1-4 x-ray characterization of materials.ppt

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.html


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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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1-4 x-ray characterization of materials.ppt

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