X RAY DIFFRACTION- XRD

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X RAY DIFFRACTION- XRD
SOLID MATTER- AMORPHOUS Atoms arranged in a
random manner , like in liquids- eg
Glass CRYSTALLINE Atoms arranged in a regular
pattern. Smallest volume element repeats in three
dimensions describing the crystal. The smallest
volume element is UNIT CELL. Dimensions of the
unit cell described by the edges a,b, and c and
the angles between them alpha, beta and gamma.
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X - RAYS

• German scientist Rontgen discovered X-rays in
  1895 accidentally when working with discharge
  tube.
• Barium platinocyanide screen placed near the tube
  began to glow, Glow continued even when a wooden
  screen was placed between them.
• As cause was not known, called as X-rays.
• It could pass through opaque bodies. Wave length
  shorter than that of ultraviolet light.

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• Essential elements of a coolidge X- ray vacuum
  tube
• Cathode- tungsten filament heated to
  incandescence by a low voltage AC from a step
  down transformer/ storage battery.
• Emits large number of electrons known as
  thermions focused on a target using cylindrical
  shields (molybdenum)
• Shield maintained at a negative potential
  surrounding the cathode.
• Electrons accelerated to very high speeds by DC
  potential difference about 50kV to 100kV applied
  between cathode and anode (anticathode). The high
  DC from a step up transformer.

Electrons
Tungsten filament
Cooling water
Shield
X rays
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• The Coolidge tube (1913) is also called hot
  cathode tube
• It works with a very good quality vacuum (about
  10-4 Pa, or 10-6 Torr).
• The filament is the cathode of the tube. The high
  voltage potential is between the cathode and the
  anode, the electrons are accelerated and then hit
  the anode.
• There are two designs end-window tubes and
  side-window tubes.
• In the end-window tubes, the filament is around
  the anode, the electrons have a curved path.
• Special about side-window tubes is
• An Electrostatic lens focuses the beam onto a
  very small spot on the anode
• The anode is specially designed to dissipate the
  heat and wear resulting from this intense focused
  barrage of electrons
• Mechanically spun to increase the area heated by
  the beam.
• Cooled by circulating coolant.
• The anode is precisely angled at 1-20 degrees off
  perpendicular to the electron current so as to
  allow escape of some of the X-ray photons which
  are emitted essentially perpendicular to the
  direction of the electron current.
• The anode is usually made out of tungsten or
  molybdenum.
• The tube has a window designed for escape of the
  generated X-ray photons.
• The power of a Coolidge tube usually ranges from
  1 to 4 kW

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Introduction to X-ray Diffraction

• References
• Elements of Modern X-ray Physics, Jens
  Als-Nielsen and Des McMorrow, John Wiley Sons,
  Ltd., 2001
• (Modern x-ray physics new developments)
• X-ray Diffraction, by B.E. Warren, General
  Publishing Company, 1969, 1990
• (Classic x-ray physics book)
• Elements of X-ray Diffraction,2nd Ed., by B.D.
  Cullity, Addison-Wesley, 1978
• (Covers most techniques used in traditional
  material characterization)
• High Resolution X-ray Diffractometry and
  Topography, by D. Keith Bowen and Brian K.
  Tanner, Taylor Francis, Ltd., 1998
• (Semiconductors and thin film analysis)
• Modern Aspects of Small-Angle Scattering, by H.
  Brumberger, Editor, Kluwer Academic Publishers,
  1993
• (SAXS techniques)
• Principles of Protein X-ray Crystallography, by
  Jan Drenth, Springer, 1994
• (Crystallography)

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• The incoming beam (coming from upper left) causes
  each scatterer to re-radiate a small portion of
  its energy as a spherical wave.
• If scatterers are arranged symmetrically with a
  separation d, these spherical waves will be in
  synch only in directions where their path-length
  difference 2 d sin ? equals an integer multiple
  of the wavelength ?.
• In that case, part of the incoming beam is
  deflected by an angle 2?, producing a reflection
  spot in the diffraction pattern

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An intuitive understanding of XRD can be obtained
from the Bragg Model of Diffraction.

• In this model, a given reflection is associated
  with a set of evenly spaced sheets running
  through the crystal, usually passing through the
  centers of the atoms of the crystal lattice.
• The orientation of a particular set of sheets is
  identified by its three MILLER INDICES (h, k, l),
  and let their spacing be noted by d.
• WILLIAM LAWARENCE BRAGG proposed a model in which
  the incoming X-rays are scattered specularly
  (mirror-like) from each plane from that
  assumption, X-rays scattered from adjacent planes
  will combine constructively when the angle ?
  between the plane and the X-ray results in a
  path-length difference that is an integer
  multiple n of the X-ray wave length ?.

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• A reflection is said to be indexed when its
  Miller indices have been identified from the
  known wavelength and the scattering angle 2?.
  Such indexing gives the unit cell parameters, the
  lengths and angles of the unit-cell, as well as
  its space group. Since BRAGGS LAW does not
  interpret the relative intensities of the
  reflections, however, it is generally inadequate
  to solve for the arrangement of atoms within the
  unit-cell for that, a Fourier transform method
  must be carried out.

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BRAGGS LAW
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Theoretical Considerations
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An X-ray diffraction pattern formed when X-rays
are focused on a crystalline material, (a
protein). Each dot, called a reflection, forms
from the coherent interference of scattered
X-rays passing through the crystal. X-ray
scattering techniques are a family of
non-destructive analytical techniques which
reveal information about the crystallographic
structure, chemical composition, and physical
properties of materials and thin films. These
techniques are based on observing the scattered
intensity of an X-RAY beam hitting a sample as a
function of incident and scattered angle,
polarization, and wavelength or energy.
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X-ray diffraction techniques

• X-ray diffraction finds the geometry or shape of
  a molecule using x-rays. X-ray diffraction
  techniques are based on the elastic scattering of
  x-rays from structures that have long range
  order.
• Single-crystal X-ray diffraction is a technique
  used to solve the complete structure of
  crystalline materials, ranging from simple
  inorganic solids to complex macromolecules, such
  as proteins.
• Powder diffraction (XRD) is a technique used to
  characterize the crystallographic structure,
  crystallite size (grain size), and preferred
  orientation in polycrystalline or powdered solid
  samples. Powder diffraction is commonly used to
  identify unknown substances, by comparing
  diffraction data against a database maintained by
  the International Centre for Diffraction Data. It
  may also be used to characterize heterogeneous
  solid mixtures to determine relative abundance of
  crystalline compounds and, when coupled with
  lattice refinement techniques, such as Rietveld
  refinement, can provide structural information on
  unknown materials. Powder diffraction is also a
  common method for determining strains in
  crystalline materials.

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• Thin film diffraction and grazing incidence x-ray
  diffraction may be used to characterize the
  crystallographic structure and preferred
  orientation of substrate-anchored thin films.
• High-resolution x-ray diffraction is used to
  characterize thickness, crystallographic
  structure, and strain in thin epitaxial films. It
  employs parallel-beam optics.
• X-ray pole figure analysis enables one to analyze
  and determine the distribution of crystalline
  orientations within a crystalline thin-film
  sample.
• X-ray rocking curve analysis is used to quantify
  grain

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Scattering techniques

• Elastic scattering
• Materials that do not have long range order may
  also be studied by scattering methods that rely
  on elastic scattering of monochromatic x-rays.
• Small angle X-ray scattering (SAXS) probes
  structure in the nanometer to micrometer range by
  measuring scattering intensity at scattering
  angles 2? close to 0.
• X-ray reflectivity is an analytical technique for
  determining thickness, roughness, and density of
  single layer and multilayer thin films.
• Wide angle X-ray scattering (WAXS), a technique
  concentrating on scattering angles 2? larger than
  5.
• Inelastic scattering
• When the energy and angle of the inelastically
  scattered x-rays are monitored scattering
  techniques can be used to probe the electronic
  band structure of materials.
• Compton scattering
• Resonant inelastic x-ray scattering (RIXS)
• X-ray Raman scattering

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1. X-ray Generation Properties
2. Lattice Planes and Bragg's Law
3. Powder Diffraction
4. Thin Film Diffraction
5. Texture Measurement (Pole Figures)
6. Residual Stress Measurements
7. Small Angle X-ray Scattering (SAXS)
8. X-ray Crystallography

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1. X-ray Generation Properties

• X-rays are electromagnetic radiation with typical
  photon energies in the range of 100 eV - 100 keV.
  For diffraction applications, only short
  wavelength x-rays (hard x-rays) in the range of a
  few angstroms to 0.1 angstrom (1 keV - 120 keV)
  are used.
• Because the wavelength of x-rays is comparable to
  the size of atoms, they are ideally suited for
  probing the structural arrangement of atoms and
  molecules in a wide range of materials. The
  energetic x-rays can penetrate deep into the
  materials and provide information about the bulk
  structure.
• X-rays are produced generally by either x-ray
  tubes or synchrotron radiation. In a x-ray tube,
  which is the primary x-ray source used in
  laboratory x-ray instruments, x-rays are
  generated when a focused electron beam
  accelerated across a high voltage field bombards
  a stationary or rotating solid target. As
  electrons collide with atoms in the target and
  slow down, a continuous spectrum of x-rays are
  emitted, which are termed Bremsstrahlung
  radiation. The high energy electrons also eject
  inner shell electrons in atoms through the
  ionization process. When a free electron fills
  the shell, a x-ray photon with energy
  characteristic of the target material is emitted.
  

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• Common targets used in x-ray tubes include Cu and
  Mo, which emit 8 keV and 14 keV x-rays with
  corresponding wavelengths of 1.54 Å and 0.8 Å,
  respectively. (The energy E of a x-ray photon and
  it's wavelength is related by the equation E
  hc/l, where h is Planck's constant and c the
  speed of light)
• In recent years synchrotron facilities have
  become widely used as preferred sources for x-ray
  diffraction measurements. Synchrotron radiation
  is emitted by electrons or positrons travelling
  at near light speed in a circular storage ring.
  These powerful sources, which are thousands to
  millions of times more intense than laboratory
  x-ray tubes, have become indispensable tools for
  a wide range of structural investigations and
  brought advances in numerous fields of science
  and technology.

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2. Lattice Planes and Bragg's Law

• X-rays primarily interact with electrons in
  atoms. When x-ray photons collide with electrons,
  some photons from the incident beam will be
  deflected away from the direction where they
  original travel, much like billiard balls
  bouncing off one anther. If the wavelength of
  these scattered x-rays did not change (meaning
  that x-ray photons did not lose any energy), the
  process is called elastic scattering (Thompson
  Scattering) in that only momentum has been
  transferred in the scattering process. These are
  the x-rays that we measure in diffraction
  experiments, as the scattered x-rays carry
  information about the electron distribution in
  materials. On the other hand, In the inelastic
  scattering process (Compton Scattering), x-rays
  transfer some of their energy to the electrons
  and the scattered x-rays will have different
  wavelength than the incident x-rays.

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• Diffracted waves from different atoms can
  interfere with each other and the resultant
  intensity distribution is strongly modulated by
  this interaction. If the atoms are arranged in a
  periodic fashion, as in crystals, the diffracted
  waves will consist of sharp interference maxima
  (peaks) with the same symmetry as in the
  distribution of atoms. Measuring the diffraction
  pattern therefore allows us to deduce the
  distribution of atoms in a material.

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• The peaks in a x-ray diffraction pattern are
  directly related to the atomic distances.
  Consider an incident x-ray beam interacting with
  the atoms arranged in a periodic manner as shown
  in 2 dimensions
• The atoms, represented as green spheres in the
  graph, can be viewed as forming different sets of
  planes in the crystal (colored lines). For a
  given set of lattice plane with an inter-plane
  distance of d, the condition for a diffraction
  (peak) to occur can be written as
• known as the Bragg's law, after
  W.L. Bragg, who first proposed it.
• n is an integer representing the order of
  the diffraction peak. The Bragg's Law is one of
  most important laws used for interpreting x-ray
  diffraction data.
• Here, atoms are used as scattering points in this
  example, Bragg's Law applies to scattering
  centers consisting of any periodic distribution
  of electron density. Ie., the law holds true if
  the atoms are replaced by molecules or
  collections of molecules, such as colloids,
  polymers, proteins and virus particles

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3. Powder Diffraction

• Powder XRD (X-ray Diffraction) is perhaps the
  most widely used x-ray diffraction technique for
  characterizing materials. As the name suggests,
  the sample is usually in a powdery form,
  consisting of fine grains of single crystalline
  material to be studied. The technique is used
  also widely for studying particles in liquid
  suspensions or polycrystalline solids (bulk or
  thin film materials).

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• The term 'powder' really means that the
  crytalline domains are randomly oriented in the
  sample. Therefore when the 2-D diffraction
  pattern is recorded, it shows concentric rings of
  scattering peaks corresponding to the various d
  spacings in the crystal lattice. The positions
  and the intensities of the peaks are used for
  identifying the underlying structure (or phase)
  of the material. For example, the diffraction
  lines of graphite would be different from diamond
  even though they both are made of carbon atoms.
  This phase identification is important because
  the material properties are highly dependent on
  structure (just think of graphite and diamond).
• .

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Powder diffraction data can be collected using
either transmission or reflection geometry, as
shown below. Because the particles in the
powder sample are randomly oriented, these two
methods will yield the same data. In the MRL
x-ray facility, powder diffraction data are
measured using the Philips XPERT MPD
diffractometer, which measures data in reflection
mode and is used mostly with solid samples, or
the custom built 4-circle diffractometer, which
operates in transmission mode and is more
suitable for liquid phase samples
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MOUNTING THE CRYSTAL
DIFFRACTOMETER
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A powder XRD scan from a K2Ta2O6 sample is as
shown -as a plot of scattering intensity v/s. the
scattering angle 2theta or the corresponding
d-spacing. The peak positions, intensities,
widths and shapes all provide important
information about the structure of the material.
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4. Thin Film Diffraction

• Thin film diffraction refers not to a specific
  technique but rather a collection of XRD
  techniques used to characterize thin film samples
  grown on substrates. These materials have
  important technological applications in
  microelectronic and optoelectronic devices, where
  high quality epitaxial films are critical for
  device performance. Thin film diffraction methods
  are used as important process development and
  control tools, as hard x-rays can penetrate
  through the epitaxial layers and measure the
  properties of both the film and the substrate.
• There are several special considerations for
  using XRD to characterize thin film samples. (i)
  reflection geometry is used for these
  measurements as the substrates are generally too
  thick for transmission. (ii) high angular
  resolution is required because the peaks from
  semiconductor materials are sharp due to very low
  defect densities in the material. Multiple bounce
  crystal monochromators are used to provide a
  highly collimated x-ray beam for these
  measurements.
• Eg in the Philips MRD used in the x-ray
  facility, a 4-crystal monochromator made from Ge
  is used to produce an incident beam with less
  than 5 arc seconds of angular divergence.

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• Basic XRD measurements made on thin film samples
  include
• Precise lattice constants measurements derived
  from 2q - q scans, which provide information
  about lattice mismatch between the film and the
  substrate and therefore is indicative of strain
  stress
• Rocking curve measurements made by doing a q scan
  at a fixed 2q angle, the width of which is
  inversely proportionally to the dislocation
  density in the film and is therefore used as a
  gauge of the quality of the film.
• Superlattice measurements in multilayered
  heteroepitaxial structures, which manifest as
  satellite peaks surrounding the main diffraction
  peak from the film. Film thickness and quality
  can be deduced from the data.
• Glancing incidence x-ray reflectivity
  measurements, which can determine the thickness,
  roughness, and density of the film. This
  technique does not require crystalline film and
  works even with amorphous materials.
• Texture measurements-(discussed separately)

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• The graph shows the high resolution XRD data of
  the superlattice peaks on the GaN (002)
  reflections.
• Red line denotes results of computer simulation
  of the structure.

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5. Texture Measurement (Pole Figure)

• Texture measurements are used to determine the
  orientation distribution of crystalline grains in
  a polycrystalline sample. A material is termed
  textured if the grains are aligned in a preferred
  orientation along certain lattice planes. One can
  view the textured state of a material (typically
  in the form of thin films) as an intermediate
  state in between a completely randomly oriented
  polycrystalline powder and a completely oriented
  single crystal. The texture is usually introduced
  in the fabrication process (e.g. rolling of thin
  sheet metal, deposition,etc.) and affect the
  material properties by introducing structural
  anisotropy.

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• A texture measurement is also referred to as a
  pole figure as it is often plotted in polar
  coordinates consisting of the tilt and rotation
  angles with respect to a given crytallographic
  orientation. A pole figure is measured at a fixed
  scattering angle (constant d spacing) and
  consists of a series of f -scans (in- plane
  rotation around the center of the sample) at
  different tilt or Y -(azimuth) angles, as
  illustrated below.

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• The pole figure data are displayed as contour
  plots or elevation graphs with zero angle in the
  center. Below we show two pole figure plots using
  the same data set. An orientation distribution
  function (ODF) can be calculated using the pole
  figure data.

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6. Residual Stress Measurement

• Structural and residual stress in materials can
  be determined from precision lattice constants
  measurements. For polycrystalline samples high
  resolution powder diffraction measurements
  generally will provide adequate accuracy for
  stress evaluation. For textured (oriented) and
  single crystalline materials, 4-circle
  diffractometry is needed in which the sample is
  rotated so that measurements on multiple
  diffraction peaks can be carried out. The
  interpretation of stress measurement data is
  complicated and model dependent. Consult the
  reference literature for more details

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7. Small Angle X-ray Scattering (SAXS)

• SAXS measurements typically are concerned with
  scattering angles lt 1o. As dictated by Bragg's
  Law, the diffraction information about structures
  with large d-spacings lies in the region.
  Therefore the SAXS technique is commonly used for
  probing large length scale structures such as
  high molecular weight polymers, biological
  macromolecules (proteins, nucleic acids, etc.),
  and self-assembled superstructures (e.g.
  surfactant templated mesoporous materials).
• SAXS measurements are technically challenging
  because of the small angular separation of the
  direct beam (which is very intense) and the
  scattered beam. Large specimen-to-detector
  distances (0.5 m - 10 m) and high quality
  collimating optics are used to achieve good
  signal-to-noise ratio in the SAXS measurement.

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• The MRL x-ray facility has cutting edge
  capabilities for SAXS measurements with three
  custom-built SAXS instruments including one
  3.5-meter long ultra-small angle SAXS instrument
  with state-of-the-art optics and area detector
  for low scattering density samples (see
  instrumentation section for more details)

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8. X-ray Crystallography

• X-ray crystallography is a standard technique for
  solving crystal structures. Its basic theory was
  developed soon after x-rays were first discovered
  more than a century ago. However, over the years
  it has gone through continual development in data
  collection instrumentation and data reduction
  methods. In recent years, the advent of
  synchrotron radiation sources, area detector
  based data collection instruments, and high speed
  computers has dramatically enhanced the
  efficiency of crystallographic structural
  determination. Today x-ray crystallography is
  widely used in materials and biological research.
  Structures of very large biological machinery
  (e.g. protein and DNA complexes, virus particles)
  have been solved using this method.

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• In x-ray crystallography, integrated intensities
  of the diffraction peaks are used to reconstruct
  the electron density map within the unit cell in
  the crystal. To achieve high accuracy in the
  reconstruction, which is done by Fourier
  transforming the diffraction intensities with
  appropriate phase assignment, a high degree of
  completeness as well as redundancy in diffraction
  data is necessary, meaning that all possible
  reflections are measured multiple times to reduce
  systematic and statistical error. The most
  efficient way to do this is by using an area
  detector which can collect diffraction data in a
  large solid angle. The use of high intensity
  x-ray sources, such as synchrotron radiation, is
  an effective way to reduce data collection time.

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• One of the central difficulties in structural
  determination using x-ray crystallography is
  referred to as the "phase problem", which arises
  from the fact that the diffraction data contains
  information only on the amplitude but not the
  phase of the structure factor. Over the years
  many methods have been developed to deduce the
  phases for reflections, including computationally
  based direct methods, isomorphous replacement,
  and multi-wavelength anormalous diffraction (MAD)
  methods.

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X-ray crystallography
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Procedure

• The technique of single-crystal X-ray
  crystallography has three basic steps. The first
  and often most difficult step is to obtain an
  adequate crystal of the material under study. The
  crystal should be sufficiently large (typically
  larger than 100 micrometres in all dimensions),
  pure in composition and regular in structure,
  with no significant internal imperfections such
  as cracks or twinning. A small or irregular
  crystal will give fewer and less reliable data,
  from which it may be impossible to determine the
  atomic arrangement.

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• In the second step, the crystal is placed in an
  intense beam of X-rays, usually of a single
  wavelength (monochromatic X-rays), producing the
  regular pattern of reflections. As the crystal is
  gradually rotated, previous reflections disappear
  and new ones appear the intensity of every spot
  is recorded at every orientation of the crystal.
  Multiple data sets may have to be collected, with
  each set covering slightly more than half a full
  rotation of the crystal and typically containing
  tens of thousands of reflection intensities.

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• In the third step, these data are combined
  computationally with complementary chemical
  information to produce and refine a model of the
  arrangement of atoms within the crystal. The
  final, refined model of the atomic arrangement
  now called a crystal structure is usually
  stored in a public database.

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• A real 3-dimensional crystal contains many sets
  of planes. For diffraction, crystal must have the
  correct orientation with respect to the incoming
  beam.
• Perfect, infinite crystal and perfectly
  collimated beam diffraction condition must be
  satisfied exactly.''
• Strains, defects, finite size effects,
  instrumental resolution diffraction peaks are
  broadened.

More formally, the scattered intensity is
proportional to the square of the Fourier
transform of the charge density
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where   is the charge density.
For perfect crystals, I(q) consists of delta
functions (perfectly sharp scattering). For
imperfect crystals, the peaks are broadened. For
liquids and glasses, it is a continuous, slowly
varying function
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Features of Electron, X-ray, or Neutron
Diffraction

• For a known structure, pattern can be calculated
  exactly.
• Symmetry of the diffraction pattern given by
  symmetry of the lattice.
• Intensities of spots determined by basis of atoms
  at each lattice point.
• Sharpness and shape of spots determined by
  perfection of crystal.
• Liquids, glasses, and other disordered materials
  produce broad fuzzy rings instead of sharp spots.
  
• Defects and disorder in crystals also result in
  diffuse scattering.

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The Ultimate'' (Technically Challenging)
Experiment

• Sample is tiny (micron-sized).
• The effect is weak (light elements, small
  modulations, subtle modifications of the
  long-range order).
• Instrumental resolution (angle and energy) is
  perfect'' allowing detailed measure- ments of
  structural disorder.
• Measurement is time-resolved (nanosecond time
  scale).
• To achieve all of the above, will need lots of
  intensity in the primary beam together with
  sensitive detection systems.

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Powder vs. Single Crystal X-ray Diffraction

• SINGLE CRYSTAL
• Put a crystal in the beam, observe what
  reflections come out at what angles for what
  orientations of the crystal with what
  intensities.
• Advantages
• In principle you can learn everything there is to
  know about the structure.
• Disadvantages
• You may not have a single crystal. It is
  time-consuming and difficult to orient the
  crystal. If more than one phase is present, you
  will not necessarily realize that there is more
  than one set of reflections.

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• POWDER
• Samples consists of a collection of many small
  crystallites with random orientations. Average
  over crystal orientations and measure the
  scattered intensity as a function of outgoing
  angle.
• Disadvantage
• Inversion of the measured intensities to find the
  structure is more difficult and less reliable.
• Advantages
• It is usually much easier to prepare a powder
  sample. You are guaranteed to see all
  reflections. The best way to follow phase changes
  as a function of temperature, pressure, or some
  other variable.

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Overview of single-crystal X-ray diffraction

• The oldest and most precise method of X-ray
  crystallography is single-crystal X-ray
  diffraction, in which a beam of X-rays are
  reflected from evenly spaced planes of a single
  crystal, producing a diffraction pattern of spots
  called reflections.1 Each reflection
  corresponds to one set of evenly spaced planes
  within the crystal. The density of electrons
  within the crystal is determined from the
  position and brightness of the various
  reflections observed as the crystal is gradually
  rotated in the X-ray beam this density, together
  with supplementary data, allows the atomic
  positions to be inferred. For single crystals of
  sufficient purity and regularity, X-ray
  diffraction data can determine the mean chemical
  bond lengths and angles to within a few
  thousandths of an Ångström and to within a few
  tenths of a degree, respectively. The data also
  allow the static and dynamic disorder in the
  atomic positions to be estimated, which is
  usually less than a few tenths of an Ångström.

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Limitations

• As the crystal's repeating unit, its unit cell,
  becomes larger and more complex, the atomic-level
  picture provided by X-ray crystallography becomes
  less well-resolved (more "fuzzy") for a given
  number of observed reflections. Two limiting
  cases of X-ray crystallography are often
  discerned, "small-molecule" and "macromolecular"
  crystallography. Small-molecule crystallography
  typically involves crystals with fewer than 100
  atoms in their asymmetric unit such crystal
  structures are usually so well resolved that its
  atoms can be discerned as isolated "blobs" of
  electron density.
• By contrast, macromolecular crystallography often
  involves tens of thousands of atoms in the unit
  cell. Such crystal structures are generally less
  well-resolved (more "smeared out") the atoms and
  chemical bonds appear as tubes of electron
  density, rather than as isolated atoms. In
  general, small molecules are also easier to
  crystallize than macromolecules however, X-ray
  crystallography has proven possible even for
  viruses with hundreds of thousands of atoms.

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• The three-dimensional structure of penicillin,
  for which Dorothy Crowfoot Hodgkin was awarded
  the Nobel Prize in Chemistry in 1964. The green,
  white, red and blue spheres represent atoms of
  carbon, hydrogen, oxygen and nitrogen,
  respectively.

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The diffraction imaging layout at beamline 9.0.1
from left, coherent x-rays illuminate the sample
(center), which is mounted on a silicon nitride
window just 50 nanometers thick in a movable
frame

• Aerogels, sometimes called "frozen smoke, " can
  be made from different materials. This silicon
  aerogel is an efficient insulator.

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Published on 31st July 2008

• A 500-nanometer cube of aerogel from the interior
  of the 3-D volume, reconstructed by X-ray
  diffraction. The foam structure shows globular
  nodes that are interconnected by thin beam-like
  struts.