Diffraction methods- X rays Flashcards
What can be shown through diffraction methods
1) how atoms are arranged
2) how they bond with one
another.
3) bond distances
4) bond angles
5) understanding of structure and reactions
What is a lattice?
An infinite array of points in IDENTICAL environments.
Crystal structures use these lattice planes as a reference grid
points are called lattice points. A MOTIF is an atom/molecule that is associated with a lattice point
Translational symmetry
symmetry
An n-fold rotation axis of symmetry
is a line of rotation about which 2pie/n
produces the identical position
center of symmetry is the point when inversion occurs; opposites
mirror plane; positions are mirror images other the other side of plane
crystal structures
ordered 3D array of atoms by implication a lattice of electrons; lattice made up of unit cells.
Describe the unit cell
It has 6 parameters; 3 axial lengths A,B,C and3 interaxial angles alpha, beta, gamma.
Symmetry will decrease the number of independant parameters
It is parallelpiped with lattice points in every corner; it has six parallelogram faces
What is a primitive cell?
Single lattice point per cell at 0, 0 , 0
Name two types of primitive cells
1) primitive- when the particles are only at the corners of the unit cell. There is a Single lattice point per cell at 0, 0 , 0
2) centered- when particles present along other positions in addition to the corners.
What are the three types of centered unit cells
1) Body centered. There are 2 lattice points
2) Face centered. There is 4 lattice points
3) end centered- particles in the center of any two opposite faces
Name the seven crystal systems depending on their crystagraphic parameters
1) Triclinic
2) Monoclinic
3) Orthorhombic
4) Tetragonal
5) Trigonal
6) Hexagonal
7) Cubic
What are Bravis lattices?
14 different 3D lattices possible organised into 7 crystal structures
3 x cubic
2 x monoclinic
4 x orthorhombic
2 x tetragonal
How are there unique arrangements of crystals
There are 32 point groups; ways planes, rotations, symmetry, inversions in addition to bravais structures gives 230 unique structures.
Glide planes
A mirror plane and translation (sliding) combination
What is a space group?
represent a description of the symmetry of the crystal.
Used to identify a lattice type, through a capital letter, then point group symbols where rotation and reflection is followed by screw axis and glide planes
symmetry acts on x, y, z to give new coordinates for equivalent positions
ie, point group 1 and triclinic lattice = spacegroup P1
What is a screw axis?
A screw axis (helical axis or twist axis) is a line that is simultaneously the axis of rotation and the line along which translation of a body occurs.
What is a crystal ?
ordered3D lattice of atoms and molecules
Diamond- lattice of carbon covalent bonds
It can be closely packed CP (max contacts with 6 atoms) are not closely packed with only max 4 atoms in contact.
Can be hexagonal close packed (HCP) like Zinc (2 atoms per unit cell)
or Cubic close packed (CCP) like copper (4 atoms per unit cell; one in each face)
HOW DO YOU DESCRIBE A METAL STRUCTURE.
- Crystal system
- Lattice type
- Unit cell dimensions and angles
- Z, the atomic contents of the unit cell, i.e. number of formula units in the cell.
- Coordinates of atoms that comprise a lattice motif/structural unit.
Describe interstices
There are two types of interstitial sites in a lattice.
small space surrounded by 4 atoms: Tetrahedral, arrangement; 4 - coordinate tetrahedral interstitial site. eg, Zn blende
cavities are surrounded by 6 atoms in octahedral geometry. This is a 6 - coordinate octahedral interstitial site. eg, NaCl rock salt ionic solid
Anions are, in general bigger than cations and often convenient to consider ionic solids as close packed anions with cations occupying Oh, or T-interstices
What is miller indices? h,k,l
The parallel plane are defined by the miller indices with reference to a particular unit cell
where h = a (of the x axis) length
k = b ( of the y axis) and l= c (of the z axis)
What is d spacing?
The interplanar space; distance inbetween planes.
This is determined by miller indices
How are X rays made?
about the size of
small wavelength 0.1-100 Angstroms, and high frequency 10+18 electromagnetic radiation consisting of PHOTONS (quantums of electromagnetic radiation)
They are made by bombarding a METAL target with electrons (using voltage)
i) white radiation; electrons hit metal, slow down, lose energy, energy lost becomes heat or spectrum of wavelengths.
ii) X rays; bombarding electrons ionize electrons on target and create vacancies in the inner orbitals, outer electrons drop down levels o fill vacancies and so release energy.
higher energy transitions, decreased wavelength.
It is important to have a monochromatic beam, X-rays with a
single and known wavelength to characterise diffraction
How are X rays made 2
Synchrotron radiation; where electrons are accelerated to the speed of light in a magnetic field (particle accelerators) . This causes electrons to emit heat when they are slowed down, and a continuous spectrum of X rays radiation of very high magnitude intensity.
What is diffraction
waves are superimposed it causes constructive and destructive interference
X RAYS have wavelengths that will diffract in atoms in crystals; ie carbon to carbon bonds
Resultant X ray scattering by the lattice is down to the interaction between electric beam and the atom’s electrons.
What is Braggs Law?
some of the incident X-rays are reflected from the plane with an angle of reflection that equals the angle of incidence whilst some are transmitted through the plane and reflected by subsequent planes; planes can be TRANSPARENT OR MIRRORS.
If incidence angle is the same as brags angle, reflected beams are IN PHASE and show constructive interference.
If different from Brags angle, the beams are reflected OUT OF PHASE and so cancel out
How is the problem of increasing scattering angles solved?
Intensities vary/decrease if scattering angle increases away from Braggs angle.
Crystal is rotated so many planes are brought into the correct position to obey braggs law and Intensity(hkl) is detected.
What is a point group?
how many degrees the crystal should be rotated in order to measure complete diffraction data.
i) Point group 2 is monoclinic (circle in half at 180)
ii) Point group 4 is tetragonal (segments of 90 degrees)
iii) point group 6 is hexagonal (circle in 6 segments at 60 degrees)
What is the resolution
interplanar d spacing and scattering angle.
Higher resolution; higher scattering angle, smaller d spacing; more detail shown! Therefore smaller crystals with less space between planes show better resolution (1 A)
Describe free electron scattering
X-rays hit an electron they induce an oscillation in the same direction of the electric
vector of the incident beam. (vertical to it) If the electron is “free” then the scattering is wavelength-independent
Thomson scattering: the production of scattered
radiation with the same wavelength as the incident beam – which gives rise to the interference
effects in diffraction.
What is the scattering factor (units= e.u)
The amplitude of X rays scattered by an atom’s electrons any direction.
Scattered amplitude is reduced by interference at higher scattering angles
What is the structure factor?
The amplitude of X rays scattered by one unit cell in the scattering factors direction.
It is the RESULTANT TOTAL AMPLITUDE of all the atoms scatter factors together
The intensity of reflection is proportional to the square of the structure factors
Describe Systematic absences
This links lattice planes and intensity.
Each unit cell has unique scatter pattern; the body center scatters X rays that are 180 degrees out of phase and so there is complete cancellation and no intensity reflected.
Therefore the structure causes no intensity
What is argand diagram and complex representation?
Vector representation of a wave
Complex representation has 2 orthogonal vector components in one equation.
This combines amplitude with phase.
Used in the structure factor
What does the electron density equation show?
This is a map of electron distribution (as contours) in the crystal and so maps the atomic distributions.
What is the problem with crystallography? What is the phase problem.
X rays cannot be focussed.
Phase cannot be measured (only intensity or amplitude measured)
To achieve electron density map, amplitude is combined with phase using vectors
Describe the Heavy atom method.
If an structure contains heavier atoms (with more electrons than other atoms) like S with Cl, its position can help calculate the phase and then electron density, as this atom has a greater influence on the phase.
i) introduce heavy atom
ii) find its coordinates
iii) generate the first phases
iv) generate an electron density map combining phases with amplitudes
v) interpret the map to identify other atoms
What is the patterson function
The Patterson function is used to solve the phase problem
Patterson function gives us a map of the vectors between atoms.
In other words, if there is a peak of electron density for atom 1 at position x1 and a peak of electron density for atom 2 at position x2, then the Patterson map will have peaks at positions given by x2-x1 and x1-x2.
The height of the peak in the Patterson map depends on the number of electrons in the atoms between which the vector occurs and is proportional to their atomic numbers (Z).
peak proportional to the product of the heights of the two peaks in the electron density map.
This shows an INTENSITY difference between heavy atoms and light atoms; their vector height is square of their atomic number
No phase required to find x,y,z
some modifications into the electron density function, so that the structure factors, represented by their amplitudes, [F(hkl)] and phases Φ(hkl), are replaced by the squared amplitudes whose values are proportional to the diffracted intensities (Formula 3 below). With these modifications, the Patterson function can be directly calculated from the experimental data obtained in the diffraction experiment.
Describe different types of patterson vectors
1) vectors in the same unit in a lattice = CROSS VECTORS
2) between symmetry-related = HARKER VECTORS. These provide the key to finding heavy atom positions
3) Self vectors; vectors between atoms in a molecule
patterson function 2
The information provided by the maxima of the Patterson Function corresponds to a map of position vectors (relative positions) between each pair of atoms in the structure. The value of the function at these maxima is proportional to the product of the implied atomic numbers, which provides a clear advantage for detecting vectors between “heavy” atoms, ie atoms with a large number of electrons.
If the crystal space (where the atoms are) is defined by the value of the ρ function at every point in the unit cell given by the coordinates x, y, z, the Patterson space (also periodic and defined by a unit cell identical to the crystal unit cell) is defined by generic coordinates u, v, w, in such a way that any pair of atoms in the crystal, located at (x1, y1, z1) and (x2, y2, z2), will be shown in the Patterson map by a maximum with coordinates:
u = x1 - x2 ; v= y1 - y2 ; w = z1 - z2
Analysing patterson function
The height of the peaks is proportional to the product of atomic numbers of the atoms involved:
Co atomic number x Oxygen atomic number = expected heights of vectors on map
The largest vector should dominate, its location found, put into density map, chimera structures, crystal packing of whole compound in lattice shape found.
What is MIR?
Multiple – need more than one derivative to break the phase ambiguity (as some fail to react with protein)
Isomorphous – absolute requirement If FP varies then
cannot use it.
Replacement – heavy atoms replace light atoms, eg water
- Getting a pure sample
- Getting crystals
- Measuring data
- Finding heavy-atom derivatives or an anomalous scatterer
- Identifying positions in the unit cell
- Obtaining approximate phases for the data
What is the Fourier transform?
A series of cosine and sine terms with the appropriate coefficients that are multiples of x is called a Fourier series.
The electron density is the Fourier transform of the structure factors.
