You could look up the density of 0.1 Volume percent carbon in steel and
make an educated guess as to the volume change.
Or, you can reason that carbon fits fairly nicely into the interstitial
sites of pure iron and therefore the net volume change is _________ than
the sum of the two initial volumes.
First divide the specified volumes by the elements molar volumes - this
will give you the moles of C and Fe. If you want to work off the mass
phase diagram, you would multiply the mole numbers by the atomic weights -
this gives you grams of C and Fe. Now consult the phase diagram. If the
composition falls within the alpha iron field, then the volume of the Fe,C
alloy might be findable in tables, but because C is an interstitial solute
in iron the volume change will likely be small. If the composition falls
outside the alpha iron solubility field, then the saturated alpha iron
will be in equilibrium with Fe3C, cementite. Now the volumetrics get dicey
for cementite has its own molar volume which is different from that of
saturated alpha iron. It has been some 40 years since I last thought about
this kind of problem, so I probably omitted some details that ahve escaped
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