A method for in-situ detection of gas impurity concentration based on refractive index gas temperature measurement

Abstract

The application relates to the technical field of low-temperature measurement and gas analysis, and provides a gas impurity concentration in-situ detection method based on a refractive index gas temperature measurement method, which comprises the following steps: measuring the experimental refractive index of a mixed gas under a known thermodynamic state; constructing a Virial coefficient model of a multi-component mixed gas containing a cross interaction term; calculating the theoretical refractive index of the mixed gas based on the Virial coefficient model; minimizing the residual error of the theoretical refractive index and the experimental refractive index by using a nonlinear optimization algorithm to solve the mole fraction of each component, and realizing in-situ detection of the gas impurity concentration; the application realizes in-situ and high-precision detection of the gas impurity concentration by using an innovative method based on refractive index measurement and a Virial coefficient model, the method can accurately characterize the interaction between gas molecules, thereby improving the detection precision, and is especially suitable for micro-impurity analysis.

Description

Technical Field

[0001] This invention relates to the field of cryogenic metrology and gas analysis technology, and in particular to an in-situ detection method for gas impurity concentration based on refractive index gas thermometry. Background Technology

[0002] In fields such as low-temperature physics, primary temperature metrology, and quantum standard reproduction, the purity of high-purity working gases (such as helium-4, helium-3, and neon) is crucial to the accuracy of experimental results. The traditional refractive index gas thermometry (RIGT) is based on the quantum standard (Boltzmann constant). The primary temperature measurement method, whose core principle is to measure the refractive index of the gas... and pressure Thermodynamic temperature is determined by combining the virial coefficient of the gas. .

[0003] However, in practical applications, the working gas often inevitably contains trace impurities (such as He-3 in He-4, or He in Ne). Existing gas analysis methods (such as gas chromatography-mass spectrometry GC-MS) usually require gas samples to be extracted for offline analysis, which is not only cumbersome but also difficult to reflect the true state of the gas inside the cryogenic chamber in real time.

[0004] Current RIGT research primarily focuses on assessing the error caused by impurities in temperature measurements given their concentrations. Existing techniques have not yet been able to use RIGT systems to measure refractive index anomalies and then extrapolate the composition and proportion of unknown impurities in the gas. Summary of the Invention

[0005] This invention provides an in-situ detection method for gas impurity concentration based on refractive index gas thermometry, which solves the problem that existing low-temperature gas impurity detection methods are difficult to perform in-situ, high-precision, and real-time analysis.

[0006] This invention provides an in-situ detection method for gaseous impurity concentration based on refractive index gas thermometry, comprising the following steps: The experimental refractive index of a gas mixture is measured under known thermodynamic conditions. Construct a virial coefficient model for a multi-component mixed gas that includes cross-interaction terms; The theoretical refractive index of the mixed gas was calculated based on the virial coefficient model. By minimizing the residual between the theoretical refractive index and the experimental refractive index using a nonlinear optimization algorithm, the mole fraction of each component is obtained, thus enabling in-situ detection of gaseous impurity concentration.

[0007] According to the in-situ detection method for gas impurity concentration based on refractive index gas thermometry provided by the present invention, the mixed gas includes a main gas and at least one impurity.

[0008] According to the in-situ detection method for gas impurity concentration based on refractive index gas thermometry provided by the present invention, the number of thermodynamic state points is one or more; when detecting a single impurity, one thermodynamic state point is selected; when detecting multiple impurities, multiple thermodynamic state points covering different temperature ranges are selected.

[0009] According to the in-situ detection method for gas impurity concentration based on refractive index gas thermometry provided by the present invention, the multi-component mixed gas virial coefficient model includes a mixed magnetic virial coefficient and a first dielectric virial coefficient, both of which adopt a linear mixing rule.

[0010] According to the in-situ detection method for gas impurity concentration based on refractive index gas thermometry provided by the present invention, the multi-component mixed gas virial coefficient model includes higher-order dielectric virial coefficient, second density virial coefficient, third density virial coefficient, and fourth density virial coefficient, which respectively characterize higher-order dielectric interactions and two-body, three-body, and four-body molecular interactions.

[0011] According to the in-situ detection method for gas impurity concentration based on refractive index gas thermometry provided by the present invention, the cross-interaction term includes two-body cross-virial coefficient, three-body cross-virial coefficient, and four-body cross-virial coefficient, which respectively characterize the two-body, three-body, and four-body interactions between different molecules.

[0012] According to the in-situ detection method for gas impurity concentration based on refractive index gas thermometry provided by the present invention, the nonlinear optimization algorithm is either the Levenberg-Marquardt algorithm or the simplex method, and the residual is calculated using a least-squares objective function, the expression of which is: ; Where n calc n is the theoretical refractive index. exp，k Let be the experimental refractive index of the k-th state point, where k = 1, 2, ..., N, and N is the total number of thermodynamic state points.

[0013] According to the in-situ detection method for gas impurity concentration based on refractive index gas thermometry provided by the present invention, the density of the mixed gas is solved by the virial equation of state, the expression of which is: in, ρ The density of the mixed gas, R is the gas constant.

[0014] The in-situ detection method for gas impurity concentration based on refractive index gas thermometry provided by the present invention further replaces refractive index measurement with measurement of changes in dielectric constant or magnetic permeability to detect impurity concentration.

[0015] According to the in-situ detection method for gaseous impurity concentration based on refractive index gas thermometry provided by the present invention, the thermodynamic state is a low-temperature environment with a temperature T < 25 K, and the mole fraction of each component satisfies the normalization condition. .

[0016] According to the in-situ detection method for gas impurity concentration based on refractive index gas thermometry provided by the present invention, the experimental refractive index is obtained by a microwave resonant cavity refractive index measurement system or an optical resonant cavity measurement system.

[0017] This invention provides an in-situ detection method for gas impurity concentration based on refractive index gas thermometry, comprising: measuring the experimental refractive index of a mixed gas under known thermodynamic conditions; constructing a multi-component mixed gas virial coefficient model including cross-interaction terms; calculating the theoretical refractive index of the mixed gas based on the virial coefficient model; minimizing the residual between the theoretical and experimental refractive indices using a nonlinear optimization algorithm to obtain the mole fraction of each component, thereby achieving in-situ detection of gas impurity concentration. This invention achieves in-situ, high-precision detection of gas impurity concentration through an innovative method based on refractive index measurement and a virial coefficient model. Firstly, by measuring the experimental refractive index of the mixed gas, this method avoids the cumbersome operations of traditional sampling analysis and can reflect the true state of the gas under low-temperature conditions in real time. By introducing a multi-component virial coefficient model to calculate the theoretical refractive index, this method can accurately characterize the interactions between gas molecules, thereby improving detection accuracy, especially suitable for the analysis of trace impurities. By using an optimization algorithm to minimize the difference between the experimental and theoretical refractive indices, this method achieves a non-destructive solution for impurity concentration without consuming or removing the gas sample. This versatile design is applicable to handling single or multiple impurity scenarios. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0019] Figure 1 This is a flowchart of an in-situ detection method for gas impurity concentration based on refractive index gas thermometry, provided by an embodiment of the present invention.

[0020] Figure 2This is a schematic flowchart of an in-situ detection method for gas impurity concentration based on refractive index gas thermometry provided in an embodiment of the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0022] The following is combined Figures 1-2 This invention describes an in-situ detection method for gas impurity concentration based on refractive index gas thermometry.

[0023] This invention provides an in-situ detection method for gaseous impurity concentration based on refractive index gas thermometry, comprising the following steps: Step S1: Under known thermodynamic conditions, measure the experimental refractive index of the gas mixture.

[0024] Specifically, in a low-temperature constant-temperature environment, a microwave resonant cavity refractive index measurement system or an optical resonant cavity measurement system is used to measure the refractive index of a resonant cavity. Different thermodynamic state points (in Experimental measurement of the refractive index of a gas mixture Experimental refractive index The calculation formula is: in These are the resonant frequencies under vacuum and pressure conditions, respectively. The effective compression factor.

[0025] Step S2: Construct a virial coefficient model for a multi-component mixed gas containing cross-interaction terms.

[0026] Step S3: Calculate the theoretical refractive index of the mixed gas based on the virial coefficient model.

[0027] Step S4: Minimize the residual between the theoretical refractive index and the experimental refractive index using a nonlinear optimization algorithm to obtain the mole fraction of each component, thereby achieving in-situ detection of gaseous impurity concentration.

[0028] As can be seen from the above scheme, this invention achieves in-situ, high-precision detection of gas impurity concentration through an innovative method based on refractive index measurement and virial coefficient model. This method first avoids the cumbersome operation of traditional sampling analysis by measuring the experimental refractive index of the mixed gas, and can reflect the real state of the gas in a low-temperature environment in real time. By introducing a multi-component virial coefficient model to calculate the theoretical refractive index, this method can accurately characterize the interaction between gas molecules, thereby improving the detection accuracy, especially suitable for the analysis of trace impurities. By using an optimization algorithm to minimize the difference between the experimental and theoretical refractive indices, this method achieves non-destructive solution of impurity concentration without consuming or removing the gas sample. This universal design is applicable to handling single or multiple impurity scenarios.

[0029] In this embodiment, in step S1, the number of thermodynamic state points is one or more; when detecting a single impurity, one thermodynamic state point is selected; when detecting multiple impurities, multiple thermodynamic state points covering different temperature ranges are selected, and the differences in the temperature dependence of the virial coefficient of different impurities are used for differentiation.

[0030] In other words, when detecting a single impurity, there is only one unknown variable in the gas mixture, namely the mole fraction of the impurity. A single thermodynamic state point can provide a set of experimental refractive index data. Combined with the virial coefficient model, the impurity concentration can be accurately deduced through a nonlinear optimization algorithm without the need for additional state point measurements. This simplifies the operation process, reduces detection time, and achieves efficient detection.

[0031] When detecting multiple impurities, there are multiple unknown variables in the gas mixture, namely the mole fraction of each impurity. The constraints provided by a single state point are insufficient to distinguish the contribution of different impurities to the refractive index. Therefore, it is necessary to select multiple state points that must cover different temperature ranges so that the characteristics of each impurity are differentiated in different temperature ranges, forming multiple sets of independent constraint equations, which provide sufficient basis for solving the concentration of multiple impurities at the same time.

[0032] On the one hand, the single-state-point design for a single impurity scenario avoids redundant measurements, and selecting the temperature range with the greatest difference between the impurity and the main gas virial coefficient further improves detection sensitivity. On the other hand, the multi-temperature-range state-point design for multiple impurity scenarios can adapt to mixed scenarios of any number of impurities (such as He-4 containing He-3, Ar, and Ne simultaneously) simply by adjusting the temperature distribution of the state points, without needing to design a dedicated detection scheme for specific impurity combinations. Simultaneously, the multi-temperature-range state points provide rich data for virial coefficient models with cross-action terms, which can more fully constrain model parameters, reduce computational uncertainties caused by higher-order cross-actions, further improve the accuracy of solving for multiple impurity concentrations, and allow the entire detection method to maintain stable high-precision detection performance in both single-impurity and multi-impurity scenarios.

[0033] This setup allows for the differentiation of temperature sensitivity among different impurities and their interactions with the main gas, as well as among impurities themselves. For instance, the virial coefficient of He-3 exhibits a significantly different behavior in low-temperature ranges (e.g., T < 25 K) compared to inert gases like Ar and Ne. The quantum effect of He-3 causes the virial coefficient to fluctuate rapidly with temperature, while the polarizability-dominated characteristics of Ar and Ne result in a more gradual change in the virial coefficient. By setting state points in different temperature ranges, this difference in characteristics can be fully revealed. Through cross-validation of multiple sets of data, the contributions of different impurities can be effectively separated, avoiding the confusion in concentration calculations caused by the superposition of the effects of multiple impurities.

[0034] In some embodiments, the mixed gas in step S2 comprises a primary gas and at least one impurity, wherein the primary gas is He-4 and the impurity is one or more of He-3, Ar, and Ne. For example, suppose the mixed gas is composed of... The composition consists of several components, with component 1 being a main gas such as He-4, and component... ( ) are impurities to be tested (such as He-3, Ar, Ne, etc.).

[0035] Define the mole fraction of each component as And it satisfies the normalization condition: in, For the first i The mole fraction of each component.

[0036] This setup allows the low-temperature environment to amplify the differences in virial coefficients between different components, especially isotopic impurities and conventional inert gas impurities. For example, as a quantum gas, the quantum effects of intermolecular interactions of He-3 are more pronounced in the low-temperature range (usually T<25K), which is significantly different from the virial coefficient variation of He-4. The differences in polarizability between impurities such as Ar and Ne and the main gas are also more clearly reflected at low temperatures through changes in density and refractive index, thereby greatly improving detection sensitivity and ensuring that the detection results can directly reflect the true state of the gas in the scene.

[0037] The mole fraction represents the proportion of each component in the gas mixture. The sum of the proportions of all components must be 1 (with no other components missing), and the proportion cannot be negative. This constraint ensures that the final output of impurity concentration results has practical reference value.

[0038] In step S2, a virial coefficient model for a multi-component mixed gas containing cross-interaction terms is constructed, including: establishing the macroscopic physical parameters and component concentrations of the mixed gas according to statistical mechanics mixing rules. x The functional relationship.

[0039] In some embodiments, the multi-component mixed gas virial coefficient model includes a mixed magnetic virial coefficient and a first dielectric virial coefficient, both of which employ a linear mixing rule.

[0040] Specifically, the expression for the hybrid magnetic virial coefficient is: in, For the first The magnetic susceptibility of a pure component, where m is the number of gas species. For the first i The mole fraction of each component.

[0041] The expression for the first dielectric virial coefficient is: in, For the first The first dielectric virial coefficient of a pure component, where m is the number of gas species. For the first i The mole fraction of each component.

[0042] In some embodiments, the multi-component mixed gas virial coefficient model includes higher-order dielectric virial coefficients, second-density virial coefficients, third-density virial coefficients, and fourth-density virial coefficients, which respectively characterize higher-order dielectric interactions and two-body, three-body, and four-body molecular interactions.

[0043] Specifically, the expression for the higher-order dielectric virial coefficient is: in xi、xj The first i, j mole fraction of the components Components i and j The cross-dielectric virial coefficient.

[0044] Second density virial coefficient (characterizing two-body interactions): in, The virial coefficient of a pure substance. The cross-virial coefficient characterizes the interaction between different molecules, such as the He-4 and Ar interaction.

[0045] Third density virial coefficient (characterizing three-body interactions): Fourth density virial coefficient (characterizing four-body interactions): With this configuration, the mixed magnetic virial coefficient characterizes the macroscopic magnetic susceptibility of the mixed gas, while the first dielectric virial coefficient reflects the fundamental dielectric properties of the mixed gas. Essentially, both are the macroscopic superposition of the inherent physical properties of each individual component in the mixed system, and the magnetic susceptibility of each component... Basic dielectric properties These are inherent parameters of the substance itself and are not affected by the mixing ratio. Therefore, adopting the linear mixing rule is an objective physical description of the fundamental magnetic and dielectric properties of the gas mixture, avoiding the model approximation error caused by complex mixing rules. This design, on the one hand, eliminates the need to introduce additional fitting parameters or empirical correction terms for linear mixing rules, requiring only that the pure components are known. and Basic data can be obtained through component mole fractions. xi Directly calculating the corresponding parameters of the mixed system significantly simplifies the model's computational complexity and reduces the computational load of subsequent iterative solutions, thus supporting the real-time nature of the detection. On the other hand, the linear rules are highly universal. Regardless of whether the main gas and impurities are isotope combinations such as He-4 and He-3, or combinations of different inert gases such as Ne and Ar, as long as the basic physical parameters of the single component are obtained, the rules can be directly applied to construct the model without adjusting the mixing logic for specific gas combinations, thereby enhancing the applicability of the entire detection method.

[0046] In this embodiment, the cross-interaction term includes two-body cross-virial coefficients, three-body cross-virial coefficients, and four-body cross-virial coefficients, which respectively characterize two-body, three-body, and four-body interactions between different molecules.

[0047] Specifically, in multi-component gas mixtures, intermolecular interactions are not limited to molecules within the same component, such as between host gases or between impurities. Intercomponent interactions between molecules of different components, such as between He⁻⁴ and He⁻³, or between He⁻⁴ and Ar, are also key factors influencing the macroscopic physical properties of the gas, such as density and refractive index. The two-body cross-virial coefficient... Describing pairwise interactions between two different molecules is the fundamental form of cross-component molecular interaction; the three-body cross-virial coefficient ( Cijk,i、 j、k Not entirely the same) characterizes the cooperative interaction when three different molecules coexist; the four-body cross-virial coefficient ( Dijks, i, j, k, s (Not entirely the same) further covers the joint interactions between four different types of molecules, adapting to more complex multi-component mixing scenarios. These three types of coefficients fully cover different levels of cross-component molecular interactions and are an objective reflection of the laws governing the movement of molecules in real mixed gases.

[0048] Traditional ideal mixing models or simplified models typically only consider interactions between molecules of the same component, neglecting cross-component interactions. This leads to discrepancies between theoretical calculations and actual gas properties in trace impurity detection scenarios, as the interactions between the main gas and impurity molecules are not characterized, ultimately affecting the accuracy of concentration calculations. In contrast, the two-body cross-virial coefficient in this invention serves as a fundamental form of cross-component molecular interaction, covering most scenarios dominated by cross-component interactions. Three-body and four-body cross-virial coefficients are designed for special conditions such as low temperature and high pressure, where intermolecular distances are smaller and the probability of simultaneous multi-molecule interactions is significantly increased. Since the influence of higher-order cross-interactions on gas density and refractive index is not negligible, their inclusion makes the model more realistic and avoids calculation errors caused by higher-order interactions. Furthermore, the linearity rules of these three types of coefficients complement those of the mixed magnetic virial coefficient and the first dielectric virial coefficient, ensuring both high efficiency in calculating basic properties and accurate characterization of complex interactions.

[0049] This setup offers several advantages. First, it significantly improves detection accuracy. By fully characterizing the interactions between different molecules at various levels, it greatly enhances the alignment between the theoretical refractive index calculation and experimental measurements, enabling subsequent residual optimization algorithms to accurately infer trace impurity concentrations. Second, it adapts to complex multi-component scenarios. When a gas mixture contains multiple impurities, such as He-4 containing He-3, Ar, and Ne simultaneously, the interactions between different impurities and the main gas, as well as between impurities themselves, can be characterized by corresponding coefficients. This eliminates the need to adjust the model for specific impurity combinations, enhancing the method's versatility. Furthermore, it adapts to specific operating conditions, particularly in applications like cryogenic metrology and quantum standard reproduction, typically in low-temperature environments (T < 25 K) where higher-order interactions are more pronounced. The presence of these three types of coefficients allows the model to stably adapt to these conditions, avoiding detection distortion caused by environmental changes.

[0050] In this embodiment, the nonlinear optimization algorithm is either the Levenberg-Marquardt algorithm or the simplex method. The residuals are calculated using a least-squares objective function, the expression of which is: in n calc Theoretical refractive index, n exp，k Let be the experimental refractive index of the k-th state point, where k = 1, 2, ..., N, and N is the total number of thermodynamic state points.

[0051] That is, using nonlinear optimization algorithms such as the Levenberg-Marquardt algorithm or the simplex method, under constraints... and The following solution makes F(x) Minimum vector This refers to the concentration of each impurity component.

[0052] Furthermore, the density of the gas mixture is solved using the virial equation of state, which is expressed as follows: in, ρ The density of the mixed gas, R is the gas constant.

[0053] Theoretical calculated refractive index Calculated by the following formula: In some embodiments, the dielectric constant can also be measured. or permeability The change of refractive index is used to replace the refractive index measurement for impurity concentration detection. The detection principle is the same as that of refractive index detection, and will not be elaborated here.

[0054] The following specific example illustrates the practical application of this method. The working gas is mainly He-4, and the impurity to be tested is only He-3. Other heavy atom impurities such as Ne and Ar have been completely removed by cold trap.

[0055] Step S10: Let the mole fraction of He-3 be... Then the mole fraction of He-4 is (1- Since it only involves a single unknown quantity. Only at a specific thermodynamic state point Perform measurements, for example, select T In the temperature range of <25K, the difference in virial coefficients between He-3 and He-4 is the greatest, resulting in the highest sensitivity.

[0056] At temperature ,pressure The experimental refractive index was measured below. .

[0057] Step S20: Construct a virial coefficient model for a multi-component mixed gas containing cross-interaction terms.

[0058] Expanding the general summation formula above for a binary system, where the virial coefficients for He-3 and He-4 are given high-precision ab initio values: (1) Mixed magnetic virial coefficient : (2) First dielectric virial coefficient: (3) Second dielectric virial coefficient: (4) Second density virial coefficient: in For pure components, The cross coefficients are He-4 and He-3.

[0059] It should be noted that for extremely low concentrations of impurities ( ), The term can be ignored, and the model can be further simplified to a linear approximation.

[0060] (5) Third density virial coefficient: (6) Fourth density virial coefficient: Reference Figure 2 This will further explain the work process.

[0061] 1. Unknown to be solved: mole fraction x of He-3 in He-4 mixture. By iteratively adjusting the trial value of x, the deviation between the theoretical refractive index and the experimentally measured refractive index is minimized, and finally x that meets the accuracy requirements is obtained.

[0062] 2. Initialization Phase Parameter and range settings Based on the actual application scenario, the range of values ​​for x is set as follows: That is, the He-3 impurity content is 0~100ppm, covering the typical range of trace impurities in high-purity gases.

[0063] Set the error threshold for convergence determination It can be 10 -8 -10 -9 It corresponds to ppb-level detection accuracy and can be adjusted according to actual needs.

[0064] Measurement parameters: The experimental refractive index of the gas mixture was obtained in advance using a refractive index measurement system. n exp (It can be obtained with a single in-situ measurement, without the need to extract a gas sample).

[0065] Fixed parameters: virial coefficients of the pure components of He-4 and He-3, thermodynamic state parameters (pressure p, temperature T, which are known constants), gas constant R, etc.

[0066] 3. Iterative solution stage (bisection method or Newton's iteration method) Initialization: Set the initial guess range .

[0067] Iterative loop: taking trial values Using the above formulas to calculate mixing parameters, the density of the mixed gas is solved using the virial equation of state (9). The theoretical refractive index is then calculated using equation (8). A nonlinear fitting method is employed, with the least squares objective function... Calculation and adjustment Until (Tolerance).

[0068] Output: Convergence result This refers to the detected He-3 impurity content.

[0069] By following the steps above, the isotopic abundance of He-3 in He-4 gas can be accurately calculated using a single refractive index measurement without the need to extract a gas sample.

[0070] In the case of multiple impurities, the composition analysis of the known gas can be completed by using formulas (1)-(10).

[0071] This invention achieves the effect of gas in its original thermodynamic environment ( p, T This method directly measures the refractive index without the need to extract samples or compromise the system's seal. This design fundamentally avoids the problems of gas state distortion, system contamination, or sample loss caused by sampling in traditional offline detection methods (such as GC-MS). It is suitable for scenarios with extremely high requirements for the stability of closed systems, such as cryogenic metrology and quantum standard reproduction. It can ensure the continuity of the experimental environment during the detection process and accurately reflect the impurity concentration of the gas in its original state, avoiding detection distortion caused by the gas deviating from its original operating conditions after sampling. Secondly, by constructing a virial coefficient model for multi-component mixed gases that includes cross-interaction terms, the complex interactions between gas molecules are realistically reproduced, and the two-body, three-body, and multi-body cross-interactions between the main gas and impurities, and between impurities, are accurately characterized. This overcomes the defect of traditional ideal mixing models that ignore intermolecular interactions, and makes the calculation of theoretical refractive index more consistent with the actual physical properties of gases. By minimizing the theoretical and experimental refractive index residuals using a nonlinear optimization algorithm, the refractive index, a physical quantity sensitive to concentration changes, is transformed into a precise solution for concentration, minimizing computational errors. When detecting a single impurity, only one thermodynamic state point is needed to provide sufficient constraints. When detecting multiple mixed impurities, by selecting multiple state points covering different temperature ranges and utilizing the temperature dependence differences in the virial coefficients of different impurities, the concentrations of multiple components can be solved simultaneously. This design eliminates the need for dedicated detection modules for different impurities, enabling it to handle both single isotopic impurities containing He-3 in He-4 and mixed impurities containing He and Ar in Ne, enhancing the method's applicability and flexibility. Furthermore, the detection process of this method does not require sample pre-processing. The time-consuming steps of processing, offline transmission, and chemical reaction analysis are reduced to physical parameter measurement (refractive index) and mathematical iterative calculation (virial coefficient model, optimization algorithm). The refractive index measurement can be completed in real time, and commonly used optimization algorithms such as the Levenberg-Marquardt algorithm have extremely fast convergence speeds (usually in the millisecond to second range), enabling rapid output of impurity concentration results. This method does not rely on the specific chemical or physical characteristics of a particular gas. As long as the basic data of the virial coefficients of each component can be obtained, the concentration can be solved through model iteration. Whether it is a combination of the main gas and isotopic impurities, or a combination of the main gas and multiple inert gas impurities, this method can achieve accurate detection, enabling it to cover the high-purity gas impurity detection needs of multiple fields such as low-temperature physics, primary temperature metrology, and quantum standard reproduction.

[0072] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for in-situ detection of gaseous impurity concentration based on refractive index gas thermometry, characterized in that, Includes the following steps: The experimental refractive index of a gas mixture is measured at one or more known thermodynamic points of state. Construct a virial coefficient model for a multi-component mixed gas that includes cross-interaction terms; The theoretical refractive index of the mixed gas was calculated based on the virial coefficient model. By minimizing the residual between the theoretical refractive index and the experimental refractive index using a nonlinear optimization algorithm, the mole fraction of each component is obtained, thus enabling in-situ detection of gaseous impurity concentration.

2. The in-situ detection method for gas impurity concentration based on refractive index gas thermometry according to claim 1, characterized in that, The mixed gas comprises a main gas and at least one impurity.

3. The in-situ detection method for gas impurity concentration based on refractive index gas thermometry according to claim 2, characterized in that, When detecting a single impurity, select one thermodynamic state point; when detecting multiple impurities, select multiple thermodynamic state points covering different temperature ranges.

4. The in-situ detection method for gas impurity concentration based on refractive index gas thermometry according to claim 1, characterized in that, The multi-component mixed gas virial coefficient model includes a mixed magnetic virial coefficient and a first dielectric virial coefficient, both of which adopt a linear mixing rule.

5. The in-situ detection method for gas impurity concentration based on refractive index gas thermometry according to claim 1, characterized in that, The multi-component mixed gas virial coefficient model includes higher-order dielectric virial coefficients, second-density virial coefficients, third-density virial coefficients, and fourth-density virial coefficients, which respectively characterize higher-order dielectric interactions and two-body, three-body, and four-body molecular interactions.

6. The in-situ detection method for gaseous impurity concentration based on refractive index gas thermometry according to claim 1, characterized in that, The cross-interaction terms include two-body cross-virial coefficients, three-body cross-virial coefficients, and four-body cross-virial coefficients, which respectively characterize two-body, three-body, and four-body interactions between different molecules.

7. The in-situ detection method for gaseous impurity concentration based on refractive index gas thermometry according to claim 1, characterized in that, The nonlinear optimization algorithm is either the Levenberg-Marquardt algorithm or the simplex method. The residuals are calculated using a least-squares objective function, the expression of which is: ； Where n calc n is the theoretical refractive index. exp，k Let be the experimental refractive index at the k-th state point, where k = 1, 2, ..., N, and N is the total number of thermodynamic state points. P k Let T be the pressure at the k-th thermodynamic state point. k Let be the temperature of the k-th thermodynamic state point. x This represents the mole fraction of each component.

8. The in-situ detection method for gas impurity concentration based on refractive index gas thermometry according to claim 1, characterized in that, In the step of calculating the theoretical refractive index of the gas mixture based on the virial coefficient model, the density of the gas mixture is solved using the virial equation of state, which is expressed as follows: in, ρ The density of the mixed gas, R The gas constant is... x This represents the mole fraction of each component.

9. The in-situ detection method for gas impurity concentration based on refractive index gas thermometry according to claim 1, characterized in that, Impurity concentration can also be detected by measuring changes in dielectric constant or permeability instead of refractive index.

10. The in-situ detection method for gas impurity concentration based on refractive index gas thermometry according to claim 1, characterized in that, The experimental refractive index was obtained using a microwave resonant cavity refractive index measurement system or an optical resonant cavity measurement system.

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