X-ray Diffraction- Powder Diffraction Flashcards
Implications of Bragg law
For a given set of Miller planes and a particular diffraction order n, there is only one (incident) angle θ that satisfies the Bragg equation. If it is not satisfied, there is no diffraction
Why do you often not see X-Ray diffraction for a single crystal?
Because the diffraction condition is so strict
Solutions to problem of single crystal diffraction
Laue diffraction: use white x-ray beam with wide range of wavelengths (hard to interpret)
Rotating crystal: multi-circle goniometer to rotate crystals in full 3D or around a particular symmetrical axis
Powder sample: many (>10^9) crystals randomly oriented so always domains in right direction for diffraction from any given Miller planes
Geometry of powder diffraction
The sample is in a fine powder and packed into a suitable holder and presented to the x-ray beam. Each particle of powder is single crystal or assemblage of small crystals, oriented at random with respect to incident beam. By chance a certain number of crystallites will be at correct angle for diffraction of incident beam by a given Miller plane. This happens to all Miller planes so diffraction always occurs for all of them
Diffracted beam from powder
Form of a cone of semi-apex angle 2θ conical sheet. Separate cone for diffraction from each plane. Detected by moving appropriate detector to intercept a small arc of the diffraction cones. Diffracted beam from each plane referred to as a reflection
3 components of instrumentation required for powder diffraction
An x-ray source
A detector and counting electronics
The goniometer, sample and x-ray optics
Most common arrangement of instrumentation
Bragg-Brentano parafocussing. There are several variants
How does parafocussing work?
X-rays diverge from source onto powder specimen on arc AB. They are diffracted by planes at the Bragg angle. They scatter through the same angle 2θ. They converge and focus at a point on the other side of the circle. Perfect focussing would require a curved specimen along the arc
Arrangement for Bragg-Brentano parafocussing
Flat plate specimen on specimen table in centre of circle. Can be tilted about diffractometer axis perpendicular to diffraction circle. On one side of circle circumference is sealed X-ray tube (source). On opposite side is detector at the focal point held by detector arm
How does rotation of specimen relate to position of detector?
When specimen is moved through angle θ to bring successive (hkl) planes into a position to diffract, the detector is moved through 2θ to maintain focussing condition.
What are the x-ray optics and their purpose?
Soller slits
Divergence slits
Receiving slit
All to clean up the x-ray beam (resolution), reduce systematic aberrations (errors) and suppress background scattering.
Soller slits
Thin parallel Mo foils which stop the beam spreading along the diffractimeter axis (axial divergence). Located between divergence slits before specimen and between specimen and detector
Divergence slits
Define the area (footprint) of the beam on the sample. Important at low angles where beam may spill over onto specimen holder. Reduces irradiated area but also intensity. Use 1° slits. Located either side of Soller slits between source and specimen
Receiving slit
Defines resolution of instrument (how well closely spaced reflections can be separated). Increase resolution narrowing slits but also reduces diffracted beam intensity. Use 0.1° slit. Located in detector arm between Soller slits and detector
The 3 systematic aberrations in parafocussing arrangement and what they affect
Specimen displacement effects
Flat specimen error
Axial divergence
May affect positions/intensities of the reflections in a diffraction pattern
Origin of specimen displacement error
Specimen surface displaced from centre of diffraction circle. Could be due to misplacement. Also due to effective displacement due to specimen transparency. If low absorption coefficient x-rays May penetrate significantly below surface so effective scattering surface lies below physical surface.
Symptom and solution to specimen displacement error
A systematic shift in the position of the reflections to lower 2θ angles.
For physical displacement (misplaced) just adjust sample.
For transparency use a thin smear of sample on a suitable substrate
Origin of flat specimen error
Has form of flat plate and isn’t curved to fit focussing circle. X-rays then diffracted by parts of specimen not located on focussing circle. Appear to be diffracted at angles lower than true Bragg angle
Symptom and solution to flat specimen error
A systematic shift in the positions of the reflections to low angle.
Close the incident beam divergence slits to control footprint on specimen and focus on sample centre (loss of intensity though)
Axial divergence origin, symptom and solution
Divergence of the x-ray beam along the axis of the diffractometer. Reflection asymmetry (long tails observed on the low angle side of reflections). Particularly important at low angles. Soller slits solve it
