Kuliah-10 XRD-2024
Kuliah-10 XRD-2024
Kuliah-10 XRD-2024
X-Ray Diffraction
Objectives:
1. Students are able to explain how X-ray diffraction works and its basic
principles (C3)
2. Students are able to predict the type of crystal structure of a material in
according to its X-ray diffraction pattern (C3).
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Topik Bahasan
1. Pendahuluan
2. What is X-ray
3. X-ray Production
4. Basic XRD
5. Applications of X-Ray Diffraction
6. Indexing Pattern
7. Crystallite Size
1. Pendahuluan
• Material characterization is a central activity of materials science.
• The general approach: to probe the material with a beam of radiation or high-
energy particles.
• X-rays are a form of electromagnetic radiation having a short wavelength (λ≈0.1
nm).
• X-ray diffraction (XRD) is used to obtain structural information about crystalline
solids.
• Useful in biochemistry to solve the 3D structures of complex bio-molecules.
• Bridge between physics, chemistry, and biology.
Components
• X-ray source
• Device for
restricting
wavelength range
“goniometer”
• Sample holder
• Radiation
detector
• Signal processor
and readout
4.3. How XRD works: Schematic
Example-1
Step 1: Identify the peaks and their proper 2θ values. 8 peaks for this pattern
Step 4. Select the result from step 3 that yields h2+ k2+ l2 as a series of integers
Step 5. Compare results with the sequences of h2+ k2+ l2 values to identify the
Bravais lattice
Step 4. Identify the lowest commont quotient from step 3 and identify the
integers to which it corresponds. Let the lowest common quotient be K
Step 5: Devide sin2θ by K for each peak.
This will give you a list of integers
corresponding to h2+ k2+ l2 Step 6: Select the appropriate pattern
h2+ k2+ l2 values and identify the
Bravais lattice
2 variables
4
Tetragonal System
• In this system, the sin2θ values obey the following relation:
• sin2θ = A (h2+ k2) + C l2
• where A(= λ2/4a2) and C (= λ2/4c2) are constants for any pattern.
• First of all, these constants (A and C) are found which will then disclose the cell
parameters a and c and enable the line indices to be calculated. The value of A is obtained
from the hk0 lines. When l= 0 the above equation becomes:
• sin2θ= A (h2+ k2)
• The permissible values of (h2 + k2) are 1, 2, 4, 5, 8, 9, etc. Therefore, the hk0 lines must
have sin2θ values in the ratio of these integers and A will be some number which is 1, 1/2,
1/4, 1/5, 1/8, 1/9, etc., times the sin2θ values of these lines. C is obtained from the other
lines on the pattern and by the use of the following equation.
• Sin2θ − A (h2+ k2) = C l2
• Differences represented by the left-hand side of the equation are set up, for various
assumed values of h and k, in an attempt to find a consistent set of C l2 values, which must
be in the ratio of 1, 4, 9, 16, etc. Once these values are found, C can be calculated.
Autoindexing
If tetragonal:
Now, we assume the 2nd peak is (001) The next step find the common factor
so all 1/d2 will be divided by 0.069 that separates the 2 different peaks.
Assume the first peak is the c axis and
the 2nd peak is a axis
Peak 1
If tetragonal : 1, 2, 4, 5, 8, 9, …… Peak 2
Peak 3
Peak 4
Peak 5
Example-3 for hexagonal
Lattice parameter c X2
7. Crystallite Size
• Sometimes, crystallite and grain sizes are
considered to be the same.
• It is important to note that a grain consists of
a single material but may be crystalline, or
polycrystalline.
• An individual crystallite consists of a single
phase.
• Crystallite and grain are both single crystals.
• A crystallite is a single crystal in powder
form.
• A grain is a single crystal within a bulk form.
• A particle is also thought of as an
agglomerate; small enough in size to not
consider it as a bulk or thin film but Diffraction pattern based on crystallite size
composed of 2 or more individual
crystallites.
• The size of the crystallite will affect the peak
of X-ray diffraction as illustrate in the
following schematic figure.
Pengaruh ukuran partikel
• where D is the crystallite size (nm), K is the Scherrer constant (0.9), 𝜆 is the wavelength
of the X-rays used (Cu: 0.15406 𝑛𝑚), 𝛽 is the Full Width at Half Maximum (𝐹𝑊𝐻𝑀,
radians), and 𝜃 is the peak position (radians).
• The steps for identifying crystal size using XRD are as follows:
1) Step 1: Identify the K value
2) Step 2: Identify the 𝜆 value
3) Step 3: Identify FWHM (β)
Fig 4. Illustration of half
Fig 3. The peak at the the maximum peak
maximum intensity with intensity.
certain 2θ.
In short, by performing a curve selection of the diffraction peaks of each plane crystal at
position 2θ, we can see half-peak curve widening value diffraction (FWHM), then with a value
of is put into the equation Scherrer to determine the size crystal.
Crystallinity Index