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
  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

                                                      Only crystallites that are in
                                                      the symmetrical reflection
                                                 2q   condition and fulfill Bragg’s
                                                      law contribute to diffraction
 Powder diffraction
                                      X-ray powder diffraction pattern for cubic ZrW2O8


  Incident    Sample
  radiation                4000

2q is the Bragg angle      3000

 2dsinq=l             or   2000


                                  1       1.5    2     2.5     3     3.5    4     4.5     5
Common sample geometries
A  slab of material in symmetrical
 reflection geometry                      q   q
 – Most laboratory x-ray measurement
 – 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            2q
 – Sample easily sealed and less
   susceptible to texture
 – 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 a1/a2 splitting in
          powder diffraction patterns
   Diffraction normally used the
    emission lines not the
   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
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                       Pulsed source peak flux

      Select narrow band for                 Use wide band for time of
     monochromatic diffraction                   flight diffraction
Powder diffraction at a reactor


Pictures courtesy of Alan Hewat
Time-of-flight diffraction
                                          L1   2q
     Source                    Detector
    Time from source to detector is determined by neutron
                     and                  so
    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
SEPD – Special Environment
Powder Diffractometer
                                          2 theta   Solid angle
                                          ± 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              Time resolution in this cement
  experiments                      hydration experiment is ~5
    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
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”
  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   X’Celerator

                  Divergence slit

                         Polycrystalline sample

                                             Thanks to Panalytical
1 D detector with capillary sample

                sample or                Focus on
                 sample                (X’Celerator)
               on/between                detector

                            Thanks to Panalytical
Capillary stage

                  Thanks to Panalytical

                                 0.05 - 1 mm
 X-ray tube
(point focus)   Mono capillary

                                      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

                                                           Soller slits
                                                                             Curved crystal
                                                 Receiving slit              monochromator

  X-ray tube       Soller slits                               Anti scatter slit
  (line focus)

                                   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”
   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
   Effective resolution of lab instruments can be improved by
    using Ka1 radiation only
Parallel beam geometry

 X-ray mirror

                                         Parallel plate
                                          + detector

                Polycrystalline sample
Parallel beam geometry

 X-ray mirror

                                         Parallel plate
                                          + detector

                Polycrystalline sample
Even a 1 mm displacement does not
cause shifts!

  Data taken from
    T.R Watkins,
 Oak Ridge National
  Laboratory, USA
The a1-Reflection System


                                                                            Soller slit

                                                                 Anti-scatter shield

                                              Soller slits
           Irradiation slit
    X-ray tube
    (line focus)

                                                                           Polycrystalline sample
                              Incident beam
                                               divergence slit
Alpha-1 vs standard diffractometer
                       Single peak


           Low background
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
   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
    – Fluorescence, Kb, Bremmstrahlung…..
   Can be eliminated using a diffracted beam
    – Typically graphite
    – Cheap, but you loose useful signal as well
   Can be eliminated using an energy discriminating
    – 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

                                           Diffraction patterns are
                                           obtained only for the
                                           volume subtended by the
 Courtesy of                               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
 Thereare lots of experimental possibilities
 each one of which represents a trade off
  – Consider carefully which compromise works best
    for you

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