A method for measuring material surface energy based on grain boundary triple junction curvature

Abstract

The application relates to a material surface energy measurement method based on grain boundary triple point curvature, and belongs to the field of material surface engineering. The test material grain size of the application is generally above 10 nm, and the material system can be pure metal, alloy, ceramic and the like. The measurement method is only based on surface morphology and hardness distribution, the three-dimensional surface morphology can be measured by an atomic force microscope and an atom probe and the like, and the material surface hardness can be measured by a tapping mode of the atomic force microscope and a nanoindentation and the like. The surface energy is indirectly estimated by using the grain boundary surface profile, the measurement method does not need to be implemented in a vacuum state, and the measurement method is simple.

Description

Technical Field

[0001] This invention belongs to the field of materials surface engineering, specifically, it relates to a method for indirectly calculating the surface energy of materials by measuring the surface profile distribution using atomic force microscopy and other methods. Background Technology

[0002] Compared to bulk materials, free atoms on a material surface are less constrained and possess excess energy; this energy associated with surface atoms is called surface free energy. The presence of surface energy significantly impacts the physical, chemical, and mechanical properties of nanostructures and materials, such as elastic modulus, melting temperature, and electromagnetic properties. In traditional continuum mechanics, surface atoms are considered to occupy only a small portion, thus the effect of surface energy is negligible. However, in reality, when the scale of materials shrinks to the nanoscale, the presence of the surface significantly influences the performance of nanostructures. The measurement of material surface energy can be divided into direct and indirect measurement techniques. Direct measurement methods obtain surface energy by measuring the breaking of released chemical bonds, while indirect methods require information such as surface tension and contact angle to measure surface energy. Current methods for measuring solid surface energy generally require vacuum conditions to obtain relatively accurate results. Furthermore, methods that extrapolate solid surface energy based on the surface tension of a molten solid are also relatively complex.

[0003] The material surface energy measurement method of the present invention is an indirect measurement method that does not require a vacuum. Summary of the Invention

[0004] In order to estimate the surface energy of a material surface, the object of the present invention is to provide a method for indirectly obtaining the surface energy of a material by measuring the profile near the grain boundary trigone point.

[0005] The technical solution adopted in this invention is: a method for measuring the surface energy of materials based on the curvature of grain boundary triple points, comprising the following steps:

[0006] S1. Cleaning of material surfaces;

[0007] S2. Using atomic force microscopy, obtain the groove profile and surface stress at the grain triangular points near the grain boundaries on the material surface. distributed;

[0008] S3. Obtain surface curvature using atomic force microscopy or atomic probe microscopy. ;

[0009] S4. Based on the surface chemical potential and grain boundary chemical potential, derive the relationship between stress, surface curvature, and surface energy, and then calculate the surface energy of the material; this specifically includes the following sub-steps:

[0010] S4.1, The chemical potential of a single atom is ;

[0011] in, The chemical potential is given by k, the Boltzmann constant is given by T, the thermodynamic temperature is given by a, the activity is given by p, and the vapor pressure is given by p. for Vapor pressure at that time;

[0012] Then according to ;

[0013] in, Indicates surface curvature. Represents surface energy. Indicates atomic volume;

[0014] The relationship between surface atomic chemical potential and surface energy is obtained as follows: ;

[0015] S4.2, The chemical potential of the grain boundary is: ;

[0016] in, It is surface stress. Indicates atomic volume;

[0017] The chemical potential difference between the surface and the grain boundary is: ;

[0018] Once steady state is reached , to obtain surface energy ;

[0019] The surface stress obtained from the above steps and surface curvature That is, to obtain the surface energy of the material.

[0020] Furthermore, in step S1, the material surface is cleaned with alcohol and acetone solution, rinsed with deionized water, and dried at low temperature.

[0021] Furthermore, in step S2, the three-dimensional morphology and hardness of the surface are measured using the tapping mode of an atomic force microscope; the maximum fluctuation of the sample within the test range is required to be no more than 12 μm.

[0022] Atomic force microscopy is used to measure two-dimensional undulations; in the original morphology data, the area near the grain boundary to be measured is found, and a two-dimensional contour map of the groove formed near the grain boundary is obtained. The data is exported and processed to obtain a surface contour map near the grain boundary.

[0023] Furthermore, the material is a metal, alloy, or ceramic.

[0024] Furthermore, the near-surface grain size of the measured material is greater than 10 nm.

[0025] This invention employs techniques such as atomic force microscopy to characterize the surface profile of the triangular points near the grain boundaries of the sample under test. A two-dimensional surface profile curve near the triangular points is obtained. The two-dimensional profile curve is then processed to obtain a curvature curve, and the stress distribution near the profile is measured.

[0026] The specific principles and steps for estimating the surface energy of a material are as follows.

[0027] The chemical potential of a single atom is: ,in The chemical potential is given by k, the Boltzmann constant is given by T, the thermodynamic temperature is given by a, the activity is given by p, and the vapor pressure is given by p. for The vapor pressure at that time.

[0028] According to the Gibbs-Thompson equation: ,in, Indicates surface curvature. Represents surface energy. Indicates atomic volume.

[0029] Combining the two equations above, we can obtain the relationship between surface atomic chemical potential and surface energy. This established the correlation between surface chemical potential, surface energy, and the curvature of the trigone point.

[0030] According to Herring's expression, the chemical potential of the grain boundary is: ,in It is surface stress. Indicates atomic volume.

[0031] Therefore, a chemical potential difference exists between the surface and the grain boundary, and this chemical potential difference is: Once a steady state is reached, Organizing can yield ,in Represents surface energy. This is surface stress. This simplifies the relationship between surface energy and the curvature of the triangular point.

[0032] Surface stress can be obtained by converting Tabor relations to hardness or by methods such as X-ray diffraction. Hardness measurement based on Tabor relations can be obtained through methods such as atomic force microscopy in tapping mode or based on Oliver-Parr nanoindentation experiments. Its hardness resolution determines the accuracy of surface energy assessment near grain boundary junctions. X-ray diffraction, on the other hand, mainly measures surface stress based on the drift and broadening of characteristic diffraction lines caused by lattice and defects, and depends on reflection geometry.

[0033] The curvature of a surface can be obtained using techniques such as atomic force microscopy and atomic probes, and its three-dimensional topological structure can be used to directly establish three-dimensional surface energy distribution information.

[0034] The beneficial effects of this invention are as follows: This method indirectly estimates surface energy by utilizing the curvature of the grain boundary triangular point. It is a method that does not depend on the measurement environment and can directly estimate the surface energy of a material based on grain boundary characteristics. It provides a method for measuring the surface energy distribution of materials with resolvable grain boundaries. Attached Figure Description

[0035] Figure 1 This is a surface profile diagram near grain boundaries in a thin film material.

[0036] Figure 2 This represents the stress distribution calculated based on the surface curvature.

[0037] Figure 3 The corresponding surface energy is calculated for each data point. Detailed Implementation

[0038] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0039] The three-dimensional morphology and hardness of the surface were measured using the tapping mode of an atomic force microscope. The maximum variation of the sample within the test range was required to be no more than 12 μm.

[0040] like Figure 1 As shown, atomic force microscopy is used to measure specific two-dimensional undulations. From the original morphology data, the vicinity of the grain boundary to be measured is located, and a two-dimensional contour map of the groove formed near the grain boundary is obtained. The data is exported, processed, and then a surface contour map of the vicinity of the grain boundary is obtained.

[0041] like Figure 2 The figure shows the stress distribution obtained by inversion based on atomic force microscopy and the stress characteristics obtained by inversion based on surface profile characteristics of the fourth-order partial differential surface diffusion equation. The two are in good agreement.

[0042] The stress calculated by inverting the surface profile features using the fourth-order partial differential diffusion equation is as follows:

[0043] First, in the diffusion-dominated evolution of surface profiles, the surface chemical potential gradient is the driving force for surface diffusion. The surface chemical potential is determined by the surface curvature:

[0044]

[0045] This gradient will cause the drift of surface atoms, the average velocity of which is given by the Nernst-Einstein relation:

[0046]

[0047] in, V is the surface diffusion coefficient, and s is the arc length of the profile. The atomic flux J of the surface is V multiplied by the surface area. The product of the number of atoms:

[0048]

[0049] If we take the surface divergence as -J, we can obtain the increase in the number of atoms per unit area per unit time. As mentioned earlier, this can be obtained by multiplying by... To convert to the speed at which a surface element moves along its normal. Combining equation (3), we can obtain:

[0050]

[0051] In the case of a general surface, equation (4) Replaced with ,Right now The surface Laplacian operator. Geometric projection of velocity. and The relationship is The differential sign in the upper right corner represents the partial differential with respect to x. Furthermore, according to the definition, And according to Transform equation (4) into The final partial differential equation for the surface profile evolution dominated by surface diffusion is as follows:

[0052]

[0053] in, Approximating the equation with a small slope, i.e. We can obtain:

[0054]

[0055] The boundary conditions for this fourth-order partial differential equation are as follows:

[0056]

[0057]

[0058]

[0059] Under the condition of equation (7), perform a Laplace transform on equation (6) ( ), we can get:

[0060]

[0061] Then, boundary conditions (8) and (9) will become

[0062]

[0063]

[0064] By solving equation (10) (solving a fourth-order linear differential equation) and substituting the boundary conditions (11) and (12), we find that it is an exponentially damped trigonometric function as follows:

[0065]

[0066] In principle, for any The values ​​can all be used to perform Laplace inversion on equation (13). Take... Then equation (13) becomes

[0067]

[0068] The corresponding time-domain function is:

[0069]

[0070]

[0071]

[0072]

[0073] The solution to the partial differential equation can be written in the following form:

[0074]

[0075] make for ,So for Then Substituting into equation (6), we can obtain the following ordinary differential equation.

[0076]

[0077] Approximating Z(u) using a power series:

[0078]

[0079] Substituting into equation (20), if the sum of the coefficients of each term after integration is 0, then equation (20) obviously holds true, from which we can obtain The recursive relationship between them:

[0080]

[0081] If the coefficients of the first four terms are known, all the coefficients can be calculated. The coefficients of the first four terms can be obtained from equations (15) to (18) according to Taylor's theorem:

[0082]

[0083] Then all the coefficients can be obtained using the above recursive formula. And an approximate solution to equation (6) can be obtained:

[0084]

[0085] Surface curvature can be calculated from the surface profile:

[0086]

[0087] According to the formula This allows for the inverse calculation of the stress characteristics corresponding to the surface profile. For example... Figure 2 As shown, the calculation results are in agreement with the results measured by atomic force microscopy.

[0088] based on The formula is used to calculate the surface energy distribution in the region, such as... Figure 3 As shown, the specific values ​​are 0.82, 1.48, 2.86, 4.19, 0.03, 0.28, 0.72, 1.076, 0.75, 0.52, 0.171, 2.285, 1.072, 0.967, and 1.289, with an average value of 1.234. Therefore, the surface energy of the material is 1.234.

[0089] Compared with the surface energy of the material, the known surface energy of the material is 1.175, and the surface energy indirectly measured by measuring the surface profile is 1.234. The relative error is 0.059, which is 5%.

[0090] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for measuring the surface energy of materials based on the curvature of grain boundary tripartite points, characterized in that, Includes the following steps: S1. Cleaning of material surfaces; S2. Using atomic force microscopy, obtain the groove profile and surface stress at the grain triangular points near the grain boundaries on the material surface. distributed; S3. Obtain surface curvature using atomic force microscopy or atomic probe microscopy. ; S4. Based on the surface chemical potential and grain boundary chemical potential, derive the relationship between stress, surface curvature, and surface energy, and then calculate the surface energy of the material; this specifically includes the following sub-steps: S4.1, The chemical potential of a single atom is ; in, The chemical potential is given by k, the Boltzmann constant is given by T, the thermodynamic temperature is given by a, the activity is given by p, and the vapor pressure is given by p. for Vapor pressure at that time; Then according to ; in, Indicates surface curvature. Represents surface energy. Indicates atomic volume; The relationship between surface atomic chemical potential and surface energy is obtained as follows: ; S4.2, The chemical potential of the grain boundary is: ; in, It is surface stress. Indicates atomic volume; The chemical potential difference between the surface and the grain boundary is: ; Once steady state is reached , to obtain surface energy ; The surface stress obtained from the above steps and surface curvature That is, to obtain the surface energy of the material.

2. The method for measuring the surface energy of a material based on the curvature of a grain boundary triple point according to claim 1, characterized in that: In step S1, the material surface is cleaned with alcohol and acetone solution, rinsed with deionized water, and dried at low temperature.

3. The method for measuring the surface energy of a material based on the curvature of a grain boundary triple point according to claim 1, characterized in that: In step S2, the three-dimensional morphology and hardness of the surface are measured using the tapping mode of an atomic force microscope; the maximum fluctuation of the sample within the test range is required to be no more than 12 μm. Atomic force microscopy is used to measure the two-dimensional undulation changes; in the original morphology data, the area near the grain boundary that needs to be measured is found, and a two-dimensional contour map of the groove formed near the grain boundary is obtained. The data is exported and processed to obtain a surface contour map near the grain boundary.

4. The method for measuring the surface energy of a material based on the curvature of a grain boundary triple point according to claim 1, characterized in that: The materials are metals, alloys, or ceramics.

5. The method for measuring the surface energy of a material based on the curvature of a grain boundary triple point according to claim 1, characterized in that, The near-surface grain size of the measured material is greater than 10 nm.

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