Method for evaluating stability of plutonium-based perovskite crystal structure

Abstract

The invention relates to the technical field of chemical analysis, in particular to a method for evaluating the stability of a plutonium-based perovskite crystal structure. The evaluation method provided by the invention comprises the following steps: carrying out structure optimization on a plutonium-based perovskite crystal structure; according to a first principle, calculating the crystal formation enthalpy of the plutonium-based perovskite crystal structure after structure optimization; according to a first principle, calculating an elastic constant Cij of the structurally optimized plutonium-based perovskite crystal structure, and according to the elastic constant, judging whether the crystal structure meets a Born stability criterion; calculating the phonon dispersion frequency of the structurally optimized plutonium-based perovskite crystal structure, and judging whether all phonon frequencies are greater than zero or not; and if the crystal formation enthalpy is less than zero, the Born stability criterion is met, and the frequencies of all phonons are greater than zero, proving that the plutonium-based perovskite crystal structure is a stable structure. The stability evaluation method can accurately judge the stability of the Pu-TM-O system formed by the plutonium oxide and the impurity elements.

Description

Technical Field

[0001] The present invention relates to the technical field of chemical analysis, and in particular to a method for evaluating the stability of a plutonium-based perovskite crystal structure. Background Art

[0002] At present, mixed oxide materials (mixed uranium and plutonium oxide fuel, MOX for short) are an important type of plutonium material research. They are important nuclear reactor fuels for plutonium recycling and improving uranium resource utilization. However, in the processing, production and storage of plutonium oxide, common transition metal elements such as Ga, Fe, V, Cr, and Ni are inevitably introduced. It is well known that the addition of appropriate transition metals can improve and enhance the various properties of the structural system. Therefore, in order to achieve the purpose of stable service, long-term storage and non-diffusion of plutonium-based materials, converting them into plutonium-based ceramic materials is an effective technical approach. Among them, the perovskite-like structure of Pu- TM -O (TM = Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn..., abbreviated as Pu- TM As an important class of plutonium-based compounds, Pu-O plays an important role in the recycling of weapon-grade plutonium and plutonium in nuclear reactor nuclear fuel (MOX). TM The stability research of Pu-TM-O system has important theoretical significance and application value for improving the performance quality of MOX fuel and increasing the efficiency and service life of nuclear reactors. However, there is currently no method to judge the structural stability of Pu-TM-O system. Summary of the invention

[0003] In order to solve the problems existing in the prior art, the present invention provides a method for evaluating the stability of the plutonium-based perovskite crystal structure. The stability evaluation method provided by the present invention can accurately determine the Pu- TM -O system stability.

[0004] In order to achieve the above-mentioned object of the invention, the present invention provides the following technical solutions: The present invention provides a method for evaluating the stability of a plutonium-based perovskite crystal structure, comprising the following steps: Structural optimization is performed on the plutonium-based perovskite crystal structure to obtain a structurally optimized plutonium-based perovskite crystal structure; Based on the first principles, the crystal formation enthalpy of the plutonium-based perovskite crystal structure after structural optimization is calculated; Calculation of the elastic constants of the optimized plutonium-based perovskite crystal structure based on first principles Cij , and based on the elastic constants, determine whether the crystal structure meets the Born stability criterion; Calculate the phonon dispersion frequency of the plutonium-based perovskite crystal structure after structural optimization to determine whether all phonon frequencies are greater than zero; If the crystal formation enthalpy is less than zero, satisfies the Born stability criterion, and all phonon frequencies are greater than zero, it proves that the plutonium-based perovskite crystal structure is a stable structure.

[0005] Preferably, when the structure is optimized, the atomic force standard of the plutonium-based perovskite crystal structure is 0.01 eV Å -1 , the energy convergence criterion is 10 -6 eV / atom, the cutoff energy was set to 520 eV, and 2π×0.03 Å was used. -1 of k Point mesh; the Hubbard parameter U of the 5f electrons of the Pu element is set to 4 eV.

[0006] Preferably, during structural optimization, the inner core electrons of the plutonium-based perovskite crystal structure are described by PAW pseudopotentials; and the exchange correlation functional adopts PBE functional under the generalized gradient approximation (GGA) framework.

[0007] Preferably, when calculating the crystal formation enthalpy of the plutonium-based perovskite crystal structure after structural optimization, the synthesis path of the plutonium-based perovskite crystal structure is performed according to Formula I; the calculation formula of the crystal formation enthalpy is performed according to Formula II; Formula I; Formula II; In formula I and formula II, the space group of Pu is Fm m, O2 is an oxygen molecule in a cubic box with a side length of 10Å, TM It is a transition metal element; The Pu TM O3, Pu, TM , the energy of O2 is obtained by self-consistent calculation.

[0008] Preferably, the transition metal element includes Mn, Ti, V, Cr, Fe, Co, Ni, Cu, Zn or Ga.

[0009] Preferably, the elastic constants of the plutonium-based perovskite crystal structure after the calculation structure optimization are C ij When calculating the stress-strain method or the stress-energy method in the first principles,

[0010] Preferably, the finite displacement method or density functional perturbation theory is used to calculate the phonon dispersion frequency of the plutonium-based perovskite crystal structure after structural optimization.

[0011] The present invention provides a stability evaluation method for a plutonium-based perovskite crystal structure, comprising the following steps: optimizing the plutonium-based perovskite crystal structure to obtain a plutonium-based perovskite crystal structure after structural optimization; calculating the crystal formation enthalpy of the plutonium-based perovskite crystal structure after structural optimization according to first principles; calculating the elastic constant of the plutonium-based perovskite crystal structure after structural optimization according to first principles. C ij , and according to the elastic constant, determine whether the crystal structure meets the Born stability criterion; calculate the phonon dispersion frequency of the plutonium-based perovskite crystal structure after structural optimization, and determine whether all phonon frequencies are greater than zero; if the crystal formation enthalpy is less than zero, meets the Born stability criterion and all phonon frequencies are greater than zero, it is proved that the plutonium-based perovskite crystal structure is a stable structure. The stability evaluation method provided by the present invention can accurately determine the Pu- TM -O system stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 A schematic diagram of a process for evaluating the stability of a plutonium-based perovskite crystal structure provided in an embodiment of the present application; Figure 2 For the present embodiment PuMnO3 (Pna2 ) Schematic diagram of the crystal structure; Figure 3 For the present embodiment PuMnO3 (Pna2 ) Phonon dispersion curve of crystal structure. DETAILED DESCRIPTION

[0013] like Figure 1 As shown, the present invention provides a method for evaluating the stability of a plutonium-based perovskite crystal structure, comprising the following steps: Structural optimization is performed on the plutonium-based perovskite crystal structure to obtain a structurally optimized plutonium-based perovskite crystal structure; Based on the first principles, the crystal formation enthalpy of the plutonium-based perovskite crystal structure after structural optimization is calculated; Calculation of the elastic constants of the optimized plutonium-based perovskite crystal structure based on first principles C ij , and based on the elastic constants, determine whether the crystal structure meets the Born stability criterion; Calculate the phonon dispersion frequency of the plutonium-based perovskite crystal structure after structural optimization to determine whether all phonon frequencies are greater than zero; If the crystal formation enthalpy is less than zero, satisfies the Born stability criterion, and all phonon frequencies are greater than zero, it proves that the plutonium-based perovskite crystal structure is a stable structure.

[0014] The present invention optimizes the plutonium-based perovskite crystal structure to obtain a plutonium-based perovskite crystal structure after structural optimization.

[0015] As an embodiment, when the structure is optimized, the atomic force standard of the plutonium-based perovskite crystal structure is 0.01 eV Å -1 , the energy convergence criterion is 10 -6 eV / atom, the cutoff energy was set to 520 eV, and 2π×0.03 Å was used. -1 of k Point grid; Hubbard parameter U (U) of the 5f electron of Pu element eff ) is set to 4 eV.

[0016] As an implementation mode, during structural optimization, the inner core electrons of the atoms constituting the plutonium-based perovskite crystal are described by PAW pseudopotentials; and the exchange correlation functional adopts the PBE functional under the generalized gradient approximation (GGA) framework.

[0017] After obtaining the structurally optimized plutonium-based perovskite crystal structure, the present invention calculates the crystal formation enthalpy of the structurally optimized plutonium-based perovskite crystal structure according to the first principles.

[0018] As an implementation manner, the calculation is performed using first-principles calculation software, and the software includes VASP, CP2K or Materials Studio.

[0019] As an implementation mode, when calculating the crystal formation enthalpy of the plutonium-based perovskite crystal structure after structural optimization, the synthesis path of the plutonium-based perovskite crystal structure is performed according to Formula I; the calculation formula of the crystal formation enthalpy is performed according to Formula II; Formula I; Formula II; In formula I and formula II, the space group of Pu is Fm m, O2 is an oxygen molecule in a cubic box with a side length of 10Å, TM It is a transition metal element; The Pu TM O3, Pu, TM , the energy of O2 is obtained by self-consistent calculation.

[0020] If the crystal formation enthalpy is negative, it proves that the structure is thermodynamically stable, otherwise it is not thermodynamically stable.

[0021] The present invention calculates the elastic constants of the plutonium-based perovskite crystal structure after structural optimization based on the first principles. C ij , and based on the elastic constants, determine whether the crystal structure satisfies the Born stability criterion.

[0022] As an embodiment, the elastic constants of the plutonium-based perovskite crystal structure after the calculation structure optimization are C ij When calculating the stress-strain method or the stress-energy method in the first principles,

[0023] The present invention calculates the phonon dispersion frequency of the plutonium-based perovskite crystal structure after structural optimization, and determines whether all phonon frequencies are greater than zero.

[0024] If the crystal formation enthalpy is less than zero, satisfies the Born stability criterion, and all phonon frequencies are greater than zero, it proves that the plutonium-based perovskite crystal structure is a stable structure.

[0025] As an implementation mode, the finite displacement method or density functional perturbation theory is used to calculate the phonon dispersion frequency of the plutonium-based perovskite crystal structure after structural optimization.

[0026] As an implementation method, when calculating the structure optimization, crystal formation enthalpy, elastic constants and phonon dispersion frequency, the temperature and pressure are set to 0K and 0GPa respectively.

[0027] The technical solutions provided by the present invention are described in detail below in conjunction with the embodiments, but they should not be construed as limiting the protection scope of the present invention.

[0028] In the embodiment of the present invention, the software calculation part involved is based on density functional theory, and adopts the VASP (Vienna ab initio Simulation Package) program and Phonopy program commonly used in the industry to combine with each other to perform calculations to obtain the data required in each step of the present invention.

[0029] Example 1 This example takes the PuMnO3 structure as an example to introduce the plutonium-based perovskite structure stability evaluation method. PuMnO3 belongs to the orthorhombic system and its space group is Pna2 The unit cell parameters are shown in Table 1, and the structure is shown in Figure 2 shown.

[0030] Table 1 Unit cell parameters of PuMnO3 structure

[0031] 1) Crystal structure optimization During structural optimization, the atomic force standard of the PuMnO3 structure was 0.01 eV Å -1 , the energy convergence criterion is 10 -6 eV / atom, the cutoff energy was set to 520 eV, and 2π×0.03 Å was used. -1 of k Point grid, U was selected for the 5f electrons of the Pu element eff =4eV.

[0032] For Pu element, the space group is Fm m, whose atomic force standard is 0.01 eV Å -1 , the energy convergence criterion is 10 - 6 eV / atom, the cutoff energy was set to 520 eV, and a 12×12×12 k Point grid.

[0033] For Mn element, the space group is Im m, whose atomic force standard is 0.01 eV Å -1 , the energy convergence criterion is 10 - 6 eV / atom, the cutoff energy was set to 520 eV, and a 17×17×17 k Point grid.

[0034] For the O2 molecule, the atomic force standard is 0.001 eV Å -1 , the energy convergence criterion is 10 -6 eV / atom, the cutoff energy was set to 520 eV, and a 3×3×3 k Point grid.

[0035] 2) Thermodynamic stability calculation After structural optimization, self-consistent calculations were performed on the four structures of PuMnO3, Pu, Mn and O2, from which the energy values ​​of the four structures were obtained. The calculation results are shown in Table 2. The formation enthalpy of PuMnO3 can be obtained from the energy value.

[0036] Table 2 Energy values ​​of elements and compounds obtained by self-consistent calculation

[0037] The formation enthalpy of PuMnO3 is: = -14.127 (eV / fu); Because the formation enthalpy of PuMnO3 is less than zero, it is thermodynamically stable.

[0038] 3) Mechanical stability calculation The elastic constants of the PuMnO3 structure were calculated using the stress-strain method using a 4×6×7 k Point grid. PuMnO3 belongs to the orthorhombic system and has 9 independent elastic constants. The calculation results are shown in Table 3. The unit of elastic constant is GPa.

[0039] Table 3 Elastic constants of PuMnO3

[0040] For the orthorhombic crystal system, according to the Born stability criterion, its mechanical stability condition is:

[0041] Calculations show that the elastic constants of PuMnO3 satisfy the Born stability criterion, so it has mechanical stability.

[0042] 4) Dynamic stability calculation VASP combined with Phonopy software uses the finite position method to calculate the structural phonon spectrum. The expansion cell size is 2×2×2. The calculated PuMnO3 phonon dispersion curve is as follows: Figure 3 Obviously, the phonon frequencies of this structure are all positive, so it is dynamically stable.

[0043] 5) Evaluation of the stability of the crystal structure of plutonium-based perovskites Based on steps 1) to 4), the formation enthalpy of the PuMnO3 crystal structure is less than zero, satisfies the Born stability criterion, and all phonon frequencies are greater than zero, so PuMnO3 is a stable structure with thermodynamic, mechanical and kinetic stability.

[0044] Note: When calculating the structure optimization, crystal formation enthalpy, elastic constants and phonon dispersion frequency, the temperature and pressure are set to 0K and 0GPa respectively.

[0045] Although the above embodiment describes the present invention in detail, it is only a part of the embodiments of the present invention, not all of the embodiments. Other embodiments can be obtained based on this embodiment without creativity, and these embodiments all fall within the protection scope of the present invention.

Claims

1. A method for evaluating the stability of a plutonium-based perovskite crystal structure, characterized in that: The following steps are involved: Structural optimization is performed on the plutonium-based perovskite crystal structure to obtain a structurally optimized plutonium-based perovskite crystal structure; Based on the first principles, the crystal formation enthalpy of the plutonium-based perovskite crystal structure after structural optimization is calculated; Calculation of the elastic constants of the optimized plutonium-based perovskite crystal structure based on first principles C ij , and based on the elastic constants, determine whether the crystal structure meets the Born stability criterion; Calculate the phonon dispersion frequency of the plutonium-based perovskite crystal structure after structural optimization to determine whether all phonon frequencies are greater than zero; If the crystal formation enthalpy is less than zero, satisfies the Born stability criterion, and all phonon frequencies are greater than zero, it proves that the plutonium-based perovskite crystal structure is a stable structure.

2. The stability evaluation method according to claim 1, characterized in that: When the structure is optimized, the atomic force standard of the plutonium-based perovskite crystal structure is 0.01 eV Å -1 , the energy convergence criterion is 10 -6 eV / atom, the cutoff energy was set to 520 eV, and 2π×0.03 Å was used. -1 of k Point mesh; the Hubbard parameter U of the 5f electrons of the Pu element is set to 4 eV.

3. The stability evaluation method according to claim 1, characterized in that: During structural optimization, the inner core electrons of the plutonium-based perovskite crystal structure are described by PAW pseudopotentials; and the exchange correlation functional adopts the PBE functional under the generalized gradient approximation (GGA) framework.

4. The stability evaluation method according to claim 1, characterized in that: When calculating the crystal formation enthalpy of the plutonium-based perovskite crystal structure after structural optimization, the synthesis path of the plutonium-based perovskite crystal structure is performed according to Formula I; the calculation formula of the crystal formation enthalpy is performed according to Formula II; Formula I; Formula II; In formula I and formula II, the space group of Pu is Fm m, O2 is an oxygen molecule in a cubic box with a side length of 10Å, TM It is a transition metal element; The Pu TM O3, Pu, TM , the energy of O2 is obtained by self-consistent calculation.

5. The stability evaluation method according to claim 4, characterized in that: The transition metal element includes Mn, Ti, V, Cr, Fe, Co, Ni, Cu, Zn or Ga.

6. The stability evaluation method according to claim 1, characterized in that: The elastic constants of the plutonium-based perovskite crystal structure after the calculation structure optimization C ij When calculating the stress-strain method or the stress-energy method in the first principles, 7. The stability evaluation method according to claim 1, characterized in that: When calculating the phonon dispersion frequency of the plutonium-based perovskite crystal structure after structural optimization, the finite displacement method or density functional perturbation theory is used.

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