Method for determining the phase boundary and structure of a piezoelectric solid solution oxide crystal and system based on the method

Abstract

The application discloses a method for determining a piezoelectric solid solution oxide crystal phase boundary and structure and a system based on the method, and the method comprises the following steps: acquiring a powder X-ray diffraction pattern of a piezoelectric solid solution oxide to be analyzed and a space group of the piezoelectric solid solution oxide to be analyzed; performing fitting and refining on the acquired powder X-ray diffraction pattern by using the space group of the piezoelectric solid solution oxide to be analyzed, so as to obtain refined residual error factors of different space groups; determining the space group to which the piezoelectric solid solution oxide to be analyzed belongs according to the refined residual error factors; and determining the phase boundary of the piezoelectric solid solution oxide to be analyzed according to the space group to which the piezoelectric solid solution oxide to be analyzed belongs. The method can accurately determine the phase boundary of the material to be analyzed by multiple single-phase space group refining, clearly defines the homotype phase boundary, and determines the space group of the pseudo-cubic phase.

Description

Technical Field

[0001] This invention belongs to the field of crystallography and relates to a method for determining the phase boundaries and structure of piezoelectric solid solution oxide crystals and a system based on this method. Background Technology

[0002] Materials structure research is a crucial part of materials science, essential for understanding material properties, designing novel materials, and developing high-performance products. Studying the structure of crystalline materials provides insights into their properties, preparation processes, and applications. As the composition of a material changes, its phase also changes. Near quasi-isomorphic phase boundaries, materials exhibit superior dielectric and piezoelectric properties; therefore, quasi-isomorphic phase boundaries have become a highly regarded physical concept in piezoelectricity and have been extensively and deeply studied in oxide perovskite piezoelectric materials. In recent years, significant progress has been made in high-performance magnetostrictive materials, electrostatic materials, and energy storage materials based on quasi-isomorphic phase boundary design research. The concept of quasi-isomorphic phase boundaries has also been successfully applied to organic (polymer) functional materials. However, currently, effective measurement methods or accurate differentiation methods are lacking for the quasi-isomorphic phase boundary region and its adjacent quasi-cubic phase region. Therefore, determining the quasi-isomorphic phase boundary region and its adjacent quasi-cubic phase structure is of great significance, as it will contribute to a better understanding of the relationship between material structure and properties and provide strong support for the functional design of materials. For example, Pb(Zr) x Ti 1-x Taking PZT (Pr:Ti) as an example, PZT is one of the most widely studied and applied ferroelectric piezoelectric ceramics. In this material system, with the increase of Ti content, it transforms from a trigonal to a tetragonal crystal system at room temperature. In the finite transformation region near Zr:Ti = 53:47, PZT exhibits high dielectric constant and piezoelectric properties. Theoretically, a quasi-isomorphic phase boundary appears when the free energies of the trigonal and tetragonal phases are equal. Compositions deviating from this point will cause one phase to have a lower free energy and thus exist stably. In reality, various changes during material preparation can lead to energy fluctuations. Therefore, the quasi-isomorphic phase boundary is a finite region, not a clear boundary. Many scholars believe that the structure of the quasi-isomorphic phase boundary is the coexistence of the trigonal and tetragonal phases (or a complex model of quasi-cubic and tetragonal phases), but theoretically, an intermediate phase should exist between the trigonal and tetragonal phases. There is currently no definitive method for determining the structure of the quasi-cubic phase immediately adjacent to the quasi-isomorphic phase boundary. More importantly, there is still no definitive method to determine whether a material is at or near a quasi-isomorphic phase boundary. These controversies and uncertainties pose many challenges to the development, performance improvement, and related theories of materials based on quasi-isomorphic phase boundaries. Summary of the Invention

[0003] To address the problems existing in the prior art, the present invention provides a method for determining the phase boundary and structure of piezoelectric solid solution oxide crystals and a system based on the method, thereby solving the technical problem that the prior art cannot determine whether a material is at a quasi-isomorphic phase boundary or near a quasi-isomorphic phase boundary.

[0004] This invention is achieved through the following technical solution:

[0005] A method for determining the phase boundaries and structure of piezoelectric solid solution oxide crystals includes the following steps:

[0006] S1: Obtain the powder X-ray diffraction pattern of the piezoelectric solid solution oxide to be analyzed and the space group of the piezoelectric solid solution oxide to be analyzed;

[0007] S2: Using the space group of the piezoelectric solid solution oxide to be analyzed as a model, the obtained powder X-ray diffraction pattern is fitted and refined to obtain the refinement residual factor of different space groups.

[0008] S3: Determine the space group to which the piezoelectric solid solution oxide to be analyzed belongs based on the refined residual factor;

[0009] S4: Determine the crystal phase boundaries and structure of the piezoelectric solid solution oxide to be analyzed based on the space group to which it belongs.

[0010] Preferably, the refinement residual factor includes a weighted full-spectrum factor; the weighted full-spectrum factor is not greater than 15%; if the weighted full-spectrum factor is greater than 15%, the powder X-ray diffraction pattern of the piezoelectric solid solution oxide to be analyzed is re-acquired, and steps S1 to S2 are repeated.

[0011] Preferably, the space group of the piezoelectric solid solution oxide to be analyzed is any one of the parent phase space group, the sub-space group of the parent phase, and the high-temperature phase space group of the parent phase.

[0012] Preferably, the process of determining the space group to which the piezoelectric solid solution oxide to be analyzed belongs based on the refinement residual factor in step S3 is as follows: by comparing the refinement residual factors of different space groups, the space group corresponding to the smallest refinement residual factor is the space group to which the piezoelectric solid solution oxide to be analyzed belongs.

[0013] Preferably, in step S4, the process of determining the crystal phase boundaries and structure of the piezoelectric solid solution oxide to be analyzed based on the space group to which the piezoelectric solid solution oxide to be analyzed specifically includes:

[0014] If the space group to which the piezoelectric solid solution oxide to be analyzed belongs has the lowest symmetry, then the piezoelectric solid solution oxide to be analyzed belongs to the quasi-isomorphic phase boundary region.

[0015] Preferably, after step S4, the method further includes using a position splitting method to determine the offset direction and offset distance of the metal atoms in the piezoelectric solid solution oxide relative to the average position or cubic equilibrium position, based on the space group to which the piezoelectric solid solution oxide to be analyzed belongs.

[0016] A system for determining the phase boundaries and structure of piezoelectric solid solution oxide crystals, comprising:

[0017] The data acquisition unit is used to acquire the powder X-ray diffraction pattern of the piezoelectric solid solution oxide to be analyzed and the space group of the piezoelectric solid solution oxide to be analyzed.

[0018] The data fitting unit is used to fit and refine the obtained powder X-ray diffraction pattern using the space group of the piezoelectric solid solution oxide to be analyzed as a model, so as to obtain the refinement residual factor of different space groups.

[0019] The first data processing unit is used to determine the space group to which the piezoelectric solid solution oxide to be analyzed belongs based on the refined residual factor.

[0020] The second data processing unit is used to determine the crystal phase boundaries and structure of the piezoelectric solid solution oxide to be analyzed based on the space group to which the piezoelectric solid solution oxide to be analyzed belongs.

[0021] A terminal device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method described above.

[0022] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the above-described method.

[0023] Compared with the prior art, the present invention has the following beneficial technical effects:

[0024] This invention discloses a method for determining the phase boundaries and structure of piezoelectric solid solution oxide crystals. First, the space group of the piezoelectric solid solution oxide to be analyzed is used as a model to fit and refine the obtained powder X-ray diffraction pattern, obtaining refinement residual factors for different space groups. Then, the space group to which the piezoelectric solid solution oxide belongs is determined based on the refinement residual factors. Finally, the crystal phase boundaries and structure of the piezoelectric solid solution oxide are determined based on the space group to which it belongs. This method, through a rigorous process, accurately determines the phase boundaries, clarifying whether the prepared material is atMPB (located at a quasi-isomorphic phase boundary) or near MPB (near a quasi-isomorphic phase boundary), resolving the controversy and uncertainty regarding quasi-isomorphic and pseudo-cubic phase boundary regions, determining the structure of the pseudo-cubic phase region, and clarifying the quasi-isomorphic phase boundaries.

[0025] Furthermore, the refinement residual factor includes a weighted full-spectrum factor, which can effectively judge the refinement result.

[0026] Furthermore, the weighted full-spectrum factor is no greater than 15%. If the weighted full-spectrum factor is greater than 15%, the powder X-ray diffraction pattern of the piezoelectric solid solution oxide to be analyzed is re-acquired, and steps S1 to S2 are repeated. Setting the weighted full-spectrum factor to a threshold of 15% effectively ensures the reliability of the refined structure and the accuracy of subsequent judgments.

[0027] Furthermore, the process of determining the space group to which the piezoelectric solid solution oxide to be analyzed belongs based on the refinement residual factor in step S3 is as follows: by comparing the refinement residual factors of different space groups, the space group corresponding to the smallest refinement residual factor is the space group to which the piezoelectric solid solution oxide to be analyzed belongs. This method can simply and effectively determine the space group to which the piezoelectric solid solution oxide to be analyzed belongs.

[0028] Furthermore, in step S4, the process of determining the phase boundary of the piezoelectric solid solution oxide to be analyzed based on its space group is as follows: if the space group to which the piezoelectric solid solution oxide to be analyzed belongs has the lowest symmetry, then the piezoelectric solid solution oxide to be analyzed belongs to a quasi-isomorphic phase boundary region. Since a quasi-isomorphic phase boundary is a phase transition process between two phases, and the phase transition process of crystal structure involves the redirection of atomic distortion, resulting in a decrease in the symmetry of the crystal material, the symmetry of the space group can be used to effectively and accurately determine the phase of the crystal material.

[0029] Furthermore, after step S4, the method further includes using a positional decomposition method. Based on the space group to which the piezoelectric solid solution oxide to be analyzed belongs, and for the quasi-isomorphic phase boundary region, based on the cubic phase space group, the offset direction and offset distance of the metal atoms in the piezoelectric solid solution oxide relative to the average position or cubic equilibrium position are determined. This process, using the positional decomposition method and based on the space group to which the piezoelectric solid solution oxide to be analyzed belongs, determines the offset direction and offset distance of the metal atoms in the piezoelectric solid solution oxide relative to the average position or cubic equilibrium position, effectively verifying the accuracy of the judgment result in step S4 and improving the precision of the judgment result. This is because the quasi-isomorphic phase boundary region is a region of two-phase transformation, where the space group in the material will be distorted, and the metal atoms in the material will be offset. Therefore, by judging the offset direction and offset distance of the metal atoms in the material relative to the average position or cubic equilibrium position, the accuracy of the aforementioned judgment is effectively verified. Attached Figure Description

[0030] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0031] Figure 1 This is a flowchart illustrating a method for determining phase boundaries in piezoelectric solid solution oxide crystals according to the present invention.

[0032] Figure 2 This is a schematic diagram of the structure of a piezoelectric solid solution oxide crystal phase boundary determination system according to the present invention;

[0033] Figure 3 The Rwp values ​​of the (1-x)BiFeO3-xBaTiO3 ceramic powder in Example 2 of this invention are the results of refinement under different space group models.

[0034] Figure 4 The Rwp factor of the R3c model for 0.8BiFeO3-BaTiO3 in Example 2 of this invention varies with the deviation of (a) A-site ions from their average position d and (c) B-site ions. (b) and (d) are magnified views of (a) and (c), respectively.

[0035] Figure 5 The Bi-O3 obtained from 0.8BiFeO3-BaTiO3 in Example 2 of this invention based on the R3c space group position partitioning method. 12 Ba-O 12 Schematic diagrams of Fe-O6 and Ti-O6;

[0036] Figure 6 The 0.65BiFeO3-BaTiO3 in Example 2 of this invention The model's Rwp factor varies with the magnitude of ion deviation from the mean position;

[0037] Figure 7 The XRD patterns of 0.8BiFeO3-BaTiO3 and 0.73BiFeO3-BaTiO3 at room temperature in Example 2 of this invention are shown. Detailed Implementation

[0038] To enable those skilled in the art to understand the features and effects of the present invention, the terms and expressions used in the specification and claims are explained and defined in general below. Unless otherwise specified, all technical and scientific terms used herein have the ordinary meaning understood by those skilled in the art regarding the present invention, and in case of conflict, the definitions in this specification shall prevail.

[0039] The theories or mechanisms described and disclosed herein, whether right or wrong, should not in any way limit the scope of the invention, that is, the contents of the invention can be implemented without being limited by any particular theory or mechanism.

[0040] In this document, all features defined by numerical ranges or percentage ranges, such as numerical values, quantities, contents, and concentrations, are for the sake of brevity and convenience only. Accordingly, descriptions of numerical ranges or percentage ranges should be considered as covering and specifically disclosing all possible sub-ranges and individual numerical values ​​(including integers and fractions) within those ranges.

[0041] In this article, unless otherwise specified, “contains,” “includes,” “containing,” “has,” or similar terms cover the meanings of “composed of” and “mainly composed of,” for example, “A contains a” covers the meanings of “A contains a and others” and “A contains only a.”

[0042] For the sake of brevity, not all possible combinations of the technical features in each implementation scheme or embodiment are described herein. Therefore, as long as there is no contradiction in the combination of these technical features, the technical features in each implementation scheme or embodiment can be combined arbitrarily, and all possible combinations should be considered within the scope of this specification.

[0043] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined by the appended claims.

[0044] The following examples use instruments and equipment conventional in the art. Experimental methods in the following examples, unless otherwise specified, are generally performed under conventional conditions or as recommended by the manufacturer. All raw materials used in the following examples are conventional commercially available products with specifications conventional in the art. In this specification and the following examples, unless otherwise specified, "%" refers to weight percentage, "parts" refers to parts by weight, and "ratio" refers to weight proportion.

[0045] Example 1

[0046] like Figure 1 As shown, the present invention provides a method for determining the phase boundaries and structure of piezoelectric solid solution oxide crystals, comprising the following steps:

[0047] S1: Obtain powder X-ray diffraction data, structural model, and instrument parameters of the piezoelectric solid solution oxide to be analyzed, and obtain the powder X-ray diffraction pattern of the piezoelectric solid solution oxide to be analyzed through the obtained powder X-ray diffraction data.

[0048] Here, the space group in the structural model of the piezoelectric solid solution oxide to be analyzed can be any one of the parent phase space group, the sub-space group of the parent phase, and the high-temperature phase space group of the parent phase.

[0049] The structural model is stored in a structural model file, which contains information about the crystal structure, including space group, unit cell parameters, atomic coordinates, atomic types, symmetry operations, and other information.

[0050] The space group in the structural model of the piezoelectric solid solution oxide to be analyzed can be any one of the parent phase space group, the sub-space group of the parent phase, and the high-temperature phase space group of the parent phase.

[0051] The X-ray diffraction data is stored in an X-ray diffraction data file.

[0052] The instrument parameters are stored in an instrument parameter file, which contains some basic parameters and information of the X-ray diffractometer, including the wavelength of the X-rays, the type of target material, and the peak shape function.

[0053] S2: The space group of the piezoelectric solid solution oxide to be analyzed is used to fit and refine the obtained powder X-ray diffraction pattern to obtain the refinement residual factor of different space groups.

[0054] The refined residual factor includes a weighted full-spectrum factor. The weighted full-spectrum factor is no greater than 15%. If the weighted full-spectrum factor is greater than 15%, the powder X-ray diffraction pattern of the piezoelectric solid solution oxide to be analyzed is re-acquired, and steps S1 to S2 are repeated.

[0055] S3: Determine the space group to which the piezoelectric solid solution oxide to be analyzed belongs based on the refined residual factor; specifically, by comparing the refined residual factors of different space groups, the space group corresponding to the smallest refined residual factor is the space group to which the piezoelectric solid solution oxide to be analyzed belongs.

[0056] S4: Determine the phase boundary of the piezoelectric solid solution oxide to be analyzed based on its space group. Specifically, if the space group to which the piezoelectric solid solution oxide to be analyzed belongs has the lowest symmetry, then the piezoelectric solid solution oxide to be analyzed belongs to a quasi-isomorphic phase boundary region.

[0057] S5: To further verify the accuracy of the above method, the position splitting method is also used. Based on the space group to which the piezoelectric solid solution oxide to be analyzed belongs, the cubic phase space group is used to determine the offset direction and offset distance of the metal atoms in the piezoelectric solid solution oxide relative to the average position or cubic equilibrium position.

[0058] This invention discloses a method for determining the phase boundaries and structure of piezoelectric solid solution oxide crystals. First, the space group of the piezoelectric solid solution oxide to be analyzed is used to fit and refine the obtained powder X-ray diffraction pattern, obtaining refinement residual factors for different space groups. Then, the space group to which the piezoelectric solid solution oxide belongs is determined based on the refinement residual factors. Finally, the phase boundary of the piezoelectric solid solution oxide is determined based on the space group to which it belongs. This method accurately determines quasi-isomorphic phase boundary regions and pseudo-cubic phase space groups through refinement using multiple single-phase space groups and positional splitting methods, thereby determining the phase diagram. This resolves the controversy and uncertainty surrounding quasi-isomorphic and pseudo-cubic phase boundary regions in materials, reducing confusion and failures in material research and design based on the concept of quasi-isomorphic phase boundaries.

[0059] Piezoelectric solid solution oxides are piezoelectric materials composed of two or more inorganic oxide crystals. Commonly used inorganic piezoelectric materials include solid solutions formed from lead titanate (PbTiO3) and lead zirconate (PbZrO3).

[0060] At the same time, such as Figure 2 As shown, the present invention also provides a system for determining the phase boundary of a piezoelectric solid solution oxide crystal, comprising:

[0061] The data acquisition unit is used to acquire the powder X-ray diffraction pattern of the piezoelectric solid solution oxide to be analyzed and the space group of the piezoelectric solid solution oxide to be analyzed.

[0062] The data fitting unit is used to fit and refine the obtained powder X-ray diffraction pattern using the space group of the piezoelectric solid solution oxide to be analyzed as a model, so as to obtain the refinement residual factor of different space groups.

[0063] The first data processing unit is used to determine the space group to which the piezoelectric solid solution oxide to be analyzed belongs based on the refined residual factor.

[0064] The second data processing unit is used to determine the crystal phase boundaries and structure of the piezoelectric solid solution oxide to be analyzed based on the space group to which the piezoelectric solid solution oxide to be analyzed belongs.

[0065] Example 2

[0066] To further illustrate the technical solution of the present invention, the following embodiments are provided.

[0067] Step 1: Prepare the material to be analyzed, such as BiFeO3-BaTiO3 ceramic, and use this ceramic as the research object to explain the technical solution of the present invention. The specific preparation process is as follows:

[0068] Based on the general chemical formula (1-x)BiFeO3-xBaTiO3, where 0.2≤x≤0.90, the chemical raw materials were weighed according to the stoichiometric ratio of each component. The weighed raw materials were placed in a nylon container, and ball-milled for 4–6 hours in a planetary ball mill with anhydrous ethanol as the dispersant and agate balls as the milling medium at a speed of 220 r / min. Afterward, the mixture was dried in a constant temperature drying oven for 3 hours. The dried powder was then placed in a sealed corundum dry pot and kept at a suitable temperature for 2 hours. The pre-synthesized product was mixed with anhydrous ethanol and agate balls, and then wet-milled again for 4–6 hours, followed by drying. After drying, the powder is granulated by adding an appropriate amount of 6% wt polyvinyl alcohol (PVA) as a binder. After being thoroughly ground in a mortar and passed through a 60-mesh sieve, it is pressed into a circular sheet with a diameter of 12 mm and a thickness of 1-2 mm under uniaxial pressure. The sheet is heated to 773 K at a heating rate of 2 K / min and held for 5 hours to remove the binder. The sheet after removing the binder is sintered into ceramic in a muffle furnace using an appropriate sintering regime.

[0069] The samples prepared here include 0.8BiFeO3-BaTiO3, 0.73BiFeO3-BaTiO3, 0.65BiFeO3-BaTiO3, 0.55BiFeO3-BaTiO3, 0.5BiFeO3-BaTiO3, 0.4BiFeO3-BaTiO3, 0.35BiFeO3-BaTiO3, and 0.1BiFeO3-BaTiO3.

[0070] Step 2: Analyze the crystal structure of the material using a combination of experimental techniques and theoretical methods. Experimental techniques include X-ray diffraction, and theoretical methods include group theory. These methods allow us to obtain information about the material's crystal structure.

[0071] The process of acquiring X-ray diffraction data includes the following steps:

[0072] (1) Preparation of powder samples for X-ray diffraction testing

[0073] The sintered ceramic sample is sanded on sandpaper to remove surface impurities, then ground and passed through a 200-mesh sieve to obtain powder with a particle size of tens of micrometers. Special attention should be paid to the following when preparing samples for powder X-ray diffraction testing: First, the sample should not have obvious large particles, meaning it should feel like "flour" to the touch; generally, a particle size of 10 μm is optimal. Second, the sample slots on the X-ray diffraction test slide should be completely filled and compacted during sample preparation to minimize sample displacement errors.

[0074] Since the quality of X-ray diffraction data acquisition is generally high nowadays, a refinement result with a refinement margin of error (Rwp) of less than 15% can be considered reliable. However, differences in testing instruments and refinement software can cause variations in Rwp.

[0075] (2) X-ray diffraction testing equipment and conditions (other equipment may also be used)

[0076] X-ray diffraction phase analysis of the prepared ceramic samples was performed using a Bruker D8 ADVANCE X-ray diffractometer (Germany). The X-ray diffraction experimental conditions were as follows: experimental voltage: 40 kV; current: 100 mA; target material: Cu target; scanning range (2θ) for Rietveld structure refinement: 15–120°; scanning speed: 1° / min.

[0077] Secondly, based on group theory analysis, the subspace groups of the parent phase are determined. For example, in BiFeO3-BaTiO3 ceramics, BiFeO3 is a trigonal phase and BaTiO3 is a tetragonal phase. The subspace groups or subgroups of the subspace groups include R3c, Pm, Pc, Cm, Cc, etc. In this patent, 230 space groups are first screened to select the parent phase space group, the subspace group of the parent phase, and the high-temperature phase space group of the parent phase of the piezoelectric solid solution oxide to be analyzed. Then, the screened space groups are used to refine and fit the powder X-ray diffraction pattern. Table 1 lists the space groups with high fitting degree.

[0078] Table 1. Spatial group obtained after refinement in this embodiment.

[0079]

[0080]

[0081] Step 3: Using the selected space groups as the space groups in the structural model, refine the acquired X-ray diffraction data to obtain the residual factors (Rwp factor) of different space group refinement results. By comparing the refinement results, the optimal structural model can be determined, that is, the space group that best matches the experimental results.

[0082] The fitting factors of the single-phase model refinement of sample 0.65BiFeO3-BaTiO3 are compared in Table 2. As can be seen from Table 2, the Rwp factor of space group P1 is the smallest, so 0.65BiFeO3-BaTiO3 is located at the quasi-isomorphic phase boundary, rather than near the quasi-isomorphic phase boundary.

[0083] The P1 space group is the simplest space group, containing no symmetry elements. In the P1 space group, each atom is independent and unrestricted, and the crystal structure can be a disordered structure of arbitrary shape and size. The P1 space group is also called the translation group or the asymmetry-free group.

[0084] Table 2 Comparison of fitting factors for the refined 0.65BiFeO3-BaTiO3 single-phase model

[0085]

[0086]

[0087] The Rwp values ​​of samples 0.55BiFeO3-BaTiO3, 0.5BiFeO3-BaTiO3, 0.4BiFeO3-BaTiO3, and 0.35BiFeO3-BaTiO3 under different space group models are shown in [reference needed]. Figure 3 The Rwp factors are compared. The Rwp factor of the quasi-isomorphic phase boundary region is larger than that of the pseudo-cubic region. The space group with the smallest Rwp factor in the quasi-isomorphic phase boundary region has lower symmetry than the space group in the pseudo-cubic region. Figure 3 It can be seen that the space groups of 0.55BiFeO3-BaTiO3, 0.5BiFeO3-BaTiO3, 0.4BiFeO3-BaTiO3, and 0.35BiFeO3-BaTiO3 are Cc, located in the pseudocubic region, and belong to the monoclinic crystal system. The crystal structure and phase transformation pathways of the materials in different composition ranges can be determined using the above method.

[0088] In judging the XRD refinement results, since the quality of XRD data acquisition is generally high nowadays, a refinement result with an Rwp factor of less than 15% can be considered reliable. Different companies' instruments typically have different commercial software versions, which may result in slightly different results.

[0089] Step 4: Using the position splitting method, based on the space group to which the piezoelectric solid solution oxide to be analyzed belongs, determine the offset direction and offset distance of the metal atoms in the piezoelectric solid solution oxide relative to the average position or cubic equilibrium position. That is, using the position splitting method, based on the selected space group, refine the acquired X-ray diffraction data.

[0090] In the trigonal phase region, the A-site ions of the material have a displacement difference along the c-axis of the trigonal phase, the Bi ions deviate from the high symmetry position, and the Ba ions do not deviate from the high symmetry position. Figure 4 (a) is the Rwp factor of 0.8BiFeO3-BaTiO3 based on the R3c space group, which varies with the A-site ion (Bi, Ba, Bi / Ba) along the c-axis. H ( <111> cubic (a) shows the change in distance d from the average position of Bi / Ba, and (b) is a magnified view. Figure 4 (a) It can be seen that the A-site ions (Bi, Ba, Bi / Ba) are positively oriented. <111> cubic The direction shift, i.e., the Rwp factor increases rapidly when d≥0. Figure 4 In (b), only Ba is negative. <111> cubic With directional shift, and Bi still at the average position of Bi / Ba, the Rwp factor is... It decreases over time, while Increases when only Bi or Bi / Ba is negative. <111> cubic When the orientation shifts, the obtained Rwp factors are all higher than their Rwp values ​​at the average Bi / Ba position. Therefore, it can be determined that Ba deviates from the average Bi / Ba position by approximately [missing information].

[0091] Here, the metal atoms contained in the ABO3 type perovskite structure are referred to as A-site atoms and B-site atoms, respectively. BiFeO3 is ABO3 type, and BaTiO3 is also ABO3 type. A-site atoms and B-site atoms can be collectively referred to as heavy atoms or metal atoms. Compared with oxygen atoms, oxygen atoms are light atoms.

[0092] Figure 5 Bi-O3 obtained from 0.8BiFeO3-BaTiO3 based on the R3c space group position partitioning method 12 Ba-O 12 Schematic diagram. This shows that the Ba ion is located in a highly symmetric position, while the Bi ion has displacement along the c-axis in three directions.

[0093] In the quasi-isomorphic phase boundary region, the positional decomposition method based on the cubic space group model is refined, and the A-site ions of the material deviate in the

[111] cubic direction, while the B-site ions deviate from their cubic equilibrium positions in the

[110] cubic direction. For example... Figure 6As shown, the cubic space group of 0.65BiFeO3-BaTiO3 is... The model Rwp factor varies with the magnitude of ion deviation from the average position.

[0094] in addition, Figure 7 The X-ray diffraction patterns of 0.8BiFeO3-BaTiO3 and 0.73BiFeO3-BaTiO3 ceramics at room temperature are shown by [the data provided]. Figure 7 It is evident that the diffraction patterns of 0.8BiFeO3-BaTiO3 and 0.73BiFeO3-BaTiO3 ceramics exhibit distinct peak splits around 30° and 39° at 2θ. The {111} plane diffraction lines of the trigonal perovskite structure should show peak splits, with an intensity ratio of 1:3. Both 0.8BiFeO3-BaTiO3 and 0.73BiFeO3-BaTiO3 ceramics can be identified as trigonal structures with space group R3c. The shift in peak position in the diffraction pattern of 0.73BiFeO3-BaTiO3 compared to the corresponding peak position in 0.8BiFeO3-BaTiO3 indicates a larger lattice parameter in the 0.73BiFeO3-BaTiO3 ceramic crystal.

[0095] Using the above methods, it can be determined that in the BiFeO3-BaTiO3 ceramic system, 0.8BiFeO3-BaTiO3 and 0.73BiFeO3-BaTiO3 are located in the tri-directional region. 0.65BiFeO3-BaTiO3 is located at the quasi-isomorphic phase boundary. 0.55BiFeO3-BaTiO3, 0.5BiFeO3-BaTiO3, 0.4BiFeO3-BaTiO3, and 0.35BiFeO3-BaTiO3 are located in the pseudo-cubic region, belonging to the monoclinic crystal system, space group Cc.

[0096] The XRD data refinement method used in this application is Rietveld refinement, and the software is Topas 4.2, TOPAS Academic.

[0097] The refinement strategy adopted is as follows:

[0098] Scale factors

[0099] Zero shift (peak shift)

[0100] Background

[0101] FWHM (Full-Width at Half Maximum)

[0102] Shape, X, Y, (peak shape)

[0103] Lattice parameters

[0104] Atomic coordinates (atomic positions)

[0105] Temperature factors, occupancy (thermal parameters, percentage)

[0106] Preferred orientation

[0107] Rwp factor and GOF of Rietveld refinement

[0108] The goodness of fit of Rietveld refinement can be judged using the Rwp factor and / or GOF (Good of fit). A smaller Rwp factor indicates a better fit. A GOF value should be greater than 1; the closer to 1, the better the fit. The definitions of Rwp factor and GOF used in Topas software are as follows:

[0109] R-pattern: R P

[0110]

[0111] R-pattern,background corrected:R' p :

[0112]

[0113] R-weighted pattern:R wp

[0114]

[0115] R-weighted pattern,background corrected:R' wp

[0116]

[0117] Goodness of fit:GOF

[0118]

[0119] R-Bragg, R B

[0120]

[0121] In the Rietveld refinement process, the selection of the correct peak shape function is crucial for successful refinement. In this embodiment, the peak shape function chosen is Split Pearson VII (SPVII), whose expression is:

[0122] SPVII = PVII_Left + PVII_R

[0123] In the formula:

[0124] PVII_Left=(1+b1x 2 ) -m1 / a, when (-∞ <x<0)

[0125] PVII_Right=(1+b2x 2 ) -m2 / a, when (0 <x<∞)

[0126]

[0127] b1 = (2 -m1 -1) / h1 2 b2=(2 -m2 -1) / h2 2

[0128] Where h1 and h2 satisfy

[0129] fwhm1=2h1

[0130] fwhm2=2h2

[0131] fwhm=h1+h2

[0132] fwhm is the half-width at half-maximum, fwhm1 and fwhm2 are the left and right composite functions respectively, and m1 and m2 are the exponents of the composite function respectively.

[0133] Compared to existing technologies, current methods do not strictly distinguish between quasi-isomorphic phase boundaries (MPBs) and pseudo-cubic phases, thus failing to accurately determine phase boundaries. This leads to confusion, uncertainty, and controversy in experimental research, the theories used, and the analyses. The method in this application rigorously and precisely determines phase boundaries, identifying whether the prepared material is at MPB (located at a quasi-isomorphic phase boundary) or near MPB (near a quasi-isomorphic phase boundary). Furthermore, existing methods generally employ 1-3 individual space groups or 1-3 two-phase coexisting space group models. Using 1-3 individual space groups cannot determine the overall pattern, resulting in low accuracy or even incorrect space groups. While using 1-3 two-phase composite space groups is mathematically feasible (for fitting), it does not conform to theory and is, in fact, an incorrect method. The method in this application is equivalent to using all individual space groups, comparing all possible structures, and obtaining the most accurate results.

[0134] Specifically, existing methods do not rigorously determine the space group of the pseudocubic phase. For example, for the BiFeO3-BaTiO3 system, the method in this application accurately determines the space group, i.e., the structure, of the pseudocubic phase. In the determination process, this application verified all structures and found the most suitable structure, resulting in higher accuracy.

[0135] Furthermore, regarding positional partitioning methods, although these methods have been reported, existing methods still rely on cubic phase-based methods for studying materials with significant distortion. For example, 0.8BiFeO3-BaTiO3 shows obvious peak separation in its spectra. Moreover, the space group R3c exhibits rotational distortion of oxygen octahedra. Using the cubic space group... At this point, c / a = 1, and this model does not describe the rotation and twisting of the oxygen octahedron, meaning it makes too many approximations. The method in this application refines the trigonal phase region using a positional decomposition method based on the trigonal phase space group, the tetragonal phase region using the same method, and so on, refining the orthorhombic phase region using the same method. For pseudocubic phases or cubic phase space groups, we refine the positional decomposition method based on the cubic phase space group. The method in this application is more accurate and scientific.

[0136] Furthermore, while some studies have explored materials near or adjacent to quasi-isomorphic phase boundaries using different offset directions for different heavy atoms, these studies are all based on cubic phase space groups. However, existing methods do not link this to quasi-isomorphic phase boundaries, i.e., to phase transitions. In this application, based on the fact that phase transitions are essentially distortion redirections—that is, different heavy atoms have different offset directions—the material undergoing heavy atom offsets is identified as being located in a quasi-isomorphic phase boundary region, thus clearly defining the material's phase boundary.

[0137] Example 3

[0138] A schematic diagram of a terminal device according to an embodiment of the present invention. The terminal device of this embodiment includes: a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps in the various method embodiments described above. Alternatively, when the processor executes the computer program, it implements the functions of each module / unit in the various device embodiments described above.

[0139] The computer program can be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention.

[0140] The terminal device may be a desktop computer, laptop, handheld computer, or cloud server, etc. The terminal device may include, but is not limited to, a processor and a memory.

[0141] The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.

[0142] The memory can be used to store the computer program and / or module. The processor implements various functions of the terminal device by running or executing the computer program and / or module stored in the memory and calling the data stored in the memory.

[0143] If the modules / units integrated into the terminal device are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0144] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

[0145] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the essence and scope of the technical solutions of the present invention.

Claims

1. A method for determining the phase boundaries and structure of piezoelectric solid solution oxide crystals, characterized in that, Includes the following steps: S1: Obtain the powder X-ray diffraction pattern of the piezoelectric solid solution oxide to be analyzed and the space group of the piezoelectric solid solution oxide to be analyzed; S2: Using the space group of the piezoelectric solid solution oxide to be analyzed as a model, the obtained powder X-ray diffraction pattern is fitted and refined to obtain the refinement residual factor of different space groups. S3: Determine the space group to which the piezoelectric solid solution oxide to be analyzed belongs based on the refined residual factor; S4: Determine the crystal phase boundaries and structure of the piezoelectric solid solution oxide to be analyzed based on the space group to which it belongs; The refined residual factor includes a weighted full-spectrum factor; If the weighted full spectrum factor is not greater than 15%, the powder X-ray diffraction pattern of the piezoelectric solid solution oxide to be analyzed is re-acquired, and steps S1 to S2 are repeated. The space group of the piezoelectric solid solution oxide to be analyzed is any one of the parent phase space group, the sub-space group of the parent phase, and the high-temperature phase space group of the parent phase. The process of determining the space group to which the piezoelectric solid solution oxide to be analyzed belongs based on the refinement residual factor in step S3 is as follows: by comparing the refinement residual factors of different space groups, the space group corresponding to the smallest refinement residual factor is the space group to which the piezoelectric solid solution oxide to be analyzed belongs. In step S4, the process of determining the crystal phase boundary and structure of the piezoelectric solid solution oxide to be analyzed based on the space group to which the piezoelectric solid solution oxide to be analyzed belongs is specifically as follows: If the space group to which the piezoelectric solid solution oxide to be analyzed belongs has the lowest symmetry, then the piezoelectric solid solution oxide to be analyzed belongs to the quasi-isomorphic phase boundary region. After step S4, the method further includes using a position splitting method to determine the offset direction and offset distance of metal atoms in the piezoelectric solid solution oxide relative to the average position or cubic equilibrium position, based on the space group to which the piezoelectric solid solution oxide to be analyzed belongs.

2. A system for determining the phase boundaries and structure of piezoelectric solid solution oxide crystals, characterized in that, A method for determining the phase boundaries and structure of a piezoelectric solid solution oxide crystal as described in claim 1; comprising: The data acquisition unit is used to acquire the powder X-ray diffraction pattern of the piezoelectric solid solution oxide to be analyzed and the space group of the piezoelectric solid solution oxide to be analyzed. The data fitting unit is used to fit and refine the obtained powder X-ray diffraction pattern using the space group of the piezoelectric solid solution oxide to be analyzed as a model, so as to obtain the refinement residual factor of different space groups. The first data processing unit is used to determine the space group to which the piezoelectric solid solution oxide to be analyzed belongs based on the refined residual factor. The second data processing unit is used to determine the crystal phase boundaries and structure of the piezoelectric solid solution oxide to be analyzed based on the space group to which the piezoelectric solid solution oxide to be analyzed belongs.

3. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in claim 1.

4. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in claim 1.

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