# High Definition X-Ray Fluorescence: Principles and Techniques

Authors: Z. W. Chen; Walter M. Gibson; Huapeng Huang
Journal: X-Ray Optics and Instrumentation
 (2008)

---

## Abstract

Energy dispersive X-ray fluorescence (EDXRF) is a well-established and powerful tool for nondestructive elemental analysis of virtually any material. It is widely used for environmental, industrial, pharmaceutical, forensic, and scientific research applications to measure the concentration of elemental constituents or contaminants. The fluorescing atoms can be excited by energetic electrons, ions, or photons. A particular EDXRF method, monochromatic microfocus X-ray fluorescence (MμEDXRF), has proven to be remarkably powerful in measurement of trace element concentrations and distributions in a large variety of important medical, environmental, and industrial applications. When used with state-of-the-art doubly curved crystal (DCC) X-ray optics, this technique enables high-sensitivity, compact, low-power, safe, reliable, and rugged analyzers for insitu, online measurements in industrial process, clinical, and field settings. This new optic-enabled MμEDXRF technique, called high definition X-ray fluorescence (HD XRF), is described in this paper.


---

## Body

## 1. Introduction

X-ray fluorescence is a
well-established and powerful tool for nondestructive elemental  analysis of
virtually any material. It is widely used for environmental, industrial, pharmaceutical, forensic, and scientific
research applications to determine the presence or absence and in some cases to
measure the concentration of elemental constituents or contaminants. The fluorescing atoms can be excited by
energetic electrons, ions, or photons.
The fluorescent X-rays are in general measured by two types of detection
systems: wavelength dispersive detection (WDXRF) and energy dispersive
detection (EDXRF). In the former, the
fluorescence X-rays are diffracted from a single crystal or multilayer optic to
select a particular and often very narrow wavelength  (or X-ray energy) range, often corresponding
to characteristic X-rays from an element of interest. This provides high elemental specificity and,
because of the high signal-to-background ratio, often high sensitivity. EDXRF permits detection of a broad range of
elements simultaneously. The measurement
resolution (elemental specificity) depends in this case on the detector X-ray
energy resolution and counting rate performance. A particular EDXRF method, monochromatic
microfocus X-ray fluorescence (MμEDXRF),
has proven to be remarkably powerful in measurement of trace element
concentrations and distributions for a large variety of important medical,
environmental, and industrial applications [1].
In contrast with conventional X-ray fluorescence in which a broad
spectrum of X-ray energies are incident on the sample, including the continuum
Bremsstrahlung radiation resulting from electron scattering in the anode of a
high-voltage X-ray tube, excitation with monochromatic X-rays has greatly improved
signal-to-noise ratio for measurement of
secondary characteristic X-rays from the sample of interest. This is shown in Figure 1, which shows an XRF
spectrum from an NIST SRM 2783 sample excited with a direct beam from a molybdenum
X-ray tube and a spectrum from the same sample excited with a monochromatic beam from a doubly
curved crystal (DCC) optic of the type described in this paper.Figure 1
Comparison of XRF spectra taken from an
NIST SRM 2783 standard reference sample using the monochromatic XRF method (black) and conventional XRF method (red).The Bremsstrahlung background in the conventional XRF spectrum is from scattering
of source radiation in the sample. This
can be avoided by selecting a characteristic X-ray line from a target
irradiated by the source to excite fluorescent X-rays in the sample. This secondary excitation technique is used
in several commercial XRF systems [2] but requires a very high primary X-ray
source intensity to accommodate the large decrease in the X-ray intensity on
the sample due to the secondary production process. High-energy synchrotron sources are sometimes
used to produce an intense beam of tunable monochromatic X-rays which are used
for important material and medical XRF applications [3]. Another way to carry out X-ray fluorescence
free of the Bremsstrahlung background is to use an ion beam to excite
fluorescent X-rays in the sample of interest.
This is the origin of the much studied particle-induced X-ray excitation
(PIXE) technique [4]. All of these
approaches illustrate the value of monochromatic excitation. However, they all require large, expensive,
fixed, or laboratory-based facilities.
Another approach to monochromatic X-ray fluorescence is the use of
radioactive radiation sources such as C
109d and A
241m
[5]. Effective use of a A
241m
isotopic source provided elemental composition measurements on the famous
Explorer Mars Lander and other planetary and lunar probes [6]. Terrestrial and even portable [7] analyzers
utilizing radioactive sources have been used for environmental, industrial, and
mineralogical applications but safety and regulatory considerations have
constrained their widespread use. In addition,
the need to keep the amount of radioactive material low often leads to reduced
sensitivity and inconveniently large measurement time and sampling area. In addition, there is degradation and the
ultimate need to replace the radioactive source.The limitations
of the techniques described above can be dramatically overcome by the use of
state-of-the-art doubly curved crystal (DCC) X-ray optics which enable
high-sensitivity, compact, low-power, safe, reliable, and rugged analyzers for in-situ, online measurements in
industrial process, clinical, and field settings [8, 9]. In addition to the greatly improved
signal-to-background ratio shown in Figure 1, it should be noted that the
focused excitation beam from the DCC optic used in this example is more than
200 times smaller in area (0.20 mm diameter) than the 3 mm diameter beam needed
for the direct excitation measurement to obtain the same incident beam flux as
measured by the scattered Mo Kα (elastic and inelastic) beam intensity. This new optic-enabled, monochromatic,
microfocus, energy dispersive X-ray
fluorescence (OEMμEDXRF)
technique is the subject of this paper and for brevity is called High
Definition X-Ray Fluorescence (HD XRF).


## 2. Doubly Curved Crystal (DCC) X-Ray Optics

### 2.1. Bragg Diffraction

Doubly curved crystal (DCC) optics are based on the well-known Bragg law [10, 11] n
λ
=
2
d
sin
θ, where λ is the
wavelength of the diffracted beam, n is an integer indicting the order of
diffraction from crystal planes of spacing d, and θ is the
angle between the incident beam and the Bragg planes. For a highly collimated X-ray beam diffracted
from a symmetric (with the diffracting planes parallel to the surface) perfect
(flat) single crystal, the peak reflectivity reaches nearly unity over a small
range of angles near the Bragg angle. From the dynamical theory [12], the range of angles over which this
occurs is Ω
=
2
R
λ
2
(
√
F
h
F
h
−
)
/
π
V
sin
2
θ, where R is the classical electron radius
(2.818
×
10
−
15 m), λ is the
X-ray wavelength, the Fs are the structure factors for the reflections (hk1)
and (−
h
−
k
−
1), V is the
unit cell volume, and θ is the
Bragg angle. This distribution can be
modified by polarization effects (1 for σ polarized X-rays and cos2θ for π polarized X-rays), and can be broadened (and
reduced in intensity) by mosaic spread w
(
Δ
) and crystal distortion effects.  In addition, the peak reflectivity is
reduced by absorption in the crystal which also makes the reflectivity curve
asymmetric. Even small distortions can
greatly perturb the behavior of perfect single crystals. Although there is no general theory that can
handle arbitrary distortions, there are approximate treatments for special
cases [13–15]. A summary of the
intrinsic energy resolution for selected crystals and reflections for 1 Å(12.4 keV) X-rays is shown in
Table I from Siddons [16]. The best
possible energy and wavelength resolution is δ
E
/
E
=
δ
λ
/
λ
=
cot
θ
δ
θ
+
δ
τ, where δ
E and E are the energy band pass and the center energy of the beam,
respectively, θ is the
Bragg angle, and δ
τ is the intrinsic
width of the crystal reflection as shown in Table 1. The actual energy resolution is typically 2-3
times the calculated Δ
E
/
E due to the effects discussed above.Table 1
Selected monochromator crystals with selectedd-spacings and reflection widths for 1 Å(12.4 keV) X-rays.
Crystal
Reflection
d-spacing (nm)
Refl. width (μrad)
Intrinsic resolution,δ
τ
Silicon
(111)
0.31355
22.3
1.36
×
10
−
4
(220)
0.19201
15.8
5,37×
10
−
5
Germanium
(111)
0.32664
50.1
3.1
×
10
−
4
(220)
0.20002
37.4
1.37
×
10
−
4
Diamond
(111)
0.20589
15.3
5.8
×
10
−
5
(400)
0.089153
5.2
7.4
×
10
−
6
Graphite
(0002)
0.3354
Sample dependent
Sample dependent


### 2.2. Curved Crystal Diffraction

There are three reasons to apply a uniform curvature to a single crystal plate used as a
monochromator: (1) to increase the
diffracted beam intensity from a point X-ray source by meeting the Bragg
condition over a larger range of incident angles from the divergent incident
beam, (2) to improve the energy resolution for a divergent beam, and (3) to provide
output beam concentration or focusing.
For Bragg reflections, the most common geometry is based on the Roland circle
principle which relies on the well-known property of a circle that an arc
segment subtends a constant angle for any point on the circle. In this geometry, the incidence angle for the
local Bragg plane must be constant. The
result of this was shown by Johansson [17] to require the radius of curvature
to be twice the radius of the crystal surface.
This can be achieved by a combination of bending and machining the
crystal as shown in Figure 2(a). For
applications requiring a small aperture, aberrations introduced by omitting the
machining step are small and acceptable.
This is the familiar Johann geometry [18] shown in Figure 2(b), which is
the one used in the studies reported here.(a) The Johansson focusing monochromator, (b) the
Johann focusing monochromator.
(a)
(b)Although the geometry shown in Figure2 is symmetrical, it is possible to
place the crystal anywhere on the circle and, therefore, achieve a (de)magnification
of the source spot other than unity. In
this case, the surface of the diffracting crystal must be cut at an angle to
the Bragg planes in order to maintain the Bragg condition across the range of
incidence angles. Depending on the
source geometry, the bending radius, and symmetry of the crystal, the bending
can improve or degrade the energy resolution of the monochromator. Each case must be considered in detail but it
is possible to make some general observations.
(1) If the angular aperture of the crystal as seen from the source is
large enough to cover
the intrinsic width (almost always true for perfect single crystals), the
Roland circle geometry will improve the energy resolution. (2) When the absorption length becomes larger
than the extinction distance for the X-rays inside the crystal, the X-rays can
travel deeply into the bent crystal so that the incidence angle changes with
depth leading to a broader energy band pass. (3) If the bending radius is small enough that the Bragg angle changes
more than the intrinsic width, the peak reflectivity will decrease and the
energy band pass will broaden. In
practice, if the energy resolution is important, it should be measured
experimentally.


### 2.3. Doubly Curved Crystal Diffraction

There is additional intensity benefit if the crystal is also curved in a plane
perpendicular to the Roland circle as shown in Figure3. The profile of the diffracted beam is shown
in Figure 4. In the case of a toroidally
curved crystal, the bending radius of the crystal perpendicular to the Roland circle
is R
V
=
2
R
sin
2
θ
B. This geometry gives point-to-point focusing
on the Roland circle and the source spot S is imaged at the image point I. As discussed below, other curvature
geometries such as elliptical, logarithmic, and parabolic can be used to accommodate
different source or image spot geometries.
Toroidal curvature is frequently used in mirrors at synchrotron X-ray
sources [19] which use small angle scattering rather than diffraction and is
occasionally used in diffraction-based monochromators on synchrotrons where
(because the curvature is facilitated by cutting grooves in the back of thick
crystals) it is referred to as sagittal-focusing geometry.Figure 3
Geometry of a toroidally curved doubly
curved crystal (DCC) optic.Figure 4
Beam profile at two points for toroidal DCC monochromator.Use of focusing geometries for producing
a point image from a point X-ray source for analytical use was described and
investigated during the 1950s [20, 21].
In the 1980s and 1990s, the X-ray optical properties of DCC optics were
systematically studied by using a ray tracing method [22–26]. Fabrication and application of DCC optics
were also reported in the early 1990s by Wittry et al. [27, 28]. However, widespread use and practical
applications of DCC optics for monochromatic beam applications was impeded by
the difficulty of fabricating DCC optics.An important development was reported in 1997 and 1998 [29, 30]. In these reports, an intense micro Cu Kα1 beam was obtained using a Johann-type
doubly curved mica crystal for monochromatic microfocus XRF applications. The high intensity gain of the mica DCC was
based on a novel crystal-bending technology.
This technology can provide elastic bending of crystals into various
complex shapes with precise figure control.
The proprietary technology used has been refined and extended at X-Ray
Optical Systems, Inc., (XOS) to produce the instruments and results summarized
in the companion paper to this review [31].Because of the
large collection solid angle of DCC optics, intense monochromatic beams can be
obtained even with low-power compact X-ray sources. Characteristics of selected monochromatic,
focused, DCC-based X-ray beams are shown in Table2.Table 2
Examples of nominal operating parameters for focusing, monochromatic X-ray beams integrated with microfocus X-ray sources.
Optic crystal X-ray line
Energy (keV)
Source power (W)
Bragg angle (θ
B)
Capture angle (sr)
Nominal focal spot size, FWHM (μm)
Flux (cps)
Working distance (mm)
Ge 220
Cr Kα1
5.4
14
35.1
0.03
80
2
×
10
9
120
Si 111
Cu Kα1
8.0
14
14.2
0.015
50
1
×
10
9
150
Si 111
Cu Kα1
8.0
50
14.2
0.01
150
2
×
10
9
150
Si 220
Cu Kα1
8.0
14
22.8
0.01
50
3
×
10
8
135
Si 220
W Lα1
8.4
10
22.6
0.01
20
1
×
10
8
80
Si 220
Mo Kα1
17.5
14
10.6
0.01
60
1
×
10
8
120A principal benefit of doubly curved crystal optics is the ability to
provide an intense monochromatic focused beam.
Various crystal materials can be used for DCC optics including Si, Ge,
quartz, graphite, and mica. The
collection solid angle of DCC optics is determined by the capture angle in the
dispersive plane and the included rotational angleϕ. Figures 3, 4, and Table 2
are for symmetrical toroidal optics. For
such cases, the spot size is an image of the source.In the Johan geometry, the optic can be placed nonsymmetrically on the
Roland circle as shown in Figure5. In
this case, the crystal planes must be tilted with respect to the crystal
surface an appropriate amount γ depending on the displacement from the symmetry position. This can be used
to demagnify the beam to obtain a smaller beam spot. Such demagnification has been used to produce
a beam spot of 20 μm diameter with a small spot Oxford Apogee source [32]. In the reverse mode, beam magnification can be
achieved to obtain a weakly convergent beam while retaining a large input
collection angle. This has been
particularly useful for diffraction (XRD) studies which also benefit from the
use of a monochromatic beam and can be especially useful for simultaneous
XRD/XRF measurements for example in metallurgical and mineralogical (planetary)
applications. In order to increase the
monochromatic beam intensity, multiple diffracting crystals can be used as
shown in Figure 6. The collection solid
angle and, therefore, the beam intensity can also be increased by using
noncircular profiles for the optic bending in the dispersive plane such as
elliptical, parabolic, or inverse logarithmic spiral as shown in Figure 7. This is particularly useful at low X-ray
energies where the Bragg diffraction angle is large and has been used with
multiple tiled optic elements to obtain collection angles up to 30
×
20 degrees
for sulfur (2.3 keV) X-rays [33]. For
higher X-ray energies where the Bragg angle becomes small, the collection solid
angle can be increased by the use of multiple optics wrapped around the
included rotational angle ϕ as shown in Figures 8 and  9.Figure 5
Asymmetric placement of DCC monochromator crystal for beam spot
magnification.Figure 6
Use of multiple DCC crystals to increase focused beam intensity.(a) Drawing of a revolving logspiral DCC optic for S
Kα (2.3 keV); (b) schematic of logarithmic curved DCC optic with X-rays ray from source on right to detector on left; (c) photograph of multisegment DCC optic used in SINDIE analyzer for Sulfur in diesel.
(a)
(b)
(c)Figure 8
Schematic of rotationally wrap around DCC monochromators to increase
focused beam intensity.Figure 9
Beam profile from eleven-segment Cu Kα rotationally wrap around
demagnifying DCC optic with photograph of X-beam assembly (height of
X-beam is 8 inches).The capture angle in the dispersive plane is typically 1–5 degrees and the
rotational angle can be 5–300 degrees. The large potential collection efficiency in
the rotational angle (~300°) is made possible by the rotational
symmetry around the S-I axis shown in Figure 2.
The large solid angle of collection results in a monochromatic X-ray
beam intensity produced with a low power (20–50 W) X-ray
source comparable to the intensity of a monochromatic beam obtainable from a
high power (5–10 kW) rotating
anode source using conventional optics.
As noted above, the focal spot size of the diffracted beam is mainly
determined by the X-ray source size. The
capabilities of commercially available DCC optics [34] are summarized in Table
3.Table 3
Characteristics of current DCC optics.
Output beam energies (keV)
Mo Lα1, 2.29 keV; Cr Kα1, 5.41 keV; Cu Kα1, 8.05 keV; WL
β1, 8.40 keV;WL
β1, 9.67 keV;
Mo Kα1, 17.48 keV; or Ag Kα1, 22.16 keV
Reflection efficiency
5% to 20%
Collection solid angle
0.005 to 0.1 steradians
Convergent angles
0.2–5 degrees (dispersive plane) x 0.2–45 degrees (rotational plane)
Focused beam size
20–300μm depending on the source size and optic
design


## 2.1. Bragg Diffraction

Doubly curved crystal (DCC) optics are based on the well-known Bragg law [10, 11] n
λ
=
2
d
sin
θ, where λ is the
wavelength of the diffracted beam, n is an integer indicting the order of
diffraction from crystal planes of spacing d, and θ is the
angle between the incident beam and the Bragg planes. For a highly collimated X-ray beam diffracted
from a symmetric (with the diffracting planes parallel to the surface) perfect
(flat) single crystal, the peak reflectivity reaches nearly unity over a small
range of angles near the Bragg angle. From the dynamical theory [12], the range of angles over which this
occurs is Ω
=
2
R
λ
2
(
√
F
h
F
h
−
)
/
π
V
sin
2
θ, where R is the classical electron radius
(2.818
×
10
−
15 m), λ is the
X-ray wavelength, the Fs are the structure factors for the reflections (hk1)
and (−
h
−
k
−
1), V is the
unit cell volume, and θ is the
Bragg angle. This distribution can be
modified by polarization effects (1 for σ polarized X-rays and cos2θ for π polarized X-rays), and can be broadened (and
reduced in intensity) by mosaic spread w
(
Δ
) and crystal distortion effects.  In addition, the peak reflectivity is
reduced by absorption in the crystal which also makes the reflectivity curve
asymmetric. Even small distortions can
greatly perturb the behavior of perfect single crystals. Although there is no general theory that can
handle arbitrary distortions, there are approximate treatments for special
cases [13–15]. A summary of the
intrinsic energy resolution for selected crystals and reflections for 1 Å(12.4 keV) X-rays is shown in
Table I from Siddons [16]. The best
possible energy and wavelength resolution is δ
E
/
E
=
δ
λ
/
λ
=
cot
θ
δ
θ
+
δ
τ, where δ
E and E are the energy band pass and the center energy of the beam,
respectively, θ is the
Bragg angle, and δ
τ is the intrinsic
width of the crystal reflection as shown in Table 1. The actual energy resolution is typically 2-3
times the calculated Δ
E
/
E due to the effects discussed above.Table 1
Selected monochromator crystals with selectedd-spacings and reflection widths for 1 Å(12.4 keV) X-rays.
Crystal
Reflection
d-spacing (nm)
Refl. width (μrad)
Intrinsic resolution,δ
τ
Silicon
(111)
0.31355
22.3
1.36
×
10
−
4
(220)
0.19201
15.8
5,37×
10
−
5
Germanium
(111)
0.32664
50.1
3.1
×
10
−
4
(220)
0.20002
37.4
1.37
×
10
−
4
Diamond
(111)
0.20589
15.3
5.8
×
10
−
5
(400)
0.089153
5.2
7.4
×
10
−
6
Graphite
(0002)
0.3354
Sample dependent
Sample dependent


## 2.2. Curved Crystal Diffraction

There are three reasons to apply a uniform curvature to a single crystal plate used as a
monochromator: (1) to increase the
diffracted beam intensity from a point X-ray source by meeting the Bragg
condition over a larger range of incident angles from the divergent incident
beam, (2) to improve the energy resolution for a divergent beam, and (3) to provide
output beam concentration or focusing.
For Bragg reflections, the most common geometry is based on the Roland circle
principle which relies on the well-known property of a circle that an arc
segment subtends a constant angle for any point on the circle. In this geometry, the incidence angle for the
local Bragg plane must be constant. The
result of this was shown by Johansson [17] to require the radius of curvature
to be twice the radius of the crystal surface.
This can be achieved by a combination of bending and machining the
crystal as shown in Figure 2(a). For
applications requiring a small aperture, aberrations introduced by omitting the
machining step are small and acceptable.
This is the familiar Johann geometry [18] shown in Figure 2(b), which is
the one used in the studies reported here.(a) The Johansson focusing monochromator, (b) the
Johann focusing monochromator.
(a)
(b)Although the geometry shown in Figure2 is symmetrical, it is possible to
place the crystal anywhere on the circle and, therefore, achieve a (de)magnification
of the source spot other than unity. In
this case, the surface of the diffracting crystal must be cut at an angle to
the Bragg planes in order to maintain the Bragg condition across the range of
incidence angles. Depending on the
source geometry, the bending radius, and symmetry of the crystal, the bending
can improve or degrade the energy resolution of the monochromator. Each case must be considered in detail but it
is possible to make some general observations.
(1) If the angular aperture of the crystal as seen from the source is
large enough to cover
the intrinsic width (almost always true for perfect single crystals), the
Roland circle geometry will improve the energy resolution. (2) When the absorption length becomes larger
than the extinction distance for the X-rays inside the crystal, the X-rays can
travel deeply into the bent crystal so that the incidence angle changes with
depth leading to a broader energy band pass. (3) If the bending radius is small enough that the Bragg angle changes
more than the intrinsic width, the peak reflectivity will decrease and the
energy band pass will broaden. In
practice, if the energy resolution is important, it should be measured
experimentally.


## 2.3. Doubly Curved Crystal Diffraction

There is additional intensity benefit if the crystal is also curved in a plane
perpendicular to the Roland circle as shown in Figure3. The profile of the diffracted beam is shown
in Figure 4. In the case of a toroidally
curved crystal, the bending radius of the crystal perpendicular to the Roland circle
is R
V
=
2
R
sin
2
θ
B. This geometry gives point-to-point focusing
on the Roland circle and the source spot S is imaged at the image point I. As discussed below, other curvature
geometries such as elliptical, logarithmic, and parabolic can be used to accommodate
different source or image spot geometries.
Toroidal curvature is frequently used in mirrors at synchrotron X-ray
sources [19] which use small angle scattering rather than diffraction and is
occasionally used in diffraction-based monochromators on synchrotrons where
(because the curvature is facilitated by cutting grooves in the back of thick
crystals) it is referred to as sagittal-focusing geometry.Figure 3
Geometry of a toroidally curved doubly
curved crystal (DCC) optic.Figure 4
Beam profile at two points for toroidal DCC monochromator.Use of focusing geometries for producing
a point image from a point X-ray source for analytical use was described and
investigated during the 1950s [20, 21].
In the 1980s and 1990s, the X-ray optical properties of DCC optics were
systematically studied by using a ray tracing method [22–26]. Fabrication and application of DCC optics
were also reported in the early 1990s by Wittry et al. [27, 28]. However, widespread use and practical
applications of DCC optics for monochromatic beam applications was impeded by
the difficulty of fabricating DCC optics.An important development was reported in 1997 and 1998 [29, 30]. In these reports, an intense micro Cu Kα1 beam was obtained using a Johann-type
doubly curved mica crystal for monochromatic microfocus XRF applications. The high intensity gain of the mica DCC was
based on a novel crystal-bending technology.
This technology can provide elastic bending of crystals into various
complex shapes with precise figure control.
The proprietary technology used has been refined and extended at X-Ray
Optical Systems, Inc., (XOS) to produce the instruments and results summarized
in the companion paper to this review [31].Because of the
large collection solid angle of DCC optics, intense monochromatic beams can be
obtained even with low-power compact X-ray sources. Characteristics of selected monochromatic,
focused, DCC-based X-ray beams are shown in Table2.Table 2
Examples of nominal operating parameters for focusing, monochromatic X-ray beams integrated with microfocus X-ray sources.
Optic crystal X-ray line
Energy (keV)
Source power (W)
Bragg angle (θ
B)
Capture angle (sr)
Nominal focal spot size, FWHM (μm)
Flux (cps)
Working distance (mm)
Ge 220
Cr Kα1
5.4
14
35.1
0.03
80
2
×
10
9
120
Si 111
Cu Kα1
8.0
14
14.2
0.015
50
1
×
10
9
150
Si 111
Cu Kα1
8.0
50
14.2
0.01
150
2
×
10
9
150
Si 220
Cu Kα1
8.0
14
22.8
0.01
50
3
×
10
8
135
Si 220
W Lα1
8.4
10
22.6
0.01
20
1
×
10
8
80
Si 220
Mo Kα1
17.5
14
10.6
0.01
60
1
×
10
8
120A principal benefit of doubly curved crystal optics is the ability to
provide an intense monochromatic focused beam.
Various crystal materials can be used for DCC optics including Si, Ge,
quartz, graphite, and mica. The
collection solid angle of DCC optics is determined by the capture angle in the
dispersive plane and the included rotational angleϕ. Figures 3, 4, and Table 2
are for symmetrical toroidal optics. For
such cases, the spot size is an image of the source.In the Johan geometry, the optic can be placed nonsymmetrically on the
Roland circle as shown in Figure5. In
this case, the crystal planes must be tilted with respect to the crystal
surface an appropriate amount γ depending on the displacement from the symmetry position. This can be used
to demagnify the beam to obtain a smaller beam spot. Such demagnification has been used to produce
a beam spot of 20 μm diameter with a small spot Oxford Apogee source [32]. In the reverse mode, beam magnification can be
achieved to obtain a weakly convergent beam while retaining a large input
collection angle. This has been
particularly useful for diffraction (XRD) studies which also benefit from the
use of a monochromatic beam and can be especially useful for simultaneous
XRD/XRF measurements for example in metallurgical and mineralogical (planetary)
applications. In order to increase the
monochromatic beam intensity, multiple diffracting crystals can be used as
shown in Figure 6. The collection solid
angle and, therefore, the beam intensity can also be increased by using
noncircular profiles for the optic bending in the dispersive plane such as
elliptical, parabolic, or inverse logarithmic spiral as shown in Figure 7. This is particularly useful at low X-ray
energies where the Bragg diffraction angle is large and has been used with
multiple tiled optic elements to obtain collection angles up to 30
×
20 degrees
for sulfur (2.3 keV) X-rays [33]. For
higher X-ray energies where the Bragg angle becomes small, the collection solid
angle can be increased by the use of multiple optics wrapped around the
included rotational angle ϕ as shown in Figures 8 and  9.Figure 5
Asymmetric placement of DCC monochromator crystal for beam spot
magnification.Figure 6
Use of multiple DCC crystals to increase focused beam intensity.(a) Drawing of a revolving logspiral DCC optic for S
Kα (2.3 keV); (b) schematic of logarithmic curved DCC optic with X-rays ray from source on right to detector on left; (c) photograph of multisegment DCC optic used in SINDIE analyzer for Sulfur in diesel.
(a)
(b)
(c)Figure 8
Schematic of rotationally wrap around DCC monochromators to increase
focused beam intensity.Figure 9
Beam profile from eleven-segment Cu Kα rotationally wrap around
demagnifying DCC optic with photograph of X-beam assembly (height of
X-beam is 8 inches).The capture angle in the dispersive plane is typically 1–5 degrees and the
rotational angle can be 5–300 degrees. The large potential collection efficiency in
the rotational angle (~300°) is made possible by the rotational
symmetry around the S-I axis shown in Figure 2.
The large solid angle of collection results in a monochromatic X-ray
beam intensity produced with a low power (20–50 W) X-ray
source comparable to the intensity of a monochromatic beam obtainable from a
high power (5–10 kW) rotating
anode source using conventional optics.
As noted above, the focal spot size of the diffracted beam is mainly
determined by the X-ray source size. The
capabilities of commercially available DCC optics [34] are summarized in Table
3.Table 3
Characteristics of current DCC optics.
Output beam energies (keV)
Mo Lα1, 2.29 keV; Cr Kα1, 5.41 keV; Cu Kα1, 8.05 keV; WL
β1, 8.40 keV;WL
β1, 9.67 keV;
Mo Kα1, 17.48 keV; or Ag Kα1, 22.16 keV
Reflection efficiency
5% to 20%
Collection solid angle
0.005 to 0.1 steradians
Convergent angles
0.2–5 degrees (dispersive plane) x 0.2–45 degrees (rotational plane)
Focused beam size
20–300μm depending on the source size and optic
design


## 3. X-Beam

Efficient use of
DCC optics requires a close match between the optic and the electron
bombardment X-ray source spot on the anode. As noted in Section2, for a well-made symmetrical toroidal optic, the
source spot size is imaged at the optic focal point. For asymmetrical optics and for optic figures
different from circular toroidal optics, a more complex relationship between the
source spot size and the image focal spot size exists. For example, the focal spot for an inverse
logarithmic spiral optic of the type shown in Figure 7 is much larger than the source spot
size. For some applications this is
acceptable, especially if the detector used has an input area larger than the
spot size. It should be noted that it is
not possible to reverse this optic in order to achieve a small spot size from a
large source since X-rays from each part of the source are incident on each
part of the optic.Virtually in every application,
precise alignment of the optic with the source position is critical. This can often be a problem since the source
spot position on the anode can vary as the source warms up or if the source
power is changed, causing the alignment to change and the optic output
intensity to vary. To alleviate this
problem, proprietary X-beams have been developed at XOS in which a thermal
management system is used to keep the source spot constant during warm up of
the source (which in some cases can take as long as two hours) or the source
power is changed. In the X-beam assembly,
the optic is prealigned and the desired beam intensity can be obtained within
less than two or three minutes and held constant (usually within 0.3%) for
extended periods. Furthermore, the
desired intensity can be reproduced through multiple on-off cycles of the X-ray
system. In addition, X-Beams are
internally shielded against radiation leakage and can contain an internal
shutter and filter wheel assembly. Also,
X-Beams with coupled DCC optics are air cooled, compact, and can be operated in
any arbitrary orientation. A typical DCC
X-Beam, about eight inches high and weighing less than five kilograms, is shown
in the inset in Figure9. This compact, low-power,
safe, rugged, and reliable X-ray source-optic assembly is at the heart of most
HD XRF analyzers discussed in the accompanying paper [31].


## 4. Fundamental Parameters Analysis

The ability to measure the intensity of X-ray fluorescence from individual elemental
constituents in complex materials even when the amount present is low provides
the possibility for rapid, nondestructive elemental analysis. As shown in Figure1, such measurements are
greatly facilitated by the use of a monochromatic excitation beam. This has been recognized for decades. For very thin samples such as for air
particulates collected on thin filters, quantitative analysis is
straightforward. Such first principle
calculations for thin samples require measurement of the integrated peak
intensity for each element and application of experimentally determined
detector response functions and experimental [35] or calculated [36]
fluorescent X-ray yields for pure samples of the elements of interest for a monochromatic
excitation X-ray beam of the appropriate energy. The excitation probability is highest for
elements with fluorescent X-rays just below the energy of the exciting
photons. An example of an experimental
fluorescent X-ray excitation curve is shown in Figure 10 for a secondary ZrKα
1Kβ (15.7–17.7 keV) excitation beam from Nielson [35]. For accurate measurement, it is still
necessary in such measurements to make corrections for absorption and
scattering from the measured elements and from the filter collector. Such corrections are more important for light
elements such as sulfur but normally are still less than 10% of the uncorrected
measurement [37]. For thicker samples,
matrix scattering and absorption effects become much more important and
suitable corrections and adjustment are crucial for quantitative application of
X-ray fluorescence.Figure 10
Experimental X-ray excitation curve measured for a Zr secondary
source by the use of thin metal samples evaporated on thin Mylar substrate
films from [35].Since the seminal
work of Compton
[38], methods have been explored to make matrix corrections for X-ray
fluorescence analysis. These have
traditionally involved use of standards of known composition [39, 40] to
calibrate the measurement system which must always take into account the
detection method, geometry, and sample form.
For conventional X-ray fluorescence, the analysis is complicated by the
presence of a large Bremsstrahlung continuum which also reduces measurement
sensitivity and requires background evaluation methods [41, 42]. As noted in Section 1, introduction of monochromatic
X-ray excitation dramatically improves the signal-to-background (S/B) ratio for
trace element determinations by eliminating the background due to scattering in
the sample of Bremsstrahlung radiation from the X-ray source. The clean, background-free X-ray spectrum also
permits analysis of the ratio of the Rayleigh (coherent) and Compton scattering
(incoherent) peaks for evaluation of X-ray absorption and scattering due to
elements in the sample matrix.  This is particularly important in evaluating
the matrix effects from light elements (such as H, C, N, and O) that are not
measured in the XRF spectrum. A
comprehensive review of studies based on the use of the Compton
scattering, especially for
monochromatic (secondary and radioactive) sources, is given by Nielson [43]. A detailed analyses for matrix absorption and
scattering effects for fundamental parameter (FP) analysis of a variety of
materials from low Z substrates such as petroleum to plant, mineral, and metal
substrates using single (Zr) [44] and double (Zr and Ti) secondary X-ray
sources [45] is described by Nielsen using an iterative analysis procedure
[35].An HD XRF
analysis software package built upon and extending the previous work is
currently under development at XOS based on the fundamental parameter approach
[46]. This fundamental parameter (FP) approach
has already achieved notable success in analysis of thin, filter or impact
membrane collected air particulate samples.  As discussed in the accompanying paper, the
use of HD XRF is particularly valuable for measurements of small particle
fractions of importance for health studies and for the small sampling volumes
and small sample sizes needed for portable personal environmental
monitors. Measurement of ultratrace
element concentrations in calibration samples prepared and characterized at the
Trace Elements Laboratory at Wadsworth Center
of the New York
State Health Laboratory for evaluation of body fluids (urine, blood, and
plasma) has shown excellent agreement with inductively coupled plasma-mass
spectroscopy (ICP-MS) characterized samples for lead and arsenic at concentrations from 10 ppb to less than 50 ppb. These studies are part
of an ongoing NIH funded study that has also shown the ability to analyze a
variety of other elements (Fe, Cu, Zn) of particular interest for studies of
Alzheimer's Disease (AD) and other neurodegenerative disorders in collaboration
with Alzheimer’s Center at Albany Medical Center and the Wadsworth Center in
Albany, NY, USA. A separate NIH funded
study of trace metal deposits in autopsied brain and spinal cord tissues by use
of HD XRF is also underway. Examples
from these FP HD XRF studies as well as other studies are discussed in the
accompanying paper [31].Computer-based
simulations are very useful to understand the X-ray scattering and absorption
processes and the role of detector response functions and measurement
geometries that lead to monochromatic EDXRF spectra for a variety of analyte
elements over a wide range of concentrations in different sample matrices and
thicknesses. This has been abundantly demonstrated
in an extensive systematic program based on a Monte Carlo—Library
Least-Squares method developed by Gardener et al. at North Carolina
State University over more than two decades [47–53]. A detailed summary of this method is given by
Li et al. [54].A very efficient analytical simulation method for HD XRF measurements is under
development [46]. An example of such a
simulation for a polyethylene standard sample containing controlled amounts of
Cr, Hg, Pb, and Br is shown in Figure 11. This simulation is being refined to more completely account for
secondary scattering effects. Analyses
of thick plastic standards are shown in Table 4 with concentrations of
observed heavy element constituents obtained from fitting of simulated peak intensities
as shown in Figure 11. Even without
further refinement, agreement with the reference values is very close and
provides a basis for reverse FP analyses for thin or thick water or plastic-matrix
homogeneous samples. The analysis is
currently being refined for other plastic, organic, or metallic homogeneous
matrices.Table 4
Reference and measured values for three polyethylene standards. The experimental uncertainty
(at 95% level) includes estimated systematic uncertainty plus Poisson counting statistical uncertainty.
Cr
Hg
Pb
Br
Uncertainty
PE_5398_N
Ref.
1001
1000
1000
500
4% (95% level)
Mea.
1020
950
981
442
10% (95% level)
PE_H_18A
Ref.
1000
1100
1200
1100
4% (95% level)
Mea.
1020
1150
1220
1090
10% (95% level)
PE_L
Ref.
400
200
400
500
4% (95% level)
Mea.
401
185
419
508
10% (95% level)Figure 11
HD XRF spectrum from polyethylene standard PE 5398 L sample and
analytical simulated spectrum from fundamental parameters analysis.  A background subtraction was made for
the spectrum below 15.2 keV.The physical constants used in the FP analysis are the incident and exit angle, the energy
of the incident monochromatic X-ray beam, tabulated mass attenuation
coefficients [55], fluorescence yields [56], absorption jump ratios [57],
intensity ratios of lines within a given series (e.g., Kα/Kβ ratio), and
energies of absorption edges and emission lines [58].The effects
of particle size in inhomogeneous matrices and samples with layers of differing
materials and constituents are under examination. A special but important class of layered
inhomogeneous samples is paint on a thick homogeneous substrate. Both experimental and analytical studies are
underway for FP analysis of such cases.
Preliminary results show promise for such applications and are discussed
in the accompanying paper on HD XRF applications [31].


## 5. Conclusions

A new HD XRF
system based on the use of proprietary DCC X-ray optics coupled with low-power
X-ray tube sources in a proprietary, compact, portable, safe, stable, X-beam
assembly for monochromatic, microfocus, energy dispersive, X-ray fluorescence
enables a broad variety of in situ, online, clinical, or remote applications in
science, medicine, and industry. The
principles and techniques as well as the basis for automated fundamental
parameter (FP) (standardless) analysis that is enabled by this new analytical
tool are discussed in this report.
Selected applications are reviewed in an accompanying paper [31]. A schematic diagram of a laboratory-based HD
XRF system of the type used for the measurement shown in Figure 11 and Table 4
is shown in Figure 12. Development of
specialized HD XRF analyzers based on this approach is discussed in the
companion paper [31].Figure 12
Schematic of laboratory benchtop HD XRF
analyzer.



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*Source: 318171-2008-05-26.xml*