An introduction to Powder Diffraction and Powder Diffraction Hardware

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An Introduction to the Powder
Diffraction Experiment
Angus P. Wilkinson
School of Chemistry and Biochemistry
Georgia Institute of Technology
Outline
Diffraction from a crystal
 What is a “powder” in the context of diffraction?
 Representing the powder diffraction pattern

– I(2q), I(d), I(Q) etc.
 Radiation
sources
 Recording powder patterns:
–
–
–
–
–
–
Monochromatic neutron diffraction
Time-of-flight neutron diffraction
Monochromatic X-rays 2D detectors
Monochromatic X-rays with point detectors
Monochromatic X-rays with 1D detectors
White x-ray beams
Diffraction from ordered atoms


Consider a 3D array of atoms
arranged on planes
Get constructive interference
between x-rays scattered from
atoms P and K in same plane
when there is no path
difference for the scattered rays
– Need to have symmetrical diffraction so that QK-PR =
PKCosq –PKCosq = 0
– Get constructive interference between x-rays scattered from
atoms in different planes when the path length is a multiple
of l. Consider atoms K and L.
– ML + LN = d’sinq + d’sinq = 2d’sinq = nl
– 2dsinq = nl is Bragg’s law
What is a powder?

In the context of powder diffraction, a powder is a sample that
consists of many small crystallites with a wide range of
different orientations in space.
– Ideally, a random and uniform distribution of orientations

Only some small fraction of the crystallites in the sample are in
the correct orientation to contribute to the diffracted intensity in
a given peak
2q
Only crystallites that are in
the symmetrical reflection
condition and fulfill Bragg’s
law contribute to diffraction
Powder diffraction
Scattered
radiation
X-ray powder diffraction pattern for cubic ZrW2O8
6000
2q
Incident
radiation
Sample
4000
2q is the Bragg angle
2dsinql
Q
5000
3000
or
2000
4 sin q
1000
l
0
1
1.5
2
2.5
3
Q
3.5
4
4.5
5
Common sample geometries
A
slab of material in symmetrical
reflection geometry
– Most laboratory x-ray measurements
– Absorption not usually a big problem
because of the reflection geometry
A
q
q
tube containing the sample
– Most neutron experiments
– Many synchrotron x-ray experiments and
some laboratory experiments
– Sample easily sealed and less susceptible
to texture/preferred orientation
– Absorption can be a big problem with low
energy x-rays as the beam has to pass
through the sample
2q
X-ray tube
 X-rays
are usually produced in the lab using an
x-ray tube. Electrons are accelerated onto a
metal target
Tube emission spectra

Characteristic lines (atomic
transitions) are superimposed
on a continuous
Bremsstrahlung background
– Some lines are multiplets
» This leads to a1/a2 splitting in
powder diffraction patterns


Diffraction normally uses the
emission lines not the
Bremsstrahlung
Intensity of K-line
– IK = Bi(V-Vk)n
» B proportionality constant, i
current, V accelerating
voltage, Vk threshold voltage,
n ~ 1.5
Mo tube emission spectra taken from
Cullity and Stock
Synchrotron radiation





High intensity
Plane polarized
Intrinsically collimated
Wide energy range
Has well defined time
structure
Neutron Sources
 Neutrons
for diffraction are either produced
using fission in a nuclear reactor or by spallation
Neutron sources 2
 Reactors
produce neutrons continually (usually)
 Spallation sources produce short pulses of neutrons
 Neutrons are initially very energetic
– They must be slowed down by moderation
» Typically, exchange energy with a hydrogen containing material
such as water, H2 or methane.
Reactor flux
Select narrow band for
monochromatic diffraction
Pulsed source peak flux
Use wide band for time of
flight diffraction
Powder diffraction at a reactor
D2B
Pictures courtesy of Alan Hewat
Time-of-flight diffraction
Sample
L
Source


Detector
2q
Time from source to detector is determined by neutron
wavelength
mL  L1l
v  ( L  L1) / t and mv  h / l so t 
h
Can measure I(Q) without scanning detector
4mL  L1sin q
Q

L1
ht
Use many separate detectors and sum the counts recorded
in each to measure I(Q) with good counting statistics in
less time
SEPD – Special Environment
Powder Diffractometer

2 theta
Solid angle
(str)
± 145°
0.086
± 90°
0.086
± 60°
0.052
+ 30°
0.017
- 15°
0.017
Only small fraction of total solid angle covered
GEM 2nd Generation TOF NPD
POWGEN3 at the SNS
TOF neutron data for cubic ZrMo2O8
X-rays with true 2D detectors: imaging
plates, CCD cameras, multi-wires etc.

A true 2D detector can intercept complete cones of
diffracted radiation and very efficiently record the
diffraction pattern
Fast data acquisition, but not very high resolution (Dd/d)
Maximum 2q that is readily achievable is often quite limited
Integrating 2D data
 Debye
rings from the 2D
detector are integrated
and converted into a
conventional powder
pattern using FIT 2D or
similar software
X-ray beam size, detector pixel
size and sample thickness
combine to limit the effective
resolution of the data
Why use 2D detectors?
 Rapid
acquisition of data
from normal sized samples
for time resolved or
parametric studies
– Seconds/minutes per pattern
 Reasonable
signal to noise
and sampling statistics can
be achieved even with very
small samples such as those
used in high pressure
diamond anvil cell
experiments
Time resolution in this cement
hydration experiment is ~5
minutes
Diamond anvil cell (DAC)

High pressures can be conveniently achieved
by placing the sample between the faces of
two diamonds and squeezing
– Megabar pressures are attainable

Diamond does not absorb high energy x-rays
strongly
1D detector: Debye-Scherrer camera

Can record sections on these
cones on film or some other
x-ray detector
– Simplest way of doing this is
to surround a capillary sample
with a strip of film
– Can covert line positions on
film to angles and intensities
by electronically scanning film
or measuring positions using a
ruler and guessing the relative
intensities using a “by eye”
comparison
Electronic 1D detectors
 1D
position sensitive detectors based on many
different types of technology are available.
– Fast data collection, but not as efficient as a 2D detector
– But access to high 2q by curving the detector
INEL curved detector at Cal Tech
Braun linear PSD at ORNL/HTML
X’celerator from Panalytical
•Fast data collection using RTMS (Real Time
Multiple Strip) detection technology
Thanks to Panalytical
1 D detector in use for plate sample
Scan direction
Scan direction
Line
focus
X’Celerator
Divergence slit
Polycrystalline sample
Thanks to Panalytical
1 D detector with capillary sample
Elliptical
mirror
Capillary
sample or
sample
on/between
foils
Focus on
(X’Celerator)
detector
Thanks to Panalytical
Capillary stage
Thanks to Panalytical
Micro-diffraction
0.05 - 1 mm
diameter
X-ray tube
(point focus)
Mono capillary
X’Celerator
Detector
Small (part of) sample
Microdiffraction Stage
Thanks to Panalytical
Point detectors: Powder diffractometer
 Alternatively,
you can intercept sections of the
cones using a point (0D) electronic detector
Slit is moved to different 2qs.
The x-rays passing through the
slit are recorded electronically
giving a powder pattern
Bragg Brentano diffractometer
Detector
Soller slits
Receiving slit
X-ray tube
(line focus)
Curved crystal
monochromator
(Graphite)
Anti scatter slit
Soller slits
Beam mask
Polycrystalline sample
Divergence slit
Thanks to Panalytical
X-ray optics

Conventional x-ray powder diffractometers use diverging x-ray
beams, with the divergence limited by slits
– If the effective sample surface is not on the 2q rotation axis, the peaks
will be shifted from their correct positions by a “sample displacement”
error

Many modern laboratory diffractometers use “parallel beam
optics” that eliminate the problems of sample height
displacement errors
– Multilayer x-ray mirror on the incident beam side and Soller collimator
on the diffracted beam side

Synchrotrons provide an inherently parallel beam on the
incident side
– Equipped with analyzer crystals on the diffracted beam side very high
angular resolution can be achieved (see later). Insensitive to sample
displacement.

Effective resolution of lab instruments can be improved by
using Ka1 radiation only
Parallel beam geometry
X-ray mirror
Slit
Parallel plate
collimator
+ detector
Polycrystalline sample
Parallel beam geometry
X-ray mirror
Slit
Parallel plate
collimator
+ detector
Polycrystalline sample
Even a 1 mm displacement does not
cause shifts!
1000
400
displacem ent = 0 mm
displacem ent = -1 m m
displacem ent = 0 mm
displacem ent = -1 m m
350
800
Al O powder
Al O powder
300
2
Intensity (cts)
3
600
400
3
250
200
150
100
200
50
1600
0
24
24.5
25
25.5
140026.5
26
2Theta (°)
Data taken from
T.R Watkins,
Oak Ridge National
Laboratory, USA
Al O powder
2
3
0
27
74
displacem ent = 0 mm
displacem ent = -1 m m
75
76
77
2Theta (°)
1200
Intensity (cts)
Intensity (cts)
2
1000
800
600
400
200
0
20
30
40
50
2Theta (°)
60
70
80
78
79
The a1-Reflection System
X’Celerator
Soller slit
Anti-scatter shield
Soller slits
Irradiation slit
Anti-scatter
slit
X-ray tube
(line focus)
Polycrystalline sample
Incident beam
monochromator
Programmable
divergence slit
Alpha-1 vs standard diffractometer
Intensity (counts)
Single peak
19600
14400
10000
No
overlap
6400
3600
1600
400
48.75
48.80
48.85
48.90
48.95
49.00
49.05
Low background
49.10
49.15
49.20
49.25
49.30
2Theta (°)
Synchrotron Diffractometer Geometry



Crystal analyzer gives very good resolution, low count rate and is insensitive
to sample displacement, useable with flat plate or capillary
Soller slits give modest resolution, good count rate and insensitivity to sample
displacement
Simple receiving slits give good count rate, easily adjustable resolution, can be
used with flat plate or capillary
Comparison of 2D and high res data
11BMB – 10min scan
1BM/MAR345 – 1sec exposure
Thanks to R. Von Dreele
Energy discrimination
 X-rays
scattered from a sample can include unwanted
wavelengths
– Fluorescence, Kb, Bremmstrahlung…..

Can be eliminated using a diffracted beam
monochromator
– Typically graphite
– Cheap, but you loose useful signal as well

Can be eliminated using an energy discriminating
detector
– Semiconductor “solid state detector”
– Expensive, but can give good count rate
Energy Dispersive Diffraction
E(keV) = 6.199 / (d_space * sin(theta_angle of Energy Dispersive detector))
Collimator and
EDX detector – at a
fixed angle
White X_ray
Beam
Courtesy of
Lachlan
Cranswick
Sample
Environment
Diffraction patterns are
obtained only for the
volume subtended by the
collimator with the
incident X-ray beam
Energy Dispersive Diffraction : Advantages

Can see “inside” unconventional sample environments
– Within limits: can have steel or other materials shielding the sample at
pressure and/or temperature
» thus samples can also be immersed in gas or liquid (hydrothermal synthesis)
» in-situ studies - reactions / explosions / properties under stress. Particle
flows within gases and fluids. Reactions in gas/fluid flow lines.
» Only see diffraction in the volume (nick-named the “lozenge”) defined where
the detector collimator subtends onto the incident white X-ray beam

Spatial Resolution inside the sample environment
– Can narrow down the beam and collimator - and move the sample : thus
obtaining diffraction patterns from different spatial volumes inside the
sample environment

Fast data collection times
– minutes to fractions of a second
Mapping phase distributions using EDXRD

Use EDXRD to record
diffraction pattern from defined
volumes inside specimens
– map out the crystalline phases in
the sample without damage
Summary
 There
are lots of experimental possibilities
each one of which represents a trade off
– Consider carefully which compromise works best
for you
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