In the design of cryogenic storage tanks, which material property is most critical due to...

At cryogenic temperatures, many materials undergo a ductile-to-brittle transition, making them susceptible to catastrophic failure from small cracks. Fracture toughness is the critical property that determines a material's ability to resist crack propagation under these extreme conditions.

Step-by-step Derivation:
Step 1: Analyze the environment. Cryogenic storage involves temperatures typically below -150°C. At these temperatures, thermal energy is low, and atomic mobility is restricted.
Step 2: Evaluate material behavior. Many structural metals (especially carbon steels) exhibit a 'Ductile-to-Brittle Transition Temperature' (DBTT). Below this temperature, the material loses its ability to deform plastically.
Step 3: Assess the options.

• Thermal conductivity (A) is important for insulation design but does not prevent structural failure.
• Corrosion resistance (C) is generally less critical at extreme low temperatures as chemical reaction rates decrease significantly.
• Electrical conductivity (D) is irrelevant to the structural integrity of a storage tank.
  Step 4: Identify the failure mode. The primary risk in cryogenic tanks is 'brittle fracture,' where a crack can propagate at the speed of sound, leading to explosive decompression or tank rupture.
  Step 5: Conclusion. Fracture toughness (the measure of a material's resistance to brittle fracture) is the most critical property to ensure the tank does not fail catastrophically.