters, and crystallographic a priori parameters, calculate the elemental bonding parameters of the material (total bond volume ζ, bond energy factor σ). μ d-electron correction factor D μ Penn correction factor A μ 5. Output the optical static refractive index through a formula; This invention fully considers the multi-chemical bond coupling effect and d-orbital electronic polarization, and also takes into account the effects of temperature and element doping in detail, which significantly improves the prediction accuracy. It is suitable for the optical performance optimization and high-throughput screening of multi-component oxide systems such as perovskite, pyrochlore, and spinel.

Description

Technical Field

[0001] This invention belongs to the field of dielectric optical material design and computational materials science, and particularly relates to a method and prediction model for quantitative prediction of static optical refractive index based on crystal structure. Background Technology

[0002] In the visible to near-infrared wavelength range, the static optical refractive index of most dielectric oxides remains constant. This crucial parameter, highly dependent on the material type and crystallographic properties, is a core element in revealing the physical nature of the interaction between static light and matter. Static optical refractive index not only provides important guidance for the design of optical components but also promotes our in-depth understanding of the electronic structure and bonding properties of materials. With the widespread application of static optical refractive index in optoelectronics, optical communication, optical sensors, and infrared detection, its research value is increasingly prominent. Therefore, accurately and effectively predicting the optical static refractive index of materials under different temperature and compositional conditions has become key to rapidly screening and identifying candidate materials that meet the needs of specific optical applications.

[0003] Currently, researchers have devoted considerable effort to predicting the optical static refractive index of materials using quantum computing and semi-empirical models. Quantum computing methods, such as density functional perturbation theory (DFPT), the Bethe-Salpeter equation (BSE), and time-dependent density functional theory (TD-DFT), while offering high accuracy, are extremely computationally expensive, limiting their feasibility for rapid screening across a wide range of materials. Therefore, the practicality of these methods in high-throughput screening of new materials with target optical properties is greatly limited. On the other hand, semi-empirical methods, such as the Moss and Ravindra models, while improving computational efficiency, typically neglect electronic transitions and specific structural factors (such as structural complexity and impurities), thus weakening the accuracy and generalizability of predictions. In contrast, models based on chemical bonding theory achieve efficient conversion from structural parameters to optical properties by dielectrically describing the chemical bonds in the crystal structure. However, these methods still face challenges in applications to complex systems, especially when considering overcorrections for systems without d-orbital electrons, empty d-orbital electron bands, temperature effects, and compositional effects. Significant discrepancies remain between the predictions of existing models and experimental observations. Furthermore, no mature model yet fully elucidates the relationship between static optical refractive index and structural parameters in complex space group structures, and its influencing mechanisms. Therefore, developing a predictive model for static optical refractive index that possesses broad applicability, high accuracy, high efficiency, few input parameters, and a clear physical picture has become an urgent need to avoid high experimental costs and complex calculations. Summary of the Invention

[0004] To address the above technical problems, this invention provides a method and model for quantitative prediction of static optical refractive index based on crystal structure. This model, by combining crystal structure, intrinsic physical quantities, and key parameters, can efficiently and accurately predict the static optical refractive index of complex oxides.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows: This invention provides a method for quantitative prediction of static optical refractive index based on crystal structure, comprising the following steps: S1: Obtain the crystal structure of the sample and deduce its intrinsic physical quantities and key parameters as input data: Key parameters: Volume per unit molecular formula V, first Bond lengths of cation and anion chemical bonds cation valence ; Intrinsic physical quantity: coordination number and The number of anions closest to the cation The number of elements corresponding to cations in the unit molecular formula cation chemical valence The number of elements corresponding to anions in a unit molecular formula , No. Average coordination number of chemical bonds between cations and anions , Calculate the stoichiometry of binary bond formulas and , and Then calculate the first Average coordination number of chemical bonds , ; Where A is a cation and B is an anion. The types of chemical bonds between cations and anions in the sample; S2: Calculate the crystallographic prior parameters of the sample: The number of effective valence electrons on a chemical bond , No. coefficients of the proportion of chemical bonds

[0006]

[0007] S3: Calculate the elemental bonding parameters of the sample: total bond volume ζ, bond energy factor , d Orbital electronic correction factor and Penn correction factor : Total bond volume ζ

[0008] bond energy factor

[0009]

[0010] Among them, the Thomas-Fermi screening factor , , ; d Orbital electronic correction factor

[0011]

[0012] for d The number of orbital holes is determined according to the periodic table. For transition elements, , , If the sample has no d-orbital electrons, then Γ = 0 and D = 1. Penn correction factor

[0013] ,in It is a constant. Electronic quality Planck constant .

[0014] S4: Calculate the static optical refractive index:

[0015] in, Electronic quality Planck constant electron charge .

[0016] Preferably, it also includes a quantitative prediction of the static optical refractive index at temperature T, incorporating the coefficient of thermal expansion. Correcting the chemical bond lengths of anions and cations And calculate the volume per unit molecular formula Then repeat steps S1-S4 to calculate the static optical refractive index at temperature T.

[0017] Preferably, the coefficient of thermal expansion is calculated. Correcting the chemical bond lengths of anions and cations And calculate the volume per unit molecular formula

[0018]

[0019] in .

[0020] in, The bond length at the initial temperature. The volume per unit molecular formula at the initial temperature. , The initial temperature. Boltzmann's constant, Here, Δ represents Avogadro's constant, and the superscript △ represents a correction parameter related to the period of cations in the periodic table. The lattice energy of a crystal can be divided into ionic components. and covalent part :

[0021] in , representing the covalent nature of crystals, and This indicates the ionic nature of the crystal.

[0022] Preferably, it further includes quantitative prediction of the static optical refractive index of the doped sample, introducing the doping degree. Calculate the chemical bond lengths of the cation and anion after doping. ,volume Repeat steps S1-S4 to calculate the static optical refractive index of the doped sample.

[0023] Preferably, the crystal structure in step S1 is obtained by first-principles calculation or by X-ray diffraction.

[0024] Based on the same inventive concept, a second aspect of the present invention provides a static optical refractive index quantitative prediction model based on crystal structure, comprising the following steps: A1: Obtain the crystal structure of the sample and deduce its intrinsic physical quantities and key parameters as input data: Key parameters: Volume per unit molecular formula V, first Bond lengths of chemical bonds between cations and anions cation valence ; Intrinsic physical quantity: coordination number and The number of anions closest to the cation The number of elements corresponding to cations in the unit molecular formula cation chemical valence The number of elements corresponding to anions in a unit molecular formula , No. Average coordination number of chemical bonds between cations and anions , Calculate the stoichiometry of binary bond formulas and , and Then calculate the first Average coordination number of bonds , ; Where A is a cation and B is an anion. The types of chemical bonds between cations and anions in the sample; A2: Calculate the crystallographic prior parameters and elemental bonding parameters of the sample. Crystallographic prior parameters: arbitrary The number of effective valence electrons on a chemical bond , any coefficients of the proportion of chemical bonds

[0025]

[0026] Elemental bonding parameters: total chemical bond volume bond energy factor , d Orbital electronic correction factor Penn correction factor Total bond volume ζ

[0027] bond energy factor

[0028]

[0029] Among them, the Thomas-Fermi screening factor , , ; d Orbital electronic correction factor

[0030]

[0031] for d The number of orbital holes is determined according to the periodic table. For transition elements, , If the sample has no d-orbital electrons, then Γ = 0, D = 1; Penn correction factor

[0032]

[0033] in, It is a constant. Electronic quality Planck constant ; A3: Calculate the static optical refractive index of the sample:

[0034] in, Electronic quality Planck constant electron charge .

[0035] Preferably, the optical refractive index at temperature T is predicted by introducing a linear coefficient of thermal expansion. Calculate the chemical bond lengths of cations and anions at different temperatures. and volume per unit molecular formula Other intrinsic physical quantities and key parameters remain unchanged.

[0036] Preferably, the intrinsic physical quantities and key parameters of the sample are obtained based on the doped crystal structure, and steps A1-A3 are repeated to obtain the doped refractive index.

[0037] Based on the same inventive concept, the third aspect of this invention provides a dielectric optical material design system, which uses the above-mentioned static optical refractive index quantitative prediction method based on crystal structure to screen high-throughput materials, obtain materials with target refractive indices, and optimize optical performance.

[0038] Because the present invention adopts the above technical solution, it has the following advantages and positive effects compared with the prior art: Validated by experimental data from 41 complex oxides and 5 doped systems, the prediction model of this invention demonstrates high accuracy and broad applicability. Compared with existing models such as Moss and Ravindra, the model of this invention has a significant advantage in prediction accuracy.

[0039] This invention fully considers the multi-bond coupling effect and d Orbital electron polarization significantly improves prediction accuracy and is applicable to the optimization of optical properties and high-throughput screening of multi-component oxide systems such as perovskite, pyrochlore, and spinel. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of the workflow of the static optical refractive index quantitative prediction method based on crystal structure of the present invention; Figure 2 This invention provides a comparison of its prediction model with other prediction methods. Figure 3 The crystal structure of cubic pyrochlore Gd₂Zr₂O₇ used for model verification in this embodiment of the invention is shown in Figure (a). Gd 2 Zr Crystal structure of O₂: purple: Gd, green: Zr, flesh-colored: O 48f Pink: O 8b In the figure (b) Gd6O 48f 2O 8b In the figure, (c) Gd6O 48f In the figure, (d)O 48f 2Gd2Zr, (e)O in the figure 8b 4Gd. Detailed Implementation

[0041] This invention establishes a predictive model for optical static refractive index based on the Phillips, Van Vechten, and Levine (PVL) chemical bond theory. This model quantifies the influence of chemical bonds on dielectric properties and, by combining parameters such as bond type, bond length, and volume per unit molecular formula in the crystal structure, establishes an expression for the optical static refractive index.

[0042] in, For optical static refractive index, Volume per unit molecular formula The proportionality constant of chemical bonds, For d-orbital electron correction factor, The number of effective valence electrons, This represents the total volume of chemical bonds. Penn correction factor The length of the cation-anion chemical bond, It is the bond energy factor. .

[0043] The following detailed description, in conjunction with the accompanying drawings and specific embodiments, provides a further detailed explanation of the static optical refractive index quantitative prediction method and prediction model based on crystal structure proposed in this invention. The advantages and features of this invention will become clearer from the following description.

[0044] 1. See Figure 1 A method for quantitative prediction of static optical refractive index based on crystal structure includes the following steps: S1: Obtain the crystal structure of the sample and deduce its intrinsic physical quantities and key parameters as input data: Key parameter: Unit molecular formula volume V (unit molecular formula volume is the ratio of the volume of the unit cell to the number of chemical formulas contained in the unit cell. For example, the smallest unit cell of NaCl is a cube, in which Na...) + The ions are located at the vertices and face centers of the cube, Cl. - The ions are located at the edge center and body center of the cube, or vice versa. Each NaCl unit cell has 4 "NaCl" molecular formulas. The volume of a unit formula of NaCl is the volume of the NaCl unit cell divided by 4. Bond lengths of cation and anion chemical bonds cation valence ; Intrinsic physical quantity: coordination number and The number of anions closest to the cation The number of elements corresponding to cations in the unit molecular formula cation chemical valence The number of elements corresponding to anions in a unit molecular formula , No. Average coordination number of chemical bonds between cations and anions , Calculate the stoichiometry of binary bond formulas and , and Then calculate the first Average coordination number of chemical bonds , ; Where A is a cation and B is an anion. The types of chemical bonds between the cations and anions in the sample.

[0045] The crystal structure of the sample can be obtained in the following two ways: First-principles calculations can be used: Utilizing methods such as density functional theory (DFT), the crystal structure of a material can be optimized to obtain its most stable lattice structure, atomic coordination, and chemical bond information. For example, software such as VASP and QuantumESPRESSO can be used to calculate the unit molecular volume V and bond lengths of the crystal structure. Information such as these serve as input data for our model; Alternatively, experimental measurements: If the crystal structure has already been obtained through experimental techniques such as X-ray diffraction (XRD), these experimental data can be used directly.

[0046] S2: Based on the known parameters, calculate the crystallographic prior parameters of the sample: The number of effective valence electrons on a chemical bond , No. coefficients of the proportion of chemical bonds

[0047]

[0048] S3: Based on the known intrinsic physical quantities, key parameters, and crystallographic a priori parameters, calculate the elemental bonding parameters of the sample: total bond volume ζ, bond energy factor. , d Orbital electronic correction factor and Penn correction factor : Total bond volume ζ

[0049] bond energy factor

[0050]

[0051] Among them, the Thomas-Fermi screening factor , , ; d Orbital electronic correction factor

[0052]

[0053] for d The number of orbital holes is determined according to the periodic table. For transition elements, , , If the sample has no d-orbital electrons, then Γ = 0 and D = 1. Penn correction factor

[0054] ,in Electronic quality Planck constant .

[0055] S4: Calculate the static optical refractive index:

[0056] in, Electronic quality Planck constant electron charge .

[0057] 2. Considering the effect of temperature on refractive index, this also includes a quantitative prediction of the static optical refractive index at temperature T, by introducing the coefficient of thermal expansion. Correcting the chemical bond lengths of anions and cations And calculate the volume per unit molecular formula Then repeat steps S1-S4 to calculate the static optical refractive index at temperature T.

[0058] Calculate the coefficient of thermal expansion Correct bond length and calculation of volume per unit molecular formula

[0059]

[0060] in .

[0061] in, The bond length at the initial temperature. The volume per unit molecular formula at the initial temperature. , The initial temperature. Boltzmann's constant, Here, Δ represents Avogadro's constant, and the superscript △ represents a correction parameter related to the period of cations in the periodic table. The lattice energy of a crystal can be divided into ionic components. and covalent part :

[0062] in , representing the covalent nature of crystals, and This indicates the ionic nature of the crystal.

[0063] Specifically, the refractive index at temperature T: in, The total volume of chemical bonds is temperature-dependent. , , The temperature-dependent Penn correction factor. .

[0064] 3. The model also considers the effect of elemental doping on the optical static refractive index. Doping elements occupy positions of the intrinsic atoms in the crystal structure, causing changes in the crystal structure of the doped material. Therefore, the intrinsic physical quantities and key parameters calculated based on the crystal structure may change. Thus, it is necessary to obtain the crystal structure of the doped sample, calculate the intrinsic physical quantities and key parameters, and repeat steps S1-S4 to obtain the refractive index, or introduce a different doping degree. Doping degree is the molar ratio of the number of dopant atoms to a certain type of atom in the parent crystal structure. For example, when La is doped into cubic pyrochlore Gd₂Zr₂O₇, La will occupy the Gd sites in the cubic pyrochlore Gd₂Zr₂O₇ crystal structure, thus introducing doping degree. The chemical formula after doping can be written as Gd 2-x La x Zr2O7; Calculate the bond length after doping ,volume and chemical bond ratio This allows for the prediction of the refractive index after doping.

[0065] Derivation of the formula for refractive index after doping:

[0066] in, , , , , and , .

[0067] 4. Model Validation: To illustrate the model of the present invention, cubic pyrochlore Gd2Zr2O7 (such as...) Figure 3 As shown, the cubic symmetric structure has the following space group: Let's take No. 227 as an example. In this crystal structure, the unit cell contains 8 molecular formulas, Z=8. If we take the lattice site where the M atom is located as the origin, then the +3 valent rare earth element Gd and the +4 valent metal Zr occupy the 16d (1 / 8, 1 / 8, 1 / 8) and 16c (0, 0, 0) symmetry sites in the unit cell, respectively. Depending on the lattice site they occupy, the O atom can be divided into O... 48f and O 8b Two types. Rare earth element Gd forms a polyhedron with eight coordinating oxygen atoms, six of which are oxygen atoms. 48f 2 are O 8b M forms a twisted octahedron with 6 coordinating O atoms, while the remaining 6 O atoms are all O atoms. 48f ;O 48f It coordinates with two Gd atoms and two Zr atoms respectively, while O 8b It coordinates with only 4 Gd atoms. Due to the high symmetry of the positions occupied by each atom, two parameters (i.e., the cell parameter a and the O' coordinate parameter x occupying the 48f lattice position) can determine the atomic coordinates within the cell.

[0068] Oxygen atoms (O) occupy two different lattice positions: O 48f Located at 48f (x, 1 / 8, 1 / 8), O 8b Located at 8b(3 / 8, 3 / 8, 3 / 8). O 48f With O 8b The ratio is 6:1. Because O 48f -Gd and O 48f The number of oxygen atoms in the -Zr bond is 100%. For O 8b -Gd key, .

[0069] Based on the above analysis, cubic pyrochlore Gd 2 Zr 2O7 can be rewritten using the following formula, where Gd 2 Zr 2O7 is decomposed into a series of bond types.

[0070]

[0071] Table 1. List of intrinsic physical parameters and key parameters of the optical static refractive index prediction model for Gd₂Zr₂O₇ (cations: Gd, Zr; anions: O).

[0072] here , , is the The stoichiometric ratio of binary bonds in a type of chemical bond. , and These are the number of nearest-neighbor A atoms of a B atom and the coordination number between A and B atoms, respectively. Inputting the parameters in Table 1 yields...

[0073]

[0074]

[0075]

[0076]

[0077]

[0078] Therefore, cubic pyrochlore was obtained. The bonding formula is as follows:

[0079] Based on the intrinsic physical quantities and key parameter data in Table 1 and the bonding formula according to the model of this invention, the following parameters are obtained, as detailed in Table 2. Table 2 Parameter list

[0080] Burning greenstone into cubes Doping The chemical formula of the doped La is (x = 0, 0.02, 0.06, 0.1), The crystal structure of (x = 0, 0.02, 0.06, 0.1) is cubic Fd. m-space group. There exist two inequivalent O sites (O... 48f and O 8b ), O 48f With two equivalent Gd 3+ Atoms and two equivalent Zr 4+ Atoms bond together to form a hybrid structure consisting of twisted edges and shared-angle OGd2Zr2 tetrahedra. 8b With four equivalent Gd 3+ Atoms bond together, forming a mixture of OGd4 atoms sharing edges and angles.

[0081] The binary bonding formula after doping is shown as follows:

[0082] The predicted refractive indices for both undoped and doped samples were obtained using the refractive index formula. Then, the refractive indices of cubic pyrochlore with the same doping composition as the predicted refractive indices were detected using both ellipsometer and spectroscopic methods. The predicted and experimental values ​​are listed in Table 3. (See Table 3 for details.) Table 3 ( Experimental and predicted values ​​for (e.g., 0, 0.02, 0.06, 0.1)

[0083] Table 3 shows that the experimental and predicted values ​​are largely the same, indicating that the prediction model used in this application has high accuracy. Then, by comparing the predicted data for 41 complex oxides with predictions from quantum computing and semi-empirical models, the results are as follows... Figure 2 As shown, the prediction model of this invention exhibits high accuracy and wide applicability. Compared with existing models such as Moss and Ravindra, the model of this invention has a significant advantage in prediction accuracy.

[0084] This invention, based on chemical bond theory, integrates intrinsic physical quantities, electron configuration information, temperature, and doping element information of materials to develop an autonomous predictive model for optical static refractive index. This model can accurately and efficiently predict the optical static refractive index of materials under various temperature and composition conditions. It quantifies the intrinsic physical quantities affecting the static optical refractive index of materials from a physical mechanism perspective. Compared with traditional prediction models that rely on fitting parameters, this invention's model does not require any structural fitting parameters, significantly improving prediction efficiency and applicability. For materials with known crystal structures and elemental compositions, this model only requires crystal volume and chemical bond lengths to efficiently and reliably predict the optical static refractive index. Experimental verification in 41 different intrinsic materials and 5 doped material systems shows that the model has high accuracy, reliability, and wide applicability, filling the research gap in predicting the optical static refractive index of complex oxide systems at finite temperatures. Compared with traditional chemical bond dielectric theory, this invention corrects for d-orbital electron empty bands, temperature effects, and doping effects, significantly improving the model's prediction performance under various temperature and composition conditions.

[0085] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to the above embodiments. Even if various changes are made to the present invention, if these changes fall within the scope of the claims of the present invention and their equivalents, they shall still fall within the protection scope of the present invention.

Claims

1. A method for the quantitative prediction of static optical refractive indices based on crystal structure, characterized in that, Includes the following steps: S1: Obtain the crystal structure of the sample and deduce its intrinsic physical quantities and key parameters as input data: Key parameters: Volume per unit molecular formula V, first Bond lengths of cation and anion chemical bonds cation valence ; Intrinsic physical quantity: coordination number and The number of nearest-neighbor anions of a cation The number of elements corresponding to cations in the unit molecular formula The number of elements corresponding to anions in a unit molecular formula cation chemical valence , No. Average coordination number of chemical bonds between cations and anions ; Calculate the stoichiometry of binary bond formulas and , and Then calculate the first Average coordination number of chemical bonds , ; in, A It is a cation. B It is an anion. The types of chemical bonds between cations and anions in the sample; S2: Calculate the crystallographic prior parameters of the sample: The number of effective valence electrons on a chemical bond , No. coefficients of the proportion of chemical bonds S3: Calculate the elemental bonding parameters of the sample: total bond volume ζ, bond energy factor , d Orbital electronic correction factor and Penn correction factor : Total bond volume ζ bond energy factor Among them, the Thomas-Fermi screening factor , , ; d Orbital electronic correction factor for d The number of orbital holes is determined according to the periodic table. For transition elements, If the sample has no d-orbital electrons, then Γ = 0 and D = 1. Penn correction factor in It is a constant. Electronic quality Planck constant ; S4: Calculate the static optical refractive index: in, electron charge .

2. The method for quantitative prediction of static optical refractive index based on crystal structure according to claim 1, characterized in that, It also includes the quantitative prediction of the static optical refractive index at temperature T, introducing the coefficient of thermal expansion. Amendment No. Chemical bond lengths of anions and cations And calculate the volume per unit molecular formula Then repeat steps S1-S4 to calculate the static optical refractive index at temperature T.

3. The method for quantitative prediction of static optical refractive index based on crystal structure according to claim 2, characterized in that, Calculate the coefficient of thermal expansion Amendment No. Chemical bond lengths of anions and cations And the volume per unit molecular formula, V(T). in in, The bond lengths of the cation and anion at the initial temperature. The volume per unit molecular formula at the initial temperature. , The initial temperature, Boltzmann's constant, Here, Δ represents Avogadro's constant, and the superscript △ indicates a correction parameter related to the period of cations in the periodic table. The lattice energy of a crystal can be divided into ionic components. and covalent part : in , representing the covalent nature of crystals, and This indicates the ionic nature of the crystal.

4. The method for quantitative prediction of static optical refractive index based on crystal structure according to claim 1, characterized in that, It also includes quantitative prediction of the static optical refractive index of the doped sample, introducing the doping degree. Calculate the doped first Chemical bond lengths of anions and cations Unit molecular formula volume Repeat steps S1-S4 to calculate the static optical refractive index of the doped sample.

5. The method for quantitative prediction of static optical refractive index based on crystal structure according to claim 1, characterized in that, The crystal structure in step S1 is obtained by first-principles calculation or by X-ray diffraction.

6. A dielectric optical material design system, characterized in that, The static optical refractive index quantitative prediction method based on crystal structure described in any one of claims 1-5 is used to screen high-throughput materials, obtain materials with target refractive indices, and optimize optical performance.

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