ME 240 Chapter 3

What is the difference between crystalline and noncrystalline solids?

• Crystalline: atoms arranged in periodic, 3D arrays (metals, many ceramics, some polymers).

• Noncrystalline (amorphous): atoms have no periodic arrangement (complex structures, rapid cooling)

Why are crystalline structures more stable?

Ordered structures are nearer the minimum in bonding energy

What are the three common metallic crystal structures?

Simple Cubic (SC), Body-Centered Cubic (BCC), and Face-Centered Cubic (FCC). Also Hexagonal Close-Packed (HCP)

What is the coordination number?

The number of nearest-neighbor (touching) atoms

What is the Atomic Packing Factor (APF)?

Ratio of volume of atoms in unit cell to the volume of the unit cell

What are the APF values for SC, BCC, FCC, and HCP?

• SC = 0.52 (1 atom/unit cell, coord. # = 6).

• BCC = 0.68 (2 atoms/unit cell, coord. # = 8).

• FCC = 0.74 (4 atoms/unit cell, coord. # = 12).

• HCP = 0.74 (6 atoms/unit cell, coord. # = 12)

What is the equation for theoretical density of metals?

ρ = nA / (VcNA)

• n = # atoms/unit cell

• A = atomic weight

• Vc = unit cell volume

• NA = Avogadro’s number

General density comparison of materials?

Metals > Ceramics > Polymers; Composites = moderate

What is the difference between single crystals and polycrystalline materials?

• Single crystal: uninterrupted periodic arrangement across specimen (e.g., turbine blades, quartz).

• Polycrystalline: many small grains, random or textured orientations

What are anisotropy and isotropy?

• Anisotropy: property values depend on crystallographic direction (single crystals).

• Isotropy: properties are same in all directions (random polycrystals)

What are polymorphism and allotropy?

• olymorphism: two or more distinct crystal structures for the same material.

• Allotropy: more than one crystal structure in an elemental solid (e.g., graphite vs. diamond, α-Fe vs. γ-Fe)

How many crystal systems exist?

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

How are crystallographic directions denoted?

By indices [uvw], reduced to smallest integers, based on lattice coordinates

What is a family of directions?

All directions crystallographically equivalent (e.g., <100>)

What are Miller Indices (hkl)?

Integers derived from reciprocals of plane intercepts with axes, reduced to smallest integers

What does {hkl} represent?

A family of crystallographic planes that are equivalent (same atomic packing)

What are linear and planar densities?

• Linear Density (LD): # atoms centered on direction vector / vector length.

• Planar Density (PD): # atoms centered on plane / plane area

What is Bragg’s Law for X-ray diffraction?

nλ = 2dsinθ, where λ = X-ray wavelength, d = interplanar spacing, θ = diffraction angle

How can X-ray diffraction distinguish crystal structures?

Reflection rules differ:

• BCC: (h + k + l) even.

• FCC: h, k, l all odd or all even.

• SC: all reflections present

Summary – key points of crystalline solids?

• Atoms can be crystalline or amorphous.

• Density depends on crystal structure, atomic weight, unit cell size.

• FCC, BCC, HCP common in metals.

• Crystallographic points/directions/planes indexed.

• Some materials show polymorphism/allotropy.

• X-ray diffraction identifies structure.

• Anisotropy in single crystals; isotropy in random polycrystals