MEC207 Metals Lecture 4 Notes

Review of Lecture 3

• Briefly looked at metal powder processing routes, their applicability, advantages, disadvantages and future developments.

Properties

• Material properties are influenced by atomic arrangement and microstructure.
• Defining properties is essential.

Microstructure

• Microstructure varies at different scales as shown in the example of Aluminium alloy 2024.
• Examples include:
  • Single crystal (0.4 nm)
  • Grain (100 μm)

Scale and Length

• Scale and length are crucial in materials science.
• Understanding atomic scale phenomena helps in comprehending micro or macroscale behavior.

Mechanical Properties

• Mechanical properties describe a metal's response to applied force.
• Important mechanical properties:
  • Stiffness
  • Strength
  • Ductility
  • Hardness
  • Toughness
  • Fatigue
  • Creep
• Except for stiffness, these properties are sensitive to composition, microstructure, and temperature.
• Strength and toughness will be discussed later.

Bonding

• Properties related to bond energy.

Types of Bonding

• Primary:
  • Ionic
  • Covalent
  • Metallic
• Secondary:
  • Van der Waals
  • Hydrogen
• Primary bonds are strong, resulting from transfer or sharing of outer orbital electrons.
• Secondary bonds are weak.

Bond Energy Curve

• Dependence of potential energy on atomic spacing.
• Long-range attraction versus short-range repulsion.
• Superposition of attractive and repulsive potentials.
• The bond-energy curve determines engineering properties:
  • Melting temperature
  • Elastic modulus (stiffness)
  • Thermal expansion coefficient
• Potential Energy E
  • $E_D$ is the dissociation energy.
• Attractive energy $E<em>A$, Repulsive energy $E</em>R$, Net energy $E_N$.

Bonding Types and Properties

• Ionic:
  • High melting point.
  • Examples: NaCl, MgO.
• Covalent:
  • High melting point.
  • Examples: Si, C(diamond).
• Metallic:
  • Variable melting point.
  • Examples: Al, Fe, W, Hg
• Van der Waals:
  • Low melting point.
  • Example: Ar.
• Hydrogen:
  • Low melting point.
  • Examples: $NH<em>3$, $H</em>2O$

Melting Point vs Binding Energy

• The graph shows the relationship between melting point (K) and binding energy (kJ/mol).

Thermal Expansivity

• Thermal expansion results from changes in average separation between atoms or molecules.
• As temperature increases, the amplitude of molecular vibrations increases, causing expansion.

Coefficient of Linear Expansion

• $\alpha$ is the coefficient of linear expansion and depends on the material.
• Area and volume expansion also occur.

Coefficient of Thermal Expansion Values

• Examples:
  • Steels: ~12 x $10^{-6}/°C$
  • Aluminium Alloys: ~23 x $10^{-6}/°C$
  • Copper Alloys: ~18 x $10^{-6}/°C$
  • Magnesium Alloys: ~26 x $10^{-6}/°C$
  • Titanium Alloys: ~9 x $10^{-6}/°C$
  • Tungsten: ~4.5 x $10^{-6}/°C$

Thermal Expansion and Bonding Energy

• The graph illustrates how the coefficient of thermal expansion relates to bonding energy (kJ/mol).

Thermal Expansion Example

• DAOB-D Length 61.7m, AA2618, $\alpha$ = 24 x 10-6/ °C, $\Delta$T 180°C
• $\Delta$l = $\alpha$($T<em>1-T</em>i$) = 61.7 x 24 x $10^{-6}$ x 180 = 0.267m

Elastic Modulus

• Different materials have different elastic modulus values. Material E/MN/$m^2$
• Examples:
  • Rubber: 1
  • Polythene/nylon: 400
  • Plywood: 7 000

Stiffness

• Bond energy only partially explains differences in stiffness because there is another factor that needs to be considered.

Atomic Packing

• Packing of atoms in metals contributes to macroscopic stiffness.
• Simple cubic packing.
• Close-packed directions.
• Close packed atoms (2D plane) (many engineering metals).

3D Close-Packed Structures

• Plane A, Plane B, Plane C
  • ABCABC…
  • ABABAB…

Close-Packed Hexagonal (c.p.h.) Structure

• The stacking sequence ABAB… corresponds to the close-packed hexagonal structure (e.g. Mg, Zn, Ti).

Face-Centred Cubic (f.c.c.) Structure

• The stacking sequence ABCABC… corresponds to the face-centred cubic structure (e.g. Al, Cu, Ni, Fe-y).

Atomic Arrangement and Crystallographic Structure

• Atomic arrangement influences crystallographic structure.

Simple Cubic Structure

• Close packed directions are cube edges
• Lattice parameter = a = 2R
• Co-ordination number = 6
• 1 atom/unit cell: 8 corners x 1/8
• Rare due to low packing density, Only Polonium (Po) has this structure; No "metals" have this structure.

Face Centred Cubic Structure (fcc)

• Atoms touch each other along face diagonals. e.g: Al, Cu, Au, Pb, Ni, Pt, Ag, Pd
• Lattice parameter = a = $2\sqrt{2}$R
• Co-ordination number = 12
• 4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8

Body Centred Cubic Structure (BCC)

• BCC is not a close packed structure
• Atoms touch each other along cube diagonals. e.g. Cr, W, Fe (a), Ta, Mo
• Lattice parameter = a = 4R/$\sqrt{3}$
• Co-ordination number = 8.
• 2 atoms/unit cell: 1 centre + 8 corners x 1/8
• Close-packed directions: length = 4R = $\sqrt{3}$a

Importance of Atomic Arrangement

• Atomic arrangements of atoms and ions determine the microstructure and properties of a material.
• Controls tensile behavior, fracture behavior, and density.
• Materials with similar atomic arrangements behave similarly when loaded.
• Crystal structure can cause anisotropy in properties.

Polymorphism & Allotropy

• Polymorphism: a material may have more than one crystal structure (i.e. BCC, FCC & HCP).
• A material that shows polymorphism exists in more than one type of space lattice in the solid state.
• Allotropy: Polymorphic change is reversible with temperature or pressure.
• The prevailing crystal structure depends on both temperature and external pressure.

Allotropic Forms of Iron

• Iron can exist in more than one crystal structure.
• Changes are reversible.
• Different allotropes are designated with Greek letters.
• Low temperature iron is BCC (ALPHA iron, $\alpha$-Fe).
• At 912°C, $\alpha$-Fe changes to GAMMA iron ($\gamma$-Fe) which is FCC (causes contraction).
• At 1394°C, $\gamma$-Fe reverts to the BCC form (DELTA iron, $\delta$-Fe) stable up to the melting point of iron (1538°C).
• Upon cooling, the reverse changes occur.

Polymorphism in Tin

• White ($\beta$) tin converts to Gray ($\alpha$) tin upon cooling with substantial volume change.

Next Lecture

• Link between atomic arrangement and properties.