In the first series of experiments, the primary spot was characterized. For that purpose, the detector is positioned in direct view of the primary beam. The detector entry is shrunk using a 5-μm diameter lead pinhole placed on the X, Y, Z piezo stages. The pinhole is positioned in the polycapillary lens focal plane and is displaced along the beam spot diameter in the same plane. For each pinhole position, a primary beam spectrum is acquired. Figure
shows the X-ray photon flux variations with the pinhole centre position within different incident energy ranges. The incident spot profile has a Gaussian shape, and the radius as well as the maximum flux depends on the photon energy. The lens providing the spot consists in a monolithic system made of a great number of monocapillary micrometric glass tubes bent together
]. Because the Rh low power source is not monochromatized, the total external reflection critical angle of glass θc
should vary with source energy E
in agreement with the following equation:
is the glass capillary density. This is the reason why the incident spot radius provided by the polycapillary lens depends on the photon energy range, as can be seen in Figure
. The average spot radius measured at 1/e is 22 μm, and the total photon flux within this spot area is about 1.7 × 109
Lateral photon flux profile for different X-ray energy ranges.
Then, the geometry of the fluorescence emitting volume in the cobalt sample was defined using the confocal XRF configuration shown in Figure
by scanning the cylindrical capillary used for detection along the X-ray fluorescence emitting zone. At each cylindrical capillary position, an X-ray spectrum is acquired that exhibits the two characteristic Co-Kα
lines at 6.9 and 7.6 keV, respectively. We then reported in Figure
peak area measured for each capillary position using various capillary radii from 5 to 50 μm. All the curves exhibit identical shape which are not expected to be Gaussian. The primary beam is not perpendicular to the surface so that it penetrates inside the sample with an attenuation length xRh-Kα/Co
= 43 μm
] inducing X-ray fluorescence, itself reabsorbed and leading to secondary emission. This means that the collected fluorescence comes from a deep excited volume schematically shown in Figure
. However, the fluorescence emitted within this deep volume cannot be entirely detected since the attenuation length of Co-Kα
rays in Co (xCo-Kα/Co
= 18 μm
]) is shorter than the penetration depth of Rh-Kα
rays in Co. From simple geometrical considerations, neglecting the secondary emission, a signal is detected over a capillary travel Φa
Fluorescence zone profile. The cobalt sample is placed in the focal plane of the polycapillary lens used to focus the rhodium source beam. The capillary inner radius is 5, 10, 25 or 50 μm.
where rspot is the primary spot radius measured at 1/e, rcap is the capillary radius and WD is the detection capillary working distance. However, as can be seen in Figure
, the fluorescence magnitude collected from point A, located at the cobalt sample surface, is obviously different from that collected from in-depth point B. This is due to the absorption of the primary beam before reaching point B and to strong fluorescence reabsorption in the path through the sample. Thus, in order to compare the theoretical and experimental values of Φa, we must consider this discrepancy. Taking into account the actual value of the primary beam flux Fmax/e at rspot from the spot centre (see Figure
), the fluorescence maximum flux F (B) escaping from the sample emitted at a depth of xCo-Kα/Co = 18 μm (point B)? should be given by:
is the path length of the primary beam in Co till a depth of xCo-Kα/Co
is the total fluorescence yield of Cobalt. With the value of τ
= 33% taken from
] the value of F
(B) is expected to be about 0.02 Fmax
. From this, we arbitrary choose the significant fluorescence flux above 0.02 Fmax
to define the capillary travel Φa
along which fluorescence was detected from the sample surface. Point A’ must thus be chosen instead of point A, to fit with this condition:
Consequently, point A’ in Figure
is positioned at a distance rA’ = 1.7 rspot from the beam centre. To compare the expected and measured values of Φa, we have thus replaced 2 rspot in Equation 1 by distance A’B = 1.7 rspot + rspot. With these considerations, Φa values of 258, 208, 178 and 168 μm are expected for a capillary radius of 50, 25, 10 and 5 μm, respectively. These values are in good agreement with the experimental values of Φa = 240, 205, 172 and 168 μm.
We have then reported in Figure
the variations of the maximum flux collected at the centre of the fluorescent zone as a function of capillary radius for a constant WD of 1 mm. The maximum collected flux increases as rcap1.8. This variation has to be compared to the ideal case of fluorescence collection from a point source using a thin capillary of length L placed at a working distance WD from the emitter. Figure
clearly shows that the collected signal level should remain constant if the capillary radius is reduced, providing the WD is reduced by the same factor by increasing the capillary length and assuming an ideal transmission coefficient of 100%. Obviously, the capillary only collects a part of fluorescence, nearly proportional to its section. In our case, the observed variations of the signal magnitude with the capillary radius are due to the fact that the fluorescent zone has dimensions higher or of the same order of magnitude than the capillary radius.
Maximum fluorescence flux dependence on the capillary radius during capillary scan. Experimental and simulated data.
X-ray collection using cylindrical monocapillary. Dependence of the collected flux on capillary radius and length. In both configurations, the signal magnitude is the same.
Is it possible to increase this signal by decreasing WD?
It is well known that cylindrical capillaries allow to significantly increase the collected signal by comparison with a pinhole with the same radius placed at the detector entry and positioned at the same WD + L
]. At high WD, the capillary nozzle is seen under a solid angle θ1
from a point source (Figure
b). Thus, all X-rays emitted by the point source within this solid angle will be transmitted through the capillary, assuming a total reflection of X-rays below the critical angle. The capillary gain G
regarding a pinhole of the same radius is given by the equation
Figure 7 X-ray collection using cylindrical monocapillary. Dependence of the collected flux on capillary working distance WD at constant sample detector distance. The detection through a capillary increases the collection solid angle. (a) Detection through a pinhole. (more ...)
If WD decreases, keeping WD + L constant, the collected signal magnitude first increases since the collection solid angle increases until it reaches θ2 = θc value. At this point (Figure
c), WD reaches WDc value given by:
In this case, the capillary gain is given by:
If WD is further decreased, the solid angle θ3 under which the capillary nozzle is seen from the point source is higher than θc (Figure
d). The collected signal is no more limited by the capillary acceptance: the capillary gain as well as the collected signal remain constant. Because the WDc value depends on the capillary radius and the smallest value of WDc is 1 mm for the capillaries tested in this work, this optimum value was chosen and taken constant in all these experiments.
Because the fluorescent emitting source in the experiments is not punctual, we have started simulations to estimate the flux collected with a 0.5-μm radius capillary positioned at a WD of 1 mm. These simulations are based on a finite element method calculation from fundamental parameter equations and will be presented elsewhere. Figure
shows the dependence of the collected signal with the capillary radius in the range of 0.5 to 50 μm. The calculated values are in good agreement with the experimental ones. The estimated flux with a 0.5-radius capillary is 0.07 photons/s. This value is obtained at 1 mm WD. However, the maximum signal should be reached at 100 μm WDc
value. For this WDc
value, about 0.7 counts/s flux can be expected. Note that increasing the acquisition time should lead to significant signal level enhancement with our EDX-SDD device. These results show that it is possible to collect the fluorescence signal using a thinner capillary without any loss on the signal level if it is close enough to the surface. Of course, using a brighter primary source such as a rotating anode or a liquid-metal jet anode electron-impact X-ray source
], a significantly higher signal (up to 100 times) can be expected Moreover, replacing the cylindrical capillary at the entry of the detector by an elliptical one would lead to an extra gain of 20
]. Thus sub-micro-resolution XRF would be possible with an in-lab excitation source. Of course, working with a synchrotron source would lead to higher signal magnitude which could allow to further shrink the capillary radius, and a sub-100-nm lateral resolution could probably be reached. The short capillary-sample working distance suggests that the cylindrical capillary could act as a scanning probe microscope tip to acquire simultaneously sample topography and chemical mapping by XRF analysis
], as already demonstrated for simultaneous SNOM-XAS XEOL
] apparatus. Moreover, within this perspective, the spatial resolution of the detection would not be limited by the critical angle θc
because the extremity of the glass tube would be approached in mechanical near-field interaction with the sample.