quantitative correction

A correction to obtain the correct concentration values of the constituent elements in an unknown specimen using the characteristic X-rays generated by electron beam irradiation. The correction is applied to the first approximate concentration value, which is calculated using the intensity ratio (K ratio = C^U/C^Std) of the characteristic X-rays from the unknown specimen and the standard specimen (mass concentrations of the constituent elements are known).

The constituent elements and their abundance ratio of the unknown specimen are different from those of the standard specimen. As a result, the measured K ratio is not equal to the concentration ratio of the unknown specimen to the standard specimen. Thus, corrections are needed to obtain the correct concentrations of the unknown specimen. The correction factor G is composed of the following three corrections: 1) Atomic number correction G^Z due to the difference of characteristic X-ray generation efficiencies, 2) Absorption correction G^A due to the difference of absorption of the characteristic X-rays when they run in the specimen and 3) Fluorescence correction G^F due to the difference of fluorescence X-ray generation efficiencies (Fig. 1). Methods for calculating these correction factors include the ZAF correction method and the Phi-Rho-Z method (φ(ρz) method).

The workflow of the quantitative correction (in standard quantification) is shown in Fig. 2. To obtain the correction factor G, first, all the characteristic X-rays generated from the unknown specimen are measured and the constituent elements (N = A, B, C,…) of the specimen are identified. In the following, we explain how to obtain the mass concentrations of the elements in the unknown specimen with the corrections described above.

The first approximate concentration value C_A⁰ of element A in the unknown specimen is calculated by multiplying the measured K-ratio K_A = C_A^U /C^Std_A by the mass concentration C^Std_A of element A in the standard specimen. By the same procedure, the first approximate concentrations C_B⁰, C_C⁰… of elements B, C...in the unknown specimen are calculated. Then, the correction factor G_N⁰ (_{N=A, B, C…}) is calculated using the first approximate concentrations C_N⁰ of all the constituent elements contained in the unknown specimen. The second approximate mass concentration C_N¹ is calculated by multiplying G_N⁰ by the first approximate concentration C_N⁰ (= C^Std_N x K_N). Next, using the corrected mass concentration C_N¹, G_N¹ is obtained, and C_N² is calculated by multiplying C_N⁰ by G_N¹. By repeating this procedure, when the calculated mass concentration C_Nⁱ⁺¹ becomes very close to the previous C_Nⁱ, the value is taken as the true value.

There are two methods for determining the K ratio and C_N⁰: (1) standard quantification, in which a standard specimen is prepared and the characteristic X-ray intensity is actually measured, and (2) standard-less quantification, in which a theoretical calculation or reference data prepared by the EDS manufacturer is used.

When the difference in the average atomic number of the constituent elements is large between the unknown specimen and the standard specimen, the correction amount becomes large because the difference of the characteristic X-ray generation efficiency and of the absorption in the specimen becomes large. In general, the effect of absorption correction is largest, followed by the atomic number correction and the fluorescence correction. In particular, when the accelerating voltage is high (e.g. 20 kV, 30 kV), the electron beam penetrates deeper into the specimen while generating the characteristic X-rays. Thus, the X-rays run a longer distance in the specimen, and then, the absorption correction becomes important. Fluorescence correction can often be neglected because the fluorescence effect is small except for the combinations of specific elements. For the detailed explanations of the absorption correction, atomic number correction and fluorescence correction, refer to the term “ZAF correction”.

Fig. 1 Three correction factors used for quantitative correction

A part of electrons incident into the specimen is scattered elastically and inelastically with the constituent atoms (elements) (①). Some electrons are backscattered and emitted outside the specimen as reflected electrons. The electrons penetrating into the specimen generate continuous X-rays and the characteristic X-rays of element A (②). The penetrating electrons also generate the characteristic X-rays of element B (③). In this inelastic scattering process, these electrons lose their energy. The difference in the characteristic X-ray generation efficiency between the unknown specimen and the standard specimen in such scattering process is corrected as the atomic number correction factor G^Z.

A part of the generated characteristic X-rays is absorbed by the specimen. Since the magnitude of absorption for the characteristic X-rays depends on the constituent elements and their abundance, the difference between the unknown specimen and the standard specimen is corrected by the absorption correction factor G^A (④).

In some cases, the characteristic X-rays of element A are excited by the characteristic X-rays of the other element B (③) or by continuous X-rays, and the X-rays of the same energy as the characteristic X-rays of element A (fluorescence X-rays) are generated (⑤). The difference in the fluorescence X-rays between the unknown specimen and the standard specimen is corrected by the fluorescence correction factor G^F.

Fig. 2 Workflow of quantitative correction of constituent-elements concentrations in an unknown specimen.

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