21-Mat-A4 Deformation Behaviour and Properties of Materials · December 2018
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Exams, December 2018 — 10-Met-A4, Structure of Materials. Three hours, closed book, one approved calculator (Casio or Sharp). Seven questions of 20 marks each (Roman numerals I–VII); the rubric asks for any five, with only the first five in the answer book marked. All seven are solved here, because this set is a study resource rather than an exam script. All necessary equations, constants and an error-function table are provided in the exam's own appendix (reproduced where used below).
Note on the exam title. The printed exam header reads 10-Met-A4, Structure of Materials. Only Question VI.2(c) (grain-size strengthening) touches mechanical/deformation properties directly; the paper as a whole is a broad introductory materials-science survey — atomic structure, bonding, crystal structure/directions/planes, point defects, XRD, dislocations and phase diagrams — and is answered as such below.
Reference texts. The answers below are keyed to the works normally recommended for this syllabus code:
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Metallic bonding is the non-directional electrostatic attraction between a lattice of positive ion cores and a delocalized "sea" of shared valence electrons (e.g. Cu, Al, Fe); it is a strong primary bond, typically several eV/atom, and the electron sea's mobility is also what gives metals their high electrical and thermal conductivity and their ability to deform plastically without fracturing. Van der Waals bonding is a weak secondary bond arising from fluctuating or permanent electric dipoles between already electrically neutral atoms or molecules (e.g. the bonding between solid Ar atoms, or between adjacent polymer chains, or between graphite sheets); it is typically only a few hundredths of an eV/atom. Metallic bonding has the much higher bonding energy of the two. Consequently, van der Waals-bonded solids correlate with the lower melting point — solid argon melts at 84 K, while a metallically bonded solid like copper melts at 1358 K — because melting only requires supplying enough thermal energy to overcome the (weaker) bond holding the structure together.
In silica, each silicon atom is covalently bonded to four oxygen atoms arranged at the corners of a tetrahedron (the SiO₄ tetrahedron, $sp^3$-like hybridisation at Si), with Si–O–Si bond angles near 145° at the bridging oxygen. Crucially, every corner oxygen is shared between two adjacent tetrahedra (a "bridging" oxygen), so each oxygen atom is itself bonded to two silicon atoms. This corner-sharing propagates the tetrahedral motif through all three dimensions, producing a fully covalent, three-dimensional network solid (as in quartz) rather than discrete SiO₂ molecules — and correctly reproduces the 1:2 silicon-to-oxygen stoichiometry, since each of the 4 oxygens per tetrahedron is only "half owned" by that tetrahedron ($4\times\tfrac12=2$ O per Si). This all-covalent, fully cross-linked network is the structural reason silica has such a high melting point ($\sim$1710°C) and is used as a network-forming glass former.
| Material | Dominant bond type | Why |
|---|---|---|
| a. NaCl | Ionic | Electron transfer Na→Cl gives Na⁺/Cl⁻, held by electrostatic (Coulombic) attraction. |
| b. CH₄ | Covalent (intramolecular) | Each C–H bond is a shared electron pair; separate CH₄ molecules are then held together only by weak secondary (van der Waals) forces in the solid/liquid state. |
| c. Polymer chains | Covalent (backbone) + secondary (between chains) | Strong covalent C–C bonds run along each chain; adjacent chains are held to one another only by weak van der Waals/hydrogen bonding — the same strong-in-plane/weak-between-planes topology as graphite (Question II.1's contrast). |
