21-Mat-B6 Ceramic Materials · May 2013
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
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.
The exam states the sample's carbon content is below the eutectoid composition (0.77 wt% C), i.e. this is a hypoeutectoid steel. On slow cooling through the austenite (γ) field, such a steel always deposits its excess-over-eutectoid ferrite FIRST, as a proeutectoid phase, before the remaining (now eutectoid-composition) austenite transforms at 727 °C. That two-population story is exactly what the micrograph shows.
[Figure not reproduced: Micrograph of a hypoeutectoid steel as printed on the exam, with the two boxed/arrowed regions. See the official exam paper or the cited reference text.]
The left arrow/box sits inside the fine, dark, closely spaced needle/plate-textured region that fills most of the field — this is pearlite, the lamellar eutectoid mixture of ferrite and cementite (α + Fe3C) formed when the carbon-enriched residual austenite crossed 727 °C. The fine alternating lamellae scatter light at this magnification and read dark/textured rather than as two distinct grey levels. The right arrow/box sits on a lighter, blockier patch that is part of a continuous light-toned network tracing what were the prior-austenite grain boundaries — this is proeutectoid ferrite (α), the primary phase that nucleated and grew along those boundaries while the steel was still above 727 °C.
The specimen was first fully austenitized — heated above its upper critical (A3) temperature into single-phase γ — then cooled slowly (furnace-cooled/full-annealed, or at most air-cooled) through the α+γ two-phase field down past 727 °C. Slow, near-equilibrium cooling gives carbon time to diffuse: proeutectoid ferrite nucleates heterogeneously at the prior-austenite grain boundaries (the lowest-energy, easiest nucleation site) and grows inward, rejecting carbon into the shrinking pool of untransformed austenite as it does. By the time the sample reaches 727 °C, the remaining austenite has been enriched to the eutectoid composition (0.77 wt% C) and transforms there by the eutectoid reaction γ → α + Fe3C (pearlite), filling the grain interiors. The continuous, boundary-hugging character of the light ferrite network (rather than isolated equiaxed grains or acicular/Widmanstätten plates driven into the grain interior) is itself evidence of a slow, diffusion-controlled anneal rather than a fast air- or oil-quench.
By the lever rule on the Fe–Fe3C diagram, the proeutectoid-ferrite weight fraction expected in a hypoeutectoid steel of composition C0 just below 727 °C is
A steel at exactly the 0.4 wt% C threshold named in the question would give $W_\alpha=(0.77-0.40)/(0.77-0.022)\approx0.49$, i.e. proeutectoid ferrite should occupy roughly half the field. The micrograph instead shows pearlite as the overwhelming majority phase and ferrite confined to a thin grain-boundary network — nowhere near 50%. That is only consistent with a carbon content higher than 0.4 wt% (closer to, but still below, the 0.77 wt% eutectoid composition — the ∼10% ferrite estimate above corresponds to roughly 0.7 wt% C by the same lever rule, offered as an illustrative order-of-magnitude figure rather than a graded number).
