The Determination of Molecular Structure by Diffraction Method

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The Determination of MolecularStructure by
Diffraction Method

• 93/2Advanced Inorganic Chemistryby HML, NCUE

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X-ray

• Optical microscopy - resolution restricted by
  Wavelength (l)
• Smaller l required for greater resolution
• For resolution at atomic level need l 10-10 m (1
  Å)
• X-rays discovered in 1895 (Roentgen)

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Electromagnetic Spectrum
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Sealed X-ray tube
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X-ray production
Collision with weakly-bound electrons slows
electron beam and produces x rays.
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Heat generation

• Only about 0.1 of the electrical energy input is
  converted to X-rays. The rest is dissipated as
  heat. A constant supply of cooling water is
  circulated through the X-ray tube to keep it from
  melting. (The x-ray machine is a very inefficient
  apparatus.)
• The accelerated electrons interact with the
  valence electrons of the target atoms but do not
  transfer sufficient energy to these outer-shell
  electrons to ionize them. The outer-shell
  electrons are simply raised to an excited, or
  higher, energy level. The outer-shell electrons
  immediately drop back to their normal energy
  state with the emission of infrared radiation.
  The constant excitation and re-stabilization of
  outer-shell electrons generates heat in the
  anodes of x-ray tubes.

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White radiation

• Bremsstrahlung (braking) continuous spectrum of
  X-ray
• X-rays are generated by the acceleration of
  electrons by an electric field towards a metal
  target.
• The collisions of the accelerated electrons with
  the nuclei of the target atoms give rise to white
  radiation. The kinetic energy of the accelerated
  electron is partially converted into
  electromagnetic energy.

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A graph of the l of the X-rays emitted against
their intensity for varying applied accelerating
voltages
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• The distribution of the radiation is similar to
  the Boltzman distribution. This is a function of
  the potential and has little to do with the
  target material
• A sharp cut-off at short wavelength. This minimum
  wavelength, lmin, corresponds to the maximum
  efficiency of conversion of the kinetic energy to
  electromagnetic radiation.

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lmin

• Emax h?max eV
• where h Plank's constant, ?max the largest
  frequency, e charge of an electron, V applied
  voltage. This maximum energy or minimum
  wavelength is called the Duane-Hunt limit.
• h?max hc/?min eV
• ?min hc / eV 12398 / V (volts)

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The intensity of the white radiation

• The highest intensity of emitted white radiation
  spectrum is obtained at a wavelength that is
  about 1.5 time lmin. The white radiation
  intensity curve may be fit to an expression of
  the form
• Iw A i Z Vn, n 2
• where i is the applied current, Z is the atomic
  number of the target, V is the applied voltage
  and A is a proportionality constant.

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Characteristic x-rays produced by photo-electric
absorption of tightly-bound electrons
K-shell electron ejected
L shell
K shell
L electron fills K shell
Characteristic X Ray
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Electronic energy levels of an atom of the anode

• Ka radiation
• L ? K
• (2s ? 1s) Ka1
• (2p ? 1s) Ka2
• Kb radiation
• M ? K

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Typical x-ray spectrum
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Characteristic radiation

• The Ka1 line is about twice as intense as the Ka2
  line. At low resolution (low scattering angle)
  the Ka wavelength is considered as a weighted
  average of the Ka1 and Ka2 lines with ?(Kaave)
  2(?(Ka1)) ?(Ka2)/3. The Ka line is about 5 -
  10 times as intense as the Kß line.
• The intensity of the Ka line can be approximately
  calculated by
• Ik B i (V - Vk)1.5
• where i applied current, Vk excitation
  potential of the target material, V applied
  voltage.
• The ratio Ik / Iw is a maximum if the
  accelerating voltage is chosen to be about 4
  times the excitation potential of the anode.

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Selected X-ray Wavelengths and Excitation
Potentials.
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Choice of radiation

• Ka lines highest intensity, used for standard
  X-ray diffraction
• Two metal targets are frequently used (Cu Ka ?
  1.5 Å and Mo Ka ? 0.7 Å).
• Copper radiation used for macromolecular
  structures of large unit cell and organic
  molecules. Diffracted beams are more separated on
  a detector if a longer wavelength is used.
  Organic molecules do not absorb strongly the Cu
  radiation. Mo radiation with small wavelength
  gives higher resolution data inaccessible to Cu
  radiation.
• Choice of radiation also depends on detector
  used. Films are better for Cu than Mo.
  Diffractometer counters have a very high counting
  efficiency with Mo radiation.

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Cu vs. Mo

• Copper radiation is preferred when the crystals
  are small or when the unit cells are large.
  Copper radiation (or softer) is required when the
  absolute configuration of a compound is needed
  and the compound only contains atoms with atomic
  numbers lt 10. A copper source is preferred for
  most types of powder diffraction.
• Molybdenum radiation is preferred for larger
  crystals of strongly absorbing materials and for
  very high resolution, sin (?) / ? lt 0.6 Å, data.

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Focal spot geometry
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Rotating anode X-ray generator

• Sealed-tube X-ray generators are inefficient in
  producing X-rays.
• The power is limited by the amount of heat that
  can be dissipated by water cooling.
• One way to increase the heat dissipating ability
  of the system, and thus increase the X-ray beam
  intensity, is to move or rotate the anode surface
  so that the beam of electrons continually hits a
  new region of the anode. These rotating-anode
  generators typically yield about 5 times the flux
  of X-rays as is routinely produced by sealed-tube
  generators with normal-focus X-ray tubes.
• Rotating anode protein
• Sealed X-ray tube small molecule

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X-ray absorption

• X-rays can be absorbed by solids
• The absorption of X rays follows Beer's Law
• I / Io exp(-µ t)
• where I transmitted intensity, Io incident
  intensity, t thickness of material, µ linear
  absorption coefficient of the material.

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A plot of m against l

• A smooth curve in this plot is followed by very
  sharp jumps. These discontinuities are called
  absorption edges and they occur at the wavelength
  corresponding to the energy needed to knock an
  electron out of an atomic orbital in the material
  that is doing the absorbing.

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K absorption edge

• the K absorption edge of an element lies very
  slightly to the short wavelength side of the K
  beta lines for that element.
• Like the characteristic lines, the absorption
  edge shifts to longer wavelength with decrease in
  atomic number.

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Filters

• If another substance can be found that has an
  absorption edge between the Ka and Kß lines of
  the incident photon beam, this other substance
  can be used to significantly reduce the intensity
  of the Kß line relative to the Ka line. The
  absorption edges of elements with ZFilter
  ZTarget - 1 (or - 2) meet this requirement.

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Monochromators

• To diffract the incident beam from a single
  crystal of known lattice dimensions.
• X-Ray photons of different wavelengths are
  diffracted from a given set of planes in a
  crystal at different scattering angles according
  to Bragg's Law.
• A narrow band of wavelengths can be chosen by
  selecting a particular scattering angle for the
  monochromatic crystal.
• Mostly used graphite(0002) face germanium,
  lithium fluoride crystals.

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Diffraction of light
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Wave interferences
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Braggs Law
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Braggs law

• Crystal is treated as planes (or layers) which is
  semi transparent to X-rays.

xy yz d sin q Thus, xyz 2d sin q But for
constructive interference to occur xyz
nl Therefore 2d sin q nl Braggs
Law Variation of 0.1 enough for complete
destructive interference.
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Instrument setup
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X-ray diffractometers
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Siemens Diffractometer (1995)
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Bruker Diffractometer (1999)
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Parts of the Instruments

• CCD detector
• X-ray generator
• N2cryostat
• Goniometer head
• Goniostat
• Video-microscope
• X-ray tube
• X-ray optics
• Computer

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CCD Detectors

• CCD stands for charge-coupled device
• Diffracted X-rays from sample strike a phosphor
• Fiber-optic cables route light to a specific
  pixel on CCD chip
• 1024 x 1024 pixels are active and binned 512 x
  512

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X-Ray Generators

• Generator power is set in KV and mA
• Operation at 40KV / 50 mA

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N2 Cryostats

• Siemens has a LT-2 cryostat 173 K min.
• Bruker has a Oxford Cryostream 600 series
  cryostat 80 K min.
• Both cryostats feed liquid nitrogen into the
  device and provide a stable temperature for data
  collection

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Goniometer head

• Goniometer heads have x and y adjustments at the
  base and z at top.
• The specimen is placed at a location known as
  thesphere of confusion
• Collimator to right
• Beam stop to left

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Goniostats

• The goniostat has three independent axes
• The Phi and Omega axes position the specimen
• The 2-Theta axis places the CCD detector at the
  position required for data collection

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Video-telescope

• The video-telescope allows us to position the
  specimen
• It also allows us to monitor phase transitions
  this sample undergoes a spin transition at 204
  where a deep purple color is observed

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X-Ray tube
Anode Mo target

• These X-ray tube have Mo targets.
• Monochromator selects 0.71073 Å
• Collimator provides 0.5 mm diameter beam at
  sphere of confusion
• Use of X-ray sources requires special training.

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Crystal centering
With silicon grease
glass capillary
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Computer
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Specimen Mounting
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Air-Sensitive Sample Mounting
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Low-Temperature Specimen Mounting
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Data Collection

• Standard sets of frames are collected most
  usually to cover a complete hemisphereto desired
  resolution

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Data Reduction

• Reflections from frames must be integrated with
  the SAINT program.
• The geometric polarization and Lorentz
  corrections are applied.
• An absorption correction is made with the SADABS
  program.
• The program SHELXL-XPREP is used to determine the
  space group and to create files for structure
  solution.
• SHELXL-XS provides complete structure solution
  with direct methods or a partial solution using
  the Patterson method.

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XP Structure Evaluation

• XP drawing of XS structure solution
• All non-hydrogen atoms are present along with a
  few false peaks
• Remove false peaks

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XP Retaining Real Atoms

• Sucrose has the formula C12H22O11
• Once the non-hydrogen atoms are properly placed,
  then these parameters are refined with
  least-squares.
• Hydrogen atoms are either placed geometrically
  or, if data is acceptable, located in difference
  Fourier map

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XP Thermal Ellipsoid Drawings

• One of the final things to do with a structure is
  to create the art work
• Thermal ellipsoid drawing as seen in XP

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XP Unit Cell Drawing