Triple junction solute segregation in Al-based polycrystals

Solute segregation is a crucial means of stabilizing nanostructured alloys, and at very small grain sizes, this requires consideration of triple junctions (TJs), which attain a meaningful volume fraction and thus become relevant for bulk material behavior. Here, the solute segregation spectra for grain boundary (GB) and TJ sites are calculated for a large number of dilute Al-based binary systems with available interatomic potentials. A defect-identifying algorithm is applied to quantify the average GB thickness and classify the intergranular site spectra into GB and junction subspectra. The algorithm is also applied to a hybrid electronic-level database for GB segregation of various solutes in Al, yielding polycrystalline TJ solute segregation spectra from first principles. The results suggest that TJ segregation is alloy or interatomic potential dependent and can exhibit either boundary or junction preference. With these spectra as inputs, the spectral GB segregation model gives quantitative predictions of segregation as a function of grain size, temperature, and total solute concentration, suitable for alloy screening and design.

Figure 1

(a) Misorientation plot for all 39 grain boundaries (GBs) in the polycrystalline samples explored here. (b)–(e) Self-similarly scaled Al(Sm) [59] polycrystals from 13–20 nm systems are visualized with the bulk atoms omitted. The atomic defect types are labeled via the color shade (dark green for GBs, light green for triple junctions, and yellow for quadruple nodes).

Figure 2

(a) Intergranular site population identified by the algorithm with varying cutoff radius. The dashed vertical line indicates the cutoff where the population reaches 99.5% of the large cutoff limit. The structures shown in (b) and (c) are examples of the overdetermined and appropriately determined cases, respectively, with cutoff radii of 10 and $5.18\AA$, respectively, in the case of Al(Sm) [59].

Figure 3

Segregation subspectra predicted by 23 EAM potentials [43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60] in kJ/mol with the junction indices labeled at the top-right corner of the plots.

Figure 4

Periodic table plot of the junction segregation index $J_X$ as defined in Eq. (5), based on quantum-accurate segregation spectra rather than potentials. The systems with an index of higher than 0.1 in the magnitude are bordered in red.

Figure 5

A comparison of embedded atom method (EAM) potentials (in color) with quantum-accurate quantum mechanical–molecular mechanical (QM-MM) segregation spectra (in black). Grain boundary (GB) and triple junction (TJ) subspectra are labeled with solid and dashed lines, respectively. (a) Defect subspectra of Al(Ni) EAM systems (Refs. [53, 54]), (b) Al(Zr) [47], and (c) Al(Ag) [43]. The QM-MM data from Ref. [61] for each corresponding system are also plotted in (a)–(c). The vertical lines indicating the mean are also plotted to demonstrate the GB/TJ relative shifts.

Figure 6

(a) Atomic volume and (b) coordination number distribution of grain boundary (GB) and triple junction (TJ) sites. The scatter plot of both (a) and (b) are combined in (c) for Al(Ti) and (d) for Al(Hf). The colormap in (c) and (d) denotes the average site-wise segregation energy of the sites within the box range.

Figure 7

Intergranular, grain boundary, and triple junction defect fraction fitted from the self-similarly scaled polycrystals.

Figure 8

Physical junction effects or the differences between the solutions with scaled [triple junction (TJs) included] and nonscaled [only grain boundaries (GBs)] spectra at $T$ = 450 K are plotted in (a) for the solute enrichment (β) and (b) for the effective segregation energy ($\mathrm{\Delta }{\overline{E}}_{\mathrm{eff}}^{\mathrm{seg}}$). (a) and (b) are normalized with the “w/o TJs” solutions to demonstrate the relative increments if TJs are included.