The Crystallography of Diverse IntermetallicPhases in Binary La-Ni Alloy Obtained by Melting and Its Structural Evolution under HighTemperature Sintering

Abstract

In this study, we have investigated thestructural evolution of binary La-Ni alloy under different heat treatments bycombing single crystal X-ray diffraction (SXRD) as well as scanning electronmicroscope (SEM) and transmission electron microscopy (TEM). It has been foundthat LaNi and La₇Ni₃ can be successfully synthesizedthrough the arc melting method. Then it was found that LaNi₅ appearsin the binary La-Ni mixture wrapped by a Tantalum sheet, followed byhigh-temperature sintering. Next, some pilot experiments have been carried outon the La-Ni mixture by sealing tube technique with some residual oxygen.Serendipitously, oxidation has not been found while La₃Ni₃Si₂ and La₂NiSi besides LaNi phase show up. Meanwhile, the detailedcrystal structure information and their topological features of theaforementioned phases as well as their high-resolution TEM images, have beenobtained. Furthermore, the orientation relationships of the Si-contaminatedmixed phases have been thoroughly investigated by advanced precession images ofSXRD patterns.

Keywords

LaNi / La₇Ni₃ / LaNi₅ / La₃Ni₃Si₂ / La₂NiSi / Single crystal / Crystal structure / Orientation relationship

Supplementary Materials

The following supporting information can be found at: https://www.sciepublish.com/article/pii/658, Figure S1: Reciprocal lattice patterns of the La₇Ni₃ phase projected in three axes: (a) a^∗ axis; (b) b^∗ axis; (c) c^∗ axis and its crystal structure projected in c axis (d); Figure S2: Reciprocal lattice patterns of the LaNi phase projected in three axes: (a) a^∗ axis; (b) b^∗ axis; (c) c^∗ axis, and its crystal structure projected in c axis (d); Figure S3: Reciprocal lattice patterns of the LaNi₅ phase projected in three axes: (a) a^∗ axis; (b) b^∗ axis; (c) c^∗ axis, and its crystal structure projected in c axis (d); Figure S4: (a) The Phi360 diffraction pattern collected in the process of single crystal testing, (b) the powder diffraction pattern obtained by integrating the Phi360 diffraction pattern; Figure S5: Powder diffraction pattern of the remaining 1094 diffraction points (margin). Figure S6: Reciprocal lattice patterns of the LaNi phase projected in three axes: (a) a^∗ axis; (b) b^∗ axis; (c) c^∗ axis, and its crystal structure projected in c axis (d); Figure S7: Reciprocal lattice patterns of the La₃Ni₃Si₂ phase projected in three axes: (a) a^∗ axis; (b) b^∗ axis; (c) c^∗ axis, and its crystal structure projected in c axis (d); Figure S8: Reciprocal lattice patterns of the La₂NiSi phase projected in three axes: (a) a^∗ axis; (b) b^∗ axis; (c) c^∗ axis, and its crystal structure projected in c axis (d); Figure S9: The precession images (a) (0kl), (b) (h0l), (c) (hk0) crystal planes of LaNi phase in the SXRD test, LaNi phase simulated diffraction pattern with axes in (d) [100], (e) [010], and (f) [001]; Figure S10: The precession images (a) (0kl), (b) (h0l), (c) (hk0) crystal planes of La₃Ni₃Si₂ phase in the SXRD test, La₃Ni₃Si₂ phase simulated diffraction pattern with axes in (d) [100], (e) [010], and (f) [001]; Figure S11: The precession images (a) (0kl), (b) (h0l), (c) (hk0) crystal planes of La₂NiSi phase in the SXRD test, La₂NiSi phase simulated diffraction pattern with axes in (d) [100], (e) [010], and (f) [001]; Figure S12: Scanning electron microscope (SEM) micrographs of a single crystal sample. EDX analysis was performed for various locations as indicated in Table S1; Table S1: The EDX results conducted at every scanning location in Figure S12; Figure S13: Scanning electron microscope (SEM) micrographs of single crystal sample. EDX analysis was performed for various locations as indicated in Table S2; Table S2: The EDX results conducted at every scanning location in Figure S13; Figure S14: The precession images: (a) LaNi (1kl), (b) LaNi (h1l), (c) LaNi (hk1), (d) La₃Ni₃Si₂ (1kl), (e) La₃Ni₃Si₂ (h1l), (f) La₃Ni₃Si₂ (hk1); Figure S15: The precession images: (a) LaNi (2kl), (b) LaNi (h2l), (c) LaNi (hk2), (d) La₃Ni₃Si₂ (2kl), (e) La₃Ni₃Si₂ (h2l), (f) La₃Ni₃Si₂ (hk2); Figure S16: The precession images: (a) LaNi (3kl), (b) LaNi (h3l), (c) LaNi (hk3), (d) La₃Ni₃Si₂ (3kl), (e) La₃Ni₃Si₂ (h3l), (f) La₃Ni₃Si₂ (hk3); Figure S17: The precession images: (a) La₃Ni₃Si₂ (1kl), (b) La₃Ni₃Si₂ (h1l), (c) La₃Ni₃Si₂ (hk1), (d) La₂NiSi (1kl), (e) La₂NiSi (h1l), (f) La₂NiSi (hk1); Figure S18: The precession images: (a) La₃Ni₃Si₂ (2kl), (b) La₃Ni₃Si₂ (h2l), (c) La₃Ni₃Si₂ (hk2), (d) La₂NiSi (2kl), (e) La₂NiSi (h2l), (f) La₂NiSi (hk2); Figure S19: The precession images: (a) La₃Ni₃Si₂ (3kl), (b) La₃Ni₃Si₂ (h3l), (c) La₃Ni₃Si₂ (hk3), (d) La₂NiSi (3kl), (e) La₂NiSi (h3l), (f) La₂NiSi (hk3); Figure S20: (a)La-Ni binary convex hull, (b) La-Ni binary phase diagram; Figure S21: La-Ni-Si ternary phase diagram; Table S3: Crystallographic and experimental data of La₃Ni₃Si₂ phase in another sample; Table S4: Fractional atomic coordinates and equivalent isotropic displacement parameters (Ų) of La₃Ni₃Si₂ phase in another sample.

Appendix A

During data processing, the orientation matrix is a 3 × 3 matrix, which specifies the component values and orientations of the three reciprocal axes based on the x, y, and z coordinates on the goniometer. This matrix therefore contains the basic data that defines the reciprocal cell and its spatial orientation. The orientation matrix in reciprocal space can be described as:

http://www.w3.org/1998/Math/MathML" display="block">R=(ax∗bx∗cx∗ay∗by∗cy∗az∗bz∗cz∗) \mathrm{R} = \begin{pmatrix} a_{x}^{∗} & b_{x}^{∗} & c_{x}^{∗} \\ a_{y}^{∗} & b_{y}^{∗} & c_{y}^{∗} \\ a_{z}^{∗} & b_{z}^{∗} & c_{z}^{∗} \end{pmatrix}R=​ax∗​ay∗​az∗​​bx∗​by∗​bz∗​​cx∗​cy∗​cz∗​​​

(A1)

a∗a^{∗} a∗corresponds to the first column, b∗b^{∗}b∗ to the second, c∗c^{∗}c∗ to the third. The subscripts x, y, and z indicate the Cartesian coordinates of the diffractometer.

The orientation matrix of LaNi, La₃Ni₃Si₂ and La₂NiSi phases in the reciprocal space was recorded using APEX3 software, where the orientation matrix of LaNi phase in the reciprocal space is:

http://www.w3.org/1998/Math/MathML" display="block">(+0.08751311−0.00740845−0.21358819+0.23488939+0.02130833+0.07239119+0.04850991−0.08981182+0.03479378)\begin{pmatrix} + 0 . 08751311 & - 0 . 00740845 & - 0 . 21358819 \\ + 0 . 23488939 & + 0 . 02130833 & + 0 . 07239119 \\ + 0 . 04850991 & - 0 . 08981182 & + 0 . 03479378 \end{pmatrix}​+0.08751311+0.23488939+0.04850991​−0.00740845+0.02130833−0.08981182​−0.21358819+0.07239119+0.03479378​​

(A2)

The orientation matrix of La₃Ni₃Si₂ phase in reciprocal space is:

http://www.w3.org/1998/Math/MathML" display="block">(+0.06037243+0.00620812−0.06503084+0.12217132−0.08172383+0.01862565−0.09075078−0.10588900−0.01818771)\begin{pmatrix} + 0 . 06037243 & + 0 . 00620812 & - 0 . 06503084 \\ + 0 . 12217132 & - 0 . 08172383 & + 0 . 01862565 \\ - 0 . 09075078 & - 0 . 10588900 & - 0 . 01818771 \end{pmatrix}​+0.06037243+0.12217132−0.09075078​+0.00620812−0.08172383−0.10588900​−0.06503084+0.01862565−0.01818771​​

(A3)

The orientation matrix of La₂NiSi phase in reciprocal space is:

http://www.w3.org/1998/Math/MathML" display="block">(+0.01006662−0.01470755−0.21359995+0.05206853−0.01050337+0.07254676−0.04672600−0.06833122+0.03482372)\begin{pmatrix} + 0 . 01006662 & - 0 . 01470755 & - 0 . 21359995 \\ + 0 . 05206853 & - 0 . 01050337 & + 0 . 07254676 \\ - 0 . 04672600 & - 0 . 06833122 & + 0 . 03482372 \end{pmatrix}​+0.01006662+0.05206853−0.04672600​−0.01470755−0.01050337−0.06833122​−0.21359995+0.07254676+0.03482372​​

(A4)

From the basic correspondence between reciprocal space and real space:

http://www.w3.org/1998/Math/MathML" display="block">a∗⋅a=b∗⋅b=c∗⋅c=1 a^{∗} \cdot a = b^{∗} \cdot b = c^{∗} \cdot c = 1a∗⋅a=b∗⋅b=c∗⋅c=1

(A5)

One can derive the orientation matrix of these two phases in real space. Where the orientation matrix of LaNi phase in real space is:

http://www.w3.org/1998/Math/MathML" display="block">(+1.34253892+3.60343910+0.74419088−0.86394990+2.48490911−10.4735680−4.10186403+1.39023996+0.66819876)\begin{pmatrix} + 1 . 34253892 & + 3 . 60343910 & + 0 . 74419088 \\ - 0 . 86394990 & + 2 . 48490911 & - 10 . 4735680 \\ - 4 . 10186403 & + 1 . 39023996 & + 0 . 66819876 \end{pmatrix}​+1.34253892−0.86394990−4.10186403​+3.60343910+2.48490911+1.39023996​+0.74419088−10.4735680+0.66819876​​

(A6)

The orientation matrix of La₃Ni₃Si₂ phase in real space is:

http://www.w3.org/1998/Math/MathML" display="block">(+2.25216729+4.55754897−3.38541900+0.34624554−4.55798760−5.90575284−13.25342951+3.79594931−3.70669660)\begin{pmatrix} + 2 . 25216729 & + 4 . 55754897 & - 3 . 38541900 \\ + 0 . 34624554 & - 4 . 55798760 & - 5 . 90575284 \\ - 13 . 25342951 & + 3 . 79594931 & - 3 . 70669660 \end{pmatrix}​+2.25216729+0.34624554−13.25342951​+4.55754897−4.55798760+3.79594931​−3.38541900−5.90575284−3.70669660​​

(A7)

The orientation matrix of La₂NiSi phase in real space is:

http://www.w3.org/1998/Math/MathML" display="block">(+4.64935674+15.29827923−3.35226173−5.26866880−9.751584356−12.00163398−4.09975509+1.39243421+0.66839289)\begin{pmatrix} + 4 . 64935674 & + 15 . 29827923 & - 3 . 35226173 \\ - 5 . 26866880 & - 9 . 751584356 & - 12 . 00163398 \\ - 4 . 09975509 & + 1 . 39243421 & + 0 . 66839289 \end{pmatrix}​+4.64935674−5.26866880−4.09975509​+15.29827923−9.751584356+1.39243421​−3.35226173−12.00163398+0.66839289​​

(A8)

Through the orientation matrix of LaNi, La₃Ni₃Si₂ and La₂NiSi phases in real space, the comprehensive models of LaNi, La₃Ni₃Si₂ and La₂NiSi described with cell edges in real space can be constructed. As shown in Figure 17a of the main text.

Now we can add the specific atoms for both phases to the orientation models described with cell edges by acknowledging the experimental orientation matrix and the Crystallographic Information File (CIF) related orientation matrix. Firstly, the positions of the atoms of the LaNi phase in real space are introduced. We named the experimental orientation matrix of the phase in the real space as matrix B. The CIF-related orientation matrix corresponding to the LaNi is described as:

http://www.w3.org/1998/Math/MathML" display="block">A=(3.921300010.79700004.3833) \mathrm{A} = \begin{pmatrix} 3 . 9213 & 0 & 0 \\ 0 & 10 . 7970 & 0 \\ 0 & 0 & 4 . 3833 \end{pmatrix}A=​3.921300​010.79700​004.3833​​

(A9)

Based on matrix A and matrix B, one can find the transformation relationship between the two matrices, let AC = B, then the matrix C is:

http://www.w3.org/1998/Math/MathML" display="block">C=(+0.34235872+0.91891647+0.18977683−0.08002272+0.23016517−0.97011617−0.93585766+0.31718914+0.15245238) \mathrm{C} = \begin{pmatrix} + 0 . 34235872 & + 0 . 91891647 & + 0 . 18977683 \\ - 0 . 08002272 & + 0 . 23016517 & - 0 . 97011617 \\ - 0 . 93585766 & + 0 . 31718914 & + 0 . 15245238 \end{pmatrix}C=​+0.34235872−0.08002272−0.93585766​+0.91891647+0.23016517+0.31718914​+0.18977683−0.97011617+0.15245238​​

(A10)

Then the cartesian coordinates of the atoms in the CIF of LaNi are multiplied by the matrix C, resulting the coordinate positions of the atoms of the LaNi phase in real space. Secondly, the coordinate positions of the atoms of the La₃Ni₃Si₂ phase and La₂NiSi phase in real space are also obtained in the same way. Finally, the comprehensive oriented structural models of LaNi, La₃Ni₃Si₂ and La₂NiSi phases in real space are obtained, Figure 17b, 17c and 17d in the main text are the projection of the orientation matrix in a, b and c after filling the atoms, respectively.

Acknowledgments

The authors express gratitude to the Fund of National Natural Science Foundation of China (grant No. 52173231; grant No. 51925105), Hebei Natural Science Foundation (grant No. E2022203182; grant No. E2020203158), Project of Hebei Provincial Department of Human Resources and Social Security (grant No. E2020100006), The Innovation Ability Promotion Project of Hebei supported by Hebei Key Lab for Optimizing Metal Product Technology and Performance (grant No. 22567609H) for providing financial support for this study.

Author Contributions

Conceptualization, C.F., B.W. and L.Z.; methodology, Y.L. and C.F.; investigation, Y.L., T.R., Z.X. and Y.W., C.F.; writing—original draft preparation, Y.L. and T.R.; writing—review and editing, Z.X., Y.W., C.F., B.W. and L.Z.; supervision, C.F., B.W. and L.Z.; funding acquisition, C.F., B.W. and Z.X. All authors have read and agreed to the published version of the manuscript.

Ethics Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data will be made available on request.

Funding

This research was funded by National Natural Science Foundation of China (grant No. 52173231; grant No. 51925105), Hebei Natural Science Foundation (grant No. E2022203182; grant No. E2020203158), Project of Hebei Provincial Department of Human Resources and Social Security (grant No. E2020100006), and The Innovation Ability Promotion Project of Hebei supported by Hebei Key Lab for Optimizing Metal Product Technology and Performance (grant No. 22567609H).

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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