5. X-ray Spectrometry5.1 X-ray Fluorescence Analysis5.2 Total Reflection X-ray Fluorescence Analysis5.3 Extended X-ray Absorption Fine Structure5.4 X-ray Microprobe Analysis

5.1 X-ray Fluorescence AnalysisX-ray fluorescence (XRF) is the emission of characteristic "secondary" (or fluorescent) X-raysfrom a material that has been excited by bombarding with high-energy X-rays or gamma rays. The phenomenon is widely used for elemental analysis and chemical analysis, particularly in the investigation of metals, glass, ceramics and building materials, and for research in geochemistry, forensic science and archaeology

A Philips PW1606 X-ray fluorescence spectrometer

Energy dispersive spectrometry

Wavelength dispersive spectrometry

5.1 X-ray Fluorescence Analysis

The physics of XRF

Electronic transitions in a calcium atom andCharacteristic x-ray radiations

The term fluorescence is applied to phenomena in which the absorption of higher-energy radiation results in the re-emission of lower-energy radiation

Characteristic radiations

Typical wavelength dispersive XRF spectrum

5.1 X-ray Fluorescence Analysis

i) Conventional x-ray tubes: most commonly used, because their output can readily be "tuned" for the application, and because very high power can be deployed.

ii) γ- ray sources: used without the need for an elaborate power supply, allowing use in smallportable instruments.

iii) Synchrotron: focused by an optic, the x-ray beam can be very small and very intense, and atomic information on the sub-micrometer scale can be obtained.

Source of radiation

End-window tube

Side-window tube

Target transmission tube

5.1 X-ray Fluorescence Analysis

DispersionIn energy dispersive analysis, the fluorescent x-rays emitted by the material sample are directed into a solid-state detector which produces a continuous distribution of pulses, the voltages of which are proportional to the incoming photon energies. This signal is processed by a multi-channel analyzer (MCA) which produces an accumulating digital spectrum that can be processed to obtain analytical data.

In wavelength dispersive analysis, the fluorescent x-rays emitted by the material sample are directed into a diffraction grating monochromator. The diffraction grating used is usually a single crystal. By varying the angle of incidence and take-off on the crystal, a single x-ray wavelength can be selected. The wavelength obtained is given by the Bragg Equation:

X-ray intensityThe secondary radiation is much weaker than the primary beam. Furthermore, the secondary radiation from lighter elements is of low energy (long wavelength) and has low penetrating power, and is severely attenuated if the beam passes through air for any distance. Because of this, for high-performance analysis, the path from tube to sample to detector is maintained under high vacuum. This means in practice that most of the working parts of the instrument have to be located in a large vacuum chamber.

5.1 X-ray Fluorescence AnalysisEnergy dispersive spectrometryIn energy dispersive spectrometers (EDX or EDS), the detector allows the determination of the energy of the photon when it is detected. Detectors historically have been based on silicon semiconductors, in the form of lithium-drifted silicon crystals, or high-purity silicon wafers.

Si(Li) detectors:These consist essentially of a 3-5 mm thick silicon junction type p-i-n diode with a bias of -1000 v across it. The lithium-drifted centre part forms the non-conducting i-layer. When anx-ray photon passes through, it causes a swarm of electron-hole pairs to form, and this causes a voltage pulse. To obtain sufficiently low conductivity, the detector must be maintained at low temperature, and liquid-nitrogen must be used for the best resolution. With some loss of resolution, the much more convenient Peltiercooling can be employed without liquid nitrogen.

5.1 X-ray Fluorescence Analysis

Wavelength dispersive spectrometryIn wavelength dispersive spectrometers (WDX or WDS), the photons are separated by diffraction on a single crystal before being detected. Although wavelength dispersive spectrometers are occasionally used to scan a wide range of wavelengths, producing a spectrum plot as in EDS, they are usually set up to make measurements only at the wavelength of the emission lines of the elements of interest.

Analyzer (Monochromator)

Flat crystal with Soller collimators Curved crystal with slits

5.1 X-ray Fluorescence Analysis

Commonly used analyzer crystal: LiF, ADP (ammonium dihydrogen phosphate), Ge, graphite, InSb, PE (tetrakis-(hydroxymethyl)-methane: penta-erythritol), KAP (potassium hydrogen phthalate), RbAP (rubidium hydrogen phthalate) and TlAP (thallium(I) hydrogen phthalate). In addition, synthetic multilayer is used to detect the light elements in the range Li to Mg.

material plane d nm min λ nm max λ nm intensity thermal expansion

durability

LiF 200 0.2014 0.053 0.379 +++++ +++ +++

LiF 220 0.1424 0.037 0.268 +++ ++ +++

LiF 420 0.0901 0.024 0.169 ++ ++ +++

ADP 101 0.5320 0.139 1.000 + ++ ++

Ge 111 0.3266 0.085 0.614 +++ + +++

graphite 001 0.3354 0.088 0.630 ++++ + +++

InSb 111 0.3740 0.098 0.703 ++++ + +++

PE 002 0.4371 0.114 0.821 +++ +++++ +

KAP 1010 1.325 0.346 2.490 ++ ++ ++

RbAP 1010 1.305 0.341 2.453 ++ ++ ++

Si 111 0.3135 0.082 0.589 ++ + +++

TlAP 1010 1.295 0.338 2.434 +++ ++ ++

6 nm SM - 6.00 1.566 11.276 +++ + ++

Detectors: used for wavelength dispersive spectrometry need to have high pulse processing speeds in order to cope with the very high photon count rates that can be obtained. In addition, they need sufficient energy resolution to allow filtering-out of background noise and spurious photons from the primary beam or from crystal fluorescence. There are three common types of detector: i) Gas flow proportional counters, ii) Sealed gas detectors, iii) Scintillation counters.

5.1 X-ray Fluorescence Analysis

Gas flow proportional counters are used mainly for detection of longer wavelengths >0.5nm. The gas is usually 90% argon, 10% methane ("P10"), although the argon may be replaced with neon or helium where very long wavelengths (over 5 nm) are to be detected.

Sealed gas detectors are similar to the gas flow proportional counter, except that the gas does not flow though it. The gas is usually krypton or xenon at a few atmospheres pressure. They are applied usually to wavelengths in the 0.15-0.6 nm range.

Scintillation counters; The crystal produces a group of scintillations for eachphoton absorbed, the number being proportional to the photon energy. This translates into a pulse from the photomultiplier of voltage proportional to the photon energy. The crystal must be protected with a relatively thick beryllium foil window, which limits the use of the detector to wavelengths below 0.25 nm.

5.1 X-ray Fluorescence Analysis

Other spectroscopic methods using the same principleIt is also possible to create a characteristic secondary X-ray emission with other incident radiation to excite the sample:

•Electron beam : electron microprobe•Ion beam: particle induced X-ray emission (PIXE).

When radiated by an x-ray beam, the sample also emits other radiations that can be used for analysis:

•Electrons ejected by photoelectric effect: X-ray photoelectron spectroscopy (XPS), Electron spectroscopy for chemical analysis (ESCA)

•Auger electrons: Auger electron spectroscopy (AES)

5.1 X-ray Fluorescence Analysis

AED Auger electron diffractionAES Auger electron spectroscopyAFM Atomic force microscopeAPS Appearance potential spectroscopyCAICISS Coaxial impact collision ion scattering spectroscopyCL CathodoluminescenceCDI Coherent Diffraction ImagingDVS Dynamic vapour sorptionEBIC Electron beam induced currentEBSD Electron backscatter diffractionEDX Energy dispersive X-ray spectroscopyEID Electron induced desorptionEPMA Electron Probe MicroanalysisESCA Electron spectroscopy for chemical analysisEPR Electron paramagnetic resonance spectroscopyESD Electron stimulated desorptionESR Electron spin resonance spectroscopyEXAFS Extended x-ray absorption fine structureFEM Field emission microscopyFIM-AP field ion microscopy-Atom probeFTIR Fourier transform infrared absorption spectroscopyGDMS Glow discharge mass spectrometryGDOS Glow discharge optical spectroscopyGISAXS Grazing Incidence Small Angle X-ray ScatteringGIXD Grazing Incidence X-ray Diffraction

GIXR Grazing Incidence X-ray ReflectivityHAS Helium atom scatteringHREELS High resolution electron energy loss spectroscopyHRTEM High-resolution transmission electron microscopyIAES Ion induced Auger electron spectroscopyIGA Intelligent gravimetric analysisIIX Ion induced X-ray analysisINS Ion neutralization spectroscopyIRS Infra Red spectroscopyISS Ion scattering spectroscopyLEED Low energy electron diffractionLEEM Low-energy electron microscopyLEIS Low energy ion scatteringLIBS Laser induced breakdown spectroscopy: LOES Laser optical emission spectroscopy LS Light (Raman) scatteringMEIS Medium energy ion scattering MTA Microthermal analysis NDP Neutron depth profiling

NEXAFS Near edge X-ray absorption fine structure

NMR Nuclear magnetic resonance spectroscopyNSOM Near-field optical microscopePD PhotodesorptionPDEIS Potentiodynamic electrochemical impedance spectroscopy

List of materials analysis methods

5.1 X-ray Fluorescence AnalysisSE Spetroscopic ellipsometrySEIRA Surface enhanced infrared absorption spectroscopySEM Scanning electron microscopySERS Surface Enhanced Raman SpectroscopySEXAFS Surface extended X-ray absorption fine structureSICM Scanning ion-conductance microscopySIMS Secondary ion mass spectrometrySNMS Sputtered neutral species mass spectroscopy SNOM Scanning Near-Field Optical Microscopy SPM Scanning probe microscopySTM Scanning tunneling microscopySTEM Scanning transmission electronmicroscopy

TEM Transmission Electron MicroscopyTXRF Total Reflection X-ray fluorescenceanalysis

UPS UV-photoelectron spectroscopyWAXS Wide angle X-ray ScatteringXAES X-ray induced Auger electron spectroscopy X-CTR X-ray crystal truncation rod scattering XDS X-ray diffuse scatteringXPEEM X-ray photoelectron emission microscopy XPS X-ray photoelectron spectroscopyXR X-ray reflectivityXRD X-ray diffractionXRF X-ray fluorescence analysis

XSW X-ray standing wave techniqueRBS Rutherford backscattering spectroscopyREM Reflection electron microscopy RHEED Reflection high energy electron diffractionSAXS Small Angle X-ray ScatteringSCANIIR Surface composition by analysis of neutral species and ion-impact radiation PED Photoelectron diffractionPIXE Particle (or proton) induced X-ray spectroscopyPTMS Photothermal microspectroscopy

5.1 X-ray Fluorescence Analysis

In simple cases quite unequivocal assignments of spectral lines can be made based on a library of Kα or Lα, or in case of doubt, when overlapping exists, Kβ or other L or M lines are checked to confirm or reject a line assignment.

Qualitative Analysis:

Quantitative Analysis:In the very low concentration range, quasi-linear relationship are found between intensity and concentration. As concentration of element increases, the fluorescent intensity candepart from proportionality to the amount present. These deviation from linearity mainly due to (i) Matrix absorption, and (ii) Enhancement by multiple excitation

Effect of iron concentration on the intensity of Fe Kα

5.1 X-ray Fluorescence AnalysisMatrix absorption: As the composition of the sample changes, so does its absorption coefficient. The absorption coefficients of an Fe-Al alloy is less than that of an Fe-Ag. The over-all is shown in figure.

Enhancement due to multiple excitation: : If the primary radiation causes element B in thespecimen to emit its characteristic radiation, of wavelength λB, and if λB is less than λK,A,

Then fluorescent K radiation from A will excited not only by the incident beam but also by fluorescent radiation from B. This effect is evident in Fe-Ni and Fe-Ag alloy. These effects so complicate the calculation of fluorescent intensities that quantitative analysis is usually performed on an empirical basis by the use of standard samples of known composition.

K-shell absorption edge of Fe

Primary fluorescence

Secondary fluorescence

5.1 X-ray Fluorescence Analysis

The ratio of the secondary fluorescent photon

More than tertiary fluorescent intensity is less than1% of the total intensity; negligible

As shown the above examples, quantitative analysis is quite complicate. Many methodological process are developed for accurate analysis of the compositionssuch as (i) Comparative method; •absorption correction method, •attenuation method, •compensation method, (ii) Mathematical method; •fundamental parameter method,•influence coefficient method, •empirical coefficient method.

5.1 X-ray Fluorescence AnalysisSynchrotron radiation induced x-ray emission

Source: • focused microprobe• continuum and mono-energetic excitation

Applications;• Collimated x-ray microscopes• Focused x-ray microscopes• Tomography• EXAFS and XANES

5.1 X-ray Fluorescence AnalysisDetection Limit: The lowest concentration level that can be determined to be statisticallysignificant from an analytical blank. The detection limit is expressed as a concentration CL

and is derived from the smallest measure xL, x being the instrumental reading.

Reading x versus C;

i mCx +=

where m is the slope and i is the intercept. If C=0, i=xB.

background (i or xB)

signal (x)

5.1 X-ray Fluorescence AnalysisFor background, is a mean value in the center of a symmetrical distribution curve (normal distribution or Gaussian distribution). The standard deviations for finite number of observation, n, calculated as the square root of the variance;

Bx

1n

xxs

n

1j BB2B

j

−

−=∑ =

2)(

The International Union of Pure and Applied Chemistry (IUPAC) determines the limit of detection

BBL sxx k+=

The attributed concentration is

mk

mBBL s)x(x

=−

= LL Cor , C

where k is a factor depending on confidence level desired. For k=3, the value recommended by IUPAC [confidence level; 1sB(68.27%), 2sB(95.45%) 3sB(99.73%)].

5.1 X-ray Fluorescence Analysis

Since the shaded area α is o.13%, the signal valuehas a probability of 0.13% to belong to

the population of values determining the mean value xB.BBL 3sxx +≥

Different values for CL are encountered when the distribution of errors is not normal. The standard deviation of s for counting of photons emitted at completely random intervals of time t obeys for an average number of accumulated counts N the equation (Poisson’sdistribution)

NsN =The detection limit can be expressed as a function of intensity IB with t as the countingtime for relative concentration unit of standard sample, m=IP/Cstandard

P

BdardsL I

tICC

/3 tan=

A standard format used by most manufacturers is to give CL for t=100sec.