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17-Phys-B7 Structure of Materials · December 2018

Question 2 of 7: Chemical Bonding

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format. 17-Phys-B7 Structure of Materials, National Examination December 2018 — a closed-book examination (Casio or Sharp approved calculators only; all necessary equations, constants and diagrams supplied in the paper's own appendix). Candidates attempt any five of the seven questions, each worth 20 marks; every question is nonetheless answered in full below so the paper remains a complete study resource.

Reference texts. W. D. Callister Jr. & D. G. Rethwisch, Materials Science and Engineering: An Introduction, 10th ed. (atomic bonding, crystal structure and packing, point defects, diffusion, dislocations and slip, mechanical properties, phase diagrams and the lever rule, precipitation hardening, X-ray diffraction).

Check — two points on the printed paper. (1) Question I.2 prints the ion as "Cl- (Z = 16)"; Z = 16 is sulfur, not chlorine (Cl is Z = 17) — a printed typo. The electronic structure below uses the correct Z = 17 for chlorine. (2) Question III.1(d) prints the hexagonal plane as $(2\bar{2}10)$, i.e. Miller–Bravais indices $h=2,\,k=-2,\,i=1$; the third index of a valid Miller–Bravais symbol is never independent — it is fixed by $i=-(h+k)$, here $i=-(2-2)=0$, not 1. Reducing the self-consistent index $(2\bar200)$ by its common factor of 2 gives $(1\bar100)$, a standard prism-type plane. The drawing below uses the symmetry-equivalent, non-degenerate face $(10\bar10)$ of the same $\{1\bar100\}$ family (chosen because it renders visibly in the cell projection used here) and states this substitution explicitly.

Question II: Chemical Bonding (20 marks)

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.

Part (a) — metallic vs. van der Waals bonds. A metallic bond is a PRIMARY bond: the metal's valence electrons are delocalized into a shared "electron gas" that permeates the whole lattice of positive ion cores, non-directionally binding every ion to every neighbour; typical bonding energies are $68$–$850$ kJ/mol (e.g. copper $\approx 323$ kJ/mol, tungsten $\approx 850$ kJ/mol). A van der Waals bond is a SECONDARY bond: a weak electrostatic attraction between induced or permanent dipoles on otherwise electrically neutral atoms/molecules (fluctuating-dipole, polar-molecule, or hydrogen-bond type); typical energies are only $\approx 2$–$10$ kJ/mol (e.g. condensed argon $\approx 7.7$ kJ/mol; between graphite sheets). The metallic bond has the much higher bonding energy of the two. Because melting requires supplying roughly the bond energy to pull the structure apart, the WEAKER bond — van der Waals — is the one that correlates with a lower melting point (solid argon melts at $84$ K, versus copper at $1358$ K).

Part (b) — silica's covalent network. In 100%-covalent SiO₂, every silicon atom is covalently bonded to FOUR oxygen atoms, arranged tetrahedrally around it (the $\text{SiO}_4^{4-}$ tetrahedron, Si–O bond $\approx0.16$ nm); every oxygen atom, in turn, BRIDGES exactly two silicon atoms, so each tetrahedron shares each of its four corners with a neighbouring tetrahedron. This corner-sharing repeats indefinitely in three dimensions, building a continuous, open, three-dimensional covalent network (with an $\text{Si:O}$ atom ratio of $1:2$, since each of the 4 O per tetrahedron is shared between 2 Si, contributing $4\times\tfrac12 =2$ oxygens per silicon). The 2-D schematic below simplifies the true 3-D tetrahedral network to triangles for clarity.

SiO₂ network (corner-sharing SiO₄ tetrahedra, 2-D schematic) Si (tetrahedron centre, coordination 4) O (bridging corner, shared by 2 tetrahedra)
Each Si (filled blue) sits at the centre of a tetrahedron of four O (open circles); every O corner is shared with the next tetrahedron, propagating the covalent network in 3-D (only 2-D corner-sharing is drawn here for clarity — each real corner is shared, not merely adjacent).

Part (c) — bonding type identification.

Final results — Question II
ItemAnswer
Higher bonding energyMetallic bond
Correlates with lower melting pointvan der Waals bond
NaClIonic
CH₄Covalent (intramolecular)
Polymer chainsCovalent backbone + secondary (van der Waals/H) between chains