Final answer:
The diffusion coefficient for carbon is expected to be larger in γ-iron (FCC) at 900°C than in α-iron (BCC) due to the increased availability of interstitial sites and higher symmetry in the FCC crystal structure.
Step-by-step explanation:
The question involves calculating the diffusion coefficients for carbon in both α-iron (BCC) and γ-iron (FCC) at 900°C and identifying which one is larger. The calculation of diffusion coefficients usually requires experimental data or empirical formulas based on factors such as temperature, atomic mass, crystal structure, and the characteristics of interstitial sites.
However, without specific values or formulas, we cannot calculate the exact diffusion coefficients directly from the information provided. Nonetheless, we can discuss the factors that affect diffusion and make a qualitative comparison between α-iron and γ-iron.
Diffusion coefficients increase with temperature because molecular speed increases, leading to faster diffusion rates. Iron transforms from BCC (α-iron) to FCC (γ-iron) at high temperatures, a phase change associated with an increase in available interstitial sites for carbon atoms to diffuse.
Given the increased interstitial site availability and symmetry in the FCC structure, diffusion typically occurs faster in γ-iron than in α-iron at the same temperature.
Therefore, even without exact coefficients, we would expect the diffusion coefficient for carbon in γ-iron at 900°C to be larger than that in α-iron