crystallography

Question 1

absorption correction

Answer 1

• 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

Question 2

anomolous dispersion

Answer 2

• 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.

Question 3

absorption edge

Answer 3

• X-ray energy that is strongly absorbed by an atom in crystal
• creates sharp increase in absorbance

Question 4

asymmetric unit

Answer 4

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

Question 5

Atomic Displacement/thermal displacement Parameters

Answer 5

define the thermal vibrations/deviation of atoms. i.e. parameters of ellipsoid

Question 6

Body centered unit cell

Answer 6

A unit cell having a lattice point at its center as well as at each corner

Question 7

Bravais Lattice

Answer 7

three-dimensional array of points with the surroundings of each point being identical

Question 8

Crystal System

Answer 8

cubic, tetragonal, orthorhombic, rhombohedral, hexagonal, monoclinic, triclinic

Question 9

point group

Answer 9

set of symmetry operations

Question 10

data reduction

Answer 10

Conversion of measured intensities over pixels to structure factors

Question 11

direct method

Answer 11

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

Question 12

disorder

Answer 12

when atoms in the unit cell exist in more than one position

Question 13

Friedel’s Law

Answer 13

The structure factor of reciprocal reflections (h,k,l and -h,-k,-l) have the same intensity but opposite phase

Question 14

miller indices

Answer 14

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.

Question 15

Fourier Analysis

Answer 15

Decomposing a periodic function into it’s component cos and sin functions

Question 16

phase problem

Answer 16

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

Question 17

Method of Least Squares

Answer 17

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

Question 18

R factor

Answer 18

• 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.

Question 19

resolution

Answer 19

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

Question 20

Space Group

Answer 20

• 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

Question 21

Structure Factor, F

Answer 21

• 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.

Question 22

Flack Parameter

Answer 22

measure of absolute configuration.

• 0 suggests model is correct configuration
• 1 suggests inverse

Question 23

wR2

Answer 23

r factor calculated on the weighted squares of the structure factors (which are what’s used for refinement). Always larger than R1

Question 24

Goodness of Fit

Answer 24

Measure of agreement between model and observations related to standard deviation of atom positions (i.e. how reliable). Should be close to 1.

Question 25

I/sigma(I)

Answer 25

the average Signal to noise.

- Should be above 5 at highest resolution

Question 26

Completeness

Answer 26

• percent of total unique reflections collected.

- Each reflection affects every atom and so missing reflections can have significant effect.

Question 27

Rint

Answer 27

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)

Question 28

SQUEEZE

Answer 28

• 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)

Question 29

Systematic Absences

Answer 29

• extinction of a reflection due to the symmetry of the unit cell.
• Directly relate to symmetry elements

Question 30

polymorphism

Answer 30

crystals of the same compound with different unit cells

Question 31

isomorph

Answer 31

different compounds with the same unit cell

Question 32

unit cell

Answer 32

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.

Question 33

Z

Answer 33

number of “formula units” in the unit cell

Question 34

Z’

Answer 34

number of molecules in the asymmetric unit.

Question 35

Geometric Index

Answer 35

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

Question 36

Cubic

Answer 36

a = b = c, α = β = γ = 90

Question 37

Tetragonal

Answer 37

a = b ≠ c, α = β = γ = 90

Question 38

Orthorhombic

Answer 38

a ≠ b ≠ c, α = β = γ = 90

Question 39

rhombohedral

Answer 39

a = b = c, α = β = γ ≠ 90

Question 40

hexagonal

Answer 40

a = b ≠ c, α = β = 90, γ = 120

Question 41

monoclinic

Answer 41

a ≠ b ≠ c, α = γ = 90, β ≠ 90

Question 42

triclinic

Answer 42

a ≠ b ≠ c, α ≠ β ≠ γ