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7/30/2019 1-4 X-Ray Characterization of Materials.ppt
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X-Ray Characterization of Materials
Dr. Saad B. H. Farid
Former ly: Chief Researchers
Currently: Assistant Professor
University of Technology
Department of Materials Engineering
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Generation of Monochromatic X-ray
Schematic Electronic transitions in an atom
Emission processes indicated by arrows
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The schematic of a typical x-ray emission spectrum, for
clarity indicating only the presence of continuous background
and three characteristic wavelengths: K1, K2, and K,
which have high intensities.
Left- the schematic of the x-ray emission spectrum shown as the solid line overlapped with the
schematic of the ()function of the properly selected -filter material (dotted line).
Right- the resultant distribution of intensity after filtering as a function of the wavelength.
The spectra of the unfiltered beams from a copper target
(Z=29) filtered by nickel (Z=28)
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Modern filtration technique utilizing divergent Monochromators
(Crystal monochromators include pyrolitic graphite, Si, Ge, and
LiCl). Usually graphite Monochromator is employed.
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A point Lattice, each point may
represent atom(s) or molecule
A unit cell, the bold a, b and c
represents vectors of the unit cell. 5
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Crystal Systems and Bravais Lattices
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Crystal Diffraction
Max von Laue
(1879-1960)
1914 Nobel prize
Laue 1912
Lattice spacing
typicallyo
1010 m 1
In 1912, the German physicist von Lauereasoned that, if crystals were
composed of regularly spaced atoms, and if x-rays were electromagnetic
waves of wavelength about equal to the inter-atomic distance in crystals,
then it should be possible to diffract x-rays by means of crystals.
Under his direction, experiments to test this hypothesis were carried
out: a crystal of copper sulfate was set up in the path of a narrow beam ofx-rays and a photographic plate was arranged to record the presence of
diffracted beams, if any. The very first experiment was successful and
showed without doubt that x-rays were diffracted by the crystal out of the
primary beam to form a pattern of spots on the photographic plate.
These experiments proved, at one and the same time, the wave nature
of x-rays and the periodicity of the arrangement of atoms within a crystal. 7
http://nobelprize.org/physics/laureates/1914/laue-bio.htmlhttp://nobelprize.org/physics/laureates/1914/laue-bio.html7/30/2019 1-4 X-Ray Characterization of Materials.ppt
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Laue X-ray diffraction YAlO3c-axis normal to picture
Typical Laue X-ray diffraction pattern
Symmetryof the crystal
Symmetryof the pattern
Each spot corresponds to a
different crystal plane
Some Applications:alignment of single crystal
info on unit cell
info on imperfections,
defects in crystal8
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The account of these experiments was
read with great interest by two English
physicists, W. H. Bragg and his son W. L.
Bragg.
The latter, although only a young studentat the time it was still the year 1912
successfully analyzed the Laue
experiment and was able to express the
necessary conditions for diffraction in a
somewhat simpler mathematical form
than that used by von Laue.
He also attacked the problem of crystal
structure with the new tool of x-ray diffraction
and, in the following year, solved the structures
of NaCl, KC1, KBr, and KI, all of which have
the NaCl structure; these were the first
complete crystal-structure determinations evermade.
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SymmetryThere are 32 unique combinationof symmetry elements called point groups
Glide planes: is the combination of a mirror reflection plane with a corresponding
translations (1/2 or 1/4 units) parallel to the plane, results in a total of five possible
crystallographic glide (shift) planes occurs.
Screw axes: Screw axes perform a rotation simultaneously with a translation along therotation axis. In other words, the rotation occurs around the axis, while the translation occurs
parallel to the axis. Crystallographic screw axes include, only two-, three-, four- and six-fold
rotations
When glide planes and screw axes is added to them, we have 230 unique space symmetry
called space groups
All are listed in I nternational tables for crystallography 10
Systematic absences:
It is the absence of
certain (h k l) diffracted
x-ray due to cancelationsof out of phase
equivalent reflections
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Reciprocal lattice
The concept of a reciprocal lattice was first
introduced by Ewald and it quickly became an
important tool in the illustrating and
understanding of both the diffraction geometry
and relevant mathematical relationships. Let a,
b and c be the elementary translations in a
three-dimensional lattice (called here a direct
lattice)A second lattice, reciprocalto the direct lattice,
is defined by three elementary translations a*,
b* and c*, which simultaneously satisfy the
following two conditions:
Diffraction methods
What is V, V* ?!
Where is the reciprocal lattice ?!
Reciprocal Lattice and Ewald's Sphere
Where and when the Bragg's condition is
met
Which is the possible Braggs reflections
(Related to the symmetry and beyond thescope of this lecture) 11
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Oscillating, Weissenberg, precession
and de Jongh Bouman photographs
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Intensity of powder diffraction peaks
1. Integrated intensity: The area under the peak fitted to Gaussian or Lorentz Distribution
2. Scale factor: to compensate diffraction geometry and Sample shape
3. Multiplicity factor: equivalent Braggs angle for reflections such as h00, -h00
4. Lorentz-polarization factor : intensity that reaches the detectors 1/sin2
5. Absorption factor: dependent on both the geometry and properties of the sample and the
focusing method
6. Preferred orientation: departure from random distribution of the orientations of crystallites
7. Extinction factor: back-reflection within the same crystallite and multiple crystallites
For single crystals
Structure factor1. Structure amplitude: Shared by multiple
atoms in the unit cell
2. Population factor: In general, gi =1/n,
where n is the multiplicity of the symmetry
element
3. Temperature factor: also known as "atomic
displacement parameters; atoms are in a
continuous oscillating motion about their
equilibrium positions
4. Atomic scattering factor: the ability to
scatter radiation varies depending on thetype of an atom
5. Phase angle: "phase problem" in diffraction
analysis; due to lost phase angles in
measurable intensities
Single Crystal X-ray
Crystallography is a complete solution
of Crystal Structure.Also called The Phase Problem of
X-ray Crystallography (FC calculations)
This is beyond the Scope of this
presentation
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Crystallite size,
not crystal or
particle size !!!
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The chief problem in determining
particle size from line breadths is
to determine B from the measured
breadth B of the diffraction line.
Of the many methods proposed,
Warren's is the simplest. Theunknown is mixed with a standard
which has a particle size greater
than 1000A, and which produces a
diffraction line near that line from
the unknown which is to be used
in the determination.
B2=B2Measured-B2Standard then
B=0.9/tcos
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Two powder diffraction patterns ofLaB6 collected using different 's
The simulated powder diffraction pattern of copper
(space group Fm3m, a =3.615 A, Cu K1, K2 radiation,
Cu atom in 4(a) position withx = 0, y = 0, z= 0). 17
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Qualitative XRD Analysis
Basic principles. The powder pattern of a substance is characteristic of that substance and
forms a sort of fingerprint by which the substance may be identified. 18
The experimental diffraction pattern of a silicon and
Al2O3 mixture. Numbers with three digits mark the
Miller indices of corresponding crystallographic planes
A powder diffraction file (PDF) of hydroxyapatite.(Reproduced with permission from the
International Centre for Diffraction Data, ICDD.)
Diffraction pattern of a powder specimen of hydroxyapatite
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details are given of the method used for
obtaining the pattern (radiation, camera
diameter, method of measuring intensity, etc.),
and a reference to the original experimental
work. The rest of the left hand portion of the
card contains room for various crystallographic,
optical, and chemical data which are fullydescribed on introductory cards of the set.
A typical card from the ASTM
file is reproduced in Fig. 14-1.
At the upper left appear the d
values for the three strongest
lines (2.28, 1.50, 1.35A) and, in
addition, the largest d value
(2.60A) for this structure.
The lower right-hand portion of
the card, gives d values listed
versus the relative intensities
I /I1, expressed as percentages of
the strongest line in the pattern.
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Analysis
1- Manual analysis and match
2- Computerized match followed by manual
analysis. The computer program is supplied
with database of standard x-ray patterns of
inorganic and/or organic compounds.
Search criteria should be applied like expected
number of elements and element types.
In all analysis, nothing can be accomplishedfrom scratch !!!
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Quantitative XRD Analysis
Quantitative analysis by diffraction is based on the fact that the intensity of the diffraction
pattern of a particular phase in a mixture of phases depends on the concentration of that
phase in the mixture. The relation between intensity and concentration is not generallylinear, since the diffracted intensity depends markedly on the absorption coefficient of the
mixture and this itself varies with the concentration.
Methods
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5. Rietveld refinement: of multiple phase samples may be
used for relatively accurate quantitative analysis. It requires
knowledge of the atomic structure for each phase present in
the mixture. It refines the difference between observed and
calculated Ihkl6. Full pattern decomposition: does not require the atomicstructure to be known and it produces intensities of
individual Bragg peaks. Thus, multiple reflections from
each phase can be used to compute intensity ratios required
in methods described in items 1 through 4 above, which
increases the accuracy of the analysis. The use of multiple
Bragg peaks in evaluating an average intensity ratio, to
some extent diminishes the detrimental influence of
preferred orientation as long as it remains small to
moderate.
This method, however, requires lattice parameters and
therefore, is applicable to indexed patterns only. The phase
composition is actually determined using any of the first
four methods listed above by using intensities of several
strong or all Bragg peaks instead of a single reflection.
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X-ray fluorescenceThe most intense lines of this spectrum are
the K
and K lines if the element werebombarded with x-rays of high enough energy
(fluorescence). They are always called
"characteristic lines" to emphasize the fact that
their wavelengths are fixed and characteristic
of the emitting element.
The primary radiation (Fig. 15-1) causes the
sample to emit secondary fluorescent
radiation, which is then analyzed in aspectrometer. This method, commonly known
asfluorescent analysis, give information about
the chemical elements present in the sample,
irrespective of their state of chemical
combination or the phases in which they exist.
The wavelength of each spectral line iscalculable from the corresponding Bragg angle
and the interplanar spacing of the analyzing
crystal used.
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The useful range of fluorescent wavelengths extends from
about 0.5 to about 2.5A. The lower limit is imposed by the
maximum voltage which can be applied to the x-ray tube,
which is 50 kv in commercial instruments.
The two main problems in fluorescent analysis, namely the
achievement of adequate intensityand adequate resolution.
There is a common
Mistake; it is the calculation
of relative contents by
simply dividing intensities !
Quali tative analysis
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Quali tative analysis
In qualitative work sufficient accuracy can be obtained by automatic scanning of the
spectrum, with the counter output fed to a chart recorder. Interpretation of the recorded
spectrum will be facilitated if the analyst has on hand (a) a table of corresponding values of
and 2 for the particular analyzing crystal used, and (b) a single table of the principal K and L
lines of all the elements arranged in numerical order of wavelength.Since it is important to know whether an observed line is due to an element in the sample
or to an element in the x-ray tube target, a preliminary investigation should be made of the
spectrum emitted by the target alone. For this purpose a substance like carbon or plexiglass is
placed in the sample holder and irradiated in the usual way; such a substance merely scatters
part of the primary radiation into the spectrometer, and does not contribute any observable
fluorescent radiation of its own. The spectrum so obtained will disclose the L lines of tungsten,if a tungsten-target tube is used, as well as the characteristic lines of whatever impurities
happen to be present in the target.
Quanti tative analysis
In determining the amount of element A in a sample, the single-line method is normally
used: the intensity Iu of a particular characteristic line of A from the unknown is compared
with the intensity Is of the same line from a standard, normally pure A.
The way in which the ratio Iu / Is varies with the concentration of A in the sample
depends markedly on the other elements present and cannot in general be predicted by
calculation. It is therefore necessary to establish the variation by means of measurements
made on samples of known composition.
Figure 15-8 illustrates typical curves of this kind for three binary mixtures containing
iron.
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Matri x Ef fect in X-ray F luorescence Analysis:
These curves show that the intensity of a fluorescent line from element A is not in general
proportional to the concentration of A. This nonlinear behavior is due mainly to two effects:
(1) Matrix absorption: As the composition of the alloy changes, so does its absorption
coefficient As a result there are changes both in the absorption of the primary radiation
traveling into the sample and in the absorption of the fluorescent radiation traveling out.
(2) Multiple excitation: If the primary radiation causes element B in the specimen to emit its
characteristic radiation, of wavelength fB, and iffB is less than KA, then fluorescent Kradiation from A will be excited not only by the incident beam but also by fluorescentradiation from B.
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Measurements of film thickness,
stress measurements, micro-
crack detection, topography,
structure of thin films, textureanalysis, etc. They are not mere
characterization of materials but
tests for produced parts
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