Method for measuring the thermal expansion coefficient of a layered two-dimensional material and applications

Abstract

This invention provides a method and application for measuring the surface thermal expansion coefficient of a layered two-dimensional material. The method includes: measuring the flexural stiffness δ of the layered two-dimensional material in a direction perpendicular to the plane, and the thermal expansion coefficient α of the chemical bonds in the layered two-dimensional material. bond Substituting into equation (1), we obtain the surface thermal expansion coefficient α of the layered two-dimensional material. s ;α s =2α bond –50 / δ(1). This invention proposes for the first time that the thermal expansion coefficient of a two-dimensional material can be obtained by combining these two testing schemes and converting them. This measurement method has the advantages of simple operation, transferable test data, wide temperature coverage, and stable results.

Description

Technical Field

[0001] This invention relates to the field of measurement technology, specifically to a method and application for measuring the surface thermal expansion coefficient of a layered two-dimensional material. Background Technology

[0002] With the miniaturization and micro-miniaturization of electronic devices and the development of flexible electronic materials, there is an urgent need for the research and development of next-generation nanofunctional devices. Two-dimensional materials, represented by graphene, black phosphorus, and molybdenum disulfide, possess natural nanoscale thickness, good flexibility, and rich functional properties, making them highly promising for applications. However, two-dimensional materials typically exhibit layered characteristics, with strong covalent bonds within the layers and weak van der Waals forces between them. This layered nature dictates that two-dimensional materials inevitably employ stacked structures from processing and fabrication to application, leading to heterojunctions between the two-dimensional material and the matrix or between different two-dimensional materials. The thermal matching between these different materials becomes a key issue determining their functional properties, necessitating the measurement or evaluation of the thermal expansion coefficients of different two-dimensional materials.

[0003] The coefficient of thermal expansion is defined as the rate of change of a material's dimensions with temperature. Therefore, for bulk materials, measuring the coefficient of thermal expansion is simple, requiring only the measurement of the material's dimensions (length, area, volume, etc.) at different temperatures. However, for two-dimensional materials, the small size causes significant thermal fluctuations, making accurate temperature measurement difficult. Furthermore, the transparency of these materials often hinders accurate dimensional measurement, making it challenging to directly measure the coefficient of thermal expansion like for bulk materials. Existing methods for directly measuring the coefficient of thermal expansion primarily involve thermal bubbling, which involves heating a suspended material, measuring its deflection, and then calculating the corresponding coefficient of thermal expansion. Indirect methods are more commonly used, such as Raman spectroscopy and electron energy loss spectroscopy, which map the system's temperature or dimensions to the target observation to obtain the coefficient of thermal expansion. However, most indirect testing methods struggle to eliminate the influence of the substrate material on thermal expansion properties. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method and application for measuring the surface thermal expansion coefficient of layered two-dimensional materials. This method utilizes mechanical property testing, specifically testing the bending stiffness of suspended two-dimensional materials. By combining this with the intrinsic thermal expansion properties of chemical bonds, the thermal expansion behavior of two-dimensional materials can be evaluated.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] This invention provides a method for measuring the surface thermal expansion coefficient of a layered two-dimensional material. The method includes: measuring the flexural stiffness δ of the layered two-dimensional material in a direction perpendicular to the plane, and the thermal expansion coefficient α of the chemical bonds in the layered two-dimensional material. bond Substituting into equation (1), we obtain the surface thermal expansion coefficient α of the layered two-dimensional material. s ;α s =2α bond –50 / δ(1). This invention proposes for the first time that the thermal expansion coefficient of two-dimensional materials can be obtained by combining these two test schemes and converting them.

[0007] Furthermore, the unit for bending stiffness is eV, and the unit for the coefficient of thermal expansion is 10. -6 ·K -1 If other units are used, the conversion can be performed, and this relationship can be used to evaluate the coefficient of thermal expansion of the material.

[0008] Furthermore, the bending stiffness δ of the layered two-dimensional material in the direction perpendicular to the plane is measured using the pressure bubbling method.

[0009] Furthermore, the coefficient of thermal expansion α of the chemical bonds in the layered two-dimensional material... bond X-ray absorption fine structure spectroscopy was used for measurement.

[0010] Furthermore, the method specifically includes the following steps: preparing layered two-dimensional materials; and measuring the thermal expansion coefficient α of the chemical bonds in the layered two-dimensional materials by X-ray absorption fine structure spectroscopy. bond The layered two-dimensional material was transferred to a substrate material with perforations, and the flexural stiffness δ of the layered two-dimensional material in the direction perpendicular to the plane was measured by pressure bubbling method; the measured coefficient of thermal expansion of chemical bonds α was then used to measure the flexural stiffness δ of the layered two-dimensional material. bond Substituting the bending stiffness δ into equation (1) for calculation, the surface thermal expansion coefficient α of the layered two-dimensional material is obtained. s ;α s =2α bond –50 / δ(1). This invention primarily aims to protect the evaluation of the thermal expansion coefficient of two-dimensional layered materials through bending stiffness and chemical bond properties. This scheme provides only a simple and feasible approach for the preparation of two-dimensional materials, the testing of bending stiffness, and the testing of chemical bond thermal expansion behavior. However, when using other methods (physical or chemical vapor deposition) to prepare two-dimensional materials and measure their mechanical properties and chemical bond thermal expansion coefficients, the quantitative relationship presented in this invention can also be used to obtain the material's thermal expansion coefficient.

[0011] Furthermore, the preparation of the layered two-dimensional material includes: preparing the layered two-dimensional material using mechanical exfoliation, physical vapor deposition, or chemical vapor deposition.

[0012] The present invention also provides the application of the method for measuring the surface thermal expansion coefficient of layered two-dimensional materials as described above in the field of measuring or evaluating the thermal expansion coefficient of different two-dimensional materials.

[0013] Compared with the prior art, the technical solution provided by the present invention has at least the following advantages:

[0014] 1. Simple operation: This invention transforms complex thermal performance testing into mechanical performance testing. It eliminates the need to analyze the material's flexural morphology and only requires measuring the height of the bubbles, thus greatly reducing the testing difficulty and improving the accuracy of the test.

[0015] 2. Test data is transferable. This mainly concerns the thermal expansion behavior of covalent bonds. For the same system, only one test is needed for recording. This invention reveals that the thermal expansion behavior of covalent bonds is an intrinsic property of the bond and is almost unrelated to the material's size, state, or dimensions. Once the database is established, this testing step can be omitted, significantly reducing testing costs.

[0016] 3. Wide temperature range coverage. Within the range of 0-500K (covering the service temperature range of most two-dimensional materials), the changes in physical quantities such as the bending stiffness and coefficient of thermal expansion of the material are very small. Therefore, only one test is needed to evaluate the thermal expansion behavior of the material over a wide range.

[0017] 4. Stable results. The quantitative relationship between flexural stiffness and coefficient of thermal expansion in layered two-dimensional materials is stable and reliable, and applicable to different material systems. Attached Figure Description

[0018] One or more embodiments are illustrated by way of example with reference to the accompanying drawings. These illustrations do not constitute a limitation on the embodiments, and unless otherwise stated, the figures in the drawings are not to be limited by scale.

[0019] Figure 1 This is a flowchart of the testing method provided in an embodiment of the present invention;

[0020] Figure 2 These are the values ​​of the covalent bond length of graphene and MoS2 with different layer thicknesses in the embodiments of the present invention as a function of temperature.

[0021] Figure 3 This refers to the changes in the dimensions of different two-dimensional materials with temperature in the embodiments of the present invention;

[0022] Figure 4 This describes the quantitative relationship between the coefficient of thermal expansion and bending stiffness of different materials in the embodiments of the present invention. Detailed Implementation

[0023] The inventors discovered that existing experimental methods for determining the coefficient of thermal expansion of two-dimensional materials can be divided into two categories: direct methods and indirect methods.

[0024] The direct method involves measuring the dimensional changes of a material at different temperatures to directly determine its coefficient of thermal expansion. A common practice is to heat a suspended two-dimensional material, causing it to flex due to thermal expansion. The dimensional change is then determined by measuring the length of the flexed material. The main problems with this method are the complexity of sample preparation, low success rate, and the need to observe changes in the material's morphology, which is not only cumbersome but also introduces human error. This increases testing costs and reduces efficiency and accuracy.

[0025] Indirect methods involve using techniques such as Raman spectroscopy and electron energy loss spectroscopy to establish a mapping between the system's temperature or size and the target observable, and then calculating its coefficient of thermal expansion. However, most indirect testing methods struggle to eliminate the influence of the substrate material on thermal expansion properties. Furthermore, the thermal expansion properties of materials differ significantly on different substrates, and the thermal expansion behaviors of different materials on the same substrate cannot be directly compared. Therefore, the results obtained by this method do not represent the intrinsic properties of the material, and the measurement results have poor transferability and comparability.

[0026] This invention is based on the discovery of a quantitative relationship between the coefficient of thermal expansion of two-dimensional materials and their mechanical properties (bending stiffness) and the intrinsic thermal expansion behavior of chemical bonds. It indirectly obtains the coefficient of thermal expansion of two-dimensional materials using mature bending stiffness testing techniques and chemical bond thermal expansion performance testing techniques. This method has the advantages of simple operation, lower cost, and higher efficiency. It is particularly noteworthy that the intrinsic thermal expansion behavior of chemical bonds is independent of the material's dimensionality (number of layers). Therefore, for the same material system, this property only needs to be tested once, which can greatly reduce testing costs and improve efficiency.

[0027] This invention provides a method for measuring the surface thermal expansion coefficient of a layered two-dimensional material, the method comprising:

[0028] The bending stiffness δ of the layered two-dimensional material in the direction perpendicular to the plane was measured, as well as the coefficient of thermal expansion α of the chemical bonds in the layered two-dimensional material. bond Substituting into equation (1), we obtain the surface thermal expansion coefficient α of the layered two-dimensional material. s ;

[0029] α s =2α bond –50 / δ (1).

[0030] The present invention will now be described in detail with reference to specific embodiments.

[0031] Example

[0032] This invention provides a method for indirectly obtaining the thermal expansion coefficient of a two-dimensional material. Specifically, it involves first measuring the bending stiffness δ and the thermal expansion coefficient α of the chemical bonds in the two-dimensional material. bond Then, the coefficient of thermal expansion of the material is calculated using the quantitative relationship (Equation (1)) discovered in this invention. The specific test procedure flowchart is as follows: Figure 1 As shown.

[0033] Figure 1 This is a flowchart of the testing method provided in this embodiment of the invention. The testing scheme of this invention consists of four steps. Step 1 is the preparation of layered two-dimensional materials, which uses a mechanical exfoliation method, capable of preparing most layered two-dimensional materials. Step 2 is the measurement of the thermal expansion coefficient of chemical bonds in the material using X-ray absorption fine structure spectroscopy. Step 3 is the measurement of the flexural stiffness of the material using a bubbling method. Before measurement, the material should be transferred to a substrate material with small holes. Step 4 is the calculation of the obtained thermal expansion coefficient α of the chemical bonds. bond If the bending stiffness δ is directly substituted into equation (1) for calculation, the thermal expansion coefficient of the material can be obtained directly.

[0034] α s =2α bond –50 / δ (1).

[0035] First, there are various methods for preparing two-dimensional materials, and this invention selects the most widely used exfoliation method. This method can obtain almost all layered two-dimensional materials. The two-dimensional materials prepared by this method have advantages such as large area, few defects, easy transfer, and controllable number of layers.

[0036] Secondly, X-ray absorption fine structure spectroscopy was performed on the bulk material to measure the change in covalent bond length with temperature, thereby obtaining the thermal expansion coefficient α of the chemical bond. bond It is worth noting that we did not directly measure the X-ray absorption fine structure spectrum of two-dimensional materials, but rather directly measured bulk materials. This is because the covalent bonds within layered two-dimensional materials are the same as those in bulk materials. The testing difficulty and cost of bulk materials are significantly reduced compared to layered two-dimensional materials. Furthermore, this invention also found that the thermal expansion coefficient of covalent bonds does not exhibit a significant layer thickness dependence (e.g., ...). Figure 2 (As shown). Therefore, α of bulk materials can be used. bond It should be noted that, in contrast to two-dimensional materials, there are bulk materials, meaning materials possessing length characteristics in three dimensions. Two-dimensional materials refer to materials whose in-plane dimensions are much larger than their dimensions perpendicular to the plane. Two-dimensional materials can be prepared using mechanical exfoliation methods; the state before exfoliation corresponds to a bulk material, such as graphene, whose bulk material is graphite.

[0037] Figure 2 In the figures (a) and (b), the covalent bond lengths of graphene and MoS2 with different layer thicknesses vary with temperature, respectively. These bond length changes are the results of molecular dynamics simulations. The slope of the dashed line in the figure corresponds to the α-coefficient of change for each material. bond It is directly proportional. Calculations show that although the thickness of the material layers varies, its α... bond There is almost no difference.

[0038] Third, the flexural stiffness of layered two-dimensional materials is measured using the bubbling method. The basic principle is to cover the two-dimensional material with a small hole and achieve bubbling by applying a pressure difference p on both sides of the hole. The pressure difference p, the radius a of the hole, the thickness t of the material, and the height h of the bubble are all observables. According to equation (2), the relationship between these observables and the Young's modulus E and the flexural stiffness δ of the material can be obtained.

[0039]

[0040] In the formula, A(v)≈(0.7179-0.1406v-0.1495v²)⁻³ is a function of the material's Poisson's ratio ν. Therefore, by measuring the bubble height of the material under different pressure differences, the bending stiffness δ of the material can be obtained.

[0041] Finally, by substituting the measured bending stiffness of the material and the thermal expansion coefficient of the chemical bonds into equation (1), the thermal expansion coefficient of the layered two-dimensional material can be obtained.

[0042] Figure 3 The changes in the dimensions of different two-dimensional materials with temperature are presented. Within a given temperature range, the material dimensions change linearly, indicating that their coefficient of thermal expansion is constant. Figure 3 The dimensions of (a) a single layer of hBN, (b) a single layer of PbTe, (c) 1-3 layers of graphene, and (d) 1-3 layers of MoS2 vary with temperature. A stable linear relationship indicates that the material has a constant coefficient of thermal expansion within a given temperature range.

[0043] from Figure 4 It can be seen that the thermal expansion coefficient and bending stiffness of different materials all satisfy the quantitative relationship shown in equation (1).

[0044] Those skilled in the art will understand that the above embodiments are specific examples of implementing this application, and in practical applications, various changes in form and detail can be made without departing from the spirit and scope of this application. Any person skilled in the art can make their own modifications and alterations without departing from the spirit and scope of this application; therefore, the scope of protection of this application should be determined by the scope defined in the claims.

Claims

1. A method for measuring the surface thermal expansion coefficient of a layered two-dimensional material, characterized in that, The method includes: The bending stiffness δ of the layered two-dimensional material in the direction perpendicular to the plane was measured, as well as the coefficient of thermal expansion α of the chemical bonds in the layered two-dimensional material. bond Substituting into equation (1), we obtain the surface thermal expansion coefficient α of the layered two-dimensional material. s ; a s =2a bond –50 / δ(1).

2. The method for measuring the surface thermal expansion coefficient of layered two-dimensional materials according to claim 1, characterized in that, The unit of flexural stiffness δ is eV, and the unit of thermal expansion coefficient is 10. -6 ·K -1 .

3. The method for measuring the surface thermal expansion coefficient of layered two-dimensional materials according to claim 1, characterized in that, The bending stiffness δ of the layered two-dimensional material in the direction perpendicular to the plane was measured using the pressure bubbling method.

4. The method for measuring the surface thermal expansion coefficient of layered two-dimensional materials according to claim 1, characterized in that, The coefficient of thermal expansion α of the chemical bonds in the layered two-dimensional material bond X-ray absorption fine structure spectroscopy was used for measurement.

5. The method for measuring the surface thermal expansion coefficient of layered two-dimensional materials according to claim 1, characterized in that, The method specifically includes the following steps: Preparation of layered two-dimensional materials; The coefficient of thermal expansion α of chemical bonds in the layered two-dimensional material was measured by X-ray absorption fine structure spectroscopy. bond ; The layered two-dimensional material was transferred onto a substrate material with small holes, and the bending stiffness δ of the layered two-dimensional material in the direction perpendicular to the plane was measured by the pressure bubbling method. The measured coefficient of thermal expansion α of the chemical bond bond Substituting the bending stiffness δ into equation (1) for calculation, the surface thermal expansion coefficient α of the layered two-dimensional material is obtained. s ; a s =2a bond –50 / δ(1).

6. The method for measuring the surface thermal expansion coefficient of layered two-dimensional materials according to claim 5, characterized in that, The preparation of the layered two-dimensional material includes: preparing the layered two-dimensional material by mechanical exfoliation, physical vapor deposition, or chemical vapor deposition.

7. The method for measuring the surface thermal expansion coefficient of layered two-dimensional materials as described in any one of claims 1 to 6, and its application in the field of measuring or evaluating the thermal expansion coefficient of different two-dimensional materials.

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