L17 Lattices, Vectors and Miller planes

Differences between single crystal and powder X-ray diffraction

Key Differences Between SCXRD and PXRD:

• Sample Type: SCXRD requires a single, pure, well-ordered crystal. PXRD utilizespolycrystalline powders, bulk solids, or thin films.

• Data Produced: SCXRD yields 3D atomic positions, bond lengths, and angles(absolute structure). PXRD produces a 1D "fingerprint" pattern of intensity vs. 2𝜃, primarily for phase identification.

• Information Obtained: SCXRD gives detailed molecular structure. PXRD provides information on phase (polymorph), crystallinity, and crystallite size.

• Time and Complexity: SCXRD is often time-intensive (hours to days) and highly dependent on growing high-quality crystals. PXRD is generally faster (minutes to hours) and user-friendly.

• Sensitivity: SCXRD is sensitive to the specific crystal chosen, which may not represent the bulk. PXRD is a bulk technique, reflecting the average structure of the entire sample.

What are crystals, lattices, motifs and unit cells

Lattice point placement conventions

the unit cell origin can be placed anywhere but convention states they should be put in a way that gives max rotational symmetry and the smallest number of lattice points if that does not distinguish.

What are the lattice parameters

How are lattice vectors written

Blue example lattice vector on right = [100]

Lattice symmetry elements

mirror planes and rotational symmetry in lattices

Allowed rotational symmetry orders

Rotary inversion symmetry

What is a centrosymmetric object

One that has a centre of inversion

Screw axes and glide planes

What does a 2₁ screw axis mean

What are crystal systems

Features of the 7 possible crystal systems

The 14 Bravais lattices

The 230 space groups

Miller indices and Miller planes

What letters do we use in a Miller index

How do you determine hkl for a Miller plane

What does the (111) Miller plane look like

What does this Miller plane look like

Indices of direction [UVW]

They are written as integers always

Lattice plane spacing formulas (on formula sheet)