X-ray Diffraction- Powder Diffraction

Question 1

Implications of Bragg law

Answer 1

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

Question 2

Why do you often not see X-Ray diffraction for a single crystal?

Answer 2

Because the diffraction condition is so strict

Question 3

Solutions to problem of single crystal diffraction

Answer 3

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

Question 4

Geometry of powder diffraction

Answer 4

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

Question 5

Diffracted beam from powder

Answer 5

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

Question 6

3 components of instrumentation required for powder diffraction

Answer 6

An x-ray source
A detector and counting electronics
The goniometer, sample and x-ray optics

Question 7

Most common arrangement of instrumentation

Answer 7

Bragg-Brentano parafocussing. There are several variants

Question 8

How does parafocussing work?

Answer 8

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

Question 9

Arrangement for Bragg-Brentano parafocussing

Answer 9

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

Question 10

How does rotation of specimen relate to position of detector?

Answer 10

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.

Question 11

What are the x-ray optics and their purpose?

Answer 11

Soller slits
Divergence slits
Receiving slit
All to clean up the x-ray beam (resolution), reduce systematic aberrations (errors) and suppress background scattering.

Question 12

Soller slits

Answer 12

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

Question 13

Divergence slits

Answer 13

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

Question 14

Receiving slit

Answer 14

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

Question 15

The 3 systematic aberrations in parafocussing arrangement and what they affect

Answer 15

Specimen displacement effects
Flat specimen error
Axial divergence
May affect positions/intensities of the reflections in a diffraction pattern

Question 16

Origin of specimen displacement error

Answer 16

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.

Question 17

Symptom and solution to specimen displacement error

Answer 17

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

Question 18

Origin of flat specimen error

Answer 18

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

Question 19

Symptom and solution to flat specimen error

Answer 19

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)

Question 20

Axial divergence origin, symptom and solution

Answer 20

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