J. Mater. Sci. Technol. ›› 2022, Vol. 101: 234-241.DOI: 10.1016/j.jmst.2021.05.058
• Research Article • Previous Articles Next Articles
Fu-Zhi Dai, Yinjie Sun, Yixiao Ren, Huimin Xiang, Yanchun Zhou*(
)
Received:2021-04-08
Revised:2021-05-21
Accepted:2021-05-22
Published:2022-02-28
Online:2021-08-05
Contact:
Yanchun Zhou
About author:* E-mail address: yczhou@alum.imr.ac.cn (Y. Zhou).Fu-Zhi Dai, Yinjie Sun, Yixiao Ren, Huimin Xiang, Yanchun Zhou. Segregation of solute atoms in ZrC grain boundaries and their effects on grain boundary strengths[J]. J. Mater. Sci. Technol., 2022, 101: 234-241.
Fig. 1. Schematic illustration on coincident site lattice (CSL) and CSL grain boundaries. Red and blue points represent lattice points of two mis-oriented crystals. Green line illustrates the position of grain boundary, and green points are coincident sites at the boundary.
Fig. 2. Atomic structure of symmetric tilt grain boundaries studied in this work: (a) Σ3_{111}, (b) Σ3_{112}, (c) Σ5_{210}, and (d) Σ9_{221}. Site 0 indicates site in a grain, while site 1, 2, and 3 are grain boundary sites.
| Name | Tilt Axis | Boundary Plane | γ (J/m2) |
|---|---|---|---|
| Σ3_{111} | [ | ($1\bar{1}1$)r|($\bar{1}$11)b | 0.674 |
| Σ3_{112} | [ | (1$\bar{1}\bar{2}$)r|($1\bar{1}2$)b | 2.379 |
| Σ5_{210} | [ | ($\bar{2}10$)r|(210)b | 2.381 |
| Σ9_{221} | [ | (2$\bar{2}\bar{1}$)r|($\bar{2}21$)b | 2.445 |
Table 1 Crystallographic features and grain boundary energies (γ) of selected grain boundaries.
| Name | Tilt Axis | Boundary Plane | γ (J/m2) |
|---|---|---|---|
| Σ3_{111} | [ | ($1\bar{1}1$)r|($\bar{1}$11)b | 0.674 |
| Σ3_{112} | [ | (1$\bar{1}\bar{2}$)r|($1\bar{1}2$)b | 2.379 |
| Σ5_{210} | [ | ($\bar{2}10$)r|(210)b | 2.381 |
| Σ9_{221} | [ | (2$\bar{2}\bar{1}$)r|($\bar{2}21$)b | 2.445 |
| Sc | Ti | V | Cr | Y | Nb | Mo | Hf | Ta | W | |
|---|---|---|---|---|---|---|---|---|---|---|
| Σ3_{111}_1 | 0.21 | 0.03 | 0.75 | 1.33 | 0.26 | 0.19 | 0.82 | -0.02 | 0.20 | 0.72 |
| Σ3_{112}_1 | -0.67 | -0.36 | -0.71 | -0.26 | -1.13 | -0.14 | -0.77 | 0.20 | 0.04 | -0.44 |
| Σ3_{112}_2 | -0.44 | -1.08 | -2.00 | -2.72 | 0.30 | -0.79 | -1.68 | 0.06 | -0.65 | -1.63 |
| Σ3_{112}_3 | -0.40 | 0.07 | -0.05 | -0.48 | -1.01 | 0.24 | 0.01 | 0.04 | 0.25 | 0.11 |
| Σ5_{210}_1 | -0.12 | -0.13 | -0.22 | -0.34 | -0.68 | 0.05 | -0.07 | 0.10 | 0.13 | -0.01 |
| Σ5_{210}_2 | -0.58 | -0.86 | -1.58 | -2.12 | -0.45 | -0.43 | -1.14 | 0.18 | -0.27 | -0.99 |
| Σ5_{210}_3 | -0.04 | 0.07 | 0.03 | -0.04 | -0.45 | 0.16 | 0.05 | 0.00 | 0.10 | 0.09 |
| Σ9_{221}_1 | -0.42 | 0.30 | 0.43 | 0.26 | -1.06 | 0.42 | 0.36 | 0.09 | 0.42 | 0.61 |
| Σ9_{221}_2 | -0.74 | -1.03 | -1.99 | -2.76 | -0.13 | -0.70 | -1.63 | 0.11 | -0.60 | -1.50 |
| Σ9_{221}_3 | -0.32 | 0.22 | 0.32 | 0.03 | -0.96 | 0.37 | 0.26 | 0.04 | 0.35 | 0.48 |
Table 2 Segregation energies (Eseg) of solute atoms (Sc, Ti, V, Cr, Y, Nb, Mo, Hf, Ta, W) in different boundary sites. The position of each site is illustrated in Fig. 2.
| Sc | Ti | V | Cr | Y | Nb | Mo | Hf | Ta | W | |
|---|---|---|---|---|---|---|---|---|---|---|
| Σ3_{111}_1 | 0.21 | 0.03 | 0.75 | 1.33 | 0.26 | 0.19 | 0.82 | -0.02 | 0.20 | 0.72 |
| Σ3_{112}_1 | -0.67 | -0.36 | -0.71 | -0.26 | -1.13 | -0.14 | -0.77 | 0.20 | 0.04 | -0.44 |
| Σ3_{112}_2 | -0.44 | -1.08 | -2.00 | -2.72 | 0.30 | -0.79 | -1.68 | 0.06 | -0.65 | -1.63 |
| Σ3_{112}_3 | -0.40 | 0.07 | -0.05 | -0.48 | -1.01 | 0.24 | 0.01 | 0.04 | 0.25 | 0.11 |
| Σ5_{210}_1 | -0.12 | -0.13 | -0.22 | -0.34 | -0.68 | 0.05 | -0.07 | 0.10 | 0.13 | -0.01 |
| Σ5_{210}_2 | -0.58 | -0.86 | -1.58 | -2.12 | -0.45 | -0.43 | -1.14 | 0.18 | -0.27 | -0.99 |
| Σ5_{210}_3 | -0.04 | 0.07 | 0.03 | -0.04 | -0.45 | 0.16 | 0.05 | 0.00 | 0.10 | 0.09 |
| Σ9_{221}_1 | -0.42 | 0.30 | 0.43 | 0.26 | -1.06 | 0.42 | 0.36 | 0.09 | 0.42 | 0.61 |
| Σ9_{221}_2 | -0.74 | -1.03 | -1.99 | -2.76 | -0.13 | -0.70 | -1.63 | 0.11 | -0.60 | -1.50 |
| Σ9_{221}_3 | -0.32 | 0.22 | 0.32 | 0.03 | -0.96 | 0.37 | 0.26 | 0.04 | 0.35 | 0.48 |
| Site | ΔLI | Element | ΔLM |
|---|---|---|---|
| Σ3_{111}_1 | 0.753 | Sc | -0.540 |
| Σ3_{112}_1 | -0.644 | Ti | -7.936 |
| Σ3_{112}_2 | -2.264 | V | -11.6550 |
| Σ3_{112}_3 | 2.716 | Cr | -13.641 |
| Σ5_{210}_1 | -0.448 | Y | 9.838 |
| Σ5_{210}_2 | -1.527 | Nb | -4.781 |
| Σ5_{210}_3 | 1.367 | Mo | -7.322 |
| Σ9_{221}_1 | 1.921 | Hf | 0.0624 |
| Σ9_{221}_2 | -4.365 | Ta | -2.9951 |
| Σ9_{221}_3 | 2.135 | W | -7.0471 |
Table 3 Bond length excess (%) of grain boundary sites and solute elements.
| Site | ΔLI | Element | ΔLM |
|---|---|---|---|
| Σ3_{111}_1 | 0.753 | Sc | -0.540 |
| Σ3_{112}_1 | -0.644 | Ti | -7.936 |
| Σ3_{112}_2 | -2.264 | V | -11.6550 |
| Σ3_{112}_3 | 2.716 | Cr | -13.641 |
| Σ5_{210}_1 | -0.448 | Y | 9.838 |
| Σ5_{210}_2 | -1.527 | Nb | -4.781 |
| Σ5_{210}_3 | 1.367 | Mo | -7.322 |
| Σ9_{221}_1 | 1.921 | Hf | 0.0624 |
| Σ9_{221}_2 | -4.365 | Ta | -2.9951 |
| Σ9_{221}_3 | 2.135 | W | -7.0471 |
Fig. 3. (a) Qualitative correlation between size effect and segregation tendency. Comparison of SVR predicted Esegs and Esegs from first-principles calculation: (b) leaving one element out and (c) leaving one grain boundary site out. Rp is Pearson correlation coefficient.
Fig. 5. Atomic structure, bond lengths and electron density difference map of Σ5_{210} grain boundary: (a) site 2 occupied by Cr, (b) no segregation, (c) site 1 occupied by Y.
| Trivial solubility (<1%) | Limited solubility (1%∼10%) | |
|---|---|---|
| Influence | Usually harmful | harmful or helpful |
| Dominate mechanism | Chemical bonding | Atomic size |
| Interface selectivity | Prefers particular surface | Limited preference |
| Phenomena | Grain boundary embrittlement Abnormal grain growth Grain boundary pre-melting Enhanced anisotropic grain growth | Grain boundary pinning Grain boundary strengthening Grain boundary weakening |
Table 4 Interaction between grain boundaries and impurities with trivial and limited solubility.
| Trivial solubility (<1%) | Limited solubility (1%∼10%) | |
|---|---|---|
| Influence | Usually harmful | harmful or helpful |
| Dominate mechanism | Chemical bonding | Atomic size |
| Interface selectivity | Prefers particular surface | Limited preference |
| Phenomena | Grain boundary embrittlement Abnormal grain growth Grain boundary pre-melting Enhanced anisotropic grain growth | Grain boundary pinning Grain boundary strengthening Grain boundary weakening |
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