1.18.4.2.1 Dilute alloy models

RIS measurements in dilute alloys are less numerous than in concentrated alloys because the required grain boundary concentrations are usually smaller. However, some of the first RIS observations concerned the seg­regation of a dilute element, Si, in austenitic steels. In this specific case, observations were easy because the RIS of Si was accompanied by precipitation of Ni3Si.

The first mechanism that was proposed to explain the observed solute segregation was the diffusion of solute-point defect complexes towards sinks.105 Since then, more rigorous models that rely on the linear response theory have been established and applied to the RIS description of Mn and P in nickel108 and P in ferritic steels.87,107 Although good precision of the microscopic parameters was still missing, the formu­lation of the kinetic equations was general enough to be used almost without modification.105 Recent ab initio calculations not only provided accurate atomic jump frequencies of P in Fe,7,70 but they also called into question the jump interstitial diffusion mechanism that had to be considered.7 Indeed, the octahedral and the (110) mixed dumbbell configura­tions have almost the same stability and migration enthalpies. The resulting effective diffusion energy estimated by the transport model was found to be smaller than the self-interstitial atom migration enthalpy, confirming the classical statement that a solute atom with a negative size effect tends to segre­gate at the grain boundary. However, as emphasized in Meslin et a/.,7 the current interpretation of the interstitial contribution to RIS in terms of size effects is certainly oversimplified. A very large ab initio value of 1.05 eV for the binding energy between a mixed dumbbell and a substitutional P atom may lead to a large activation energy for P interstitials and a drastic reduction of P segregation predictions.7 To consider this new blocking configuration with two P atoms, a concentrated alloy diffusion model including short — range-order effects is required.

It is interesting to note that the same solute seems to have a positive coupling with the vacancy also (although the calculation was not as precise as for the interstitials as it was based on an empirical poten — tial).117 In the same way, recent ab initio calculations showed that a Cu solute is also expected to be dragged by vacancy at low temperatures in Fe.11 ,119