Crystal Structures

Thermal expansion refers to the increase in volume of a material as a result of an increase in temperature.
Key Formula: The expansion of a material can be calculated using the coefficient of thermal expansion, which scales the change in temperature.
Coefficient of Thermal Expansion: A material property determined by bonding types; different materials expand differently based on this coefficient.
Practical Example: Sidewalks have breaks that accommodate expansion to prevent buckling during heat waves.

Definition: Ashby plots are graphical representations used to visualize the relationship between two properties of materials.
Example Axis: In the discussed example, one axis represents the coefficient of thermal expansion and the other stiffness (Young's modulus).
Applications: Selecting materials based on desired properties (e.g., high stiffness and low thermal expansion for sidewalks).

Four Main Categories:
1. Polymers: Organic compounds made mainly of carbon and hydrogen; low stiffness and low thermal conductivity.
2. Metals: Characterized by metallic bonding; typically high melting points, strong, good heat/electricity conductors.
3. Ceramics: Composed of metal and non-metal bonding; often high strength but low toughness and sometimes insulating.
4. Composites: Mixtures of two or more materials to combine their properties (e.g., fiberglass is a polymer mixed with glass fibers).

Metals: High strength, toughness, excellent conductors of electricity and heat, often ductile (can be deformed without breaking).
Polymers: Generally low strength and conductivity; flexible yet weak compared to metals.
Ceramics: Typically brittle, high in compression strength, low in tension strength; not good electrical conductors.

Conductivity:
- Metals exhibit low electrical resistivity due to the free movement of electrons in metallic bonds (sea of electrons).
- Ceramics show high resistivity because of ionic bonds where electrons are not free to move.

Toughness vs. Strength:
- Toughness: Ability to absorb energy and deform without fracturing. Related to the material's capacity to withstand impacts.
- Strength: Resistance to being deformed or broken under load; it focuses on the material's maximum force application.

Importance: The arrangement of atoms in crystal structures significantly affects the properties of materials.
Types of Crystal Structures:
1. Simple Cubic: Least common; has low packing density.
2. Body-Centered Cubic (BCC): Common in metals like steel; has two atoms per unit cell, showing strong ductility at high temperatures.
3. Face-Centered Cubic (FCC): Atoms on the faces and vertices; high packing efficiency and often found in ductile materials like aluminum and copper.
4. Hexagonal Close-Packed (HCP): Common in materials like titanium; exhibits anisotropic properties (different properties in different directions).

Definition: A notation to describe crystal planes and directions in a crystal lattice through a set of three integers.
Calculation:
- Determine intercepts on axes, take reciprocals, and simplify to whole numbers.
- Use square brackets for directions and parentheses for planes (e.g., [110] for direction, (111) for a plane).

Density can be calculated using the formula:
Density ($
ho$) = Mass of the atoms in a unit cell / Volume of unit cell
Density predictions from crystal structures can help in identifying suitable materials for applications.
Example Calculation: For FCC copper (4 atoms per unit cell, atomic weight = 63.55 g/mol), leads to a density value consistent with experimental results.

Materials that lack long-range order (e.g., glass) are termed amorphous; they possess different properties compared to crystalline structures.
Short-range order might exist, but not consistently throughout the material.
Application: Amorphous structures can serve specific roles where uniformity and energy minimize properties are not critical.