The Röntgen Radiation and its application in studies of ... - Mansic

The Röntgen Radiation and its application in
studies of advanced materials
written by Mihaela Alexandru
“Petru Poni” Institute of Macromolecular Chemistry, Iasi, Romania,aleaahim@yahoo.com
Abstract
and Alexandra Nistor
“Gh. Asachi” Technical University Iasi, Romania, anistor@ch.tuiasi.ro
based on the lecture of Prof. Tomasz Goryczka
University of Silesia, Poland, goryczka@us.edu.pl
The wave-particle dual nature of the electromagnetic radiation was emphasized
through the discovery of X-rays. The X-rays are, posses the same nature as light
has, electromagnetic waves, but in comparison to the light rays, the X radiation
has a much higher frequency. According to Planck’s formula, the energy of X
photon is correspondingly higher. It explains why properties of the X radiations
manifest more evidently in comparison to those of the light. On this occasion
another important particle-like property of the photon will be highlighted and that
is the impulse.
1. Introduction
On November 8th 1890, Professor Wilhelm
Conrad Röntgen (1845-1923) was working
alone in his room from the Physics Laboratory
of the Wurzburg University, as always. Although
he was in his fifties at the time and he had by
then published numerous articles. Röntgen
decided to approach a new field of science – the
field of gas electrical discharges.
In order to study fluorescence phenomena, he
carried out experiments in a Crooke’s tube
using an electrical discharge obtained form an
induction coil. Röntgen covered the tube with a
black cardboard to increase luminescence
phenomena. By chance, besides the Crookes
tube, there was a screen covered with barium
platinocyanide. Röntgen was amazed seeing the
Crookes tube, which was under tension, and the screen mysteriously became
fluorescent, although nothing seemed to fall on it. The property of the barium
platinocyanide as a fluorescent material was well-known. Despite, the
fluorescence phenomena there were other kinds of radiation, which made
negatives stacked in a laboratory’s corner completely dark. He realized that it
must have been new radiation. From that, the rays became known as a Roentgen
radiation. Röntgen studied its properties and found a lot of practical applications.
One of them is possibility to be absorbed at different rates by the soft tissues
and bones [1]. On this occasion, Röntgen made the first radiography that
represents the left hand of his wife.
Physics of Advanced Materials Winter School 2008 1

In this radiography the hand bones show up very obvious, just as the ring that
his wife was wearing on her finger. On the day of March 28th 1895, Röntgen
presented his results to the Medical-Physical Society from Wurzburg. In the
course of a few days, the experiments of Röntgen were repeated in numerous
laboratories around the world and after a few weeks attempts were made to use
the X rays in medicine. After a couple of months from the discovery of X-rays, the
Romanian physicist Dragomir Hurmuzescu (1865-1954) built a very sensitive
electroscope, that was named after him, especially for the study of these
radiations. This electroscope has proved to be very useful for the study of
ionisation phenomenons caused by different radioactive substances. Röntgen’s
discovery became famous in a very short time.
Almost all scientific journals were preoccupied on it. Indeed what could be more
amazing than its invisibility for the human eye? Such property can be used to
“see” the skeleton of a human body and other animals. Of course, one cannot
deny that Röntgen had a struck of luck when he discovered the X rays. Other
physicists have had a chance, but they didn’t know how to take advantage of that.
In the book “The History of the Ether and of the Matter Theories”, Whittaker tells
of a physicist from Oxford who had realized that a latent image forms on the
photographic plates only when they are close to a gas discharge tube. He found
that X-rays are emitted by the part of a tube which is bombarded by electrons
obtained from a cathode. Based on this observation, Röntgen built a generator
and the tube, which provides the most favorable way for obtaining and using
X - rays. Röntgen knew that cathode rays leave the cathode along a normalised
direction Based on this he built a concave cathode that focused the emitted beam
in one point. Because most of the energy brought by cathode rays turn into a
heat strongly increasing temperature of the anode, presenting even the danger of
melting it, Röntgen introduced in the tube a special plate made from heat
resistant material, on which he focused the beam.
This plate, that was given the name of anticathode, was placed at an angle of 45º
from the axle of the tube in order to make the use of the emitted X-rays more
comfortable. This way, Röntgen built the tube that bears his name and which
construction remained essentially unchanged until today.
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The next improvement was introduced by William David Coolidge in 1913. He
invented the X-ray tube with heated cathode. The tube is vacuumed and the
cathode emits electrons through the heating with an auxiliary electric current.
The cause of the electrons emission is not the bombardment with electrons as it
was in the previous cases. The acceleration of the electrons emission process is
done by applying a high tension electric current, through the tube. When the
voltage increases, the wavelength of the radiation decreases.
The American physicist Arthur Holly Compton (1892 - 1962), a Nobel Prize winner,
discovered through his studies the so-called Compton Effect in the year 1922. His
theory demonstrates that the wavelengths of the X and gamma radiations
increase. This phenomenon also proves the particle-like nature of the X rays.
In 1913, physicists: Sir W. H. Bragg and his son Sir W.L. Bragg developed a
formula, which explains diffraction effect when crystals reflects X-ray beams at a
certain incidence angle (theta, θ). Now it is known as Bragg’s Law:
2 ⋅ d hkl ⋅ sinθ
= n ⋅ λ
⋅ λ
=
2 ⋅sinθ
n
d
The variable d is an interplanar distance between atomic layers in a crystal, and
λ is the wavelength of the X-ray beam; n is an integer. This observation is an
example of X-ray wave interference, commonly known as X-ray diffraction (XRD),
and was direct evidence for the periodic atomic structure of crystals postulated
for several centuries.
The Braggs were awarded the Nobel Prize in physics in 1915 for their work in
determining crystal structures beginning with NaCl, ZnS and diamond. Although
Physics of Advanced Materials Winter School 2008 3

Bragg’s Law was used to explain the interference pattern of X-rays scattered by
crystals, diffraction has been developed to study the structure of all states of
matter with any beam, e.g., ions, electrons, neutrons, and protons, with a
wavelength comparable to the distance between the atomic or molecular
structure.
Bragg’s Law: n ⋅ λ = 2 ⋅ d ⋅ sinθ
Figure 1. The reflection of the X-rays on the crystal planes
Constructive interference occurs only when difference of between rays is
proportional to the wavelength:
n ⋅ λ = AB + BC
AB=BC
n ⋅ λ = 2 ⋅ AB
sin θ = AB / d
AB = d ⋅ sinθ
n ⋅ = 2 ⋅ d ⋅
λ sinθ
λ = 2 ⋅ d ⋅ sinθ
hkl
P.P. Ewald published in 1916 a more simple and more elegant theory of the Xray
diffraction, by introducing the concept of reciprocal network. Comparison of
Bragg’s Law (left), Bragg Modified Law (middle) and Ewald Law (right):
⋅ λ
=
2 ⋅sinθ
n
d
Physics of Advanced Materials Winter School 2008 4
hkl
1/
d
sinθ
=
2 / λ
σ
sinθ
=
1
2 ⋅
λ

2. The production of X-rays
The X rays, that are currently being used for different purposes, can be obtained
with help of the X-ray tube. The X-ray tube is a vacuumed space (10 -6 torr) inside
of which there are two electrodes, a hot cathode (tungsten filament) and an
anode between which a 10 ÷ 200 kV voltage is applied. The electrons emitted by
the filament are accelerated due to the voltage differential and when they hit the
anode X radiation is emitted. Because through the collision with the anode over
98% from the energy of incoming electrons is turned into heat (the rest consist of
energy radiated as X-rays), the anode has to be water cooled (Figure 2) [2]. For
higher power (5 ÷ 60 kW) of X-ray radiation, the tube equipped with rotating
anode is in use. On the X-ray tube used for structural studies, the electrons
emitted by the filament are focused, only on a rectangular surface of the anode
(tubes with Gotze linear focal point).
Figure 2. The scheme of the tube with rotating anode
Figure 3. The principle of X-ray diffraction [3]
3. X-ray spectrum - continuous and characteristic
Roentgen radiation, produced with the help of X-ray tubes, is the result of the
accelerated electrons interaction with the atoms from surface of the anode. There
are two types of interactions that lead to the apparition of a continuous spectrum
or a characteristic spectrum [4].
a. The continuous spectrum. An electron that moves at a high speed can be
decelerated when pass near of atom nuclei. As a result of this interaction the
Physics of Advanced Materials Winter School 2008 5

kinetic energy of the electron is transformed totally or partially, into a photon of
X-ray, with its frequency ν given by Einstein’s equation:
2 2 ( v − v ) = ⋅ϑ
⎛ m ⎞
∆E = ⎜ ⎟ ⋅ 1 2 h
⎝ 2 ⎠
b. The characteristic spectrum. Another type of interaction of the accelerated
electron with an atom could result in the expulsion of an electron from the
interior electronic orbits of the target atom and then the atom remains in an
excited, ionized state. In order to come back to the normal state the jump of one
electron from higher orbital is needed. Excess of energy is emitted as a photon of X-ray
whit constant value of the wavelength.
X-ray diffraction is used for:
• Measuring the average spacing between crystallographic plains
• Determination of the orientation of a single crystal or grain
• Quantitative and qualitative phase analysis
• Finding the crystal structure of an unknown material
• Measuring the size, shape and internal stress of small crystalline regions.
Properties of X-rays
The importance of X-ray in diffraction studies is generation when high-energy
electrons impinge a metal target. The most useful metal for anode construction is
iron, copper, cobalt and molybdenum. At a sufficiently high voltage the X-ray
emits a beam, which is shown in Figure 4 [5]. It consists of two parts, a broad
band of continuously varying wavelengths with a broad energy maximum in the
neighborhood of 0,5 Å and a characteristic spectrum superposed on it combined
from two series: Kα and Kβ. The Kα line is always 2/3 more intense than Kβ.
Scheme of Kα and Kβ emission is shown in Figure 5. Actually the Kα line is itself a
doublet with components Kα1 and Kα2 separated by such a small interval that is
most X-ray diffraction patterns they are resolved only at higher range of 2θ.
Figure 4. Intensity curve for X-rays from a molybdenum target operated at 35kV
Physics of Advanced Materials Winter School 2008 6

Due to the fact that Kβ and Kα2 are diffracted on the same crystallographic plane,
they cause appearance of additional peaks in XRD pattern. Such inconvenience
can be easy eliminated by adding filters.
4. Interaction with matter
The absorption of the X rays
Figure 5. An atom from the material of the anode
One of the important properties of X-rays is their ability to pass through opaque
substances. At the passing of X-rays through a substance, their intensity is
reduced and for monochromatic radiation the next equation can be written:
I = I 0 ⋅ e
Where: I0 is the intensity of a primary beam, I – the intensity of the transmitted
radiation through an absorbent shield, x- thickness of absorbent and µ – linear
absorption coefficient.
Due to the fact, that the linear absorption coefficient depends on the physical
status of the X ray absorbing substance, the µ/ρ mass absorption coefficient is
introduced which, for a monochromatic beam, is a constant, independently on the
nature of absorbent material [4]. Thus, the graphite and the diamond, as
allotropic variations of carbon, have different values for their linear absorption
coefficients, but both have the same value of the mass absorption coefficient.
Physics of Advanced Materials Winter School 2008 7
−µ
x
The secondary fluorescence. The Auger effect
The X rays beam, which passes through a substance, can cause several effects:
fluorescence, scattering of X-ray (coherent and incoherent-Compton effect),
increase of the heat and electrons (recoil electrons and photoelectron).
One of these effects, discussed above, is the secondary fluorescence that consists
in the emission of an X ray characteristic spectrum as a result of the atoms
passing in an excited state due to their interaction with the incoming X-ray
photons. When an X ray photon of a certain energy collides with a target atom,
an electron from the interior orbits of the atom is expulsed and the energy of the
absorbed photon can be found as excitation energy of the ionized atom and as
kinetic energy of the expulsed photoelectron:
mv
h Eleg
2
+ = ⋅ϑ
(Eleg represents the bounding energy of the expulsed photon).
2

When, through the occupation of the free orbital by an electron from the exterior
orbits the ionized atom comes back to its normal state, a secondary X radiation is
emitted, known as fluorescence radiation. The fluorescence radiation spectrum is
a spectrum of lines that is characteristic for the material subjected to the
radiation. From the equation it is obvious that the wavelength of the fluorescence
radiation Has higher value, than that, of the incoming radiation.
h
∆λ
= ⋅ 2
m ⋅ c
( 1− cos θ )
The incoherent scattering of the X rays. The incoherent scattering (or
Compton effect) was explained by A.H. Compton as an elastic collision between
an X photon and free or lose tide electron. During the collision, some of energy of
the incoming photon is passed to electron. After the collision, the energy of the
photon is slightly smaller. In consequence, scattered radiation has a wavelength
slightly bigger than that of the incoming radiation.
The coherent scattering of the X rays. Also, the scattering of the X rays by
electrons on an atom can take place coherently.
According to J. J. Thomson’s theory of coherent scattering, electron is put in
oscillating motion by incoming electromagnetic wave (the X radiation). In this
forced oscillating movement, with its frequency equal to that of the electric field
of the electromagnetic wave, electron is continuously accelerated or decelerated
and as a result of that it emits an electromagnetic wave having a wavelength the
same as incoming radiation.
Although X rays are scattered by the electron in all directions, the intensity of the
radiation according to J. J. Thomson’s equation, depends on the scattering angle:
⎛
I = I ⋅ ⎜ 0
⎝ r
2
e
⋅ m
4
2
⋅ c
4
⎞ ⎛ 2 2 ⋅θ
⎞
⎟ ⋅⎜1
+ cos ⎟
⎠ ⎝ 2 ⎠
In this equation, I0 represents the intensity of primary beam, I – the intensity of
scattered radiation, 2θ – the scattering angle.
⎛ 2 2 ⋅θ
⎞
The factor ⎜1+
cos ⎟
⎝ 2 ⎠
is called polarization factor due to the fact that
crystallographic planes play role of polarizator for X-ray.
5. Basics of Crystallography
A crystal consists of a periodic arrangement of the unit cell into a lattice. The unit
cell can contain a single atom, ion or molecular in a fixed arrangement.
Figure 6. : The structure of CsCl crystal
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Crystal net is built from planes of atoms that are spaced at a distance d. Many
atomic planes can be distinguished, however, each one with a different d-spacing.
In the unit cell, a, b and c (length) and α, β and γ angles between a, b and c are
lattice constant or parameters, which can be determined from X-ray diffraction
measurement.
5.1. Crystal Systems and Space Lattices
Depending on the atom arrangement in the lattice a given structure can be
assigned to one of six crystal systems characterized by the ratios of the lattice
parameters: a, b and c-and the three angles defined by those edges –α =

Figure 8. Graphic interpretation of the Miller indices
Figure 9. Several atomic planes and their Miller indexes in a cubic unit cell
6. Basics of Bragg-Brentano geometry
The Bragg-Brentano geometry is frequently used like a tool for the most of the
diffractometers. This geometry was applied in analytical instrument -
diffractometer (Figure 10), which was an ingenious invention. It is a commonly
used instrument where the samples reveal polycrystalline nature.
The Bragg-Brentano diffractometer combines a high efficiency with high
resolution.
Figures 11 and 12 present the Bragg-Brentano geometry for X-ray beam focusing
and its principle. The main idea is that, focus of the X-ray tube, sample and
detector are placed on the same focusing circle.
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Figure 10. A Modern Automated X-ray Diffractometer
Figure 11. The Bragg-Brentano Geometry
Figure 12. Bragg - Brentano Focus Geometry
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In order to improve parallelism of the primary beam is application of the Göbel
mirrors (or Parallel Beam) – these capture in a large solid angle, the X radiations
from the source and produce an intense parallel beam without the Kβ radiations
(Figure 13).
Parallel beam diffractometers have became more common in the use, in the
recent years and have captured some applications from traditional Bragg-
Brentano diffractometers (in thin films measurements and reflectometry).
Multilayer parabolic mirrors proved their efficiency as they collimate incident
beams and are used in a variety of applications [10].
Figure 13. Beam forming by use of the Göbel mirror
Figure 14. Comparison Bragg-Brentano Geometry versus Parallel Beam Geometry
The results are obtained in the form of X-ray diffraction pattern, which shows
dependence of collected intensity versus scattering angle θ (Figure 15).
For the computation of the data different existing programs are being used (such
as the TOPAZ software for the DIFFRAC plus ). Figure 16 shows an example of the
qualitative phase analysis supported by computer phase filtering. Also X-ray diffraction
pattern can be collected versus change of some external parameter applied to
the sample such as temperature, pressure, magnetic or electric field ect. Figure
17 reveals set for X-ray diffraction patterns collected versus temperature change.
Physics of Advanced Materials Winter School 2008 12

a) b)
Intensity
20 40 60 80 100 120
2θ
Figure 15. Example of the X-ray diffraction pattern registered for (a) amorphous and (b)
polycrystalline material.
Physics of Advanced Materials Winter School 2008 13
2500
2000
1500
1000
Figure 16. Results of the qualitative phase analysis
Figure 17. High Temperature XRD Patterns of the Decomposition of YBa2Cu3O7-d
500

7. Applications of XRD
The study of the X radiations has played a vital part in physics, especially for the
development of the advanced material characterization. As a mean of research,
the X radiations have allowed the scientists to experimentally confirm structural
properties of materials. By using the diffraction method, the crystalline
substances can be identified and their structure determined. The method can also
be applied for powders that do not posses a crystalline structure, but they are
amorphous. By these means, chemical compounds can be identified and the size
of the ultramicroscopic particles can be established. Besides the applications from
physics, chemistry, mineralogy, metalurgy and biology, which mainly base on
effect of diffraction another feature of X-rays – its possibility to go thorough
materials - is used in industry. Especially it is applied for the non-destructive
reflecting of some metallic alloys. Some tests are being done in different phases
of the production cycle and the defects are eliminated. The soft X-rays are used
for establishing the authenticity of some works of art or for the restoration of
paintings. In medicine, the radiographs and the fluoroscopes are used for
diagnosis. The computerized machine, the axial tomograph (CAT or CT scanner)
was invented in 1972 by the electronics engineer Godfrey Hounsfield and came
into use on large scale after 1979.
Despite of structural studies, X-rays are used for chemical analysis of materials.
An X-ray source is used to irradiate the specimen. It causes emission (or
fluoresce) of characteristic X-rays from the elements presented in a specimen. A
detection system (wavelength dispersive) is used to measure the peaks of the
emitted X-rays for qual/quant measurements of the elements and their amounts.
However, the main part of the X-ray application is structural investigation, that’s several
technique and methods are applied for single crystals as well as polycrystalline materials.
Some of them are discussed as follow:
-To identify crystalline phases and orientation
A condition in which the distribution of grains orientation is non-random.
Figure 18. Preferred Orientation in a powder sample
The first evidence of preferentially oriented grains in studied materials are
anomalies in diffraction peak intensity. Example is shown in Figure 18, which
compare X-ray diffraction patterns collected for material with randomly oriented
grains (blue) and sample revealing texture. Preferred orientation of grains can
introduce anisotropy of material properties. In case of single crystal Laue
Physics of Advanced Materials Winter School 2008 14

technique is used for determination of its orientation (Figure 19). From
stereographic projection appropriate crystallographic directions can be find.
Figure 19. Basics of the Laue method for single crystals studies
-To determine structural data: lattice parameters, strain, grain size, phase
composition, preferred orientation, order-disorder transformation, and thermal
expansion.
As an example we mention the use of X-ray analysis to make phase and structure
analysis on the polycrystalline Cd0,5Ge0,5Cr2Se4 and CdCr1,9Ge0,075Se4 compounds.
Both compounds crystallized in cubic, normal spinel structure, Fd3m [11].
Another example is phase identification in multi-phase sample - the oxidation
states of copper applied for roof covering (Figure 20). The major phase is quartz
(red), also a significant amount of Cu (green). Perhaps some Cu2O (blue) and
other unidentified phases are also present.
Figure 20. The phases of the material
-To measure the thickness of thin films and multi-layers
Physics of Advanced Materials Winter School 2008 15

The strong relationship of the physical, chemical, metallurgical and electronic
structure of thin film micro and nanomaterials with the physical properties of thin
materials has led to development of a large number of microanalytical
characterization techniques for thin films (Figures 21). The techniques based on
X-ray beam have dominated the field mainly because of their simplicity, more
reliability, quantitative and nondestructive nature. X-ray technique – reflectivity -
has played a leading role, as a fundamental tool for material characterization. It
allows to determine thickness, roughness and density of layer or multi-layers.
a) b)
Figure 21. Thin films – (a) single layer and (b) multilayer.
Figure 22. Effect of a layer thickness on a shape of reflectivity curve.
-To determine atomic arrangement
The atomic arrangements can be determined from X-ray diffraction patterns,
which are analyzed using the Rietveld method and LeBail. Figure 23 shows set of
X-ray diffraction pattern registered versus temperature change. Change of the
intensity of diffraction and their position peak as well as peak vanishing and new
one appearing are evidence of the phase transformation occurrence. During the
transformation, caused by temperature lowering, atoms change their position in
the unit cell leading to new structure forming. Particular analyze of each
diffraction pattern allows to obtain Patterson maps (Figure 24), from which
position of atoms can be derived.
Physics of Advanced Materials Winter School 2008 16

In
te
ns
it
y
Temperature 0 C 2θ
Figure 23. Set of diffraction patterns registered during cooling of shape memory alloy –
NiTi.
a) b)
Figure 24. Patterson maps calculated from diffraction pattern registered at 45 0 C (a) and
14 0 C (b).
Despite of structural studies, X-rays are used for chemical analysis of materials.
An X-ray source is used to irradiate the specimen. It causes emission (or
fluoresce) of characteristic X-rays from the elements presented in a specimen. A
detection system (wavelength dispersive) is used to measure the peaks of the
emitted X-rays for qual/quant measurements of the elements and their amounts.
Acknowledgements
This research occurred in the frame of Projects CNCSIS Nr. 5 and Nr. 64/2007.
Physics of Advanced Materials Winter School 2008 17

9. References
[1] http://www.chass.utoronto.ca/ipst/html/rontgen.html
[2] http://physics.pdx.edu/~pmoeck/phy381/Topic5a-XRD.pdf
[3] www.micro.magnet.fsu.edu/primer/java/interface/index.html
[4] E.Luca, M. Chiriac, M. Strat, V. Barboiu, Analiza structurala prin metode
fizice, II, Editura Academiei, Bucuresti, 1985, 103-171.
[5] Ulrey, Phys.Rev.,11,401 (1918)
[6] L. E. Alexander, X- Ray Diffraction Methods in Polymer Science, John
Wiley&Sons, Inc., 1969
[7] M. Von Laue, Sitz. math. phys. Klasse bayer, Akad. Wiss., p. 303(1912),
Ann. Physik, 41, 971 (1913)
[8] W. L Bragg, Proc. Cambridge Phil. Soc., 17, 43, (1913).
[9] http://www.chass.utoronto.ca/ipst/html/rontgen.html
[10] B. Verman, B. Kim, Analytical Comparison of Parallel Beam and Bragg-
Brentano Diffractometer Performance, Material Science Forum Vols.
443-444, pp.167-170, 2004
[11] E. Maciazek, T. Goryczka, I. Jendrzejewska, X-ray Analysis of the
Cd0,5Ge0,5Cr2Se4 and CdCr1,9Ge0,075Se4 Compounds, Solid State
Phenomena Vol. 130, pp.93-96, 2007
Physics of Advanced Materials Winter School 2008 18