Diapositiva 1

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Prima Scuola Nazionale di Metodologie
Chimico-Fisiche per lo studio dei Sistemi
Biologici Martina Franca 5-9 Settembre 2005
Larea cristallografica e i suoi metodi
by Carmelo Giacovazzo CNR Istituto di
Cristallografia Bari
E-mail carmelo.giacovazzo_at_ic.cnr.it
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About Crystallography

• Crystallography is usually associated to ordered
  systems ( crystals ).
• Crystals are nothing else but the
  three-dimensional repetition of a motive (the
  content of the the unit cell)
• The tool of the crystallographic investigation is
  the diffraction.

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When neutrons or X-Rays are used diffraction
intensities are collected When electron radiation
is used the phase is not lost
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The phase is lost
The phase is not lost
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• Atomic scattering factors for
• Electrons( they see the electric field)
• X-Rays ( they see the electrons)
• Neutrons ( they see the nuclei)

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MODERN CRYSTALLOGRAPHY The application
field from ordered systems (crystals)
to polymers, fibres, etc
to amorphous materials (solid, liquid, gas)
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CRYSTAL STRUCTURE SOLUTION

• In the practice
• where
• and
• It depends on the interatomic coordinates

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About the basic tools

• The information one can use to solve a crystal
  structure is
• A) the positivity of the electron density
• B) the atomicity
• The phase problem is practically solved for
  structures up to 200 atoms in the asymmetric
  unit.
• The phase problem is still open for the proteins

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About the experimental information

• The experimental information is contained in the
  data.
• As a rule of thumb, data up to 1Å resolution are
  full informative.
• For proteins this resolution is only seldom
  attained . Therefore supplementary data are
  necessary , which are provided by the following
  techniques
• A) isomorphous derivatives
• B) anomalous dispersion
• C) molecular replacement

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Diffuse
scattering

• 
  It is due to
• Inelastic scattering generated by electronic
  excitations
• thermal diffuse scattering related to atomic
  motion (TDS)
• scattering from disorder and/or from crystal
  defects (DDS)

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Experimental and calculated difraction pattern
from tRNA crystals
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Experimental and calculated diffraction patterns
from crystals of Calmodulin
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Modulated crystal
structures

• They are perfect crystals with periodic
  distorsion from some basic structure.
• The modulated atomic parameters may be one or
  several of the following
• Coordinates (displacive modulation)
• b) Occupancy factors on displacement parameters
  (density modulation)
• c) Orientation of the magnetic moments ( magnetic
  structure)
• d) Two or more intergrown periodic structures
  with mutually incommensurated lattices (
  composite structures).

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Experimental evidence satellite
reflections, main reflections
One-dimensional modulated structure Sketch of a
section of the three-dimensional Diffraction
pattern, showing main and satellite reflections
From S4 to S3. Main and satellite reflections
are denoted by M and W respectively
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Quasicrystals
Diffraction pattern of a decagonal Al-Co-Ni
quasicrystal. Computer reconstruction of the
second layer from 720 images
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X-Ray Laue photograph of an icosahedral Al-Mn-Pd
quasicrystal with fivefold symmetry
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The mathematical basis
of quasi crystals
1) f(x1,x2) A1sin2?x1 A2sin2?x2
Let us assume x2 ?x1 where ? is an irrational
number, then
f(x1) A1sin2?x1 A2sin2??x1
is not periodic.
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where
is the golden mean. Since a and a?/2 are
incommensurate numbers the structure is not
periodic.
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The aperiodic long-range ordered structure and
its periodic approximants
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Powder diffraction If single crystals
of sufficient size are not available ,
then Powders may be used for diffraction. Three-d
imensional data Collapse in a one-dimensional
Pattern. Intensities overlap. X-Ray and
neutron radiations are frequently used.
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Via powder diffraction data

• Crystallinity degree
• Qualitative analysis
• Quantitative analysis
• Residual stress

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Liquid crystals
They constitute an intermediate state between
liquid and crystals

• uniaxial nematic system made up by
• rod-like molecules
• b) its typical diffraction pattern

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Typical cholesteric mesophase organisation
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• Arrangements of a simple
• lipid-water system
• lamellar L
• rectangular P

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Fiber diffraction
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CRYSTALLOGRAPHY
AND LIQUIDS The distribution function P(u) for a
linear arrangement of objects of length a and of
increasing compactness, according to Zernicke
Prins. The ratio between a and the length l
varies from 0.5 to 0.90.
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Liquid Mercury Distribution p(u)
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Liquid nitrogen at 89K. Average number of atoms
at a distance x for a given atom.
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Crystallography and Material Science Defects in
crystal may be studied the kinematic
approximation in no more sufficient. Dynamical
theory of diffraction is necessary
X-Ray section topograph of a dislocations in
silicon
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X-Ray topograph of quartz showing A great number
of dislocations
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Crystal structure determination via HREM and
Crystallographic Image Processing

• The crystal structure may be determined by back
  Fourier transforming the image and/or by using
  electron diffraction data
• STEPS
• Crystal Symmetry
• Elimination of the noise due to lattice
  averaging
• Correction for defocusing and astigmatism
• Compensation for the crystal tilt
• 3D crystal structure determination

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Data perturbation

• Dynamical scattering
• Secondary scattering
• Crystal bending (causing incoherence of the
  diffracted beam)
• Radiation damage

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Electron diffraction Pattern from Gas . Working
temperature about 353 K
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Gas electron diffraction for C6H5-NO2 gas
Molecular intensity curves E, experimental T,
theoretical Two camera distances
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Radial distribution curves For C6H5-NO2 E,
experimental T, theoretical