ZAF correction

1. Atomic number effect

The atomic number effect is the effect of the difference in the constituent elements of an unknown specimen and of the standard specimen, namely the difference in the average atomic number between the two specimens, on the generation amount of the characteristic X-rays. The effect consists of backscattering factor and penetration factor.

The backscattering factor is to correct the difference in the number of backscattered electrons that do not contribute to the characteristic X-ray generation, which depends on the average atomic number. As the average atomic number of the unknown specimen is larger, the number of the electrons backscattered out of the specimen increases, and the number of the electrons penetrating into the specimen contributing to the X-ray generation decreases.

The penetration factor is to correct the difference in the number of the penetrating electrons contributing to the characteristic X-ray generation, which depends on the magnitude of the mass stopping power.

The penetrating electrons excite and ionize the electrons in the atoms of the specimen, and generate characteristic X-rays while losing their energy due to these inelastic scattering processes. The energy loss of a penetrating electron, when it passes through a unit mass depth (mass thickness) [1], is expressed by the energy-loss ratio, namely the mass stopping power. As the average atomic number of the unknown specimen is larger, the mass stopping power becomes smaller. Then, the generation efficiency of the characteristic X-rays by the penetrating electrons increases.

Thus, the backscattering factor and the penetrating factor behave to cancel out each other for the characteristic X-ray generation efficiency when the average atomic number of the unknown specimen is different from that of the standard specimen.

The atomic number correction factor G^Z_A for calculating the concentration of element A in the unknown specimen is expressed by the following equation using the backscattering factor and the penetration factor.

2. Absorption effect

The absorption effect is an effect, where the characteristic X-rays generated in the specimen are absorbed by the other elements in the specimen until the X-rays are emitted from the specimen, thereby reducing the X-ray intensity.

In particular, the low-energy characteristic X-rays generated from the elements with small atomic numbers suffer greatly absorption by the elements with large atomic numbers. To the contrary, the high-energy characteristic X-rays generated from the elements with large atomic numbers, suffer less absorption by the elements with small atomic numbers, thus, the decrease in the X-ray intensity being almost negligible. Therefore, the absorption correction is important in quantitative analysis of the elements with small atomic numbers.

The magnitude of absorption of the characteristic X-rays is expressed as the function f (χ) of the variable χ = (μ/ρ) cosecθ defined by the mass absorption coefficient (μ/ρ) of the specimen and the take-off angle θ of the X-ray detector. It is noted that the variable χ is related to the degree of X-ray attenuation of the constituent elements, and the path length of the characteristic X-rays in the specimen.

When the take-off angle of the detector is low, the variable χ becomes large and the generated X-rays run a longer distance through the specimen, thus, the X-rays suffer a greater absorption. The absorption correction factor G^A_A for element A is expressed by the following equation as the ratio of the absorption for the standard specimen to that for the unknown specimen.

3. Fluorescence excitation effect

The fluorescence excitation effect is an effect, where the high-energy characteristic X-rays from the other elements in the specimen secondary generate the characteristic X-rays of the element A to be measured, thereby, arising the addition of the characteristic X-ray intensity of element A. The difference in the magnitude of fluorescence excitation of the characteristic X-rays for element A between the standard specimen and the unknown specimen, is corrected using the fluorescence excitation correction factor. The fluorescence excitation correction factor G^F_A is expressed by the following equation using the fluorescence excitation ratio γ between the amount of the characteristic X-rays generated from element A by the incident electron-beam and the amount of the X-rays (fluorescence X-rays) from element A due to the other elements.