Acta Metallurgica Sinica (English Letters) ›› 2018, Vol. 31 ›› Issue (2): 113-126.DOI: 10.1007/s40195-017-0693-1
Special Issue: 2017-2018高温合金专辑； 2018-2019高温合金专辑
• Orginal Article • Next Articles
Wen-Sheng Xu1(
), Xiao-Peng Yang2(), Wen-Zheng Zhang1()
Received:2017-12-19
Revised:2017-12-19
Online:2018-02-20
Published:2018-03-20
Wen-Sheng Xu, Xiao-Peng Yang, Wen-Zheng Zhang. Interpretation of the Habit Plane of δ Precipitates in Superalloy Inconel 718[J]. Acta Metallurgica Sinica (English Letters), 2018, 31(2): 113-126.
| Phase | γ | δ |
|---|---|---|
| Compound | Ni | Ni3Nb |
| Structure | FCC (A1) | Orthorhombic (DOa) |
| Space group | \({\text{Fm}}\bar{3}{\text{m}}\) (225) | Pmmn (59) |
| Parallel vectors | \([1 \;\bar{1} \;0]_{\gamma }\) | \([1\;0\;0]_{\delta }\) |
| Parallel planes | \((1\; 1\; 1)_{\gamma }\) | \((0 \;1 \;0)_{\delta }\) |
| Lattice parameters (nm) | \(a_{\gamma } = 0.3616\) | \(a_{\delta } = 0.5141\) |
| \(b_{\delta } = 0.4231\) | ||
| \(c_{\delta } = 0.4534\) |
Table 1 Initial OR and lattice parameters of the superalloy 718
| Phase | γ | δ |
|---|---|---|
| Compound | Ni | Ni3Nb |
| Structure | FCC (A1) | Orthorhombic (DOa) |
| Space group | \({\text{Fm}}\bar{3}{\text{m}}\) (225) | Pmmn (59) |
| Parallel vectors | \([1 \;\bar{1} \;0]_{\gamma }\) | \([1\;0\;0]_{\delta }\) |
| Parallel planes | \((1\; 1\; 1)_{\gamma }\) | \((0 \;1 \;0)_{\delta }\) |
| Lattice parameters (nm) | \(a_{\gamma } = 0.3616\) | \(a_{\delta } = 0.5141\) |
| \(b_{\delta } = 0.4231\) | ||
| \(c_{\delta } = 0.4534\) |
Fig. 1 According to the initial OR, the simulated diffraction patterns with zone axis: a$[1\overline{1}0]_{\gamma}$//$[100]_{\delta}$, b $[111]_{\gamma}$//$[010]_{\delta}$
| Matrix | |
|---|---|
| \({\mathbf{G}}_{\gamma }^{\gamma }\) | \(\left[ {\begin{array}{*{20}c} 1 & 1 & 1 \\ {\bar{1}} & {\bar{1}} & 1 \\ 2 & {\bar{2}} & 0 \\ \end{array} } \right]\) |
| \({\mathbf{G}}_{\delta }^{\delta }\) | \(\left[ {\begin{array}{*{20}c} 0& 2& 0\\ 0& 0& 2\\ 4& 0& 0\\ \end{array} } \right]\) |
| \({\mathbf{G}}_{\gamma }\) | \(\left[ {\begin{array}{*{20}c} {4.7900} & 0 & 0 \\ { - 1.5967} & {4.5160} & 0 \\ 0 & 0 & {7.8220} \\ \end{array} } \right]\) |
| \({\mathbf{G}}_{\delta }\) | \(\left[ {\begin{array}{*{20}c} { 4. 7 2 7 0} & 0& 0\\ 0& { 4. 4 1 1 1} & 0\\ 0& 0& { 7. 7 8 0 6} \\ \end{array} } \right]\) |
Table 2 Matrices used for OR calculations
| Matrix | |
|---|---|
| \({\mathbf{G}}_{\gamma }^{\gamma }\) | \(\left[ {\begin{array}{*{20}c} 1 & 1 & 1 \\ {\bar{1}} & {\bar{1}} & 1 \\ 2 & {\bar{2}} & 0 \\ \end{array} } \right]\) |
| \({\mathbf{G}}_{\delta }^{\delta }\) | \(\left[ {\begin{array}{*{20}c} 0& 2& 0\\ 0& 0& 2\\ 4& 0& 0\\ \end{array} } \right]\) |
| \({\mathbf{G}}_{\gamma }\) | \(\left[ {\begin{array}{*{20}c} {4.7900} & 0 & 0 \\ { - 1.5967} & {4.5160} & 0 \\ 0 & 0 & {7.8220} \\ \end{array} } \right]\) |
| \({\mathbf{G}}_{\delta }\) | \(\left[ {\begin{array}{*{20}c} { 4. 7 2 7 0} & 0& 0\\ 0& { 4. 4 1 1 1} & 0\\ 0& 0& { 7. 7 8 0 6} \\ \end{array} } \right]\) |
| Matrices and vectors | ||
|---|---|---|
| Initial deformation matrix | \({\mathbf{A}}_{ 0}\) | \(\left[ {\begin{array}{*{20}c} {1.0133} & 0 & 0 \\ { - 0.3620} & {1.0238} & 0 \\ 0 & 0 & {1.0053} \\ \end{array} } \right]\) |
| Rotation matrix | R | \(\left[ {\begin{array}{*{20}c} {0.9999996} & { - 0.0009} & 0 \\ {0.0009} & {0.9999996} & 0 \\ 0 & 0 & 1 \\ \end{array} } \right]\) |
| Final deformation matrix | A | \(\left[ {\begin{array}{*{20}c} {1.0136} & { - 0.0009} & 0 \\ { - 0.3611} & {1.0238} & 0 \\ 0 & 0 & {1.0053} \\ \end{array} } \right]\) |
| Rotation angle | θ | 0.05°(clockwise) |
| HP normal on lattice basis | \({\mathbf{n}}_{\gamma }^{\gamma } /\Delta {\mathbf{g}}'{\text{s}}\) | \((1.15 \;1.15\; 1)_{\gamma }\) |
Table 3 Calculated results of the OR and HP
| Matrices and vectors | ||
|---|---|---|
| Initial deformation matrix | \({\mathbf{A}}_{ 0}\) | \(\left[ {\begin{array}{*{20}c} {1.0133} & 0 & 0 \\ { - 0.3620} & {1.0238} & 0 \\ 0 & 0 & {1.0053} \\ \end{array} } \right]\) |
| Rotation matrix | R | \(\left[ {\begin{array}{*{20}c} {0.9999996} & { - 0.0009} & 0 \\ {0.0009} & {0.9999996} & 0 \\ 0 & 0 & 1 \\ \end{array} } \right]\) |
| Final deformation matrix | A | \(\left[ {\begin{array}{*{20}c} {1.0136} & { - 0.0009} & 0 \\ { - 0.3611} & {1.0238} & 0 \\ 0 & 0 & {1.0053} \\ \end{array} } \right]\) |
| Rotation angle | θ | 0.05°(clockwise) |
| HP normal on lattice basis | \({\mathbf{n}}_{\gamma }^{\gamma } /\Delta {\mathbf{g}}'{\text{s}}\) | \((1.15 \;1.15\; 1)_{\gamma }\) |
Fig. 2 Parallel ?g’s and HP of the final OR in reciprocal space with zone axis \([1 \;\bar{1} \;0]_{\gamma } //[1\; 0 \;0]_{\delta }\)
Fig. 3 Distribution of GMSs in the central GMS clusters and different lattice points on different planes: a plane \((1 \;1 \;1)_{\gamma } //(0 \;1 \;0)_{\delta }\), b plane \((1 \;\bar{1} \;0)_{\gamma } //(1\; 0 \;0)_{\delta }\)
Fig. 4 Large-scale distribution of GMS clusters on different planes: a plane \((1 \;1 \;1)_{\gamma } //(0\; 1 \;0)_{\delta }\), b plane \((1 \;\bar{1}\; 0)_{\gamma } //(1 \;0\; 0)_{\delta }\). \({x}//\left[ {0 \;1\; 0} \right]_{\delta } //[1 \;1 \;1]_{\gamma }\), \({y}//\left[ {0 \;0 \;1} \right]_{\delta } //[1 \;1\; \bar{2}]_{\gamma }\), and \({z}//[1 \;0\; 0]_{\delta } //[1\; \bar{1} \;0]_{\gamma }\)
Fig. 5 Configuration of GMS clusters on different terrace planes connected by steps on the stepped interface
Fig. 6 a CCSL and CDSCL on zero layer of δ phase, b CDSCL on the next layer, c CDSCL and CCSL perpendicular to the terrace plane
| δ | γ | |
|---|---|---|
| CCSL on lattice basis | \(\left[ {\begin{array}{*{20}c} 0 & 0 & 1 \\ 3 & 0 & 0 \\ 0 & 1 & 0 \\ \end{array} } \right]\) | \(\left[ {\begin{array}{*{20}c} 2 & {1/2} & 1 \\ 2 & {1/2} & {\bar{1}} \\ 2 & {\bar{1}} & 0 \\ \end{array} } \right]\) |
| CDSCL on lattice basis | \(\left[ {\begin{array}{*{20}c} 0 & 0 & {1/2} \\ {1/2} & 0 & 0 \\ 0 & {1/3} & 0 \\ \end{array} } \right]\) | \(\left[ {\begin{array}{*{20}c} { 1 / 3} & { 1 / 6} & { 1 / 2} \\ { 1 / 3} & { 1 / 6} & {\overline{ 1 / 2} } \\ { 1 / 3} & {\overline{ 1 / 3} } & 0\\ \end{array} } \right]\) |
| CCSL on the orthonormal basis (\({\mathbf{S}}_{\delta }^{\text{II}}\),\({\mathbf{S}}_{\gamma }^{\text{II}}\)) | \(\left[ {\begin{array}{*{20}c} {1.2693} & 0 & 0 \\ 0 & {0.4534} & 0 \\ 0 & 0 & {0.5141} \\ \end{array} } \right]\) | \(\left[ {\begin{array}{*{20}c} {1.2526} & 0 & 0 \\ 0 & {0.4429} & 0 \\ 0 & 0 & {0.5113} \\ \end{array} } \right]\) |
| Transformation matrix \({\mathbf{A}}^{\text{II}}\) | \(\left[ {\begin{array}{*{20}c} {1.0133} & 0 & 0 \\ 0 & {1.0238} & 0 \\ 0 & 0 & {1.0053} \\ \end{array} } \right]\) |
Table 4 Choice of CCSL, CDSCL, and the transformation matrix
| δ | γ | |
|---|---|---|
| CCSL on lattice basis | \(\left[ {\begin{array}{*{20}c} 0 & 0 & 1 \\ 3 & 0 & 0 \\ 0 & 1 & 0 \\ \end{array} } \right]\) | \(\left[ {\begin{array}{*{20}c} 2 & {1/2} & 1 \\ 2 & {1/2} & {\bar{1}} \\ 2 & {\bar{1}} & 0 \\ \end{array} } \right]\) |
| CDSCL on lattice basis | \(\left[ {\begin{array}{*{20}c} 0 & 0 & {1/2} \\ {1/2} & 0 & 0 \\ 0 & {1/3} & 0 \\ \end{array} } \right]\) | \(\left[ {\begin{array}{*{20}c} { 1 / 3} & { 1 / 6} & { 1 / 2} \\ { 1 / 3} & { 1 / 6} & {\overline{ 1 / 2} } \\ { 1 / 3} & {\overline{ 1 / 3} } & 0\\ \end{array} } \right]\) |
| CCSL on the orthonormal basis (\({\mathbf{S}}_{\delta }^{\text{II}}\),\({\mathbf{S}}_{\gamma }^{\text{II}}\)) | \(\left[ {\begin{array}{*{20}c} {1.2693} & 0 & 0 \\ 0 & {0.4534} & 0 \\ 0 & 0 & {0.5141} \\ \end{array} } \right]\) | \(\left[ {\begin{array}{*{20}c} {1.2526} & 0 & 0 \\ 0 & {0.4429} & 0 \\ 0 & 0 & {0.5113} \\ \end{array} } \right]\) |
| Transformation matrix \({\mathbf{A}}^{\text{II}}\) | \(\left[ {\begin{array}{*{20}c} {1.0133} & 0 & 0 \\ 0 & {1.0238} & 0 \\ 0 & 0 & {1.0053} \\ \end{array} } \right]\) |
Fig. 7 Edge-on view of the stepped interface and its association with GMS clusters connected by up-steps. \({x}//\left[ {0 \;1 \;0} \right]_{\delta } //[1 \;1\; 1]_{\gamma }\) and \({y}//\left[ {0 \;0 \;1} \right]_{\delta } //[1 \;1 \;\bar{2}]_{\gamma }\)
Fig. 8 Another group of parallel ? g’s and the corresponding HP trace with zone axis \([1 \;\bar{1} \;0]_{\gamma } //[1 \;0 \;0]_{\delta }\)
| Matrices and vectors | |
|---|---|
| \({\mathbf{G}}_{\gamma }^{\gamma }\) | \(\left[ {\begin{array}{*{20}c} 1 & 1 & 1 \\ {\bar{1}} & {\bar{1}} & 1 \\ 1 & {\bar{1}} & 0 \\ \end{array} } \right]\) |
| \({\mathbf{G}}_{\delta }^{\delta }\) | \(\left[ {\begin{array}{*{20}c} 0& 2& 0\\ 0& {{\bar{\text{1}}}} & 2\\ 2& 0& 0\\ \end{array} } \right]\) |
| \({\mathbf{G}}_{\gamma }\) | \(\left[ {\begin{array}{*{20}c} {4.7900} & 0 & 0 \\ { - 1.5967} & {4.5160} & 0 \\ 0 & 0 & {3.9110} \\ \end{array} } \right]\) |
| \({\mathbf{G}}_{\delta }\) | \(\left[ {\begin{array}{*{20}c} {4.7270} & 0 & 0 \\ { - 2.3640} & {4.4111} & 0 \\ 0 & 0 & {3.8903} \\ \end{array} } \right]\) |
| \({\mathbf{A}}_{0}^{'}\) | \(\left[ {\begin{array}{*{20}c} { 1. 0 1 3 3} & 0& 0\\ { 0. 1 8 1 0} & { 1. 0 2 3 8} & 0\\ 0& 0& { 1. 0 0 5 3} \\ \end{array} } \right]\) |
| R | \(\left[ {\begin{array}{*{20}c} {0.999998} & {0.0018} & 0 \\ { - 0.0018} & {0.999998} & 0 \\ 0 & 0 & 1 \\ \end{array} } \right]\) |
| A′ | \(\left[ {\begin{array}{*{20}c} {1.0136} & {0.0018} & 0 \\ {0.1792} & {1.0238} & 0 \\ 0 & 0 & {1.0053} \\ \end{array} } \right]\) |
| θ | - 0.10° |
| \(n_{\gamma }^{\gamma } /\Delta {\mathbf{g}}'{\text{s}}\) | \([1 \;1 \;1.31]_{\gamma }\) |
Table 5 Results in the calculation process of HPII
| Matrices and vectors | |
|---|---|
| \({\mathbf{G}}_{\gamma }^{\gamma }\) | \(\left[ {\begin{array}{*{20}c} 1 & 1 & 1 \\ {\bar{1}} & {\bar{1}} & 1 \\ 1 & {\bar{1}} & 0 \\ \end{array} } \right]\) |
| \({\mathbf{G}}_{\delta }^{\delta }\) | \(\left[ {\begin{array}{*{20}c} 0& 2& 0\\ 0& {{\bar{\text{1}}}} & 2\\ 2& 0& 0\\ \end{array} } \right]\) |
| \({\mathbf{G}}_{\gamma }\) | \(\left[ {\begin{array}{*{20}c} {4.7900} & 0 & 0 \\ { - 1.5967} & {4.5160} & 0 \\ 0 & 0 & {3.9110} \\ \end{array} } \right]\) |
| \({\mathbf{G}}_{\delta }\) | \(\left[ {\begin{array}{*{20}c} {4.7270} & 0 & 0 \\ { - 2.3640} & {4.4111} & 0 \\ 0 & 0 & {3.8903} \\ \end{array} } \right]\) |
| \({\mathbf{A}}_{0}^{'}\) | \(\left[ {\begin{array}{*{20}c} { 1. 0 1 3 3} & 0& 0\\ { 0. 1 8 1 0} & { 1. 0 2 3 8} & 0\\ 0& 0& { 1. 0 0 5 3} \\ \end{array} } \right]\) |
| R | \(\left[ {\begin{array}{*{20}c} {0.999998} & {0.0018} & 0 \\ { - 0.0018} & {0.999998} & 0 \\ 0 & 0 & 1 \\ \end{array} } \right]\) |
| A′ | \(\left[ {\begin{array}{*{20}c} {1.0136} & {0.0018} & 0 \\ {0.1792} & {1.0238} & 0 \\ 0 & 0 & {1.0053} \\ \end{array} } \right]\) |
| θ | - 0.10° |
| \(n_{\gamma }^{\gamma } /\Delta {\mathbf{g}}'{\text{s}}\) | \([1 \;1 \;1.31]_{\gamma }\) |
Fig. 9 Experimental results of the interface of δ phase: a contrast of two groups of steps associated with dislocations, b high-resolution image of the HP, c extended schematic diagram corresponding to b [11]
Fig. 10 Configuration of GMS cluster under different view directions using the atomic points, a atomic figure of Fig. 4a, b atomic figure of Fig. 4b, c partical enlarged view of b. \({x}//\left[ {0\; 1 \;0} \right]_{\delta } //[1\; 1 \;1]_{\gamma }\), \({y}//\left[ {0 \;0 \;1} \right]_{\delta } //[1 \;1\; \bar{2}]_{\gamma }\), and \({z}//[1 \;0\; 0]_{\delta } //[1\; \bar{1} \;0]_{\gamma }\)
Fig. 11 Based on atomic points: a CCSL and CDSCL on zero atomic layer of δ phase, b CDSCL on the next atomic layer, c CDSCL and CCSL perpendicular to the terrace plane
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