Method for predicting domain switching path and loading and unloading characteristics of ferroelastic material

Abstract

The application discloses a kind of ferroelastic material domain flipping path and load-unload characteristic prediction method, and relates to ferroelastic material technical field.The method includes obtaining the spontaneous strain orientation of ferroelastic material in turn to construct unit cell with different compression or tension strain;Using density functional theory, the geometry structure optimization is carried out to each unit cell, and stable configuration is obtained;The atomic migration process of domain flipping is obtained;The stress size corresponding to each stable configuration under different strain conditions is extracted in turn, and the stress-strain curve of ferroelastic material is drawn, so as to obtain the critical mechanical load of domain flipping.The atomic migration process of domain flipping can be obtained according to stable configuration;The stress-strain curve of material can be accurately drawn, and the critical mechanical load of domain flipping is obtained.

Description

Technical Field

[0001] This invention relates to the field of ferroelastic material technology, specifically to a method for predicting domain flipping paths and loading / unloading characteristics of ferroelastic materials. Background Technology

[0002] Ferroelastic toughening is a unique property of ferroelastic materials. Under stress, ferroelastic grains spontaneously form regions oriented according to stress, known as ferroelastic domains. The orientation of these domains absorbs some of the energy for crack propagation, leading to stress-strain hysteresis and significantly improving the fracture toughness of the material. Therefore, ferroelastic toughening provides structural stability assurance for the application of materials and devices. Notably, ferroelasticity is a rare toughening mechanism suitable for high-temperature environments, and thus it is widely used in the field of high-temperature ceramic coatings.

[0003] In the thermal barrier coatings of high-performance aero-engines, the high-temperature brittleness of ceramic materials is a significant factor leading to coating spalling failure. Introducing a ferroelastic toughening mechanism can effectively improve the fracture toughness of the ceramic coating, thereby extending its service life. Therefore, yttrium-stabilized zirconia (YSZ), with its excellent ferroelastic toughening properties, is currently the only coating material that has reached practical application. Furthermore, some novel thermal barrier coating materials have also been found to possess excellent ferroelastic toughening properties, such as rare earth tantalates (RETaO4), rare earth aluminates (REAlO3), and their modified materials.

[0004] Current research on ferroelastic domain flipping mainly falls into two categories: experimental methods and theoretical calculation methods. In terms of experimental methods, existing techniques primarily include in-situ transmission electron microscopy loading and indentation methods, while theoretical calculation methods mainly include phase-field methods and transition state calculation methods.

[0005] 1) In-situ transmission electron microscopy loading method: Professor Gao Peng of Peking University experimentally confirmed using in-situ transmission electron microscopy that PbTiO3 can be loaded under compressive stress. c → a Domain transformation, and with the continued increase of mechanical load, the newly formed a Domains will permeate the entire film and continue to "grow". However, in-situ transmission electron microscopy requires the transmission electron microscope to be equipped with in-situ nanomechanical testing equipment, and the preparation of the test samples is highly demanding and expensive.

[0006] 2) Indentation method: Professor Zhou Yichun of Xiangtan University observed 90°C cracks at the crack tips of Vickers indentations on the surface of yttrium-stabilized zirconia single-crystal epitaxial films. o The arranged ferroelastic domains are presumably caused by external forces in the indentation region, resulting in some of the ferroelastic domains in the single-crystal thin film. c domain transformation aDomain transformation helps prevent further crack propagation, thus achieving toughening. However, indentation can only observe the final morphology of the domain structure in a non-in-situ manner near the crack tip of ferroelastic materials, and cannot obtain the domain inversion process, nor can it accurately measure the critical load for domain inversion.

[0007] 3) Phase-Field Method: Professor Luo Jun of Huazhong University of Science and Technology, using the phase-field method, defined variants with different crystallographic orientations as order parameters. Based on the volume and energy conservation during domain flipping, he theoretically studied the crack propagation process in tetragonal yttrium oxide-stabilized zirconia single crystals under different external loads, revealing the influence of crystal orientation and loading type on domain flipping. Although the phase-field method can study a wider range of material systems compared to density functional theory methods, it requires experimental measurement of the coercivity of domain flipping to set the energy barrier for domain flipping during the phase-field simulation. This simulation method cannot obtain the stress-strain curves of ferroelastic materials, thus requiring additional experimental data (coercivity) to assist in modeling, resulting in low efficiency.

[0008] 4) Transition State Calculation Method: Professor Jinsong Huang of the University of North Carolina, using density functional theory, calculated the domain flipping process between two orientations in two-dimensional inorganic-organic hybrid perovskites by searching for transition states. Theoretically, he predicted that its ferroelasticity originates from the inorganic octahedral distortion caused by the rotation of aspherical methylammonium cations. While transition state calculations can accurately obtain the change in total energy of the system in any intermediate state, they cannot obtain the stress-strain curve of the material, nor can they specify the critical mechanical load for domain flipping. Furthermore, transition state calculations require the variant structures before and after domain flipping; therefore, the obtained domain flipping path is related to the pre-given domain orientation, and the results have a certain degree of randomness, so the predicted results may deviate from reality.

[0009] The above methods all have limitations. Therefore, this invention reports a simpler method for predicting the domain flipping path and loading / unloading characteristics of ferroelastic materials, which can provide theoretical guidance for the design and development of high-performance materials, devices, and coatings. Summary of the Invention

[0010] To address the shortcomings of the aforementioned background technologies, this invention primarily solves the problem of simultaneously obtaining the domain flipping path and critical load of ferroelastic materials. This invention provides a method for predicting the domain flipping path and loading / unloading characteristics of ferroelastic materials. Based on density functional theory, this method studies the process of spontaneous strain transformation within the crystal by calculating the ferroelastic material under applied mechanical load. The magnitude and direction of the mechanical load are controllable, allowing not only the acquisition of the atomic migration process of ferroelastic domain flipping but also the precise acquisition of the critical mechanical load for domain flipping and the stress-strain curve of the material.

[0011] The first objective of this invention is to provide a method for predicting the domain flipping path and loading / unloading characteristics of ferroelastic materials, comprising the following steps: To obtain the spontaneous strain orientation of ferroelastic materials; Based on the spontaneous strain orientation of the ferroelastic material, cell cells with different compressive or tensile strains are constructed sequentially along the tensile or compressive strain direction. Density functional theory was used to optimize the geometry of each unit cell to obtain a stable configuration; Based on the stable configuration, a ball-and-stick model was drawn and arranged in order of increasing strain to obtain the atomic migration process of domain flipping. By sequentially extracting the stress magnitudes corresponding to each stable configuration under different strain conditions, the stress-strain curves of the ferroelastic material are plotted, thereby obtaining the critical mechanical load for domain flipping.

[0012] Preferably, the critical mechanical load for domain flipping is the stress corresponding to the first peak of the stress-strain curve deviating from the linear region.

[0013] Preferably, the ferroelastic material includes YTaO4, YSZ, BaTiO3, LaNbO4, BiFeO3, WO3, or a two-dimensional inorganic-organic hybrid perovskite.

[0014] Preferably, the spontaneous strain orientation of the ferroelastic material is obtained based on the crystal symmetry of the ferroelastic material.

[0015] Preferably, the strain of the constructed unit cell is consistent with the spontaneous strain orientation of the ferroelastic material, with a strain value range of ±0~50%.

[0016] Preferably, the strain interval of each unit cell is less than 2%.

[0017] Preferably, when optimizing the geometry of each unit cell, only the unit cell size in the spontaneous strain direction is fixed.

[0018] Compared with the prior art, the beneficial effects of the present invention are: This invention provides a method for predicting the domain flipping path and loading / unloading characteristics of ferroelastic materials. Based on the crystal symmetry of the ferroelastic material, the spontaneous strain orientation of the ferroelastic material is determined, and unit cells with different compressive / tensile strains are constructed along the tensile / compressive strain direction. Density functional theory is used to effectively predict the domain flipping path and loading / unloading characteristics of the ferroelastic material. The atomic migration process of domain flipping can be obtained based on the stable configuration. The stress-strain curve of the material can be accurately plotted, and the critical mechanical load of domain flipping can be obtained.

[0019] This invention, based on density functional theory, studies the spontaneous strain transformation process within a ferroelastic material under applied mechanical loads. The magnitude and direction of the mechanical load are controllable, allowing for the acquisition of not only the atomic migration process of ferroelastic domain flipping but also the precise acquisition of the critical mechanical load for domain flipping and the material's stress-strain curve. Compared to in-situ transmission electron microscopy and indentation methods, the computational method described in this invention is low-cost and highly efficient. Compared to the phase-field method, this method accurately acquires the critical mechanical load for domain flipping and the material's stress-strain curve. Compared to transition state calculations, this method does not require simultaneously providing both pre- and post-domain flipping variants, making it simpler and more convenient, and accurately predicting the material's stress-strain curve. Attached Figure Description

[0020] Figure 1 Here are ball-and-stick model diagrams of YTaO4 crystals in Example 1: (a) a schematic diagram of tensile strain applied along the

[001] direction, and (b) a schematic diagram of compressive strain applied along the

[100] direction. Figure 2 This is the stress-strain curve of the YTaO4 crystal under tension along the

[001] direction in Example 1; Figure 3 This is a diagram of the ferroelastic domain flipping process of the YTaO4 crystal in the

[001] direction under stretching conditions in Example 1; Figure 4 This is the stress-strain curve of the YTaO4 crystal under compression along the

[100] direction in Example 1; Figure 5 This is a diagram of the ferroelastic domain flipping process of the YTaO4 crystal under compression along the

[100] direction in Example 1; Figure 6 Here are model diagrams of the LaNbO4 crystal stretching process in Example 2: (a) is a schematic diagram of tensile strain applied along the

[001] direction, and (b) is the stress-strain curve of the LaNbO4 crystal under stretching along the

[100] direction. Figure 7 This is a diagram of the ferroelastic domain flipping process of the LaNbO4 crystal under stretching along the

[001] direction in Example 2; Figure 8 Here are model diagrams of the BaTiO3 crystal stretching process in Example 3. (a) is a schematic diagram of applying tensile strain along the

[100] direction, and (b) is the stress-strain curve of the BaTiO3 crystal under stretching along the

[100] direction. Figure 9 This is a diagram of the ferroelastic domain flipping process of the BaTiO3 crystal in the

[100] direction under stretching conditions in Example 3. Detailed Implementation

[0021] To enable those skilled in the art to better understand and implement the technical solutions of the present invention, the present invention will be further described below in conjunction with specific embodiments and accompanying drawings. However, the embodiments described are not intended to limit the present invention.

[0022] The main objective of this invention is to study the process of spontaneous strain transformation within a crystal of a ferroelastic material under external mechanical load by calculating density functional theory. The magnitude and direction of the mechanical load are controllable, which can not only obtain the atomic migration process of ferroelastic domain flipping, but also accurately obtain the critical mechanical load for domain flipping and the stress-strain curve of the material.

[0023] To achieve the above objectives, the present invention provides a method for predicting domain flipping paths and loading / unloading characteristics of ferroelastic materials, comprising the following steps: To obtain the spontaneous strain orientation of ferroelastic materials; Based on the spontaneous strain orientation of the ferroelastic material, cell cells with different compressive or tensile strains are constructed sequentially along the tensile or compressive strain direction. Density functional theory was used to optimize the geometry of each unit cell to obtain a stable configuration; Based on the stable configuration, a ball-and-stick model was drawn and arranged in order of increasing strain to obtain the atomic migration process of domain flipping. By sequentially extracting the stress magnitudes corresponding to each stable configuration under different strain conditions, and plotting the stress-strain curves of the ferroelastic material, the critical mechanical load for domain flipping can be obtained.

[0024] It should be noted that each stable configuration of strain has a corresponding stress.

[0025] The critical mechanical load for domain flipping is the stress corresponding to the first peak of the stress-strain curve deviating from the linear region.

[0026] The ferroelastic material includes YTaO4, YSZ, BaTiO3, LaNbO4, BiFeO3, WO3, or two-dimensional inorganic-organic hybrid perovskite.

[0027] The spontaneous strain orientation of the ferroelastic material is obtained based on the crystal symmetry of the ferroelastic material.

[0028] Specifically, the space group of the crystal structure is used to determine whether the material under study has ferroelastic properties, the crystal symmetry of the ferroelastic body under study is analyzed, and the spontaneous strain orientation of the ferroelastic body is determined.

[0029] The strain of the constructed unit cell is consistent with the spontaneous strain orientation of the ferroelastic material, with a strain value range of ±0~50%.

[0030] The strain interval of each unit cell is less than 2%.

[0031] When optimizing the geometry of each unit cell, only the cell size along the spontaneous strain direction is fixed; the size in other directions is not fixed. The geometry optimization is based on density functional theory and is performed by adjusting the atomic coordinates of the input system to obtain a relatively stable unit cell structure.

[0032] It should be noted that, unless otherwise specified, the experimental methods used in this invention are all conventional methods.

[0033] Example 1 A method for predicting the YTaO4 ferroelastic domain flipping path and loading / unloading characteristics includes: (1) Based on the crystal structure symmetry, it is determined that the monoclinic phase YTaO4 under study has ferroelastic properties. The crystal symmetry of the ferroelastic body under study is analyzed, and it is determined that the YTaO4 ferroelastic body has spontaneous compressive strain along the

[001] crystal direction and spontaneous tensile strain along the

[100] crystal direction.

[0034] (2) Based on the spontaneous strain characteristics, along the

[001] crystal direction, unit cells with different tensile strains are constructed sequentially; or along the

[100] crystal direction, unit cells with different compressive strains are constructed sequentially.

[0035] (3) Using density functional theory, the geometric structure of the above series of unit cells is optimized to obtain the final stable configuration.

[0036] (4) Draw the ball-and-stick model of stable YTaO4 configuration under different strain states and arrange them in order of strain from small to large, so as to obtain the atomic migration process of YTaO4 domain flipping.

[0037] (5) Extract the stress magnitude corresponding to each stable configuration under different strain conditions in sequence, and plot the stress-strain curves of YTaO4 under tensile or compressive conditions, so as to obtain the critical mechanical load for the overturning of ferroelastic domains in YTaO4.

[0038] The strain value range of the unit cell constructed in step (2) is ±30%; The strain interval of the unit cell constructed in step (2) is 1%; In step (3), in the tensile strain cell, only the cell size in the

[100] direction is fixed, and the other directions are not fixed; in the compressive strain cell, only the cell size in the

[001] direction is fixed, and the other directions are not fixed. In step (5), the critical mechanical load for domain flipping is the stress corresponding to the first peak of the stress-strain curve deviating from the linear region.

[0039] Figure 1Here are ball-and-stick model diagrams of YTaO4 crystals in Example 1: (a) a schematic diagram of tensile strain applied along the

[001] direction, and (b) a schematic diagram of compressive strain applied along the

[100] direction.

[0040] Figure 2 The figure shows the stress-strain curve of the YTaO4 crystal under tension along the

[001] direction in Example 1. The fitted curve shows that when the tensile strain is 3.5%, the stress-strain curve deviates from the linear region. The load corresponding to this point is the critical mechanical load for ferroelastic domain flipping, with a magnitude of 2.47 GPa. When the strain is greater than 5%, the tension of the YTaO4 crystal is linear elastic. When the strain is greater than 30%, plastic deformation occurs, indicating that the material is about to break.

[0041] Figure 3 This is a diagram illustrating the ferroelastic domain flipping process of the YTaO4 crystal under tensile stress along the

[001] direction in Example 1. As the tensile strain increases, the monoclinic YTaO4 crystal... a , c The included angle between the axes is 91.47°. o It became 87.96 o This explains why it was originally along the

[100] direction. a Domains, under tensile load along the

[001] direction, will gradually flip, forming domains along the

[001] direction. c Fields.

[0042] Figure 4 The figure shows the stress-strain curve of the YTaO4 crystal under compression along the

[100] direction in Example 1. The fitted curve shows that when the compressive strain is -4.0%, the stress-strain curve deviates from the linear region. The load corresponding to this point is the critical mechanical load for ferroelastic domain flipping, with a magnitude of 4.20 GPa. When the strain is greater than -6%, the compression of the YTaO4 crystal is linear elastic. When the strain is greater than -20%, plastic deformation occurs, and the stress decreases rapidly, indicating that the material is crushed.

[0043] Figure 5 This is a diagram illustrating the ferroelastic domain flipping process of the YTaO4 crystal under compression along the

[100] direction in Example 1. As the compressive strain increases, the monoclinic YTaO4 crystal... a , c The included angle between the axes is 91.47°. o It became 84.05 o This explains why it was originally along the

[100] direction. a Domains, under compressive load along the

[100] direction, will gradually flip, forming domains along the

[001] direction. c Fields.

[0044] Example 2 Methods for predicting the LaNbO4 ferroelastic domain flipping path and loading / unloading characteristics include: (1) Based on the crystal structure symmetry, it is determined that the monoclinic phase LaNbO4 under study has ferroelastic properties. The crystal symmetry of the ferroelastic body under study is analyzed, and it is determined that the LaNbO4 ferroelastic body has spontaneous compressive strain along the

[001] crystal direction.

[0045] (2) Based on the characteristics of spontaneous compressive strain, cell cells with different tensile strains are constructed sequentially along the

[001] crystal orientation.

[0046] (3) Using density functional theory, the geometric structure of the above series of unit cells is optimized to obtain the final stable configuration.

[0047] (4) Draw the ball-and-stick model of the stable configuration of LaNbO4 under different strain states and arrange them in order of strain from small to large, so as to obtain the atomic migration process of LaNbO4 domain flipping.

[0048] (5) Extract the stress magnitudes corresponding to each stable configuration under different strain conditions in sequence, and plot the stress-strain curve of LaNbO4 under tensile conditions to obtain the critical mechanical load for the overturning of ferroelastic domains in LaNbO4.

[0049] The strain value range of the unit cell constructed in step (2) is ±32%; The strain interval of the unit cell constructed in step (2) is 1%; In step (3), only the cell size in the

[001] direction is fixed in the tensile strained cell, while the cell size in the other directions is not fixed; In step (5), the critical mechanical load for domain flipping is the stress corresponding to the first peak of the stress-strain curve deviating from the linear region.

[0050] Figure 6 This is a model diagram of the LaNbO4 crystal stretching process in Example 2. (a) is a schematic diagram of applying tensile strain along the

[001] direction, and (b) is the stress-strain curve of the LaNbO4 crystal under stretching along the

[100] direction. The fitted curve shows that when the compressive strain is 8.0%, the stress-strain curve deviates from the linear region. The load corresponding to this point is the critical mechanical load for ferroelastic domain flipping, with a magnitude of 2.87 GPa. When the strain is greater than 12%, the stretching of the LaNbO4 crystal is linear elastic. When the strain is greater than 27%, plastic deformation occurs, and the stress decreases rapidly, indicating that the material is broken.

[0051] Figure 7 This is a diagram illustrating the ferroelastic domain flipping process of the LaNbO4 crystal under tensile stress along the

[001] direction in Example 2. As the tensile strain increases, the monoclinic LaNbO4 crystal...a , c The included angle between the axes is 93.02. o It became 85.13 o This explains why it was originally along the

[100] direction. a Domains, under tensile load along the

[001] direction, will gradually flip, forming domains along the

[001] direction. c Fields.

[0052] Example 3 Methods for predicting BaTiO3 ferroelastic domain flipping paths and loading / unloading characteristics include: (1) Based on the crystal structure symmetry, it is determined that the tetragonal phase BaTiO3 under study has ferroelastic properties. The crystal symmetry of the ferroelastic body under study is analyzed, and it is determined that the BaTiO3 ferroelastic body has spontaneous tensile strain along the

[001] crystal direction.

[0053] (2) Based on the characteristics of spontaneous tensile strain, cell cells with different tensile strains are constructed sequentially along the

[100] crystal orientation.

[0054] (3) Using density functional theory, the geometric structure of the above series of unit cells is optimized to obtain the final stable configuration.

[0055] (4) Draw the ball-and-stick model of the stable configuration of BaTiO3 under different strain states and arrange them in order of strain from small to large, so as to obtain the atomic migration process of BaTiO3 domain flipping.

[0056] (5) Extract the stress magnitude corresponding to each stable configuration under different strain conditions in sequence, and plot the stress-strain curve of BaTiO3 under tensile conditions, so as to obtain the critical mechanical load for the overturning of ferroelastic domains in BaTiO3.

[0057] The strain value range of the unit cell constructed in step (2) is ±40%; The strain interval of the unit cell constructed in step (2) is 1%; In step (3), only the cell size in the

[100] direction is fixed in the tensile strain cell, while the cell size in the other directions is not fixed; In step (5), the critical mechanical load for domain flipping is the stress corresponding to the first peak of the stress-strain curve deviating from the linear region.

[0058] Figure 8This is a model diagram of the BaTiO3 crystal stretching process in Example 3. (a) is a schematic diagram of applying tensile strain along the

[100] direction, and (b) is the stress-strain curve of the BaTiO3 crystal under stretching along the

[100] direction. The fitted curve shows that when the tensile strain is 3.5%, the stress-strain curve deviates from the linear region. The load corresponding to this point is the critical mechanical load for ferroelastic domain flipping, with a magnitude of 3.62 GPa. When the strain is greater than 5%, the stretching of the BaTiO3 crystal is linear elastic. When the strain is greater than 16%, plastic deformation occurs, indicating that the material is about to break.

[0059] Figure 9 This is a diagram illustrating the ferroelastic domain flipping process of the BaTiO3 crystal under tensile stress along the

[100] direction in Example 3. As the tensile strain increases, the long axis of the tetragonal BaTiO3 crystal gradually shifts from the

[001] direction to the

[100] direction. This indicates that the original domains along the

[001] direction... c Domains, under tensile load along the

[100] direction, will gradually flip, forming domains along the

[100] direction. a Fields.

[0060] This invention describes preferred embodiments and their effects. However, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to include both the preferred embodiments and all changes and modifications falling within the scope of this invention.

[0061] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for predicting domain flipping paths and loading / unloading characteristics of ferroelastic materials, characterized in that, Includes the following steps: To obtain the spontaneous strain orientation of ferroelastic materials; Based on the spontaneous strain orientation of the ferroelastic material, cell cells with different compressive or tensile strains are constructed sequentially along the tensile or compressive strain direction. Density functional theory was used to optimize the geometry of each unit cell to obtain a stable configuration; Based on the stable configuration, a ball-and-stick model was drawn and arranged in order of increasing strain to obtain the atomic migration process of domain flipping. The stress magnitudes corresponding to each stable configuration under different strain conditions are extracted sequentially, and the stress-strain curves of the ferroelastic material are plotted to obtain the critical mechanical load for domain flipping. The critical mechanical load for domain flipping is the stress corresponding to the first peak of the stress-strain curve deviating from the linear region. The spontaneous strain orientation of the ferroelastic material is obtained based on the crystal symmetry of the ferroelastic material; The strain of the constructed unit cell is consistent with the spontaneous strain orientation of the ferroelastic material, with a strain value range of ±0~50%. When optimizing the geometry of each unit cell, only the unit cell size in the spontaneous strain direction is fixed.

2. The method for predicting domain flipping paths and loading / unloading characteristics of ferroelastic materials according to claim 1, characterized in that, The ferroelastic material includes YTaO4, YSZ, BaTiO3, LaNbO4, BiFeO3, WO3, or two-dimensional inorganic-organic hybrid perovskite.

3. The method for predicting domain flipping paths and loading / unloading characteristics of ferroelastic materials according to claim 1, characterized in that, The strain interval of each unit cell is less than 2%.

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