X-ray diffraction(XRD)

1. Advance Characterization Techniques
X-ray diffraction(XRD)
Theory and applications to materials science and
smart textiles
Kanhaya lal kumawat
M.tech.
Ict (UDCT), Mumbai

2. What is X-Ray and how it is concerned with XRD ?
 In 1895, W.C. Röntgen discovered mysterious rays capable of passing
through the human body. Because of its unknown nature, he called them X-
rays.
 Interaction of an EM wave (X-Ray) with an object having size dimension
comparable with the period of the wave
or
 The atomic planes of a crystal cause an incident beam of X-rays to interfere
with one another as they leave the crystal. The phenomenon is called X-ray
diffraction
or
 X-ray diffraction pattern is the fingerprint of periodic atomic arrangements
in a given material

3. Application of XRD
 Phase identification
 Crystal structure determination
 Radialdistribution functions
 Thin film quality
 Crystallographic texture
 Percent crystalline/amorphous
 Crystal size
 Residual stress/strain
 Defect studies
 In situ analysis (phase transitions, thermal expansion coefficients, etc)
 Superlattice structure

4. X-Ray Diffractometer
1
• X-ray tube or cathode Ray tube
2 • Sample holder
3
• X-ray detector

5. Schematic diagram of a diffractometer system

6. Cross section of sealed-off filament X-ray tube
X-rays are produced whenever high-speed electrons collide with a metal target. A source of
electrons – hot W filament, a high accelerating voltage between the cathode (W) and the
anode and a metal target, Cu, Al, Mo, Mg. The anode is a water-cooled block of Cu containing
desired target metal.

7. Pathway to produce characteristic X-ray spectra
I. X-rays generation in a cathode ray tube by heating a filament to
produce electrons.
II. Accelerating the electrons toward a target by applying a voltage, and
bombarding the target material with generated electrons
III. When electrons have sufficient energy to dislodge inner shell electrons
of the target material, characteristic X-ray spectra are produced
Production →Diffraction → Detection → Interpretation
 Thus, X-rays are generated by a cathode ray tube, filtered to produce
monochromatic radiation, collimated to concentrate and directed toward
the sample to produce characteristic X-ray spectra

8. Principle of XRD
It works on Bragg’s law
Statement -
when the x-ray is incident onto a crystal surface, its angle of
incidence(θ) will reflect back with a same angle of scattering(θ) if the
path difference(2dsinθ) is equal to a whole number of wavelength it
would cause constructive interference
2dsinθ = nλ or 2dhklsinθhkl=nλ
where n is an integer called order of differaction, λ is the wavelength of the X-
rays, d is the interplanar spacing generating the diffraction, and u is the
diffraction angle where hkl are Miller indices of a crystal lattice

9. Bragg’s law
2dhklsinθhkl=nλ
where
For a simple cubic (a = b = c = ao)
for example for NaCl, 2θ220=46o, θ220=23o d220 =1.9707Å,
ao=5.5739Å

10. •

11. SCHERRER FORMULA
Note- K actually varies from 0.62 to 2.08

12. How to find BM ?

13. Concept of constructive interference
• X-ray diffraction peaks are produced by constructive interference of a
monochromatic beam of X-rays scattered at specific angles from each set
of lattice planes in a sample

14. Miller indices
 Miller indices are used to specify directions and planes
 How to find Miller Indices for Planes?
3. Take the reciprocals of the fractional intercepts.
2. Specify intercepts in fractional coordinates. 3. Take the
1.Identify the plane intercepts on the x, y and z-axes.
Example, plane intercepts (1, ¾ ,½ ) will be expressed as (432) as its Miller indices

15. How to designate Miller Indices for Planes
 For x axis, The plane intersects the x-axis at point a and runs parallel along
y and z axes , plane can be designated as (1,∞,∞) likewise for (∞,1,∞)
(∞,∞,1) for y and z axis respectively
Note- Pink Face = (1/1, 1/∞, 1/∞) = (100) Green Face = (1/∞, 1/∞, 1/1) = (001) Yellow Face = (1/∞, 1/1, 1/∞) = (010)

16. 7 crystal systems

17. 14 Bravais lattices
(Bravais lattice is an infinite array of discrete points with identical environment)

18. How to compare the obtained data ?
Obtain XRD pattern →Measure d-spacings → Obtain integrated intensities →
Compare data with known standards in the JCPDS file
Note-The JCPDS (Joint Committee on Powder Diffraction Standards) is the
"old name" of our ICDD (International Centre for Diffraction Data).

19. JCPDS Card
1.file number 2.three strongest lines 3.lowest-angle line 4.chemical formula and name 5.data on
diffraction method used 6.crystallographic data 7.optical and other data 8.data on specimen 9.data on
diffraction pattern1.file number 2.three strongest lines 3.lowest-angle line 4.chemical formula and name
5.data on diffraction method used 6.crystallographic data 7.optical and other data 8.data on specimen
9.data on diffraction pattern

20. Example

21. XRD pattern of NaCl

22. Examples
•

23. Question

24. Limitations
 Instrumental Sources of Error Specimen displacement, Instrument
misalignment, Error in zero 2q position
 Homogeneous and single-phase material is best for identification of an
unknown
 Access to a standard reference file of inorganic compounds is required
 Material, in tenths of a gram quantity, must be ground into a powder
 For mixed materials, detection limit is » 2% of sample
 For unit cell determinations, indexing of patterns for non isometric crystal
systems is complicated
 Peak overlay may occur and worsens for high angle “reflections”