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Chapter 12
Atomic X-ray Spectrometry
X-ray emission, absorption, scattering,
fluorescence, diffraction.
12A Fundamental Principles
12A-1 Emission of X-rays: continuum and line spectra
Short-wavelength limit (0): depend
on accelerating voltage, but
independent of target material.
h0 = hc/0 = Ve (Duane-Hunt law)
0 (Å) = 12398/V
Continuum radiation results from
collision between the electrons of
the beam and the atoms of the
target material.
FIGURE 12-1 Distribution of continuum radiation from an X-ray tube with a tungsten
target. The numbers above the curves indicate the accelerating voltages.
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0.63 Å 0.71 Å
+ lines in 4~6Å
FIGURE 12-2 Line spectrum for an X-ray with a molybdenum target.
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TABLE 12-1 Wavelengths in Angstroms of the More Intense Emission
Lines for some Typical Elements
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Minimum acceleration voltage
required for the excitation of line
emission increases with atomic
number.
Fig.12-1 W: no line at <50kV
0.18Å and 0.21Å at 70kV
Moseley’s Law:
√1/ = K(Z-S)
Z: 原子序
Fig.12-2 Mo: no line at <20kV
FIGURE 12-3 Relationship between X-ray emission
frequency and atomic number for Kα1 and Lα1 lines.
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Electron transitions in the
innermost atomic orbitals.
Wavelengths of
characteristic X-ray lines
are independent of the
physical and chemical
states.
FIGURE 12-4 Partial
energy level diagram
showing common
transitions producing
X-rays. The most
intense lines are
indicated by the wider
arrow.
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TABLE 12-2 Common Radioisotopic Sources for X-ray Spectroscopy
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12A-2 Absorption Spectra
ln(P0/P) =x = x
: linear absorption
coefficient
: mass absorption
coefficient
wii (additive)
Absorption edge
FIGUER 12-5 X-ray absorption spectra for lead and silver.
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12A-4 Diffraction of X-rays
1) Spacing between atom layers is roughly
the same as radiation wavelength.
2) The scattering centers must be spatially
distributed in a highly regular way.
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(Why in X-ray?)
If AP + PC = n →
constructive interference
AP = PC = dsin
Bragg’s equation:
n = 2d sin
FIGURE 12-6 Diffraction of X-ray by a crystal.
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12B Instrument Components
12B-1 Sources
* The X-ray Tube
* Radioisotopes
* Secondary Fluorescent Sources
12B-2 Filters for X-ray
12B-3 X-ray Monochromators
energy or 
12B-4 X-ray Transducers and
Signal Processors
* gas-filled transducers
* scintillation counters
* semiconductor transducers
intensity
FIGURE 12-7 Schematic of an X-ray tube.
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12B-2 Filters for X-ray
FIGURE 12-8 USE of a filter to produce monochromatic radiation.
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12B-3 X-ray monochromators
Bragg’s equation:
n = 2dsin
準直器
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FIGURE 12-9 An X-ray
monochromator and detector.
Note that the angle of the
detector with respect to the
beam (2θ) is twice that of the
crystal face. For absorption
analysis, the source is an X-ray
tube and the sample is located
in the beam as shown. For
emission measurements, the
sample becomes a source of Xray fluorescence as shown in
the insert.
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X-ray spectrograph.
Scan of a Molybdenum specimen.
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TABLE 12-3 Properties of Typical diffracting Crystals
X-ray range 0.1~10Å:
require at least two interchangeable crystals.
n = 2dsin
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Dispersion: d/d = n/2dcos
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12B-4 X-ray Transducers and Signal Processors
• gas-filled transducers (充氣式傳感器)
• scintillation counters (閃爍計數器)：NaI + 0.2% Thallium iodide
• semiconductor transducers （半導體傳感器）
FIGURE 12-10 Cross section of a gas-filled detector.
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FIGURE 12-11
Gas amplification for various
types of gas-filled detectors.
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Semiconductor transducers
FIGURE 12-12 Vertical cross section of a lithium-drifted silicon detector for X-rays
and radiation from radioactive sources. (鋰漂移矽偵測器)
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12C X-Ray Fluorescence Methods (XRF)
Excitation is by irradiating the sample with a beam of X-rays from an
X-ray tube or a radioactive source.


Wavelength-dispersive X-ray fluorescence (WDXRF)- Fig. 12-9
* single channel (sequential): two targets: Cr for long wavelength
and W for short wavelength.
* multichannel (simultaneous): simultaneous detection of 24 elements.
Energy-dispersive X-ray fluorescence (EDXRF):
* simple and no moving parts in the excitation and detection components,
* without collimator and crystal diffractor.
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FIGURE 12-13 Energy-dispersive X-ray fluorescence spectrometer. Excitation by Xrays from (a) an X-ray tube and (b) a radioactive substance (curium-244, a 5.81
MeV alpha particle and X-ray source) as shown in the sensor head for the Mars
alpha proton X-ray spectrometer. The X-ray detector is a new room-temperature
type.
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FIGURE 12-14 X-ray spectrum obtained on Mars together with the deconvolution
model components. The main elemental characteristic peaks (Kα lines) are
labeled and Kβ lines are unlabeled.
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FIGURE 12-15(a) MiniPal 4 benchtop X-ray fluorescence spectrometer
showing removable turntable for up to twelve samples.
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FIGURE 12-15(b) Diagram showing the X-ray source, filter wheel, detector, and
sample turntable from the bottom.
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FIGURE 12-15(c) X-ray fluorescence spectrum of a rice sample. The shaded areas
under the curves are proportional to the amount of each element in the sample.
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FIGURE 12-15(d) Calibration curve obtained from nine rice samples. Integrated
areas from spectra similar to the one in (c) are plotted against the certified
concentrations of iron in the samples.
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FIGURE 12-16 Spectrum of an iron sample obtained with an energy-dispersive
instrument with a Rh anode X-ray tube source. The numbers above the peaks are
energies in keV.
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12D-1 X-ray Diffraction Method
1) Arrangement and spacing of atoms in crystalline materials: clearer
understanding of physical properties of metals, polymeric
materials, and other solids.
2) Qualitative identification and quantitative information about the
compounds present in a solid sample. (ex. KBr + NaCl)



Sample preparation: ground to a fine homogeneous powder.
Automated diffractometer like Figure 12-9, with the powdered
sample replaces the single crystal on its mount.
Photographic recording: Debye-Scherrer powder camera, d = 5.73
cm or 11.46 cm  1 mm = 1.0° or 0.5°.
3) Interpretation of Diffraction Patterns:
* based on the position of lines ( or 2) and their relative
intensities. Crystals are identified empirically (database:
477,000reference materials).
* determination of % crystallinity of materials (polymers & fibers)
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FIGURE 12-17 Schematic of (a) a Debye-Scherrer powder camera; (b) the film strip
after development. D2, D1, and T indicate positions of the film in the camera.
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If a monochromatic X-ray beam is directed at a
single crystal, then only one or two diffracted
beams may result.
If the sample consists of some tens of randomly
orientated single crystals, the diffracted beams
are seen to lie on the surface of several cones.
The cones may emerge in all directions,
forwards and backwards.
result
A sample of some hundreds of crystals (i.e. a
powdered sample) show that the diffracted
beams form continuous cones.
A circle of film is used to record the diffraction
pattern as shown. Each cone intersects the film
giving diffraction lines. The lines are seen as
arcs on the film.
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The powder method is used to determine the value of the lattice parameters
accurately. Lattice parameters are the magnitudes of the unit vectors a, b and c
which define the unit cell (單位晶胞) for the crystal.
X-ray diffraction pattern of zinc oxide
nanoparticles.
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FIGURE 12-18 APXS calibration curve for Fe corrected for attenuation coefficient.
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FIGURE IA2-1 Cold-vapor atomic fluorescence system for ultratrace
determinations of mercury.
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