Exercises: Internal structure and properties

Explain what the three main types of atomic bonding (ionic, covalent and metallic) consist of and give a representative material example for each, indicating a property of that material that is explained by its bonding.

Copper conducts electric current and polyethylene does not. Explain this difference using the "sea of electrons" model of metallic bonding and the structure of polymers.

The figure shows the unit cell of a crystalline metal: there are atoms at the eight vertices of the cube and an additional atom inside it. State the name of this crystal lattice and explain, based on it, why metals are usually dense and deformable.

Explain what a composite material is and how it differs from an alloy: in the former, two phases can be distinguished with the naked eye or under a microscope, whereas in the latter, the atoms mix within a single lattice. Give an example of each.

Ceramic materials (porcelain, alumina, brick) combine ionic and covalent bonds. State three typical properties of ceramics related to these bonds and an application that makes use of each one.

Explain using the crystal lattice model why a metal can be rolled into thin sheets without breaking while an ionic crystal (such as salt) shatters when struck: what happens to the atomic planes and the charges in each case?

Qualitatively compare body-centred cubic (BCC) and face-centred cubic (FCC) lattices: how many atoms each atom touches (coordination number) and which typical metals crystallise in each (iron at room temperature versus aluminium or copper).

Explain the difference in internal structure between a thermoplastic polymer (independent chains) and a thermosetting polymer (cross-linked chains), and reason why the former can be recycled by melting while the latter cannot.

Diamond and graphite are both composed solely of carbon atoms, yet the former is the hardest natural material and the latter is used as a lubricant and in pencil leads. Explain this difference based on how the carbon atoms are bonded and arranged in each structure.

A glass bottle and a quartz crystal have very similar chemical compositions (both silica-based), but glass is amorphous while quartz is crystalline. Explain what these two terms mean and reason why glass breaks into irregular fragments whereas quartz exhibits flat faces.

Predict, reasoning from the type of bonding, the behaviour of these three materials: common salt (NaCl), copper (Cu) and quartz (SiO₂). For each one, state whether you expect it to conduct electric current in the solid state, whether it will have a high or low melting point, and whether it will be brittle or ductile.

Distinguish between a substitutional alloy and an interstitial alloy at the atomic level: what relative size the added atoms must have in each case, and a real example of each type (bronze with tin versus steel with carbon).

Steel is iron with up to $2\,\%$ carbon. Explain qualitatively what ferrite and cementite (iron carbide) are in its microstructure and reason why steel with a higher carbon content is harder but less weldable.

A wind turbine blade is manufactured using carbon fibre in epoxy resin. Explain what each component contributes (strength and stiffness from the fibres; shape, protection and load transmission from the matrix) and why the orientation of the fibres is designed according to the dominant stresses.

Relate thermal conductivity to internal structure: why metals conduct heat well (free electrons), why diamond conducts it even better without conducting electricity (lattice vibrations in a perfect covalent structure), and why polymers are thermal insulators.

Explain what the glass transition temperature of an amorphous polymer is and what happens to the material above and below it. Reason why an elastic rubber band becomes rigid and brittle if it is cooled with liquid nitrogen.

A technical team proposes replacing conventional high-voltage cables (ACSR: steel core with helical aluminum strands) with a solid homogeneous copper conductor having identical overall electrical resistance, claiming that it simplifies assembly and reduces the outer diameter.

Technically rebut this proposal by analyzing three aspects based on bonding and internal structure:

1) Relate the atomic mass and crystal structure of copper versus aluminum to the resulting density, predicting how the self-weight of the cable would affect the sag (catenary) between towers and the tensile stresses.

2) Justify why the skin effect at 50 Hz favors placing aluminum on the periphery and reserving steel exclusively for the central core.

3) Predict the risk of mechanical failure if steel were omitted and only pure aluminum were used, considering creep and the plastic deformation mechanisms of aluminum at operating temperature.

Three covalent material wafers are analyzed to design a resistive temperature sensor over a range from 150 °C to 350 °C: diamond ($E_g \approx 5,5\ \text{eV}$), silicon ($E_g \approx 1,1\ \text{eV}$), and germanium ($E_g \approx 0,67\ \text{eV}$).

1. a) A technician suggests using germanium doped with phosphorus ($10^{16}\ \text{atoms/cm}^3$). Interpret using the band model why, when raising the temperature above a certain threshold, the intrinsic carrier concentration exceeds that provided by the dopants (intrinsic regime), causing the conductivity to go out of control and invalidating the sensor calibration.
2. b) Predict with reasoning which of the three base materials would offer the greatest stability against uncontrolled thermal generation of electron-hole pairs in this temperature range, and argue whether diamond would behave as a semiconductor or as an insulator at 350 °C considering its bandgap width.

For the manufacture of friction bushings subjected to load, a quality report shows that Cu-Sn bronze (10 wt% Sn) exhibits a significantly higher yield strength than annealed pure copper. An operator proposes replacing tin with zinc in the same proportion (Cu-Zn brass at 10 wt% Zn), claiming that the strengthening will be exactly the same because both are substitutional solid solutions.

1. a) Given the atomic radii ($r_{\text{Cu}} = 128\ \text{pm}$, $r_{\text{Zn}} = 133\ \text{pm}$, $r_{\text{Sn}} = 151\ \text{pm}$), justify using crystal lattice distortion theory and elastic stress fields why the operator's claim is incorrect, predicting which of the two alloys will offer greater resistance to dislocation movement.
2. b) Explain how the ductility and electrical conductivity of copper are affected when adding these solutes, relating both changes to electron scattering and the pinning of dislocation motion.

In a total hip replacement (femoral stem, femoral head, and acetabular cup), a surgeon detects two long-term revision issues: bone resorption around the femoral stem due to stress shielding and adhesive/abrasive wear at the articulating friction pair.

You have the following materials available: Ti-6Al-4V alloy ($E \approx 110\ \text{GPa}$), 316L stainless steel ($E \approx 200\ \text{GPa}$), polycrystalline alumina $\text{Al}_2\text{O}_3$ ($E \approx 380\ \text{GPa}$, very high hardness), and ultra-high-molecular-weight polyethylene UHMWPE ($E \approx 1\ \text{GPa}$, low coefficient of friction). Cortical bone has $E \approx 18\ \text{GPa}$.

1. a) Justify the selection of the ideal material for the stem between titanium and 316L steel, explaining quantitatively and biomechanically how the difference in elastic modulus influences stress shielding.
2. b) Design the articulating friction pair (femoral head and inner cup liner), selecting the optimal combination of materials and justifying at the bonding and microstructural level why you would rule out direct metal-on-metal or polymer-on-polymer contact.

To lighten a beam that will work outdoors over a thermal range from $-10\,^\circ\text{C}$ to $+40\,^\circ\text{C}$, substituting the steel bars ($\alpha = 12 \cdot 10^{-6}\ \text{K}^{-1}$, tensile strength $500\ \text{MPa}$) with aluminium alloy bars ($\alpha = 24 \cdot 10^{-6}\ \text{K}^{-1}$, tensile strength $300\ \text{MPa}$) is evaluated. The concrete has $\alpha = 10 \cdot 10^{-6}\ \text{K}^{-1}$, an allowable compressive strength of $30\ \text{MPa}$, and an allowable tensile strength of only $2,5\ \text{MPa}$.

1. a) Predict the type of internal stress (tensile or compressive) that would be induced in the concrete and in the aluminium bars upon experiencing a heating of $\Delta T = +30\,^\circ\text{C}$ during the summer. Justify why the discrepancy in the $\alpha$ coefficients would cause cracking and premature spalling of the concrete around the reinforcement.
2. b) Analyse what would happen during a winter frost ($\Delta T = -20\,^\circ\text{C}$) regarding the mechanical bond at the aluminium-concrete interface and how this would affect stress transfer when the beam is subjected to bending.

In a catalytic converter to neutralize polluting gases, substituting platinum microspheres of diameter $d_1 = 10\ \mu\text{m}$ with spherical platinum nanoparticles of diameter $d_2 = 10\ \text{nm}$ is proposed.

1. a) Quantitatively demonstrate by what factor the specific surface area (area per unit mass) is multiplied when reducing the diameter from $10\ \mu\text{m}$ to $10\ \text{nm}$. Interpret at the atomic level why atoms located on the surface of a nanoparticle have a lower coordination number and how this translates into their reactivity and catalytic activity.
2. b) During the thermal regeneration process, nanoparticles tend to agglomerate (surface sintering). Predict how this phenomenon affects the performance of the catalyst and justify why, from a toxicological and occupational hygiene point of view, accidental inhalation of free nanoparticles poses a much more severe biological risk than that of micrometric particles of the same chemical substance.

On a coastal pedestrian footbridge, structural carbon steel beams were joined using stainless steel bolts and aluminium alloy rivets. After two years of service, two severe pathologies are observed: the aluminium rivets have disintegrated due to galvanic corrosion, while the steel beams show intense localized pitting at the points where the protective paint layer suffered scratches during assembly.

1. a) Using the galvanic series of potentials and the surface area balance (anode/cathode area ratio), justify the rapid destruction of the aluminium rivets in contact with stainless steel in a saline atmosphere, explaining why their natural alumina ($\text{Al}_2\text{O}_3$) passivation layer was not sufficient to prevent the attack.
2. b) Refute the suitability of the paint coating compared to hot-dip galvanizing (zinc coating). Justify electrochemically why a scratch in the paint accelerates localized corrosion of the base steel, whereas on galvanized sheet the steel remains protected even if the coating suffers a similar gouge.

The structural frame for a lightweight rescue drone is being designed. It must maximize flight endurance, ensure stiffness against wind gusts, and absorb impacts in forced landings without catastrophic failure. Three candidate materials are presented:

• Candidate A (Polyamide 66 with 30% short glass fibre): $\rho = 1,35\ \text{g/cm}^3$, $E = 8,5\ \text{GPa}$, Izod impact strength $= 11\ \text{kJ/m}^2$, low cost, recyclable by thermoforming.

• Candidate B (Forged AZ91D magnesium alloy): $\rho = 1,81\ \text{g/cm}^3$, $E = 45\ \text{GPa}$, yield strength $\sigma_y = 160\ \text{MPa}$, fracture toughness $K_{1c} = 17\ \text{MPa}\cdot\text{m}^{1/2}$, medium cost, recyclable by casting.

• Candidate C (Unidirectional continuous carbon fibre epoxy laminate / CFRP): $\rho = 1,55\ \text{g/cm}^3$, $E = 135\ \text{GPa}$ (in the longitudinal direction), brittle under transverse point impacts, very high cost, not thermally recyclable.

1. a) Calculate the specific stiffness ($E/\rho$) of the three candidates and interpret which one best optimizes the ratio between structural stiffness and mass in flight.
2. b) If the drone must operate in rocky environments with a high risk of accidental collision, justify which material you would select, reasoning the microstructural pros and cons of candidates B and C (ductility and plastic deformation versus elastic-brittle behaviour with delamination). Argue which priority criterion would force you to discard Candidate A despite its lower density and cost.