PERFORMANCE OF TXRF and GI-XRF ANALYSES - Total-Reflection X-Ray Fluorescence Analysis and Related Methods - page 252

cylinders consisting of a matrix of metal-salts in accord with a formula similar
to Equation 4.1.
A deviation from linearity of 20% was generally reached for a deposition
less than 1 × 10 14 metal atoms and a deviation of 10% for an amount less than
2 × 10 13 atoms. With an average area of 1.5 × 10

3 cm 2 for the circular wall the
area-related mass is about 6 μ g/cm 2 for a systematic deficit a rel = 10%, and
about 1 μ g/cm 2 for a rel = 5%. Both specifications roughly correspond with the
restrictions cited for the maximum mass of thin layers in Section 4.4.3.1. In
general, the deposition of microliter droplets is not well suited for quantitative
TXRF; the dynamic range of a linear calibration is restricted to less than 3 μ g/
cm 2 for thin layers of metallic coverings and less than 2 μ g/cm 2 for ring-shaped
metal-salt residues of microliter droplets. However, the dynamic range can be
extended for film-like residues of nano- and moreover of picoliter droplets
already dealt with in Sections 4.1.3.2, 4.1.3.3 and 4.1.3.4.

4.4.3.3CoherenceLengthofRadiation

Constructive and destructive interference lead to the standing wave fields treated
in Chapter 2. This two-beam interference, however, is only possible under the
condition of coherence, that is, both beams, or strictly speaking their waves,
should have a phase difference that is constant with regard to time and space. The
first condition,“temporal constancy,”is always met for TXRF experiments. The
second condition,“spatial coherence,”however, is limited for two reasons:

1. The two beams do not come from a punctual source but from a source
with a certain extension w beam .
2. The two beams are not completely monochromatic but have a certain
bandwidth Δ E or Δ λ , respectively. The monochromaticity can be defined
by E / Δ E .

As a result, the interference pattern of Figure 2.8 with maxima and minima is
not completely sharp within the total triangle above the surface but is restricted
in height.
The two kinds of spatial coherence are called transversal and longitudinal
coherence and are represented in Figure 4.18 [47,59]. For Figure 4.18a we
assume two waves with the same wavelength but originating from different
points A and B of the source. Their wave fronts with distance λ cross over in
direction of the observation point P , with a small deviation Δ α . In a lateral
distance ± ξ t from point P , both wave fronts coincide and are completely out of
phase. Δ α is given by

λ
2 ξ t

tan Δ α (4.18)