Iron Carbide \(Fe_3C\), \(Z=3*26+6\), density \(7640\,kgm^{-3}\), molar mass \(179.54\,gmol^{-1}\),
\(v_{rms}=3.4354*\cfrac{density}{Z}\)
\(v_{rms}=3.4354*\cfrac{7640}{3*26+6}=312.46\,ms^{-1}\)
and
\(T_{boom}=v^2_{rms}*\cfrac{Molar\,mass}{3*8.3144}\)
\(T_{boom}=312.46^2*\cfrac{179.54*10^{-3}}{3*8.3144}=702.75\,K\) or \(429.25\,^oC\)
It would seems that \(T_{boom}\) for \(Fe_3C\) has nothing to do with annealing of steel nor its critical temperature.
\(T_{p}\) however,
\(T_{p}=v^2_{rms}*\cfrac{Molar\,mass}{2*8.3144}\)
\(T_{p}=312.46^2*\cfrac{179.54*10^{-3}}{2*8.3144}=1054.12\,K\) or \(780.97\,^oC\)
It could be that clusters of \(Fe_3C\) with the effective density of \(7640\,kgm^{-3}\) are broken up in steel at \(780.97\,^oC\) and that gives it strength.
\(v_{p}\) is more relevant here because, instead of multiple collisions to gain the required kinetic energy input to set off a boom effect, in this non-homogeneous medium, only one collision on the quasi-nucleus of \(Fe_3C\) can be expected to deliver energy at the rate required. Multiple collisions on the quasi-nucleus do not add up to \(v_{boom}\).
Maybe, \(T_{boom}=429.25\,^oC\) is just as effective annealing, it is simply not experimented with before.
Just when \(T_{boom}\) was deemed more relevant (post "RMS Than Most Probable" dated 1 Jan 2018).
Note: For annealing steel is heated up \(20-50^oC\) above critical temperature at \(723^oC\).
