Question in material structure.

[M.masarwy]

Assuming atoms pack together as hard spheres , find the largest intenstihal atom that can fit in a BCC arrangement of iron atoms . Take the radius of the irom atoms as 1,21 Å . Carry out the same calculations for an FCC arrangment of iron atoms . On the basis of these caluclation would you expect carbon with an atomc radius of 0,77Å to occur as an intenstihal in BCC iron ? or FCC iron?

 

[Mapes]

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[M.masarwy]

This is my solve

I) for BCC :-
assumming 2 unitcells :

a= ( 4r )\[tex]\sqrt{}3[/tex] =2.86 A

a) for the plane ( 0 1 0 ) ( the plane between the 2 cubics )

the free length between each 2 oppiste atoms = a[tex]\sqrt{}2[/tex] - 2r = 1.56 A



b) the free length between the 2 central atoms = a - 2r = 0.38 A


from a , b the largest radius = 0.38 A


II) for FCC :

assumming unitcell :

a = 2a [tex]\sqrt{}2[/tex] =3.507 A

the free space between each 2 oppiste face central atoms = a - 2r = 1.0272 A

the largest radius = 1.0272 A


III) If I have carbon with r = 0.77 A it's possible to occur as an intastitial in a FCC




May I have ur comments ??!:!)