Iron(ρ=7.86 g.cm-3)crystallizes in a BCC unit cell
Iron(ρ=7.86 g.cm-3)crystallizes in a BCC unit cell at room temperature.Calculate the radius of an iron atom in this crystal.At temperatures above 910℃ iron prefers to be FCC.If we neglect the temperature dependence of the radius of the iron atom on the grounds that it is negligible,we can calculate the density of FCC iron.Use this to determine whether iron expands or contracts when it undergoes transformation from the BCC to the FCC structure.
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InBCCthereare2atoms/unitcell,so2/a3=Nav/Vmolar,whereVmolar=A/ρ(Aisatomicmassofiron).a=r=1.24×10-8cmIfweassumethatchangeofphasedoesnotchangetheradiusoftheironatom,thenwerepeatthecalculationinthecontextofanFCCcrystalstructure,i.e.,4atomsperunitcellanda=2ρ==8.60g.cm-3FCCironismorecloselypackedthanBCCsuggestingthatironcontractsuponchangingfromBCCtoFCC.
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