On Peierls Nabarro stress in Iron

It is well known that Iron is polymorphic, it exists as α Iron (ferrite), which is BCC up to 912°C after which γ Iron (austenite), which is FCC is formed, being stable up to 1394°C, at which temperature it reverts back to a BCC phase known as δ Iron (δ ferrite), which finally melts at 1538°C. Plastic deformation can be due to crystallographic slip mechanism or twinning. The slip system for FCC crystal is {111}〈110〉 in which 12 combinations exist. In BCC crystal, the slip systems are {110}〈111〉, {112}〈111〉 and {123}〈111〉 of which 48 combinations are feasible. Therefore, a FCC crystal has 12 slip systems and BCC has 48 slip systems. Several decades back, Von Mises proposed that minimum five independent slip systems are required for plastic deformation by slip to occur in crystals. From this criterion it can be argued that the BCC crystal is more ductile than FCC crystal due to the presence of more slip systems. However, experimentally it is found that FCC crystal is more ductile than BCC crystal. The scientific reason for this anomaly is attributed to the higher Peierls Nabarro stress in BCC crystals as compared to FCC crystals. In this paper, calculations are presented to calculate the Peierls Nabarro stress in α Iron and γ Iron. This Peierls Nabarro is related to the cohesive energy of the crystal.