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Lesson 14
Finish Discussion of Symmetry and Reciprocal Space
Growing Crystals Collecting Data
Fourier Series
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
x=0 y=anything z=0 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 k=2n
In general
For a d dimensional screw axis If along c then 0,0,l l=dn (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 3
2).
If along a then h,0,0 h=dn For a 63 since the translation involves 3/6 or ½
the cell the presences are 2n not 6n
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 l=2n
For the n-glide the translation is along the diagonal moving to x=1/2+x, z=1/2+z so the presence is h,0,l h+l=2n
A point not in the plane does not undergo a simple translation so there is no general presences.
Centering
Centering is applied to every point. For c centering for every point x,y,z there is an
equivalent point a 1/2+x,1/2+y,z. The presence is hkl,h+k=2n For a centering k+l=2n For b centering h+l=2n For i centering h+k+l=2n For f centering a and b and c
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.
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.
The Energetics of Crystal Growth
For a process to occur spontaneously we know that ΔG must be negative
ΔG=ΔH-TΔS 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.
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 Π-Π interactions Van der Waals interactions
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
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.
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.
Look at some methods
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.
Polarizing Microscope
General Position
Interference Colors
A function of the thickness of the crystal and the difference in therefractive indices in the two directions.
As crystals get thicker these colors disappear.
The more light that comes through the better the crystal
Layered crystals will not be bright because of internal reflection betweenthe layers.
Extinction
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 polarizer—dichroism.
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 Remember—The quality of the final
structure depends almost entirely on the quality of the crystal studied!
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.
Goniometer Head
Magnetic Caps
Fiber is glued into copper tube.A magnet on the goniometer head holds the cap in placeCan easily and quickly be removed from diffractometer
Film Methods
Rotation Photograph
Weissenberg Photos
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
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.
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 anymore—in fact it is hard to find
good quality film.
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.
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.
