An element measurement method based on an improved multi-energy correction method

Abstract

The application provides an element measurement method based on an improved multi-energy correction method, the Boltzmann expression is linearized by using a Taylor expansion, the spectral line intensity and the product of the spectral line intensity and the excitation energy are used as independent variables, and then the multi-energy correction method is used to calculate the unknown sample element concentration according to the spectral line intensity coefficient, so that the quantitative error caused by the change of the light source temperature is reduced, the process of calculating the plasma temperature is avoided, and the quantitative interference error caused by the calculation error of the plasma temperature is avoided.

Description

Technical Field

[0001] This invention belongs to the field of analytical technology such as atomic spectroscopy, mass spectrometry, and flame atomic absorption spectroscopy. It relates to an element measurement method, specifically, a measurement method for quantitative analysis of element content using spectral line intensity information corresponding to multiple wavelengths or multiple energies of the element to be measured. Background Technology

[0002] For techniques such as optical emission spectroscopy / mass spectrometry and flame atomic absorption spectrometry, calibration is a crucial step in quantitative analysis. Inappropriate calibration methods can degrade quantitative results. In common applications, calibration is performed by measuring the analytical signals of multiple standard reference solutions and establishing a calibration curve equation between the instrument response and the analyte concentration. Ideally, the physicochemical environment of the analyte should be identical to that of the standard reference solution and the sample. However, in practice, achieving perfect matrix matching between the reference solution and the sample is difficult, thus posing challenges to quantitative determination. To address the problems caused by matrix effects, commonly used calibration strategies include single-wavelength calibration methods such as external standard methods, internal standard methods, and standard addition methods, as well as the recently proposed multi-energy calibration method.

[0003] Traditional external standard methods are effective for simple matrix determinations. They assume that the reference solution and sample have the same or similar matrix, or that differences in matrix composition have negligible impact on the analytical signal.

[0004] The internal standard method involves adding an internal standard of the same concentration to blank, standard, and sample solutions. A standard curve is established by using the relationship between the ratio of the analytical line intensity to the internal standard intensity and the concentration. Since the selected internal standard has similar physicochemical properties to the analyte and is affected by the same nebulization, transmission, atomization, excitation, and ionization, it can correct signal fluctuations caused by instrument conditions, sampling errors, and some matrix effects.

[0005] The standard addition method is the most commonly used method for complex matrix analysis. This method involves adding equal volumes of sample to a blank and a standard solution of known concentration, and then calculating the concentration of the analyte in the sample using a standard curve. Since the calibration solution and the sample are prepared in the same matrix, matrix effects can be minimized.

[0006] Multi-energy calibration, proposed by Alex Virgilio et al., is a novel calibration method that utilizes multiple wavelengths of the analyte for calibration. Different wavelengths correspond to different excitation energies, hence the names Multi-energy Calibration Method (Analytica Chimica Acta 2017, 982, 31-36), Multi-wavelength Calibration Method (Microchemical journal 2019, 146, 381-386), and Multi-isotope Calibration Method (Analytical and Bioanalytical Chemistry 2018, 410, 1157-1162). This method requires only two calibration solutions, has high throughput, and the calibration solutions contain the same sample concentration, thus exhibiting matrix matching capabilities similar to the standard addition method. Furthermore, it easily identifies potential spectral interferences on specific analytical lines based on outliers observed on the calibration curve for different wavelengths.

[0007] The external standard method is inaccurate when the sample matrix is ​​complex, resulting in significant deviations.

[0008] The standard addition method is a time-consuming and sample-intensive method. For the determination of each sample, 4 to 5 standard solutions must be prepared to establish a standard curve. At the same time, it is difficult to effectively correct for spectral interference.

[0009] The difficulty of the internal standard method lies in the selection of the internal standard. It requires that the internal standard be absent in the sample, ideally have a concentration range consistent with the analyte, and possess physicochemical properties (ionization energy) consistent with the analyte. In practice, the selection of the internal standard is determined by indicators such as recovery rate. Furthermore, the internal standard method still cannot address severe matrix effects.

[0010] The multi-energy correction method is susceptible to systematic errors caused by solution preparation. Inaccurate results will occur if the concentration of the reference standard added to solution 1 is incorrect. It is only applicable to analytes that can generate multiple analytical lines, with at least three analytical lines for each element. Similar to the standard addition method, it cannot adequately correct for additive interferences. Furthermore, a calibration curve needs to be established for each sample and each element. It cannot identify errors introduced by variations in light source parameters, which are difficult to determine simply by the R² value of the linear regression coefficient of the calibration curve. Summary of the Invention

[0011] To address the inability of multi-energy correction methods to effectively identify interference caused by changes in light source temperature, an element measurement method based on an improved multi-energy correction approach is proposed. This method effectively identifies quantitative errors caused by changes in light source temperature, while avoiding quantitative errors caused by calculating plasma temperature.

[0012] First, let me explain the working principle of this invention:

[0013] Under conditions of optical thinness and thermodynamic / local thermodynamic equilibrium, the relationship between the instrument response or emission intensity of the analyte at a specified characteristic wavelength and the concentration and excitation energy of the analyte is as follows:

[0014]

[0015] Where the subscripts j and i represent the upper and lower energy levels of the element being measured, respectively; I is the intensity of the characteristic spectral line of the element received by the detector; F represents the instrument parameters, which are constants for given experimental conditions; C is the concentration of the element to be measured; λ k A, g, and U(T) represent the characteristic wavelength (k = 1, 2, 3, ..., n), transition probability, statistical weight of excited state, and partition function, respectively, and E, k B T represents the element excitation energy, Boltzmann constant, and plasma temperature, respectively.

[0016] In the calibration process, two calibration solutions are prepared for each sample.

[0017] Calibration solution 1 contains the sample and a calibration solution of an element with a known concentration; calibration solution 2 contains the sample and a blank. For example, calibration solution 1 contains a 50% v / v sample and a 50% v / v calibration solution of an element with a known concentration, while calibration solution 2 contains a 50% v / v sample and a 50% v / v blank sample. Other mixing ratios are also acceptable as long as both solutions contain equal amounts of sample. The following derivation process only applies to the case of a 1:1 dilution ratio.

[0018] By acquiring the spectral information of the two solutions using a spectrometer, the following relationship exists between the two solutions:

[0019] For solution 1:

[0020] For solution 2:

[0021] Where I(λ) k ) Sam+Std With I(λ) k ) Sam These are solutions 1 and 2 at a specific wavelength λ. k The instrument response at position, T1 and T2 are the plasma temperatures when measuring solution 1 and solution 2, respectively, in °C. Sam With CStd These are the element concentrations in the sample and the spiking concentrations in solution 1, respectively. m1 and m2 are the instrument response constants for the corresponding elements. Since the temperatures in the two solutions may be different, m1 and m2 may not be the same.

[0022] Combining formulas 2 and 3, we get:

[0023]

[0024] In general, the temperature change of the plasma source is small during the measurement process, and the change in the partition function of some elements is also very small due to temperature. The change in the partition function is far less than the change in the exponential term in the above equation. In this case, the change in the partition function can be ignored, and the above equation can be rewritten as:

[0025]

[0026] Let plasma temperature be the independent variable, and consider the exponential term in Formula 5. The position is approximated by a second-order Taylor expansion:

[0027]

[0028] Where ΔT = T2 - T1, Formula 6 can be rewritten as:

[0029] I(λ k ) Sam+Std =a0I(λ k ) Sam +a1I(λ k ) Sam E j +a2I(λ k ) Sam E j 2 +b (7)

[0030] in, b is the fitting constant term.

[0031] If I(λ) k ) Sam 、I(λ k ) Sam E j 、I(λ k ) Sam E j 2 Let I(λ) be the independent variable. k ) Sam+Std If we perform a multiple linear fit for the dependent variable, we can directly calculate the parameters a0, a1, a2, b, where a0 is a quantity that is independent of temperature and directly related to concentration.

[0032] Due to the spiking concentration C of the target element Std Given that the concentration of the analyte in the sample is known, it can be calculated using the following formula:

[0033]

[0034] Similarly, based on the above derivation process, Formula 7 can also be written as:

[0035] I(λ k ) Sam =a0I(λ k ) Sam+Std +a1I(λ k ) Sam+Std E j +a2I(λ k ) Sam+Std E j 2 +b (9)

[0036] in, b is the fitting constant term.

[0037] At this point, I(λ) k ) Sam+Std 、I(λ k ) Sam+Std E j 、I(λ k ) Sam+Std E j 2 Let I(λ) be the independent variable. k ) Sam To perform a multiple linear fit for the dependent variable, the parameters a0, a1, a2, and b can be directly calculated. Here, a0 is a quantity independent of temperature but directly related to concentration. The concentration of the analyte in the sample can be calculated using the following formula:

[0038]

[0039] This invention can be achieved through the following technical solutions:

[0040] An element measurement method based on an improved multi-energy correction method, comprising the following steps:

[0041] 1) Prepare two calibration solutions for each sample. Calibration solution 1 contains a volume ratio of V Sam V Std The sample and concentration of C Std Solution 1 contains the spiked solution; Solution 2 contains the same volume ratio of sample and blank, and both solutions contain equal amounts of sample.

[0042] 2) Obtain the emission spectra of the two calibration solutions, and calculate the intensity I(λ) of multiple atomic and / or ionic characteristic spectral lines of the element to be measured. k ) Sam+Std With I(λ) k ) Sam The intensity of a spectral line can be either the peak area or the peak height.

[0043] 3) The intensity I(λ1, λ2…) of the spectral lines at multiple wavelengths (λ1, λ2…) of the element to be measured in solution 2 k ) Sam 、I(λ k ) Sam E j 、I(λ k ) Sam E j 2 …I(λ k ) Sam E j n As the independent variable, the intensity I(λ) of the spectral line at the wavelength position of the element to be measured in solution 1 is... k ) Sam+Std Multiple linear fitting was performed on the dependent variable to obtain the relevant fitting parameters, and the relationship is as follows: Where E j For the energy level of the upper energy level, n≥1, preferably n=2;

[0044] 4) Take the fitting coefficient a0, and predict the concentration of the element to be measured in the sample according to the following formula:

[0045]

[0046] Another technical solution of the present invention is:

[0047] An element measurement method based on an improved multi-energy correction method, comprising the following steps:

[0048] 1) Prepare two calibration solutions for each sample. Calibration solution 1 contains a volume ratio of V Sam V Std The sample and concentration of C Std Solution 1 contains the spiked solution; Solution 2 contains the same volume ratio of sample and blank, and both solutions contain equal amounts of sample.

[0049] 2) Obtain the emission spectra of the two calibration solutions, and calculate the intensity I(λ) of multiple atomic and / or ionic characteristic spectral lines of the element to be measured. k ) Sam+Std With I(λ) k ) Sam The intensity of a spectral line can be either the peak area or the peak height.

[0050] 3) The intensity I(λ1, λ2…) of the spectral lines at multiple wavelengths (λ1, λ2…) of the element to be measured in solution 1 k ) Sam+Std 、I(λ k ) Sam+Std E j 、I(λ k ) Sam+Std E j 2 …I(λ k ) Sam+Std E j n As the independent variable, the intensity I(λ) of the spectral line at the corresponding wavelength position of the element to be measured in solution 2. k ) Sam Multiple linear fitting was performed on the dependent variable to obtain the relevant fitting parameters, and the relationship is as follows: Where E j For the energy level of the upper energy level, n≥1, preferably n=2;

[0051] 4) Take the fitting coefficient a0, and predict the concentration of the element to be measured in the sample according to the following formula:

[0052]

[0053] Beneficial effects

[0054] This method requires only two calibration solutions, offers high throughput, and contains identical sample concentrations, thus providing simple matrix matching capabilities. It easily identifies potential spectral interferences on specific analytical lines based on outliers on the calibration curve for different wavelengths. Furthermore, the use of a multiple linear regression method considering excitation energy reduces quantitative errors caused by variations in light source temperature, improving measurement accuracy. Since this method eliminates the need to calculate plasma temperature, it reduces the need for calculations of elemental atomic parameters (such as transition probabilities A). ji The errors introduced by uncertainties in plasma temperature calculation methods also avoid the need for spectral response correction of the spectrometer due to plasma temperature calculation. Attached Figure Description

[0055] Figure 1 This is a multi-energy correction curve based on the intensity of 10 Cr spectral lines in this invention. Detailed Implementation

[0056] The following specific embodiments illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification.

[0057] This invention provides an element measurement method based on an improved multi-energy correction method, the method comprising the following steps:

[0058] 1) Prepare two calibration solutions for each sample. Calibration solution 1 contains V... Sam V Std The sample and concentration of C Std Solution 1 contains the spiked solution; Solution 2 contains the same volume ratio of sample and blank, and both solutions contain equal amounts of sample.

[0059] 2) Obtain the emission spectra of the two calibration solutions, and calculate the intensity I(λ) of multiple atomic and / or ionic characteristic spectral lines of the element to be measured. k ) Sam+Std With I(λ) k ) Sam The intensity of a spectral line can be either the peak area or the peak height.

[0060] 3) The intensity I(λ1, λ2…) of the spectral lines at multiple wavelengths (λ1, λ2…) of the element to be measured in solution 2 k ) Sam 、I(λ k ) Sam E j 、I(λ k ) Sam E j 2 …I(λ k ) Sam E j n As the independent variable, the intensity I(λ) of the spectral line at the wavelength position of the element to be measured in solution 1 is... k ) Sam+Std Multiple linear fitting was performed on the dependent variable to obtain the relevant fitting parameters, and the relationship is as follows: Where E j For the energy level of the upper energy level, n≥1, preferably n=2;

[0061] 4) Take the fitting coefficient a0, and predict the concentration of the element to be measured in the sample according to the following formula:

[0062]

[0063] Optionally, in another technical solution of the present invention, steps 3) and 4) above can also be modified as follows:

[0064] 3) The intensity I(λ1, λ2…) of the spectral lines at multiple wavelengths (λ1, λ2…) of the element to be measured in solution 1 k ) Sam+Std 、I(λ k ) Sam+Std E j 、I(λ k ) Sam+Std E j 2 …I(λ k ) Sam+Std E jn As the independent variable, the intensity I(λ) of the spectral line at the corresponding wavelength position of the element to be measured in solution 2. k ) Sam Multiple linear fitting was performed on the dependent variable to obtain the relevant fitting parameters, and the relationship is as follows: Where E j For the energy level of the upper energy level, n≥1, preferably n=2;

[0065] 4) Take the fitting coefficient a0, and predict the concentration of the element to be measured in the sample according to the following formula:

[0066]

[0067] Example

[0068] The following is a specific conceptual example to illustrate the execution process and effects of this invention:

[0069] The sample contains C Sam A solution of Cr element with a concentration of 0.50 μg / L;

[0070] Solution 1 was prepared using 5.00 mL of C Std It was prepared using a Cr standard of 10.0 μg / L and a 5.00 mL sample.

[0071] Solution 2 was prepared by mixing 5.00 mL of the same sample with 5.00 mL of blank.

[0072] Assume a 10.0 μg / L Cr solution will produce 1000 Cr free atoms. Therefore, solutions 1 and 2 will produce 525 and 25 free atoms, respectively. However, due to the change in light source temperature, the spectral line intensities at different wavelengths will change. Table 1 shows the spectral line intensities of 10 Cr atoms for the two solutions, including atomic parameter information. Solutions 1 and 2 correspond to plasma temperatures T1 = 5000 K and T2 = 5500 K, respectively; the partition functions are U(T1) = 10.40 and U(T2) = 11.44, respectively.

[0073] Table 1

[0074]

[0075] The intensity of the spectral lines at multiple wavelength positions of the element to be measured in solution 2 is I(λ). k ) Sam 、I(λ k ) Sam E j 、I(λ k ) Sam E j 2 …I(λ k ) Sam Ej n As the independent variable, the intensity I(λ) of the spectral line at the wavelength position of the element to be measured in solution 1 is... k ) Sam+Std Multiple linear fitting was performed on the dependent variable to obtain the relevant fitting parameters, and the relationship is as follows: Where E j Let n = 2, which is the energy of the upper energy level. The multivariate fitting data are shown in Table 2. The subscripts 1 and 2 represent the spectral intensities from solution 1 and solution 2, respectively.

[0076] Table 2

[0077] <![CDATA[λ ji (nm)]]> <![CDATA[E j (eV)]]> <![CDATA[I1]]> <![CDATA[I2]]> <![CDATA[I2*E j ]]> <![CDATA[I2*E j 2 ]]> 302.1559 5.13 7.14E-13 9.12E-14 4.68E-13 2.40E-12 357.87038 3.46 1.21E-11 1.08E-12 3.75E-12 1.30E-11 359.35021 3.45 9.78E-12 8.76E-13 3.02E-12 1.04E-11 360.53446 3.44 7.72E-12 6.90E-13 2.37E-12 8.16E-12 425.43517 2.91 7.74E-12 6.19E-13 1.80E-12 5.25E-12 427.48117 2.90 6.03E-12 4.81E-13 1.39E-12 4.04E-12 428.97307 2.89 4.52E-12 3.60E-13 1.04E-12 3.01E-12 520.44981 3.32 1.32E-12 1.15E-13 3.82E-13 1.27E-12 520.84094 3.32 3.06E-12 2.67E-13 8.88E-13 2.95E-12 540.97834 3.32 3.62E-13 3.15E-14 1.05E-13 3.48E-13

[0078] According to the multiple linear regression, the fitting coefficient a0 = 22.085;

[0079] Given C std =10.0 μg / L, V Sam =V Std =5.00mL, according to Predict the concentration of the element to be measured in the solution from the sample: C Sam =0.474 μg / L, a deviation of -5.1% from the true concentration of 0.50 μg / L;

[0080] In contrast. Figure 1 The calibration curves prepared using the traditional multi-energy correction method are given:

[0081] Based on the linear regression slope Slope = 0.0878 and R² = 0.9922, according to Predict the concentration of the element to be measured in the solution from the sample: C Sam =0.96μg / L, quantitative deviation 92.5%, indicating that plasma temperature seriously affects the quantitative accuracy of traditional multi-energy correction methods, while the method proposed in this invention can effectively suppress the influence of this factor.

[0082] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An elemental measurement method based on an improved multi-energy correction method, characterized by, The method comprises the following steps: 1) Two calibration solutions are prepared for each sample, calibration solution 1 contains sample and spike solution in a volume ratio of V Sam :V Std , where C Std is the concentration of the spike solution; solution 2 contains sample and blank in the same volume ratio, both solutions contain the same amount of sample; 2) Obtain the emission spectrum of the two calibration solutions and calculate the intensity of the atomic and / or ionic characteristic lines of the element to be determined I(λ k ) Sam+Std of the calibration solutions and calculate the intensity of the atomic and / or ionic characteristic lines of the element to be determined I(λ k ) Sam , the line intensity being the peak area or the peak height; 3) with solution 2 the intensity of the spectrum line I(λ k ) Sam , I(λ k ) Sam E j , I(λ k ) Sam E j 2 I(λ k ) Sam E j n , I(λ k ) Sam+Std as the dependent variable, the multiple linear fitting is carried out to obtain the related fitting parameters, and the relationship is wherein E j is the energy of the upper energy level, and n≥1. 4) taking the fitting coefficient a0, and predicting the concentration of the element to be detected in the sample according to the following formula:

2. An elemental measurement method based on an improved multi-energy correction method, characterized by, The method comprises the following steps: 1) Two calibration solutions are prepared for each sample, calibration solution 1 contains sample in a volume ratio of V Sam : V Std to a spiked solution with concentration C Std ; solution 2 contains the same volume ratio of sample to blank, both solutions contain the same amount of sample; 2) Obtain the emission spectrum of the two calibration solutions and determine the intensity of several atomic and / or ionic characteristic lines of the element to be determined I(λ k ) Sam+Std and I(λ k ) Sam , the line intensity is the peak area or the peak height; 3) with solution 1 the element to be determined multi-wavelength (λ1, λ2...) position spectrum line intensity I(λ k ) Sam+Std , I(λ k ) Sam+Std E j , I(λ k ) Sam+Std E j 2 … I(λ k ) Sam+Std E j n , I(λ k ) Sam as the dependent variable for multiple linear fitting to get the relevant fitting parameters, the relationship is where E j is the upper level energy, n≥1, 4) taking the fitting coefficient a0, and predicting the concentration of the element to be detected in the sample according to the following formula:

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