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(2), 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 = PKCos –PKCos = 0

– Get constructive interference between x-rays scattered from atoms in different planes when the path length is a multiple of . Consider atoms K and L.– ML + LN = d’sin + d’sin = 2d’sin = n

– 2dsin = n 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

Only crystallites that are in the symmetrical reflection condition and fulfill Bragg’s law contribute to diffraction

Powder diffraction

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X-ray powder diffraction pattern for cubic ZrW2O8

Q

Sample

Scattered radiation

Incident radiation

is the Bragg angle

sin4

Q

dsinor

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 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

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 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 SourcesNeutrons 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.Pulsed source peak fluxReactor flux

Select narrow band for monochromatic diffraction

Use wide band for time of flight diffraction

Powder diffraction at a reactor

Pictures courtesy of Alan Hewat

D

Time-of-flight diffraction

Time from source to detector is determined by neutron wavelength

Can measure I(Q) without scanning detector

Use many separate detectors and sum the counts recorded in each to measure I(Q) with good counting statistics in less time

LL1Source

Sample

Detector

tLLv /)1( /hmv and so h

LLmt

1

ht

LLmQ

sin14

SEPD – Special Environment Powder Diffractometer

Only small fraction of total solid angle covered

2 theta Solid angle

(str)

± 145° 0.086

± 90° 0.086

± 60° 0.052

+ 30° 0.017

- 15° 0.017

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 (d/d)

Maximum 2 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 2 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

Polycrystalline sample

X’Celerator

Line focus

Divergence slit

Scan directionScan direction

1 D detector in use for plate sample

Thanks to Panalytical

1 D detector with capillary sample

Focus on Focus on (X’Celerator) (X’Celerator)

detectordetector

Elliptical Elliptical mirrormirror

Capillary Capillary sample or sample or

sample sample on/between on/between

foilsfoils

Thanks to Panalytical

Capillary stage

Thanks to Panalytical

X’CeleratorDetector

Small (part of) sample

Mono capillaryX-ray tube

(point focus)X-ray tube

(point focus)

0.05 - 1 mmdiameter

Microdiffraction Stage

Micro-diffraction

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 2s. The x-rays passing through the slit are recorded electronically giving a powder pattern

Bragg Brentano diffractometer

Anti scatter slit

Detector

Curved crystalmonochromator(Graphite)

Receiving slit

Polycrystalline sample

Soller slits

X-ray tube(line focus)

Divergence slit

Soller slits

Beam mask

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 2 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 K1 radiation only

Parallel beam geometry

Parallel plate collimator + detector

Polycrystalline sample

Slit

X-ray mirror

Parallel beam geometry

Parallel plate collimator + detector

Polycrystalline sample

Slit

X-ray mirror

Even a 1 mm displacement does not cause shifts!

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Al2O

3 powder

displacement = 0 mmdisplacement = -1 mm

Inte

nsity

(cts

)

2Theta (°)

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Al2O

3 powder

displacement = 0 mmdisplacement = -1 mm

Inte

nsity

(cts

)

2Theta (°)

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Al2O

3 powder

displacement = 0 mmdisplacement = -1 mm

Inte

nsity

(cts

)

2Theta (°)

Data taken fromT.R Watkins,

Oak Ridge National Laboratory, USA

The 1-Reflection System

X-ray tube(line focus)

Incident beam monochromator

Irradiation slit

Programmable divergence slit

Soller slits

Polycrystalline sample

Soller slit

X’Celerator

Anti-scatter shield

Anti-scatter slit

48.75 48.80 48.85 48.90 48.95 49.00 49.05 49.10 49.15 49.20 49.25 49.302Theta (°)

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nsity

(co

unts

)

Low background

Single peak

No overlap

Alpha-1 vs standard diffractometer

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

11BMB – 10min scan 1BM/MAR345 – 1sec exposure

Comparison of 2D and high res data

Thanks to R. Von Dreele

Energy discrimination X-rays scattered from a sample can include unwanted

wavelengths– Fluorescence, K, 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))

Courtesy of Lachlan

Cranswick

White X_ray

Beam

SampleEnvironment

Collimator andEDX detector – at afixed angle

Diffraction patterns areobtained only for thevolume subtended by thecollimator with theincident 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