A diffusion–precipitation model for gaseous nitriding of Fe-2wt.% V alloy

Coupling Inward Diffusion and Precipitation Kinetics; the Case of Nitriding Iron-Based Alloys

“…Then the nucleation and growth (including coarsening) of M y N z (i.e., (N i ) k j and (R i ) k j for each class i of M y N z at every depth) are calculated as described in Eqs. [7] through [17]). Classes with (R i ) k j less than the radius corresponding to the size of one M y N z molecular unit are removed from the PSD and the M and N components are added to the solutes content of the matrix.…”

“…Therefore, it would be highly beneficial to have at one's disposal a model that links the inward diffusion of I with the (depth-and time-dependent) precipitation state (volume fraction, number density, and size distribution) of the M y I z particles so that the microstructure of the alloys can be predicted and optimized. [1] Until now a series of attempts have been made to simulate inward diffusion of I and simultaneous precipitation of M y I z , [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] usually focusing on one specific (extreme) case of inward diffusion and precipitation. A simple model of coupled diffusion and precipitation was thus developed for the case of internal oxidation [2,3] and later applied to nitriding [4] and carburizing.…”

“…The model was generalized by considering a finite solubility of I, leading to some amount of dissolved I ahead of the reaction front during the precipitation; [6] in this variant, the model has been widely applied to carburizing [7][8][9] and nitriding. [10][11][12][13][14][15][16][17][18][19] A serious shortcoming of the type of models introduced earlier [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] is the disregard of the kinetics (the time and temperature dependencies) of the precipitation reaction. Moreover, these models describe the evolution of only the total amount of precipitated M y I z and cannot predict number density and size (distribution) of the precipitates.…”

“…[25,26] In some investigations, this effect was taken into account, [10,12,16,18] but it has been disregarded in many other studies, [11,[13][14][15]17,19,20] where instantaneous establishment of a (equilibrium) dissolved N concentration at the surface was assumed.…”

“…[31] * Yet, most of the diffusion-precipitation coupled models for internal nitriding published until now ignore this distinct role of excess N. [10,12,[16][17][18]20] The purpose of this study is to develop a, in the sense of the earlier discussion, complete model for coupling the inward diffusion of I and the precipitation of M y I z , for the case of nitriding iron-based alloys, which serves as a model for similar other thermochemical surface treatments. The nitride-precipitation kinetics will be described by a time-and temperature-dependent model for nucleation and growth of second-phase particles, based on a description of the evolution of the PSD, as a function of nitriding depth.…”