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XRD Principles and Interpretation
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XRD Principles and Interpretation
Lecture 6
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1
Question
What is the primary purpose of X-ray Diffraction (XRD) in materials characterization?
Answer
XRD is used to determine the crystal structure of a material by analyzing the arrangement of atoms and the resultant diffraction pattern, rather than directly identifying the composition.
2
Question
How is a crystallographic plane defined in three dimensions?
Answer
A crystallographic plane is defined by its intercepts with the x, y, and z axes and expressed by the equation x/a + y/b + z/c = 1, where a, b, and c are the intercepts on the respective axes.
3
Question
What are Miller Indices and how are they determined?
Answer
Miller Indices (hkl) are a set of three integers representing the orientation of crystallographic planes, found by taking the reciprocals of the axial intercepts of the plane, clearing fractions and reducing to the smallest integers.
4
Question
What is Bragg's Law and what does it describe?
Answer
where n is an integer, λ is the wavelength, d_hkl the interplanar spacing, and θ the incident angle.
5
Question
How is Bragg's Law expressed for the first order reflection (n=1) in terms of wavelength λ, lattice constant a, Miller indices (h,k,l), and diffraction angle θ?
Answer
λ = (2a / sqrt(h² + k² + l²)) * sin(θ)
6
Question
Why are X-ray wavelengths particularly suitable for crystallography?
Answer
Because X-ray wavelengths are comparable to atomic spacings (on the order of angstroms), allowing them to diffract from crystal planes and reveal atomic structure.
7
Question
What role does absorption and filtering play in preparing X-rays for crystallography?
Answer
Absorption and filtering reduce intensity of unwanted continuous and secondary characteristic X-rays to isolate monochromatic radiation necessary for precise diffraction measurements.
8
Question
Formula for intensity I_x of X-rays passing through an absorption layer of thickness x.
Answer
9
Question
How to index crystal planes from XRD peaks?
Answer
10
Question
What factors affect peak instensity?
Answer
11
Question
Why is monochromatic X-ray radiation preferred for crystallography experiments?
Answer
Monochromatic radiation produces sharp, well-defined diffraction peaks and avoids overlapping reflections from multiple wavelengths, improving measurement accuracy.
12
Question
What is the formula for the intensity of X-rays scattered by a single electron
Answer
13
Question
What is the atomic scattering factor fa formula?
Answer
14
Question
Lattice types and requirements for diffraction
Answer
15
Question
According to the extinction rules table, which diffraction peaks are necessarily absent in a face-centered cubic (FCC) lattice?
Answer
In FCC lattices, diffraction peaks are necessarily absent when the Miller indices \(h, k, l\) are mixed (some even and some odd). Only those peaks with all indices unmixed (all even or all odd) can be present.
16
Question
Lorentz Factor (trigometric) equations
Answer
17
Question
How does temperature affect the intensity and position of X-ray diffraction peaks?
Answer
18
Question
What is the formula representing the cumulative effect of all factors on peak intensity in X-ray diffraction?
Answer
where (|F|^2\) is the structure factor squared, (p_{hkl}) is the multiplicity factor, and (e^{-2M}) is the temperature factor.
19
Question
Peak width size changes due to crystallite size
Answer
Smaller crystallite sizes cause increased peak broadening. Peak width is inversely correlated to grain size, D (grain size reduces with increasing width) as given by Scherrer’s equation, where B (or β) is the FWHM, and K is a proportionality factor (that depends on crystal structure and other factors).
20
Question
What are microstrains in the crystal lattice, and how do they affect X-ray diffraction peaks?
Answer
Microstrains are small distortions or variations (due to deformation) in the crystal lattice spacing. They cause changes by shifting and broadening peaks due to local variations in d-spacing.