A method for plasma temperature calculation for CF-LIPS quantitative analysis

Abstract

This invention discloses a plasma temperature calculation method for CF-LIPS quantitative analysis, relating to the field of elemental composition detection technology. The method includes: S1, assuming n elements and m data points participate in the calculation, establishing a linear model of the elements based on their spectral lines and related spectral parameters; S2, constructing a model matrix based on the m data points; S3, constructing a target loss function using the least squares method; S4, calculating the optimal model parameters of the target loss function constructed in step S3; and S5, calculating the relative abundance of the elements using the Saha-Boltzmann plot method. The method provided by this invention is based on the consistency of plasma temperature for each element under local thermodynamic equilibrium conditions in the CF-LIPS method. It can solve the problems of difficulty in determining plasma temperature for trace components due to sparse spectral lines and large temperature differences between different components, and can effectively improve the quantitative accuracy of CF-LIPS.

Description

Technical Field

[0001] This invention belongs to the field of elemental composition detection technology, specifically relating to a plasma temperature calculation method for quantitative analysis using CF-LIPS. Background Technology

[0002] Laser-induced plasma spectroscopy (LIPS, also known as laser-induced breakdown spectroscopy, LIBS) is an atomic emission spectroscopy technique with advantages such as in-situ, rapid, non-contact, and simultaneous multi-element detection, showing great potential for in-situ real-time online analysis of elemental composition. Traditional LIPS quantitative methods are often limited by matrix effects, requiring the construction of calibration curves based on matrix-matched standard samples, which to some extent restricts their application range. Calibration-free laser-induced plasma spectroscopy (CF-LIPS), on the other hand, does not require calibration curves based on standard samples, effectively avoiding the influence of matrix effects and exhibiting better applicability. It is particularly suitable for the detection of substances where standard samples are difficult to obtain and has been gradually applied in fields such as metallurgy, geology, archaeology, biomedicine, materials science, and environmental monitoring.

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

[0004] To ensure a good linear fit, the coordinate points used for line fitting need to be highly reliable and sufficient in number. However, in practical applications, especially for trace elements, the number of spectral lines is often insufficient, leading to increased errors in plasma temperature calculation and consequently affecting the accuracy of CF-LIPS. The CF-LIPS method with a standard reference line (SRL) uses the plasma temperature calculated for the matrix element as the plasma temperature for other elements, avoiding the impact of insufficient spectral lines leading to inadequate plasma temperature calculations or large errors in the results. However, this method comes at the cost of sacrificing some spectral information, resulting in less accurate calculations for some elements. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide a plasma temperature calculation method for quantitative analysis of trace components using CF-LIPS. This method can solve the problems of difficulty in determining plasma temperature due to the scarcity of spectral lines for trace components and the large temperature differences between different components, and can effectively improve the quantitative accuracy of components in CF-LIPS.

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

[0007] A method for calculating plasma temperature for quantitative analysis in CF-LIPS includes the following steps:

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

[0009] h i =ax i,0 +b1x i,1 +b2x i,2 +···+b n x i,n (1)

[0010] In equation (1), h i Here, 'a' represents the model estimate, 'i' represents the slope, and 'i' represents the data point in the Saha-Boltzmann plane plot. i,0 Let b be the x-coordinate of the data point, {i∈Z|0<i≤m}; for elements j of different types, b j x is the intercept. 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, represented as follows:

[0012] H = XB (2)

[0013] In equation (2), H = [h1h2h3···h m ] T It is an m×1 dimensional vector composed of model estimates; The data is represented by the x-axis in the Saha-Boltzmann plane plot. * A vector of m×(n+1) dimensions consisting of the types of elements; B = [ab1b2···b n ] T It is the slope a and the intercept b1~b n The resulting (n+1)×1 dimensional vector;

[0014] S3. Construct the target loss function using the least squares method:

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

[0016] In equation (3), L(a,b) i ) represents variables a and b i The target loss function is Y = [y1y2y3···y m ] T The data is represented by the y-axis in the Saha-Boltzmann plot. * A vector of m×1 dimensions;

[0017] S4. Calculate the optimal model parameters of the target loss function constructed in step S3, obtain the intercept and slope of the best fitted line, and then calculate the plasma temperature based on the slope.

[0018] S5. Based on the intercept of the best-fit line obtained in step S4 and the plasma temperature, calculate the relative content of the elements according to the Saha-Boltzmann diagram method.

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

[0020] For L(a,b) i Find the partial derivatives. The variable values ​​corresponding to the partial derivatives being equal to 0 are the best-fit parameters. At this point, L(a,b) i The model corresponding to the smallest variable value is the best-fit model. The values ​​of the variable parameter matrix B obtained through matrix transformation and calculation are shown in the following formula:

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

[0022] In equation (4), B = [ab1b2···b n ] T The parameters included are the intercept and slope of the best-fit line for each element, which are calculated uniformly using a matrix containing spectral information of various elements; the plasma temperature is calculated from the slope.

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

[0024]

[0025] In equations (5) and (6), j represents an element atom or a monovalent ion, and U j (T) is the partition function of element particle s at plasma temperature T, and F is an experimental parameter. It is calculated by equation (5). The relative atomic fraction of element atom or monovalent ion is obtained by equation (6). The relative mass content is obtained by converting the relative atomic mass.

[0026] A CF-LIPS spectral analysis processing program, the program being based on the plasma temperature calculation method for CF-LIPS quantitative analysis as described above, includes 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 specifically involves: correcting the relative spectral conversion efficiency at each wavelength of the input raw spectrum, subtracting the continuous background formed by bremsstrahlung and recombination radiation, and then correcting and stitching the non-uniformity of the plasma light collected in each channel.

[0032] Furthermore, in the CF-LIPS spectral analysis processing program described above, the spectral line identification and selection specifically includes: 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 through comparison with the spectral line information database; and selecting the spectrum for CF-LIPS calculation, i.e., selecting interference-free spectral lines as reliable data for subsequent calculations.

[0033] Furthermore, in the CF-LIPS spectral analysis processing procedure described above, the plasma electron density calculation specifically involves: obtaining Stark broadening by performing Lorentz fitting on the H-α spectral profile and then calculating the plasma electron density.

[0034] Furthermore, in the CF-LIPS spectral analysis processing procedure described above, the calculation of plasma temperature and sample element content specifically involves: selecting the spectral line intensities and corresponding atomic spectral data for calculation and analysis, calculating the slope and intercept of the fitted straight line for each element using the CF-LIPS method at a uniform temperature, and then performing subsequent calculations to obtain the relative content of the elements.

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

[0036] Compared with existing technologies, the plasma temperature calculation method and program for quantitative analysis of CF-LIPS provided by this invention have the following advantages:

[0037] The plasma temperature calculation method provided by this invention is based on the consistency of plasma temperatures for each element under the local thermodynamic equilibrium (LTE) condition in the CF-LIPS method. It constructs a matrix model by correlating the spectral line information of different elements and uses the least squares method to determine a unified plasma temperature. This method can solve the problems of difficulty in determining plasma temperature for trace components due to sparse spectral lines and large temperature differences between different components, and effectively improves the accuracy of component quantification in CF-LIPS. Attached Figure Description

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

[0039] Figure 2 Here is a flowchart of the CF-LIPS analysis procedure;

[0040] Figure 3 Saha-Boltzmann diagrams of aluminum alloy samples obtained using the uniform temperature method;

[0041] Figure 4 The plasma temperature of the aluminum alloy sample was calculated using two different methods.

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

[0043] Figure 6 CF-LIPS analysis results for aluminum alloy samples whose plasma temperature was calculated using matrix element slopes;

[0044] Figure 7 A comparison chart of elemental analysis results obtained by calculating plasma temperature using matrix element slope and standard values;

[0045] Figure 8 This is a comparison chart of elemental analysis results obtained using the uniform temperature method with standard values. Detailed Implementation

[0046] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0047] This invention provides a method for calculating plasma temperature for quantitative analysis using CF-LIPS. This method assumes that all elements have the same plasma temperature under the local thermodynamic equilibrium condition in the CF-LIPS method, that is, they have the same slope in the Saha-Boltzmann diagram. For linear fitting of data points with different intercepts but the same slope, the least squares method is used to establish an estimation model.

[0048] Both the Boltzmann diagram method and the Saha-Boltzmann diagram method are acceptable. The following text will only use the Saha-Boltzmann diagram method as an example to explain this method in detail. Figure 1 This invention provides a flowchart of a plasma temperature calculation method for quantitative analysis using CF-LIPS, which includes the following steps:

[0049] S1. Establish a linear model of elements.

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

[0051] h i =ax i,0 +b1x i,1 +b2x i,2 +···+b n x i,n (1)

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

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

[0054] Assume there are m data points involved in the calculation, and all data points can be represented by a matrix.

[0055] H = XB (2)

[0056] In equation (2), H = [h1 h2 h3···h m ] T , is an m×1 dimensional vector composed of model estimates; The data is represented by the x-axis in the Saha-Boltzmann plane plot. * A vector of m×(n+1) dimensions consisting of the types of elements; B = [a b1 b2···b n ] T , is the slope a and the intercept b1~b n The resulting (n+1)×1 dimensional vector.

[0057] S3. Construct the target loss function

[0058] The least squares method posits that the model that minimizes the sum of squared errors between predicted and measured values ​​best approximates the true situation. For normally distributed data, minimizing the sum of squared errors using the least squares method is equivalent to maximizing the likelihood function; that is, the least squares method is the maximum likelihood estimate of data with normally distributed errors.

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

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

[0061] In equation (3), L(a,b) i ) represents variables a and b i The target loss function is Y = [y1y2y3···y m ] T The data is represented by the y-axis in the Saha-Boltzmann plot. * A vector of length m×1.

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

[0063] For L(a,b) i Find the partial derivatives. The variable values ​​corresponding to the partial derivatives being equal to 0 are the best-fit parameters. At this point, L(a,b) i The model corresponding to the smallest variable value is the best-fit model. Through certain matrix transformations and calculations, the numerical values ​​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 equation (4), B = [ab1b2···b n ] T The parameters included are the intercept and slope of the best-fit line for each element, calculated uniformly using a matrix containing spectral information of various elements. The plasma temperature can be calculated from the slope.

[0066] S5. Based on the intercept of the best-fit line obtained in step S4 and the plasma temperature, calculate the relative content of the elements according to the Saha-Boltzmann diagram method.

[0067] The relative content of elements can be obtained by using formulas (5) and (6) in the subsequent calculations according to the Saha-Boltzmann diagram method.

[0068]

[0069] In equations (5) and (6), j represents an element atom or a monovalent ion, and U j (T) is the partition function of element particle s at plasma temperature T, and F is an experimental parameter. It is calculated by equation (5). The relative atomic fraction of element atom or monovalent ion is obtained by equation (6). The relative mass content is obtained by converting the relative atomic mass.

[0070] Based on the above inventive concept, this invention employs Python to develop a CF-LIPS spectral analysis processing program using a unified temperature method. The calculation flow of the spectral analysis program is as follows: Figure 2 As shown, the specific steps include:

[0071] 1) Spectral data preprocessing

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

[0073] 2) Spectral line identification and selection

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

[0075] 3) Plasma electron density calculation

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

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

[0078] The spectral line intensities and corresponding atomic spectral data used for calculation and analysis are selected. The slope and intercept of the fitted line for each element are calculated using the CF-LIPS method at a uniform temperature. Then, the relative abundance of the elements is obtained through subsequent calculations.

[0079] Example

[0080] The aluminum alloy standard material was analyzed by CF-LIPS using the above-mentioned unified temperature method, and the method of calculating plasma temperature using matrix element slope was used as a control.

[0081] The test samples used in the experiment were high-silicon, high-copper cast aluminum alloy spectral standard materials, numbered GBW02238 to GBW02243. The composition of these standard materials is primarily aluminum (Al), and also includes six other elements: silicon (Si), magnesium (Mg), manganese (Mn), iron (Fe), copper (Cu), and zinc (Zn). The reference component contents of these standard materials are shown in Table 1. These elements are arranged in a gradient cross-coupling pattern, which can be used for the evaluation of measurement methods.

[0082] Table 1. Elemental composition and content of standard materials for high-silicon and high-copper cast aluminum alloys

[0083]

[0084] The test results identified seven elements in the aluminum alloy samples: aluminum (Al), silicon (Si), magnesium (Mg), manganese (Mn), iron (Fe), copper (Cu), and zinc (Zn), with a total of 21 spectral lines used for CF-LIPS calculations. The Saha-Boltzmann plots of the aluminum alloy samples obtained using the unified temperature method are shown below. Figure 3 As shown, the corresponding intercepts can also be calculated for the four elements Fe, Mn, Zn, Cu, and Si, which have insufficient spectral lines.

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

[0086] The results of element content calculation 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 even closer to the standard values ​​than the analysis results calculated using the slope of the matrix element.

[0087] This invention provides a plasma temperature calculation method for CF-LIPS quantitative analysis. Based on the consistency of plasma temperatures for each element under the local thermodynamic equilibrium (LTE) condition in the CF-LIPS method, it constructs a matrix model by correlating the spectral line information of different elements and uses the least squares method to determine a unified plasma temperature, solving the problem of difficulty in temperature determination for trace components due to the scarcity of spectral lines. This method improves the calculation quality of plasma temperature while ensuring that all elemental spectral lines generate only one plasma temperature, addressing the problem of large temperature differences between different components and effectively improving the accuracy of CF-LIPS component quantification. Furthermore, the calculation results of this invention include not only the plasma temperature but also the intercepts corresponding to all elemental spectral lines, quickly connecting the subsequent calculation of elemental content in the CF-LIPS method without recalculating the intercepts after calculating the plasma temperature. This invention achieves a tight connection and efficient integration of the CF-LIPS calculation process.

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

Claims

1. A method for calculating plasma temperature for quantitative analysis in CF-LIPS, comprising the following steps: S1. Assuming there are n types of elements and m data points involved in the calculation, establish a linear model for each element based on its spectral lines and related spectral parameters; the estimated model for all element points is expressed as: h i =ax i,0 +b1x i,1 +b2x i,2 +···+b n x i,n (1) In equation (1), h i Here, 'a' represents the model estimate, 'i' represents the slope, and 'i' represents the data point in the Saha-Boltzmann plane plot. i,0 Let b be the x-coordinate of the data point, {i∈Z|0<i≤m}; for elements j of different kinds, b j x is the intercept. 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, represented as follows: H = XB (2) In equation (2), H = [h1h2h3···h m ] T It is an m×1 dimensional vector composed of model estimates; The data is represented by the x-axis in the Saha-Boltzmann plane plot. * A vector of m×(n+1) dimensions consisting of the types of elements; B = [ab1b2···b n ] T It is the slope a and the intercept b1~b n The resulting (n+1)×1 dimensional vector; S3. Construct the target loss function using the least squares method: L(a,b i )=||H-Y|| 2 (3) In equation (3), L(a,b) i ) represents variables a and b i The target loss function is Y = [y1y2y3···y m ] T The data is represented by the y-axis in the Saha-Boltzmann plot. * A vector of m×1 dimensions; S4. Calculate the optimal model parameters of the target loss function constructed in step S3, obtain the intercept and slope of the best fitted line, and then calculate the plasma temperature based on the slope. S5. Based on the intercept of the best-fit line obtained in step S4 and the plasma temperature, calculate the relative content of the elements according to the Saha-Boltzmann diagram method. Step S4 specifically involves: For L(a,b) i Find the partial derivatives. The variable values ​​corresponding to the partial derivatives being equal to 0 are the best-fit parameters. At this point, L(a,b) i The model corresponding to the smallest variable value is the best-fit model. The values ​​of the variable parameter matrix B obtained through matrix transformation and calculation are shown in the following formula: B=(X T X) -1 X T Y (4) In equation (4), B = [a b1 b2 ··· b n ] T The parameters included are the intercept and slope of the best-fit line for each element, which are calculated uniformly using a matrix containing spectral information of various elements; the plasma temperature is calculated from the slope.

2. The plasma temperature calculation method for quantitative analysis of CF-LIPS according to claim 1, characterized in that, The formula for calculating the relative content of elements in step S5 is as follows: In equations (5) and (6), j represents an element atom or a monovalent ion, and U j (T) is the partition function of element particle s at plasma temperature T, and F is an experimental parameter. It is calculated by equation (5). The relative atomic fraction of element atom or monovalent ion is obtained by equation (6). The relative mass content is obtained by converting the relative atomic mass.

3. A CF-LIPS spectral analysis processing method, characterized in that, Includes the following steps: 1) Spectral data preprocessing; 2) Spectral line identification and selection; 3) Calculation of plasma electron density; 4) The plasma temperature and sample element content are calculated using the plasma temperature calculation method for CF-LIPS quantitative analysis as described in claim 1 or 2.

4. The CF-LIPS spectral analysis and processing method according to claim 3, characterized in that, The spectral data preprocessing specifically involves: correcting the relative spectral conversion efficiency at each wavelength of the input raw spectrum, subtracting the continuous background formed by bremsstrahlung and recombination radiation, and then correcting the inhomogeneity of the plasma light collected in each channel and splicing them together.

5. The CF-LIPS spectral analysis and processing method according to claim 4, characterized in that, The spectral line identification and selection specifically includes: 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 through comparison with the spectral line information database; and selecting the spectrum for CF-LIPS calculation, i.e., selecting interference-free spectral lines as reliable data for subsequent calculations.

6. The CF-LIPS spectral analysis and processing method according to claim 5, characterized in that, The plasma electron density calculation specifically involves: obtaining Stark broadening by performing Lorentz fitting on the H-α spectral profile and then calculating the plasma electron density.

7. The CF-LIPS spectral analysis and processing method according to claim 6, characterized in that, The calculation of plasma temperature and sample element content is specifically as follows: select the spectral line intensity and corresponding atomic spectral data for calculation and analysis, calculate the slope and intercept of the fitted line of each element using the plasma temperature calculation method for CF-LIPS quantitative analysis, and then calculate the relative content of the elements.

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