Question 7 of 7: Borosilicate Glass Design and Cermets

Question 7: Borosilicate Glass Design and Cermets (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.

Given. Binary SiO$_2$–B$_2$O$_3$ glass; atomic masses (page-1 table) $M_{Si}=28.01$, $M_O=16.0$, $M_B=10.81$ g/mol, giving $M_{SiO_2}=60.01$ g/mol and $M_{B_2O_3}=69.62$ g/mol; constraint: total O:Si atomic ratio $\le2.5$.

Find. (a) Maximum wt% B$_2$O$_3$ consistent with O:Si$\,\le2.5$. (b) A definition of cermets, their manufacture, and typical applications.

Approach

Assume B$_2$O$_3$ acts as a true network former (BO$_3$ triangular units contribute all three of their oxygens to the network, alongside the SiO$_4$ tetrahedra of the silica network) and that "O:Si ratio" means all oxygen atoms (from both oxides) divided by only the silicon atoms (B contributes no Si). Working per 100 g of glass, express both mole counts in terms of the unknown wt% B$_2$O$_3=x$ and solve the ratio constraint at equality (the maximum addition is the one that just reaches the $2.5$ limit).

1. (a) Set up the oxygen balance. Per $100$ g glass, moles $n_{SiO_2}=(100-x)/60.01$ contribute $2n_{SiO_2}$ oxygen atoms and $n_{SiO_2}$ silicon atoms; moles $n_{B_2O_3}=x/69.62$ contribute $3n_{B_2O_3}$ oxygen atoms and no silicon. The O:Si constraint at its maximum (equality): $$\frac{2n_{SiO_2}+3n_{B_2O_3}}{n_{SiO_2}}=2.5\quad\Rightarrow\quad \frac{n_{B_2O_3}}{n_{SiO_2}}=\frac{0.5}{3}=\frac16$$
2. (a) Solve for the maximum wt% B$_2$O$_3$. Substituting the mole expressions: $$\frac{x/69.62}{(100-x)/60.01}=\frac16\quad\Rightarrow\quad6(60.01)x=69.62(100-x)$$ $$360.06x+69.62x=6962\quad\Rightarrow\quad429.68x=6962$$ $$\boxed{x\approx16.2\ \text{wt}\%\ \text{B}_2\text{O}_3\ \text{(maximum)}}$$ (Check: at $x=16.2$, $n_{SiO_2}=1.397$, $n_{B_2O_3}=0.2327$ mol/100 g, giving O:Si $=(2\times1.397+3\times0.2327)/1.397=2.500$, confirming the limit is exactly met.)
3. (b) Cermets — what they are. A cermet ("ceramic" $+$ "metal") is a composite material combining a hard, brittle ceramic phase (commonly a carbide, oxide, boride, or nitride — e.g. WC, TiC, Al$_2$O$_3$) with a ductile metallic binder phase (commonly Co, Ni, or an Fe-based alloy) to obtain the ceramic's hardness/wear/high-temperature resistance together with the metal's toughness, which neither constituent has alone.
4. (b) Manufacture. Cermets are made by powder metallurgy: ceramic and metal powders are blended, cold-pressed into a green compact, and then liquid-phase sintered (heated to a temperature at which the metallic binder melts and wets/infiltrates the ceramic grains, then cooled to solidify a continuous metal matrix binding the ceramic particles). This route is necessary because the very high melting points and brittleness of the ceramic phase make conventional melting/casting impractical.
5. (b) Typical applications. Because they combine wear/abrasion resistance, hot hardness, and thermal-shock tolerance with usable fracture toughness, cermets (especially WC–Co) are used for cutting-tool inserts and drill bits, wear-resistant dies and nozzles, and, for oxide-based cermets, high-temperature structural and turbine-related components where pure ceramics would be too brittle and pure metals too soft or too temperature-limited.