Method for analyzing doped stable structure of lutetium silicate crystal

Abstract

The invention relates to an analysis method of a lutetium silicate crystal doped stable structure, which comprises the following steps: firstly constructing a lutetium silicate pure crystal and a doping defect structure model containing doping elements, and then carrying out structural relaxation optimization by using density functional theory calculation software to obtain an optimized structure and total energy. Calculating an image charge correction Ecorr value, a potential alignment correction value and a reference chemical potential value, and constructing a defect structure formation energy value by combining total energy and a charge state; then forming a relation curve by taking the Fermi level as a horizontal coordinate, the defect formation energy as a vertical coordinate and different charge states of the defect as slopes, and selecting a line segment with the lowest energy as a formation energy-Fermi level curve; and finally summarizing the curves, taking the midpoint of the band gap as a Fermi level reference value, and taking the minimum value as the most stable defect structure. According to the method, calculation and analysis are combined, a dual correction mechanism is introduced, and a good correction effect on the cerium-doped lutetium silicate system is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of materials science, and in particular to an analysis method for the doped stable structure of a lutetium silicate crystal. Background Art

[0002] Cerium-doped lutetium silicate (LSO:Ce) is a widely recognized scintillator material with broad application prospects in high-energy physics and digital medical imaging. The matrix material lutetium silicate (LSO) has a high density (7.4g / cm 3 ) and chemical stability, its luminescence center Ce 3+ The 5d-4f transition has a typical decay time of 10-50 ns, enabling modern scintillators to achieve high temporal resolution. LSO:Ce (LSO:Ce) exhibits high light output (26,000 photons / MeV) and a short decay time (approximately 40 ns). However, experimental studies have shown that LSO:Ce crystals exhibit a significant afterglow phenomenon, which severely impacts their scintillation performance. This afterglow effect is associated with defect levels caused by intrinsic oxygen vacancies and various other defects.

[0003] Among the various defects in lutetium silicate crystals, oxygen vacancies are an intrinsic defect that can significantly degrade the luminescence performance by capturing excited electrons from cerium centers, resulting in reduced light output and prolonged decay time. In order to suppress the harmful afterglow and adjust the scintillation performance, researchers have developed a variety of strategies, including: forming an isostructural lutetium yttrium silicate (LYSO) solid solution by doping with yttrium, thermal annealing treatment, and co-doping with elements such as lithium, calcium, copper, aluminum, and carbon. Among these methods, co-doping has shown significant effects in simultaneously shortening the decay time and improving the light output. However, multiple dopants may lead to complex charged or neutral defects, which makes it difficult to understand the intrinsic mechanism between the defect structure and the luminescence performance.

[0004] Accurately determining the distribution and stability of doping elements in LSO:Ce crystals remains a significant challenge in current doping studies. Experiments often use a series of concentration gradients for comparison, but actual doping concentrations often deviate significantly from theoretical values. The specific location of doping elements in the crystal lattice is difficult to determine directly; dopants may occupy lutetium sites, silicon sites, or form interstitial atoms, even with multiple possible configurations under different growth conditions. Furthermore, establishing a quantitative relationship between doping and afterglow is difficult, making it difficult to experimentally distinguish the specific contributions of various defects to afterglow. Summary of the Invention

[0005] Aiming at the problem that it is difficult to accurately determine the distribution position of doping elements and their stable state in the current research on doping of LSO:Ce crystals, the present invention provides a method for analyzing the doping stable structure of lutetium silicate crystals.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] A method for analyzing the doped stable structure of lutetium silicate crystals, the method comprising:

[0008] S1. Construct a structural model of pure lutetium silicate crystals and a doping defect structure model containing doping elements;

[0009] S2. Performing structural relaxation optimization on the pure crystal structure model of lutetium silicate and the doping defect structure models containing various doping elements using density functional theory calculation software to obtain the optimized structure model and the related total energy;

[0010] S3. Calculate the image charge (IC) correction E related to the formation energy corr value, the potential alignment (PA) correction value of each defect structure, and the reference chemical potential value μ of each defect state i , combining the total energy and charge state of the pure crystal and the defect structure to construct the formation energy value of each defect structure;

[0011] S4. With the Fermi level as the abscissa and the defect formation energy as the ordinate, the defect structure formation energy is taken as the formation energy value of the Fermi level at 0, and different charge states are taken as slopes to form a series of intersecting relationship curves. The line segment with the lowest energy among the intersections is selected as its formation energy-Fermi level curve;

[0012] S5. Select the defect structure formation energy-Fermi level curves under study and summarize them. Take the midpoint of the band gap as the reference value of the Fermi level. Observe the intersection of the dotted line at the midpoint of the band gap and the formation energy curve of each defect type. The minimum value of the intersection is the most stable defect structure.

[0013] Furthermore, the model of the lutetium silicate crystal in S1 is obtained from the open source database Crystallography OpenDatabase, and the lattice parameters of the lutetium silicate crystal are α=γ=90°, β=122.22°.

[0014] Furthermore, the doping element in S1 is one or more of lithium, sodium, and potassium.

[0015] Furthermore, the density functional theory calculation software described in S2 is the Vienna ab initio simulation package.

[0016] Furthermore, when calculating the doping defect structure model containing dopant elements in S2, a 2×2×1 Monkhorst-Pack k-grid is used, and the electronic interaction is described by the Perdew-Burke-Ernzerhof exchange-correlation functional.

[0017] Furthermore, the convergence criterion for relaxation in S2 is set to be that the residual force per atom is less than , the plane wave cutoff energy is set to 500 eV.

[0018] Furthermore, the image charge correction E of the defect structure is calculated in S4. corr The value is calculated as:

[0019]

[0020] Among them, E corr is the Image Charge (IC) correction value used to account for long-range Coulomb potential errors in charged defect calculations. α is the Madelung constant of the lattice structure, which is dependent on the shape of the selected supercell model. q is the defect charge state; ε is the static dielectric constant of the material; and L is the effective size of the selected supercell model.

[0021] Furthermore, the calculation formula for the potential alignment correction value of the defect structure in S4 is:

[0022] ΔV NAP =V defect -V bulk

[0023] Where, ΔV NAP is the value corrected by Potential Alignment (PA), which is used to solve the short-range potential offset problem. V bulk is the average electrostatic potential of the pure crystal, V defect is the average electrostatic potential of the defect structure.

[0024] Furthermore, the calculation formula for the formation energy value of the defect structure in S4 is:

[0025]

[0026] in, is the formation energy of each defect structure, is the total energy of the defect structure, E tot(bulk) is the total energy of the pure crystal, E corr is the value of image charge (IC) correction, ΔV NAP is the value corrected by PotentialAlignment (PA), ni is the change in the amount of doping elements, μ i is the reference chemical potential value of the doping element, E F is the Fermi level.

[0027] Furthermore, the defect structure includes one or more of substitutional doping, interstitial doping, and oxygen vacancies.

[0028] Compared with the prior art, the present invention has the following advantages:

[0029] 1) High Precision: This paper combines density functional theory calculations with formation energy analysis and introduces a dual correction mechanism (image charge correction and potential alignment correction). This effectively solves the problems of long-range Coulomb potential error and short-range potential offset in charged defect calculations, and has a good correction effect on the cerium-doped lutetium silicate system.

[0030] 2) High efficiency: The modular analysis process designed by this invention simplifies the complex calculation process. Researchers do not need to master the theoretical calculation details in depth, but can complete the doping stability analysis by simply following the instructions. The formation energy calculation module includes the potential alignment (PA) correction value ΔV for different doping types of cerium, lithium, sodium, potassium doping elements and lutetium silicate intrinsic defects. NAP and the reference chemical potential μ of each defect state i , can be used to perform easy-to-operate high-precision calculations of the formation energy of defect structures containing these doping elements, and the results can be converted into intuitive, scientifically-compliant formation energy-Fermi level diagrams through the drawing module.

[0031] 3) Scalability: The analytical framework constructed in this paper is seamlessly applicable to alkali metal elements (lithium, sodium, potassium) and complex co-doping systems, and can simultaneously handle multiple combinations of doping positions and defect types. By intuitively comparing the formation energy-Fermi level diagram, the most stable doping configuration can be quickly determined, providing clear optimization directions for experimental research. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 Formation energy-Fermi level diagram provided for the embodiments. DETAILED DESCRIPTION

[0033] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0034] Example

[0035] To overcome the current difficulty in accurately determining the distribution location and stable state of doping elements in LSO:Ce crystal doping research, this embodiment provides a method for analyzing the doping stable structure of lutetium silicate crystals, including the following steps:

[0036] (1) Constructing a unit cell model: The experimentally determined model of lutetium silicate crystals was obtained from the open source database Crystallography Open Database. Its lattice parameters are α=γ=90°,β=122.22°. In this embodiment, the experimental measurement model is expanded to construct a 2x2x1 supercell model as the basis of the cell model. On the basis of this cell model, different defect types are established, and defective structures are constructed by replacing atoms or interstitial doping. When creating defects, there are two lutetium atoms with different coordination environments in the lutetium silicate system, and the coordination numbers are 6 and 7, respectively. The seven-coordinated lutetium atom is named Lu1, and the six-coordinated one is named Lu2. There are five oxygen atoms in different environments, named O1 to O5. Finally, a pure crystal cell model and a series of defective structure models of the research objects are obtained. The defective structure models selected in the embodiment are single-atom lithium replacing the seven-coordinated lutetium atom (Li Lu1 ), single-atom lithium interstitial doping (Li i ), oxygen vacancy pentad defect (VO5), lithium substituted seven-coordinated lutetium atoms and oxygen vacancy pentad coexistence (Li Lu1 -VO5), lithium interstitial doping and oxygen vacancy coexistence (Li i -VO5).

[0037] (2) Unit cell model optimization: The pure crystal and defect structures were optimized using the Vienna Ab Initio Simulation Package (VASP). In this example, a 2×2×1 Monkhorst-Pack k-grid was used for the calculation of defect structures. The electronic interaction was described by the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional. The ionic structure was described by the projected augmented wave (PAW) method. The valence electron configurations corresponding to the PAW data sets of each element are as follows: Lu is 5p 6 5d 1 6s 2 (4f 14 As the core electron is frozen), O is 2s 2 2p 4 , Ce is 5s 2 5p 6 4f 1 5d 1 6s 2 , Li is 1s 2 2s1 (the inner 1s orbital is treated as a valence state), Na is 2p 6 3s 1 , K is 3p 6 4s 1 It should be noted that the outer electrons of alkali metals are treated as valence electrons. The convergence criterion of the electronic iteration is set to 10 -6 eV; the convergence criterion for atomic relaxation is set to a residual force per atom less than The plane wave cutoff energy is set to 500 eV.

[0038] (3) The lattice parameters of the optimized pure crystal structure are β=122.00°, which is consistent with the lattice parameters of the experimentally determined model ( α=γ=90°,β=122.22°) is close, with an error of less than 0.5%. Similarly, a series of defect structure models are optimized, and finally the most stable structure model and the output file OUTCAR containing its total energy are obtained.

[0039] (4) Formation energy model parameter calculation: For this system, the formation energy calculation with special corrections is performed. The specific module refers to the following formation energy calculation formula:

[0040]

[0041] 1. Extract the total energy E of the pure crystal from the OUTCAR file obtained by the Vienna Ab Initio Simulation Package (VASP) structure optimization calculation tot(bulk) The total energy of each defect structure

[0042] 2. Extract the valence band top position of each defect structure from the OUTCAR file obtained by the Vienna Ab Initio Simulation Package (VASP) structure optimization calculation as E F Initial value of

[0043] 3. Through the formula: Substitute the Madelung constant α, lattice parameter L, and defect charge q related to the structural model to solve the image charge (IC) correction E corr value

[0044] 4. Calculate the remote electrostatic potential of pure crystal and defect structure respectively, according to the formula ΔV NAP =V defect -V bulk Calculate the potential alignment (PA) correction value of each defect structure

[0045] 5. The corresponding chemical potential value of each doping element oxide determined by experiment is added to the calculated chemical potential value of the element to obtain the reference chemical potential value μ of each doping element. i

[0046] 6. Substitute the above content into the formation energy calculation formula and calculate the formation energy of each defect structure separately, which is defined as the defect formation energy when the Fermi level is at the top of the valence band.

[0047] (5) Constructing a formation energy-Fermi level diagram model: The formation energy-Fermi level diagram is constructed with the Fermi level as the horizontal axis, the defect formation energy as the vertical axis, and the defect charge state as the slope. The Fermi level range is taken as the band gap width, which is extracted from the output file OUTCAR of the pure crystal. For a certain defect structure, the formation energy of each defect structure calculated in (4) is used as the formation energy value of the Fermi level at 0, and the different charge states are used as slopes to form a series of intersecting relationship curves. The line segment with the lowest energy in the intersection is selected as its formation energy-Fermi level curve.

[0048] (6) Predict the most stable structure: Summarize the formation energy-Fermi level curves of different defect structures obtained in (5) in one graph, take the midpoint of the band gap as the Fermi level reference value, and observe the intersection of the dotted line at the midpoint of the band gap and the formation energy curve of each defect type. The minimum value of the intersection is the most stable defect structure. Figure 1 The figure shows the substitution of a single lithium atom for a seven-coordinated lutetium atom (Li Lu1 ), single-atom lithium interstitial doping (Li i ), oxygen vacancy pentad defect (VO5), lithium substituted seven-coordinated lutetium atoms and oxygen vacancy pentad coexistence (Li Lu1 -VO5), lithium interstitial doping and oxygen vacancy coexistence (Li i -VO5) formation energy, with the change of Fermi level. The formation energy of the midpoint of the band gap is from small to large, respectively. Lu1 , Li i ,VO5,Li i -VO5 and Li i -VO5, the formation energy values ​​are 3.32eV, 5.52eV, 6.56eV, 12.14eV, and 7.55eV respectively. The comparison of formation energy usually selects structures containing the same defects, that is, when lithium is doped alone in lutetium silicate, its most stable structure is Li Lu1 , that is, lithium replaces the seven-coordinated lutetium atom. For the composite defect Li i -VO5 and Li i -VO5, which exhibits the same properties, i.e., substitution sites are more stable than doping sites.

[0049] These conclusions have played a significant role in the progress of experiments and provide a theoretical basis for subsequent material optimization design. This method can be further extended to the analysis of other doping elements (such as alkali metals such as sodium and potassium) and complex co-doping systems, helping experimental researchers to precisely control doping strategies and specifically improve the afterglow characteristics and light output performance of LSO:Ce scintillator materials, significantly shortening the research and development cycle from theory to practical application.

[0050] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other manner. Any person skilled in the art may utilize the above-disclosed technical content to modify or modify the present invention into equivalent embodiments. However, any simple modifications, equivalent variations, and modifications to the above embodiments that do not depart from the technical content of the present invention and are based on the technical essence of the present invention remain within the scope of protection of the present invention.

Claims

1. A method for analyzing the doped stable structure of lutetium silicate crystals, characterized in that: The analytical method includes: S1. Construct a structural model of pure lutetium silicate crystals and a doping defect structure model containing doping elements; S2. Performing structural relaxation optimization on the pure crystal structure model of lutetium silicate and the doping defect structure models containing various doping elements using density functional theory calculation software to obtain the optimized structure model and the related total energy; S3. Calculate the image charge correction E related to the formation energy respectively corr value, potential alignment correction value of each defect structure, reference chemical potential value μ of each defect state i , combining the total energy and charge state of the pure crystal and the defect structure to construct the formation energy value of each defect structure; S4. With the Fermi level as the abscissa and the defect formation energy as the ordinate, the defect structure formation energy is taken as the formation energy value of the Fermi level at 0, and different charge states are taken as slopes to form a series of intersecting relationship curves. The line segment with the lowest energy among the intersections is selected as its formation energy-Fermi level curve; S5. Select the defect structure formation energy-Fermi level curves under study and summarize them. Take the midpoint of the band gap as the reference value of the Fermi level. Observe the intersection of the dotted line at the midpoint of the band gap and the formation energy curve of each defect type. The minimum value of the intersection is the most stable defect structure.

2. The method for analyzing the doped stable structure of lutetium silicate crystals according to claim 1, wherein: The model of the lutetium silicate crystal in S1 was obtained from the open source database Crystallography Open Database. The lattice parameters of the lutetium silicate crystal are α=γ=90°, β=122.22°.

3. The method for analyzing the doped stable structure of lutetium silicate crystals according to claim 1, wherein: The doping element in S1 is one or more of lithium, sodium, and potassium.

4. The method for analyzing the doped stable structure of lutetium silicate crystals according to claim 1, wherein: The density functional theory calculation software described in S2 is the Vienna ab initio simulation package.

5. The method for analyzing the doped stable structure of lutetium silicate crystals according to claim 1, wherein: When calculating the doping defect structure model containing dopant elements in S2, a 2×2×1 Monkhorst-Pack k-grid is used, and the electronic interaction is described by the Perdew-Burke-Ernzerhof exchange-correlation functional.

6. The method for analyzing the doped stable structure of lutetium silicate crystals according to claim 1, wherein: The convergence criterion for relaxation in S2 is set to a residual force per atom smaller than The plane wave cutoff energy is set to 500 eV.

7. The method for analyzing the doped stable structure of lutetium silicate crystals according to claim 1, wherein: Image charge correction E of defect structure calculated in S4 corr The value is calculated as: Among them, E corr is the value of the image charge (IC) correction, which is used to resolve the long-range Coulomb potential error in the calculation of charged defects; α is the Madelung constant of the lattice structure, which is related to the shape of the selected supercell model; q is the defect charge state; ε is the static dielectric constant of the material; L is the effective size of the selected supercell model.

8. The method for analyzing the doped stable structure of lutetium silicate crystals according to claim 1, wherein: The calculation formula for the potential alignment correction value of the defect structure in S4 is: ΔV NAP =V defect -V bulk Where, ΔV NAP is the value corrected by Potential Alignment (PA), which is used to solve the short-range potential offset problem. V bulk is the average electrostatic potential of the pure crystal, V defect is the average electrostatic potential of the defect structure.

9. The method for analyzing the doped stable structure of lutetium silicate crystals according to claim 1, wherein: The calculation formula for the formation energy value of the defect structure in S4 is: in, is the formation energy of each defect structure, is the total energy of the defect structure, E tot(bulk) is the total energy of the pure crystal, E corr is the image charge correction value, ΔV NAP is the potential alignment correction, n i is the change in the amount of doping elements, μ i is the reference chemical potential value of the doping element, E F is the Fermi level.

10. The method for analyzing the doped stable structure of lutetium silicate crystals according to claim 1, characterized in that: The defect structure includes one or more of substitutional doping, interstitial doping, and oxygen vacancies.

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