CN113744818B - Prediction method for ternary rare earth oxide composite point defects - Google Patents

Abstract

The invention discloses a prediction method of a ternary rare earth oxide composite point defect, which relates to the technical field of ternary rare earth oxides, in particular to S1, construction of a ternary rare earth oxide defect model; s2, calculating the formation energy of the isolated point defect, determining the defect position, and predicting the dominant composite defect type S3. The method for predicting the composite point defects of the ternary rare earth oxide is calculated based on the first principle, only the basic crystal structure information of the ternary rare earth oxide is needed to be known, the defect formation energy of the stoichiometric ratio and the non-stoichiometric ratio can be calculated without other parameters, the prediction of the dominant defect type and the concentration is completed, and the adopted calculation simulation method is low in cost and high in efficiency without adding experimental equipment and raw materials except a computer.

Description

A prediction method for composite point defects in ternary rare earth oxides

Technical field

The present invention relates to the technical field of ternary rare earth oxides, specifically a method for predicting composite point defects in ternary rare earth oxides.

Background technique

Materials are the foundation of all walks of life in the national economy. With the rapid development of the modern industrial revolution, the industry has increasingly higher requirements for the performance of new inorganic non-metallic materials. Ternary rare earth oxides have high temperature structural stability and excellent mechanical properties. / The comprehensive physical/chemical properties have become a new type of material that has attracted much attention in the scientific community in recent years and has broad application prospects in the industry. For example, because of its low thermal conductivity and good high-temperature phase stability, three-dimensional Rare earth oxides are considered to be potential thermal barrier and environmental barrier coating materials; their excellent ionic conductivity and defect accommodation capabilities make them widely used in fields including electrolyte materials for solid oxide fuel cells and nuclear waste solids. The properties such as ionic conductivity, radiation resistance and thermal conductivity involved in the application of ternary rare earth oxides can all be explained through point defects. Therefore, the analysis and research of point defects is very necessary.

Although research on ternary rare earth oxides is becoming more and more extensive, experimental and theoretical calculation studies related to defects are not complete enough. Traditional theoretical research on defects is mainly based on the isolated point defect model. Due to the inability to maintain electrical neutrality and ignore defects, defects Interactions lead to contradictions between predicted results and experiments.

Contents of the invention

In view of the shortcomings of the existing technology, the present invention provides a method for predicting composite point defects of ternary rare earth oxides, which solves the problem that the existing research on ternary rare earth oxides proposed in the above background technology is becoming more and more extensive, but the defects Relevant experimental and theoretical calculation research is not perfect enough. Traditional defect theory research is mainly based on the isolated point defect model. Due to the inability to maintain electrical neutrality and ignore defects and defect interactions, the prediction results are inconsistent with the experiment.

In order to achieve the above objectives, the present invention is realized through the following technical solutions: a method for predicting composite point defects of ternary rare earth oxides. The prediction method for composite point defects of ternary rare earth oxides includes the following steps:

S1. Construction of ternary rare earth oxide defect model:

Construct a complete structure supercell of ternary rare earth oxide and perform structural optimization. Based on the optimized supercell, construct its isolated point defect structure supercell model, referred to as the isolated point defect model, and convert the ternary rare earth oxide supercell model is the three-dimensional atomic coordinate information;

S2. Calculation of isolated point defect formation energy and determination of defect location:

Set the input parameters, perform structural optimization on all isolated point defect models, calculate the defect formation energy of the isolated point defect, and select the most stable defect position by comparing the supercell formation energies of all structures of the same isolated point defect;

S3. Prediction of dominant composite defect types:

Consider all possible competing phases, list the chemical potential limiting conditions of ternary rare earth oxides and draw a chemical potential phase diagram containing competing phases, and find out the region and boundary chemical potential conditions where ternary rare earth oxides can stably exist; based on this , write down the possible defect chemical reactions and corresponding composite defect types under each chemical potential condition, obtain the composite defect formation energy by calculating the defect chemical reaction ability, and predict the dominant composite defect type and concentration at different temperatures.

Optionally, in step S1, the complete structure of the ternary rare earth oxide supercell is optimized and the structure is optimized. In the optimized complete supercell structure of the ternary rare earth oxide, an internal atom is removed to form an isolated vacancy defect model, as follows One cation occupies the position of another cation to form an anti-structural defect model, and an atom is added to occupy an interstitial position to form an interstitial defect model.

Optionally, for all isolated point defects, the valence state adopts the standardized valence of the corresponding element. For isolated point defect types with multiple possibilities, all possible structural supercells are constructed here.

Optionally, in step S2, first principles calculations based on density functional are used for calculations.

Optionally, in step S2, the calculation software used for calculation is VASP, which is called Vienna Ab-initioSimulation Package software.

Optionally, the exchange correlation functional uses the generalized gradient approximation PBEsol method, all calculations consider spin polarization, the cutoff energy of the plane wave pseudopotential is set to above 500eV, and the convergence criterion of the structural optimization is set to Ensure that the calculation results of the system achieve sufficient calculation accuracy within a controllable calculation amount.

Optionally, all processes are calculated as follows:

k-points are generated using the Monkhorst-Pack method, and the generated k-point grid density is set to less than This method can generate grid points simply and quickly and improve calculation efficiency.

Optionally, the above-mentioned drawing of chemical potential limiting conditions and phase diagrams needs to consider all possible single, binary and ternary key competing phases of the constituent elements of the ternary rare earth oxide material, and the supercell volume remains unchanged during the optimization of the defect model structure. , allowing all atomic positions to relax.

Optionally, in step S2, the defect formation energy is calculated by the formula E _f =E _d +E _p +∑ n _i μ _i +q( _ΔEF +E _VBM ), where E _d and E _p are respectively the defect-containing and the total energy of the supercell without defects, n _i is the number of atoms to be removed or added, μ _i is the chemical potential of the corresponding element, q is the valence state of the point defect, E _VBM is the valence band top, that is, valence band maximum , abbreviated as the energy level of VBM, ΔE _F is based on the Fermi level measured by VBM.

Optionally, in step S3, the concentrations at different temperatures are calculated as follows:

Under thermodynamic equilibrium conditions, the Arrhenius equation is used to calculate the concentration of various composite defects at different temperatures, namely Among them, N _s and N _c are the number of sites and the equivalent configuration number of composite defects in unit volume respectively, k _B is Boltzmann's constant, T is the temperature, and E _f is the defect formation energy.

The present invention provides a method for predicting composite point defects of ternary rare earth oxides, which has the following beneficial effects:

1. This method for predicting composite point defects in ternary rare earth oxides is based on first-principles calculations. It only needs to know the basic crystal structure information of the ternary rare earth oxide, and its stoichiometric ratio and non-stoichiometric ratio can be calculated without the need for other parameters. The defect formation energy of the stoichiometric ratio can be used to predict the dominant defect type and concentration, and the computational simulation method adopted does not require the investment of experimental equipment and raw materials other than computers, which is low-cost and high-efficiency.

2. This method for predicting composite point defects of ternary rare earth oxides can simulate the actual chemical environment of the material by considering the competing phases of the ternary rare earth oxides, and accordingly predict the most likely defect chemical reactions and corresponding composites in each chemical environment. The defect types and defect concentrations at different temperatures will provide a theoretical basis for the regulation of defect types during the experimental synthesis process to promote the optimization of defect-related physical properties of the material.

Description of the drawings

Figure 1 is a schematic flow diagram of the present invention;

Figure 2 is a chemical potential diagram of A-Zr-O of the present invention;

Figure 3 is a schematic diagram of the formation energy of Schottky defects, Frenkel defects and cation anti-site defects in the ternary rare earth zirconate A ₂ Zr ₂ O ₇ (A=La, Pr, Pm, Eu) of the present invention;

Figure 4 is a schematic diagram of the dominant defect reaction equation and its reaction formation enthalpy under different chemical environments of the present invention;

Figure 5 is a schematic diagram of the chemical potential of RE ₂ Si ₂ O ₇ of the present invention;

Figure 6 is a schematic diagram of the formation energy of Schottky, Frenkel and anti-structure composite defects of RE ₂ Si ₂ O ₇ of the present invention;

Figure 7 is a schematic diagram of the dominant defect reaction equation and its reaction enthalpy in Yb ₂ Si ₂ O ₇ and Lu ₂ Si ₂ O ₇ under different chemical environments depending on the present invention.

Detailed ways

Referring to Figures 1 to 7, the present invention provides a technical solution: a method for predicting composite point defects in ternary rare earth oxides. The method for predicting composite point defects in ternary rare earth oxides includes the following steps:

S1. Construction of ternary rare earth oxide defect model:

Construct a complete structure supercell of ternary rare earth oxide and perform structural optimization. Based on the optimized supercell, construct its isolated point defect structure supercell model, referred to as the isolated point defect model, and convert the ternary rare earth oxide supercell model is the three-dimensional atomic coordinate information;

S2. Calculation of isolated point defect formation energy and determination of defect location:

Set the input parameters, perform structural optimization on all isolated point defect models, calculate the defect formation energy of the isolated point defect, and select the most stable defect position by comparing the supercell formation energies of all structures of the same isolated point defect;

S3. Prediction of dominant composite defect types:

Consider all possible competing phases, list the chemical potential limiting conditions of ternary rare earth oxides and draw a chemical potential phase diagram containing competing phases, and find out the region and boundary chemical potential conditions where ternary rare earth oxides can stably exist; based on this , write down the possible defect chemical reactions and corresponding composite defect types under each chemical potential condition, obtain the composite defect formation energy by calculating the defect chemical reaction ability, and predict the dominant composite defect type and concentration at different temperatures.

In step S1, the complete supercell structure of the ternary rare earth oxide is optimized and the structure is optimized. In the optimized complete supercell structure of the ternary rare earth oxide, an internal atom is removed to form an isolated vacancy defect model, and one cation occupies the other. The cation position forms an antistructural defect model, and an atom is added to occupy the interstitial position to form an interstitial defect model.

For all isolated point defects, the valence state adopts the standard valence of the corresponding element. For isolated point defect types with multiple possibilities, all possible structural supercells are constructed here.

In step S2, the calculations are all based on first principles calculations based on density functional.

In step S2, the calculation software used in the calculation is VASP, whose full name is Vienna Ab-initio SimulationPackage software.

The exchange correlation functional adopts the generalized gradient approximation PBEsol method, all calculations consider spin polarization, the cutoff energy of the plane wave pseudopotential is set to above 500eV, and the convergence criterion of the structural optimization is set to Ensure that the calculation results of the system achieve sufficient calculation accuracy within a controllable calculation amount.

All processes are calculated as follows:

k-points are generated using the Monkhorst-Pack method, and the generated k-point grid density is set to less than This method can generate grid points simply and quickly and improve calculation efficiency.

To draw chemical potential constraints and phase diagrams, all possible single, binary, and ternary key competing phases of the constituent elements of ternary rare earth oxide materials need to be considered. During the structure optimization process of the defect model, the supercell volume remains unchanged and all atomic positions are allowed to be modified. Relaxation.

In step S2, the defect formation energy is calculated by the formula E _f =E _d +E _p +∑ n _i μ _i +q( _ΔEF +E _VBM ), where E _d and E _p are defective and defect-free respectively. The total energy of the supercell, n _i is the number of atoms to be removed or added, μ _i is the chemical potential of the corresponding element, q is the valence state of the point defect, E _VBM is the valence band top, that is, valence band maximum, abbreviated as the energy of VBM level, ΔE _F is based on the Fermi level measured by the VBM.

In step S3, the concentration at different temperatures is calculated as follows:

Under thermodynamic equilibrium conditions, the Arrhenius equation is used to calculate the concentration of various composite defects at different temperatures, namely Among them, N _s and N _c are the number of sites and the equivalent configuration number of composite defects in unit volume respectively, k _B is Boltzmann's constant, T is the temperature, and E _f is the defect formation energy.

Case number one:

Construct a complete structural supercell of A ₂ Zr ₂ O ₇ (A=La, Pr, Pm, Eu) and perform structural optimization. Based on the optimized perfect super cell, a structural super cell model containing isolated point defects is constructed, and A ₂ Zr _{The 2} O ₇ supercell model is converted into three-dimensional atomic coordinate information. In the optimized A ₂ Zr ₂ O ₇ perfect supercell structure, one internal A, Zr and O atom is deleted to form _VA , V _Zr and V _O vacancies. Defect; an A atom occupies the Zr position or a Zr atom occupies the A position to form two anti-structural defects of A _Zr and Zr _A respectively; adding an A, Zr and O atom to the gap position forms A _i , Zr _i and O _i respectively. A kind of interstitial defect, for all isolated point defects in the A ₂ Zr ₂ O ₇ structure, the valence state adopts the standardized valence of the corresponding element;

Set the input parameters, perform structural optimization on all isolated point defect models, calculate the defect formation energy of the isolated point defect, and select the most stable defect position by comparing the formation energy of all structural supercells of the same isolated point defect. All calculations are based on density generalization. First principles calculation of functional theory, the calculation software is VASP (Vienna Ab-initioSimulation Package) software, the exchange correlation functional uses the generalized gradient approximation GGA-PBEsol method, all calculations consider spin polarization, plane wave pseudopotential The cutoff energy is set to 520eV, and the convergence criterion for structural optimization is set to The calculation method uses the Monkhorst-Pack method to generate k points during calculation. The generated k-point grid density is set to 2×2×2. The defect formation energy can be calculated through the formula E _f =E _d +E _p +∑n _i μ _i +q (ΔE _F +E _VBM ) calculation, where E _d and E _p are the total energy of defective and defect-free supercells respectively, n _i is the number of atoms to be removed or added, μ _i is the chemical potential of the corresponding element, q is the valence state of the point defect, E _VBM is the energy level of the valence band top (VBM), ΔE _F is the Fermi level measured based on VBM;

Considering all possible competing phases in ternary rare earth zirconates: ternary phase A ₂ Zr ₂ O ₇ , binary phases A ₂ O ₃ , ZrO ₂ and monophase A, Zr and O ₂ , list the ternary rare earth zirconium The chemical potential limiting conditions between the monobasic, binary and ternary phases in the acid salt, obtain and draw the chemical potential phase diagram containing competing phases in A ₂ Zr ₂ O ₇ , and find out the stable existence of the ternary rare earth zirconate Region ABCD and boundary chemical potential conditions; based on this, write down the possible defect chemical reactions and corresponding composite defect types under each chemical potential condition, obtain the composite defect formation energy by calculating the defect chemical reaction energy, and predict the dominant composite defect types and Concentrations at different temperatures, and the chemical potential constraints are as follows:

Schottky defects:

Frenkel defects:

Anti-structural flaws:

Under thermodynamic equilibrium conditions, the Arrhenius equation can be used to calculate the concentration of various composite defects at different temperatures: Among them, N _s and N _c are the number of sites and the equivalent configuration number of composite defects in unit volume respectively, k _B is Boltzmann's constant, T is temperature, E _f is defect formation energy, according to the different chemical potential environments, It can be divided into two situations: stoichiometric ratio and non-stoichiometric ratio. The non-stoichiometric ratio situation may be further subdivided into different chemical environments based on the amount of relevant competing phases. Under ZrO _2- rich and A ₂ O _3- rich conditions The leading defects in non-stoichiometric ratios are as follows:

Rich ZrO ₂ conditions:

Rich A ₂ O ₃ conditions:

Case 2:

Construct a RE ₂ Si ₂ O ₇ complete structural supercell and perform structural optimization. Based on the optimized supercell, construct its isolated point defect structure supercell model, and convert the RE ₂ Si ₂ O ₇ supercell model into three-dimensional atomic coordinate information. In the optimized complete supercell structure of RE ₂ Si ₂ O ₇ , RE, Si and O are deducted to form V _RE , V _Si and _VO vacancy defects; one RE occupying the Si position or one Si occupying the RE forms RE Si and _RE respectively. Si _RE two anti-structural defects; search the entire potential energy surface to find the gap configuration of each element with the lowest energy, thereby determining the gap position of each element, and adding RE, Si and O atoms at the gap position to form three RE _i , Si _i and O _i A kind of interstitial defect, for all isolated point defects in the RE ₂ Si ₂ O ₇ structure, the valence state adopts the normalized valence of the corresponding element;

Calculation of isolated point defect formation energy and determination of defect location: Set the input parameters, perform structural optimization on all isolated point defect models, calculate the defect formation energy of isolated point defects, and select the supercell formation energy of all structures of the same isolated point defect by comparing them. For the most stable defect position, all calculations adopt first-principles calculations based on density functional. The calculation software is VASP (Vienna Ab-initio Simulation Package) software, RE ₂ Si ₂ O ₇ composite point defect prediction method, exchange correlation general The function uses the generalized gradient approximation GGA-PBEsol method. All calculations consider spin polarization. The cutoff energy of the plane wave pseudopotential is set to 520eV. The convergence criterion of the structural optimization is set to The calculation method uses the Monkhorst-Pack method to generate k points during calculation, and the generated k-point grid density is set to 2×2×2. The supercell volume is kept unchanged during the defect model structure optimization process, and all atomic positions are allowed to relax. The defect formation energy is calculated by the formula E _f =E _d +E _p +∑n _i μ _i +q( _ΔEF +E _VBM ), where E _d and E _p are the total energies of the defective and defect-free supercells, respectively. , n _i is the number of atoms to be removed or added, μ _i is the chemical potential of the corresponding element, q is the valence state of the point defect, E _VBM is the energy level of the valence band top (VBM), ΔE _F is measured based on VBM Fermi level;

Consider all possible competing phases in ternary rare earth silicates: ternary phase RE ₂ Si ₂ O ₇ , binary phase RE ₂ O ₃ , SiO ₂ , monophase RE, Si, O ₂ , and in the binary phase RE The ternary impurity phase RE ₂ SiO ₅ produced when ₂ O ₃ is excessive List the chemical potential limiting conditions of ternary rare earth silicate, draw a chemical potential phase diagram containing competing phases, and find out the area ABCD and boundary chemical potential conditions where ternary rare earth silicate can stably exist. Based on this, write The possible defect chemical reactions and corresponding composite defect types under each chemical potential condition are determined. The composite defect formation energy is obtained by calculating the defect chemical reaction ability, and the dominant composite defect types and concentrations at different temperatures are predicted. The chemical potential limiting conditions are as follows :

Ternary phase:

One element:

Binary phase:

Ternary competition phase:

Schottky defects:

Frenkel defect:

Anti-structural flaws:

Under thermodynamic equilibrium conditions, the Arrhenius equation can be used to calculate the concentration of various composite defects at different temperatures: Among them, N _s and N _c are the number of sites and the equivalent configuration number of composite defects in unit volume respectively, k _B is Boltzmann's constant, T is temperature, E _f is defect formation energy, according to the different chemical potential environments, It can be divided into two situations: stoichiometric ratio and non-stoichiometric ratio. The non-stoichiometric ratio situation may be further subdivided into different chemical environments based on the amount of relevant competing phases.

Summary: Based on first-principles calculations, you only need to know the basic crystal structure information of the ternary rare earth oxide. Without other parameters, you can calculate the defect formation energy of its stoichiometric ratio and non-stoichiometric ratio, and complete the dominant defect types and Prediction of concentration, and the computational simulation method used, does not require the investment of experimental equipment and raw materials other than computers, is low-cost and highly efficient. By considering the competitive phase of ternary rare earth oxides, the actual chemical environment of the material can be simulated, and predictions can be made accordingly The most likely defect chemical reactions in each chemical environment and the corresponding composite defect types and defect concentrations at different temperatures will provide a theoretical basis for the regulation of defect types during the experimental synthesis process to promote the improvement of defect-related physical properties of materials. optimization.

Claims (10)

1. A method for predicting the composite point defect of a ternary rare earth oxide is characterized by comprising the following steps: the method for predicting the composite point defect of the ternary rare earth oxide comprises the following operation steps:

s1, constructing a ternary rare earth oxide defect model:

constructing a supercell of a complete structure of the ternary rare earth oxide, performing structural optimization, constructing a supercell model of an isolated point defect structure of the supercell based on the optimized supercell, namely an isolated point defect model for short, and converting the supercell model of the ternary rare earth oxide into three-dimensional atomic coordinate information;

s2, calculating the formation energy of isolated point defects and determining the defect positions:

setting input parameters, carrying out structural optimization on all the isolated point defect models, calculating defect formation energy of the isolated point defects, and selecting the most stable defect position by comparing the sizes of supercell formation energy of all structures of the same isolated point defect;

s3, predicting dominant composite defect types:

taking all possible competing phases into consideration, listing chemical potential limiting conditions of the ternary rare earth oxide, and drawing a chemical potential phase diagram containing the competing phases to find out the region and boundary chemical potential conditions where the ternary rare earth oxide can stably exist; according to the method, possible defect chemical reactions and corresponding composite defect types under each chemical potential condition are written, the composite defect formation energy is obtained by calculating the defect chemical reaction capacity, and the type of the dominant composite defect and the concentration at different temperatures are predicted.

2. The method for predicting the composite point defect of the ternary rare earth oxide according to claim 1, wherein the method comprises the following steps: in the step S1, the three-element rare earth oxide has a complete structure supercell and is subjected to structural optimization, one atom in the optimized three-element rare earth oxide has been removed to form an isolated vacancy defect model, one cation occupies one cation position to form an inverse structure defect model, and one atom occupies a gap position to form a gap defect model.

3. The method for predicting the composite point defect of the ternary rare earth oxide according to claim 2, wherein the method comprises the following steps: for all isolated point defects, the valence state is the standard valence of the corresponding element, and for isolated point defect types with multiple possibilities, all possible structural supercells are constructed for the isolated point defect types.

4. The method for predicting the composite point defect of the ternary rare earth oxide according to claim 1, wherein the method comprises the following steps: in the step S2, the calculation adopts a first sexual principle calculation based on a density functional.

5. The method for predicting the composite point defect of the ternary rare earth oxide according to claim 1, wherein the method comprises the following steps: in the step S2, the calculation software used in calculation is VASP, and is called Vienna Ab-initio Simulation Package software.

6. The method for predicting the composite point defect of the ternary rare earth oxide according to claim 1, wherein the method comprises the following steps: the generalized gradient approximation PBEsol method is adopted for the exchange correlation functional, spin polarization is considered in all calculation, the cutoff energy of the plane wave pseudopotential is set to be more than 500eV, and the convergence standard of structure optimization is set to beThe calculation result of the system is ensured to reach enough calculation precision in controllable calculation amount.

7. The method for predicting the composite point defect of the ternary rare earth oxide according to claim 5, wherein the method comprises the following steps: the calculation method of all the processes is as follows:

generating k points by using a Monkhorst-Pack method, wherein the density of the generated k point grids is set to be smaller than that of the generated k point gridsThe method can simply and quickly generate grid points and improve the calculation efficiency.

8. The method for predicting the composite point defect of the ternary rare earth oxide according to claim 1, wherein the method comprises the following steps: all possible monobasic, dibasic and tribasic critical competing phases of the ternary rare earth oxide material composition elements are considered in the drawing of chemical potential limiting conditions and phase diagrams, the supercell volume is kept unchanged in the defect model structure optimization process, and all atomic positions are allowed to relax.

9. The method for predicting the composite point defect of the ternary rare earth oxide according to claim 1, wherein the method comprises the following steps: in the step S2, the defect formation can be performed by the formula E _f ＝E _d +E _p +∑n _i μ _i +q(ΔE _F +E _VBM ) Calculation of E _d And E is _p Respectively contain defectsAnd the total energy of supercells without defects, n _i The number of atoms, mu, to be removed or added _i Is the chemical potential of the corresponding element, q is the valence of the point defect, E _VBM For valance band cap, i.e. valence band maximum, abbreviated as energy level of VBM, ΔE _F Is based on the fermi level measured by VBM.

10. The method for predicting the composite point defect of the ternary rare earth oxide according to claim 1, wherein the method comprises the following steps: in the step S3, the concentration calculation modes at different temperatures are as follows:

under thermodynamic equilibrium conditions, the Arrhenius equation is used to calculate the concentration of various composite defects at different temperatures, i.eWherein N is _s And N _c The number k is the equivalent configuration of the sum of the number of sites of the composite defect in unit volume _B Is Boltzmann constant, T is temperature, E _f Is the defect formation energy.