MCEN90014 · Materials Engineering
Structure of Metals & Ceramics
Structure of Metals & Ceramics is the Week-1 foundation of MCEN90014 Materials Engineering at the University of Melbourne, where the whole subject follows a Process → Structure → Property logic. This chapter covers the interatomic bonds that hold solids together and the crystal geometry that follows — unit cells, atomic packing, theoretical density, Miller indices and the allotropy of iron — the atomic-scale vocabulary every later topic (defects, phase diagrams, diffusion) is built on.
What this chapter covers
- 01Classify the four interatomic bond types (ionic, covalent, metallic, secondary) and link bond stiffness to modulus and melting point
- 02Identify the SC, BCC, FCC and HCP unit cells and count atoms per cell using corner (1/8) and face (1/2) sharing
- 03Compute the atomic packing factor (APF) and reproduce the FCC result of 0.74
- 04Relate cube edge length to atomic radius: a = 2√2 r for FCC and a = 4r/√3 for BCC
- 05Calculate theoretical density from ρ = nA/(V_C N_A) with correct nm-to-cm conversion
- 06Assign Miller indices to crystal planes (hkl) and directions [uvw], and reduce to smallest integers
- 07Convert hexagonal indices to the Miller-Bravais 4-index system using i = -(h+k)
- 08State ceramic coordination numbers for CsCl (8), NaCl (6) and ZnS (4)
- 09Describe the allotropy of iron: BCC α-ferrite, FCC γ-austenite and BCC δ-ferrite, with transition temperatures
Theoretical density of a BCC metal
- +1Atoms per cell: BCC has 8 corners x 1/8 + 1 body-centre = 2, so n = 2.
- +1Edge length from radius: BCC atoms touch along the body diagonal, so a = 4r/sqrt(3) = 4 x 0.124 / 1.732 = 0.2864 nm.
- +1Convert to cm before cubing: a = 2.864 x 10^-8 cm, so V_C = a^3 = 2.348 x 10^-23 cm^3.
- +1Substitute into the density formula: rho = nA / (V_C N_A) = (2 x 55.85) / ((2.348 x 10^-23)(6.022 x 10^23)).
- +1Evaluate numerator and denominator: numerator = 111.7 g/mol; denominator = 14.14 cm^3/mol.
- +1Result: rho = 111.7 / 14.14 = 7.90 g/cm^3.
Key terms
- Unit cell
- The smallest repeating block of a crystal; stacking identical unit cells builds the whole lattice. Defined by an edge length a and the atom positions inside it.
- Atomic packing factor (APF)
- The fraction of unit-cell volume occupied by atoms, APF = (volume of atoms in the cell) / (cell volume). FCC and HCP reach the maximum of 0.74; BCC is 0.68; SC is 0.52.
- Theoretical density
- Density predicted from crystal geometry, rho = nA/(V_C N_A), where n is atoms per cell, A is atomic weight (g/mol), V_C is cell volume (cm^3) and N_A is Avogadro's number.
- Miller indices
- A shorthand for crystal geometry: planes (hkl) come from the reciprocals of the axial intercepts; directions [uvw] come from the head-minus-tail vector, each reduced to smallest integers.
- Miller-Bravais indices
- The four-index (h k i l) system for hexagonal crystals, where the redundant third index is fixed by i = -(h+k) to make the hexagonal symmetry explicit.
- Coordination number
- The number of nearest-neighbour ions surrounding a central ion in a ceramic. Set by the cation-to-anion size ratio: CsCl gives 8, NaCl gives 6, and ZnS (zinc blende) gives 4.
- Allotropy
- The ability of a pure element to adopt different crystal structures with temperature or pressure. Iron is BCC alpha-ferrite below 912 C, FCC gamma-austenite from 912 to 1394 C, and BCC delta-ferrite up to melting at 1538 C.
- Bond stiffness
- The slope of the force-separation curve at the equilibrium spacing, S = dF/dr at r0. A stiffer bond gives a higher Young's modulus and a higher melting temperature.
Structure of Metals & Ceramics FAQ
Why does FCC iron dissolve more carbon than BCC iron even though FCC packs more tightly?
Although FCC has the higher packing factor (0.74 versus 0.68 for BCC), its octahedral interstitial holes are larger than those in BCC, so a carbon atom fits more comfortably. This is why steel is austenitised into the FCC gamma phase to take carbon into solution before heat treatment.
What is the difference between Miller indices for planes and for directions?
Planes (hkl) are found by taking the reciprocals of the axial intercepts, then clearing fractions; a plane parallel to an axis has intercept infinity, giving an index of 0. Directions [uvw] are found from the head-minus-tail vector components, without reciprocals. Both are reduced to the smallest integers, and negatives are shown with an overbar.
Can AI help me with the structure of metals and ceramics in MCEN90014?
Yes, within the University of Melbourne academic-integrity rules. An AI tutor like Sia can explain crystal-structure concepts step by step, walk through how a packing factor or theoretical density is derived, and check your reasoning on a Miller-indexing practice question. It cannot sit your invigilated exam or guarantee a mark, and MCEN90014's assessed work must be your own; always confirm what tools are permitted on Canvas.
Studying with AI? Sia — free AI mechanical engineering tutor works through MCEN90014 step by step.
Exam move
Treat Week 1 as vocabulary you must own cold, because every later topic leans on it. Start with the bond types and the four unit cells, then drill the mechanical steps until they are automatic: count atoms per cell using corner (1/8) and face (1/2) sharing, get a from r with the right relation, and always convert nm to cm before computing a density. Practise Miller indexing by sketching a plane or direction and reading off the indices, then reversing the process. Because the final exam is worth 50%, is a hurdle you must pass, and provides a formula sheet, the highest-value habit is showing method and carrying units through every line, since these structure items are self-contained marks you can bank early. Confirm the exam duration and format on Canvas.
