Thermal stability of nanocrystalline Fe–Zr alloys

Stability of binary nanocrystalline alloys against grain growth and phase separation

“…These suggest that equilibrium solute segregation lowers the grain boundary energy to varying degrees. Experimentally, a reduction in the propensity for grain growth in nanocrystalline materials has been observed in a variety of binary alloys [21][22][23][24][25][26][27][28][29][30][31]. There are many indications in experimental systems that there is a "preferred" grain size which emerges during processing which is closely linked to the solute content [2,24,30,32,33]; this is considered significant evidence for a thermodynamic contribution to stabilization.…”

“…Using experimental data from these systems as input, they predicted the distribution of solute, an increase in solute solubility with a decrease in grain size, and that the precipitation temperature of an ordered compound can be suppressed for these systems [37]. Darling and coworkers adapted a model of surface segregation energy to evaluate potential alloying elements with iron on the basis of their propensity to lower grain boundary energy [26,28,38].A more general, and generalizable, model is that of Trelewicz [39], who proposed a regular nanocrystalline solution (RNS) model for the free energy of mixing in binary alloys with both crystalline and intercrystalline atomic environments. The RNS model reduces properly to a regular solution model for the crystalline phase in the limit of infinite grain size, and to a standard grain boundary segregation isotherm in the dilute limit.…”

Phase transitions in stable nanocrystalline alloys

“…Pure nanocrystalline materials undergo rapid grain growth into micron-scale grain sizes at relatively low homologous temperatures, [1][2][3][4] but with the addition of alloying elements grain growth can be greatly hindered. [5][6][7][8][9][10][11][12][13] Two mechanisms for suppressing grain growth by alloying have been proposed: alloying elements can either kinetically impede grain growth by increasing the activation energy for grain boundary motion (effectively decreasing grain boundary mobility) or decrease the grain boundary energy thermodynamically through grain boundary segregation (or both). The latter mechanism is particularly promising, as substantial decreases to the grain boundary energy from grain boundary segregation could stabilize nanoscale grain sizes to higher temperatures and for longer times.…”

“…The latter mechanism is particularly promising, as substantial decreases to the grain boundary energy from grain boundary segregation could stabilize nanoscale grain sizes to higher temperatures and for longer times. [8][9][10][11][12][13] There is an even more enticing prospect when alloying to reduce the grain boundary energy: if the excess energy of the grain boundary is eliminated by grain boundary segregation, grain growth can be entirely avoided and a thermodynamically stable grain size in the nanocrystalline regime could exist. This concept was put forth by Weissmüller,14,15 with an accompanying analytical model that revealed that a system with an enthalpy of grain boundary segregation large enough to offset the pure grain boundary energy should have such a stable nanocrystalline state.…”

“…Several of these alloy systems have shown considerable nanometer-scale grain size stability in experiments, including Ni-P, Ni-W, Fe-Zr, and W-Ti. [8][9][10][11][12][13] While these models are able to identify systems with potential stability through energetic considerations of grain boundary segregation, the accurate accounting of entropic effects has been limited by assumptions needed to make the analytical models tractable, i.e., dilute limit or regular solution assumptions. A number of analytical [20][21][22][23] and atomistic models 24,25 have been developed for determining the change in free energy associated with grain boundary segregation under a variety of conditions, but typically do not allow the grain size to change during disordering.…”