background also changes. The background produced in WDXRF is always appreciably high. In addition, the distance between the sample and the detector is also larger in WDXRF (a few centimeters) compared to that in EDXRF (a few millimeters). This reduces the sensitivity of a WDXRF spectrometer, due to the attenuation of X‐ray intensity by air and spectrometer components, the crystal analyzer placed between the sample and the detector, and also due to the smaller solid angle subtended by the detector on the sample. These factors limit the applicability of XRF ‐ EDXRF as well as WDXRF, especially for those samples which contain trace levels of analyte (in a sub‐ppm level ) or where the sample amount available is less, e.g. forensic, precious, biological samples, etc. [7].
4.4 Modifying XRF to Make it Suitable for Elemental Determinations at Trace Levels: Total Reflection X‐Ray Fluorescence (TXRF) Spectrometry
Now the question arises: How can XRF be made suitable for trace element determinations? The answer is: by removing the limiting factors stated above. This can be done by taking care of the problems mentioned above: (i) minimizing the spectral background, (ii) making the matrix effects negligible and (iii) reducing the distance between the sample and detector to the minimum possible level. All these features can be achieved in total reflection X‐ray fluorescence (TXRF) spectrometric analysis, which is comparatively a new and advanced version of EDXRF. The possibility of using TXRF for trace elemental determinations was put forward by two Japanese scientists, Y. Yoneda and T. Horiuchi in the year 1971. They proposed that the total reflection of the exciting beam on optically flat supports reduces the background drastically and results in much improved detection limits for a thin film of Cr placed on it when excited by X‐ray beam in TXRF conditions. TXRF is now considered as a distinct X‐ray spectrometric technique [4–8].
4.4.1 Principles of TXRF
As stated above, the idea of TXRF application for trace element analysis was first put forward by two Japanese scientists, Yoneda and Horiuchi. Since then this technique has found applications in newer and advanced areas of material characterization [9]. The principles of TXRF analysis are based on the following three fundamental instrumentation changes to tradtional EDXRF:
1 In TXRF, the primary beam falls on the sample/support at an angle less than the critical angle which is <1° for almost all materials and depends on the energy of the X‐ray beam as well as density and atomic number (Z) of the reflector materials. This feature of TXRF ensures that the incident X‐rays do not penetrate deep into the sample supports and hence the scattered background is drastically reduced and leads to far better detection limits compared to conventional XRF.
2 As the primary parallel incident X‐ray beam falls on the sample support at an angle less than the critical angle, the sample support has to be a flat polished surface so that a fixed angle below the critical angle of support can be maintained for the impinging beam to totally reflect from it. In this situation, if a thin film of the sample having thickness of a few nanometers is deposited on the intersection area of the incident and reflected beams, it will be excited by the incident as well as by the totally reflected beams from the support. This arrangement results in almost double excitation of the sample compared to that in EDXRF and thus, increases the intensity of fluorescent X‐rays compared to that in EDXRF by about two times.
3 Since the glancing as well as the reflection angles are generally below one degree (very near to zero degree) the detector can be brought very close to the sample deposited on the support ensuring the angle between the incident X‐ray beam and the detector to be about 90°. This arrangement leads to 0–90° geometry of beam and detector, required for attaining a low background in XRF (here in TXRF).
The above geometrical arrangement takes care of the problems, associated with EDXRF, which are responsible for higher (inferior) detection limits and provides excellent elemental detection limits in TXRF comparable with other trace determination techniques, e.g. ICP‐OES, ICP‐MS, etc. In addition, the sample thickness is very small (a few nm) and hence the matrix effects associated are also negligible [8–10].
4.4.2 Theoretical Considerations
X‐rays are electromagnetic radiation and follow the law of refraction in a similar manner as any other electromagnetic radiation when traveling from one medium (e.g. air) to another (e.g. glass) as shown in Figure 4.1. The refraction of the X‐rays is governed by the formula:
In Eq. (4.1), n1 and α1 are the refractive index and the glancing angle of the incident X‐rays in medium 1, respectively, whereas n2 and α2 are these values for medium 2.
Figure 4.1 X‐rays undergoing reflection and refraction.
Figure 4.2 Depiction of total reflection of X‐rays on the sample support containing sample ( yellow colour).
For X‐rays, any medium is rarer than air or vacuum and hence, n1 (air) > n2 (medium). This means that when X‐rays pass from a denser medium (e.g. air) to a rarer medium (e.g. glass) then, cosα2 > cos α1 thereby α2 < α1. So, if the glancing angle α1 is reduced continuously, at one value of α1, α2 shall be zero and the refracted beam shall be just touching the supports surface and passing over it. Since the glancing angle in this situation is almost near to zero degree, the reflected beam shall also pass almost touching over the surface after reflection.This situation is depicted in the Figure 4.2 and is known as the condition of total reflection; the glancing angle at this stage is called the critical angle. The critical angle is very crucial in TXRF analysis as total reflection of X‐rays happen when the glancing angle of the X‐ray beam is equal to or less than the critical angle. The critical angle ( α crit ) can be expressed by the following Eq. (4.2):
where, E is the energy of incident X‐ray beam (in keV) undergoing total reflection, ρ is the density in g/cm3 of the second medium, and Z and A are the atomic number and atomic mass of the second medium, respectively. The above formula holds true only for the X‐ray energies above the absorption edges of the medium [8–10].
It is clear from the above elaboration that for a glancing angle lower than the critical angle, there will be no refraction and the X‐ray beam falling on the sample is totally reflected from the second medium back to first medium. This means that the penetration of X‐rays in the medium, when the glancing angle is below the critical angle, is negligible and this is very advantageous for TXRF analysis. Thus, three physical quantities: critical angle, reflectivity, and penetration depth, are important parameters
