This document provides an overview of x-ray techniques, including: 1. X-rays were discovered in 1895 by Roentgen and have wavelengths between 0.1-10nm, similar to atomic sizes. Bragg's law from 1912 describes x-ray diffraction from atomic lattices in crystals. 2. X-ray fluorescence analysis uses x-rays to excite elements and analyze chemical compositions with parts-per-million sensitivity but limited spatial resolution. Electron microprobes use focused electron beams for higher 1-micron spatial resolution but lower detection limits of 0.01%. 3. Quantitative analysis with electron microprobes requires corrections for matrix effects including atomic number, absorption, and fluorescence to accurately determine elemental concentrations.

1. X-Ray
Techniques
Prof. Samirsinh.P.Parmar
Department of Civil Engineering
Dharmasinh Desai University, Nadiad

2. Electron Beam

3. X-rays Discovered by Roentgen, 1895
λ = 0.1 – 10 nm

4. Energy versus Wavelength of Photons
E = h .  ergs per single photon
E = h . c /  ergs per single photon
h = Planck's constant = 1.38 10-16 erg sec
Fundamental Equivalency
For light, the minimum resolvable distance between 2 points:
=  / NA Limiting case for light  200m or nm
The smaller wavelengths of X-Rays (0.1 – 10 nm) are similar to the size of atoms (0.1 – 0.2 nm),
and have energies that correspond to the energy differences between the inner atomic orbitals.

5. Black Body Radiation:
All matter emits continuous background
electromagnetic radiation whose energy
is a function of its temperature.
Total emitted radiant energy:
Etotal =  . T4 = ergs/sec/m2
= Stefan-Boltzmann constant = 5.672  10-16 erg/K
Eλ = 2hc2/λ5×1/(e(hc/λ(T-1))
Energy of most abundant photon:
E = hm = hc/m  3 .  . T
= Boltzmann factor = 1.38  10-16 erg/K
T = hc/3m
T = (2897.8 / m) K = Wien’s Law, where m is the wavelength of the most abundant photons
Our eyes are tuned to the Sun
whose Photosphere is 5780 K

6. Characteristic Spectral Lines

7. Characteristic Spectral Lines

8. X-Ray Tubes

9. 60 kV Rhodium K lines and continuous spectrum
Rh Kα
Rh K

10. Braggs Law (1912)
n × λ = 2 × d × sin(θ)
X-Ray diffraction by atomic
lattice planes of crystals

12. 2 θ degrees
Counts
Antigorite
X-ray Diffractogram
n × λ = 2 × d × sin(θ)

13. X-ray Diffractogram
n × λ = 2 × d × sin(θ)

14. I = illite
S = smectite
Chl = chlorite
Q = quartz
K = kaolinite
Clay Minerals
X-ray Diffractogram
n × λ = 2 × d × sin(θ)
Scanning electron
microscope image of a
clay mineral

15. n × λ = 2 × d × sin(θ)

16. Illite Crystallinity
n × λ = 2 × d × sin(θ)

17. Mapping Alteration
“Halos”

18. Characteristic Spectral Lines
Chemical Analysis

20. excitation
emission
emission
emission
excitation emission

21. X-Ray Fluorescence Analysis
The excitation is produced by X-rays. The advantage of XRF
analysis is that it can analyze many elements down to levels of
ppm. The disadvantage of XRF analysis is that X-rays are
difficult to focus, and thus it is difficult to analyze small volumes.
XRF is the method of choice for obtaining the chemical
compositions of powdered or fused bulk rock samples.

22. Electron Microprobe
Electrons can be focused with
magnetic fields to spot sizes on the
order of 1 micron or less. By using
an electron beam as the excitation
source, one can analyze very small
spots on mineral grains, and thus
investigate phenomena such as
compositional zoning in crystals,
partitioning of elements between
coexisting phases, etc.
The disadvantage of electron beam
excitation is that a relatively high
background radiation is created by
the electrons, which makes the
detection limits for most elements
~0.01 wt.%.

23. Secondary electrons are produced by inelastic
collisions of electrons from beam with valence
electrons. These secondary electrons typically have
lower energies than backscattered electrons.
Auger electrons are produced by the interaction
between the characteristic X-rays produced by an
element with electrons in higher energy orbitals.
Auger electrons typically have energies that are the
difference between the energy of the initial electronic
transition that produced the characteristic radiation and
the ionization energy of the element.
Back-scattered electrons are those which interact with
atomic nucleii electrostatically and are flung back out
of the sample, in much the same way that a comet
interacts gravitationally with the sun.
Interaction between the Electron Beam and Sample Surface
Bremsstrahlung X-rays are the radiation that is emitted when electrons
are decelerated by a target. Accelerated charges give off electromagnetic
radiation, and when the energy of the bombarding electrons is high
enough, that radiation is in the X-ray region and is characterized by a
continuous distribution of radiation which becomes more intense and
shifts toward higher frequencies as the energy of the bombarding
electrons is increased. This background radiation is the principle
limitation in analyzing elements at very low concentrations with the
electron microprobe.

24. Interaction between the Electron Beam and Sample Surface
~ 1 micron
spot

25. WDS: Wavelength Dispersive Analysis
Electron Microprobe Analysis X-Ray Fluorescence Analysis

26. The counter is a chamber containing a
gas that is ionized by x-ray photons. A
central electrode is charged at ~ +1700 V
with respect to the conducting chamber
walls, and each photon triggers a pulse-
like cascade of electrons across this field.
The signal is amplified and transformed
into an accumulating digital count.
Gas-Flow Proportional Counter

27. In energy dispersive analysis, the
dispersion and detection of X-rays is a
single operation. The fluorescent X-
rays emitted by the 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. These detectors consist of a 3-
5 mm thick silicon junction type p-i-n
diode with a bias of ~ -1000 Volts
across it. The lithium-drifted centre part
forms the non-conducting i-layer.
When an x-ray photon passes through,
it causes a swarm of electron-hole pairs
to form, and this causes a voltage pulse.
The detector must be maintained at low
temperature with liquid-nitrogen for the
best energy resolution.
Energy Dispersive Analysis (EDS)
The electrical pulses generated by the detector are
processed by amplifiers and significant computer
power is required to correct for pulse-pile up and for
extraction of peaks from poorly-resolved spectra.
P-type Si is doped with 3+cation such as Al to provide
electron holes.
N-type Si is doped with 5+ cation such as P to provide
excess electrons.
I-type intrinsic semiconductor

28. Olivine
(Mg,Fe)2SiO4
Diopside
Ca(MgFe)Si2O6
Hornblende
Energy Dispersive Analysis
EDS

29. Wavelength dispersive analysis (WDS) is inherently more precise because of the better resolution of the spectral
peaks. The disadvantage of WDS is that peaks must be occupied sequentially by the spectrometer, which slows
the analytical process. With 4 spectrometers, a 10 element major analysis takes approximately ~ 4 minutes of data
acquisition. WDS is the method of choice for high-quality quantitative analysis.
Energy dispersive analysis (EDS) has less energy resolution, but has the advantage that all spectral lines are
accumulated simultaneous, giving a complete analysis in ~ 20 seconds. EDS is the method of choice for
qualitative “identification” analyses.

30. Conc(I)unkn ~ (Count(IPeak)unkn -(Bkgd)) / (Count(IPeak)Std – (Bkgd))
Quantitative Analysis

31. Matrix effects can affect the X-ray spectrum produced in an electron microprobe
analysis and have to be corrected for an accurate analysis. These matrix corrections
are called ZAF corrections, in reference to their three components: atomic number
(Z), absorption (A), and fluorescence (F).
Matrix Corrections
Atomic Number Correction
X-ray emission is dependent on atomic number because of the stopping power of the target and
backscattering from the target. Stopping power is the ability of a material to reduce the energy
of an electron by inelastic scattering. This property is a function of A/Z, in which A is the
atomic mass and Z is the atomic number. A/Z increases with increasing Z, as a result, the X-ray
intensity per unit concentration increases with Z.
Some of the electrons hitting the sample will be ejected back
out. This process is known as backscattering and it is strongly
affected by atomic number. The effect of backscattering is to
decrease the X-ray intensity with increasing Z, which is
opposite to the effect of stopping power. However, the
backscattering effect is greater and, therefore, the overall
atomic number correction follows the same trend. Minerals
with high mean atomic number appear brighter in back-
scattered electron images because they backscatter more
electrons.
Fe-rich
Mg-rich
Back-scattered electron image of
olivine phenocryst

32. Back Scattered Electron Image Showing Compositional Zoning in Tourmaline

33. Back-scattered electron image
of zoned clinopyroxene
phenocryst with superimposed
chemical analysis of Al content
and Mg# (Mg/(Mg+Fe))

34. Absorption Correction
X-rays are generated throughout the analytical
volume during a probe analysis. Those X-rays
produced at depth must pass through a certain
distance within the sample and risk being
absorbed, reducing the X-ray signal of the
element of interest.
Fluorescence Correction
The critical excitation energy (Ec) of an element is the energy threshold needed to dislodge
inner electrons and generate characteristic X-rays. In addition to the incident electrons,
however, X-rays from the ionization of elements with higher Ec will also ionize atoms of
elements with lower Ec, whose own characteristic X-ray emission lines will then be enhanced.
There is also fluorescence caused by the X-ray continuum or continuous X-ray background
emission produced by electron deflections. As an electron passes near an atomic nucleus, it may
be slowed by the electric field of the nucleus, causing a quantum jump to a lower energy state
and the emission of more X-rays.