A pole piece surface density measurement method based on a double exponential model

Abstract

The application discloses a kind of based on double exponential model pole piece surface density measurement method, comprising: first, the X-ray source is started, the ray intensity when not placing pole piece is measured;Second, replace different surface density standard pole piece to be measured, and measure the ray intensity;Again, different coating surface density corresponding mass attenuation coefficient is obtained according to attenuation formula, and mass attenuation coefficient is corrected according to double exponential model calibration data;Finally, the ray intensity after measuring through the pole piece to be measured, according to the ray intensity attenuation model and the mass attenuation coefficient after calibration, the pole piece surface density measurement can be realized.This application uses the method of double exponential model to correct the mass attenuation coefficient of pole piece to realize the measurement of pole piece surface density, compared with the method of directly calibrating the measured ray intensity and standard surface density value, the problem of the influence of X-ray beam hardening and Compton scattering on pole coating surface density measurement is overcome, and the precision of pole piece surface density measurement is improved.

Description

Technical Field

[0001] This invention relates to the field of lithium battery electrode areal density measurement, specifically a method for measuring electrode areal density by calibrating the mass decay coefficient of lithium battery electrodes using a double exponential model. Background Technology

[0002] The uniformity of the areal density of lithium-ion battery electrodes directly affects the internal resistance, capacity, and safety of the battery; therefore, precise control of the areal density of the electrode coating is necessary. Currently... X-ray surface density measuring instrument, utilizing The intensity of X-rays after penetrating an object is attenuated relative to the incident X-ray intensity. This attenuation ratio has a negative exponential relationship with the surface density of the penetrated object. Therefore, the surface density of the object can be calculated by measuring the intensity of the X-rays. Currently, most lithium battery electrode surface density testers use a method of directly fitting the detected X-ray intensity value to the actual surface density value of the electrode coating. However, in practical applications, due to… The energy distribution of X-rays is continuous, and beam hardening occurs when they interact with the electrode under test. This causes the mass attenuation coefficient to be a variable rather than a fixed constant. Therefore, current measurement methods do not consider the impact of variations in the mass attenuation coefficient on areal density detection, thus affecting the accuracy of areal density measurement. Summary of the Invention

[0003] To overcome the shortcomings of existing technologies, this invention provides a method for measuring electrode surface density based on a double-exponential model, aiming to reduce the influence of ray hardening on surface density measurement, thereby improving the accuracy and reliability of lithium battery electrode surface density measurement.

[0004] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0005] This invention discloses a method for measuring electrode areal density based on a double-exponential model, which is applied in the lithium battery electrode areal density detector and includes: a high-voltage power supply, X-ray source, ionization chamber, host computer, lithium battery electrode to be tested, A lithium battery electrode to be calibrated, and the ionization chamber and the... The X-ray sources are symmetrically arranged; the lithium battery electrode is composed of a substrate and a coating; the areal density of the substrate is a known quantity, the areal density of the coating is the areal density of the lithium battery electrode, and the areal density of the lithium battery electrode to be calibrated is a known quantity. The integer is a positive integer not less than 6, characterized in that the measurement method includes the following steps:

[0006] Step 1: The high-voltage power supply supplies power to the... The anode input of the radiation source is used for control. DC high voltage to the X-ray source The cathode of the X-ray source is inputted for control Adjustable AC current to the X-ray spectrum distribution; so that the X-ray source outputs initial X-rays matching the high voltage power supply

[0007] Step 2, the ionization chamber obtains the intensity of the initial X-rays and the intensity of the X-rays after passing through the lithium battery pole piece to be calibrated, and transmits to the upper computer Step 3, the upper computer constructs the X-ray intensity model according to the intensity of the initial X-rays

[0008] and the intensity of the X-rays after passing through the lithium battery pole piece to be calibrated, using formula (1) Step 4, according to the X-ray intensity model, the mass attenuation coefficients of the lithium battery pole pieces to be calibrated are obtained

[0009] (1)

[0010] In formula (1), is the intensity of the X-rays after passing through the i-th lithium battery pole piece to be calibrated, is a positive integer not greater than i, is the mass attenuation coefficient of the i-th lithium battery pole piece to be calibrated, is the density of the coating of the i-th lithium battery pole piece to be calibrated, is the thickness of the coating of the i-th lithium battery pole piece to be calibrated, is the area density of the coating of the i-th lithium battery pole piece to be calibrated, denotes the density of the substrate of the lithium battery pole piece, denotes the thickness of the substrate of the lithium battery pole piece, is the area density of the substrate of the lithium battery pole piece, is a natural constant; Step 4, according to the X-ray intensity model, the mass attenuation coefficients of the lithium battery pole pieces to be calibrated are obtained

[0011] Step 4, according to the X-ray intensity model, the mass attenuation coefficients of the lithium battery pole pieces to be calibrated are obtained

[0012] Step 5, the mass attenuation coefficients of the lithium battery pole pieces to be calibrated are obtained ​​​​​​​​​​​​​​​​The corrected mass attenuation coefficient is obtained by performing correction. ;

[0013] Step 6: Measure the lithium battery electrode to be tested to obtain the intensity value of the radiation transmitted through the electrode. ;

[0014] Step 7: Use equation (2) to obtain the coating areal density of the lithium battery electrode to be tested. :

[0015] (2)

[0016] In equation (2), The density of the coating on the lithium battery electrode to be tested. The thickness of the coating on the lithium battery electrode to be tested. This represents the areal density of the coating on the lithium battery electrode to be tested.

[0017] The method for measuring the areal density of pole pieces based on a double-exponential model described in this invention is also characterized in that step 5 includes:

[0018] Step 5.1: Obtain using equation (3) The total areal density of the lithium battery electrode to be calibrated :

[0019] (3)

[0020] In equation (3), for The thickness of the coating on the lithium battery electrode to be calibrated; express The density value of a lithium battery electrode to be calibrated. express The thickness of the lithium battery electrode to be calibrated;

[0021] Step 5.2: Use the double exponential model described in equation (4) to... The mass decay coefficient of a lithium battery electrode to be calibrated The corrected mass attenuation coefficient is obtained by performing correction. :

[0022] (4)

[0023] In equation (4), All have 6 calibration parameters.

[0024] The electronic device comprises a memory and a processor, and is characterized in that the memory is used for storing a program supporting the processor to execute the pole piece surface density measurement method, and the processor is configured to execute the program stored in the memory.

[0025] The computer readable storage medium stores a computer program, and the computer program is executed by a processor to execute the steps of the pole piece surface density measurement method.

[0026] Compared with the prior art, the beneficial effects of the present application are reflected in that:

[0027] 1. Compared with the traditional surface density detector calibration method which needs manual stamping sampling to determine the surface density value of the sample, the method of using the standard surface density pole piece to be calibrated improves the timeliness of the calibration method and saves the pole piece surface density measurement time and labor cost.

[0028] 2. Compared with the measurement method of directly linearly fitting the relationship between the ray intensity attenuation value and the surface density, the present application considers the influence of the ray hardening phenomenon on the mass attenuation coefficient in the calibration process, corrects the influence of the ray hardening phenomenon on the pole piece surface density measurement result, and improves the reliability of the surface density detection.

[0029] 3. Compared with the calibration method of performing polynomial fitting model on the relationship between the ray intensity attenuation value and the surface density, the present application requires relatively fewer parameters, which is convenient for solving the calibration parameters.

[0030] 4. The measurement method of using a double exponential model to correct the mass attenuation coefficient of the to-be-measured pole piece effectively reduces the influence of the interaction between multi-energy rays and matter on the pole piece surface density measurement result, and therefore has high measurement accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 It is a schematic diagram of a lithium battery pole piece surface density detector in the present application.

[0032] Figure 2 It is a flowchart of the method of the present application.

[0033] Figure 3 It is a schematic diagram of the ray hardening effect.

[0034] Figure 4 It is a schematic diagram of the ray hardening effect curve in the surface density detection in the present application. DETAILED DESCRIPTION

[0035] In this embodiment, a pole piece surface density measurement method based on a double exponential model is applied to a lithium battery pole piece surface density detector, such as the lithium battery pole piece surface density detector shown in FIG. 1. Figure 1 ​As shown, it includes: high-voltage power supply, X-ray source, ionization chamber, host computer, lithium battery electrode to be tested, A lithium battery electrode to be calibrated, and the ionization chamber and The X-ray source is symmetrically arranged; the lithium battery electrode consists of a substrate and a coating; the areal density of the substrate is known, the areal density of the coating is the areal density of the lithium battery electrode, and the areal density of the lithium battery electrode to be calibrated is also known. The value is a positive integer not less than 6. The measurement method involves calibrating the lithium battery electrode to be calibrated using the areal density value and the measured radiation intensity value during the calibration process of the areal density detector. This allows for the correction of the mass decay coefficient of the lithium battery electrode to be calibrated using a double exponential model. The areal density value of the electrode to be tested is then calculated using the calibrated mass decay coefficient and the measured radiation intensity value passing through the electrode. Specifically, for example... Figure 2 As shown, the method is performed according to the following steps:

[0036] Step 1: The high-voltage power supply is directed to... The anode input of the radiation source is used for control. A DC high voltage with high radiation intensity, directed towards The cathode input of the radiation source is used for control. A tunable alternating current with a variable X-ray energy spectrum distribution; thus enabling Initial matching of X-ray source output with high-voltage power supply ray;

[0037] Step 2: Obtain initial ionization chamber intensity of rays as well as The ray source passes through After the lithium battery electrode to be calibrated The intensity of the radiation is measured and transmitted to the host computer. Through analysis... The areal density of the electrode is indirectly measured by the degree of intensity attenuation of the radiation, while the initial... The intensity of radiation can avoid interference from ambient radiation during measurement, thus ensuring the accuracy of the measurement to the greatest extent.

[0038] Step 3: The host computer calculates the initial... Intensity of rays and the process The intensity of the radiation behind the lithium battery electrode to be calibrated is constructed using equation (1). Ray intensity model;

[0039] (1)

[0040] In equation (1), For the first The radiation intensity behind the lithium battery electrode to be calibrated. Not greater than positive integers, For the first The mass degradation coefficient of a lithium battery electrode to be calibrated. For the first The density of the coating on a lithium battery electrode to be calibrated. For the first The thickness of the coating on the lithium battery electrode to be calibrated. For the first The areal density of the coating of a lithium battery electrode to be calibrated. This indicates the density of the substrate used in lithium-ion battery electrodes. This indicates the thickness of the substrate used in lithium-ion battery electrodes. The areal density of the substrate for lithium battery electrodes, wherein... Given a value This is a natural constant. It allows us to obtain the corresponding ray intensity under a lithium battery electrode with a known areal density, preparing for subsequent correction of the mass decay coefficient.

[0041] exist The theoretical basis for correcting the mass attenuation coefficient in a X-ray surface density measuring instrument is: mass attenuation coefficient This measures the probability of absorption per gram of absorbing material per square centimeter of X-ray beam. In the X-ray surface density measurement system, It can be represented as:

[0042] (2)

[0043] In formula (2): The electron density of the object, The cross section of the electron photoelectric effect. The Compton effect cross section of the electron. This is the density of the object.

[0044] Electron density of an object and object density Not following The cross section of the photoelectric effect changes with the energy of the photon. and Compton effect cross section All The total cross-section decreases as photon energy increases. Follow The mass line attenuation coefficient decreases as photon energy increases. Follow The energy of a photon decreases as its energy increases; that is, the energy decreases as its energy increases. Photons interact more readily with electrons in an object. When the object is irradiated by the rays, the low-energy photons are easily absorbed by the object, so that the proportion of low-energy photons in the transmitted photons decreases, the proportion of high-energy photons increases, the average energy of the beam increases, the peak of the energy spectrum moves to the right (the energy spectrum becomes hard), that is, the beam hardening effect occurs, as shown in Figure 3 .

[0045] In an ideal case, the mass attenuation coefficient of the measured substance can be expressed as:

[0046] (3)

[0047] In formula (3), N represents the Avogadro constant, h represents the Planck constant, c represents the speed of light, A represents the relative atomic mass, K represents a constant, Z represents the atomic number of the absorbing element, λ represents the wavelength of the incident rays, E represents the energy of the incident rays. Due to the beam hardening effect, the energy of the transmitted rays increases, and the wavelength decreases, thereby causing the mass attenuation coefficient to decrease. Therefore, when measuring the area density of the plate, the mass attenuation coefficient must be corrected to obtain a more accurate measurement result in the measurement.

[0048] For the continuous spectrum of the ray intensity, it should be:

[0049] (4)

[0050] In formula (4), S represents the spectrum of the incident rays, E represents the peak energy, and the calculated is the initial ray intensity.

[0051] Therefore, the logarithmic attenuation of the ray intensity during the measurement can be expressed as:

[0052] (5)

[0053] wherein, ρ represents the density of the measured object, t represents the thickness of the measured object, μ represents the area density of the measured object, μ represents the mass attenuation coefficient thereof, ​​​​​​After passing through the object to be tested As for the radiation intensity, the logarithmic decay of the radiation intensity can be seen from the above formula. areal density A monotonically increasing function, that is, as the surface density increases... As the value increases, logarithmic decay occurs. The larger it is. Then compare its density to the surface density. Differentiation yields:

[0054] (6)

[0055] The logarithmic attenuation value of the ray intensity can be obtained with respect to the surface density. The monotonically decreasing function, that is, as the surface density of the measured object increases... As the value increases, logarithmic decay occurs. The rate of increase gradually decreases, such as Figure 4 As shown.

[0056] As can be seen from equation (1), the slope of the curve showing the logarithmic attenuation of radiation intensity as a function of surface density represents the mass attenuation coefficient of the electrode under test. The areal density is affected by changes in surface density, specifically by the effect of ray hardening during the measurement process, which leads to a change in the mass attenuation coefficient. Therefore, for areal density detection, due to... The existence of radiation hardening causes photons of different energies to exhibit different attenuation rates when penetrating objects; that is, low-energy photons attenuate faster when penetrating thicker materials, while high-energy photons attenuate relatively slower. This different attenuation rate can be described by a double exponential decay model, which considers two different attenuation constants and their corresponding amplitudes in the model to more accurately reflect the physical phenomena in the actual detection process.

[0057] Therefore, in order to satisfy the above equations (5) and (6) for the continuous spectrum Theoretical derivation of the variation of ray intensity with surface density and consideration of ray hardening phenomenon occurring when photons of different energies penetrate objects are presented. A double-exponential model correction method for the mass attenuation coefficient is proposed, namely:

[0058] (7)

[0059] In equation (7), These represent the attenuation constant and amplitude value of photons with lower and higher energies, respectively.

[0060] Step 4, according to The ray intensity model yields... That is, to obtain The mass decay coefficient of a lithium battery electrode to be calibrated ;

[0061] Step 5.1, obtaining the total area density of the lithium battery pole piece to be calibrated by using formula (8) ; ;

[0062] Step 5.1, obtaining the total area density of the lithium battery pole piece to be calibrated by using formula (8) : :

[0063] (8)

[0064] In formula (8), is the thickness of the coating of the lithium battery pole piece to be calibrated; represents the density value of the lithium battery pole piece to be calibrated, represents the thickness of the lithium battery pole piece to be calibrated. Step 5.2, correcting the mass attenuation coefficient of the lithium battery pole piece to be calibrated by using the double exponential model of formula (9), which considers the influence of the hardening of the rays on the mass attenuation coefficient, corrects the influence of the hardening of the rays on the measurement results, improves the reliability of the area density detection, and corrects the mass attenuation coefficient :

[0065] :

[0066] (9)

[0067] In formula (9), all are 6 correction parameters, respectively representing the attenuation constants and amplitude values of the lower-energy photons and the higher-energy photons;

[0068] The parameter solving of the mass attenuation coefficient of the double exponential model is a nonlinear curve fitting problem, and the data of the mass attenuation coefficient corresponding to the 6 area densities are substituted into the double exponential model formula (9). The optimal solution is found by iteratively searching the parameter space, that is, the residual sum of squares is minimized, so as to obtain the parameters of the attenuation constants and amplitude values of the lower-energy photons and the higher-energy photons .

[0069] Step 6, measuring the lithium battery pole piece to be measured to obtain the ray intensity value after the lithium battery pole piece to be measured is transmitted ;

[0070] ​​​​​​​​Step 7, using formula (10) to obtain the coating area density of the lithium battery pole piece to be tested :

[0071] (10)

[0072] In formula (10), is the density of the coating of the lithium battery pole piece to be tested, is the thickness of the coating of the lithium battery pole piece to be tested, is the area density of the coating of the lithium battery pole piece to be tested.

[0073] In this embodiment, an electronic device includes a memory for storing a program supporting the processor to execute the above method, and a processor configured to execute the program stored in the memory.

[0074] In this embodiment, a computer readable storage medium has a computer program stored thereon, and the computer program is run by a processor to execute the steps of the above method.

Claims

1. A method for measuring electrode areal density based on a double-exponential model, applied in a lithium battery electrode areal density detector, comprising: High voltage power supply X-ray source, ionization chamber, host computer, lithium battery electrode to be tested, A lithium battery electrode to be calibrated, and the ionization chamber and the... The X-ray sources are symmetrically arranged; the lithium battery electrode is composed of a substrate and a coating; the areal density of the substrate is a known quantity, the areal density of the coating is the areal density of the lithium battery electrode, and the areal density of the lithium battery electrode to be calibrated is a known quantity. The value is a positive integer not less than 6, characterized in that the measurement method includes the following steps: Step 1: The high-voltage power supply supplies power to the... The anode input of the radiation source is used for control. A DC high voltage with high radiation intensity, directed towards The cathode input of the radiation source is used for control. A tunable alternating current with a variable X-ray energy spectrum distribution; thereby enabling the... The initial output of the radiation source is matched with the high-voltage power supply. ray; Step 2: The ionization chamber obtains the initial... Intensity of rays and the The ray source passes through After the lithium battery electrode to be calibrated The intensity of the radiation is measured and transmitted to the host computer. Step 3: The host computer, based on the initial... Intensity of rays and the process The intensity of the radiation behind the lithium battery electrode to be calibrated is constructed using equation (1). Ray intensity model; (1) In equation (1), For the first The radiation intensity behind the lithium battery electrode to be calibrated. Not greater than positive integers, For the first The mass degradation coefficient of a lithium battery electrode to be calibrated. For the first The density of the coating on a lithium battery electrode to be calibrated. For the first The thickness of the coating on the lithium battery electrode to be calibrated. For the first The areal density of the coating of a lithium battery electrode to be calibrated. This indicates the density of the substrate used in lithium-ion battery electrodes. This indicates the thickness of the substrate used in lithium-ion battery electrodes. The areal density of the substrate for lithium battery electrodes. It is a natural constant; Step 4, according to The ray intensity model yields... The mass decay coefficient of a lithium battery electrode to be calibrated ; Step 5, for The corrected mass attenuation coefficient is obtained by performing correction. ; Step 6: Measure the lithium battery electrode to be tested to obtain the intensity value of the radiation transmitted through the electrode. ; Step 7: Use equation (2) to obtain the coating areal density of the lithium battery electrode to be tested. : (2) In equation (2), The density of the coating on the lithium battery electrode to be tested. The thickness of the coating on the lithium battery electrode to be tested. This represents the areal density of the coating on the lithium battery electrode to be tested.

2. The method for measuring the areal density of pole pieces based on a double-exponential model according to claim 1, characterized in that, Step 5 includes: Step 5.1: Obtain using equation (3) The total areal density of the lithium battery electrode to be calibrated : (3) In equation (3), for The thickness of the coating on the lithium battery electrode to be calibrated; express The density value of a lithium battery electrode to be calibrated. express The thickness of the lithium battery electrode to be calibrated; Step 5.2: Use the double exponential model described in equation (4) to... The mass decay coefficient of a lithium battery electrode to be calibrated The corrected mass attenuation coefficient is obtained by performing correction. : (4) In equation (4), All have 6 calibration parameters.

3. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports the processor in executing the pole sheet areal density measurement method of claim 1 or 2, and the processor is configured to execute the program stored in the memory.

4. A computer-readable storage medium storing a computer program thereon, characterized in that, The computer program is executed by the processor to perform the steps of the electrode surface density measurement method according to claim 1 or 2.

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