Method for measuring elastic constants of cubic crystal materials based on brillouin scattering spectrum

Abstract

A method for measuring elastic constants of cubic crystal materials based on Brillouin scattering spectrum, comprising: S1. obtaining a spatial rotation angle of a cubic crystal material sample according to an angle of rotation of the cubic crystal material sample around a surface normal; S2. obtaining a Brillouin scattering spectrum of the cubic crystal material sample according to the spatial rotation angle, containing two Brillouin scattering characteristic peaks; S3. obtaining a frequency shift of the scattering peak by Lorentz fitting based on the Brillouin scattering spectrum characteristic peak; S4. calculating an experimental value of an acoustic characteristic curve of the cubic crystal material sample; and S5. fitting a theoretical value and the experimental value of the acoustic characteristic curve of the cubic crystal material to obtain a complete elastic constant tensor of the cubic crystal material. The method can improve the detection efficiency and realize nondestructive detection of the complete elastic constant tensor of the cubic crystal material.

Description

Technical Field

[0001] This invention relates to the field of Brillouin scattering nondestructive testing technology, and in particular to a method for measuring the elastic constants of cubic crystal materials based on Brillouin scattering spectroscopy. Background Technology

[0002] For single-crystal materials, elastic constants are crucial parameters. For example, measuring properties such as Young's modulus, shear modulus, bulk modulus, and Poisson's ratio can determine the material's mechanical properties and infer its structural information. Currently, common methods for measuring the elastic constants of crystalline materials, both domestically and internationally, primarily rely on traditional mechanical tests such as tension, compression, bending, torsion, and shear. However, these methods inevitably involve destructive experiments and are difficult to obtain a complete elastic constant tensor.

[0003] Due to the limitations of mechanical testing methods, non-destructive testing (NDT) techniques have gradually replaced traditional mechanical testing methods in the field of material elastic constant detection. Brillouin scattering spectroscopy is a typical non-contact, non-destructive spectroscopic detection method. Brillouin scattering studies the inelastic light scattering caused by thermoacoustic modes in materials. It utilizes the interaction between the monochromatic, directional, and coherent spatial light emitted by a laser and the acoustic phonons of the medium to produce an inelastic scattering effect. By capturing the scattered signal, a Brillouin scattering spectrum is formed, and then the properties and structural characteristics of the material under test are analyzed using this spectrum. This method has the advantage of being able to detect materials with small dimensions; furthermore, the six-channel Fabry-Perot interferometer used in Brillouin scattering spectroscopy has extremely high resolution (less than 0.5 GHz), which can also meet the requirements of experimental precision.

[0004] Brillouin scattering can be used to calculate the elastic constants of single-crystal materials by detecting their acoustic anisotropy. Among the practical applications of single-crystal materials, cubic crystals are the most widely used. The elastic constant tensor c of cubic crystal materials... ij This can be simplified as follows:

[0005]

[0006] For cubic crystal materials, there are only three independent elastic constants, namely c 11 c 12 and c 44 Conventional Brillouin scattering spectroscopy typically employs a backscattering geometry: incident light is focused onto the sample surface, generating scattered light, which is then collected back along the same optical path as the incident light into the interferometer. However, this method lacks a complete Brillouin scattering spectral signal, making it impossible to obtain all independent elastic constants. Furthermore, the focusing experiment itself is very cumbersome, hindering practical applications.

[0007] Patent document CN111855614A discloses a method for analyzing the refractive index of trigonal materials using in-situ Brillouin scattering spectroscopy. This method improves the scattering configuration by altering the angle between the incident and scattered light; it uses a Fabry-Perot interferometer to detect the trigonal material sample; and it analyzes the spectrum of the detected trigonal material sample to obtain its refractive index. However, although this method improves the scattering geometry, it still cannot use a fixed external scattering angle for experiments with a symmetrical scattering geometry. Multiple adjustments to the incident and scattering angles are still required; that is, for each Brillouin spectrum collected, the scattering geometry must be redefined, the sample focused, and the Fabry-Perot interferometer calibrated, significantly limiting the efficiency of Brillouin scattering spectrum acquisition. Furthermore, this scheme is only suitable for measuring refractive index and cannot meet the requirements for detecting elastic constants. For solid materials, their acoustic properties include both refractive index and elastic constants; therefore, research on the measurement of elastic constants is necessary. Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for measuring the elastic constants of cubic materials based on Brillouin scattering spectroscopy. A symmetrical scattering geometry is designed for the optical path. By fixing the external scattering angle and changing the rotation angle of the sample on the vertical sample stage, the angle value is directly read from the micrometer scale, achieving non-destructive Brillouin scattering spectroscopy detection. This method improves detection efficiency and measures the complete elastic constants of cubic materials.

[0009] The technical solution of the present invention is as follows:

[0010] A method for detecting the elastic constants of cubic materials based on Brillouin scattering spectroscopy includes:

[0011] S1. Obtain the spatial rotation angle of the cubic crystal system material sample based on the angle of rotation of the cubic crystal system material sample around the surface normal;

[0012] S2. Based on the spatial rotation angle, obtain the Brillouin scattering spectrum of the cubic crystal system material sample, which includes two Brillouin scattering characteristic peaks, QTA and QLA;

[0013] S3. The frequency shift Δω of the scattering peak is obtained by Lorentz fitting based on the characteristic peaks of the Brillouin scattering spectrum;

[0014] S4. Calculate the experimental value V of the acoustic characteristic curve of the cubic crystal system material sample, using the following formula:

[0015]

[0016] In the formula, λ0 is the wavelength of the incident light, and θ *It is the scattering angle between the incident light and the scattered light of the cubic crystal system material sample;

[0017] S5. Fit the theoretical and experimental values ​​of the acoustic characteristic curves of cubic crystal system materials to obtain the complete elastic constant tensor of cubic crystal system materials.

[0018] Further, step S1, obtaining the spatial rotation angle of the cubic crystal material sample based on the angle of rotation of the cubic crystal material sample around the surface normal, specifically includes:

[0019] S1.1 Select cubic crystal system material sample: Polish both the front and back surfaces of the sample and cut it into (010) orientation;

[0020] S1.2 Selection of sample stage: Select an optical vertical sample stage, and the working slot of the optical vertical sample stage has a light-transmitting hole for placing the sample;

[0021] S1.3 A microscope camera with monitoring function is selected to monitor the focal bright spot of the incident light inside the sample;

[0022] S1.4 Constructing a symmetrical scattering geometry spatial optical path: Determine the incident angle and scattering angle, fix all optical elements on the test platform and ensure that their relative positions remain unchanged, pass the laser into the light-transmitting hole on one side of the working slot, and after being scattered by the sample, it exits from the other side of the light-transmitting hole;

[0023] S1.5 The spatial rotation angle of the sample is obtained by rotating an optical vertical sample stage around the normal to the sample surface, with the scattering angle equal to the incident angle.

[0024] Further, in step S2, the Brillouin scattering spectrum of the cubic crystal material sample is obtained according to the spatial rotation angle, which includes two Brillouin scattering characteristic peaks, QTA and QLA. Specifically, the Brillouin scattering photon signals at the corresponding frequencies of different spatial rotation angles are collected using a Fabry-Perot interferometer to obtain the Brillouin scattering spectrum.

[0025] Furthermore, in step S5, the theoretical and experimental values ​​of the acoustic characteristic curves of the cubic crystal system material are fitted to obtain the complete elastic constant tensor of the cubic crystal system material, as shown in the following formula:

[0026]

[0027]

[0028] In the formula, V QLA and V QTA These are the two Brillouin scattering characteristic peaks QTA and QLA, respectively, where χ is the spatial rotation angle, and c is the angle of rotation. 11 c 12 and c 44There are three complete elastic constant tensors.

[0029] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0030] 1) By fixing the external scattering angle and changing the rotation angle of the sample on the vertical sample stage, the angle value can be read directly from the micrometer dial, thus achieving non-destructive Brillouin scattering spectroscopy detection.

[0031] 2) By detecting the Brillouin scattering spectrum of the cubic crystal system material, the acoustic characteristic curve is obtained, and the experimental values ​​are fitted and iterated with the theoretical function to obtain the complete elastic constant tensor of the material.

[0032] 3) The method of the present invention is simple to operate, accurate in measurement, easy to set up, requires no destructive testing, requires no repeated testing, and has high detection efficiency. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of the spatial orientation of the sample under a symmetrical scattering geometry configuration according to an embodiment of the present invention.

[0034] Figure 2 This is a Brillouin scattering spectrum according to an embodiment of the present invention.

[0035] Figure 3 This is a sound speed distribution characteristic curve diagram of an embodiment of the present invention.

[0036] Figure 4 This is a schematic diagram of the symmetrical scattering spatial optical path according to an embodiment of the present invention. Detailed Implementation

[0037] The present invention will be further described below with reference to the accompanying drawings and embodiments, but this should not be construed as limiting the scope of protection of the present invention.

[0038] A method for detecting the elastic constants of cubic materials based on Brillouin scattering spectroscopy includes:

[0039] (1) Select an optical vertical sample stage and place the cubic crystal material on the sample stage.

[0040] (2) Select a microscope camera with a monitor to monitor the focal bright spot of the incident light inside the sample.

[0041] (3) Construct a symmetrical scattering geometry configuration for the spatial optical path: Fix all optical elements on the test platform to determine the incident angle and scattering angle, and ensure that the relative positions remain unchanged.

[0042] See Figure 4 , Figure 4This is a schematic diagram of the symmetrical scattering spatial optical path according to an embodiment of the present invention. As shown in the figure, a first polarizer, a set of mirrors, a first lens, an optical vertical sample stage, a set of lenses, a second polarizer, and an interferometer are placed sequentially along the laser output optical path on the test platform. The two surfaces of the sample are polished and cut into (010) orientation, and placed into the light-transmitting hole of the working slot of the optical vertical sample stage. The laser is passed into the light-transmitting hole on one side of the working slot, and after being scattered by the sample, it exits from the other side of the light-transmitting hole.

[0043] (4) Change the rotation angle of the sample placement on the vertical sample stage (see...) Figure 1 (Rotate the sample around the Y-axis) and read the angle value.

[0044] (5) Use a Fabry-Perot interferometer to collect Brillouin scattered photon signals at frequencies corresponding to different rotation angles to obtain Brillouin scattering spectra.

[0045] (6) Determine the experimental values ​​of the acoustic characteristic curve of the cubic crystal material based on the frequency change of the Brillouin scattering spectrum in step (5).

[0046] (7) Based on the experimental values ​​of the acoustic characteristic curves from step (6), and combined with the theoretical function of the acoustic characteristic curves of cubic crystal materials, the experimental values ​​are fitted using the least squares method to obtain the complete elastic constant tensor of the cubic crystal material.

[0047] In a preferred embodiment of the present invention, the operation of placing a cubic crystal material on the sample stage includes:

[0048] The cubic crystal material is placed in the working slot inside the optical vertical sample stage, the working slot containing a light-transmitting hole with a diameter of 5 mm.

[0049] Adjust the sample position to completely cover the light-transmitting hole, fix it with adhesive, and then tighten the threaded cap on the outside of the working groove.

[0050] In a preferred embodiment of the present invention, the operation of collecting Brillouin scattered photon signals at different frequencies using a Fabry-Perot interferometer includes:

[0051] The mirror spacing is preset to 4mm and the scanning amplitude to 600nm. The mirror spacing is adjusted according to the scattering signal to obtain the optimal collection range in the free spectral region.

[0052] In a preferred embodiment of the invention, the procedure before testing includes:

[0053] A 532nm spatial laser is output on the optical testing platform, and the pitch angle of all optical components is adjusted to make the optical path in the experimental space completely parallel to the optical testing platform.

[0054] In a preferred embodiment of the present invention, the operation of constructing a symmetrical scattering geometry configuration spatial optical path includes:

[0055] A Cartesian coordinate system is established based on the surface normal of the double-sided polished cubic crystal sample (corresponding to the (010) crystal axis direction);

[0056] The laser is passed through a light-transmitting hole on one side of the working slot, and then emitted from the other side of the light-transmitting hole through the sample. The sample is placed using an optical vertical sample stage so that it is completely perpendicular to the test platform and the scattering angle is equal to the incident angle.

[0057] Rotate the sample about the normal to the sample surface.

[0058] In a preferred embodiment of the present invention, the operation of determining the experimental values ​​of the acoustic characteristic curve of the cubic crystal material includes:

[0059] The sound velocity of the sample is obtained by fitting the frequency shift of the characteristic peak of the Brillouin scattering spectrum using Lorentz fitting.

[0060] The spatial rotation angle of the sample is obtained by rotating the sample around the surface normal.

[0061] Example:

[0062] This embodiment provides a method for measuring the elastic constants of cubic crystal materials based on Brillouin scattering spectroscopy, including the following steps:

[0063] The sample selected was a high-purity (99.9%) cubic single crystal MgO with a size of 10mm×10mm×1mm. Both the front and back surfaces of the sample were polished to meet the optical quality requirements and cut into (010) orientation.

[0064] refer to Figure 1 In this embodiment, detection is performed using a symmetrical scattering geometry configuration, and the operation steps include:

[0065] In the XY plane, the sample position is adjusted and fixed using a micrometer. The incident light is incident into the sample at a 60° angle to the normal of the sample surface, and the angle of the scattered light is kept at 60°.

[0066] If the laser polarization state is not vertical (or horizontal), a polarizing plate or polarizing prism can be used to adjust the polarization state to vertical (or horizontal).

[0067] The sample was rotated around the surface normal as an axis, ranging from 0 to 90°. A set of data was measured every 5°, for a total of 19 sets of Brillouin scattering spectra. All Brillouin scattering spectra were plotted on the same graph.

[0068] Experimental test analysis:

[0069] In this example, the Brillouin scattering spectrum of the cubic single-crystal MgO sample obtained through the above steps is shown. Two characteristic Brillouin scattering peaks (QTA and QLA) are obtained, thus enabling a complete measurement of the elastic constants of cubic materials. See also... Figure 2 By applying a symmetric scattering geometry configuration, the speed of sound V and the Brillouin frequency shift Δω have a simple relationship:

[0070]

[0071] Where λ0 is the wavelength of the incident light, θ * It is the scattering angle between the incident and scattered light from outside the sample, Δω is based on Figure 2 The characteristic peaks of the Brillouin scattering spectrum shown are frequency shift values ​​obtained through Lorentz fitting. The experimental value V of the acoustic characteristic curve of the material can be calculated using equation (2).

[0072] like Figure 3 The figure shows the acoustic characteristic curves calculated by equation (2) according to the method of the present invention. For the cubic crystal system (010) crystal plane, the two sound velocity anisotropy curves (QTA and QLA) in the figure satisfy the following equations respectively:

[0073]

[0074]

[0075] In the formula, the sound speed V obtained by solving is a function of the spatial rotation angle χ;

[0076] refer to Figure 3 After obtaining the experimental values ​​of the acoustic characteristic curves, an iterative fitting operation can be performed between the theoretical and experimental values ​​of the acoustic characteristic curves. According to equations (3) and (4), by iteratively fitting the sound velocity V and spatial rotation angle χ corresponding to 19 sets of Brillouin scattering spectra using the least squares method, all three complete independent elastic constants c can be obtained. 11 c 12 and c 44 The test results of the samples are shown in the table below:

[0077]

[0078] The embodiments of the present invention have now been described in detail. To avoid obscuring the concept of this disclosure, some details known in the art have not been described. Those skilled in the art can fully understand how to implement the technical solutions of the present invention based on the above description.

[0079] The embodiments of the present invention have been described above in conjunction with the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made according to the purpose of the invention. Any changes, modifications, substitutions, combinations or simplifications made based on the spirit and principle of the technical solution of the present invention shall be equivalent substitutions. As long as they meet the purpose of the invention and do not deviate from the technical principle and inventive concept of the present invention, they shall fall within the protection scope of the present invention.

Claims

1. A method for detecting the elastic constants of cubic materials based on Brillouin scattering spectroscopy, comprising: S1. Obtain the spatial rotation angle of the cubic crystal system material sample based on the angle of rotation of the cubic crystal system material sample around the surface normal; S2. Based on the spatial rotation angle, obtain the Brillouin scattering spectrum of the cubic crystal system material sample, which includes two Brillouin scattering characteristic peaks, QTA and QLA; S3. The frequency shift ∆ω of the scattering peak is obtained by Lorentz fitting based on the characteristic peaks of the Brillouin scattering spectrum; S4. Calculate the experimental value V of the sound velocity of the acoustic characteristic curve of the cubic crystal system material sample, using the following formula: In the formula, λ0 is the wavelength of the incident light, and θ * It is the scattering angle between the incident light and the scattered light of the cubic crystal system material sample; S5. Fit the theoretical and experimental values ​​of the acoustic characteristic curves of cubic crystal system materials to obtain the complete elastic constant tensor of cubic crystal system materials; Step S5 involves fitting the theoretical and experimental values ​​of the acoustic characteristic curves of the cubic material to obtain the complete elastic constant tensor of the cubic material, as shown in the following formula: In the formula, and The sound velocities of the two Brillouin scattering characteristic peaks, QTA and QLA, are respectively. Let c be the angle of spatial rotation. 11 c 12 and c 44 There are three complete elastic constant tensors.

2. The method for detecting the elastic constant of cubic materials based on Brillouin scattering spectroscopy according to claim 1, wherein step S1, obtaining the spatial rotation angle of the cubic material sample based on the angle of rotation of the cubic material sample around the surface normal, specifically includes: S1.1 Select a cubic crystal system material sample: Polish both the front and back surfaces of the sample and cut it into (010) orientation; S1.2 Selection of sample stage: Select an optical vertical sample stage, and the working slot of the optical vertical sample stage has a light-transmitting hole for placing the sample; S1.3 A microscope camera with monitoring function is selected to monitor the focal bright spot of incident light inside the sample; S1.4 Constructing a symmetrical scattering geometry spatial optical path: Determine the incident angle and scattering angle, fix all optical components on the test platform, ensuring their relative positions remain unchanged, and pass the laser beam through a light-transmitting aperture on one side of the working slot. After being scattered by the sample, the laser beam exits from the other side of the light-transmitting aperture. S1.5 The spatial rotation angle of the sample is obtained by rotating an optical vertical sample stage around the normal to the sample surface, with the scattering angle equal to the incident angle.

3. The method for detecting the elastic constant of cubic crystal materials based on Brillouin scattering spectroscopy according to claim 1, wherein step S2. obtaining the Brillouin scattering spectrum of the cubic crystal material sample according to the spatial rotation angle, including two Brillouin scattering characteristic peaks QTA and QLA, specifically by using a Fabry-Perot interferometer to collect Brillouin scattering photon signals at frequencies corresponding to different spatial rotation angles to obtain the Brillouin scattering spectrum.

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