1. EBB245 Material Characterisations
Lecture 1. X-ray Diffraction Methods
Dr Zainovia Lockman, PPKBSM, USM

2. Contents of the lecture
Introduction to XRD
Elements of XRD
2.1. X-ray generator
2.2. Specimen
2.3. Detection
Data Acquisition
Distortion of diffraction spectra
Classwork and problem based learning

3. 1. Introduction to XRD Previously you have seen:
Now you are given 4 bottles of white powders:
What are these powders?
The easiest and quickest way to determine the phase present in these powders is by x-ray diffraction method.

4. Definition
XRD method is one of the most effective methods for determining a crystal structure of a given material. From the crystal structure phase identification of an unknown specimen can be performed.
XRD is based on the diffraction of incident X-ray on a specimen. The diffraction occurs by the reticular planes that form the atoms of the crystal

5. What is XRD? X-ray Detector Sample Data acquisition Questions to ask:
What is being plotted?
How does it do it?
What does XRD do?
What is its limitation?
Phase identification

6. XRD: spectroscopic technique
XRD methods can be classified into: spectroscopic and photographic
The photographic technique has not be used in modern laboratories but is still use to determine unknown crystals (phase identification)
The spectroscopic technique is known as x-ray diffractometry and this will be the main topic discussed in this lecture

7. Applications of XRD Phase identification Quantitative measurement
XRD can be used to identify crystalline substance and crystalline phases in a specimen.
XRD is perhaps the best method for phase identification.
Quantitative measurement
Quantitative analysis can be done by XRD to determine relative amounts of compounds or phases in a sample of compound/phase mixture.
Lattice parameters and Bravais lattice symmetry
Lattice parameters can vary as a function of diffraction angle and therefore information about phase purity, alloying, doping, solid solutions and strain can be deduced.

8. Applications of XRD Crystal Structure Epitaxy/Texture/Orientation
By Rietveld refinement of the entire diffraction pattern an unknown crystal structure of a given compound can be determined by XRD
Epitaxy/Texture/Orientation
XRD can be used to measure the texture and preferred orientation of sample. This is especially important for thin film analysis.
Crystallite Size and Microstrain
Crystallite size and microstraining are indicated by peak broadening
Other defects (stacking faults, etc.) can be measured by analysis of peak shapes and peak width

9. 2. Elements of XRD 3 elements in XRD:
Radiation generator (emits X-ray)
Specimen (diffracting X-ray)
Radiation detector (diffracted X-ray detected)
(1) Radiation generator
(2) specimen
(3) Radiation detector
This figure shows the path of x-ray from the generator to when it impinge on the specimen and after it being diffracted from the specimen and detected by the detector

10. The components of XRD X-ray tube: the source of X Rays
Incident-beam optics: condition the X-ray beam before it hits the sample
The goniometer: the platform that the sample, optics, detector, and/or tube
The sample & sample holder
Receiving-side optics: condition the X-ray beam after it has encountered the sample
Detector: count the number of X Rays scattered by the sample

11. 2.1. Generation of X-ray
X-ray can be produced by high speed electrons accelerated by a high voltage field colliding with a metal target.
Rapid deceleration of the electrons on the target enable the kinetic energy of electrons to be converted to the energy of x-ray radiation.
X-ray can be generated in an x-ray tube

12. There are windows which guide the x-ray put of the tube
X-ray tube
There are windows which guide the x-ray put of the tube
The generated x-ray will have range of wavelengths and can be plotted as x-ray intensities vs. wavelength plot as will be seen in the next slide.
Cooling is necessary to avoid overheating as most kinetic energy of the electron are transferred to heat

13. X-ray spectra
There is sharp intensity maxima superimposed on a continuous x-ray radiation.
This is characteristic x-rays
XRD requires monochromatic x-ray which comes from this characteristic x-ray
In this figure, the characteristic radiations are labeled as K and K
What are K and K?
Which one would be used for an XRD?

14. Characteristic x-ray radiation
Consider an atom, when an incident electron has sufficient energy to excite electron in the inner shell of an atom to a higher energy state, the vacancy left in the inner shell will be filled by electron in an out shell.
As the electron falls from the outer shell to the inner shell, energy will be released by emitting an x-ray with specific wavelength.
The k-shell vacancy will be filled by either M or L electron. This would then emit K and K respectively
As L is closer to K then K  would have higher intensity than K 

15. K
K has the highest intensity because the probability of electron from L to fill in the vacancy in K is higher than M (distance wise).
Now consider the K, recall that K is produced when electron from L shell jump into vacant state in K.
The L shell has subshell: L1, L2 and L3
When electron from L3 goes to K, K1 will be emitted, if electron moves from L2 then K2 will be emitted. K1 and K2 (K doublet) are used monochromatic x-rays for diffraction works L3 L1 L2
K2
K1 K

16. Filter in XRD & Common Target Used
Copper is one of the most common target (anode) used in XRD work.
If copper is used as the target:
K1  of nm
K2 has  of nm
K has  nm
These strongest characteristic x-rays are used for diffraction work with the Cu K 1 as the most common used one
Recall that there is a continuous x-ray radiation being emitted along the monochromatic K 
For XRD work, we need only the K so the continuous x-ray must be filtered.
Cu target
Electron accelerator
Filter can be made by a material which can absorbed other x-rays apart from the K .

17. Apart from Cu, other metals like Cr, Fe, Co and Mo are used as target (anode) in x-ray tube

18. 2.2. Specimen & diffraction theory
K  radiation that is generated by the x-ray tube will be focused onto a specimen.
Specimen in placed on a sample holder
The x-ray bean incident on the specimen will be diffracted by the crystallographic planes within the specimen
Therefore, one of the requirement of the specimen analysed is that, it must be solid which have certain degree of crystallinity.
The wavelength of Cu K is about equal to the distance between planes of atoms in crystalline solid.
Therefore, reinforced diffraction peaks of radiation of varying intensities can be produced when a beam of x-ray strikes a crystalline solid.

19. Diffraction theory
If rays leaving a set of planes are out of phase (as in case of arbitrary angle of incidence) no reinforced beam is
produced.
If rays leaving are in phase, reinforced beams are produced.
Consider x-ray 1 and 2. For rays reflected from different planes to be in phase, the extra distance traveled by a ray should be a integral multiple of wave length λ

20. Derivation of the Bragg’s Law
Given, nλ = MP + PN
(n = 1,2…)
n is order of diffraction
If dhkl is interplanar distance,
Then MP = PN = dhkl.Sinθ
Therefore, λ = 2 dhkl.Sinθ
This is a basic law of diffraction called Bragg’s Law.
Now we are able to obtain information on the spacing between atomic planes of a crystal.
Knowing the spacing of the crystallographic planes by diffraction method, we can determine the crystal structure of the materials

21. Interpreting Diffraction Data
We know that
Since
Substituting for d,
Therefore
Note that the wavelength λ and lattice constant a are the same
For both incoming and outgoing radiation.

22. Example
This type of calculation is however unnecessary as these days, the information about materials can be gathered by International Centre for Diffraction Data (ICDD)

23. Crystal lattice
Zn: HCP
Cu:FCC
Au:FCC
Zr: HCP
Hf:HCP
W: BCC

24. Which one is BCC?

25. Ceramic Oxides & Sulphides

26. Instrumentation: Geometric arrangement of x-ray diffractometer
X-ray will be diffracted by the atomic plane
The atoms in a crystal are a periodic array of coherent scatterers and thus can diffract light
X-ray impinge on crystalline material

27. Atomic Planes
The (220) planes of atoms in NiO
The (200) planes of atoms in NiO
In a crystalline material, a unit cell is the basic repeating unit. The above examples are for NiO. The red large spheres are oxygen and the green smaller spheres are nickel.
Parallel planes of atoms intersecting the unit cell are used to define directions and distances in the crystal.
These crystallographic planes are identified by Miller indices.

28. 2.3. Detection
Look at the cross section of the instrumentation in page 26.
See that a sample is placed in a sample holder in between a detector and an X-ray generator.
The sample will be tilted at a given angle, ,  could vary from 5o to 100o.
At a certain angle , the Bragg’s Law conditions are satisfied by the d-spacing in the sample.
The angle between the sample and the detector is 2
The diffracted x-ray will be detected by the detector and will be recorded as intensity versus 2 plot (diffraction pattern) as seen in page 29.
Plotting the angular positions and intensities of the resultant diffraction peaks produces a pattern which is characterised of the sample.
The question is how to interpret the diffraction pattern?

29. An example of XRD pattern
Write down what is the significant of this plot?

30. Bragg-Brentano Arrangement
Generally the basic function of a diffractometer is to detect X-ray diffraction from a specimen and to record the diffraction intensity as a function of the diffraction angle 2.
The commercially available diffractometer used Bragg-Brentano arrangement, in which the X-ray incident beam from the generator is fixed, but the sample stage will rotate around an axis perpendicular to the plane of the previous figure.
The detector rotates around the axis perpendicular to the figure

31. A single crystal specimen in a Bragg-Brentano diffractometer would produce only one family of peaks in the diffraction pattern. 2q
At 20.6 °2, Bragg’s law fulfilled for the (100) planes, producing a diffraction peak.
(110) planes diffract at 29.3 °2; however, they are not properly aligned to produce a diffraction peak (due to the single crystal nature of the sample). Only background is observed.
The (200) planes are parallel to the (100) planes. Therefore, they also diffract for this crystal. Since d200 is ½ d100, they appear at 42 °2.

32. A polycrystalline sample should contain thousands of crystallites
A polycrystalline sample should contain thousands of crystallites. Therefore, all possible diffraction peaks should be observed. 2q
For every set of planes, there will be a small percentage of crystallites that are properly oriented to diffract (the plane perpendicular bisects the incident and diffracted beams).
Basic assumptions of powder diffraction are that for every set of planes there is an equal number of crystallites that will diffract and that there is a statistically relevant number of crystallites, not just one or two.

33. Bragg-Brentano Arrangement
Generally the basic function of a diffractometer is to detect X-ray diffraction from a specimen and to record the diffraction intensity as a function of the diffraction angle 2.
The commercially available diffractometer used Bragg-Brentano arrangement, in which the X-ray incident beam from the generator is fixed, but the sample stage will rotate around an axis perpendicular to the plane of the previous figure.
The detector rotates around the axis perpendicular to the figure

34. Thin Film Measurement
In Bragg-Brentano arrangement, when the incident beam hit the sample, a significant amount of beam will penetrate inside the sample
A thin film or a coating is a thin layer of material deposited onto a substrate.
Therefore, Bragg-Brentano arrangement is not suitable for the detection of a phase of thin film or coating.
Why do you think this is?

35. In this figure an optical arrangement for thin film diffractometry is shown.

36. 3. Data Acquisition
A diffractometer records changes of diffraction intensity starting from low 2 ending at a high 2
A spectrum will be produced consisting of several intensity peaks located at different 2. You have seen examples of the diffraction patterns.
The spectrum provide a ‘fingerprint’ for crystalline solid.
Spectrum matching is determined by:
The position of the peak
The relative peak intensities among the peaks
But what are we matching the diffraction pattern with?

37. Crystal Phase Identification
To identify the crystalline phase existing in a given specimen, the diffraction data gathered must be matching with spectrum of known substance.
X-ray diffraction data from a known substance are recorded as powder diffraction file (PDF)
The standard diffraction data is published by the international Centre for Diffraction Data (ICDD)

38. This is an older version of ICDD called JCPDS card
Joint Committee On Powder Diffraction Standard (JCPDS).
There are several important feature to be seen from this card. Label them.

39. ICDD PDFs are updated and expended from time to time
Now days computer software performs the search-match task.
All PDFs of the ICDD can be stored in a computer and a programme can be used to find all the possible matches for a specimen.

40. 4. Distortion of diffraction spectra
A diffraction spectrum of a given specimen is considered as a fingerprint for identifying the phases which present in the specimen.
The spectrum/pattern will be compared with the standard PDFs database.
The standard spectrum has been collected from pure powder sample with fine powder size in micronsize.
In matching the data, two important points must be considered: peak positions and relative peak intensities.
However sometimes there exist discrepancy between the standard data then the gathered spectrum. The discrepancies are due to:
Preferential crystal orientation
Crystallite size
Residual stress

41. Preferential Orientation. Example: Gold thin film on single crystal
Preferential Orientation. Example: Gold thin film on single crystal. The thin gold film follows the atomic arrangement of the underlying substrate. The film has preferred orientation/texture 40 50 60 70 80 90
100
Two-Theta (deg)
x10 3
2.0
4.0
6.0
8.0
10.0
Intensity(Counts)
This the XRD pattern of the gold film. Note a strong peak at 2=38o
Match XRD pattern to the stick pattern:
(111)
(311)
(200)
(220)
(222)
(400) 40 50 60 70 80 90
100
Two-Theta (deg)
x10 3
2.0
4.0
6.0
8.0
10.0
Intensity(Counts)
> Gold - Au
(111)
(311)
(200)
(220)
(222)
(400) 40 50 60 70 80 90
100
Two-Theta (deg)
x10 3
2.0
4.0
6.0
8.0
10.0
Intensity(Counts)
This is the ICDD stick pattern of # Gold - Au
Gold is FCC metal and should have the strongest peak intensity at (111) followed by (311), (200) and (220). However, in this case only (111) peak is obvious. This is because the thin film has preferred orientation (texture)

42. Crystallite Size
A Bragg diffraction peak should be just a line at a certain 2.
However, in real sample, a peak has a certain width
The width can result from instrumental factors but more importantly from the size effect of the crystals.
As the crystallite size becomes smaller and smaller, the peak will become wider
This is due to incomplete destructive interference when the crystallite size becomes much smaller.
Nanomaterials have broad diffraction peaks due to the size of the material is in nanoscale.

43. Example
Small crystallite size will give broad X-ray diffraction pattern

44. Residual stress
d-spacing in a crystal will determine the position of the diffracted angle, 2
Any factor that change the d-spacing or the lattice parameter of a specimen will distort the position of the 2 in the x-ray pattern
Residual stress in a solid specimen may shift the diffraction peak position in the pattern.
Residual stress can be generated by strain in the specimen.
There are many reasons to have strain. Strain could be due point defects
When the lattice spacing is in tensile stress, the peak shift would be to a lower 2 value
When the lattice spacing is in compression, the peak shift would be at higher 2 value.

45. 5. Classwork + problem based learning

46. Classwork 1. You are given this XRD pattern
Classwork 1. You are given this XRD pattern. Write down steps on how to identify the phase of this pattern

47. Experimental data
Reference data
(PDF # )
d-value
relative intensity

48. Problem based learning: NiO
Distortion of XRD pattern from the ICDD stick pattern.

49. Case: To identify oxide film on Ni
NiO is an important engineering material. A thin NiO film is used in many applications. NiO film can be grown on Ni foil by thermal oxidation.
Nickel foil with thickness of 10mm was oxidised in air at 1000oC. A thin NiO should form on the surface of the nickel foil. To further verify if indeed NiO is formed, XRD was performed on the sample. XRD pattern of the sample was given to you.
From the stick pattern of standard ICDD of NiO # , the strongest NiO peak should correspond to (200) NiO followed by (220) and (111).
However, from the XRD pattern of the sample only peak corresponding to (200) NiO is identified. Very small peak from (111) NiO can be seen.

50. XRD pattern of the sample

51. Problem
After performing the peak matching with ICDD # , it appears that only 2 peaks from NiO matches with strongest peak match to (200) NiO at 2 = o and a smaller peak of (111) NiO at o. Explain possible reasons to cause discrepancies between the peak intensities of this x-ray pattern and its standard data?
Moreover from the standard data, the peak position for the (200) NiO should be at o and (111) NiO should be at o. Why do you think there is a discrepancy between the measured data with the standard ICDD?

52. Stick pattern from ICDD #00 002 1216 (Bunsenite, NiO)
No. h k l d [A] 2Theta[deg] I [%]

53. Anchor Scan Parameters
Dataset Name: 1
File name: C:\X'PertData\hazhar\hafiz\1\1.xrdml
Comment: BB optics phase analysis
Measurement Date / Time: 3/26/ :02:23 AM
Operator: UNIVERSITI SAINS MAL
Raw Data Origin: XRD measurement (*.XRDML)
Scan Axis: Gonio
Start Position [°2Th.]:
End Position [°2Th.]:
Step Size [°2Th.]:
Scan Step Time [s]:
Scan Type: Continuous
Offset [°2Th.]:
Divergence Slit Type: Fixed
Divergence Slit Size [°]:
Specimen Length [mm]:
Receiving Slit Size [mm]:
Measurement Temperature [°C]: 25.00
Anode Material: Cu
K-Alpha1 [Å]:
K-Alpha2 [Å]:
K-Beta [Å]:
K-A2 / K-A1 Ratio:
Generator Settings: 30 mA, 40 kV
Goniometer Radius [mm]:
Dist. Focus-Diverg. Slit [mm]: 91.00
Incident Beam Monochromator: No
Spinning: No
Real Data from XRD
These are the information from the XRD Go through each line and try to understand what does it mean

54. This is the XRD pattern plot as in intensity vs
This is the XRD pattern plot as in intensity vs. 2 (this is considered a raw data - data must be replot)
This list is the peak position list, what does height, FWHM, d spacing and Rel. Int signify? Discuss.
The orange line signify the peak matched by , NiO
The blue signify the peak matched by Ni
Peak List
Pos.[°2Th.] Height[cts] FWHM[°2Th.] d-spacing[Å] Rel.Int.[%] Tipwidth[°2Th.] Matched by

55. Write down your discussion

56. Revision questions What is XRD? What is XRD used for?
XRD patterns gathered must be matched to a standard data, what is the standard data?
State 3 reasons why there exist discrepancies between the XRD pattern gathered from a specimen compared to the standard data.
State 2 limitation of XRD in performing phase identification of a given specimen.
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