Young modulus and Poisson's ratio detection method based on atomic force microscope

Abstract

The invention relates to the technical field of precision measurement, in particular to a Young modulus and Poisson's ratio detection method based on an atomic force microscope, which comprises the following steps: S1, preparing equipment; step S2, probe parameter calibration; s3, establishing a resonant frequency measurement device; s4, fixing the sample; step S5, resonant frequency detection: inserting a probe and contacting the sample, driving the probe with a voltage of 10-50mV by using a phase-locked amplifier in a range of 10nm, then scanning the resonant frequency # imgabs0 # of the probe through the phase-locked amplifier, and collecting a morphology result of the surface of the sample to be detected; transmitting a morphology result and a signal of resonance frequency # imgabs1 # to a PC (Personal Computer) upper computer; step S6, data processing: the PC upper computer calculates the inclination angle # imgabs2 # of the probe based on the morphology result, draws the corresponding relation between the resonance frequency # imgabs3 # and the inclination angle # imgabs4 #, and then adopts a probe-sample contact model to solve the indentation modulus and Poisson's ratio; the Young modulus can be obtained through conversion of the indentation modulus and the Poisson's ratio.

Description

Technical Field

[0001] The present invention relates to the field of precision measurement technology, and in particular to a Young's modulus and Poisson's ratio detection method based on an atomic force microscope. Background Art

[0002] Young's modulus and Poisson's ratio are two key parameters that describe the mechanical response of materials under external forces. Young's modulus is used to measure the stiffness of a material under tension or compression, reflecting the material's resistance to deformation; Poisson's ratio describes the change in strain in the perpendicular direction when a material is subjected to force in one direction. Accurate measurement of these two parameters can not only reveal the basic mechanical properties of the material, but also lay the foundation for the widespread application of the material; characterization of the mechanical properties of materials is crucial to understanding their behavior and promoting the design of new materials.

[0003] At the nanoscale, the mechanical properties of materials may differ significantly from those at the macroscale. As the size of the material decreases to the nanoscale, phenomena such as surface effects, size effects, and grain boundary effects become more significant. These effects may lead to significant changes in Young's modulus. For example, the Young's modulus of nanomaterials may be significantly different from that of macroscopic materials due to differences in surface atomic arrangement and surface energy. In addition, the Poisson's ratio may also exhibit a unique negative characteristic in certain nanostructures, known as the negative Poisson's ratio effect, that is, the material expands laterally when stretched. This phenomenon is particularly common at the nanoscale, demonstrating the complexity and diversity of the mechanical properties of nanomaterials.

[0004] Young's modulus and Poisson's ratio tests at the nanoscale not only help to deeply understand the basic physical mechanisms of materials, but also provide a scientific basis for the design and application of new materials. For example, by measuring the mechanical properties of nanomaterials, it can provide guidance for the design of high-strength and lightweight structures. In addition, materials with special Poisson's ratios, such as negative Poisson's ratio materials, have broad application prospects in energy absorption, protection, and medical devices. Due to their unique deformation characteristics, these materials can show higher impact resistance and energy absorption capacity under high strain conditions.

[0005] In order to accurately characterize the Young's modulus and Poisson's ratio of nanomaterials, current detection methods such as nanoindentation technology and atomic force microscopy (AFM) can provide high-precision mechanical property testing on an extremely small scale. Among them, nanoindentation technology is currently the most common and mainstream detection method, which can achieve high-precision detection of Young's modulus and hardness. However, on the one hand, this method is destructive to the material and requires a certain amount of intrusion to achieve detection. On the other hand, nanoindentation also requires other equipment to assist in the measurement of Poisson's ratio. Based on the AFM measurement method, high-precision non-destructive detection of modulus information can be achieved by detecting the resonant frequency, testing the micro-area force curve, or dual-frequency drive detection; the shear modulus of the sample can also be tested through torsional vibration excitation, and the Poisson's ratio can be derived in combination with the Young's modulus test results. However, these methods cannot test Young's modulus and Poisson's ratio at the same time, and replacing different mode detections also has different requirements for probes. Summary of the invention

[0006] The purpose of this technical solution is to provide a Young's modulus and Poisson's ratio detection method based on atomic force microscopy, which can realize the simultaneous detection of Young's modulus and Poisson's ratio of materials.

[0007] The purpose of this technical solution is achieved in this way:

[0008] A method for detecting Young's modulus and Poisson's ratio of a material based on an atomic force microscope specifically comprises the following steps: Step S1, preparing equipment: including a microscope, a probe, a lock-in amplifier, a tilt table, a sample to be tested, a sapphire sheet and a PC host computer; the microscope is an atomic force microscope, and the probe is an atomic force microscope probe; Step S2, probe parameter calibration: install the probe on the atomic force microscope, and use a sapphire sheet to calibrate the probe sensitivity, and then calibrate the probe stiffness by the thermal noise method; Step S3, building a resonance frequency measurement device: connecting the response signal of the four-quadrant photodetector of the atomic force microscope to the signal input port of the phase-locked amplifier, the response signal being the difference between the upper plate voltage and the lower plate voltage of the four-quadrant photodetector, and the response signal being used to reflect the longitudinal deflection of the probe; connecting the excitation signal output port of the phase-locked amplifier to the piezoelectric ceramic drive interface of the atomic force microscope probe, and the excitation signal being used to drive the probe to generate mechanical vibration; Step S4, fixing the sample: fixing the sample to be tested on the tilt table, and the sample to be tested is located in the detection area of ​​the atomic force microscope; Step S5, resonance frequency detection: select a tilt stage at any angle, record the set point of the atomic force microscope, the set point is the working deflection of the probe cantilever, and the working deflection is used to multiply the probe sensitivity in step S2 to calculate the contact force; insert the needle and contact the sample, use a phase-locked amplifier to drive the probe with a voltage of 10-50mV in the range of 10nm, and then scan the probe resonant frequency through the phase-locked amplifier After selecting the second-order resonance peak and locking the phase, the scanning range is expanded to 1um to collect the morphological results of the surface of the sample to be tested; the morphological results and the resonance frequency are compared. The signal is transmitted to the PC host computer; repeat this step, adjust different angles and use the same resonance peak for measurement; Step S6, data processing: The PC host computer calculates the tilt angle of the probe based on the topography results , and plot the resonant frequency With tilt angle The corresponding relationship is then obtained by using the probe-sample contact model to solve the indentation modulus and Poisson's ratio; the Young's modulus can be converted from the indentation modulus and Poisson's ratio.

[0009] In step S6, the probe-sample contact model equates the normal and tangential contact between the probe tip and the sample to and Two springs, the probe is installed at a fixed tilt angle due to the design of the atomic force microscope , the probe cantilever a is equivalent to the length The cantilever beam and the length of the probe tip are considered to be ; The theoretical modeling formula of its tilted cantilever is expressed as: ; in: ; ; ; In formula (1) refers to the wave number, which is determined by the resonant frequency It turns out that: ; In formula (2): , where is the Young's modulus of the cantilever, is the moment of inertia of the cantilever section, , is the cantilever width, is the cantilever thickness, is the cantilever cross-sectional area. is the cantilever n-order circular frequency, and the conversion relationship with the resonance frequency is as follows: ; In formula (1) is the cantilever stiffness, which is obtained by the thermal noise method in step S2 . is the contact stiffness between the probe and the sample, calculated as follows: ; In formula (4) is the probe contact radius, which can be obtained from electron microscope photos. is the reduced modulus of the probe and sample, calculated as follows: ; in: and are the indentation modulus of the sample and the probe respectively. The indentation modulus is a parameter used to characterize the elastic properties of a material through indentation testing. It reflects the stiffness or deformation resistance of the material when subjected to local force. ; In the formula , are Young’s modulus and Poisson’s ratio of the corresponding materials, respectively; The contact force in formula (4) can be calculated as follows: ; a is the sensitivity constant of the cantilever optical lever obtained by calibrating the probe sensitivity using a sapphire sheet in step S2; The displacement stiffness and angular stiffness of the cantilever caused by torque are expressed as follows: ; In formula (1) is the cantilever lateral stiffness and normal stiffness The ratio, ; Here According to formula (4), Related to the shear modulus of the sample, reduced shear modulus The calculation is as follows: ; in and Refers to the shear modulus of the sample and probe respectively, according to the Young's modulus of the material and Poisson's ratio The relationship calculation is: ; In step S6, the method for solving the Young's modulus and Poisson's ratio through the relationship between the angle and the resonant frequency is as follows: According to formulas (2) and (3), the measured contact resonance frequency Converted into wave numbers, formula (1) can be rewritten as follows: ; Formula (8) is used to calculate the displacement stiffness and angular stiffness of the cantilever caused by the torque, and it is substituted into formula (7) to solve the contact force corresponding to different angles under the set cantilever deflection voltage; In formula (6) and Set as a variable, combined with the result obtained by formula (7), the contact stiffness between the probe and the sample can be obtained by combining formula (4). Then, this formula is combined with (12) and fitted by the constrained linear least squares fitting algorithm to solve The minimum condition that can meet the actual test results and , the Poisson's ratio and Young's modulus of the material can be characterized.

[0010] Compared with the prior art, the technical solution has the following outstanding and beneficial technical effects:

[0011] The present invention utilizes the established model to simultaneously test the Young's modulus and Poisson's ratio of the material, has low requirements on the probe and has a wide range of applications. The method of the present invention can simultaneously detect the Young's modulus and Poisson's ratio, and has great development potential under the current demand for micro-nanoscale characterization of new materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 It is a schematic diagram of the Young's modulus and Poisson's ratio detection method of the present invention.

[0013] Figure 2 is a schematic diagram of the probe-sample contact model.

[0014] Figure 3 It is the contact resonance frequency and probe-sample angle distribution relationship of silicon (Si), gallium arsenide (GaAs), and highly oriented pyrolytic graphite (HOPG), and the Poisson's ratio and modulus test results. DETAILED DESCRIPTION

[0015] The following is combined with Figure 1-3 The specific implementation methods of this technical solution are further described in detail.

[0016] A method for detecting Young's modulus and Poisson's ratio of a material based on an atomic force microscope specifically comprises the following steps: Step S1, prepare equipment: including a microscope, a probe, a lock-in amplifier, a tilt stage, a sample to be tested, a sapphire sheet and a PC host computer; the microscope is an atomic force microscope equipped with a Tapping mode probe holder; the probe is an atomic force microscope probe; Step S2, probe parameter calibration: install the probe to the atomic force microscope, and use a sapphire sheet to calibrate the probe sensitivity, and then calibrate the probe stiffness by the thermal noise method; complete the probe sensitivity and probe stiffness calibration; if there is no sapphire sheet, high modulus materials such as silicon wafers can also be selected; Step S3, building a resonance frequency measurement device: connecting the response signal (Vertical signal) of the four-quadrant photodetector of the atomic force microscope to the signal input port of the phase-locked amplifier, the response signal is the difference between the upper plate voltage and the lower plate voltage of the four-quadrant photodetector, and the response signal is used to reflect the longitudinal deflection of the probe; connecting the excitation signal output port of the phase-locked amplifier to the piezoelectric ceramic drive interface of the atomic force microscope probe, and the excitation signal is used to drive the probe to generate mechanical vibration; outputting and collecting the frequency signal of the phase-locked amplifier for subsequent processing; Step S4, fixing the sample: the sample to be tested is adhered to the circular fixed iron sheet using structural adhesive, and after the sample is firmly bonded, the circular fixed iron sheet is fixed to the tilt table by bolts and a pressing plate, and the sample to be tested is located in the detection area of ​​the atomic force microscope; Step S5, resonance frequency detection: select a tilt stage at any angle, record the set point of the atomic force microscope, the set point is the working deflection of the probe cantilever, and the working deflection is used to multiply the probe sensitivity in step S2 to calculate the contact force; insert the needle and contact the sample, use a phase-locked amplifier to drive the probe with a voltage of 10-50mV in the range of 10nm, and then scan the probe resonant frequency through the phase-locked amplifier After selecting the second-order resonance peak and locking the phase, the scanning range is expanded to 1um to collect the morphological results of the surface of the sample to be tested; the morphological results and the resonance frequency are compared. The signal is transmitted to the PC host computer; repeat this step, adjust different angles and use the same resonance peak for measurement; the PC host computer can also be used to identify the frequency signal of the phase-locked amplifier and lock the resonance frequency In this step, you can first select an inclination table of any angle, and then perform tests based on the angle ±20 degrees. Step S6, data processing: import the test data into the MATLAB software in the PC host computer. The Chinese name of the software is Matrix Laboratory, which is a commercial mathematical software produced by MathWorks, USA; the tilt angle corresponding to the morphology result is calculated by the software; the MATLAB software calculates the tilt angle of the probe based on the morphology result , and plot the resonant frequency With tilt angle The corresponding relationship is then obtained by using the probe-sample contact model to solve the indentation modulus and Poisson's ratio; the Young's modulus can be converted from the indentation modulus and Poisson's ratio.

[0017] In step S6, the probe-sample contact model equates the normal and tangential contact between the probe tip and the sample to and Two springs, the probe is installed at a fixed tilt angle due to the design of the atomic force microscope , the probe cantilever ax is equivalent to the length The cantilever beam and the length of the probe tip are considered to be ; The theoretical modeling formula of its tilted cantilever is expressed as:

[0018] .

[0019] in:

[0020] .

[0021] .

[0022] .

[0023] In formula (1) refers to the wave number, which is determined by the resonant frequency It turns out that:

[0024] .

[0025] In formula (2): , where is the Young's modulus of the cantilever, is the moment of inertia of the cantilever section, , is the cantilever width, is the cantilever thickness, is the cantilever cross-sectional area. is the cantilever n-order circular frequency, and the conversion relationship with the resonance frequency is as follows:

[0026] .

[0027] In formula (1) is the cantilever stiffness, which is obtained by the thermal noise method in step S2 , is the contact stiffness between the probe and the sample, calculated as follows:

[0028] .

[0029] In formula (4) is the probe contact radius, which can be obtained from electron microscope photos. is the reduced modulus of the probe and sample, calculated as follows:

[0030] .

[0031] in: and are the indentation modulus of the sample and the probe respectively. The indentation modulus is a parameter used to characterize the elastic properties of a material through indentation testing. It reflects the stiffness or deformation resistance of the material when subjected to local force.

[0032] .

[0033] In the formula , are Young’s modulus and Poisson’s ratio of the corresponding materials, respectively;

[0034] The contact force in formula (4) can be calculated as follows:

[0035] .

[0036] a is the sensitivity constant of the cantilever optical lever obtained by calibrating the probe sensitivity using a sapphire sheet in step S2;

[0037] The displacement stiffness and angular stiffness of the cantilever caused by torque are expressed as follows:

[0038] .

[0039] In formula (1) is the cantilever lateral stiffness and normal stiffness The ratio,

[0040] .

[0041] Here According to formula (4), Related to the shear modulus of the sample, reduced shear modulus The calculation is as follows:

[0042] .

[0043] in and Refers to the shear modulus of the sample and probe respectively, according to the Young's modulus of the material and Poisson's ratio The relationship calculation is:

[0044] .

[0045] In step S6, the method for solving the Young's modulus and Poisson's ratio through the relationship between the angle and the resonant frequency is as follows:

[0046] According to formulas (2) and (3), the measured contact resonance frequency Converted into wave numbers, formula (1) can be rewritten as follows:

[0047] .

[0048] Formula (8) is used to calculate the displacement stiffness and angular stiffness of the cantilever caused by the torque, and it is substituted into formula (7) to solve the contact force corresponding to different angles under the set cantilever deflection voltage;

[0049] In formula (6) and Set as a variable, combined with the result obtained by formula (7), the contact stiffness between the probe and the sample can be obtained by combining formula (4). Then, this formula is combined with (12) and fitted by the constrained linear least squares fitting algorithm to solve The minimum condition that can meet the actual test results and , the Poisson's ratio and Young's modulus of the material can be characterized.

[0050] The above shows and describes the basic principle and main features of the technical solution and the advantages of the technical solution. The technicians in this industry should understand that the technical solution is not limited by the above embodiments. The above embodiments and the description are only to illustrate the principle of the technical solution. Without departing from the spirit and scope of the technical solution, the technical solution will have various changes and improvements, which fall within the scope of the technical solution to be protected. The scope of protection claimed by the technical solution is defined by the attached claims and their equivalents.

Claims

1. A method for detecting Young's modulus and Poisson's ratio of a material based on an atomic force microscope, characterized in that: The specific steps include: Step S1, preparing equipment: including a microscope, a probe, a lock-in amplifier, a tilt table, a sample to be tested, a sapphire sheet and a PC host computer; the microscope is an atomic force microscope, and the probe is an atomic force microscope probe; Step S2, probe parameter calibration: install the probe on the atomic force microscope, and use a sapphire sheet to calibrate the probe sensitivity, and then calibrate the probe stiffness by the thermal noise method; Step S3, building a resonance frequency measurement device: connecting the response signal of the four-quadrant photodetector of the atomic force microscope to the signal input port of the phase-locked amplifier, the response signal being the difference between the upper plate voltage and the lower plate voltage of the four-quadrant photodetector, and the response signal being used to reflect the longitudinal deflection of the probe; connecting the excitation signal output port of the phase-locked amplifier to the piezoelectric ceramic drive interface of the atomic force microscope probe, and the excitation signal being used to drive the probe to generate mechanical vibration; Step S4, fixing the sample: placing the sample to be tested on a tilt table, wherein the sample to be tested is located in the detection area of ​​the atomic force microscope; Step S5, resonance frequency detection: select a tilt stage at any angle, record the set point of the atomic force microscope, the set point is the working deflection of the probe cantilever, and the working deflection is used to multiply the probe sensitivity in step S2 to calculate the contact force; insert the needle and contact the sample, use a phase-locked amplifier to drive the probe with a voltage of 10-50mV in the range of 10nm, and then scan the probe resonant frequency through the phase-locked amplifier After selecting the second-order resonance peak and locking the phase, the scanning range is expanded to 1um to collect the morphological results of the surface of the sample to be tested; the morphological results and the resonance frequency are compared. The signal is transmitted to the PC host computer; repeat this step, adjust different angles and use the same resonance peak for measurement; Step S6, data processing: The PC host computer calculates the tilt angle of the probe based on the topography results , and plot the resonant frequency With tilt angle The corresponding relationship is then obtained by using the probe-sample contact model to solve the indentation modulus and Poisson's ratio; the Young's modulus can be converted from the indentation modulus and Poisson's ratio.

2. The method for detecting Young's modulus and Poisson's ratio of a material based on an atomic force microscope according to claim 1 is characterized in that: In step S6, the probe-sample contact model equates the normal and tangential contact between the probe tip and the sample to and Two springs, the probe is installed at a fixed tilt angle due to the design of the atomic force microscope , the probe cantilever a is equivalent to the length The cantilever beam and the length of the probe tip are considered to be ; The theoretical modeling formula of its tilted cantilever is expressed as: ； in: ； ； ； In formula (1) refers to the wave number, which is determined by the resonant frequency It turns out that: ； In formula (2): , where is the Young's modulus of the cantilever, is the moment of inertia of the cantilever section, , is the cantilever width, is the cantilever thickness, is the cantilever cross-sectional area, is the cantilever n-order circular frequency, and the conversion relationship with the resonance frequency is as follows: ； In formula (1) is the cantilever stiffness, which is obtained by the thermal noise method in step S2 , is the contact stiffness between the probe and the sample, calculated as follows: ； In formula (4) is the probe contact radius, which can be obtained from electron microscope photos. is the reduced modulus of the probe and sample, calculated as follows: ； in: and are the indentation modulus of the sample and the probe respectively. The indentation modulus is a parameter used to characterize the elastic properties of a material through indentation testing. It reflects the stiffness or deformation resistance of the material when subjected to local force. ； In the formula , are Young’s modulus and Poisson’s ratio of the corresponding materials, respectively; The contact force in formula (4) can be calculated as follows: ； a is the sensitivity constant of the cantilever optical lever obtained by calibrating the probe sensitivity using a sapphire sheet in step S2; The displacement stiffness and angular stiffness of the cantilever caused by torque are expressed as follows: ； In formula (1) is the cantilever lateral stiffness and normal stiffness The ratio, ； Here According to formula (4), Related to the shear modulus of the sample, reduced shear modulus The calculation is as follows: ； in and Refers to the shear modulus of the sample and probe respectively, according to the Young's modulus of the material and Poisson's ratio The relationship calculation is: 。 3. The method for detecting Young's modulus and Poisson's ratio of a material based on an atomic force microscope according to claim 1 is characterized in that: In step S6, the method for solving the Young's modulus and Poisson's ratio through the relationship between the angle and the resonant frequency is as follows: According to formulas (2) and (3), the measured contact resonance frequency Converted into wave numbers, formula (1) can be rewritten as follows: ； Formula (8) is used to calculate the displacement stiffness and angular stiffness of the cantilever caused by the torque, and it is substituted into formula (7) to solve the contact force corresponding to different angles under the set cantilever deflection voltage; In formula (6) and Set as a variable, combined with the result obtained by formula (7), the contact stiffness between the probe and the sample can be obtained by combining formula (4). Then, this formula is combined with (12) and fitted by the constrained linear least squares fitting algorithm to solve The minimum condition that can meet the actual test results and , the Poisson's ratio and Young's modulus of the material can be characterized.

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