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.
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.
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.
a. NaCl — ionic bonding. Na (electronegativity $\approx0.9$) transfers
its single valence electron to Cl (electronegativity $\approx3.0$); the resulting
Na⁺/Cl⁻ ions attract electrostatically, non-directionally, in a rock-salt lattice.
b. CH₄ (methane) — covalent bonding. Each of the four
C–H bonds is a shared, directional electron pair (small electronegativity difference,
C $\approx2.5$, H $\approx2.1$); the molecules themselves then interact only weakly, by
secondary (van der Waals, induced-dipole) forces, which is why methane is a gas at room
temperature despite its strong intramolecular covalent bonds.
c. Polymer chains — covalent bonding (chain backbone) with secondary bonding
between chains. The C–C (or C–Si, etc.) backbone of the chain itself is
covalent; adjacent chains are held to each other only by much weaker secondary (van der Waals or,
in polymers like nylon, hydrogen) bonds, which is why thermoplastics soften well below any
covalent-bond-breaking temperature.
Final results — Question II
Item
Answer
Higher bonding energy
Metallic bond
Correlates with lower melting point
van der Waals bond
NaCl
Ionic
CH₄
Covalent (intramolecular)
Polymer chains
Covalent backbone + secondary (van der Waals/H) between chains