Bremsstrahlung produced by the interaction between electron beam and sample constitutes X-ray continuous spectrum, which is the main background source that cannot be ignored and inevitable in X-ray measurement. Therefore, the background count caused by continuous spectrum must be deducted from the characteristic X-ray counting rate measured by experiments, that is, the background must be corrected. The energy distribution formula of continuous spectral intensity is:
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Where: I(E) is the average intensity of the continuous spectrum generated by each incident electron in the unit energy interval; Z is the atomic number; E0 is the energy of incident electrons; K0, K 1 and K2 are constants related to z and E0.
The background of energy spectrum analysis is high and the peak back is low, so the background value can be accurately calculated by Lifshin formula.
The peak-to-back ratio of high-content elements determined by spectral analysis is usually very high, and the background correction can sometimes be ignored. When determining low-content elements, it is necessary to accurately measure the background value. There are several ways to determine the background.
1) If the background intensity is a linear function of X-ray wavelength, measure the background value at the positions of 1nm or 2 Bragg angle on both sides of the spectral peak, and the average value is the background of the center of the spectral peak, as shown in Figure 89.6(a).
2) If there is no linear relationship between the background intensity and the wavelength, the background values of two or more points are usually measured on both sides of the spectral peak, and then the background trajectory is drawn to directly read the background intensity data of the peak position, as shown in Figure 89.6(b).
3) When testing multicomponent samples, it is often difficult to choose a suitable location measurement background because of the complex spectral lines. The background can be measured by the pure element standard sample corresponding to each component in the sample, and then one component in the sample can be calculated by the following formula.
Fig. 89.6 Relationship between background intensity and X-ray wavelength
Background intensity of BA:
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Where: B'A is the background measured at a position deviating from the peak wavelength of element A on pure element A; WA is the assumed content of element A in the sample; Bi is the background value measured by adjusting the spectrometer to the characteristic peak position of element A on pure element Bi (except element A); Wi is the assumed content of element I in the sample.
89.2. 1.2 dead time correction
Dead time refers to a period of time after a pulse arrives at the counting system, and the technical system no longer records the pulse that continues to arrive (like "dead"). The counting system of each electron probe has its own unique dead time. "Dead time makes some X-ray pulses miss, resulting in loss of counting; And the higher the counting rate, the higher the counting loss caused by dead time. In electron probe analysis, the characteristic X-ray counting rates of samples and standard samples are different, sometimes even several orders of magnitude, so it is necessary to correct the dead time. The usual dead-time correction formula is:
Investigation and analysis technology of resources and environment in the fourth volume of rock mineral analysis
Where: n' is the actually measured counting rate; N is the counting rate after dead time correction.
Here are some methods to determine the dead time.
(1) beam method
In electron probe analysis, the x-ray counting rate n is proportional to the beam current I:
Investigation and analysis technology of resources and environment in the fourth volume of rock mineral analysis
According to Formula (89.3) and Formula (89.4):
Investigation and analysis technology of resources and environment in the fourth volume of rock mineral analysis
Drawing n' from n'/i means that the intercept of the curve is k and the slope is k ",so you can get the dead time".
Or randomly select two beam values i 1 and i2, and measure the corresponding counting rates n' 1 and n'2 respectively, and obtain according to formula (89.5):
Investigation and analysis technology of resources and environment in the fourth volume of rock mineral analysis
To solve this simultaneous equation:
Investigation and analysis technology of resources and environment in the fourth volume of rock mineral analysis
(2) Different spectral line method
Select a pair of characteristic X-rays of elements whose intensity ratio is about 6∶ 1, such as FeKα and FeKβ, and determine the dead time according to the following steps.
A. adjust the beam so that the counting rate of Kα line (Nα 1) is about 1000 and that of Kβ line (Nβ 1) is about 150. At this time, the influence of dead time can be ignored, and the proportional relationship between Kα and Kβ line counting rate is nα 65438+.
B, appropriately increasing the beam current so that the counting rate of Kβ Nβ2 is about1000; At the same time, the counting rate (Nα2) of Kα is determined. At this time, it can be approximated as follows: Nβ2 (true) = nβ 2; However, because Nα2 is quite high, the influence of dead time cannot be ignored, so Nα (real) =Nα2( 1-Nα2 ").
C according to x-ray physics, when the beam current changes, the relative ratio of the spectral line intensities of Kα and Kβ of the same element should remain unchanged, that is, Nα2 (true) = nβ 2 nα 1/nβ 1, from which it is concluded that:
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(3) Standard sample method
Select a pair of standard samples containing an element, such as metallic iron (Fe) and pyrite (FeS2), or metallic palladium (Pd) and antimony palladium ore (PdSb), and measure the characteristic X-ray counting rate of an element in a pair of standard samples under exactly the same conditions. Taking iron and pyrite as examples, the counting rate of FeKα in pure iron is N 1, the counting rate of FeKα in pyrite is n 1, and the true counting rate after dead time correction is sum respectively. Then choose another current value, the counting rate of FeKα in pure iron and pyrite is N2, and the true counting rate after dead time correction is respectively
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When measuring the above two sets of data, only the light beams are different and other conditions are exactly the same, so their ZAF corrections are exactly the same, and it is concluded that:
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89.2. 1.3 spectral line interference correction
Electron probe analysis of multicomponent samples will encounter the problem of overlapping spectral lines and must be corrected. This paper discusses the physical meaning of the concepts of overlap factor and overlap quantity, as well as their experimental measurement and calculation methods.
In fig. 89.7, the Kβ line (AKβ) of element A overlaps with the Kα line (BKα) of element B, that is, the Kβ line of element A interferes with the analysis line Kα of element B. Generally, the ratio of the counting rate of AKβ line at BKα peak to the counting rate of main analysis line (AKα) of element A is defined as the overlapping factor of AKβ line and BKα line. If the X-ray spectrum is an ideal Gaussian peak, the overlap factor can be calculated mathematically. Because of the existence of low energy tail, it is generally not an ideal Gaussian peak, so the overlap factor is usually determined by experimental methods with standard samples. Assuming that pure element A is the standard sample (or a compound with known content of element A but no element B), the peak intensity IAKα of element A is measured first, and then the linear intensity IAKβ(B) of element A is measured at the peak position corresponding to element Kα, so as to obtain the overlap factor RAB of AKβ to BKα:
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Fig. 89.7 Overlap of Kβ line of element A and Kα line of element B.
Assuming that the strength of Kα line of element A is I'AKα when testing samples containing elements A and B, as an approximation, the interference QAB of AKβ line on BKα line can be calculated by the following formula:
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Then the Kα line intensity of element B measured by experiment is subtracted from QAB, and the spectral line overlapping effect of element A on element B can be corrected quantitatively.
The types of spectral line overlap and their correction can be summarized as follows.
Overlap between (1)Kα spectral lines
This overlap appears on the energy spectrometer. For Kα lines with energy less than 3keV (such as Kα lines of Si, Al, Mg, Na and other elements), the spectral line overlap between adjacent elements can not be ignored, for example, the overlap factor of MgKα and NaKα is as high as 0.027 1.
Modified formula of Kα line (reed and tile) overlapping;
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Where: z is the atomic number; IZ, IZ- 1 and IZ+ 1 are the peak intensities of elements with atomic numbers of z, Z- 1 and Z+ 1 after background correction and spectral line overlap correction, respectively (if the overlap is not serious, only IZ- 1 and iz+/kloc-can be used. I'Z is the peak intensity of element Z only after background correction; IZ- 1 and IZ+ 1 are the overlapping factors of elements Z- 1 and Z+ 1, respectively.
(2) The overlap between K β line and Kα line, Lβ line and Lα line, and different lines.
We don't have to pay attention to all spectral line overlap, but only need to study the elemental characteristic X-ray spectral line overlap that may usually occur in minerals and other substances. Generally speaking, for elements with atomic numbers between 20 and 28, the Kα line of the element with atomic number Z often overlaps with the Kβ line of the element Z- 1 (Table 89.3). For elements with atomic numbers between 45 and 50, the Lα 1 of the element with atomic number z overlaps with the Lβ 1 of the element with atomic number Z- 1. In addition, PbLα 1 and BiLβ 1 also overlap the Lβ line of some elements (Table 89.3).
Table 89.3 Overlap of Kβ Line and Kα Line among Some Elements
The atomic numbers of some sample components usually vary greatly, and there may be overlap between different line systems, such as
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In spectral analysis, in order to avoid the influence of overlapping spectral lines, other non-overlapping spectral lines can be selected as analysis lines; However, in most cases, overlap correction must be carried out. In the energy spectrum analysis, the possible overlap between various spectral lines of all elements must be considered and corrected by the following formula:
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Where: Ii is the spectral peak intensity of element I after background correction and spectral line overlap correction; "Ii" is the spectral peak intensity of element I only after background correction; Ij is the spectral peak intensity of element J after background correction and spectral line overlap correction (if the overlap is not serious, Ij is the spectral peak intensity after background correction only); Rji is the overlap factor of spectral lines from element j to element i.
(3) Overlapping of higher order lines and quadratic lines
The overlapping phenomenon between the high-order lines of some elements and the primary lines of other elements is quite common, for example:
Skα(53.73 nm)-COK α (53.73 nm) Cubic Line
The quadratic line of hflα l (15.69nm)-zrkα (15.76nm)
The Quadratic Line of Tal α L (15.22 nm) ——NBKα( 14.9 nm)
Generally speaking, the spectral line interference caused by the overlapping of high-order lines will not be too serious, because the intensity of high-order lines is relatively weak. In addition, the energy difference between the high-order line and the primary line is large, and the interference of the high-order line can be eliminated by properly selecting the baseline and track width of the pulse amplitude analyzer. In some special cases, if the interference of high-order lines cannot be eliminated by experimental methods, overlapping correction method can be used to correct it.
When analyzing platinum group minerals by electron probe, the overlapping of spectral lines is quite serious, which is not only the overlapping of β line to α line in the same spectral line system, but also the interference of high-order lines. We have studied this problem systematically, determined some overlapping factors between spectral lines, and used these overlapping factors to quantitatively correct the overlapping of spectral lines. When researching and testing new minerals, such As Emei (OsAs2), Ruas (RuAsS) and Amdo (RuAs2), the quantitative analysis results are accurate and reliable due to the overlapping correction of As by Os and As by Ir.