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Ceramics and glasses

Check ionic bonding and coordination numbers, representative crystal structures, sintering, the glass transition, strength scatter by Weibull statistics, thermal shock, and dielectric and piezoelectric materials with multiple-choice questions, including calculations with explanations.

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Thermal expansion and stress →

Ceramics and glasses: key points

Most ceramics are held together by ionic or covalent bonds, and the coordination number of the cation is roughly determined by the cation-to-anion radius ratio. Learn the structures and coordination numbers of types such as NaCl, CsCl and perovskite. Sintering, in which powders are consolidated at high temperature, is driven by the reduction in surface energy.

Ceramics fail in a brittle manner from small internal flaws, so their strength scatters widely and the probability of failure is evaluated with the Weibull distribution. Glass is a supercooled liquid whose structure has frozen in, and its glass transition temperature depends on the cooling rate. Ferroelectrics such as BaTiO₃ are indispensable in electronic components as capacitors and piezoelectric elements.

All Ceramics and glasses questions (12)
  1. Take the ionic radius of Na⁺ as 0.102 nm and that of Cl⁻ as 0.181 nm. What cation coordination number does the radius ratio predict? Take the coordination number as 4 for a radius ratio of 0.225–0.414, 6 for 0.414–0.732, and 8 for 0.732 and above.
  2. Which statement about the CsCl structure is correct?
  3. In the perovskite structure (ABO₃), as in BaTiO₃, what is the oxygen coordination number around the B-site cation (Ti⁴⁺)?
  4. Which statement about sintering of ceramic powders is correct?
  5. Which statement about the glass transition temperature Tg when a glass is cooled from the melt is correct?
  6. The strength of a ceramic follows the Weibull distribution Pf = 1 − exp[−(σ/σ₀) to the power m] with a scale parameter σ₀ = 400 MPa and a Weibull modulus m = 10. Which value is closest to the probability of failure under a load of 300 MPa?
  7. For a ceramic with a Weibull modulus m = 10, specimens of volume V had a characteristic strength of 500 MPa. Using the Weibull volume effect σ₂/σ₁ = (V₁/V₂) to the power 1/m, which value is closest to the characteristic strength of a component of volume 10V made of the same material?
  8. A ceramic has a flexural strength of 300 MPa, a Young's modulus of 380 GPa, a Poisson's ratio of 0.22 and a coefficient of linear thermal expansion of 8.0×10⁻⁶ K⁻¹. Which value is closest to the rough temperature difference at which thermal shock from rapid quenching begins to crack it, ΔTc = σf(1 − ν)/(Eα)?
  9. Why does stabilized zirconia (YSZ), ZrO₂ with Y₂O₃ dissolved in it, conduct oxide ions?
  10. Which statement about the relation between piezoelectricity and ferroelectricity is correct?
  11. Which value is closest to the capacitance of a parallel-plate capacitor with a dielectric layer of relative permittivity 3000 and thickness 2.0 µm between electrodes of area 1.0 mm²? Take the permittivity of free space as 8.85×10⁻¹² F/m.
  12. What is the main reason partially stabilized zirconia has a high fracture toughness?

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