Fan Lecture 3

Question 1

What is Ewald’s sphere or sphere of reflections?

Answer 1

Used in crystallography to visualize and understand the diffraction of x-rays by crystal lattices
1) radius of the sphere is proportional to inverse of the wavelength of the incident x-rays
2) Represents all possible scattering vectors corresponding to different diffraction angles.
- it corresponds to a diffracted x-ray beam that contributed to the diffraction pattern
3) Diffraction pattern observed = all diffracted x-ray beams that intersect ewald’s sphere

Question 2

Calculate the cell dimensions of a unit cell in orthorhombic shape, given the distance between two reflections, x-ray, and the distance from crystal to detector.

Answer 2

nλ=2dsin(θ)
1/d(hkl) = (2/λ)sin(θ)
1/d100 = reciprocal lattice spacing along to (100) direction
1/d010 = reciprocal lattice spacing along the (010) direction
1/d001 = reciprocal lattice spacing along (001) direction
d100 = distance between adjacent crystallographic planes along the (100) direction
d010 = distance between adjacent crystallographic planes along the (010) direction
d001 = distance between adjacent crystallographic planes along the (001) distance

Question 3

Calculate number of reflections collected, given the information on the unit cell and x-ray.

Answer 3

N = 33.5 * volume of unit cell/(λ^3)
1) Crystal symmetry
2) Reciprocal Lattice
3) Bragg’s Law
4) Range of angles measured
5) Miller Indices
6) Number of unique reflections within experimental range
7) Multiplicity due to crystal symmetry

Question 4

How is the crystal structure determined?

Answer 4

1) Diffraction images to reciprocal space lattice to real space lattice to unit cell
2) determination of the distribution of atoms in the structure from the intensities of the diffraction spots