lesson 14 finish discussion of symmetry and reciprocal space growing crystals collecting data

Lesson 14

Finish Discussion of Symmetry and Reciprocal Space

Growing Crystals Collecting Data

Fourier Series

http://www.youtube.com/watch?v=y6crWlxKB_E

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.