A method for calculating the grain size of nanomaterials

Abstract

The application discloses a kind of suitable for the calculation method of nanometer material grain size, belong to grain size measurement technical field.The application obtains diffraction peak half-height width and instrument half-height width by selecting two different target materials for X-ray diffraction measurement, then respectively according to peak shape follows Cauchy function distribution and Gaussian function distribution calculation, the sample half-height width of two distributions is respectively substituted into Scherrer formula to calculate nanometer grain size, compare the size of deviation, to determine the calculation mode of nanometer material grain size, the material grain size accuracy of the grain size calculation method is high, solves the problem of big result deviation of traditional nanometer material grain size measurement.

Description

Technical Field

[0001] This invention belongs to the field of grain size measurement technology, specifically relating to a method for calculating the grain size of nanomaterials. Background Technology

[0002] Currently, most methods for calculating nanocrystal size involve observing particle diameter, which cannot accurately determine the nanocrystal size. For example, SEM can only detect the grain size at local locations in the material, lacking representativeness. X-ray diffraction can more accurately calculate the average nanocrystal size, with the most commonly used methods being the Hall method and the Hall deformation method. However, for the same nanomaterial, the nanocrystal size results obtained by the two methods differ significantly. Huang Jiwu et al. pointed out that when the peak shape follows a Cauchy function, the Hall method can be used to calculate the nanocrystal size; when the peak shape follows a Gaussian function, the Hall deformation method can be used. However, it is difficult to intuitively determine which distribution the diffraction peak shape should follow from the diffraction peak shape. Directly using Gaussian or Cauchy functions to fit the peak shape and observe the residuals is also subject to interference from many factors such as measurement factors, function factors, and instrument configuration, leading to inaccurate measurements of nanomaterial grain size. Summary of the Invention

[0003] In view of the shortcomings of the prior art, the present invention provides a method for calculating the grain size of nanomaterials, which can improve the accuracy of measuring and calculating the grain size of nanomaterials.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A method for calculating the grain size of nanomaterials includes the following steps:

[0006] (1) X-ray diffraction analysis was performed on the nanomaterials using Cu targets and targets of other materials to obtain X-ray diffraction patterns. The full width at half maximum (FWHM) of the diffraction peaks was measured based on the 2θ position provided by the X-ray diffraction patterns and denoted as B. Cu B 其他 Then, select a standard sample to measure the half-width b of the instrument.

[0007] (2) Take the B obtained in step (1) Cu B 其他 Given the instrument's half-width at half-maximum (WHM) b, and according to formula (1): β = Bb, the sample's WHM β is obtained. Cu -1, β 其他 -1.

[0008] (3) Take the B obtained in step (1) Cu B 其他 And the instrument's half-height and width b, according to formula (2): The full width at half maximum (FWHM) β of the samples were obtained respectively.Cu -2, β 其他 -2; in formula (1) and formula (2), β is a sample half width, B is a diffraction peak half width, and b is an instrument half width.

[0009] (4) a sample half width β Cu -1, β 其他 -1, β Cu -2, β 其他 -2, according to formula (3): D=Kλ / βcosθ, grain sizes D Cu -1, D 其他 -1, D Cu -2, D 其他 -2; in formula (3), K is a Scherrer constant, λ is a wavelength of X-rays, β is a sample half width, and D is a grain size.

[0010] (5) a grain size D Cu -1 and D 其他 -1, a grain size D Cu -2 and D 其他 -2 according to formula (4): to obtain calculation deviations δ1 and δ2 respectively; in formula (4), δ is a grain size deviation; D Cu is a grain size of a nanomaterial under a copper target; and Dother is a grain size of a nanomaterial under other target materials.

[0011] (6) when δ1<δ2, a grain size of a nanomaterial is formula (5): (B-b)cosθ / λ=1 / D+4εsinθ / λ;

[0012] when δ1≥δ2, a grain size of a nanomaterial is formula (6):

[0013] in formula (5)-(6), B is a half width of a diffraction peak, b is an instrument half width, λ is a wavelength of X-rays, D is a grain size of a nanomaterial, and ε is a micro strain.

[0014] As a preferred embodiment of the present application, the nanomaterial is a nanomaterial with a grain size of less than 100 nm.

[0015] As a preferred embodiment of the present application, the target material of other materials can be any target material commonly used in the art.

[0016] As a preferred embodiment of the present application, the standard sample is a standard sample commonly used for XRD testing in the art, and is generally selected from a completely annealed material with stable structure, no grain refinement, no macro stress or micro stress, and no distortion.

[0017] As a preferred embodiment of the present application, the sample half-height width is in radian system, and the conversion formula is (β / 180)π.

[0018] Compared with the prior art, the present application has the following beneficial effects: the present application selects two different target materials for X-ray diffraction measurement, obtains diffraction peak half-height width and instrument half-height width, then respectively calculates according to the peak shape following Cauchy function distribution and Gaussian function distribution, substitutes the sample half-height width in the two distributions into the Scherrer formula to calculate the nanocrystalline grain size, compares the deviation, and determines the calculation method of the nanomaterial grain size, the grain size obtained by the calculation method suitable for the nanomaterial grain size is accurate, and the problem of large result deviation in the traditional nanomaterial grain size calculation is solved. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 Fig. 1 is the XRD diffraction graph of TiO2 and Si under the Cu target in Example 1 of the present application, and the XRD graphs of TiO2, TiO2 standard card, Si and Si standard card are from top to bottom.

[0020] Figure 2 Fig. 2 is the XRD diffraction graph of TiO2 and Si under the Ag target in Example 1 of the present application, and the XRD graphs of TiO2, TiO2 standard card, Si and Si standard card are from top to bottom. DETAILED DESCRIPTION

[0021] In order to better illustrate the purpose, technical scheme and advantages of the present application, the present application will be further described below in combination with specific examples.

[0022] Example 1

[0023] A calculation method suitable for nanomaterial grain size, comprising the following steps:

[0024] (1) obtaining half-height width: a certain amount of TiO2 nanometer powder is weighed, X-ray diffraction measurement is carried out on the X-ray diffractometer by selecting Cu target and Ag target to obtain the X-ray diffraction graphs of Figure 1 and Figure 2 , the selected diffraction peak is fitted, the 2θ position corresponding to the diffraction peak is obtained, and the diffraction peak half-height width is measured, and the instrument half-height width is measured by taking silicon powder as a standard sample.

[0025] In this embodiment, the TiO2 diffraction peak 2θ is selected to be 25.311° and 9.175° under the conditions of Cu target and Ag target, the measured half-height width B of the TiO2 diffraction peak obtained after fitting under the conditions of Cu target and Ag target is 0.373° and 0.326° respectively, and the instrument half-height width b is 0.135° and 0.242° respectively, as shown in Table 1.

[0026] Table 1 Sample half-width and instrument half-width table

[0027]

[0028] B(rad) is the sample half-width in radian, b(rad) is the instrument half-width in radian. The half-width is converted to radian, and the radian conversion formula is (β / 180)π. The sample half-width and instrument half-width are 0.006510 rad and 0.002356 rad under the Cu target condition, and the measured sample half-width and instrument half-width are 0.005689 rad and 0.004224 rad under the Ag target condition.

[0029] (2) Calculate the sample half-width:

[0030] In this embodiment, the diffraction peak at the position of 2θ of 25.311° and 9.175° under the Cu target and Ag target conditions is selected for TiO2, and the half-width unit is converted to radian.

[0031] ①The half-width values obtained under the Cu target and Ag target conditions are respectively brought into formula (1) to calculate, and the sample half-widths of the diffraction peak peak shape conforming to the Cauchy function under two different target material conditions are obtained, that is, β Cu -1, β Ag -1:

[0032] α=B-b (1)

[0033] The diffraction peak peak shape of formula (1) conforms to the Cauchy distribution; β is the sample half-width; B is the measured half-width of the diffraction peak, and b is the instrument half-width.

[0034] ②The half-width values obtained under the Cu target and Ag target conditions are respectively brought into formula (2) to calculate, and the sample half-widths of the diffraction peak peak shape conforming to the Gaussian function under two different target material conditions are obtained, that is, β Cu -2, β Ag -2:

[0035]

[0036] The diffraction peak peak shape of formula (2) conforms to the Gaussian distribution; β is the sample half-width; B is the measured half-width of the diffraction peak, and b is the instrument half-width.

[0037] As shown in Table 2:

[0038] Table 2 TiO2 sample half-width table

[0039]

[0040] β-1 is the sample half-width calculated by substituting the half-width value into formula (1), and β-2 is the sample half-width calculated by substituting the half-width value into formula (2). In this embodiment, when the peak shape follows the Cauchy function, the sample half-width β Cu -1 is 0.004154 rad, and the sample half-width β Ag -1 is 0.001466 rad; and the sample half-width β Cu -2 is 0.006069 rad, and the sample half-width β Ag -2 is 0.003812 rad.

[0041] (3) Calculate the nanocrystal size:

[0042] ①Substitute the sample half-width β Cu -1 and β Ag -1 into formula (3) respectively to calculate the nanomaterial crystal size D Cu -1 and D Ag -1 under the conditions of two different target materials.

[0043] D = Kλ / βcosθ (3)

[0044] In formula (3), K is the Scherre constant, which is 0.89; λ is the wavelength of X-ray (λ Cu = 0.15406 nm; λ Ag = 0.05594 nm); and β is the sample half-width calculated in step (2), rad.

[0045] ②Substitute the sample half-width β Cu -2 and β Ag -2 into formula (3) respectively to calculate the nanomaterial crystal size D Cu -2 and D Ag -2 under the conditions of two different target materials.

[0046] As shown in Table 3:

[0047] Table 3 TiO2 Crystal Size Table

[0048]

[0049] D-1 is the nanomaterial crystal size obtained by substituting the sample half-width β Cu -1 and β Ag -1 into formula (3) respectively, and D-2 is the nanomaterial crystal size obtained by substituting the sample half-width β Cu -2 and β Ag-2 respectively into equation (3) to obtain the nanomaterial grain size. In this embodiment, the grain size is calculated by equation (3), and the TiO2 grain size D Cu -1 is 33.8295 nm, and the TiO2 grain size D Ag -1 is 34.0688 nm; the TiO2 grain size D Cu -2 is 23.1554 nm, and the TiO2 grain size under the Ag target is 13.1015 nm.

[0050] (4) Calculate and compare the deviation size:

[0051] Substitute the nanocrystalline grain sizes obtained according to equation (3) into the following equation (4) to calculate the deviation of the peak shapes of the diffraction peaks under two different target conditions:

[0052]

[0053] In equation (4), δ is the grain size deviation; D Cu is the nanocrystalline grain size under the copper target; D 其他 is the nanocrystalline grain size under other target materials (silver target is selected in this embodiment).

[0054] The nanocrystalline grain size deviation results are as follows:

[0055]

[0056]

[0057] Compare δ1 and δ2 respectively, and according to the calculation results, the nanocrystalline grain size deviation δ1 is only 0.7073%, while the nanocrystalline grain size deviation δ2 is 43.4191%; therefore, the nanocrystalline grain size deviation δ1 is smaller, and therefore, the nanocrystalline grain size calculated by equation (B-b) cosθ / λ = 1 / D + 4εsinθ / λ is more accurate. Taking βcosθ / λ as the vertical coordinate and sinθ / λ as the horizontal coordinate, the intercept is 0.02631 and the slope is 1.4221, and ε is the microstrain, so the average nanocrystalline grain size of the sample is 38.0107 nm. Because the average nanocrystalline grain size is stable, in this embodiment, the calculation result is more stable when the half-height width of the sample follows the Cauchy function distribution, and the nanocrystalline grain size calculated by equation (B-b) cosθ / λ = 1 / D + 4εsinθ / λ is more accurate.

[0058] Comparative Example 1

[0059] A certain amount of TiO2 nano powder is weighed, and the sample is measured and analyzed on an X-ray diffractometer using a Cu target. The TiO2 grain size is calculated to be 33.8295 nm when the peak shape follows the Cauchy function according to the Scherrer formula, i.e., formula (3). When the peak shape follows the Gaussian function, the TiO2 grain size is 23.1554 nm according to formula (3). The calculation results differ greatly, and it cannot be determined whether it is the real value of the nano grain size.

[0060] The deviation is smaller when the peak shape of Example 1 of the present application follows the Cauchy distribution. The nano grain size of 38.0107 nm calculated by formula (B-b)cosθ / λ=1 / D+4εsinθ / λ is closer to the nano grain size of 33.8295 nm calculated by formula (3) of Comparative Example 1, further verifying that the calculation method of the present application for the nano material grain size improves the accuracy of calculating the nano grain size.

[0061] Finally, it should be noted that the above examples are only used to illustrate the technical solutions of the present application and not to limit the scope of protection of the present application. Although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or replaced by equivalents without departing from the essence and scope of the technical solutions of the present application.

Claims

1. A method for calculating the grain size of nanomaterials, characterized in that, Includes the following steps: (1) X-ray diffraction analysis was performed on the nanomaterials using Cu targets and targets of other materials to obtain X-ray diffraction patterns. The full width at half maximum (FWHM) of the diffraction peaks was measured based on the 2θ position provided by the X-ray diffraction patterns and denoted as B. Cu B 其他 Then, select a standard sample to measure the half-width (b) of the instrument. (2) Take the B obtained in step (1) Cu B 其他 Given the instrument's half-width at half-maximum (WHM) b, and according to formula (1): β = Bb, the sample's WHM β is obtained. Cu -1, β 其他 -1; (3) Take the B obtained in step (1) Cu B 其他 And the instrument's half-height and width b, according to formula (2): The full width at half maximum (FWHM) β of the samples were obtained respectively. Cu -2, β 其他 -2; In equations (1) and (2), β is the sample half-width at half maximum (FWHM), B is the diffraction peak half-width at half maximum (FWHM), and b is the instrument half-width at half maximum (FWHM); (4) Set the sample half-width β Cu -1, β 其他 -1, β Cu -2, β 其他 -2, according to formula (3): D=Kλ / βcosθ, the grain size D is obtained respectively. Cu -1、D 其他 -1、D Cu -2、D 其他 -2; where in equation (3), K is the Scherrer constant, λ is the wavelength of the X-ray, β is the full width at half maximum (FWHM) of the sample, and D is the grain size; (5) The grain size D Cu -1 and D 其他 -1. Grain size D Cu -2 and D 其他 -2 according to equation (4): The calculated deviations δ1 and δ2 are obtained respectively; in equation (4), δ is the grain size deviation; D Cu D represents the grain size of nanomaterials under a copper target; D other represents the grain size of nanomaterials under other target materials. (6) When δ1 < δ2, the grain size of the nanomaterial is given by formula (5): (Bb)cosθ / λ = 1 / D + 4εsinθ / λ; When δ1≥δ2, the grain size of the nanomaterial is given by formula (6): In equations (5)-(6), B is the half-width at half maximum (WHM) of the diffraction peak, b is the instrument half-width at half maximum (WHM), λ is the wavelength of the X-ray, D is the grain size of the nanomaterial, and ε is the microstrain.

2. The method for calculating the grain size of nanomaterials as described in claim 1, characterized in that, The nanomaterials are nanomaterials with a grain size of less than 100 nm.

3. The method for calculating the grain size of nanomaterials as described in claim 1, characterized in that, The half-width at half-maximum of the sample is in radians, and the radian conversion formula is (β / 180)π.

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