crystallography Flashcards
absorption correction
- A factor to correct for the reduction in X-ray intensity due to absorption by the crystal, i.e. ratio of intensities entering and leaving.
- Dependent on the atomic composition.
- applied during data reduction
anomolous dispersion
- change in reflection phase due to strong X-ray absorbance.
- Stronger with heavier atoms
- violates Friedel’s Law.
- The difference in intensity for Friedel pairs affected by anomolous dispersion is used to solve absolute configuration and the phase problem.
absorption edge
- X-ray energy that is strongly absorbed by an atom in crystal
- creates sharp increase in absorbance
asymmetric unit
The asymmetric unit of a space group is that part of the crystallographic unit cell which can be used to generate the complete unit cell
Atomic Displacement/thermal displacement Parameters
define the thermal vibrations/deviation of atoms. i.e. parameters of ellipsoid
Body centered unit cell
A unit cell having a lattice point at its center as well as at each corner
Bravais Lattice
three-dimensional array of points with the surroundings of each point being identical
Crystal System
cubic, tetragonal, orthorhombic, rhombohedral, hexagonal, monoclinic, triclinic
point group
set of symmetry operations
data reduction
Conversion of measured intensities over pixels to structure factors
direct method
Derives the relative phases of reflections by assigning the strongest reflections based on the assumption that the structure is composed of atoms with non-negative electron density
disorder
when atoms in the unit cell exist in more than one position
Friedel’s Law
The structure factor of reciprocal reflections (h,k,l and -h,-k,-l) have the same intensity but opposite phase
miller indices
A set of 3 integeres (hkl) that identify a lattice plane/relection order from that plane.
- The plane intercepts the unit cell axes at a/h, b/k, c/l.
- Determined from the Bragg equation.
Fourier Analysis
Decomposing a periodic function into it’s component cos and sin functions
phase problem
The problem of determining the phase angle (relative to origin) for each reflection in order to calculate the electron density map. i.e. calculating the phases rather than measuring them introduces approximation
Method of Least Squares
Minimizing the sum squared error of the model to the experimetal values. In crystallography the structure factor is fitted by sum squares. Requires at least 10 measurements for each parameter
R factor
- Measure of the disagreement between the observed data and that predicted by the model.
- Proportional to the sums of the difference in the observed and calculated structure factors divided by the observed.
resolution
The distance at which two points/features can be distinguished.
- In crystallography is the minimum distance between structural features that can be distinguished related to the distance between lattice planes (i.e. high angle small distance high resolution) though intensity decreases at higher angles.
- Limit for X-ray wavelength defined by Braggs Law
Space Group
- a group of symmetry operations with an infinitely extending, repeating pattern.
- There are 230 groups
- identified by systematic abscences in diffraction pattern.
- Formed by combining the point groups and bravais lattices
Structure Factor, F
- complex number that embodies the amplitude and phase of a reflection.
- Approximately equal to the squared intensity of the reflection.
- It’s inverse fourier transform is the electron density of the unit cell.
Flack Parameter
measure of absolute configuration.
- 0 suggests model is correct configuration
- 1 suggests inverse
wR2
r factor calculated on the weighted squares of the structure factors (which are what’s used for refinement). Always larger than R1
Goodness of Fit
Measure of agreement between model and observations related to standard deviation of atom positions (i.e. how reliable). Should be close to 1.
I/sigma(I)
the average Signal to noise.
- Should be above 5 at highest resolution
Completeness
- percent of total unique reflections collected.
- Each reflection affects every atom and so missing reflections can have significant effect.
Rint
measure of the agreement in intensity of what should be equivalent reflections for that space group. Lower is better. Used to choose space group (i.e. highest symmetry with lowest Rint)
SQUEEZE
- Removes unassigned electron density at a specific distance from the assigned structure
- Prevents atoms being distorted due to attempting to encompass unassigned electrons nearby
- Often due to solvent which is often heavily disorder and thus unable to be effectively modelled (though should be if can be)
Systematic Absences
- extinction of a reflection due to the symmetry of the unit cell.
- Directly relate to symmetry elements
polymorphism
crystals of the same compound with different unit cells
isomorph
different compounds with the same unit cell
unit cell
the smallest group of atoms which has the overall symmetry of the crystal, and from which the entire lattice can be built up by repetition in three dimensions.
Z
number of “formula units” in the unit cell
Z’
number of molecules in the asymmetric unit.
Geometric Index
measure of the distortion between two geometries of same coordination number.
- T5 is for 5-coordinate complexes, 0 = square pyramidal, 1 = trigonal bipyramidal
- T4/T4’ is for 4-coordinate, 0/0 = square planar, 1/1 = tetrahedral, inbetween = see saw
Cubic
a = b = c, α = β = γ = 90
Tetragonal
a = b ≠ c, α = β = γ = 90
Orthorhombic
a ≠ b ≠ c, α = β = γ = 90
rhombohedral
a = b = c, α = β = γ ≠ 90
hexagonal
a = b ≠ c, α = β = 90, γ = 120
monoclinic
a ≠ b ≠ c, α = γ = 90, β ≠ 90
triclinic
a ≠ b ≠ c, α ≠ β ≠ γ
