Thermo-kinetic modelling of the giant Snoek effect in carbon-supersaturated iron

Effect of substitutional Ni atoms on the Snoek relaxation in ferrite and martensite Fe-C alloys: An atomisitic investigation

“…It is shown in Ref. [21] that both τ and ∆ depend on the material parameters, carbon content and temperature. At low carbon content, the relaxation time τ has a simplified expression [33,22,21]:…”

“…The applied stress amplitude is set to 300 MPa. The latter is a relatively high value compared with the experimental usage, but technically necessary to overcome the high fluctuations present in the finite-size simulation box [21]. The site fractions of the carbon atoms (c i=1,2,3 ) are measured after each atomic jump.…”

“…In this case, only three non-equivalent carbon migration barriers are left: ω 1/2 , ω 2/3 , and ω 3/2 . The TK model is thus characterized by the following master equation of the site fraction [21]:…”

“…Note that the material parameters (i.e., the stiffness tensors and the elastic dipole tensors) are modified in Nialloyed Fe [30]. This modification should be responsible for the decrease of the peak height as the relaxation strength ∆ is sensitive to the material parameters [21]. Moreover, as mentioned before, the carbon migration barriers are largely modified by Ni-C pair interactions: in Fe-0.01C, the carbon migration enthalpy is very close to the stressfree one (H m 0 ) because C-C pair interactions are negligible and the applied stress leads to very small modification of the migration barrier; in Fe-25Ni-0.01C, the carbon migration enthalpy does not have a single value but performs a value spectrum, as presented in Fig.…”

“…A full investigation of the Ni-alloying effect on the IF behaviors should be accomplished by simulation approaches. Atomistic kinetic Monte Carlo (AKMC) simulations have been applied to compute the IF in ferrite Fe-C [20,21] and Fe-Cr-C alloys [22]. However, close studies are still lacking for ferrite Fe-Ni-C alloy.…”