Finish Discussion of Symmetry and Reciprocal Space

1
Lesson 14

• Finish Discussion of Symmetry and Reciprocal
  Space
• Growing Crystals
• Collecting Data

2
Fourier Series
3
http//www.youtube.com/watch?vy6crWlxKB_E
4
Apply to screw axis

• If a point is exactly on the screw axis then it
  will only be translated since the rotation will
  not move it at all
• For P21/c the rotation is along b so a point at
  x0 yanything z0 is on the screw axis (remember
  we do not need to consider the offset)?
• Thus in reciprocal space for 0,k,0 the point only
  has ½ cell translation resulting in the presence
  0,k,0 k2n

5
In general

• For a d dimensional screw axis
• If along c then 0,0,l ldn (i.e. For a 3 fold 3n
  Since the handedness of the 3 fold does not
  survive the Fourier transform this is also true
  for 32).
• If along a then h,0,0 hdn
• For a 63 since the translation involves 3/6 or ½
  the cell the presences are 2n not 6n

6
For a Glide Plane

• If the point sits in the plane of the mirror then
  it only undergoes translation.
• For the c-glide in P21/c the mirror is x,0,z
  (ignoring the offset) and the translation is
  along c resulting in h,0,l l2n
• For the n-glide the translation is along the
  diagonal moving to x1/2x, z1/2z so the
  presence is h,0,l hl2n
• A point not in the plane does not undergo a
  simple translation so there is no general
  presences.

7
Centering

• Centering is applied to every point.
• For c centering for every point x,y,z there is an
  equivalent point a 1/2x,1/2y,z.
• The presence is hkl,hk2n
• For a centering kl2n
• For b centering hl2n
• For i centering hkl2n
• For f centering a and b and c

8
Use Systematic Absences

• By using the systematic absences we can assign
  the possible space groups.
• Frequently more than one possible space group is
  possible.
• Use table 3.1.4 in volume A of the International
  Tables for Crystallography
• Look at space groups.

9
Program XPREP

• This is the program for working with completed
  data
• It will check for centering
• It will look at equivalent reflections to
  determine a Laue Group
• It will look at systematic absences to determine
  possible space groups
• It will transform the space group into the
  standard setting.

10
The Energetics of Crystal Growth

• For a process to occur spontaneously we know that
  ?G must be negative
• ?G?H-T?S where G is the Gibb's Free Energy H
  is the energy difference between the initial and
  final states and S is the entropy
• Since crystals are very ordered forming a crystal
  always results in a negative change in the
  entropy!
• Therefore the energy of the crystal must be lower
  than that of the system it is grown from.

11
Sources for Energy

• Ionic Interactions
• Dipole-dipole interactions
• If a molecule has a dipole than one end is and
  the other -
• Results in a head to tail interaction or
  inversion center
• Hydrogen bonding
• ?-? interactions
• Van der Waals interactions

12
Relations between cell constants and crystal
faces.

• Many, though not all crystals, crystallize on
  primary faces (1,0,0) (0,1,0) (0,0,1)?
• In general the shorter the axis the stronger the
  interaction along it. Therefore it pays to have
  as many short axis repeats in the crystal
• Therefore a crystal with one short and two long
  axes will grow as needles.
• Crystals with two short and one long one will
  grow as plates.
• Changing crystallization conditions will not
  alter this

13
What is Crystallization

• Crystallization is the process of trying to
  arrange a collection of molecules or ions to
  maximize the attractive forces and minimize the
  repulsive ones.
• This is best accomplished at equilibrium where
  the crystal components are free to enter and
  leave the lattice.
• This means it must be done slowly.

14
Crystallization involving solvents

• Choose a solvent in which the compound is
  moderately soluble. If it is too soluble the
  crystallization will occur rapidly as the last
  bit of solvent evaporates.
• If possible try to avoid solvents that hydrogen
  bond. The less stable the solution the bigger
  the difference in energy between the solution and
  the crystal.
• Avoid low boiling solvents especially diethyl
  ether.

15
Look at some methods
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Selecting Crystals

• Crystals should have well defined faces.
• They should have smooth faces without
  imperfections.
• Should not be larger than 0.5mm in the long
  direction
• If light goes through them they should be
  examined under a polarizing microscope.
• Obviously must make accommodations for the real
  world.

17
Polarizing Microscope
18
General Position
19
Interference Colors
20
Extinction
21
Some Comments on Extinction

• Cubic crystals are isotropic and hence always
  dark!
• Hexagonal, trigonal and tetragonal crystal have
  an isotropic axis (c). When looked at down that
  axis the crystals will always be dark
• In triclinic and most faces in monoclinic
  crystals the extinction directions may be a
  function of wavelength. Instead of going black
  the will get dark blue then go dark red or vice
  versa. This is ok
• Some crystals change colors under one
  polarizerdichroism.

22
Selecting a Crystal

• It is worth spending some time with the
  microscope to get the best crystal.
• Make sure the crystal is representative of the
  batch.
• Size is not as important as quality
• RememberThe quality of the final structure
  depends almost entirely on the quality of the
  crystal studied!

23
Crystal Mounting

• Crystals are typically mounted on a glass or
  quartz fiber (at Purdue I use quartz). Since
  these materials are not crystalline they do not
  diffract but they can scatter the beam.
• Crystals can be glued to the fiber with epoxy,
  super glue, or thermal glue for room temperature
  work.
• For low temperature work grease (Apeazon H) can
  be used.

24
Goniometer Head
25
Magnetic Caps
26
Film Methods
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Rotation Photograph
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Weissenberg Photos
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(No Transcript)
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Problems

• Must align about a real axis
• Alignment is fairly fast.
• Exposure takes days.
• Picture is hard to read.
• Film is curved so Polaroid cannot be used

31
How to get data?

• Must determine the intensity of the spots.
• To do this must compare the intensities to some
  scale.
• To expand the cell the camera holds six films.
  The front one is used for weak reflections while
  the last one is used for strong reflections
• The six films are scaled by common spots.
• How do you determine standard uncertainty?
• Very tedious and inexact.

32
Using Film

• Very low background can take very long exposures
• Fairly sensitive to radiation
• Covers a wide area.
• Obviously slow to expose and very tedious to
  measure the intensities off of.
• No one uses anymorein fact it is hard to find
  good quality film.

33
Next Time

• Diffractometers and area detectors
• Tour the lab and look at the equipment.
• Start to look at how the instruments are used at
  Purdue.

34
Homework

• Go to http//www.nonius.nl/manuals/index.html
• Read the KappCCD Users Manual
• Read the Collect Users Manual
• Read the Technical Users Manual
• You can skip parts dealing with installation,
  troubleshooting, maintenance, etc.