The atomic radius of iron is 0.125 nm, while that of a carbon atom is 0.070 nm. Can a carbon atom fit inside a steel bcc structure without distorting the neighboring atoms?
The Correct Answer and Explanation is :
In a body-centered cubic (BCC) structure, atoms are arranged such that there is one atom in the center of the cube and additional atoms at each corner. To determine whether a carbon atom can fit inside the BCC structure of steel without distorting the neighboring atoms, we need to analyze the atomic sizes and how they fit within the lattice.
Step 1: Atomic Radius Consideration
- The atomic radius of iron (in the BCC structure) is 0.125 nm, while the atomic radius of a carbon atom is 0.070 nm. This implies that a carbon atom is significantly smaller than an iron atom.
Step 2: Interstitial Sites in BCC
- In a BCC structure, the interstitial sites are spaces between the atoms that may accommodate smaller atoms like carbon. These interstitial sites can be either octahedral or tetrahedral.
- The octahedral site (the space between six atoms) typically has a radius that can fit atoms smaller than those of the host metal. The interstitial space in a BCC lattice is large enough to accommodate smaller atoms like carbon, without the need for significant distortion.
Step 3: Comparison of Sizes
- The size of the carbon atom (0.070 nm) is much smaller than that of the iron atom (0.125 nm), and the carbon atom can fit into the octahedral interstitial sites without causing strain. The radius of an interstitial site in a BCC structure is typically between 0.026 nm and 0.062 nm, which is less than the size of a carbon atom. Therefore, carbon atoms can fit in these spaces without significantly distorting the iron lattice.
Conclusion
Yes, a carbon atom can fit inside a steel BCC structure, specifically into the interstitial sites, without distorting the neighboring iron atoms. The carbon atom’s smaller size allows it to fit into the voids of the lattice, which does not result in substantial distortion of the neighboring atoms. This is a key feature of steel’s carbon content in alloys like carbon steel. The carbon atoms in this case contribute to the material’s overall strength by “hardening” the steel, a process known as solid solution strengthening.