A method for measuring the thickness of low-density materials based on pXRF

Abstract

This invention discloses a pXRF-based method for measuring the thickness of low-density materials, belonging to the field of chemical analysis technology. The method includes placing a standard sample containing a specific metal element in front of the pXRF instrument's measurement window; placing several low-density target samples with different known thicknesses one by one between the standard sample and the measurement window to obtain a set of thickness values ​​and a corresponding set of element content values; using a piecewise nonlinear regression method to fit calibration curve equations of different functional forms to establish a piecewise nonlinear calibration curve; placing and measuring a low-density target sample of the same type with unknown thickness to obtain new element content values, which are then substituted into the corresponding inverse function to calculate the thickness. This invention utilizes pXRF to achieve rapid, non-destructive, and low-cost measurement of the thickness of low-density materials. It is easy to operate, can be used long-term after a single calibration, and has high measurement accuracy. It is suitable for thickness determination of homogeneous low-density materials such as films, sample bags, glass, and wood panels.

Description

Technical Field

[0001] This invention relates to the field of chemical analysis technology, and in particular to a method for measuring the thickness of low-density materials based on pXRF. Background Technology

[0002] In the field of chemical analysis, portable X-ray fluorescence (pXRF) offers numerous advantages, including non-destructive testing, speed, cost-effectiveness, and multi-element measurement, significantly reducing analysis time and testing costs. To protect the instrument and facilitate operation, pXRF measurements are typically performed with samples separated by Mylar film, plastic wrap, or directly through polyethylene bags or paper sample bags. To obtain accurate results, the thickness of these films, packaging bags, and other materials needs to be measured for thickness calibration. Furthermore, obtaining thickness data is equally important for other similar homogeneous, low-density materials, such as glass and wood.

[0003] Traditional thickness measurement methods, such as calipers, ultrasonic instruments, and lasers, are relatively cumbersome. X-ray-based methods, on the other hand, typically rely on the exponential decay law described by Beer-Lambert's law to measure thickness by measuring the change in X-ray intensity before and after penetrating the material. However, these methods require specific X-ray emitting and receiving devices, which are expensive and inconvenient for field use. Summary of the Invention

[0004] The purpose of this invention is to provide a pXRF-based method for measuring the thickness of low-density materials, thereby solving the problems mentioned in the background art and providing a portable, in-situ, non-destructive, and economical new method for accurate measurement of material thickness.

[0005] To achieve the above objectives, this invention provides a method for measuring the thickness of low-density materials based on pXRF, comprising the following steps: Step 1: Place a standard sample containing a specific metal element in front of the measurement window of the pXRF instrument, use the pXRF instrument to directly measure the element content of the metal element in the standard sample, and record the measured value as the element content value. Step 2: Place several low-density target samples with different known thicknesses one by one between the standard sample and the measurement window of the pXRF instrument, and measure the element content values ​​of specific metal elements under different known thicknesses to obtain the set of thickness values ​​and the corresponding set of element content values. Step 3: Using a piecewise nonlinear regression method, fit the set of thickness values ​​and the set of element content values. Use a change point detection algorithm to determine two thickness inflection points, divide the effective measurement thickness range into three intervals, and fit calibration curve equations of different function forms respectively. When the thickness of the low-density target sample is greater than the maximum measurable thickness, the element content value is less than the instrument detection limit, thus establishing a piecewise nonlinear calibration curve. Step 4: Place a low-density target sample of the same type with unknown thickness between the standard sample and the measurement window of the pXRF instrument, and measure the content value of the specific metal element corresponding to the low-density target sample with unknown thickness. Step 5: Based on the range of element content values ​​measured in Step 4, select the inverse function of the corresponding calibration curve equation in Step 3 to calculate the thickness value of the low-density target sample with unknown thickness.

[0006] Preferably, the thickness value of the low-density target sample with known thickness in step two is obtained by measuring any one of the following tools: vernier caliper, micrometer, or laser thickness gauge.

[0007] Preferably, the change point detection algorithm in step three is a Bayesian criterion-based inflection point search method, which determines the two thickness inflection points by minimizing the following objective function. and : ; in, For the first The known thickness of a low-density target sample This corresponds to the element content value. For the first The fitted values ​​for each segment of data are calculated using the corresponding fitting function. The first data segment contains all that satisfy... The second data segment contains all data points that satisfy the following conditions. The data points in the third segment contain all data points that satisfy the following conditions: Data points, Maximum measurable thickness; , , These represent the number of data points that fall within the first, second, and third data segments, respectively. By searching different Combination, selection The combination with the smallest value is taken as the optimal turning point.

[0008] Preferably, the fitting function corresponding to the first data segment is a logarithmic function, the fitting function corresponding to the second data segment is a power function, and the fitting function corresponding to the third data segment is an exponential function.

[0009] Preferably, the complete expression for the piecewise nonlinear calibration curve in step three is: ; in, This represents the elemental content value. For low-density target sample thickness, , , The amplitude coefficients of the logarithmic, power, and exponential functions obtained through fitting are given. For the constant term of the logarithmic function, The exponent of the power function is . For the rate parameter of the exponential function, This represents the detection limit of pXRF for a specific metal element.

[0010] Preferably, the equation of the inverse function in step five is: ; in, These are the thickness inflection points. The corresponding element content values.

[0011] Preferably, the element content value corresponding to each thickness value is the arithmetic mean of three repeated measurements.

[0012] Preferably, the standard sample is a homogeneous bulk material containing a specific metal element, which is any one of lead, cerium, lanthanum, barium, antimony, molybdenum or zirconium, and the size of the standard sample is larger than the measurement window of the pXRF instrument and the thickness is greater than 1 cm.

[0013] Preferably, low-density materials include homogeneous films, sample bags, glass, or wood panels.

[0014] Therefore, the present invention employs the above-mentioned pXRF-based method for measuring the thickness of low-density materials, which has the following beneficial effects: (1) This invention does not require complex samples or large instruments and equipment, is time-saving and cost-effective, and can complete sample preparation and measurement in a simple environment.

[0015] (2) The present invention can obtain a standard calibration curve by performing a single pXRF measurement under precise thickness control, which can be applied to the measurement of the thickness of materials of the same type with arbitrary thickness.

[0016] (3) In the measurement of materials of different thicknesses, the present invention uses the method of taking the arithmetic mean of multiple measurements to reduce the random error of a single measurement and improve the measurement accuracy; at the same time, pXRF measurement has fewer restrictions on sample state and working environment and has good universality.

[0017] (4) Based on the attenuation law of characteristic X-rays in the process of passing through the material by logarithmic function, power function and exponential function, the present invention establishes a piecewise nonlinear regression equation to realize the accurate measurement of material thickness, which is a brand-new method for measuring homogeneous low-density materials.

[0018] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0019] Figure 1 This is a flowchart of a low-density material thickness measurement method based on pXRF according to the present invention; Figure 2 This is a schematic diagram illustrating the relationship between the pXRF detector, the standard sample, and the target sample in a pXRF-based method for measuring the thickness of low-density materials according to the present invention. Figure 3 The graph shows the relationship between Pb readings and film thickness obtained using lead blocks as standard samples and polyethylene films as target samples in an embodiment of the present invention. It also shows the results of piecewise fitting of the data using logarithmic, power, and exponential functions, respectively. Figure 4 The graph shows the relationship between Pb readings and film thickness obtained using lead blocks as standard samples and polyethylene films as target samples in an embodiment of the present invention. It illustrates the results of global fitting of all data using a single logarithmic function, a single power function, and a single exponential function, respectively. Detailed Implementation

[0020] The following detailed description of embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely illustrates selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0021] Example 1 like Figure 1 As shown, this invention provides a method for measuring the thickness of low-density materials based on pXRF. The low-density materials include homogeneous films, sample bags, glass, or wooden boards. The elemental content value corresponding to each thickness value is the arithmetic mean of three repeated measurements. The method includes the following steps: Step 1: Place a standard sample containing a specific metal element in front of the measurement window of the pXRF instrument, use the pXRF instrument to directly measure the element content of the metal element in the standard sample, and record the measured value as the element content value.

[0022] The standard sample is a homogeneous bulk material containing a specific metal element, which can be any one of lead, cerium, lanthanum, barium, antimony, molybdenum or zirconium. The standard sample must be larger than the measurement window of the pXRF instrument and thicker than 1 cm.

[0023] Step 2: Place several low-density target samples with different known thicknesses one by one between the standard sample and the measurement window of the pXRF instrument, and measure the element content values ​​of specific metal elements under different known thicknesses to obtain the set of thickness values ​​and the corresponding set of element content values. The low-density target samples with known thicknesses are obtained by measuring with any one of the following tools: vernier calipers, micrometers or laser thickness gauges.

[0024] Step 3: Using a piecewise nonlinear regression method, fit the set of thickness values ​​and the set of element content values. Use a change point detection algorithm to determine two thickness inflection points, divide the effective measurement thickness range into three intervals, and fit calibration curve equations of different function forms respectively. When the thickness of the low-density target sample is greater than the maximum measurable thickness, the element content value is less than the instrument detection limit, thus establishing a piecewise nonlinear calibration curve.

[0025] The change point detection algorithm is a Bayesian criterion-based inflection point search method that determines two thickness inflection points by minimizing the following objective function. and : ; in, For the first The known thickness of a low-density target sample This corresponds to the element content value. For the first The fitted values ​​for each segment of data are calculated using the corresponding fitting function. The first data segment contains all that satisfy... The second data segment contains all data points that satisfy the following conditions. The data points in the third segment contain all data points that satisfy the following conditions: Data points, Maximum measurable thickness; , , These represent the number of data points that fall within the first, second, and third data segments, respectively. By searching different Combination, selection The combination with the smallest value is taken as the optimal turning point.

[0026] The fitting function for the first data segment is a logarithmic function, the fitting function for the second data segment is a power function, and the fitting function for the third data segment is an exponential function.

[0027] The complete expression for the piecewise nonlinear calibration curve is: ; in, This represents the elemental content value. For low-density target sample thickness, , , The amplitude coefficients of the logarithmic, power, and exponential functions obtained through fitting are given. For the constant term of the logarithmic function, The exponent of the power function is . For the rate parameter of the exponential function, This represents the detection limit of pXRF for a specific metal element.

[0028] Step 4: Place a low-density target sample of the same type with unknown thickness between the standard sample and the measurement window of the pXRF instrument, and measure the content value of the specific metal element corresponding to the low-density target sample with unknown thickness.

[0029] Step 5: Based on the range of element content values ​​measured in Step 4, select the inverse function of the corresponding calibration curve equation in Step 3 to calculate the thickness value of the low-density target sample with unknown thickness.

[0030] The equation of the inverse function is: ; in, These are the thickness inflection points. The corresponding element content values.

[0031] Example 2 This embodiment uses polyethylene film as the low-density target sample and pure lead block as the standard sample to explain the specific operation process in detail.

[0032] Step 1: Select a lead block with a purity of 99% as the standard sample. Lead is a specific metal element. The standard sample is a homogeneous block material with geometric dimensions of 2.5 cm × 2.5 cm × 1.5 cm. Its size is larger than the measurement window of the pXRF instrument, and the thickness is greater than 1 cm. Place the standard sample closely outside the measurement window of the pXRF instrument (Olympus Vanta M type portable X-ray fluorescence analyzer). Turn on the pXRF instrument, with an excitation voltage of 8 - 50 kV, a current of 5 - 200 μA, the anode material is rhodium (Rh), the measurement mode is "Geochemmode", and the single measurement time is 180 seconds. Directly measure the elemental content of lead in the standard sample. After the instrument is calibrated, the elemental content value of lead (unit: μg / g) is output, and this value is recorded as the elemental content value. The ambient temperature during measurement is 22°C, and the relative humidity is 50%. Each measurement point is measured three times repetitively, and the arithmetic mean is taken as the final reading.

[0033] Step 2: First, determine the minimum layer thickness of the polyethylene film. Take commercially available tightly compacted polyethylene films and cut 5 samples with different thicknesses all greater than 1 cm. Use a vernier caliper to measure the total thickness of each sample, and record the number of polyethylene film layers of each sample at the same time. Calculate the single-layer thickness based on the total thickness and the number of layers; the single-layer thicknesses calculated for the 5 samples are 0.0078 mm, 0.0081 mm, 0.0079 mm, 0.0080 mm, and 0.0082 mm respectively. Take the arithmetic mean as the final single-layer polyethylene film thickness value, denoted as , and a series of known thickness values can be obtained by stacking different numbers of layers. For example, 1 layer corresponds to 0.008 mm, 2 layers correspond to 0.016 mm, and so on.

[0034] Place polyethylene films with different known thicknesses one by one between the standard sample (lead block) and the measurement window of the pXRF instrument, as Figure 2 shown; start with a polyethylene film about 50 mm thick. At this time, no lead signal can be detected by the pXRF (the reading is "<LOD"); then gradually peel off the polyethylene film layer by layer until a valid reading appears. At this time, record the thickness value as the maximum measurable thickness , and measure . Subsequently, measure once every 100 layers of polyethylene film peeled off. When the remaining thickness is close to 1.5 mm, change to measure once every 1 layer peeled off until there is no polyethylene film (thickness is 0), and then directly measure the standard sample. Each thickness point is measured three times, and the arithmetic mean is taken. Obtain the set of polyethylene film thickness values and the corresponding set of elemental content values of lead ; some data are as follows: when the thickness is 0 mm, ; when the thickness is 0.245 mm, ; when the thickness is 5.00 mm, When the thickness is 42.30 mm, Approaching the instrument detection limit (LOD).

[0035] Step 3: Use a piecewise nonlinear regression method to analyze the set of thickness values. With the set of element content values A fitting process is performed, and two thickness inflection points are automatically determined using a change point detection algorithm. This embodiment employs an inflection point search method based on the Bayesian information criterion, finding the optimal inflection point by minimizing the BIC objective function. The calculation result is: First Inflection Point The corresponding Pb element content value Second turning point The corresponding Pb element content value Therefore, the effective thickness measurement range is divided into three intervals: Interval 1 Interval 2 Interval 3 .

[0036] Different functional forms of calibration curve equations were obtained by fitting the data. In this embodiment, the first segment uses a logarithmic function, the second segment uses a power function, and the third segment uses an exponential function. The piecewise nonlinear calibration curve equation obtained by fitting is as follows: ; like Figure 3 and Figure 4 As shown, the fitting coefficients for each segment are as follows: Logarithmic function segment power function segment exponential function segment All of these results are superior to the global fitting effect of a single function. When the thickness of the polyethylene film is greater than the maximum measurable thickness of 42.30 mm, the element content value is lower than the instrument detection limit and there is no effective reading.

[0037] The corresponding inverse function equation is: ; Step 4: Take a polyethylene film sample from the same batch with unknown thickness. Using the same instrument parameters and geometric conditions as in Step 2, place it between the standard sample (lead block) and the pXRF measurement window to measure the lead content. Each thickness point was measured three times, and the arithmetic mean was taken.

[0038] Step 5: and the content value of inflection point elements , By comparing and determining the relevant interval, the corresponding inverse function equation is selected to calculate the thickness, for example, by measuring... ,because Between and Therefore, the inverse power function is chosen. The calculated thickness is approximately 0.409 mm.

[0039] Measurements and calculations were performed on several polyethylene film samples with unknown thicknesses, and the results are shown in Table 1. The relative error of most predicted thicknesses was less than 5%, indicating that the method in this embodiment has high measurement accuracy.

[0040] Table 1. Predicted results and relative errors of polyethylene film thickness

[0041] Therefore, the present invention adopts the above-mentioned pXRF-based method for measuring the thickness of low-density materials. It utilizes pXRF to achieve rapid, non-destructive, and low-cost measurement of the thickness of low-density materials. It is easy to operate, can be used for a long time after one calibration, and has high measurement accuracy. It is suitable for the thickness measurement of homogeneous low-density materials such as films, sample bags, glass, and wood boards.

[0042] 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 preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for measuring the thickness of low-density materials based on pXRF, characterized in that, Includes the following steps: Step 1: Place a standard sample containing a specific metal element in front of the measurement window of the pXRF instrument, use the pXRF instrument to directly measure the element content of the metal element in the standard sample, and record the measured value as the element content value. Step 2: Place several low-density target samples with different known thicknesses one by one between the standard sample and the measurement window of the pXRF instrument, and measure the element content values ​​of specific metal elements under the target samples with different known thicknesses to obtain the set of thickness values ​​and the corresponding set of element content values. Step 3: Using a piecewise nonlinear regression method, fit the set of thickness values ​​and the set of element content values. Use a change point detection algorithm to determine two thickness inflection points, divide the effective measurement thickness range into three intervals, and fit calibration curve equations of different function forms respectively. When the thickness of the low-density target sample is greater than the maximum measurable thickness, the element content value is less than the instrument detection limit, thus establishing a piecewise nonlinear calibration curve. Step 4: Place a low-density target sample of the same type with unknown thickness between the standard sample and the measurement window of the pXRF instrument, and measure the content value of the specific metal element corresponding to the low-density target sample with unknown thickness. Step 5: Based on the range of element content values ​​measured in Step 4, select the inverse function of the corresponding calibration curve equation in Step 3 to calculate the thickness value of the low-density target sample with unknown thickness.

2. The method for measuring the thickness of low-density materials based on pXRF according to claim 1, characterized in that: In step two, the thickness value of the low-density target sample with known thickness is obtained by measuring it using any one of the following tools: vernier caliper, micrometer, or laser thickness gauge.

3. The method for measuring the thickness of low-density materials based on pXRF according to claim 1, characterized in that, The change point detection algorithm in step three is a Bayesian criterion-based inflection point search method, which determines the two thickness inflection points by minimizing the following objective function. and : ； in, For the first The known thickness of a low-density target sample This corresponds to the element content value. For the first The fitted values ​​for the segmented data are calculated using the corresponding fitting function. The first data segment contains all that satisfy... The second data segment contains all data points that satisfy the following conditions. The data points in the third segment contain all data points that satisfy the following conditions: Data points, Maximum measurable thickness; , , These represent the number of data points that fall within the first, second, and third data segments, respectively. By searching different Combination, selection The combination with the smallest value is taken as the optimal turning point.

4. The method for measuring the thickness of low-density materials based on pXRF according to claim 3, characterized in that: The fitting function for the first data segment is a logarithmic function, the fitting function for the second data segment is a power function, and the fitting function for the third data segment is an exponential function.

5. The method for measuring the thickness of low-density materials based on pXRF according to claim 4, characterized in that, The complete expression for the piecewise nonlinear calibration curve in step three is: ； in, This represents the elemental content value. For low-density target sample thickness, , , The amplitude coefficients of the logarithmic, power, and exponential functions obtained through fitting are given. For the constant term of the logarithmic function, The exponent of the power function is . For the rate parameter of the exponential function, This represents the detection limit of pXRF for a specific metal element.

6. The method for measuring the thickness of low-density materials based on pXRF according to claim 5, characterized in that, The equation of the inverse function in step five is: ； in, These are the thickness inflection points. The corresponding element content values.

7. The method for measuring the thickness of low-density materials based on pXRF according to claim 1, characterized in that: The element content value corresponding to each thickness value is the arithmetic mean of three repeated measurements.

8. The method for measuring the thickness of low-density materials based on pXRF according to claim 1, characterized in that: The standard sample is a homogeneous bulk material containing a specific metal element, which can be any one of lead, cerium, lanthanum, barium, antimony, molybdenum or zirconium. The standard sample must be larger than the measurement window of the pXRF instrument and thicker than 1 cm.

9. The method for measuring the thickness of low-density materials based on pXRF according to claim 1, characterized in that: Low-density materials include homogeneous films, sample bags, glass, or wood panels.

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