A method for measuring the flexoelectric coefficient of separable piezoelectric two-dimensional materials

Abstract

The present invention discloses a method for measuring the flexoelectric coefficient of a separable piezoelectric two-dimensional material, comprising: testing N samples with different distance values ​​respectively, where the distance value is the distance from the thickness bisector of the two-dimensional material to the thickness bisector of the sample along the thickness direction of the base plate in one sample; since the distance value affects the strain state and piezoelectric polarization of the two-dimensional material, the flexoelectric contribution and the piezoelectric contribution are separated according to the total polarization difference of multiple samples, thereby accurately measuring the flexoelectric coefficient of the two-dimensional material.

Description

Technical Field

[0001] The present invention relates to the technical field of flexoelectric coefficient measurement, and more specifically, to a method for measuring the flexoelectric coefficient of a separable piezoelectric two-dimensional material. Background Art

[0002] The flexoelectric effect is a mechanoelectric coupling effect that describes the electric polarization induced by strain gradients in dielectric materials. Unlike the piezoelectric effect, which is limited to non-centrosymmetric materials, the flexoelectric effect can exist in all dielectric materials because strain gradients can break the spatial inversion symmetry of the crystal structure. The strain gradient increases with decreasing size, which makes the flexoelectric effect play a more significant role at the micro- and nanoscale. Small-sized two-dimensional materials can withstand larger deformations and produce higher strain gradients, thus having better flexoelectric properties. In recent years, various novel flexoelectric phenomena and applications have emerged in two-dimensional materials, including flexophotovoltaic effects, domain engineering, photodetectors, and self-rectifying memristors. Quantitative characterization of the flexoelectric coefficients of two-dimensional materials is crucial for understanding their flexoelectric behavior.

[0003] In the prior art, the conventional method for measuring the flexoelectric coefficient of a material is the macroscopic cantilever beam bending method, which requires that the sample to be tested be made into a beam specimen with a thickness of millimeters, and then metal electrodes of appropriate sizes are prepared on the upper and lower surfaces of the specimen, and then wires are drawn out from the metal electrodes to finally complete the sample preparation. The sample is assembled on a dynamic mechanical analyzer using a cantilever beam fixture, and dynamic deformation is generated by applying different displacement excitations to it, wherein the axial positive strain generates a strain gradient along the thickness direction. The current signal generated by the flexoelectric effect is then collected by connecting the wire to a phase-locked amplifier. The strain gradient value is derived by combining the applied displacement amplitude value with the cantilever beam bending theory, and the flexoelectric polarization value is converted from the relationship between current and polarization. The flexoelectric coefficient value of the material is obtained by fitting in combination with the above-mentioned flexoelectric effect expression.

[0004] However, conventional beam bending methods require millimeter-scale specimens to facilitate the preparation of metal electrodes and the application of dynamic mechanical loads, making this method difficult to apply to micron-scale two-dimensional materials. Furthermore, for piezoelectric two-dimensional materials, the generation of strain gradients in the specimen inevitably introduces piezoelectric effects, which can affect the accuracy of flexoelectric coefficient measurements.

[0005] Therefore, the present invention provides a method for measuring the flexoelectric coefficient of a separable piezoelectric two-dimensional material. Summary of the Invention

[0006] In view of this, the present invention provides a method for measuring the flexoelectric coefficient of a separable piezoelectric two-dimensional material, comprising:

[0007] Providing N samples, where N is an integer and N ≥ 2, wherein the samples include a stack and a top plate, wherein the stack includes a bottom plate, a bottom electrode, a micron-sized two-dimensional material, and a top electrode stacked in sequence, the top plate being located on a side of the top electrode away from the bottom plate, and the stack and the top plate being connected by an adhesive layer; wherein the distance values ​​of any two samples are different, and in one sample, the distance from a thickness bisector plane of the two-dimensional material to a thickness bisector plane of the sample along the thickness direction of the bottom plate is taken as the distance value of the sample;

[0008] Calculate the expressions corresponding to N samples respectively, including: when calculating the expression corresponding to the ith sample, i is an integer and 1≤i≤N, measure the distance value of the ith sample; perform M tests on the ith sample, each test only with a different preset displacement, M is an integer and M≥2, including: when performing the jth test on the ith sample, j is an integer and 1≤j≤M, place the ith sample between a four-point bending base and a four-point bending pressure head, the four-point bending base includes two support columns relatively arranged along the length direction of the bottom plate of the ith sample, the four-point bending pressure head includes two lower pressure columns relatively arranged along the length direction of the bottom plate of the ith sample on the side close to the four-point bending base, and the bottom plate of the ith sample abuts against the support columns; along the thickness direction of the bottom plate of the ith sample, the center point of the two-dimensional material of the ith sample, the center point of the four-point bending pressure head and the center point of the four-point bending base overlap; along the length direction of the bottom plate of the ith sample , the two-dimensional material of the i-th sample is located between the two lower pressure columns, and the lower pressure column is located between the two support columns; a phase-locked amplifier is connected to the top electrode of the i-th sample and the bottom electrode of the i-th sample, and a function generator is used to control the four-point bending head to move the preset displacement along the thickness direction of the bottom plate of the i-th sample, and the phase-locked amplifier obtains the measured current of the i-th sample at the j-th test; according to the measured current of the i-th sample at the j-th test and the preset displacement of the i-th sample at the j-th test, the j-th measured flexoelectric coefficient value of the i-th sample is obtained; the average value from the 1st measured flexoelectric coefficient value of the i-th sample to the Mth measured flexoelectric coefficient value of the i-th sample is calculated to obtain the fitted flexoelectric coefficient value of the i-th sample; according to the fitted flexoelectric coefficient value of the i-th sample, the distance value, the effective flexoelectric coefficient and the effective piezoelectric coefficient of the i-th sample, the expression corresponding to the i-th sample is constructed;

[0009] The expression corresponding to the first sample is fitted to the expression corresponding to the Nth sample by linear fitting to obtain a fitting line, and the intercept value of the fitting line is the effective flexoelectric coefficient of the two-dimensional material.

[0010] Optionally, according to the measured current of the i-th sample during the j-th test and the preset displacement of the i-th sample during the j-th test, the j-th measured flexoelectric coefficient value of the i-th sample is obtained, and is calculated as follows:

[0011]

[0012] Among them, δ ij is the preset displacement of the i-th sample during the j-th test, L is the distance between the center points of the two support columns along the length direction of the bottom plate of the i-th sample, L1 is the shortest distance from the center point of the support column to the four-point bending head along the length direction of the bottom plate of the i-th sample, i j is the measured current of the i-th sample at the j-th test, f is the excitation frequency, A i is the area of ​​the top electrode of the i-th sample, The j-th measured flexoelectric coefficient value for the i-th sample.

[0013] Optionally, an expression corresponding to the i-th sample is constructed according to the fitted flexoelectric coefficient value of the i-th sample, the distance value of the i-th sample, the effective flexoelectric coefficient and the effective piezoelectric coefficient, and is calculated in the following manner:

[0014]

[0015] in, is the fitting flexoelectric coefficient value of the i-th sample, h i is the distance value of the i-th sample, μ eff is the effective flexoelectric coefficient, e eff is the effective piezoelectric coefficient.

[0016] Optionally, the i-th sample is prepared in the following manner:

[0017] providing the stack;

[0018] applying an adhesive on one side of the stack, the adhesive covering the top electrode;

[0019] Covering the top plate on the side of the adhesive away from the bottom plate, uniformly applying pressure to the top plate along the thickness direction of the bottom plate until the thickness of the adhesive along the thickness direction of the bottom plate is equal to the preset adhesive layer thickness corresponding to the i-th sample, and curing the adhesive at room temperature to obtain the adhesive layer;

[0020] The adhesive layer is trimmed so that the adhesive layer overlaps with the base plate along the thickness direction of the base plate, thereby obtaining the i-th sample.

[0021] Optionally, the i-th sample is prepared in the following manner:

[0022] providing the stack;

[0023] applying an adhesive on one side of the stack, the adhesive covering the top electrode;

[0024] Providing the top plate, wherein the thickness of the top plate is equal to the preset top plate thickness corresponding to the i-th sample;

[0025] Covering the top plate on the side of the adhesive away from the bottom plate, uniformly applying a preset pressure to the top plate along the thickness direction of the bottom plate, and obtaining the adhesive layer after the adhesive is cured at room temperature;

[0026] The adhesive layer is trimmed so that the adhesive layer overlaps with the base plate along the thickness direction of the base plate, thereby obtaining the i-th sample.

[0027] Optionally, the stack is manufactured in the following manner:

[0028] providing the base plate;

[0029] depositing the bottom electrode on one side of the bottom plate;

[0030] The two-dimensional material is placed on a side of the bottom electrode away from the bottom plate, wherein the length of the two-dimensional material along the length direction of the bottom plate is less than the length of the bottom electrode; and the width of the two-dimensional material along the width direction of the bottom plate is equal to the width of the bottom electrode;

[0031] The top electrode is deposited on a side of the two-dimensional material away from the bottom electrode to form the stack. Along the length direction of the bottom plate, the length of the top electrode is less than the length of the two-dimensional material.

[0032] Optionally, the i-th sample is prepared in the following manner:

[0033] When i≥2, after the test of the i-1th sample is completed, a thickening layer is pasted on the side of the top plate of the i-1th sample away from the bottom plate to obtain the i-th sample.

[0034] Compared with the prior art, the present invention provides a method for measuring the flexoelectric coefficient of a separable piezoelectric two-dimensional material, which achieves at least the following beneficial effects:

[0035] 1. The present invention provides a method for measuring the flexoelectric coefficient of separable piezoelectric two-dimensional materials, which embeds micron-sized two-dimensional materials between multilayer structures to form a sample, solving the technical difficulties of electrode preparation and dynamic mechanical loading faced in the flexoelectric coefficient measurement of micron-sized two-dimensional materials.

[0036] 2. The present invention provides a method for measuring the flexoelectric coefficient of a separable piezoelectric two-dimensional material, which tests N samples with different distance values ​​respectively. The distance value is the distance from the thickness bisector of the two-dimensional material to the thickness bisector of the sample along the thickness direction of the base plate in one sample. Since the distance value affects the strain state and piezoelectric polarization of the two-dimensional material, the flexoelectric contribution and the piezoelectric contribution are separated according to the total polarization difference of multiple samples, thereby accurately measuring the flexoelectric coefficient of the two-dimensional material.

[0037] Of course, any product implementing the present invention does not necessarily need to achieve all of the technical effects described above at the same time.

[0038] Further features and advantages of the present invention will become apparent from the following detailed description of exemplary embodiments of the present invention with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention.

[0040] Figure 1 It is a structural diagram of the sample.

[0041] Figure 2 The present invention is a structural schematic diagram of a device for measuring the flexoelectric coefficient of a separable piezoelectric two-dimensional material.

[0042] Figure 3 The present invention is a flowchart of a method for measuring the flexoelectric coefficient of a separable piezoelectric two-dimensional material.

[0043] Figure 4 A comparison chart of the samples.

[0044] Figure 5 The measured electric polarization versus the applied strain gradient.

[0045] Figure 6 A schematic diagram of the fitted line.

[0046] In the figure: 1. Sample; 2. Laminated part; 3. Bottom plate; 4. Bottom electrode; 5. Two-dimensional material; 6. Top electrode; 7. Top plate; 8. Adhesive layer; 9. Metal wire; 10. Four-point bending base; 11. Support column; 12. Four-point bending pressure head; 13. Lower pressure column; 14. Function generator; 15. Phase-locked amplifier; 16. Piezoelectric brake. DETAILED DESCRIPTION

[0047] Various exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be noted that unless otherwise specifically stated, the relative arrangement of components and steps, numerical expressions and numerical values ​​set forth in these embodiments do not limit the scope of the present invention.

[0048] The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the invention, its application, or uses.

[0049] Technologies, methods, and equipment known to ordinary technicians in the relevant art may not be discussed in detail, but where appropriate, the technologies, methods, and equipment should be considered part of the specification.

[0050] In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not limiting. Therefore, other examples of the exemplary embodiments may have different values.

[0051] It should be noted that like reference numerals and letters refer to like items in the following figures, and therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0052] Example 1

[0053] Combine Figure 1 、 Figure 2 and Figure 3 , Figure 1 It is a structural diagram of the sample. Figure 2 This is a structural diagram of a device for measuring the flexoelectric coefficient of a separable piezoelectric two-dimensional material. Figure 3 The present invention provides a flow chart of a method for measuring the flexoelectric coefficient of a separable piezoelectric two-dimensional material, which illustrates a specific embodiment of the method for measuring the flexoelectric coefficient of a separable piezoelectric two-dimensional material provided by the present invention, including:

[0054] S101: Provide N samples 1, where N is an integer and N ≥ 2, and the sample 1 includes a stack 2 and a top plate 7. The stack 2 includes a bottom plate 3, a bottom electrode 4, a two-dimensional material 5 of micrometer size, and a top electrode 6 stacked in sequence. The top plate 7 is located on a side of the top electrode 6 away from the bottom plate 3, and the stack 2 and the top plate 7 are connected by an adhesive layer 8. The distance values ​​of any two samples 1 are different. In one sample 1, the distance from the thickness bisector plane of the two-dimensional material 5 to the thickness bisector plane of the sample 1 along the thickness direction Z of the bottom plate 3 is used as the distance value of the sample 1.

[0055] S102: Calculate the expressions corresponding to N samples 1 respectively, including: when calculating the expression corresponding to the i-th sample, i is an integer and 1≤i≤N, measure the distance value of the i-th sample; perform M tests on the i-th sample, each test only with a different preset displacement, M is an integer and M≥2, including: when performing the j-th test on the i-th sample, j is an integer and 1≤j≤M, place the i-th sample between the four-point bending base 10 and the four-point bending pressure head 12, the four-point bending base 10 includes Two supporting columns 11 are arranged opposite to each other in the length direction X of the bottom plate 3 of the i-th sample, and the four-point bending pressure head 12 includes two lower pressure columns 13 arranged opposite to each other in the length direction X of the bottom plate 3 of the i-th sample on one side close to the four-point bending base 10. The bottom plate 3 of the i-th sample abuts against the supporting columns 11; along the thickness direction Z of the bottom plate 3 of the i-th sample, the center point of the two-dimensional material 5 of the i-th sample, the center point of the four-point bending pressure head 12 and the center point of the four-point bending base 10 overlap; along the i-th sample On the length direction X of the base plate 3 of the i-th sample, the two-dimensional material 5 of the i-th sample is located between the two lower pressure columns 13, and the lower pressure column 13 is located between the two support columns 11; the phase-locked amplifier 15 is connected to the top electrode 6 of the i-th sample and the bottom electrode 4 of the i-th sample, and the function generator 14 is used to control the four-point bending head 12 to move a preset displacement along the thickness direction Z of the base plate 3 of the i-th sample, and the phase-locked amplifier 15 obtains the measured current of the i-th sample at the j-th test; according to the measured current of the i-th sample at the j-th test and the preset displacement of the i-th sample at the j-th test, the j-th measured flexoelectric coefficient value of the i-th sample is obtained; the average value of the 1st measured flexoelectric coefficient value of the i-th sample to the Mth measured flexoelectric coefficient value of the i-th sample is calculated to obtain the fitted flexoelectric coefficient value of the i-th sample; the expression corresponding to the i-th sample is constructed according to the fitted flexoelectric coefficient value of the i-th sample, the distance value of the i-th sample, the effective flexoelectric coefficient and the effective piezoelectric coefficient;

[0056] S103: Use linear fitting to fit the expression corresponding to the first sample to the expression corresponding to the Nth sample to obtain a fitting line, and the intercept value of the fitting line is the effective flexoelectric coefficient of the two-dimensional material 5.

[0057] It should be noted that the two-dimensional material 5 refers to a material in which electrons can only move freely in two dimensions at a non-nanoscale. In this embodiment, the material of the two-dimensional material 5 is copper indium phosphide (chemical formula: CuInP2S6). The top electrode 6 and the bottom electrode 4 are led out by a metal wire 9 to facilitate the phase-locked amplifier 15 to measure the current. Of course, it is not limited to this and can be set according to actual needs. The thickness bisector plane is the mid-plane, which can also be called the neutral plane. It refers to a plane that divides the thickness of an object such as a plate or shell into two equal parts. For a flat plate, the mid-plane is a plane; for a shell, the mid-plane is a curved surface. Figure 2In step S102, a function generator 14 is used to control the four-point bending press head 12 to move a preset displacement along the thickness direction Z of the bottom plate 3 of the i-th sample. Specifically, a piezoelectric brake 16 is provided on the side of the four-point bending press head 12 away from the four-point bending base 10. The function generator 14 is connected to the piezoelectric brake 16. The function generator 14 outputs a sinusoidal signal, and the piezoelectric brake 16 receives the sinusoidal signal and controls the four-point bending press head 12 to apply a corresponding dynamic bending load according to the sinusoidal signal, thereby moving the four-point bending press head 12 along the thickness direction Z of the bottom plate 3 of the i-th sample.

[0058] It can be understood that by applying a four-point bending deformation to the sample 1, a strain gradient is generated in the two-dimensional material 5, thereby generating a flexural current. When the same strain gradient is applied, the piezoelectric polarization changes with the distance between the two-dimensional material 5 and the neutral plane of the structure, that is, the piezoelectric polarization changes with the distance between the thickness bisector of the two-dimensional material 5 and the thickness bisector of the sample 1 in which it is located, while the flexural polarization remains unchanged. Therefore, the piezoelectric effect and the flexoelectric effect can be separated based on the embedding position of the total polarization relative to the two-dimensional material 5. This embodiment uses a method for measuring the flexoelectric coefficient of a two-dimensional material with separable piezoelectricity to successfully measure the flexoelectric coefficient of the piezoelectric two-dimensional material 5 copper indium phosphorus sulfide.

[0059] Compared with the prior art, the present invention provides a method for measuring the flexoelectric coefficient of a separable piezoelectric two-dimensional material, which has the following advantages:

[0060] The present invention provides a method for measuring the flexoelectric coefficient of a separable piezoelectric two-dimensional material, in which a micron-sized two-dimensional material 5 is embedded between a multilayer structure to form a sample 1, thereby solving the technical difficulties of electrode preparation and dynamic mechanical loading faced by the micron-sized two-dimensional material 5 in the measurement of the flexoelectric coefficient. By testing N samples 1 with different distance values, the distance value is the distance from the thickness bisector of the two-dimensional material 5 to the thickness bisector of the sample 1 along the thickness direction Z of the base plate 3 in one sample 1. Since the distance between the two-dimensional material 5 and the neutral plane of the structure in which it is located affects the strain state and piezoelectric polarization of the two-dimensional material 5, the flexoelectric contribution and the piezoelectric contribution are separated according to the total polarization difference of multiple samples 1, thereby accurately measuring the flexoelectric coefficient of the two-dimensional material 5.

[0061] Example 2

[0062] Reference Figure 1 、 Figure 2 、 Figure 3 and Figure 4 , Figure 4 A comparison diagram of samples is provided to illustrate another specific embodiment of a method for measuring the flexoelectric coefficient of a separable piezoelectric two-dimensional material provided by the present invention, comprising:

[0063] S101: Provide N samples 1, where N is an integer and N ≥ 2, and the sample 1 includes a stack 2, the stack 2 including a bottom plate 3, a bottom electrode 4, a two-dimensional material 5 of micrometer size, and a top electrode 6 stacked in sequence, and the sample 1 further includes a top plate 7 located on a side of the top electrode 6 away from the bottom plate 3, and the stack 2 and the top plate 7 are connected by an adhesive layer 8; the distance values ​​of any two samples 1 are different, and in one sample 1, along the thickness direction Z of the bottom plate 3, the distance from the thickness bisector plane of the two-dimensional material 5 to the thickness bisector plane of the sample 1 is used as the distance value of the sample 1;

[0064] S102: Calculate the expressions corresponding to N samples 1 respectively, including: when calculating the expression corresponding to the i-th sample, i is an integer and 1≤i≤N, measure the distance value of the i-th sample; perform M tests on the i-th sample, each test is different only by the preset displacement, M is an integer and M≥2, including: when performing the j-th test on the i-th sample, j is an integer and 1≤j≤M, place the i-th sample between the four-point bending base 10 and the four-point bending pressure head 12, and the four-point bending base 10 includes The base plate 3 of the i-th sample includes two supporting columns 11 that are relatively arranged along the length direction X of the base plate 3 of the i-th sample, and the four-point bending pressure head 12 includes two lower pressure columns 13 that are relatively arranged along the length direction X of the base plate 3 of the i-th sample on the side close to the four-point bending base 10. The base plate 3 of the i-th sample abuts against the supporting columns 11; along the thickness direction Z of the base plate 3 of the i-th sample, the center point of the two-dimensional material 5 of the i-th sample, the center point of the four-point bending pressure head 12 and the center point of the four-point bending base 10 overlap; along the i-th In the length direction X of the base plate 3 of the sample, the two-dimensional material 5 of the i-th sample is located between two lower pressure columns 13, and the lower pressure column 13 is located between two support columns 11; the phase-locked amplifier 15 is connected to the top electrode 6 of the i-th sample and the bottom electrode 4 of the i-th sample, and the function generator 14 is used to control the four-point bending head 12 to move a preset displacement along the thickness direction Z of the base plate 3 of the i-th sample, and the phase-locked amplifier 15 obtains the measured current of the i-th sample at the j-th test; according to the measured current of the i-th sample at the j-th test and the preset displacement of the i-th sample at the j-th test, the j-th measured flexoelectric coefficient value of the i-th sample is obtained; the average value of the 1st measured flexoelectric coefficient value of the i-th sample to the Mth measured flexoelectric coefficient value of the i-th sample is calculated to obtain the fitted flexoelectric coefficient value of the i-th sample; the expression corresponding to the i-th sample is constructed according to the fitted flexoelectric coefficient value of the i-th sample, the thickness value of the i-th sample, the effective flexoelectric coefficient and the effective piezoelectric coefficient;

[0065] S103: Use linear fitting to fit the expression corresponding to the first sample to the expression corresponding to the Nth sample to obtain a fitting line, and the intercept value of the fitting line is the effective flexoelectric coefficient of the two-dimensional material 5.

[0066] Specifically, the i-th sample is prepared as follows:

[0067] providing a stack 2;

[0068] Applying adhesive to one side of the stack 2, the adhesive covering the top electrode 6;

[0069] Place the top plate 7 over the side of the adhesive away from the bottom plate 3, and apply uniform pressure to the top plate 7 along the thickness direction Z of the bottom plate 3 until the thickness of the adhesive along the thickness direction Z of the bottom plate 3 is equal to the preset adhesive layer thickness corresponding to the i-th sample. After the adhesive is cured at room temperature, an adhesive layer 8 is obtained.

[0070] The adhesive layer 8 is trimmed so that the adhesive layer 8 overlaps with the base plate 3 along the thickness direction Z of the base plate 3 to obtain the i-th sample.

[0071] Alternatively, the i-th sample is prepared as follows:

[0072] providing a stack 2;

[0073] Applying adhesive to one side of the stack 2, the adhesive covering the top electrode 6;

[0074] Providing a top plate 7, wherein the thickness of the top plate 7 is equal to the preset top plate thickness corresponding to the i-th sample;

[0075] Cover the top plate 7 on the side of the adhesive away from the bottom plate 3, and apply a preset pressure uniformly to the top plate 7 along the thickness direction Z of the bottom plate 3, and obtain an adhesive layer 8 after the adhesive is cured at room temperature;

[0076] The adhesive layer 8 is trimmed so that the adhesive layer 8 overlaps with the base plate 3 along the thickness direction Z of the base plate 3 to obtain the i-th sample.

[0077] Alternatively, the i-th sample is prepared as follows:

[0078] When i≥2, after the test of the i-1th sample is completed, a thickening layer is pasted on the side of the top plate 7 of the i-1th sample away from the bottom plate 3 to obtain the i-th sample, and the thickening layer, bottom plate 3 and top plate 7 can be made of the same flexible material, which can be selected according to actual needs.

[0079] Of course, the manufacturing method of sample 1 is not limited to this and can be set according to actual needs. Specifically, the stack 2 is manufactured in the following manner:

[0080] Providing a bottom plate 3;

[0081] Depositing a bottom electrode 4 on one side of the bottom plate 3;

[0082] A two-dimensional material 5 is placed on the side of the bottom electrode 4 away from the bottom plate 3. Along the length direction X of the bottom plate 3, the length of the two-dimensional material 5 is less than the length of the bottom electrode 4; along the width direction of the bottom plate 3, the width of the two-dimensional material 5 is equal to the width of the bottom electrode 4.

[0083] A top electrode 6 is deposited on a side of the two-dimensional material 5 away from the bottom electrode 4 to form a stack 2 . Along the length direction X of the bottom plate 3 , the length of the top electrode 6 is smaller than the length of the two-dimensional material 5 .

[0084] It should be noted that both bottom plate 3 and top plate 7 are made of flexible materials, and the adhesive is epoxy resin. This ensures that Sample 1 can deform with the applied dynamic bending load during four-point bending. Of course, this is not a limitation. Before the four-point bending, each layer of Sample 1 is flat. It is only during the four-point bending process that each layer becomes a curved surface.

[0085] In step S102, the jth measured flexoelectric coefficient value of the i-th sample is obtained according to the measured current of the i-th sample at the j-th test and the preset displacement of the i-th sample at the j-th test, and is calculated as follows:

[0086]

[0087] Among them, δ ij is the preset displacement of the i-th sample during the j-th test, L is the distance between the center points of the two support columns 11 along the length direction X of the bottom plate 3 of the i-th sample, L1 is the shortest distance from the center point of the support column 11 to the four-point bending head 12 along the length direction X of the bottom plate 3 of the i-th sample, i j is the measured current of the i-th sample at the j-th test, f is the excitation frequency, A i is the area of ​​the top electrode 6 of the i-th sample, The j-th measured flexoelectric coefficient value for the i-th sample.

[0088] The expression corresponding to the i-th sample is constructed based on the fitted flexoelectric coefficient value of the i-th sample, the distance value of the i-th sample, the effective flexoelectric coefficient, and the effective piezoelectric coefficient, and is calculated as follows:

[0089]

[0090] in, is the fitted flexoelectric coefficient value of the i-th sample, h i is the distance value of the i-th sample, μ eff is the effective flexoelectric coefficient, e eff is the effective piezoelectric coefficient.

[0091] It should be noted that the strain gradient generated in the two-dimensional material 5 can be described by the classical elastic theory and calculated as follows:

[0092]

[0093] Here, δ is the longitudinal displacement applied by the four-point bending head 12.

[0094] When testing the i-th sample for the j-th time, replace δ with δ ij , which is used to represent the strain gradient generated by the two-dimensional material 5 in the i-th sample.

[0095] The 5-electrode polarization of a 2D material can be expressed by the measured current and calculated as follows:

[0096]

[0097] Where i is the measurement current, f is the excitation frequency of the piezoelectric device, and A is the electrode area.

[0098] When the i-th sample is tested for the j-th time, i is replaced by i j , A is replaced by A i , thereby obtaining the electric polarization representation of the two-dimensional material 5 in the i-th sample.

[0099] In order to measure the flexoelectric coefficient, it is also necessary to address the problem of interference in the measurement caused by the piezoelectric effect caused by tensile or compressive strain during the bending deformation of the piezoelectric two-dimensional material 5. Considering the flexoelectric effect and the piezoelectric effect, the electric polarization induced by the bending deformation in the two-dimensional material 5 can be expressed as follows:

[0100]

[0101] Among them, μ ijkl is the flexoelectric coefficient, e ijk is the piezoelectric coefficient, ε jk is the strain tensor.

[0102] If only the electric polarization in the thickness direction Z of the two-dimensional material 5 is considered, it can be expressed as:

[0103]

[0104] Where v is the Poisson's ratio of the two-dimensional material 5, ε 11 is the strain along the length direction X of the two-dimensional material 5.

[0105] The strain along the length direction X of the two-dimensional material 5 can be calculated as follows:

[0106]

[0107] Wherein, h is the distance between the thickness bisector plane of the two-dimensional material 5 and the thickness bisector plane of the sample 1 in which it is located.

[0108] Combining the above formulas, we can get:

[0109]

[0110] μ exp =μ eff +e eff h

[0111] Therefore, when the i-th sample is tested for the j-th time, P3 in the above formula is substituted into the electric polarization of the two-dimensional material 5 in the i-th sample, Substitute the strain gradient generated by the two-dimensional material 5 in the i-th sample to obtain μ exp That is

[0112] It is understandable that for the sake of illustration, Figure 2 and Figure 4 The structure of sample 1 is simplified in the paper. The experimentally measured flexoelectric coefficient comes from the contributions of the flexoelectric effect and the piezoelectric effect; under the same strain gradient, the piezoelectric polarization is linearly related to the distance between the two-dimensional material 5 and the neutral plane, while the flexoelectric polarization is independent of the distance between the two-dimensional material 5 and the neutral plane. In order to separate the contribution of the piezoelectric effect, a series of samples 1 can be constructed, and the distance h between the two-dimensional material 5 and the neutral plane of the multilayer structure can be changed so that under the same strain gradient, the piezoelectric polarization changes while the flexoelectric polarization remains unchanged. Then, by measuring the current difference of different multilayer structures, the contributions of flexoelectricity and piezoelectricity can be separated.

[0113] Reference Figure 4 ,exist Figure 4 Only three samples 1 are shown in the figure. The two-dimensional materials 5 of the three samples 1 gradually deviate from the neutral plane of the structure in which they are located. By measuring the thickness of each sample 1, the distance value h is calculated according to the following formula:

[0114]

[0115] Among them, t total is the total thickness of sample 1 along the thickness direction Z of the bottom plate 3, t substrate is the thickness of the bottom plate 3, t material is the thickness of the two-dimensional material 5 of the sample 1 along the thickness direction Z of the base plate 3.

[0116] By measuring the current value of each sample 1 under different strain gradients, the current value is converted into an electric polarization value, and then the experimental measured flexoelectric coefficient value of each sample 1 is fitted. Finally, a linear fit is performed on the experimental measured flexoelectric coefficient value and the distance value, where the intercept value of the fitting line is the effective flexoelectric coefficient value μ of the two-dimensional material 5 to be tested. eff .

[0117] Example 3

[0118] Combine Figure 1 、 Figure 2 、 Figure 4 、 Figure 5 and Figure 6 , Figure 5 is the measured electric polarization versus applied strain gradient, Figure 6 is a schematic diagram of a fitting line, illustrating another specific embodiment of the method for measuring the flexoelectric coefficient of the two-dimensional material 5 provided by the present invention, comprising:

[0119] This embodiment uses the piezoelectric two-dimensional material copper indium phosphorus sulfide (chemical formula: CuInP2S6, abbreviated as CIPS) as a case to verify the correctness of the method proposed in the present invention.

[0120] The details of sample 1 preparation are as follows:

[0121] The bottom plate 3 and the top plate 7 are both made of flexible sheets, and the material of the flexible sheets is polyethylene terephthalate (chemical formula: (C 10 H8O4) n , English full name: Polyethylene terephthalate, abbreviated as: PET), and epoxy resin is used as the adhesive. In order to prepare sample 1, a 188-micron-thick PET substrate was cut into rectangular sheets with a length of 25 mm and a width of 3 mm as the bottom plate 3 and the top plate 7. Electron beam evaporation was used to deposit 5-nanometer-thick chromium metal and 45-nanometer-thick gold metal on the upper surface of the PET substrate in sequence as the bottom electrode 4. 50-nanometer-thick gold metal was deposited on the upper surface of a 28-micron-thick CIPS single crystal sheet by ion sputtering as the top electrode 6. Platinum wire was used as the metal wire 9, and it was connected to the metal electrode through silver paste to collect current. Epoxy resin was used as the adhesive, and PET / CIPS / PET were continuously stacked and bonded to form a multilayer structure, and uniform longitudinal pressure was applied to form a stable flat structure.

[0122] It is possible to prepare multiple samples 1 with different distance values ​​for testing at the same time, or to gradually bond the PET layer to the top plate 7 in sequence after each flexural electrical test to change the total thickness of the sample 1. The method of changing the total thickness of the sample 1 is not limited to this and can be set according to actual needs.

[0123] In this embodiment, it is taken as an example that four samples 1 are tested separately, and the number of tests on any sample 1 is 6 times. Of course, it is not limited to this. In the 6 tests, the longitudinal displacement values ​​applied by the four-point bending head 12 are 5 microns, 10 microns, 15 microns, 20 microns, 25 microns and 30 microns respectively; the distance L1 between the four-point bending head 12 and the adjacent support column 11 is 6 mm, and the distance between the two support columns 11 is 20 mm; the excitation frequency is set to 10 Hz to ensure that the actual deflection of the multi-layer sample 1 can accurately follow the driving displacement of the piezoelectric actuator; the top electrode 6 is circular with a radius of 1 mm, and the bottom electrode 4 is rectangular, and the size is consistent with the PET substrate.

[0124] Reference Figure 5 It can be seen that with the increase of the number of PET layers, the measured polarization gradually increases, indicating that the distance between the two-dimensional material 5 and the neutral plane gradually increases, resulting in a larger in-plane strain and inducing a stronger piezoelectric polarization. Figure 5 The relationship between the neutral polarization and the strain gradient is linearly fitted to obtain the values ​​of the experimentally measured flexoelectric coefficients of different samples 1. The measured flexoelectric coefficients are fitted with the distance h between the two-dimensional material 5 and the neutral plane in different samples 1. The results are as follows: Figure 6 As shown. Figure 6 ,from Figure 6 The intercept in the magnified part shows that the effective flexoelectric coefficient of the two-dimensional material copper indium phosphide is -25.6nC / m.

[0125] It should be noted that the method for measuring the flexoelectric coefficient of separable piezoelectric two-dimensional materials provided by the present invention can be applied to the National Natural Science Foundation of China general project with project number "12172047", project name "Research on Flexoelectric Effect in Self-supporting Perovskite Films", and project leader "Hong Jiawang"; it can also be applied to the Beijing Natural Science Foundation Youth Project with project number "1244057", project name "Flexoelectric Control of Micro-Nano Mechanics and Pyroelectric Properties of Self-supporting Oxide Films", and project leader "Lun Yingchao".

[0126] From the above embodiments, it can be seen that the method for measuring the flexoelectric coefficient of a separable piezoelectric two-dimensional material provided by the present invention achieves at least the following beneficial effects:

[0127] 1. The present invention provides a method for measuring the flexoelectric coefficient of separable piezoelectric two-dimensional materials, which embeds micron-sized two-dimensional materials between multilayer structures to form a sample, solving the technical difficulties of electrode preparation and dynamic mechanical loading faced in the flexoelectric coefficient measurement of micron-sized two-dimensional materials.

[0128] 2. The present invention provides a method for measuring the flexoelectric coefficient of a separable piezoelectric two-dimensional material, which tests N samples with different distance values ​​respectively. The distance value is the distance from the thickness bisector of the two-dimensional material to the thickness bisector of the sample along the thickness direction of the base plate in one sample. Since the distance value affects the strain state and piezoelectric polarization of the two-dimensional material, the flexoelectric contribution and the piezoelectric contribution are separated according to the total polarization difference of multiple samples, thereby accurately measuring the flexoelectric coefficient of the two-dimensional material.

[0129] Although some specific embodiments of the present invention have been described in detail by way of examples, it should be understood by those skilled in the art that the above examples are for illustration only and are not intended to limit the scope of the present invention. It should be understood by those skilled in the art that modifications may be made to the above embodiments without departing from the scope and spirit of the present invention. The scope of the present invention is defined by the appended claims.

Claims

1. A method for measuring the flexoelectric coefficient of a separable piezoelectric two-dimensional material, characterized in that: include: Providing N samples, where N is an integer and N ≥ 2, wherein the samples include a stack and a top plate, wherein the stack includes a bottom plate, a bottom electrode, a micron-sized two-dimensional material, and a top electrode stacked in sequence, the top plate being located on a side of the top electrode away from the bottom plate, and the stack and the top plate being connected by an adhesive layer; wherein the distance values ​​of any two samples are different, and in one sample, the distance from a thickness bisector plane of the two-dimensional material to a thickness bisector plane of the sample along the thickness direction of the bottom plate is taken as the distance value of the sample; Calculate the expressions corresponding to N samples respectively, including: when calculating the expression corresponding to the ith sample, i is an integer and 1≤i≤N, measure the distance value of the ith sample; perform M tests on the ith sample, each test only with a different preset displacement, M is an integer and M≥2, including: when performing the jth test on the ith sample, j is an integer and 1≤j≤M, place the ith sample between a four-point bending base and a four-point bending pressure head, the four-point bending base includes two support columns relatively arranged along the length direction of the bottom plate of the ith sample, the four-point bending pressure head includes two lower pressure columns relatively arranged along the length direction of the bottom plate of the ith sample on the side close to the four-point bending base, and the bottom plate of the ith sample abuts against the support columns; along the thickness direction of the bottom plate of the ith sample, the center point of the two-dimensional material of the ith sample, the center point of the four-point bending pressure head and the center point of the four-point bending base overlap; along the length direction of the bottom plate of the ith sample , the two-dimensional material of the i-th sample is located between the two lower pressure columns, and the lower pressure column is located between the two support columns; a phase-locked amplifier is connected to the top electrode of the i-th sample and the bottom electrode of the i-th sample, and a function generator is used to control the four-point bending head to move the preset displacement along the thickness direction of the bottom plate of the i-th sample, and the phase-locked amplifier obtains the measured current of the i-th sample at the j-th test; according to the measured current of the i-th sample at the j-th test and the preset displacement of the i-th sample at the j-th test, the j-th measured flexoelectric coefficient value of the i-th sample is obtained; the average value from the 1st measured flexoelectric coefficient value of the i-th sample to the Mth measured flexoelectric coefficient value of the i-th sample is calculated to obtain the fitted flexoelectric coefficient value of the i-th sample; according to the fitted flexoelectric coefficient value of the i-th sample, the distance value, the effective flexoelectric coefficient and the effective piezoelectric coefficient of the i-th sample, the expression corresponding to the i-th sample is constructed; The expression corresponding to the first sample is fitted to the expression corresponding to the Nth sample by linear fitting to obtain a fitting line, and the intercept value of the fitting line is the effective flexoelectric coefficient of the two-dimensional material.

2. The method for measuring the flexoelectric coefficient of a separable piezoelectric two-dimensional material according to claim 1, characterized in that: According to the measured current of the i-th sample during the j-th test and the preset displacement of the i-th sample during the j-th test, the j-th measured flexoelectric coefficient value of the i-th sample is obtained, which is calculated as follows: Among them, δ ij is the preset displacement of the i-th sample during the j-th test, L is the distance between the center points of the two support columns along the length direction of the bottom plate of the i-th sample, L1 is the shortest distance from the center point of the support column to the four-point bending head along the length direction of the bottom plate of the i-th sample, i j is the measured current of the i-th sample at the j-th test, f is the excitation frequency, A i is the area of ​​the top electrode of the i-th sample, The j-th measured flexoelectric coefficient value for the i-th sample.

3. The method for measuring the flexoelectric coefficient of a separable piezoelectric two-dimensional material according to claim 1, characterized in that: The expression corresponding to the i-th sample is constructed based on the fitted flexoelectric coefficient value of the i-th sample, the distance value of the i-th sample, the effective flexoelectric coefficient and the effective piezoelectric coefficient, and is calculated in the following manner: in, is the fitting flexoelectric coefficient value of the i-th sample, h i is the distance value of the i-th sample, μ eff is the effective flexoelectric coefficient, e eff is the effective piezoelectric coefficient.

4. The method for measuring the flexoelectric coefficient of a separable piezoelectric two-dimensional material according to claim 1, characterized in that: The i-th sample is prepared in the following manner: providing the stack; applying an adhesive on one side of the stack, the adhesive covering the top electrode; Covering the top plate on the side of the adhesive away from the bottom plate, uniformly applying pressure to the top plate along the thickness direction of the bottom plate until the thickness of the adhesive along the thickness direction of the bottom plate is equal to the preset adhesive layer thickness corresponding to the i-th sample, and curing the adhesive at room temperature to obtain the adhesive layer; The adhesive layer is trimmed so that the adhesive layer overlaps with the base plate along the thickness direction of the base plate, thereby obtaining the i-th sample.

5. The method for measuring the flexoelectric coefficient of a separable piezoelectric two-dimensional material according to claim 1, characterized in that: The i-th sample is prepared in the following manner: providing the stack; applying an adhesive on one side of the stack, the adhesive covering the top electrode; Providing the top plate, wherein the thickness of the top plate is equal to the preset top plate thickness corresponding to the i-th sample; Covering the top plate on the side of the adhesive away from the bottom plate, uniformly applying a preset pressure to the top plate along the thickness direction of the bottom plate, and obtaining the adhesive layer after the adhesive is cured at room temperature; The adhesive layer is trimmed so that the adhesive layer overlaps with the base plate along the thickness direction of the base plate, thereby obtaining the i-th sample.

6. A method for measuring the flexoelectric coefficient of a separable piezoelectric two-dimensional material according to claim 1, 4 or 5, characterized in that: The stack is made in the following manner: providing the base plate; depositing the bottom electrode on one side of the bottom plate; The two-dimensional material is placed on a side of the bottom electrode away from the bottom plate, wherein the length of the two-dimensional material along the length direction of the bottom plate is less than the length of the bottom electrode; and the width of the two-dimensional material along the width direction of the bottom plate is equal to the width of the bottom electrode; The top electrode is deposited on a side of the two-dimensional material away from the bottom electrode to form the stack. Along the length direction of the bottom plate, the length of the top electrode is less than the length of the two-dimensional material.

7. The method for measuring the flexoelectric coefficient of a separable piezoelectric two-dimensional material according to claim 1, characterized in that: The i-th sample is prepared in the following manner: When i≥2, after the test of the i-1th sample is completed, a thickening layer is pasted on the side of the top plate of the i-1th sample away from the bottom plate to obtain the i-th sample.

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