Plasma temperature calculation method for CF-LIPS quantitative analysis

Abstract

The invention discloses a plasma temperature calculation method for CF-LIPS quantitative analysis, and relates to the technical field of elemental component detection.The method comprises the steps that S1, it is assumed that m data points of n elements participate in calculation, and a linear model of the elements is established according to spectral lines of the n elements and related spectral line parameters; s2, constructing a model matrix according to the m data points; s3, constructing a target loss function by adopting a least square method; s4, calculating an optimal model parameter of the target loss function constructed in the step S3; and S5, the relative content of the elements is calculated according to a Saha-Boltzmann graph method. The method provided by the invention is based on the consistency of the plasma temperature of each element under the local thermodynamic equilibrium condition in the CF-LIPS method, can solve the problems of difficulty in plasma temperature valuing and large temperature difference among different components caused by spectral line scarcity of trace components, and can effectively improve the component quantification precision of CF-LIPS.

Description

Technical Field

[0001] The invention belongs to the technical field of element composition detection, and in particular relates to a plasma temperature calculation method for CF-LIPS quantitative analysis. Background Art

[0002] Laser-induced plasma spectroscopy (LIPS, also known as laser-induced breakdown spectroscopy, LIBS) is an atomic emission spectroscopy technique that has the advantages of in-situ, rapid, non-contact, and multi-element synchronous detection. It has great development potential in the in-situ real-time online analysis of elemental composition. Traditional LIPS quantitative methods are often limited by matrix effects and rely on standard samples matching the matrix to construct calibration curves, which to a certain extent limits its scope of application. The calibration-free laser-induced plasma spectroscopy (CF-LIPS) method does not need to establish a calibration curve based on standard samples, which can effectively avoid the influence of matrix effects and has good object applicability. It is especially suitable for the detection of materials that are difficult to obtain standard samples. It has been gradually applied to metallurgy, geology, archaeology, biomedicine, materials science, and environmental monitoring.

[0003] The principle of the CF-LIPS method is to use a simplified mathematical model of the laser-induced plasma emission spectrum, and use atomic parameters such as the spontaneous emission coefficient, energy level, degeneracy, and partition function of the characteristic spectral line to directly calculate the plasma parameters and elemental composition, and finally obtain the element percentage content through normalization. The classic CF-LIPS calculation methods include the Boltzmann diagram method and the Saha-Boltzmann diagram method. Both methods require first performing a linear fit based on the data of the spectral line intensity and the corresponding particle energy level, first calculating the plasma temperature using the slope corresponding to the fitted straight line, and then using the intercept of the fitted straight line to calculate the relative content of each element. The accurate calculation of the plasma temperature is crucial for the quantitative analysis of the element content. Therefore, the quantitative accuracy of the CF-LIPS method is closely related to the accurate fitting of the straight line of the element in the Boltzmann diagram or the Saha-Boltzmann diagram.

[0004] In order to ensure that the straight line has a good fitting effect, the coordinate points used for straight line fitting need to have high reliability and sufficient number. However, in practical applications, especially for trace elements, the number of spectral lines is often insufficient, resulting in an increase in the error in the calculation of plasma temperature, which in turn affects the accuracy of CF-LIPS. The CF-LIPS method with standard reference line (SRL) uses the plasma temperature calculated by the matrix element as the plasma temperature of other elements, avoiding the influence of insufficient number of element spectral lines that lead to insufficient calculation of plasma temperature or large error in calculation results. However, this method comes at the cost of losing some spectral line information, resulting in poor accuracy of the calculation results of some elements. Summary of the invention

[0005] In view of the defects existing in the prior art, the purpose of the present invention is to provide a plasma temperature calculation method for CF-LIPS quantitative analysis. This method can solve the problems of difficulty in determining the plasma temperature due to the scarcity of spectral lines of trace components and the large temperature difference between different components, and can effectively improve the component quantification accuracy of CF-LIPS.

[0006] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0007] A plasma temperature calculation method for CF-LIPS quantitative analysis comprises the following steps:

[0008] S1. Assuming that there are n elements and m data points involved in the calculation, a linear model of the elements is established based on the spectral lines of the n elements and related spectral line parameters; the estimated model of all element points is expressed as:

[0009] h i =ax i,0 +b 1 x i,1 +b 2 x i,2 +···+b n x i,n (1)

[0010] In formula (1), h i is the model estimate, a is the slope, i represents the data point in the Saha-Boltzmann plane, x i,0 is the horizontal coordinate of the data point, {i∈Z|0<i≤m}; for different types of elements j, b j is the intercept, x i,k＝j =1,x i,k≠j =0, {k,j∈Z|0<k,j≤n};

[0011] S2. Construct a model matrix based on m data points, expressed as:

[0012] H=XB (2)

[0013] In formula (2), H = [h 1 h 2 h 3 ···h m ] T is an m×1-dimensional vector of model estimates; is the horizontal coordinate x of the data in the Saha-Boltzmann plane * and element types composed of m×(n+1) dimensional vectors; B=[ab 1 b 2 ···b n ] T is the slope a and intercept b 1 ~b n The (n+1)×1 dimensional vector;

[0014] S3. Use the least squares method to construct the target loss function:

[0015] L(a,b i )=||HY|| 2 (3)

[0016] In formula (3), L(a,b i ) indicates that the variables are a, b i The target loss function, Y = [y 1 y 2 y 3 ···y m ] T is the ordinate y of the data in the Saha-Boltzmann plot * The m×1 dimensional vector composed of

[0017] S4, calculating the optimal model parameters of the target loss function constructed in step S3, obtaining the intercept and slope of the best fitting straight line, and then calculating the plasma temperature according to the slope;

[0018] S5. Calculate the relative content of the element according to the intercept of the best fitting straight line obtained in step S4 and the plasma temperature using the Saha-Boltzmann diagram method.

[0019] Further, in the plasma temperature calculation method for CF-LIPS quantitative analysis as described above, step S4 is specifically as follows:

[0020] For L(a,b i ) to find the partial derivative. When each partial derivative function is equal to 0, the corresponding variable value is the best fitting parameter. At this time, L(a,b i) is the smallest, and the model corresponding to the variable value is the best fitting model. The value of the variable parameter matrix B obtained by matrix transformation and calculation is shown as follows:

[0021] B=(X T X) -1 X T Y (4)

[0022] In formula (4), B = [ab 1 b 2 ···b n ] T The parameters included are the intercept and slope of the best fitting straight line for each element, which are calculated uniformly through a matrix containing the spectral line information of each element; the plasma temperature is calculated from the slope

[0023] Further, in the plasma temperature calculation method for CF-LIPS quantitative analysis as described above, the relative content calculation formula of the element in step S5 is:

[0024]

[0025] In formula (5) and formula (6), j represents an element atom or a monovalent ion, and U j (T) is the distribution function of element particle s at plasma temperature T, F is an experimental parameter, which is calculated by formula (5), and the relative atomic fraction of element atoms or monovalent ions is obtained by formula (6), and the relative mass content is obtained by relative atomic mass conversion.

[0026] A CF-LIPS spectrum analysis processing program, the program is based on the plasma temperature calculation method for CF-LIPS quantitative analysis as described above, and comprises the following steps:

[0027] 1) Spectral data preprocessing;

[0028] 2) Spectral line identification and selection;

[0029] 3) Calculation of plasma electron density;

[0030] 4) Calculation of plasma temperature and sample element content.

[0031] Furthermore, in the CF-LIPS spectral analysis processing program described above, the spectral data preprocessing is specifically as follows: after correcting the relative spectral conversion efficiency at each wavelength of the input original spectrum, the continuous background formed by bremsstrahlung and recombination radiation is deducted, and then the inhomogeneity of the plasma light collected by each channel is corrected and spliced.

[0032] Furthermore, in the CF-LIPS spectral analysis processing program as described above, the spectral line identification and selection specifically include: spectral line peak finding, i.e. finding the wavelength position of the spectral line, spectral line matching, i.e. confirming the information corresponding to the spectral line by comparing with the spectral line information database, and selecting the spectrum for CF-LIPS calculation, i.e. selecting the spectral line without interference as reliable data for subsequent calculations.

[0033] Furthermore, in the CF-LIPS spectrum analysis processing program described above, the plasma electron density calculation is specifically: by performing Lorentz fitting on the H-α spectral line profile, Stark broadening is obtained and the plasma electron density is calculated.

[0034] Furthermore, in the CF-LIPS spectral analysis processing procedure described above, the plasma temperature and sample element content are calculated specifically as follows: the spectral line intensity and the corresponding atomic spectrum data used for calculation and analysis are selected, and the slope and intercept of the fitting line of each element are calculated by the CF-LIPS method with uniform temperature, and then subsequent calculations are performed to obtain the relative content of the element.

[0035] Furthermore, the CF-LIPS spectrum analysis processing program as described above is written in Python language.

[0036] Compared with the prior art, the plasma temperature calculation method and program for CF-LIPS quantitative analysis provided by the present invention have the following beneficial effects:

[0037] The plasma temperature calculation method provided by the present invention is based on the consistency of the plasma temperature of each element under the local thermodynamic equilibrium (LTE) condition in the CF-LIPS method, and constructs a matrix model by associating the spectral line information of different elements, and determines a unified plasma temperature using the least squares method. This method can solve the problem of difficulty in determining the plasma temperature due to the scarcity of spectral lines of trace components and the large temperature difference between different components, and effectively improve the component quantitative accuracy of CF-LIPS. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 A flow chart of a plasma temperature calculation method for CF-LIPS quantitative analysis provided in an embodiment of the present invention;

[0039] Figure 2 Flowchart of the CF-LIPS analysis program;

[0040] Figure 3 is the Saha-Boltzmann plot of the aluminum alloy sample using the uniform temperature method;

[0041] Figure 4 Plasma temperature of aluminum alloy samples calculated for both methods;

[0042] Figure 5 CF-LIPS analysis results of aluminum alloy samples using the uniform temperature method;

[0043] Figure 6 CF-LIPS analysis results of aluminum alloy samples using matrix element slope to calculate plasma temperature;

[0044] Figure 7 This is a comparison chart between the element analysis results obtained by calculating the plasma temperature using the matrix element slope and the standard value;

[0045] Figure 8 This is a comparison chart between the element analysis results obtained using the unified temperature method and the standard values. DETAILED DESCRIPTION

[0046] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0047] In an embodiment of the present invention, a plasma temperature calculation method for CF-LIPS quantitative analysis is provided. The method assumes that the plasma temperatures of all elements are the same under the local thermodynamic equilibrium conditions in the CF-LIPS method, that is, their slopes in the Saha-Boltzmann diagram are the same; for the straight line fitting of data points with different intercepts and the same slope, the least squares method is used to establish an estimation model.

[0048] Both the Boltzmann graph method and the Saha-Boltzmann graph method are acceptable. The following text will only take the Saha-Boltzmann graph method as an example to explain this method in detail. Figure 1 A flow chart of a plasma temperature calculation method for CF-LIPS quantitative analysis provided in an embodiment of the present invention is shown, and the method comprises the following steps:

[0049] S1. Establishing element linear model

[0050] Assuming that there are n elements involved in the calculation, the estimation model of all element points can be expressed as:

[0051] h i =ax i,0 +b 1 x i,1 +b 2 x i,2 +···+b n x i,n (1)

[0052] In formula (1), h i is the model estimate, a is the slope, i represents the data point in the Saha-Boltzmann plane, xi,0 is the horizontal coordinate of the data point, {i∈Z|0<i≤m}; for different types of elements j, b j is the intercept, x i,k＝j =1,x i,k≠j =0, {k,j∈Z|0<k,j≤n}.

[0053] S2. Build a model matrix based on data points

[0054] Assuming that there are m data points involved in the calculation, all data points can be represented by a matrix as

[0055] H=XB (2)

[0056] In formula (2), H = [h 1 h 2 h 3 ···h m ] T , is an m×1-dimensional vector of model estimates; is the horizontal coordinate x of the data in the Saha-Boltzmann plane * and element types composed of m×(n+1) dimensional vectors; B=[ab 1 b 2 ···b n ] T , is the slope a and intercept b 1 ~b n A (n+1)×1 dimensional vector.

[0057] S3. Construct target loss function

[0058] The least squares method believes that the model that minimizes the sum of squared errors between the predicted value and the measured value is the closest to the actual situation. For data that obeys the normal distribution, the error sum of squared functions of the least squares method that minimizes the least squares method is equivalent to the maximum likelihood function, that is, the least squares method is the maximum likelihood estimate of data whose errors satisfy the normal distribution.

[0059] The sum of squared errors (SSE) between the predicted values ​​and the measured values, i.e. the target loss function, can be expressed as:

[0060] L(a,b i )=||HY|| 2 (3)

[0061] In formula (3), L(a,b i ) indicates that the variables are a, b i The target loss function, Y = [y 1 y 2 y 3 ···y m ] Tis the ordinate y of the data in the Saha-Boltzmann plot * An m×1 dimensional vector.

[0062] S4. Calculate the optimal model parameters of the target loss function constructed in step S3 to obtain the intercept and slope of the best fitting straight line, and then calculate the plasma temperature according to the slope.

[0063] For L(a,b i ) to find the partial derivative. When each partial derivative function is equal to 0, the corresponding variable value is the best fitting parameter. At this time, L(a,b i ) is the smallest, and the model corresponding to the variable value is the best fitting model. Through certain matrix transformation and calculation, the value of the variable parameter matrix B can be obtained as shown in the following formula:

[0064] B=(X T X) -1 X T Y (4)

[0065] In formula (4), B = [ab 1 b 2 ···b n ] T The parameters included are the intercept and slope of the best fitting straight line for each element, which are calculated uniformly through a matrix containing the spectral line information of each element. The plasma temperature can be calculated from the slope

[0066] S5. Calculate the relative content of the element according to the intercept of the best fitting straight line obtained in step S4 and the plasma temperature using the Saha-Boltzmann diagram method.

[0067] According to the Saha-Boltzmann diagram method, the relative content of the elements can be obtained by subsequent calculation using formulas (5) and (6).

[0068]

[0069] In formula (5) and formula (6), j represents an element atom or a monovalent ion, and U j (T) is the distribution function of element particle s at plasma temperature T, F is an experimental parameter, which is calculated by formula (5), and the relative atomic fraction of element atoms or monovalent ions is obtained by formula (6), and the relative mass content is obtained by relative atomic mass conversion.

[0070] Based on the above invention concept, the present invention uses Python language to write a CF-LIPS spectrum analysis processing program using a unified temperature method. The calculation process of the spectrum analysis program is as follows: Figure 2 As shown, the specific steps include:

[0071] 1) Spectral data preprocessing

[0072] The input original spectrum is corrected for the relative spectral conversion efficiency at each wavelength, and the continuous background formed by bremsstrahlung and recombination radiation is subtracted. Then, the inhomogeneity of plasma light collected by each channel is corrected and spliced.

[0073] 2) Spectral line identification and selection

[0074] It includes spectral line peak finding (finding the wavelength position of the spectral line), spectral line matching (confirming the spectral line information such as the element type corresponding to the spectral line by comparing with the spectral line information database), and selection of spectra for CF-LIPS calculation (selecting non-interference spectral lines as reliable data for subsequent calculations).

[0075] 3) Plasma electron density calculation

[0076] By performing Lorentz fitting on the H-α spectral line profile, the Stark broadening is obtained and the plasma electron density is calculated.

[0077] 4) Calculation of plasma temperature and sample element content

[0078] The spectral line intensity and the corresponding atomic spectrum data for calculation and analysis were selected, and the slope and intercept of the fitting line of each element were calculated by the CF-LIPS method with unified temperature. Then subsequent calculations were performed to obtain the relative content of the elements.

[0079] Example

[0080] CF-LIPS analysis of aluminum alloy standard materials was carried out using the unified temperature method described above, and a method using matrix element slope to calculate plasma temperature was used as a control.

[0081] The test samples used in the experiment are high-silicon and high-copper cast aluminum alloy spectral standard materials, numbered GBW02238 to GBW02243. The composition of this standard material is mainly aluminum (Al), and also contains six elements: silicon (Si), magnesium (Mg), manganese (Mn), iron (Fe), copper (Cu) and zinc (Zn). The reference component content of this standard material is shown in Table 1. These elements are arranged in a gradient cross and can be used to evaluate the measurement method.

[0082] Table 1 Element composition and content of high silicon and high copper casting aluminum alloy standard materials

[0083]

[0084] The test results identified the elements in seven aluminum alloy samples: aluminum (Al), silicon (Si), magnesium (Mg), manganese (Mn), iron (Fe), copper (Cu) and zinc (Zn). A total of 21 spectral lines were used for CF-LIPS calculation. The Saha-Boltzmann diagram of the aluminum alloy sample using the uniform temperature method is shown below: Figure 3 As shown, for the four elements Fe, Mn, Zn, Cu and Si whose spectral lines are insufficient, the corresponding intercepts can also be calculated.

[0085] The plasma temperature of aluminum alloy samples calculated by the matrix element slope and the uniform temperature method is shown in Figure 2. Figure 4 As shown in the figure, the plasma temperatures of the samples calculated by the unified temperature method are approximately 11130, 11179, 11432, 11354, 11307 and 11507 K. For all aluminum alloy standard samples, the plasma temperatures calculated by the unified temperature method are lower than the plasma temperatures calculated by the matrix element slope, which are 292, 267, 414, 319, 459 and 143 K lower, respectively.

[0086] The calculated results of element content are as follows: Figure 5 , Figure 6 , Figure 7 and Figure 8 As shown, from Figure 5-8 It can be seen that the CF-LIPS calculation results using the unified temperature method are close to the standard values ​​and are closer to the standard values ​​than the analysis results using the matrix element slope to calculate the plasma temperature.

[0087] The plasma temperature calculation method for CF-LIPS quantitative analysis provided by the present invention is based on the consistency of the plasma temperature of each element under the local thermodynamic equilibrium (LTE) condition in the CF-LIPS method, and constructs a matrix model by associating the spectral line information of different elements, and uses the least squares method to determine a unified plasma temperature, which solves the problem of difficulty in temperature determination caused by the scarcity of spectral lines for trace components. While improving the calculation quality of plasma temperature, this method only produces one plasma temperature for all element spectral lines, which solves the problem of large temperature differences between different components, and effectively improves the component quantitative accuracy of CF-LIPS. In addition, the calculation results of the present invention include not only plasma temperature, but also intercepts corresponding to all element spectral lines, which quickly connect the subsequent process of calculating the content of each element by the CF-LIPS method, without calculating the plasma temperature and then calculating the corresponding intercepts of each element again. The present invention realizes the close connection and efficient integration of the CF-LIPS calculation process.

[0088] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A plasma temperature calculation method for CF-LIPS quantitative analysis, comprising the following steps: S1. Assuming that there are n elements and m data points involved in the calculation, a linear model of the elements is established based on the spectral lines of the n elements and related spectral line parameters; the estimated model of all element points is expressed as: h i =ax i,0 +b1x i,1 +b2x i,2 +···+b n x i,n (1) In formula (1), h i is the model estimate, a is the slope, i represents the data point in the Saha-Boltzmann plane, x i,0 is the horizontal coordinate of the data point, {i∈Z|0<i≤m}; for different types of elements j, b j is the intercept, x i,k＝j =1,x i,k≠j =0, {k,j∈Z|0<k,j≤n}; S2. Construct a model matrix based on m data points, expressed as: H=XB (2) In formula (2), H=[h1 h2 h3 ···h m ] T is an m×1-dimensional vector of model estimates; is the horizontal coordinate x of the data in the Saha-Boltzmann plane * and element types; B = [a b1 b2 ···b n ] T is the slope a and the intercept b1~b n The (n+1)×1 dimensional vector; S3. Use the least squares method to construct the target loss function: L(a,b i )=||H-Y|| 2 (3) In formula (3), L(a,b i ) indicates that the variables are a, b i The target loss function is Y = [y1 y2 y3 ···y m ] T is the ordinate y of the data in the Saha-Boltzmann plot * The m×1 dimensional vector composed of S4, calculating the optimal model parameters of the target loss function constructed in step S3, obtaining the intercept and slope of the best fitting straight line, and then calculating the plasma temperature according to the slope; S5. Calculate the relative content of the element according to the intercept of the best fitting straight line obtained in step S4 and the plasma temperature using the Saha-Boltzmann diagram method.

2. The plasma temperature calculation method for CF-LIPS quantitative analysis according to claim 1, characterized in that: Step S4 is specifically as follows: For L(a,b i ) to find the partial derivative. When each partial derivative function is equal to 0, the corresponding variable value is the best fitting parameter. At this time, L(a,b i ) is the smallest, and the model corresponding to the variable value is the best fitting model. The value of the variable parameter matrix B obtained by matrix transformation and calculation is shown as follows: B=(X T X) -1 X T Y (4) In formula (4), B = [ab1b2···b n ] T The parameters included are the intercept and slope of the best fitting straight line for each element, which are calculated uniformly through a matrix containing the spectral line information of each element; the plasma temperature is calculated from the slope 3. The plasma temperature calculation method for CF-LIPS quantitative analysis according to claim 2, characterized in that: The relative content calculation formula of the element in step S5 is: In formula (5) and formula (6), j represents an element atom or a monovalent ion, and U j (T) is the distribution function of element particle s at plasma temperature T, F is an experimental parameter, which is calculated by formula (5), and the relative atomic fraction of element atoms or monovalent ions is obtained by formula (6), and the relative mass content is obtained by relative atomic mass conversion.

4. A CF-LIPS spectrum analysis processing program, characterized in that: The program is based on the plasma temperature calculation method for CF-LIPS quantitative analysis according to any one of claims 1 to 3, and comprises the following steps: 1) Spectral data preprocessing; 2) Spectral line identification and selection; 3) Calculation of plasma electron density; 4) Calculation of plasma temperature and sample element content.

5. The CF-LIPS spectrum analysis processing program according to claim 4, characterized in that: The spectral data preprocessing is specifically as follows: after correcting the relative spectral conversion efficiency at each wavelength of the input original spectrum, the continuous background formed by bremsstrahlung and compound radiation is deducted, and then the inhomogeneity of plasma light collected by each channel is corrected and spliced.

6. The CF-LIPS spectrum analysis processing program according to claim 5, characterized in that: The spectral line identification and selection specifically include: spectral line peak finding, i.e. finding the wavelength position of the spectral line, spectral line matching, i.e. confirming the information corresponding to the spectral line by comparing with the spectral line information database, and selecting the spectrum for CF-LIPS calculation, i.e. selecting the spectral line without interference as the reliable data for subsequent calculation.

7. The CF-LIPS spectrum analysis processing program according to claim 6, characterized in that: The plasma electron density calculation is specifically as follows: Stark broadening is obtained and the plasma electron density is calculated by performing Lorentz fitting on the H-α spectral line profile.

8. The CF-LIPS spectrum analysis processing program according to claim 7, characterized in that: The plasma temperature and sample element content are calculated specifically as follows: the spectral line intensity and the corresponding atomic spectrum data used for calculation and analysis are selected, the slope and intercept of the fitting line of each element are calculated by the CF-LIPS method with uniform temperature, and then subsequent calculations are performed to obtain the relative content of the element.

9. The CF-LIPS spectrum analysis processing program according to any one of claims 4 to 8, characterized in that: The program is written in Python language.

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