L-2 Structure of Crystalline Solids

Dependency of Physical Properties

Physical properties depend of atomic arrangement as well as the bonding forces between atoms, ion, molecules.

Crystalline Solid

A solid where the atoms/ions are arranged in a

3-D repeating pattern

(Metals, Alloys, Ceramics)

Unit Cell

Small groups of atoms that form a repetitive pattern within a crystalline solid

Lattice Parameter

Describes the size and shape of a unit cell

(Side lengths & angles)

Coordinate Number

The number of atoms touching one “central” atom. Higher coordinate number = higher density

Atomic Packing Factor (APF)

The fraction of space occupied by atoms, assuming atoms are hard spheres.

Efficiency of the packing of atoms

Higher APF = Higher Density

Metallic Crystal Structures (FCC)

• Face centered cubic

• 4 total atoms, ½ in each face, 1/8 in each corner

• APF = 0.74

• CN = 12

Metallic Crystal Structure (BCC)

• Body Centered Cubic

• 2 total atoms, 1 center, 1/8 in each corner

• APF = 0.64

• CN = 8

Metallic Crystal Structure (HCP)

• Hexagonal Close Packed

• 6 Total Atoms, 1/6 each corner, ½ in each face, 3 center

• APF = 0.74

• CN = 12

Crystallographic Directions

• Direction vector between two point, determines material properties

Indices of a Family:

• choreographically
  equivalent if spacing along each direction is the same

Close-Packet planes

Maximum atomic packing density

FCC

• Planes in family {111}

HCP

• (0001) & (0002)

Single Crystal materials

periodic arrangement of atoms is perfect throughout the entire specimen without interruption

Polycrystalline Materials

These materials are composed of a collection of many small crystals or grains

Anisotropy

Properties of a substance differ based on the crystallographic direction in which measurements are taken, this directionality of properties is anisotropy.

Non-Crystalline Solids

These solids are Amorphous - lacking of systematic and regular arrangement of atoms

Can result from something like rapid cooling

X-Rays

X-ray diffraction led to the understanding of atomic and molecular arrangements

X-rays used for diffraction are “electromagnetic
waves” with:

• wave length of 0.05-0.25 nm

• a voltage of about 35 kV

  (between anode and cathode)

Bragg’s Law & X-Ray diffraction

The reflection of a single wavelength (monochromatic) x-ray beam by the (hkl) planes of a crystal is characterized by:

• No reflected beam is produced at an arbitrary angle of incidence

• At the Bragg’s law angle θ, the reflected rays are in-phase and reinforce one another