**Summary of fundamental parameter method**

**1、****X-ray fluorescence **

X-ray fluorescence spectrometer (XRF) is an instrument for quantitative analysis of elements. It is widely used in steel, cement, petrochemical, environmental protection, materials and other fields. It is superior to other analysis methods in terms of convenient, non-destructive, and fast sample preparation. However, it has been challenged in terms of quantitative accuracy and sample adaptation range.

Currently, XRF is widely used in fields that often have three characteristics: one is that the sample matrix is relatively stable, the other is that the types of analysis elements are limited, and it is often analyzed for several elements in the sample, and the third is that a series of standard samples or easily prepared fixed-value samples are required. The above characteristics are based on the basic needs of XRF quantitative analysis. Usually X-ray fluorescence spectroscopy analysis adopts multiple regression method to establish a mathematical model of the fluorescence intensity and content of each element of the standard sample to obtain a calibration curve to quantitatively analyze the element content. However, even if a series of standard samples are used to establish a calibration curve, the accuracy of quantitative analysis of unknown samples is also affected by the consistency of the matrix with the standard sample, the content relationship between elements, and whether the sample preparation reaches the physical state of the standard sample.

In general, the quantitative accuracy of XRF is affected by the following aspects:
**1）Sample preparation**

XRF sample preparation is simple, but not without sample preparation. XRF has requirements for the uniformity of element distribution in the sample, sample particle size, sample surface smoothness, surface dust, and mineral effects. These aspects will affect the analysis accuracy to varying degrees. Users can eliminate or improve these effects through relevant sample preparation methods, such as: grinding, tableting, fritting, etc. are the sample preparation methods commonly used in XRF.

**2) Quantitative model**

The establishment of the XRF quantitative model must fully consider the selection of standard samples, the matching of the matrix, the establishment of the calibration algorithm, the applicability of the target sample, etc. These aspects will affect the quantitative accuracy, and often require the analyst to have rich experience.

**3) Sample adaptability**

Even if a reliable quantitative model is established, the adaptation to the target sample is not once and for all. It is also necessary to fully consider the physical form of the target sample, the elemental content range, the consistency of the matrix and the standard sample, and other conditions, which are inconsistent with the standard sample used to establish the quantitative model, and will cause deviations in quantification to some extent.

**4) Quality Control**

In the analysis of the target sample process, the use of other laboratory analytical methods for quantitative accuracy control is necessary, the existence of deviations in different analytical methods is inevitable. When the deviation is large, the accuracy of the two analytical methods should be further fully validated, the goal is to improve the XRF quantitative accuracy.

**2、 Empirical coefficient method**

XRF element quantitative analysis has to solve two problems:

**1）**Different elements have different excitation and detection efficiency. Some elements are easy to excite and detect, and some elements are difficult to excite and detect, so the relationship between intensity and content is quite different.

**2) ** An important difficulty in X-ray fluorescence spectroscopy analysis is to solve the problem of the absorption enhancement effect between elements. The simplest method is, of course, to use a standard sample. By detecting the fluorescence intensity of the standard sample, an optimization algorithm (linear or non-linear least square regression or other optimization algorithm) is used to establish a mathematical model between the fluorescence intensity and the content. The established mathematical model is used for quantitative analysis of unknown samples. Usually we call it the empirical coefficient method. The inevitable problem of the empirical coefficient method is that standard samples are inseparable. If there is an absorption enhancement effect between elements, in order to obtain the mutual influence coefficient between the elements through the optimization algorithm, the number of standard samples will be more. Even if there are enough qualified standard samples (usually difficult), the scope of application of the obtained mathematical model will be limited, and usually cannot exceed the scope covered by the standard samples. The reason why most X-ray fluorescence analyzers analyze the types of elements is limited, is part of that standard samples cannot be found, or there is no standard sample elements. Even if the hardware is analyzable, the quantitative accuracy cannot be guaranteed. Therefore, the empirical coefficient method is usually suitable for the situation where the sample matrix is relatively stable, the element types are limited, and a series of standard samples are available. Once the above situation becomes complicated, the quantitative accuracy of the empirical coefficient method is challenged. Therefore, the empirical coefficient method limits XRF Quantitative accuracy and application range.

**3、 ****fundamental parameter method (FP)**

In view of the serious dependence of the empirical coefficient method on standard samples and the narrow applicability, the fundamental parameter method (FP) has received more and more attention.

The fundamental parameter method is to calculate the generation and filtering of X-rays, the effects of X-rays and substances, and the various effects of the detector. According to the known database and physical theory, the calculated spectrum is compared with the measured spectrum, and the real content is approached through the iterative process. Therefore, the fundamental parameter method greatly reduces the dependence on standard samples, and its goal is to carry out standard-free quantitative analysis.

The usual fundamental parameter method calculates the intensity and distribution of the X-ray tube emission spectrum, the incident sample spectrum, the spectral line fraction, elemental fluorescent rays and scattered lines, primary fluorescence intensity and secondary fluorescence intensity. However, the above calculation alone cannot obtain high-precision quantitative results. That is to say, the existing fundamental parameter library cannot cover the entire physical principle and detection process of X-ray fluorescence. For example, how to deduct the baseline? The calculation of the various effects of the detector? Calculation of physical structure condition parameters of X-ray fluorescence spectrometer, etc. The lack of these fundamental parameter libraries requires further theoretical calculations with corresponding mathematical models. That is to say, fundamental parameter method + complete mathematical model can improve the quantitative accuracy and applicability of XRF elements.

This is also the reason why the usual fundamental parameter method cannot complete quantitative analysis and has narrow adaptability! It is also the reason why most XRF analysts believe that the fundamental parameter method cannot be used for quantitative analysis!

**4、Fast fundamental parameter method (Fast FP) and advanced mathematical model (Advanced mathematical models abbreviated as Advanced MM)**

After more than ten years of accumulation, Ancoren successfully applied the fast fundamental parameter method and advanced mathematical model to XRF quantitative analysis, which greatly improved the accuracy of element quantification and sample adaptability.

Why is it called the fast fundamental parameter method? The fundamental parameter method and a series of advanced mathematical models require a lot of calculations in the calculation process. Through the optimization program, the iterative process can be completed quickly. That is why we call it the fast fundamental parameter method (Fast FP).

The difference and advantages of Fast FP with Advanced MM from the conventional basic parameter method:

**1）****Integrity**

The entire process from the intensity distribution of incident X-rays, the interaction of X-rays with the sample, the generation of elemental fluorescent rays to the detection of the detector, uses the basic parameter library and advanced mathematical models to perform theoretical calculations to obtain the theoretical content of the elements in the sample. The theoretical content has a clear physical significance, which is able to interpret the entire process of X-ray fluorescence from generation to detection。

**2）****High precision**

Fast FP with Advanced MM fully calculates matrix effects, inter-element absorption-enhancement effects, elemental spectral overlap and interference, detector effects, etc. The theoretical calculated values have a certain quantitative accuracy, and consistent quantitative accuracy can be obtained within a certain sample range (sample application method coverage range), and usually only 1-3 standard samples (or fixed value samples) are needed for calibration to correct the quantitative errors and achieve high precision elemental quantitative results.

**3）**Applicability (development support)

Fast FP with Advanced MM is used for the development of applied methods for various samples. By editing the list of quantitative elements and adjusting some of the analytical parameters, quantitative methods for various samples can be quickly established.

**4) Visualization**

The software has a visual interface, with visualization of the elemental peaks, the fit between the calculated spectrum and the detection spectrum, and the calculated elemental content, etc.

**5、 ****Applications**

Fast FP and Advanced MM can rapidly improve the quantitative accuracy of XRF elements and expand the scope of XRF applications. The analysis of elemental content in soil, inorganic elemental content in air filtration membrane, constant elemental content in cement, hazardous elemental content in solid waste, alloy composition analysis, elemental content analysis in ore, etc. have all been improved in quantitative accuracy and sample applicability.

Fast FP with Advanced MM will greatly expand the scope of XRF applications and improve the quantitative accuracy, we also sincerely hope to provide solutions for more fields of quantitative analysis of elements, if you are engaged in XRF application analysis, welcome your inquiries!

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