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.