Fan Lecture 2

Question 1

What is an unit cell?

Answer 1

basic repeating structural unit of a crystal lattice in crystallography
- can be repeated infinitely in all directions to form a crystalline solid

Question 2

What is an asymmetric unit cell?

Answer 2

Smaller portion of the crystal lattice that when repeated and combined with symmetry operations, generates the full crystal structure
- contains only part of the atoms or molecules present in the crystal

Question 3

What is a lattice?

Answer 3

it’s the ordered arrangement of points or building blocks in a crystal structure. It represents the spatial arrangement of repeating units in a crystalline material, forming a 3D framework.

Question 4

What is a real space lattice? What is reciprocal space?

Answer 4

Real space: spatial arrangement of atoms, ions, or molecules in a crystal structure, the 3D framework formed by the repetitive arrangement of structural units, defining the crystal’s shape and atomic arrangement
Reciprocal space: mathematical dual space to real space lattice where the positions of atoms in real space correspond to frequencies or wavelengths in reciprocal space

Question 5

What’s the relationship between the real space and reciprocal space?

Answer 5

Fourier transforms relate the spatial arrangement of atoms or molecules in real space to the spatial frequencies or wavelengths in reciprocal space.
Any change in one space affects the other space inversely.

Question 6

What is Bragg’s Law?

Answer 6

1) describes the condition under which x-rays scattered by different atomic planes in a crystal lattice interfere constructively, resulting in a strong diffraction peak
- when the path difference between the scattered waves from adjacent atomic planes is equal to an integer multiple of the x-ray wavelength, the waves reinforce each other.
2) By measuring angle of incidence and observing the diffraction pattern, we can determine spacing between crystal lattice planes and infer about atomic positions, bond lengths, and symmetry.
3) Used in x-ray diffraction techniques to determine structures of materials ranging from minerals and metals to macromolecules
4) assumes that crystal lattice is perfectly ordered and that the incident x-rays are monochromatic and coherent

Question 7

Explain the Bragg’s Law equation.

Answer 7

nλ=2dsin(θ)

Where:
n is an integer representing the order of the diffraction peak (e.g.,
n=1 for the first-order peak, n=2 for the second-order peak, and so on).
- λ is the wavelength of the incident X-rays. - d is the spacing between adjacent planes of atoms in the crystal lattice.
- θ is the angle between the incident X-rays and the crystal lattice planes.

Question 8

What is Miller Index?

Answer 8

They are used to describe the orientation of crystallographic planes and directions within a crystal lattice. They provide a concise and systematic way to communicate the orientation of specific planes and directions within a crystal lattice.
Planes: represented as (hkl) where hkl are reciprocals of the intercepts of the plane with the axes
Directions: [uvw] where uvw are reciprocals of the direction vector’s components along the crystallographic axes

Question 9

Know how to draw the hkl planes in unit cells.

Answer 9

1) Determine hkl and extend the plane indefinitely in all directions
2) Mark the intercepts on the respective axes of the unit cell
3) Connect the marked intercepts on the axes to form the boundaries of the plane within the unit cell.
4) Extend to continue the lattice
5) Label the plane with the corresponding hkl