JP2696965B2 - X-ray spectroscopy - Google Patents

Description

The present invention relates to a method for quantitative analysis of a multi-element sample by X-ray spectroscopy.

(Prior Art) When quantitative analysis is performed by X-ray spectroscopy, a calibration curve is created using several standard samples with known concentrations of the element to be quantified. However, in some cases it may be difficult to prepare standard samples with known concentrations of some of the elements to be quantified. In such a case, as a method of creating a calibration curve without using a standard sample, consider a model in which characteristic X-rays of the target element are emitted when an electron beam for excitation is incident on the sample, and perform simulation by a computer. The relationship between the concentration of the target element and the relative intensity of the characteristic X-ray is calculated. For example, for a sample having 100% of the target element concentration, the ratio between the measured intensity of the characteristic X-ray and the relative intensity obtained by the above calculation is determined. By multiplying the calculated relative intensity, a method of creating a calibration curve representing the relationship between the concentration of the target element and the characteristic X-ray intensity can be considered. According to this method, one kind of relatively inexpensive sample such as a pure product of the target element may be prepared, and the difficulty in preparing many kinds of standard samples is eliminated. However, this method can be applied to a two-component sample or a multi-component sample when the composition ratio of other components except one component is known and it is desired to quantify only one component. For elemental samples, combinations of component amounts become diversified, and a large number of calibration curves must be prepared, which makes it difficult to implement.

(Problem to be Solved by the Invention) The present invention provides a method for achieving a purpose by a relatively small number of simulation calculations when a calibration curve is created by a simulation method in a quantitative analysis of a multi-element sample by X-ray spectroscopy. It is something to offer.

(Means for Solving the Problems) Assuming that the component numbers of the component elements of the sample to be measured are 1, 2,... I,..., The actual measured intensity I ^o i of the characteristic X-ray of each component element and one standard of each component element the ratio K ^o between the measured characteristic X-ray intensity Isti in the sample
Determine the first approximate concentration C ^o i of each component by i = I ^o i / Isti,
Assuming a sample having the above component composition, the ratio K ¹ i of the characteristic X-ray intensity of each component to the characteristic X-ray intensity of each component in the standard sample is calculated by a simulation method, and the error rate εi = (K ¹ i−K ^o i) / K ^o i, and taking the two component elements from the larger | ε i |, leaving the other component concentration at the first approximate concentration C ^o i, A simulation is performed by changing the concentration, a calibration curve is created by calculation for the two components, and the concentrations of the two components are obtained from the measured characteristic X-ray intensities of the two components by the calibration curve. In the concentration, the new component composition obtained by replacing the two-component concentration with the concentration determined by the calibration curve is defined as the second approximate concentration C ¹ i of each component, and the above calculation performed on the first approximate concentration C ^o i is performed as C ^o i. where a and seek again the error rate εi went replaced by a C ¹ i of The calculation is repeated so as to obtain the third approximate concentration of each component, and the final approximate concentration obtained when the error rate sequentially obtained below the predetermined value is less than the predetermined value is used as the analysis value. .

(Operation) According to the above-described method, the measured characteristic X-ray intensity of each component of the sample to be measured and one type of each component (the sample is not limited to one for each component but may be a sample of a plurality of components). The first approximate concentration of each component is determined by a simple ratio from the ratio K ^o i of the characteristic X-ray intensity of each component to the characteristic X-ray intensity. Linear intensity and characteristic X of each component in the above standard sample
Calculate the ratio to the line intensity and obtain the characteristic X
A difference from the line intensity ^Koi is obtained, and for a large difference, simulation calculation is performed by changing the assumed concentration to create a calibration curve. In this way, the number of variable components at the time of creating a calibration curve by the simulation method is limited, so that the number of simulation calculations can be greatly reduced, and thereafter, the concentration of each component of the sample to be measured can be determined by successive approximation. is there.

(Embodiment) FIG. 1 is a flowchart of the operation when the method of the present invention is executed. First, the characteristic X-ray intensity I ^o i of each component element is actually measured for the sample to be measured (A). Here, i is a component number and i = 1... N. Next, the characteristic X-ray intensity Isti of each component of the pure sample of each component is actually measured (b). Thus, the preparation operation is completed, and ^Koi is calculated (C). Although ^Koi is approximately proportional to the concentration of each component in the sample, it is not exactly proportional to the concentration because it is affected by coexisting elements in the sample. Naturally ΣK ^o
Although i does not become 1, C ^o i is calculated (d) as the first approximation of each component concentration. Next, with p = o (e), the following simulation calculation is performed. The simulation calculation will be described later. Here, p indicates an approximation stage, and p = o
Means the first approximation. In step (f), the characteristic X-ray intensity I ¹ i in terms of the settlement of each component element is calculated by simulation, assuming that the component composition of the sample is ^Co i. Next, a simulation is performed for a 100% sample of each component, and the calculated characteristic X-ray intensity I ^S sti of each component pure product is calculated (g). Thus, K ¹ i = I ¹ i / I ^S sti is calculated (h). Next, the error rate εi = (K ¹ i−K ^o ) from K ^o i obtained in step (c).
i) / K ^o i is calculated (i), it is checked whether or not the absolute value of ε i is larger than a predetermined value Δ (nu). If all ε i are smaller than Δ, the first approximation C ^o i is used. As a result, the analysis operation is completed as the composition of the sample. Normally, since all εi are not smaller than Δ, the operation shifts to the step (e). In step (e), two elements k and l are taken from the larger | εi |, and a simulation is performed by changing the concentration of both elements (the other components use the first approximate composition ratio) to perform characteristic X-rays of each component. Strength ▲ I
Calculate ^{p + 1 + 1} _i ▼.

In this calculation, the concentration range of the elements k and l is C in the first approximation.
^o k, C ^o as ^{T = C o k + C o} l by l, the concentration of the element k and Ck, the concentration of each of the elements of the concentration Cl of elements l as T-Ck 0
To T. In this range, for example, the concentration of the element k is set to 3
Since the simulation is performed in stages, the simulation calculation is performed three times in total. By this calculation, a calibration curve as shown in FIG. 2 is created (W). Using this calibration curve,
The concentration of K ^o k, K ^o both elements from l k, l which has been obtained in the step
C ¹ k and C ¹ l are determined (f), 1 is added to p (y), and the operation returns to step (f). The above operation is repeated until the step (nu) turns ON.

Next, the simulation calculation will be described. FIG. 3 shows a flowchart of the simulation calculation. The sample to be measured has a thickness t, and its constituent elements are 1 to n.
N types. Assuming a combination of the concentrations of these elements, the simulation is started with the concentrations (% by weight) of these elements as C1, C2... Ci. Here, the subscript i is a component number. The sample thickness t, the scattering cross section of the atoms of each element constituting the sample with respect to the electrons, the ionization cross section, the concentration Ci of each element, the initial energy Eo of the electron, the final energy E ', the number of times of the simulation No, etc. Input to computer (a). Simulation starts at 1000
Performed on 20000 electrons. Specifically, the trajectory calculation of the trajectory of the electron when one electron is incident on the sample is performed,
This is repeated No times. When the input of data and parameters necessary for the simulation calculation is completed in the step (a), the arithmetic circuit N is set to 1 (c), and the tracking operation of the electrons incident on the sample is performed (d). This calculation is a calculation of the process from the collision of an electron with an atom in the sample to the atom in the next sample, and stochastically determines the direction in which the electron is repelled in the previous collision. Then, the atom of which element is to be collided is stochastically determined by the following equation (1) in relation to the scattering cross section of each constituent element atom and the concentration of each element. It is assumed that electrons travel by the mean free path in the sample and collide with the stochastically determined atoms, and the energy consumption in this process is calculated by the following equation (3). Where Pi is the probability that an electron collides with the atom of element i, and Pi is Here, Ai is the atomic weight of element i, σi is the scattering cross section of the atoms of element i for the electrons, and the energy E of the colliding electrons is
And the atomic number zi of each element constituting the sample, Where βi is a screening parameter, It is.

The mean free path L is in units of Å The energy loss when electrons travel through a substance is per unit flying distance, However, this is the average value of the atomic numbers in consideration of the composition ratio (% by weight) of each element in the sample, and is represented by = ΣCi · zi where ΣCi = 1. Similarly, is the average atomic weight of the elements in the sample, and ρ is the sample density.

The unit of the above equation is KeV / Å, and Ji is the ionization potential (eV) of element i.

When the tracking calculation is completed, the current depth of the electron from the sample surface by adding the depth travel distance of the electron from the sample surface during the previous and subsequent collisions to the previous depth direction travel distance in the calculation. The position d is calculated (e). In this embodiment, in the next step (f), the characteristic X-ray emission probability of the element i in the subsequent collision in the above process is calculated, and the result is input to the memory. The characteristic X-ray emission probability is E for the electron energy and Ei for the excitation energy for characteristic X-ray emission of element i.
Then, it is related to vi = E / Ei, and is proportional to φi given by the following equation.

As shown in the memory map of FIG. 4, this φi is added to the data at the address corresponding to the depth d from the sample surface in the area of the element i of the calculation sample in the memory and stored at the same address. Next, it is checked whether the electron energy E is E <E '(g). E 'is the terminal energy of the electron, and in this case, may be set to a limit energy at which atoms of any element in the sample cannot be ionized. If this check is NO, it is checked whether or not the depth d of the electrons from the sample surface is <o (protrudes from the surface) (h), and then whether or not d> t (transmits through the sample) (h). If all are NO, the operation returns to (D), and the same operation is repeated until any of the steps (G), (H), and (R) becomes NO.

As described above, when any of the steps (g), (h), and (i) becomes YES, the tracking operation for one electron is completed, N is set to N + 1 (l), and new N is N> No.
It is checked whether or not (e), and if No, the operation returns to step (c) and the above-described calculation is performed for the next electron.
Thus, for example, if 10,000 calculations are performed, N> No, the step (e) becomes YES, and the Monte Carlo simulation calculation for one sample is completed. By the operation up to this point, a histogram of characteristic X-ray radiance as shown in FIG. 5 with respect to the depth from the sample surface is formed for each element in the memory.
Characteristic X of each element formed in the memory in the above step
The X-ray emission intensity histogram is integrated by performing X-ray absorption correction based on the depth from the sample surface. This is a relative value indicating the mutual ratio of the characteristic X-ray emission intensities of the respective elements of a sample having a certain composition having a thickness t, which is the above-mentioned I ¹ i, I ^S sti or the like.

In the above embodiment, a sample having a concentration of 100% for each component is used as a standard sample. However, if a sample having a known composition ratio of each component is available, it can be used as a standard sample. In this case, the step (b) in the flow chart of FIG.
Isti is measured, and the step (c) is the component i
The concentration as CSTI in the standard sample of the ^{K o i = (I o i} / Isti) × Csti.

In the above embodiment, since the characteristic X-ray emission probability of each component is calculated for each depth from the sample surface, the invention can be applied not only to a bulk sample but also to a thin film sample having an arbitrary thickness.

(Effect of the Invention) When a calibration curve method is used to quantify each component of a multi-element sample, the combinations of the component composition ratios become diverse, so that many kinds of standard samples are required, and it is necessary to make many kinds of calibration curves. As a result, the analysis operation is extremely troublesome, and it is often difficult to obtain various standard samples. According to the present invention, only a small number of available standard samples are required, and a large part of the analysis operation is calculated by a computer, and the operation of the analysis operator is to measure each component characteristic X-ray intensity of the sample to be measured. And characteristic X of each component for a small number of standard samples
Only the operation of measuring the intensity of the line and setting the parameters necessary for the calculation in the computer are performed, and the analysis operation is also simplified.

[Brief description of the drawings]

FIG. 1 is a flowchart showing one embodiment of the method of the present invention;
2 is an example of a calculated calibration curve, FIG. 3 is a flowchart of an example of an X-ray radiation simulation operation used in the present invention, FIG. 4 is a memory map of a memory used in the simulation operation, and FIG. FIG. 4 is a distribution diagram of the frequency of occurrence of characteristic X-rays obtained from the simulation operation in the depth direction from the sample surface.

Claims (1)

(57) [Claims] 1. The ratio K ⁰ i = I ⁰ i / Isti between the measured intensity I ⁰ i of the characteristic X-ray of each component element of the sample to be measured and the actually measured characteristic X-ray intensity Isti of one standard sample of each component element. The first approximate concentration C ⁰ i of each component is determined according to the following formula. Assuming a sample having the above component composition, the ratio K ¹ i of the characteristic X-ray intensity of each component to the characteristic X-ray intensity of each component in the standard sample is determined. were calculated by simulation method, seek error rate ^{εi = (K 1 i-K} 0 i) / K 0 i, | εi | takes two of the component elements from the person who is large,
The concentration of the other ingredients as remains of the first approximation C ⁰ i, to simulate changing the concentration of the two components, a calibration curve by calculating its two components, the actual characteristic X-ray intensity of the two-component From the above calibration curve, the concentration of the two components is obtained, and a new component composition obtained by replacing the two component concentration with the concentration obtained by the above calibration curve in each of the component concentrations previously obtained is used as a second approximation, and this composition is obtained. The simulation calculation is again performed for the assumed sample, the characteristic X-ray intensity I ¹ i of each element is calculated, and further, the characteristic X-ray intensity I ^S sti of each component element for the standard sample is obtained by the simulation calculation. Is used to determine K ² i = I ¹ i / I ^S sti, K ² i is the above K ¹ i, K ¹ i is the above K ⁰ i, and the error rate εi is obtained again. Perform calculations up to where the composition is determined An operation of calculating the third approximate component composition and obtaining the error rate εi again is repeated until εi becomes equal to or less than a predetermined value, and the finally determined approximate component composition is used as an analysis value. Line spectroscopy.