J. Mater. Sci. Technol. ›› 2022, Vol. 103: 105-112.DOI: 10.1016/j.jmst.2021.07.010
• Research Article • Previous Articles Next Articles
Qian Wanga,b, Shun Xuc, Yajun Zhaod,*(
), Jean-Sébastien Lecomtea,b,*(), Christophe Schumana,b,*()
Received:2021-05-05
Revised:2021-07-03
Accepted:2021-07-05
Published:2022-03-20
Online:2021-08-27
Contact:
Yajun Zhao,Jean-Sébastien Lecomte,Christophe Schuman
About author:christophe.schuman@univ-lorraine.fr (C. Schuman).Qian Wang, Shun Xu, Yajun Zhao, Jean-Sébastien Lecomte, Christophe Schuman. Multi-dimensional morphology of hydride diffusion layer and associated sequential twinning in commercial pure titanium[J]. J. Mater. Sci. Technol., 2022, 103: 105-112.
| Orientation relationship | Interface plane | |
|---|---|---|
| OR1 | {0001}//{001},<$1\bar{2}10$>//<110> | {$10\bar{1}0$}//{$1\bar{1}0$} |
| OR2 | {0001}//{$1\bar{1}1$} (angle of 4°), <$1\bar{2}10$>//<110> | {$10\bar{1}3$}//{$1\bar{1}0$} |
| OR3 | {$10\bar{1}0$}//{$1\bar{1}1$},<$1\bar{2}10$>//<110> | {0001}//{$1\bar{1}2$} |
| OR4 | {$\bar{1}011$}//{001},<$1\bar{2}10$>//<110> | {$10\bar{1}1$}//{$1\bar{1}\bar{1}$} |
Table 1 Four orientation relationships of α-Ti/δ-hydride (FCC structured) transition.
| Orientation relationship | Interface plane | |
|---|---|---|
| OR1 | {0001}//{001},<$1\bar{2}10$>//<110> | {$10\bar{1}0$}//{$1\bar{1}0$} |
| OR2 | {0001}//{$1\bar{1}1$} (angle of 4°), <$1\bar{2}10$>//<110> | {$10\bar{1}3$}//{$1\bar{1}0$} |
| OR3 | {$10\bar{1}0$}//{$1\bar{1}1$},<$1\bar{2}10$>//<110> | {0001}//{$1\bar{1}2$} |
| OR4 | {$\bar{1}011$}//{001},<$1\bar{2}10$>//<110> | {$10\bar{1}1$}//{$1\bar{1}\bar{1}$} |
Fig. 1. (a) SEI showing section microstructure of hydride layer. (b) The higher-magnification SEM of the area in the black box. (c) TD-IPF maps of hydride layer formed on TD surface. (d) RD-IPF maps of hydride layer formed on RD surface. Grain boundaries are indicated by black lines in the IPF maps.
Fig. 2. IPF maps of hydride layer and corresponding pole figures of hydride variants in (a) Grain 1, Euler angle: 101.1°, 73.3°, 22.9°, (b) Grain 2, Euler angle: 86.7°, 57.1°, 5.2°, (c) Grain 3, Euler angle: 37.9°, 82.5°, 13.3° and (d) Grain 4, Euler angle: 166.2°, 87.1°, 26.3°. The IPF maps are colored with hydrogen diffusion direction. Grain boundaries are indicated by black line.
Fig. 3. (a) ND-IPF map of Ti matrix and hydride precipitates with corresponding color code. (b) Phase map with Ti matrix in silver and white hydride. The hydride and twin boundaries are highlighted by color lines: {$10\bar{1}2$} extension twins (green), {$11\bar{2}2$} contraction twins (orange), interface planes of OR1 hydrides (blue) and OR2 hydrides (pink). Black lines refer to grain boundaries.
| Variant 1 | Variant 2 | Variant 3 | Variant 4 | Variant 5 | Variant 6 | |
|---|---|---|---|---|---|---|
| OR1 hydride (Pi) | ($10\bar{1}0$) | ($01\bar{1}0$) | ($\bar{1}100$) | |||
| OR2 hydride (Bi) | ($10\bar{1}3$)[$10\bar{1}0$] | ($01\bar{1}3$)[$01\bar{1}0$] | ($\bar{1}103$)[$\bar{1}100$] | ($\bar{1}013$)[$\bar{1}010$] | ($0\bar{1}13$)[$0\bar{1}10$] | ($1\bar{1}03$)[$1\bar{1}00$] |
| {$10\bar{1}2$} twin (TiI) | ($10\bar{1}2$)[$\bar{1}011$] | ($01\bar{1}2$)[$0\bar{1}11$] | ($\bar{1}102$)[$1\bar{1}01$] | ($\bar{1}012$)[$10\bar{1}1$] | ($0\bar{1}12$)[$01\bar{1}1$] | ($1\bar{1}02$)[$\bar{1}101$] |
| {$11\bar{2}2$} twin (CiI) | ($11\bar{2}2$)[$11\bar{2}\bar{3}$] | ($\bar{1}2\bar{1}2$)[$\bar{1}2\bar{1}\bar{3}$] | ($\bar{2}112$)[$\bar{2}11\bar{3}$] | ($\bar{1}\bar{1}22$)[$\bar{1}\bar{1}2\bar{3}$] | ($1\bar{2}12$)[$1\bar{2}1\bar{3}$] | ($2\bar{1}\bar{1}2$)[$2\bar{1}\bar{1}\bar{3}$] |
Table 2 Variants of hydride and twin.
| Variant 1 | Variant 2 | Variant 3 | Variant 4 | Variant 5 | Variant 6 | |
|---|---|---|---|---|---|---|
| OR1 hydride (Pi) | ($10\bar{1}0$) | ($01\bar{1}0$) | ($\bar{1}100$) | |||
| OR2 hydride (Bi) | ($10\bar{1}3$)[$10\bar{1}0$] | ($01\bar{1}3$)[$01\bar{1}0$] | ($\bar{1}103$)[$\bar{1}100$] | ($\bar{1}013$)[$\bar{1}010$] | ($0\bar{1}13$)[$0\bar{1}10$] | ($1\bar{1}03$)[$1\bar{1}00$] |
| {$10\bar{1}2$} twin (TiI) | ($10\bar{1}2$)[$\bar{1}011$] | ($01\bar{1}2$)[$0\bar{1}11$] | ($\bar{1}102$)[$1\bar{1}01$] | ($\bar{1}012$)[$10\bar{1}1$] | ($0\bar{1}12$)[$01\bar{1}1$] | ($1\bar{1}02$)[$\bar{1}101$] |
| {$11\bar{2}2$} twin (CiI) | ($11\bar{2}2$)[$11\bar{2}\bar{3}$] | ($\bar{1}2\bar{1}2$)[$\bar{1}2\bar{1}\bar{3}$] | ($\bar{2}112$)[$\bar{2}11\bar{3}$] | ($\bar{1}\bar{1}22$)[$\bar{1}\bar{1}2\bar{3}$] | ($1\bar{2}12$)[$1\bar{2}1\bar{3}$] | ($2\bar{1}\bar{1}2$)[$2\bar{1}\bar{1}\bar{3}$] |
Fig. 4. (a) IPF map of Grain I (Euler angles: 116.0°, 98.2°, 21.1°) containing OR1 hydrides. The color code for the IPF maps is the same as Fig. 4. (b) {$10\bar{1}0$} pole figure, the black dots represent the planes of Ti matrix and the color ones represent the hydride planes. The dotted lines represent the traces of corresponding interface planes of hydrides. (c) IGMA distributions obtained from the misorientation angles of Grain I.
Fig. 5. (a) and (e) ND-IPF map of Grain II (Euler angles: 33.2°, 155.5°, 29.2°) containing {$10\bar{1}2$} twin-hydride pairs and Grain III (Euler angles: 100.2°, 62.6°, 25.1°) containing {$11\bar{2}2$} twin-hydride pairs. (b) and (f) Phase maps of Grain II and Grain III. (c) and (g) Pole figures of {$10\bar{1}3$}, {$10\bar{1}2$} and {$11\bar{2}2$} planes. The black dots represent the planes of Ti matrix and the color ones are the planes of hydrides or twins. The dotted lines represent the traces of corresponding interface planes of hydrides. (d) and (h) IPF contouring maps of all the grains with respective {$10\bar{1}2$} and {$11\bar{2}2$} twin-hydride pairs. The OR1 and OR2 favorable orientations are indicated by red points.
Fig. 6. Illustration of HCP-FCC structure transformations of (a) OR1 and (b) OR2 hydrides. The filled and open circles are in the different atom layers.
| Twinning (DT) | ||
|---|---|---|
| OR2 hydride (DH) | TI{$10\bar{1}2$}<$\bar{1}011$> | CI{$11\bar{2}2$}<$11\bar{2}\bar{3}$> |
| $\left[\begin{array}{ccc}0.055 & 0 & 0.384 \\ 0 & 0.055 & 0 \\ 0 & 0 & 0.086\end{array}\right]$ | $\left[\begin{array}{ccc}0 & 0 & 0.173 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right]$ | $\left[\begin{array}{ccc}0 & 0 & 0.218 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right]$ |
Table 3 Displacement gradient tensor of OR2 hydriding and twinning in α-titanium (c/a=1.587).
| Twinning (DT) | ||
|---|---|---|
| OR2 hydride (DH) | TI{$10\bar{1}2$}<$\bar{1}011$> | CI{$11\bar{2}2$}<$11\bar{2}\bar{3}$> |
| $\left[\begin{array}{ccc}0.055 & 0 & 0.384 \\ 0 & 0.055 & 0 \\ 0 & 0 & 0.086\end{array}\right]$ | $\left[\begin{array}{ccc}0 & 0 & 0.173 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right]$ | $\left[\begin{array}{ccc}0 & 0 & 0.218 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right]$ |
| Variant 1 | Variant 2 | Variant 3 | Variant 4 | Variant 5 | Variant 6 | |
|---|---|---|---|---|---|---|
| B5 (Grain I) | $\mathbf{T}_{\mathbf{1}}^{\mathbf{I}}$+0.071 | $\mathbf{T}_{\mathbf{2}}^{\mathbf{I}}$+0.063 | $\mathbf{T}_{\mathbf{3}}^{\mathbf{I}}$+0.071 | $\mathbf{T}_{\mathbf{4}}^{\mathbf{I}}$+0.066 | $\mathbf{T}_{\mathbf{5}}^{\mathbf{I}}$+0.052 | $\mathbf{T}_{\mathbf{6}}^{\mathbf{I}}$+0.065 |
| $~\text{C}_{1}^{\text{I}}$-0.038 | $\text{C}_{2}^{\text{I}}$-0.038 | $\text{C}_{3}^{\text{I}}$-0.081 | $\text{C}_{4}^{\text{I}}$-0.100 | $\text{C}_{5}^{\text{I}}$-0.100 | $\text{C}_{6}^{\text{I}}$-0.082 | |
| B2(Grain II) | $\mathbf{T}_{\mathbf{1}}^{\mathbf{I}}$ +0.004 | $\mathbf{T}_{\mathbf{2}}^{\mathbf{I}}$-0.056 | $\mathbf{T}_{\mathbf{3}}^{\mathbf{I}}$-0.008 | $\mathbf{T}_{\mathbf{4}}^{\mathbf{I}}$-0.009 | $\mathbf{T}_{\mathbf{5}}^{\mathbf{I}}$-0.044 | $\mathbf{T}_{\mathbf{6}}^{\mathbf{I}}$-0.001 |
| $~\text{C}_{1}^{\text{I}}$0.000 | $\text{C}_{2}^{\text{I}}$+0.008 | $\text{C}_{3}^{\text{I}}$-0.024 | $\text{C}_{4}^{\text{I}}$+0.063 | $\text{C}_{5}^{\text{I}}$+0.078 | $\text{C}_{6}^{\text{I}}$-0.017 |
Table 4 The values $\text{D}_{33}^{\text{S}}$ obtained by transforming displacement gradient tensors from {$10\bar{1}2$} and {$11\bar{2}2$} twinning frames into sample frame. The bold variants are more favorable.
| Variant 1 | Variant 2 | Variant 3 | Variant 4 | Variant 5 | Variant 6 | |
|---|---|---|---|---|---|---|
| B5 (Grain I) | $\mathbf{T}_{\mathbf{1}}^{\mathbf{I}}$+0.071 | $\mathbf{T}_{\mathbf{2}}^{\mathbf{I}}$+0.063 | $\mathbf{T}_{\mathbf{3}}^{\mathbf{I}}$+0.071 | $\mathbf{T}_{\mathbf{4}}^{\mathbf{I}}$+0.066 | $\mathbf{T}_{\mathbf{5}}^{\mathbf{I}}$+0.052 | $\mathbf{T}_{\mathbf{6}}^{\mathbf{I}}$+0.065 |
| $~\text{C}_{1}^{\text{I}}$-0.038 | $\text{C}_{2}^{\text{I}}$-0.038 | $\text{C}_{3}^{\text{I}}$-0.081 | $\text{C}_{4}^{\text{I}}$-0.100 | $\text{C}_{5}^{\text{I}}$-0.100 | $\text{C}_{6}^{\text{I}}$-0.082 | |
| B2(Grain II) | $\mathbf{T}_{\mathbf{1}}^{\mathbf{I}}$ +0.004 | $\mathbf{T}_{\mathbf{2}}^{\mathbf{I}}$-0.056 | $\mathbf{T}_{\mathbf{3}}^{\mathbf{I}}$-0.008 | $\mathbf{T}_{\mathbf{4}}^{\mathbf{I}}$-0.009 | $\mathbf{T}_{\mathbf{5}}^{\mathbf{I}}$-0.044 | $\mathbf{T}_{\mathbf{6}}^{\mathbf{I}}$-0.001 |
| $~\text{C}_{1}^{\text{I}}$0.000 | $\text{C}_{2}^{\text{I}}$+0.008 | $\text{C}_{3}^{\text{I}}$-0.024 | $\text{C}_{4}^{\text{I}}$+0.063 | $\text{C}_{5}^{\text{I}}$+0.078 | $\text{C}_{6}^{\text{I}}$-0.017 |
Fig. 7. Full inverse pole figure of $\text{D}_{33}^{\text{S}}$ value for (a) six {$10\bar{1}2$} twin variants and (b) {$11\bar{2}2$} twin variants
| Variant 1 | Variant 2 | Variant 3 | Variant 4 | Variant 5 | Variant 6 | |
|---|---|---|---|---|---|---|
| B5 (Grain I) | $\mathbf{T}_{\mathbf{1}}^{\mathbf{I}}$ +0.120 | $\mathbf{T}_{\mathbf{2}}^{\mathbf{I}}$+0.224 | $\mathbf{T}_{\mathbf{3}}^{\mathbf{I}}$T3I +0.120 | $\mathbf{T}_{\mathbf{4}}^{\mathbf{I}}$+0.089 | $\mathbf{T}_{\mathbf{5}}^{\mathbf{I}}$-0.193 | $\text{T}_{6}^{\text{I}}$-0.089 |
| $\text{C}_{1}^{\text{I}}$-0.108 | $\text{C}_{2}^{\text{I}}$-0.108 | $\text{C}_{3}^{\text{I}}$-0.014 | $\mathbf{C}_{\mathbf{4}}^{\mathbf{I}}$+0.080 | $\text{C}_{5}^{\text{I}}$+0.080 | $\text{C}_{6}^{\text{I}}$-0.014 | |
| B2 (Grain II) | $\text{C}_{1}^{\text{I}}$+0.080 | $\text{C}_{2}^{\text{I}}$+0.080 | $\text{C}_{3}^{\text{I}}$-0.014 | $\mathbf{C}_{\mathbf{4}}^{\mathbf{I}}$-0.108 | $\text{C}_{5}^{\text{I}}$-0.108 | $\text{C}_{6}^{\text{I}}$-0.014 |
| $\mathbf{T}_{\mathbf{1}}^{\mathbf{I}}$-0.089 | $\mathbf{T}_{\mathbf{2}}^{\mathbf{I}}$-0.193 | $\mathbf{T}_{\mathbf{3}}^{\mathbf{I}}$-0.089 | $\mathbf{T}_{\mathbf{4}}^{\mathbf{I}}$+0.120 | $\mathbf{T}_{\mathbf{5}}^{\mathbf{I}}$+0.224 | $\text{T}_{6}^{\text{I}}$+0.120 |
Table 5 The values $\text{D}_{13}^{\text{H}-\text{T}}$ obtained by transforming displacement gradient tensors from hydriding frame into the twinning frames. The bold variants are more favorable.
| Variant 1 | Variant 2 | Variant 3 | Variant 4 | Variant 5 | Variant 6 | |
|---|---|---|---|---|---|---|
| B5 (Grain I) | $\mathbf{T}_{\mathbf{1}}^{\mathbf{I}}$ +0.120 | $\mathbf{T}_{\mathbf{2}}^{\mathbf{I}}$+0.224 | $\mathbf{T}_{\mathbf{3}}^{\mathbf{I}}$T3I +0.120 | $\mathbf{T}_{\mathbf{4}}^{\mathbf{I}}$+0.089 | $\mathbf{T}_{\mathbf{5}}^{\mathbf{I}}$-0.193 | $\text{T}_{6}^{\text{I}}$-0.089 |
| $\text{C}_{1}^{\text{I}}$-0.108 | $\text{C}_{2}^{\text{I}}$-0.108 | $\text{C}_{3}^{\text{I}}$-0.014 | $\mathbf{C}_{\mathbf{4}}^{\mathbf{I}}$+0.080 | $\text{C}_{5}^{\text{I}}$+0.080 | $\text{C}_{6}^{\text{I}}$-0.014 | |
| B2 (Grain II) | $\text{C}_{1}^{\text{I}}$+0.080 | $\text{C}_{2}^{\text{I}}$+0.080 | $\text{C}_{3}^{\text{I}}$-0.014 | $\mathbf{C}_{\mathbf{4}}^{\mathbf{I}}$-0.108 | $\text{C}_{5}^{\text{I}}$-0.108 | $\text{C}_{6}^{\text{I}}$-0.014 |
| $\mathbf{T}_{\mathbf{1}}^{\mathbf{I}}$-0.089 | $\mathbf{T}_{\mathbf{2}}^{\mathbf{I}}$-0.193 | $\mathbf{T}_{\mathbf{3}}^{\mathbf{I}}$-0.089 | $\mathbf{T}_{\mathbf{4}}^{\mathbf{I}}$+0.120 | $\mathbf{T}_{\mathbf{5}}^{\mathbf{I}}$+0.224 | $\text{T}_{6}^{\text{I}}$+0.120 |
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