Suppose approximately one-third of the octahedral holes in the fcc lattice of iron (r = 126 pm)is occupied by a carbon atom (r = 77 pm).Which of the following is its probable composition?

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Quizplus · Accepted Answer

The radius ratio for filling octahedral sites in an FCC lattice is 0.414 (larger ion smaller distance minus smaller ion radius). For iron (Fe) with a radius of 126 pm and carbon (C) with a radius of 77 pm, the radius ratio is approximately 0.38 (77/126). This is small enough to allow carbon to occupy approximately one-third of the octahedral sites. Based on the options given, the only one that includes both Fe and C is option C: Fe₃C. This suggests that the iron lattice is doped with some sulfur (S) as well. The presence of the sulfur is expected to have a negligible impact on the ability of carbon to occupy octahedral sites since the radius ratio of S to Fe is similar to that of Fe to C. Thus option C is the most likely composition for the iron-carbon lattice.

Suppose Approximately One-Third of the Octahedral Holes in the Fcc