Compute the size of the largest sphere that can fit inside an \"octahedral\" voi

Question

Compute the size of the largest sphere that can fit inside an "octahedral" void in the bcc structure without distortion. Compute the size of the largest sphere than can fit in the tetrahedral void in bcc without distortion. Given your results in (a) and (b), are you surprised that interstitial atoms such as C and N occupy the octahedral voids in bcc (alpha) iron rather than the tetrahedral voids? Suggest a reason why this might be the case [Hint: which has the larger volume?] When bcc iron has a high carbon content in solution its structure is distorted and its unit cell becomes slightly tetragonal (elongated along one of the cubic axes 0. Why might you expect this?

Explanation / Answer

a)The octahedral hole is located at the center of any four spheres that form a square. If we represent the radius of a ball fitting in the octahedral holes byr, and the radius of the sphere asR, then we have the relationship:

r + R

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