The Crystallography of Diverse Intermetallic Phases in Binary La-Ni Alloy Obtained by Melting and Its Structural Evolution under High Temperature Sintering
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Other Information
1
State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, China
2
Hebei Key Lab for Optimizing Metal Product Technology and Performance, Yanshan University, Qinhuangdao 066004, China
3
School of Mechanical and Materials Engineering, North China University of Technology, Beijing 100144, China
*
Authors to whom correspondence should be addressed.
†
These authors contribute equally.
Received: 24 July 2025 Accepted: 27 August 2025 Published: 02 September 2025
© 2025 The authors. This is an open access article under the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/).
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Green Chem. Technol.
2025,
2(3), 10014;
DOI: 10.70322/gct.2025.10014
ABSTRACT:
In this study, we have investigated the
structural evolution of binary La-Ni alloy under different heat treatments by
combing single crystal X-ray diffraction (SXRD) as well as scanning electron
microscope (SEM) and transmission electron microscopy (TEM). It has been found
that LaNi and La7Ni3 can be successfully synthesized
through the arc melting method. Then it was found that LaNi5 appears
in the binary La-Ni mixture wrapped by a Tantalum sheet, followed by
high-temperature sintering. Next, some pilot experiments have been carried out
on 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 detailed
crystal structure information and their topological features of the
aforementioned phases as well as their high-resolution TEM images, have been
obtained. Furthermore, the orientation relationships of the Si-contaminated
mixed phases have been thoroughly investigated by advanced precession images of
SXRD patterns.
Keywords:
LaNi; La7Ni3; LaNi5;
La3Ni3Si2; La2NiSi; Single crystal;
Crystal structure; Orientation relationship
1. Introduction
The study of intermetallic compounds, especially those involving rare earth elements, has attracted much attention due to their interesting magnetic, electrical, and structural properties [1,2,3]. For instance, the recently reported La-F-Se compounds exhibit exceptional electronic characteristics [4,5]. Notably, the La-Ni system and the La-Ni-Si ternary system have been identified as promising materials for various applications, including hydrogen storage alloys [6,7,8,9,10], battery electrodes [11], thermoelectric materials [12], superconducting materials [13,14,15,16,17,18], and catalytic materials [19,20,21].
The La-Ni binary alloy system contains numerous compounds of various types and proportions, which have been thoroughly explored and extensively researched. These different ratios contribute to the diverse performance characteristics of the alloys. Buschow and Yamamoto synthesized a series of La-Ni binary alloys with varying ratios in their respective research teams. The alteration of the ratio resulted in changes in the crystal microstructure, ultimately impacting the hydrogen absorption and release capabilities of the alloy [22,23]. The influence of this phenomenon on the thermodynamic properties of the alloy material was further investigated in a subsequent study by Dischinger et al. [24]. In another study, Chesalkin et al. highlighted the specific synthesis parameters of various La-Ni binary compounds through detailed analysis. They also discussed the current status and future significance of the system in the context of energy sources [6]. Among these compounds, LaNi5 is recognized as one of the most promising commercial solid hydrogen storage alloys due to its high hydrogen storage capacity. Many researchers have reported that hydrogen atoms can enter the LaNi5 lattice, occupying tetrahedral or octahedral interstices, to form metal hydrides for hydrogen storage [8,9,12]. Joubert et al. provided a comprehensive overview of the properties of materials based on LaNi5 and its derivatives, including their electrochemical, thermodynamic, and kinetic properties [1]. These properties play a crucial role in the hydrogen absorption and release capacity of hydrogen storage alloys. Additionally, researchers have shown interest in the electromagnetic properties of LaNi5 alloy. Stucki et al. discussed the electromagnetic properties of LaNi5 and other materials, which positively impacted the electromagnetic applications of this alloy system [7]. Due to its unique superlattice structure, La2Ni7 exhibits better hydrogen storage performance than LaNi5. It has also been demonstrated to possess a distinctive low-temperature discharge capacity [25]. Iwase et al. studied the crystal structure changes and phase transitions of La2Ni7 during hydrogen absorption using in situ XRD, while Iwatake specifically investigated the crystal structure changes of the two coexisting La2Ni7 hydrides formed at hydrogen absorption saturation [26,27]. Additionally, several superconducting materials exist in the La-Ni binary system, such as La3Ni and La7Ni3, as reported in previous studies [13,14]. The La-Ni-Si system comprises various compound proportions, serving purposes in hydrogen storage and superconductivity. Numerous researchers have delved into the composition and performance of this system [2,3,28,29]. Mayer et al. tested the crystallographic data of rare earth silicides at high temperature using in situ XRD and found that binary compounds were generally more stable than ternary compounds, which is reflected in their performance [30]. Baisheva mentioned that in intermetallic compounds, the addition of a small amount of impurities may act as a catalyst and increase the active site [31]. Kakuta et al. explored the hydrogen absorption and discharge characteristics of several La-Na-Si ternary compounds in experiments, while Dakka et al. comprehensively compared LaNi5 with La28.9Ni67.55Si3.55. The study showed that after Si replaced Ni, the hydrogen storage would decrease slightly, but the thermodynamic and kinetic performance would greatly improve [32,33]. In the La-Ni-Si system, many superconducting materials have been discovered. Kasahara et al. found that La3Ni4Si4 is a superconducting material. Winiarski et al. compared it with La3Ni4Ge4, another superconducting material, and found that they were highly similar in many properties, providing direction and ideas for exploring more similar superconducting materials [15,34]. Furthermore, Smetana et al. recently employed single-crystal X-ray diffraction to identify four new compounds in the La-Ni-Si system. They noted the existence of unknown phases that necessitate further investigation [35]. Previous studies have shown that these two systems play an important role in material science and application, but there are few studies on the symbiosis of the two, and the rules of symbiosis have an important impact on the growth and performance of materials.
Single-crystal X-ray diffraction (SXRD) has become a powerful technique for the accurate determination of crystal structures, enabling researchers to gain insight into the arrangement and bonding of atoms in materials [36]. Deriving an unknown and complex crystal structure from powder X-ray diffraction (PXRD) data alone remains a very difficult and even impossible task. However, SXRD measurements can provide not only precise atomic coordinates, bond lengths, and bond angles but also atomic thermal displacements and occupancy rates, which are unavailable from PXRD even when measured using highly monochromatized and very intense synchrotron radiation [37]. By utilizing cutting-edge SXRD techniques, we will demonstrate how high-quality data can be obtained for solving and refining the atomic positions of each phase.
In this paper, we investigated the crystal structure evolution of La-Ni binary alloys under varying oxygen partial pressures using SXRD, EDX, and TEM. Initially, the nominal chemical composition of La3Ni2 samples produced via the arc melting method. Then the mixture was coated with a tantalum sheet as well as vacuum sealed, followed by the same high-temperature sintering conditions. The crystal structural information, their topological features, and crystallographic orientation relationships, including their microstructures of those phases during such different synthesized conditions, have been investigated.
2. Materials and Methods
High-purity La (99.99%) blocks and high-purity Ni (99.99%) blocks were weighed according to a molar ratio 3:2, with a total mass of 20 g. Argon (Ar) was used as a protective gas and introduced into a melting furnace. During arc melting, the current was set within the range of 200 A–300 A, and the pressure was maintained at 0.05 MPa. These materials underwent four melting cycles to ensure a uniform composition. After melting, the resulting alloy ingot is crushed into small pieces ranging from tens to hundreds of microns in size. First, a portion of the sample was wrapped in a tantalum sheet, placed in a heat treatment furnace, and maintained at 1100 °C for 5 h before being cooled within the furnace. Second, part of arc melted sample was placed in a quartz tube with a diameter of 6 mm and vacuum-sealed. The sealed glass tube was then subjected to heat treatment in a heat treatment furnace. Among them, the heat treatment conditions for the tantalum-coated and vacuum-sealed samples were identical. The sample was initially heated from room temperature to 200 ℃ and held for 5 min to remove any residual water, followed by heating to 1100 ℃ and maintained at that temperature for 5 h. The heating rate is consistently set at 10 °C per minute. Afterwards, the temperature of the furnaces equilibrates to room temperature. It needs to be mentioned that the stoichiometry of La3Ni2 (metastable according to the La-Ni binary phase diagram as shown in Figure S20 of the supplementary material) was initially selected as a precursor to synthesize the recently reported La3Ni2O7 superconducting material [16,17,18] with the purpose of clarifying its crystallographic features. However, a piece of single crystal with coexistence of three-phase LaNi, La3Ni3Si2 and La2NiSi (see the La-Ni-Si ternary phase diagram as shown in Figure S21 of the supplementary material) was discovered serendipitously as reported in the present work. It needs to be noted that the contamination probably originated from the quartz tube, which was cracked due to the outside pressure (1 atm) of the furnace and inside pressure of the sealed tube during the heat treatment, resulting in a large contact area of the deformed tube with the samples. Consequently, some Si diffuses into the La-Ni sample. Another group has also observed contamination of Si/SiO2 emitted from the quartz tube [38].
The La-Ni alloy samples obtained through three different treatment methods (through melting, tantalum sheet wrapping, and vacuum-sealed tube) were subsequently tested using SXRD. The diffraction was measured using a four-circle single crystal X-ray diffractometer (Bruker D8 Ventures, Bruker AXS GmbH, Karlsruhe, Germany). In order to verify the accuracy of phase measurement by SXRD, two SEM and EDX tests have been conducted on the vacuum sealed tube sample. In the first test, the electron microscope Hitachi S-3400N type equipped with EDX (EDAX Inc., Mahwah, NJ, USA) at a cathode voltage of 20 kV was used to characterize the morphology and chemical composition. In the second test, the electron microscope ZEISS Sigma 300 type equipped with EDX (Oxford, UK) at a cathode voltage of 15 kV was used to characterize the morphology and chemical composition. SEM and EDX analysis of the single crystal sample can be found in the supplementary material. The results are in good agreement with the phases tested by SXRD. TEM (JEM-F200, JEOL, Tokyo, Japan) equipped with an energy dispersive X-ray spectrometer (EDX) operated at 200 kV. The sample was prepared using the powder dispersion method for the TEM observation. The powder sample dispersed in anhydrous alcohol was sonicated to prepare a suspension, and then part of the suspension was sucked by a rubber dropper and dropped on a copper grid. After drying, a TEM test was performed.
All datasets from SXRD were processed by the APEX3 program [39], including indexing, integration, scaling, absorption correction [40], space group determination [41], structure solving, and refinement [34,42]. Structural models were plotted with the Diamond program (Version 4.6.8) [43]. Building clusters for the studied phases was analyzed by the ToposPro software package (Version 5.5.2.0) [44].
3. Results
3.1. SXRD Test of Synthesized Sample by the Melting Method
The La3Ni2 sample obtained through the melting method was analyzed using the SXRD test. The results indicated that both LaNi and La7Ni3 phases coexisted within the sample. According to the results of the SXRD test, the sample consists of several La7Ni3 and LaNi twins. Figure 1 and Figure 2 show the reciprocal points of the La7Ni3 and LaNi twins. Figure 1 presents the reciprocal points of the triple-twinned La7Ni3. Figure 1a shows the reciprocal points of the triple-twinned La7Ni3 along a random direction. Figure 1b–d sequentially illustrate the reciprocal lattice of the triple-twinned La7Ni3 along the c∗ axis. The indexed crystal parameters confirm that these are La7Ni3 twins. Figure 2 displays the reciprocal points of twinned LaNi. Figure 2a shows the reciprocal points of the LaNi twinning along a random direction. Figure 2b–d sequentially illustrate the reciprocal lattice of the LaNi twinning along the a∗ axis. The indexed crystal parameters confirm that these are LaNi twins. This method for confirming twin crystals was also employed in another paper previously published by our group [45]. In Figure 1b, there are 2662 white diffraction points. In Figure 1c, there are 2179 green diffraction points. In Figure 1d, there are 2570 yellow diffraction points. In Figure 2b, there are 1740 red diffraction points. In Figure 2c, there are 622 purple diffraction points. To facilitate the analysis and refinement of the crystal structure, the La7Ni3 phase and the LaNi phase, which have the largest number of diffraction points (without intersection with diffraction points from other grains), were selected for crystal structure refinement. The reciprocal lattices of the La7Ni3 and LaNi phases projected in three axes and their crystal structures are shown in Figure S1 and Figure S2 of the supplementary material. The reciprocal lattice is a lattice made up of points known as reciprocal points. It is a geometric approach used to describe crystal structures, having a reciprocal relationship with the spatial lattice. Each reciprocal point in the reciprocal lattice corresponds to a set of lattice planes with the same crystal plane spacing in the spatial lattice.
Detailed crystallographic data, data collection, and structural refinement details for the La7Ni3 and LaNi phases are summarized in Table 1. The crystallographic parameters of both phases adhere to the standards established by international crystallography for the rationalization of crystal structures.
Table 2 presents detailed information on La7Ni3, indicating that all atoms are fully occupied at their respective positions. The coordinate positions and occupancy of each atom are highly consistent with Olcese reported in 1973 [46].
Next, the building units in the structure of the La7Ni3 phase were analyzed using the nanocluster method in Topospro software (Version 5.5.2.0). The nanocluster method can be used to decompose the structure into construction units and describe the overall structural model in the form of combinations. This approach simplifies the structure, making it more intuitive and facilitating the identification of connections and differences between different structures. Through topology analysis, the La7Ni3 phase structure can be described by the cluster model of La1(1)(1@15). The cluster is centered on the La1 atom. Figure 3a demonstrates the cluster assembly model of the La7Ni3 phase. There are two La1(1)(1@15) clusters in the La7Ni3 cell, and the connections between clusters are collinear. Figure 3b depicts the environment diagram of the La1 atom, showing 15 surrounding atoms, including 3 La2 atoms, 9 La3 atoms and 3 Ni1 atoms. In addition, the distances between each coordination atom and the central atom La1 are indicated in Figure 3b. The longest distance, measuring 4.0553 Å, is observed between the La3 and La1 atoms, while the shortest distance, at 2.9382 Å, occurs between the Ni1 and La1 atoms.
Table 3 demonstrates the fractional atomic coordinates, atomic occupancy (Occ.) and equivalent isotropic displacement parameters (Ueq) of the LaNi phase. Notably, all atoms have an occupancy of 1. This finding is in strong agreement with the LaNi study by Raman et al. in 1968 [47]. The key distinction is that our study utilizes single crystal X-ray diffraction, whereas the 1968 paper relied on powder X-ray diffraction.
Next, the building units in the structure of the LaNi phase were analyzed using the nanocluster method in Topospro software (Version 5.5.2.0). Through topology analysis, the LaNi phase structure can be described by the cluster model of La1(1)(1@15). The cluster is a octadechedron cluster centered on the La1 atom. Figure 4a illustrates the cluster assembly model of the LaNi phase. There are two La1(1)(1@15) clusters in the LaNi cell, and the connections between clusters are collinear. Figure 4b depicts the environment diagram of the La1 atom, showing 15 surrounding atoms, including 8 La1 atoms and 7 Ni1 atoms. The distances between each coordination atom and the central atom La1 are indicated in Figure 4b. The longest distance, measuring 3.9014 Å, is observed between the La1 and La1 atoms, while the shortest distance, at 2.9743 Å, occurs between the Ni1 and La1 atoms.
3.2. SXRD Test of Tantalum Sheet Wrapped Heat Treatment Sample
Some melted samples were wrapped in tantalum sheets and heat-treated to investigate the structural transformation. Subsequently, SXRD tests were conducted on the samples. The results indicated that the samples were predominantly composed of LaNi5 twins. To facilitate crystal structural refinement, we selected a set of diffraction points exhibiting the strongest diffraction intensity for refinement. The reciprocal lattice and crystal structure of LaNi5 are shown in Figure S3 of the supplementary materials. In addition, an unknown phase is present in this batch of samples. Due to the limited number and weak intensity of the diffraction points associated with this phase, structural refinement cannot be performed. Currently, it is only known that the cell parameter obtained from its indexing are a = 7.23 Å, b = 3.96 Å, c = 6.70 Å, α = 90°, β = 94.50°, γ = 90°.
Detailed crystallographic data, data collection, and structural refinement details of the LaNi5 phase are summarized in Table 4. The crystallographic parameters of the LaNi5 phase adhere to the standards established by international crystallography for the rationalization of crystal structures.
Table 5 presents detailed information on LaNi5, indicating that La and Ni atoms are fully occupied at their respective positions. The coordinate positions and occupancy of each atom are highly consistent with Thompson et al. reported in 1987 [48].
Next, the building units in the structure of the LaNi5 phase were analyzed using the nanocluster method in Topospro software (Version 5.5.2.0). Through topology analysis, the LaNi5 phase structure can be described by the cluster model of La1(1)(1@18), which is a icosahedron cluster centered on the La1 atom. Figure 5a illustrates the cluster assembly model of the LaNi5 phase. There are eight La1(1)(1@18) clusters in the LaNi5 cell, and the connections between clusters are coplanar. Figure 5b depicts the environment diagram of the La1 atom, showing 18 surrounding atoms, including 6 Ni1 atoms and 12 Ni2 atoms. In addition, the distances between each coordination atom and the central atom La1 are indicated in Figure 5b. The longest distance, measuring 3.1996 Å, is observed between the La1 and Ni2 atoms, while the shortest distance, at 2.8954 Å, occurs between the Ni1 and La1 atoms.
3.3. SXRD Test of Vacuum Sealed Tube Samples
In this section, SXRD tests are conducted on samples of vacuum-sealed tube following heat treatment. The diffraction points in the reciprocal space of the collected sample, obtained from the 12 runs of SXRD measurements, are demonstrated in Figure 4. In Figure 6, white spots represent the LaNi phase because the cell parameters after indexing are a = 3.92 Å, b = 10.81 Å, c = 4.39 Å, α = β = γ = 90°. Green spots represent the La3Ni3Si2 phase because the cell parameters after indexing are a = 6.11 Å, b = 7.47 Å, c = 14.28 Å, α = β = γ = 90°, and yellow spots represent the La2NiSi phase because the cell parameters after indexing are a = b = 16.18 Å, c = 4.35 Å, α = β = 90°, γ = 120°. It can be clearly divided into three different sets of data sets, which means three independent different phases. Next, the three datasets were analyzed separately. The SXRD analysis of the sample involved a total of 12 runs, resulting in the collection of 8050 diffraction points in reciprocal space when the criterion of I/σ(I) equaled 3 for phase indexing. Within these diffraction points, 2437 were attributed to the LaNi phase, 3131 to the La3Ni3Si2 phase, and 1388 to the La2NiSi phase. The remaining 1094 diffraction points were associated with very small crystalline phases that could not be indexed to determine a unit cell (For a detailed description of the remaining diffraction points, see Figure S5 in Supplementary materials).
The reciprocal lattices of the LaNi, La3Ni3Si2 and La2NiSi phases projected in three axes and their crystal structures are in the Figure S6, Figure S7 and Figure S8 of the supplementary material.
Detailed crystallographic data, data collection, and structural refinement details of LaNi phase and La3Ni3Si2 phase are summarized in Table 6. The crystallographic parameters of both phases conform to the standards set by international crystallography for the rationalization of crystal structures. For the La2NiSi phase, due to the limited number of diffraction points and low intensity of the phase, structural refinement is not feasible. However, the crystal structure of La2NiSi has been previously reported [49,50]. Therefore, the crystal structure of the La2NiSi phase determined by Bodak et al. [49] is utilized in the topological analysis of the phase. It can be observed from Table 6 that the La3Ni3Si2 phase exhibits a narrow range of θ values and higher Rint, R1, and R2 values. This phenomenon is likely attributed to the presence of the three coexisting phases in the measured crystal, which contributes to the aforementioned issues in the final refinement results of the La3Ni3Si2 phase. To address this, selected samples from the same batch for SXRD tests and found a sample belonging to La3Ni3Si2 phase, the diffraction quality of this sample is quite good. After indexing the unit cell, it is found that this set of data shows a small number of La3Ni3Si2 twins. Among them, 80.8% of the diffraction points belong to the first domain La3Ni3Si2, 16.7% belong to the second domain La3Ni3Si2, and 2.5% cannot be indexed, these are crystals that are extremely small in size. Since only a small portion of the diffraction points belong to the second domain La3Ni3Si2, we refined the crystal structure of the main 80.8% of the diffraction points. The refinement results were very good, and the crystallographic data from the refined results are presented in Table S3 of the supplementary material, while the fractional coordinates and equivalent isotropic displacement parameters of the atoms are displayed in Table S4 of the supplementary material.
Since the atomic positions and topology of the LaNi phase have been detailed in Section 3.1, we will not elaborate further here.
Table 7 presents detailed information on La3Ni3Si2, indicating that the three types of atoms La, Ni, and Si are fully occupied at their respective positions. Compared with the crystal structure of La3Ni3Si2 mentioned by Pani et al. in 2022 [2], the coordinate positions and occupancy of each atom are highly consistent.
Next, the topological structure of the La3Ni3Si2 phase is analyzed. It is found that the structure of La3Ni3Si2 can be described by the model of a La2(1)(1@17) cluster, which is a centered on the La2 atom. Figure 7a illustrates the cluster assembly model in the La3Ni3Si2 unit. There are 4 La2(1)(1@17) clusters that are interleaved with each other connections. Figure 7b presents an environmental diagram of the La2 atom, showing 17 atoms around it, including 6 La1 atoms, 2 La2 atoms, 2 Ni1 atoms, 3 Ni2 atom, and 4 Si1 atoms. In addition, the distances between each coordination atom and the central atom La1 are indicated in Figure 7b. The longest distance, measuring 4.0125 Å, is observed between the La2 and La2 atoms, while the shortest distance, at 2.7952 Å, occurs between the Ni2 and La2 atoms.
As for the La2NiSi phase, the structural model of Bodak et al. is used in this paper [49]. Table 8 shows the coordinate positions and occupancy of each atom in the La2NiSi phase. It can be seen from Table 8 that there are two pairs of co-occupying atoms in the La2NiSi phase, namely Ni2/Si2 co-occupying atoms and Ni3/Si3 co-occupying atoms.
Similarly, we conducted a topological analysis of the La2NiSi phase and found that the phase can be characterized by one cluster model: La2(1)(1@15). The central atom of the La2(1)(1@15) cluster is the La2 atom. Figure 8a illustrates the cluster assembly model in the La2NiSi phase cell, while Figure 8b depicts the surrounding environment diagram of the La2 atom, which includes 15 atoms: 3 La1 atoms, 4 La3 atoms, 1 La4 atom, 2 Si1 atoms, 3 Si2/Ni2 atoms, and 2 Ni3/Si3 atoms. Additionally, the distances between each coordination atom and the central atom La2 are indicated in Figure 8b. The longest distance, measuring 4.1921 Å, is observed between the La2 and La3 atoms, while the shortest distance, at 3.0406 Å, occurs between the La2 and Ni3/Si3 atoms.
3.3.1. TEM Test
In order to verify the accuracy of our SXRD tests, transmission electron microscopy (TEM) analyses were conducted on the same batch of samples. The results are presented in Figure 9, Figure 10, Figure 11 and Figure 12. Figure 9 and Figure 10 confirm the presence of the La2NiSi phase, while Figure 11 and Figure 12 confirm the presence of the LaNi phase. It is important to note that although the atomic ratio of La to Ni in Figure 10 is approximately 3:2, the indexing results from the SAED and HRTEM images in Figure 11 are in good agreement with LaNi. Therefore, the sample is considered to be LaNi phase. In addition, only the La2NiSi and LaNi phases were identified in the TEM test, while the La3Ni3Si2 phase was not detected at this time. However, the La3Ni3Si2 phase was observed multiple times during the SXRD test. In summary, the TEM test results further confirmed the presence of silicon (Si) elements. Additionally, these findings lend support to the accuracy of our SXRD test results to some extent.
3.3.2. Construction of Structure Models for Intergrowth LaNi Phase, La3Ni3Si2 Phase and La2NiSi Phase in Real Space
According to the preceding section, it was observed that LaNi, La3Ni3Si2, and La2NiSi are three coexisting phases based on SXRD testing. However, the precise orientation of these three coexisting phases in real space remains unknown. This section aims to establish the orientation model of real space by utilizing the orientation matrices of the LaNi phase, La3Ni3Si2, and La2NiSi phase in reciprocal space. Refer to Appendix A for the detailed method of constructing the orientation model of these three coexisting phases in real space. In a diffraction experiment, the orientation matrix describes the orientation of the single crystal in space. The matrix relates the reciprocal axes of the crystal with the Cartesian coordinate system of the diffractometer. The orientation matrix of the three coexisting phases in reciprocal space is initially determined using APEX3 software. Subsequently, the orientation matrix of the three coexisting phases in real space is derived by establishing the fundamental correspondence between reciprocal space and real space. The orientation model of the interface of the three coexisting phases in real space is then deduced based on the orientation matrix of the three coexisting phases in real space. In Figure 13a, the gray, green, and yellow frames correspond to the LaNi, La3Ni3Si2, and La2NiSi phases, respectively. Finally, the ultimate orientation model depicted in Figure 13b is achieved by introducing atoms to the interface of the three coexisting phase units. Figure 13c illustrates the orientation model of LaNi and La3Ni3Si2 phases in real space, while Figure 13d displays the orientation model of LaNi and La2NiSi phases in real space. Notably, it is evident from Figure 13d that the c-axis of the LaNi phase aligns perfectly with that of the La2NiSi phase.
3.3.3. Interface between the LaNi Phase and the La3Ni3Si2 Phases
In the previous section, we obtained oriented structural models for the LaNi, La3Ni3Si2, and La2NiSi phases. However, the orientation of the three coexisting phases interface and the arrangement of atoms within the interface remain ambiguous. In this section, we will focus on addressing these issues by studying the synthetic precession images of the SXRD dataset as shown in Figure 14 and Figure 15. Figure 14a, b and c represent the precession images of the (0kl), (h0l) and (hk0) planes from the LaNi phase while the Figure 14d, e and f represent the precession images of the (0kl), (h0l) and (hk0) planes from the La3Ni3Si2 phase. In Figure 14a–c, the precession images are constructed with a thickness of 0.01 Å−1 and a resolution of 0.80 Å. While in Figure 14d–f, the precession images are constructed with a thickness of 0.05 Å−1 and a resolution of 0.80 Å. In Figure 14, the white and green circles represent the crystal planes of the LaNi and La3Ni3Si2 phases, respectively. Figure 14 directly shows the orientation relationship between the LaNi and La3Ni3Si2 phases represented by a pair of crystal planes. These diffraction points from the two phases overlap, mean that they represent crystal planes parallel to each other. In summary, five orientation relationships were obtained from Figure 14a, c, d, e and f, named OR1, OR2, OR3, OR4 and OR5, as shown in Table 9.
Figure 15a, b and c represent precession images of the (0kl), (h0l) and (hk0) planes from the La3Ni3Si2 phase, while Figure 15d, e and f represent precession images of the (0kl), (h0l) and (hk0) planes from the La2NiSi phase. In Figure 15, the green and yellow circles represent the crystal planes of the La3Ni3Si2 and La2NiSi phases, respectively. The precession image has a thickness of 0.01Å−1 and the resolution of 0.80 Å. From Figure 15a, b and f, three orientation relationships between La3Ni3Si2 and La2NiSi phases are obtained, named OR6, OR7 and OR8. These three orientation relationships are shown in Table 10.
In order to more intuitively express the five orientation relationships listed in Table 9 and the three orientation relationships listed in Table 10, they are represented by stereoscopic projection diagrams, as shown in Figure 16 and Figure 17.
As mentioned above, Figure 14 identifies five crystal orientation relationships between the LaNi and La3Ni3Si2 phases. Three crystal orientation relationships of the La3Ni3Si2 phase and La2NiSi phase can be determined from Figure 15. According to the symmetry principle of crystallography, a set of experimentally determined orientation relationships often has multiple variants. Therefore, it is necessary to determine whether the eight crystal orientation relationships observed in this experiment are equivalent. Next, we use the matrix method to analyze and discuss the experimental results. The matrix method is used to determine the conversion relationship between the crystal plane index and the crystal direction index between two phases mathematically. This involves finding the transformation matrices B and A for each type of orientation relation. If the absolute values of the nine elements in the transformation matrix are the same, it indicates that the orientation relation of the two phases belongs to the same type, even if the positive/negative signs, arrangement order, and position are different. A detailed description of the matrix approach can be found in our group’s previous research [51]. This method obtained the transformation matrix for the eight orientation relations. They are presented in Table 11 and Table 12 below. Table 11 shows the conversion matrix for the five crystal orientation relationships between the LaNi and La3Ni3Si2 phases, while Table 12 displays the conversion matrix for the three crystal orientation relationships between the La3Ni3Si2 and La2NiSi phases. Where matrix A represents the conversion matrix between crystal planes, and matrix B represents the conversion matrix between crystal directions. It can be determined that there are eight independent orientation relationships because the elements in the transformation matrix corresponding to the eight orientation relationships have different absolute values.
Furthermore, a preliminary interface model of these interface relationships was established. Take OR1 orientation relationship: [001] LaNi //[23$$\overset{-}{4}$$] La3Ni3Si2, (220) LaNi//(3$$\overset{-}{2} 0$$) La3Ni3Si2 as an example. For the (220)LaNi surface model, as shown in Figure 18a, the u and v directions are parallel to [001] and [1$$\overset{-}{1}$$0], respectively. At this time, the lattice parameters on the surface of (020)LaNi are: u = 4.383 Å, v = 11.487 Å, and θ = 90°. For the surface model of (3$$\overset{-}{2}$$0) La3Ni3Si2, as shown in Figure 18b, the u and v directions are parallel to [23$$\overset{-}{4}$$] and [2 3 13], respectively. The lattice parameters on the surface of (3$$\overset{-}{2}$$0) La3Ni3Si2 are as follows: u = 51.304 Å, v = 90.926 Å, θ = 88.43°. Considering the significant mismatch between the surfaces of (220) LaNi and (3$$\overset{-}{2} 0$$) La3Ni3Si2, it is essential to construct a supercell interface model to minimize the disparity. It was observed that utilizing the 12(u) × 8(v) (220) LaNi interface and the 1(u) × 1(v) La3Ni3Si2 interface led to relatively minor mismatches, with δ(u) = 2.52% and δ(v) = 1.07% discrepancies in the u and v directions, respectively. Figure 18c displays the atomic interface model of LaNi(220)/ La3Ni3Si2(3$$\overset{-}{2} 0$$).
Figure 1. The reciprocal points of the La<sub>7</sub>Ni<sub>3</sub> triple twins (<strong>a</strong>), the reciprocal points of the first layer of La<sub>7</sub>Ni<sub>3</sub> twins (<strong>b</strong>), the reciprocal points of the second layer of La<sub>7</sub>Ni<sub>3</sub> twins (<strong>c</strong>), the reciprocal points of the third layer of La<sub>7</sub>Ni<sub>3</sub> twins (<strong>d</strong>).
Figure 2. The reciprocal points of LaNi twins (<strong>a</strong>), the reciprocal points of the first layer of LaNi twins (<strong>b</strong>), the reciprocal points of the second layer of LaNi twins (<strong>c</strong>).
Table 1. Crystallographic and experimental data of La7Ni3 and LaNi obtained through arc melting.
| La7Ni3 | LaNi | |
|---|---|---|
| a/Å | 10.0995(18) | 3.9014(4) |
| b/Å | 10.0995(18) | 10.7782(12) |
| c/Å | 6.4490(16) | 4.3854(5) |
| α, β, γ/° | 90, 90, 120 | 90, 90, 90 |
| V/Å3 | 569.7(2) | 184.41(3) |
| Z | 8 | 2 |
| Space group | P63mc | Cmcm |
| Crystal system | Hexagonal | Orthorhombic |
| Diffractometer | Bruker D8 Venture Photon 100 COMS | |
| Monochromator | Graphite | |
| Tmeas/K | 300(2) | |
| Radiation | Mo-Kα, λ = 0.71073 (Å) | |
| Scan mode | φ and ω scan | |
| Time per step/s | 5 | |
| Absorption correction | Multi-scan | |
| F(000) | 966 | 340 |
| θ range/° | 3.93~27.50 | 3.78~27.49 |
| μ/mm−1 | 30.372 | 32.472 |
| No. measured reflections | 4501 | 2438 |
| No. unique reflections | 388 | 109 |
| No. observed reflections (I > 2σ(I)) | 337 | 104 |
| No. reflections used in refinement | 388 | 109 |
| No. parameters used in refinement | 22 | 9 |
| Reflection range | −12 ≤ h ≤ 11, −12 ≤ k ≤ 11, −6 ≤ l ≤ 7 | −4 ≤ h ≤ 4, −12 ≤ k ≤ 12, −5 ≤ l ≤ 5 |
| Rint | 0.1072 | 0.0657 |
| R(σ) | 0.0479 | 0.0192 |
| Final R indices (Fobs > 4σ(Fobs)) | R1 = 0.0316, ωR2 = 0.0615 | R1 = 0.0153, ωR2 = 0.0326 |
| R indices (all data) | R1 = 0.0359, ωR2 = 0.0615 | R1 = 0.0165, ωR2 = 0.0326 |
| Goodness of fit | 1.094 | 1.243 |
Table 2. Fractional atomic coordinates and equivalent isotropic displacement parameters (Å2) of La7Ni3.
| Label | Site | x | y | z | Occ. | Ueq |
|---|---|---|---|---|---|---|
| La1 | 2b | 0.333333 | 0.666667 | 0.7870(5) | 1 | 0.0129(7) |
| La2 | 6c | 0.12531(11) | 0.87469(11) | 0.0006(2) | 1 | 0.0145(5) |
| La3 | 6c | 0.53923(11) | 0.46077(11) | 0.8123(3) | 1 | 0.0152(5) |
| Ni1 | 6c | 0.8120(2) | 0.1880(2) | 0.0586(6) | 1 | 0.0173(10) |
Figure 3. Cluster assembly model of La<sub>7</sub>Ni<sub>3</sub> phase (<strong>a</strong>) and atomic environment diagram of La1 atom (<strong>b</strong>). Symmetry codes: (i) −<em>x</em> + 1, −<em>y</em> + 1, <em>z</em> + 1/2; (ii) <em>y</em>, −<em>x</em> + <em>y</em> + 1, <em>z</em> + 1/2; (iii) <em>x</em> − <em>y</em>, <em>x</em>, <em>z</em> + 1/2; (iv) −<em>y</em> + 1, <em>x</em>−<em>y</em> + 1, <em>z</em>; (v) −<em>x</em> + <em>y</em>, −<em>x</em> + 1, <em>z</em>; (vi) −<em>x</em> + 1, −<em>y</em> + 1, <em>z</em> − 1/2; (vii) <em>x</em> − <em>y</em>, <em>x</em>, <em>z</em>−1/2; (viii) <em>y</em>, −<em>x</em> + <em>y</em> + 1, <em>z</em>−1/2; (ix) <em>x</em>, <em>y</em>, <em>z</em> + 1; (x) −<em>x</em> + <em>y</em>, −<em>x</em> + 1, <em>z</em> + 1; (xi) −<em>y</em> + 1, <em>x</em> − <em>y</em> + 1, <em>z</em> + 1.
Table 3. Fractional atomic coordinates and equivalent isotropic displacement parameters (Å2) of LaNi.
| Label | Site | x | y | z | Occ. | Ueq |
|---|---|---|---|---|---|---|
| La1 | 4c | 0.000000 | 0.13715(5) | 0.250000 | 1 | 0.0116(2) |
| Ni1 | 4c | 0.000000 | 0.42884(16) | 0.250000 | 1 | 0.0173(4) |
Figure 4. Cluster assembly model of LaNi phase (<strong>a</strong>) and atomic environment diagram of La1 atom (<strong>b</strong>). Symmetry codes: (i) <em>x</em> − 1/2, <em>y</em> − 1/2, <em>z</em>; (ii) <em>x</em> + 1/2, <em>y</em> − 1/2, <em>z</em>; (iii) −<em>x</em> − 1/2, −<em>y</em> + 1/2, −<em>z</em>; (iv) −<em>x</em> + 1/2, −<em>y</em> + 1/2, −<em>z</em> + 1; (v) −<em>x</em> + 1/2, −<em>y</em> + 1/2, −<em>z</em>; (vi) −<em>x</em> − 1/2, −<em>y</em> + 1/2, −<em>z</em> + 1; (vii) −<em>x</em>, −<em>y</em>, −<em>z</em>; (viii) −<em>x</em>, −<em>y</em>, −<em>z</em> + 1.
Table 4. Crystallographic and experimental data of LaNi5 obtained through tantalum sheet-wrapping heat treatment.
| LaNi5 | |
|---|---|
| a, b, c/Å | 5.0149(4), 5.0149(4), 3.9751(5) |
| α, β, γ/° | 90, 90, 120 |
| V/Å3 | 86.577(18) |
| Z | 1 |
| Space group | P6/mmm |
| Crystal system | Hexagonal |
| Diffractometer | Bruker D8 Venture Photon 100 COMS |
| Monochromator | Graphite |
| Tmeas/K | 300(2) |
| Radiation | Mo-Kα, λ = 0.71073 (Å) |
| Scan mode | φ and ω scan |
| Time per step/s | 3 |
| Absorption correction | Multi-scan |
| F(000) | 197 |
| θ range/° | 4.69~27.47 |
| μ/mm−1 | 38.406 |
| No. measured reflections | 1897 |
| No. unique reflections | 47 |
| No. observed reflections (I > 2σ(I)) | 47 |
| No. reflections used in refinement | 47 |
| No. parameters used in refinement | 9 |
| Reflection range | −5 ≤ h ≤ 5, −5 ≤ k ≤ 5, −4 ≤ l ≤ 4 |
| Rint | 0.0670 |
| R(σ) | 0.0181 |
| Final R indices (Fobs > 4σ(Fobs)) | R1 = 0.0294, ωR2 = 0.0709 |
| R indices (all data) | R1 = 0.0289, ωR2 = 0.0709 |
| Goodness of fit | 1.374 |
Table 5. Fractional atomic coordinates and equivalent isotropic displacement parameters (Å2) of LaNi5.
| Label | Site | x | y | z | Occ. | Ueq |
|---|---|---|---|---|---|---|
| La1 | 1a | 0.000000 | 0.000000 | 0.000000 | 1 | 0.0061(10) |
| Ni1 | 2c | 0.333333 | 0.666667 | 0.000000 | 1 | 0.0078(12) |
| Ni2 | 3g | 0.500000 | 0.000000 | 0.500000 | 1 | 0.0063(11) |
Figure 5. Cluster assembly model of LaNi<sub>5</sub> phase (<strong>a</strong>) and atomic environment diagram of La1 atom (<strong>b</strong>). Symmetry codes: (iv) −<em>x</em>, −<em>y</em> + 1, −<em>z</em>; (v) <em>x</em>, <em>y</em> − 1, <em>z</em>; (vi) −<em>x</em> + <em>y</em> + 1, −<em>x</em> + 1, <em>z</em>; (viii) −<em>y</em>, <em>x</em> − <em>y</em>, <em>z</em>; (ix) <em>x</em>−1, <em>y</em>, <em>z</em> − 1; (x) −<em>y</em>, <em>x</em> – <em>y</em> − 1, <em>z</em> − 1.
Figure 6. Diffraction spots of the entire sample in the reciprocal space. (<strong>a</strong>) Projection of three sets of data in reciprocal space in a random direction; (<strong>b</strong>) Projection of LaNi phase and La<sub>3</sub>Ni<sub>3</sub>Si<sub>2</sub> phase along the <em>c</em><sup>∗</sup> axis of LaNi phase; (<strong>c</strong>) Projection of LaNi phase and La<sub>3</sub>Ni<sub>3</sub>Si<sub>2</sub> phase along the <em>c</em><sup>∗</sup> axis of LaNi phase; (<strong>d</strong>) Projection of La<sub>3</sub>Ni<sub>3</sub>Si<sub>2</sub> phase and La<sub>2</sub>NiSi phase along the <em>a</em><sup>∗</sup> axis of La<sub>2</sub>NiSi phase.
Table 6. Crystallographic and experimental data of LaNi and La3Ni3Si2 obtained through vacuum-sealed tube heat treatment.
| LaNi | La3Ni3Si2 | |
|---|---|---|
| a/Å | 3.9213(5) | 7.435(5) |
| b/Å | 10.7970(13) | 14.227(9) |
| c/Å | 4.3833(6) | 6.069(4) |
| α, β, γ/° | 90, 90, 90 | 90, 90, 90 |
| V/Å3 | 185.58(4) | 641.9(7) |
| Z | 2 | 8 |
| Space group | Cmcm | Pnma |
| Crystal system | Orthorhombic | Orthorhombic |
| Diffractometer | Bruker D8 Venture Photon 100 COMS | |
| Monochromator | Graphite | |
| Tmeas/K | 300(2) | |
| Radiation | Mo-Kα, λ = 0.71073 (Å) | |
| Scan mode | φ and ω scan | |
| Time per step/s | 5 | |
| Absorption correction | Multi-scan | |
| F(000) | 340 | 1132 |
| θ range/° | 3.77~27.48 | 5.46~25.38 |
| μ/mm−1 | 32.266 | 28.370 |
| No. measured reflections | 3183 | 6122 |
| No. unique reflections | 138 | 581 |
| No. observed reflections (I > 2σ(I)) | 130 | 362 |
| No. reflections used in refinement | 138 | 581 |
| No. parameters used in refinement | 9 | 40 |
| Reflection range | −5 ≤ h ≤ 5, −14 ≤ k ≤ 14, −5 ≤ l ≤ 5 | −8 ≤ h ≤ 8, −16 ≤ k ≤ 16, −7 ≤ l ≤ 7 |
| Rint | 0.0611 | 0.2268 |
| R(σ) | 0.0183 | 0.1225 |
| Final R indices (Fobs > 4σ(Fobs)) | R1 = 0.0248, ωR2 = 0.0612 | R1 = 0.0543, ωR2 = 0.1150 |
| R indices (all data) | R1 = 0.0263, ωR2 = 0.0612 | R1 = 0.1159, ωR2 = 0.1150 |
| Goodness of fit | 1.280 | 1.048 |
Table 7. Fractional atomic coordinates and equivalent isotropic displacement parameters (Å2) of La3Ni3Si2.
| Label | Site | x | y | z | Occ. | Ueq |
|---|---|---|---|---|---|---|
| La1 | 8d | 0.01646(18) | 0.60636(9) | 0.3610(2) | 1 | 0.0127(4) |
| La2 | 4c | 0.6169(2) | 0.25000 | 0.3744(4) | 1 | 0.0118(6) |
| Ni1 | 8d | 0.1292(4) | 0.4596(2) | 0.1013(5) | 1 | 0.0121(8) |
| Ni2 | 4c | 0.2745(6) | 0.25000 | 0.5646(8) | 1 | 0.0167(12) |
| Si1 | 8d | 0.3305(8) | 0.4121(4) | 0.3630(11) | 1 | 0.0087(15) |
Figure 7. Cluster assembly model of La<sub>3</sub>Ni<sub>3</sub>Si<sub>2</sub> phase (<strong>a</strong>) and atomic environment diagram of La2 atom (<strong>b</strong>). Symmetry codes: (vi) <em>x</em> + 1/2, <em>y</em>, −<em>z</em> + 1/2; (vii) <em>x</em> + 1/2, −<em>y</em> + 1/2, −<em>z</em> + 1/2; (viii) <em>x</em>, −<em>y</em> + 1/2, <em>z</em>; (ix) <em>x</em> + 1/2, <em>y</em>, −<em>z</em> + 3/2.
Table 8. Fractional atomic coordinates of La2NiSi.
| Label | Site | x | y | z | Occ. |
|---|---|---|---|---|---|
| La1 | 6h | 0.83200 | 0.82000 | 0.25000 | 1 |
| La2 | 6h | 0.60200 | 0.86400 | 0.25000 | 1 |
| La3 | 6h | 0.38700 | 0.93300 | 0.25000 | 1 |
| La4 | 2c | 0.33333 | 0.66667 | 0.25000 | 1 |
| Ni1 | 2b | 0.00000 | 0.00000 | 0.00000 | 1 |
| Si1 | 6h | 0.54700 | 0.16700 | 0.25000 | 1 |
| Ni2 | 6h | 0.75800 | 0.09200 | 0.25000 | 0.45 |
| Si2 | 6h | 0.75800 | 0.09200 | 0.25000 | 0.55 |
| Ni3 | 6h | 0.71700 | 0.21900 | 0.25000 | 0.90 |
| Si3 | 6h | 0.71700 | 0.21900 | 0.25000 | 0.10 |
Figure 8. Cluster assembly model of La<sub>2</sub>NiSi phase (<strong>a</strong>) and atomic environment diagram of La2 atom (<strong>b</strong>).
Figure 9. Microstructures of the La<sub>2</sub>NiSi phase. (<strong>a</strong>) TEM topography of La<sub>2</sub>NiSi phase. (<strong>b</strong>) SAED of La<sub>2</sub>NiSi phase. (<strong>c</strong>) HRTEM image for the area outlined by the red circle in (<strong>a</strong>). (<strong>d</strong>) HRTEM image of La<sub>2</sub>NiSi acquired from the red box in (<strong>c</strong>).
Figure 10. STEM image and elemental mappings of La, Ni and Si. (<strong>a</strong>) BF image. (<strong>b</strong>) DF image. (<strong>c</strong>) Element composition test results. (<strong>d</strong>) elemental mapping of La. (<strong>e</strong>) elemental mapping of Ni. (<strong>f</strong>) elemental mapping of Si.
Figure 11. Microstructures of the LaNi phase. (<strong>a</strong>) TEM topography of LaNi phase. (<strong>b</strong>) SAED of LaNi phase. (<strong>c</strong>) HRTEM image for the area outlined by the red circle in (<strong>a</strong>). (<strong>d</strong>) HRTEM image of LaNi acquired from the red box in (<strong>c</strong>).
Figure 12. STEM image and elemental mappings of La, Ni and Si. (<strong>a</strong>) BF image. (<strong>b</strong>) DF image. (<strong>c</strong>) Element composition test results. (<strong>d</strong>) elemental mapping of La. (<strong>e</strong>) elemental mapping of Ni. (<strong>f</strong>) elemental mapping of Si.
Figure 13. The orientation model of the single-cell border and the LaNi, La<sub>3</sub>Ni<sub>3</sub>Si<sub>2</sub>, and La<sub>2</sub>NiSi phases after adding atoms in real space is as follows: (<strong>a</strong>) single-cell border, (<strong>b</strong>) LaNi, La<sub>3</sub>Ni<sub>3</sub>Si<sub>2</sub>, and La<sub>2</sub>NiSi three coexisting phases, (<strong>c</strong>) LaNi and La<sub>3</sub>Ni<sub>3</sub>Si<sub>2</sub> two phases, (<strong>d</strong>) LaNi and La<sub>2</sub>NiSi two phases. (The green atoms are La atoms, the gray atoms are Ni atoms, and the blue atoms are Si atoms).
Figure 14. The precession images of intergrowth crystals: (<strong>a</strong>) LaNi (0<em>kl</em>), (<strong>b</strong>) LaNi (<em>h</em>0<em>l</em>), (<strong>c</strong>) LaNi (<em>hk</em>0), (<strong>d</strong>) La<sub>3</sub>Ni<sub>3</sub>Si<sub>2</sub> (0<em>kl</em>), (<strong>e</strong>) La<sub>3</sub>Ni<sub>3</sub>Si<sub>2</sub> (<em>h</em>0<em>l</em>), (<strong>f</strong>) La<sub>3</sub>Ni<sub>3</sub>Si<sub>2</sub> (<em>hk</em>0).
Figure 15. The precession images of intergrowth crystals: (<strong>a</strong>) La<sub>3</sub>Ni<sub>3</sub>Si<sub>2</sub> (0<em>kl</em>), (<strong>b</strong>) La<sub>3</sub>Ni<sub>3</sub>Si<sub>2</sub> (<em>h</em>0<em>l</em>), (<strong>c</strong>) La<sub>3</sub>Ni<sub>3</sub>Si<sub>2</sub> (<em>hk</em>0), (<strong>d</strong>) La<sub>2</sub>NiSi (0<em>kl</em>), (<strong>e</strong>) La<sub>2</sub>NiSi (<em>h</em>0<em>l</em>), (<strong>f</strong>) La<sub>2</sub>NiSi (<em>hk</em>0).
Table 9. Five crystallographic orientation relationships at the interface of LaNi and La3Ni3Si2.
| [uvw] LaNi//[uvw] La3Ni3Si2 | (hkl) LaNi //(hkl) La3Ni3Si2 | |
|---|---|---|
| OR1 | [100] LaNi//[27$$\overset{-}{22} \overset{-}{2}$$] La3Ni3Si2 | (084) LaNi//(2 1 16) La3Ni3Si2 |
| OR2 | [001] LaNi//[23$$\overset{-}{4}$$] La3Ni3Si2 | (220) LaNi//(3$$\overset{-}{2} 0$$) La3Ni3Si2 |
| OR3 | [$$\overset{-}{9} \overset{-}{3}$$2] LaNi//[$$1$$00] La3Ni3Si2 | (023) LaNi//(0$$\overset{-}{1}$$10) La3Ni3Si2 |
| OR4 | [$$\overset{-}{9}$$3$$\overset{-}{4}$$] LaNi//[$$0$$10] La3Ni3Si2 | (130) LaNi//(201) La3Ni3Si2 |
| OR5 | [$$\overset{-}{1}$$16] LaNi//[$$0$$01] La3Ni3Si2 | ($$\overset{-}{1}$$5$$\overset{-}{1}$$) LaNi//(140) La3Ni3Si2 |
Table 10. Three crystallographic orientation relationships at the interface of La3Ni3Si2 and La2NiSi.
| [uvw] La3Ni3Si2//[uvw] La2NiSi | (hkl) La3Ni3Si2//(hkl) La2NiSi | |
|---|---|---|
| OR6 | [100] La3Ni3Si2//[$$\overset{-}{17} \overset{-}{6}$$ 11] La2NiSi | (0$$\overset{-}{1}$$3) La3Ni3Si2//(1$$\overset{-}{1}$$1) La2NiSi |
| OR7 | [010] La3Ni3Si2//[3 30$$\overset{-}{41}$$] La2NiSi | (402) La3Ni3Si2//(10$$\overset{-}{1}$$0) La2NiSi |
| OR8 | [23$$\overset{-}{4}$$] La3Ni3Si2//[$$0$$01] La2NiSi | ($$\overset{-}{1}$$21) La3Ni3Si2//($$\overset{-}{4}$$50) La2NiSi |
Figure 16. Stereographic projection of the orientation relationships between LaNi and La<sub>3</sub>Ni<sub>3</sub>Si<sub>2</sub> based on the La<sub>3</sub>Ni<sub>3</sub>Si<sub>2</sub> phase: the orientation relationships between crystal directions (<strong>left</strong>), the orientation relationships between crystal planes (<strong>right</strong>).
Figure 17. Stereographic projection of the orientation relationships between La<sub>3</sub>Ni<sub>3</sub>Si<sub>2</sub> and La<sub>2</sub>NiSi based on the La<sub>3</sub>Ni<sub>3</sub>Si<sub>2</sub> phase: the orientation relationships between crystal directions (<strong>left</strong>), the orientation relationships between crystal planes (<strong>right</strong>).
Table 11. Orientation relationships and corresponding conversion matrixes between LaNi and La3Ni3Si2 interfaces.
| Orientation Relationship | Conversion Matrix B | Conversion Matrix A | |
|---|---|---|---|
| OR1 | (084) LaNi//(2 1 16) La3Ni3Si2 [100] LaNi//[27 $$\overset{-}{22}$$ $$\overset{-}{2}$$] La3Ni3Si2 |
$$\begin{pmatrix} + 1 . 08 & - 1 . 32 & - 0 . 44 \\ + 0 . 38 & + 0 . 42 & + 0 . 51 \\ - 0 . 27 & - 0 . 60 & + 2 . 96 \end{pmatrix}$$ | $$\begin{pmatrix} + 0 . 45 & - 0 . 37 & - 0 . 03 \\ + 1 . 21 & + 0 . 90 & + 0 . 29 \\ - 0 . 14 & - 0 . 21 & + 0 . 28 \end{pmatrix}$$ |
| OR2 | (220) LaNi//(3$$\overset{-}{2} 0$$) La3Ni3Si2 [001] LaNi //[23$$\overset{-}{4}$$] La3Ni3Si2 |
$$\begin{pmatrix} + 0 . 17 & - 1 . 05 & + 0 . 07 \\ + 0 . 19 & - 0 . 2 2 & - 0 . 07 \\ + 0 . 84 & + 1 . 87 & - 9 . 12 \end{pmatrix}$$ | $$\begin{pmatrix} + 1 . 11 & + 0 . 87 & + 0 . 28 \\ - 4 . 93 & - 8 . 18 & - 2 . 13 \\ + 0 . 0 5 & + 0 . 07 & - 0 . 09 \end{pmatrix}$$ |
| OR3 | (023) LaNi//(0$$\overset{-}{1}$$10) La3Ni3Si2 [$$\overset{-}{9} \overset{-}{3}$$2] LaNi//[100] La3Ni3Si2 |
$$\begin{pmatrix} - 1 . 37 & + 1 . 90 & + 0 . 69 \\ - 0 . 46 & - 0 . 71 & - 0 . 11 \\ + 0 . 31 & + 0 . 33 & + 1 . 5 1 \end{pmatrix}$$ | $$\begin{pmatrix} - 0 . 38 & + 0 . 2 4 & + 0 . 02 \\ - 0 . 97 & - 0 . 84 & + 0 . 38 \\ + 0 . 11 & - 0 . 17 & + 0 . 68 \end{pmatrix}$$ |
| OR4 | (130) LaNi//(201) La3Ni3Si2 [$$\overset{-}{9}$$3$$\overset{-}{4}$$] LaNi//[$$0$$10] La3Ni3Si2 |
$$\begin{pmatrix} + 1 . 10 & - 2 . 51 & + 0 . 15 \\ + 0 . 43 & + 0 . 84 & + 0 . 35 \\ - 0 . 01 & - 1 . 12 & + 1 . 30 \end{pmatrix}$$ | $$\begin{pmatrix} + 0 . 50 & - 0 . 19 & - 0 . 16 \\ + 1 . 04 & + 0 . 48 & + 0 . 42 \\ - 0 . 33 & - 0 . 11 & + 0 . 68 \end{pmatrix}$$ |
| OR5 | ($$\overset{-}{1}$$5$$\overset{-}{1}$$) LaNi//(140) La3Ni3Si2 [$$\overset{-}{1}$$16] LaNi//[$$0$$01] La3Ni3Si2 |
$$\begin{pmatrix} + 1 . 28 & - 2 . 07 & - 0 . 21 \\ + 0 . 55 & + 0 . 84 & + 0 . 21 \\ - 0 . 38 & - 1 . 12 & + 1 . 27 \end{pmatrix}$$ | $$\begin{pmatrix} + 0 . 39 & - 0 . 23 & - 0 . 09 \\ + 0 . 86 & + 0 . 46 & + 0 . 67 \\ - 0 . 08 & - 0 . 12 & + 0 . 66 \end{pmatrix}$$ |
Table 12. Orientation relationships and corresponding conversion matrixes between La3Ni3Si2 and La2NiSi interfaces
| Orientation Relationship | Conversion Matrix B | Conversion Matrix A | |
|---|---|---|---|
| OR6 | (0$$\overset{-}{1}$$3) La3Ni3Si2//(1$$\overset{-}{1}$$1) La2NiSi [100] La3Ni3Si2//[$$\overset{-}{17}\, \overset{-}{6}$$ 11] La2NiSi |
$$\begin{pmatrix} - 2 . 02 & + 0 . 36 & + 0 . 11 \\ + 0 . 14 & - 1 . 76 & - 0 . 74 \\ + 0 . 73 & - 1 . 27 & + 0 . 44 \end{pmatrix}$$ | $$\begin{pmatrix} - 0 . 51 & - 0 . 18 & + 0 . 33 \\ - 0 . 09 & - 0 . 29 & - 0 . 68 \\ + 0 . 0 2 & - 0 . 44 & + 1 . 03 \end{pmatrix}$$ |
| OR7 | (402) La3Ni3Si2//(10$$\overset{-}{1}$$0) La2NiSi [010] La3Ni3Si2//[3 30 $$\overset{-}{41}$$] La2NiSi |
$$\begin{pmatrix} + 2 . 43 & - 0 . 68 & - 0 . 32 \\ - 0 . 45 & + 1 . 07 & - 0 . 11 \\ - 0 . 18 & + 0 . 89 & + 0 . 64 \end{pmatrix}$$ | $$\begin{pmatrix} + 0 . 44 & + 0 . 17 & - 0 . 12 \\ + 0 . 09 & + 0 . 85 & - 1 . 17 \\ + 0 . 24 & + 0 . 24 & + 1 . 30 \end{pmatrix}$$ |
| OR8 | ($$\overset{-}{1}$$21) La3Ni3Si2//($$\overset{-}{4}$$50) La2NiSi [23$$\overset{-}{4}$$] La3Ni3Si2//[$$0$$01] La2NiSi |
$$\begin{pmatrix} - 0 . 78 & - 1 . 82 & + 0 . 30 \\ - 1 . 75 & + 1 . 04 & + 0 . 45 \\ - 0 . 43 & - 0 . 05 & - 0 . 60 \end{pmatrix}$$ | $$\begin{pmatrix} - 0 . 22 & - 0 . 43 & + 0 . 13 \\ - 0 . 38 & + 0 . 21 & + 0 . 29 \\ - 0 . 39 & - 0 . 06 & - 1 . 40 \end{pmatrix}$$ |
Figure 18. (<strong>a</strong>): (220) surface of the LaNi phase; (<strong>b</strong>): (3$$\overset{-}{2}$$0) surface of the La<sub>3</sub>Ni<sub>3</sub>Si<sub>2</sub> phase; (<strong>c</strong>): the atomic interface model of LaNi(220)/ La<sub>3</sub>Ni<sub>3</sub>Si<sub>2</sub>(3$$\overset{-}{2} 0$$) (The green atoms are La atoms, the gray atoms are Ni atoms, and the blue atoms are Si atoms).
4. Summary
We conducted SXRD tests on La-Ni alloys obtained through three different treatment methods in this experiment. Firstly, the La3Ni2 samples produced by the melting method consist of La7Ni3 and LaNi phases. The space group corresponding to La7Ni3 is P63mc, with the following cell parameters: a = b = 10.0995(18) Å, c = 6.4490(16) Å, α = β = 90°, γ = 120°. Topological analysis demonstrates that the La7Ni3 phase consists of La1(1)(1@15) type clusters, with the La1 atom serving as the central atom. The corresponding space group for LaNi is Cmcm, and its cell parameters are as follows: a = 3.9014(4) Å, b = 10.7782(12) Å, c = 4.3854(5) Å, α = β = γ = 90°. Topological analysis demonstrates that the LaNi phase consists of La1(1)(1@15) type clusters, with the La1 atom serving as the central atom.
Secondly, the phase composition of the La3Ni2 sample, after coating with a tantalum sheet and subsequent heat treatment, primarily consists of the LaNi5 phase. The corresponding space group is P6/mmm, and the cell parameters are as follows: a = b = 5.0149(12) Å, c = 3.9751(5) Å, α = β = 90°, γ = 120°. The crystal structure can be described as composed of La1(1)(1@18) type clusters, with the La1 atom serving as the central atom.
Finally, the phase composition of the La3Ni2 sample after vacuum-sealed tube heat treatment consists of LaNi, La3Ni3Si2, and La2NiSi phases, which coexist in three distinct phases. Among these, the space group corresponding to LaNi is Cmcm, with the following cell parameters: a = 3.9213(5) Å, b = 10.7970(13) Å, c = 4.3833(6) Å, α = β = γ = 90°. The corresponding space group for La3Ni3Si2 is Pnma, with cell parameters of a = 7.435(5) Å, b = 14.227(13) Å, c = 6.069(6) Å, α = β = γ = 90°. The crystal structure can be described as composed of La2(1)(1@17) type clusters, with the La2 atom at the center. Due to the limited and weak number of diffraction points, the crystal structure of the La2NiSi phase cannot be refined. However, the cell parameters of the La2NiSi phase, after indexing, are known to be a = b = 16.18 Å, c = 4.35 Å, α = β = 90°, and γ = 120°. Furthermore, the synthetic precession images of the SXRD data set were studied to obtain the orientation relationship of the three coexisting phases interface. By analyzing the (0kl), (h0l), and (hk0) planes of the three coexisting phases, eight independent orientation relationships were obtained for OR1, OR2, OR3, OR4, OR5, OR6, OR7, and OR8, respectively. Taking OR2 as an example, the preliminary interface model illustrates the arrangement of atoms within the interface.
This study analyzed the phase composition of La-Ni alloys under various treatment methods, which plays an important role in the future study of the La-Ni and La-Ni-Si systems.
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 (Å2) 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:
$$a^{∗} $$corresponds to the first column, $$b^{∗}$$ to the second, $$c^{∗}$$ 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:
The orientation matrix of La3Ni3Si2 phase in reciprocal space is:
The orientation matrix of La2NiSi phase in reciprocal space is:
From the basic correspondence between reciprocal space and real space:
One can derive the orientation matrix of these two phases in real space. Where the orientation matrix of LaNi phase in real space is:
The orientation matrix of La3Ni3Si2 phase in real space is:
The orientation matrix of La2NiSi phase in real space is:
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:
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:
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.
```latex \mathrm{R} = \begin{pmatrix} a_{x}^{∗} & b_{x}^{∗} & c_{x}^{∗} \\ a_{y}^{∗} & b_{y}^{∗} & c_{y}^{∗} \\ a_{z}^{∗} & b_{z}^{∗} & c_{z}^{∗} \end{pmatrix}```
```latex\begin{pmatrix} + 0 . 08751311 & - 0 . 00740845 & - 0 . 21358819 \\ + 0 . 23488939 & + 0 . 02130833 & + 0 . 07239119 \\ + 0 . 04850991 & - 0 . 08981182 & + 0 . 03479378 \end{pmatrix}```
```latex\begin{pmatrix} + 0 . 06037243 & + 0 . 00620812 & - 0 . 06503084 \\ + 0 . 12217132 & - 0 . 08172383 & + 0 . 01862565 \\ - 0 . 09075078 & - 0 . 10588900 & - 0 . 01818771 \end{pmatrix}```
```latex\begin{pmatrix} + 0 . 01006662 & - 0 . 01470755 & - 0 . 21359995 \\ + 0 . 05206853 & - 0 . 01050337 & + 0 . 07254676 \\ - 0 . 04672600 & - 0 . 06833122 & + 0 . 03482372 \end{pmatrix}```
```latex a^{∗} \cdot a = b^{∗} \cdot b = c^{∗} \cdot c = 1```
```latex\begin{pmatrix} + 1 . 34253892 & + 3 . 60343910 & + 0 . 74419088 \\ - 0 . 86394990 & + 2 . 48490911 & - 10 . 4735680 \\ - 4 . 10186403 & + 1 . 39023996 & + 0 . 66819876 \end{pmatrix}```
```latex\begin{pmatrix} + 2 . 25216729 & + 4 . 55754897 & - 3 . 38541900 \\ + 0 . 34624554 & - 4 . 55798760 & - 5 . 90575284 \\ - 13 . 25342951 & + 3 . 79594931 & - 3 . 70669660 \end{pmatrix}```
```latex\begin{pmatrix} + 4 . 64935674 & + 15 . 29827923 & - 3 . 35226173 \\ - 5 . 26866880 & - 9 . 751584356 & - 12 . 00163398 \\ - 4 . 09975509 & + 1 . 39243421 & + 0 . 66839289 \end{pmatrix}```
```latex \mathrm{A} = \begin{pmatrix} 3 . 9213 & 0 & 0 \\ 0 & 10 . 7970 & 0 \\ 0 & 0 & 4 . 3833 \end{pmatrix}```
```latex \mathrm{C} = \begin{pmatrix} + 0 . 34235872 & + 0 . 91891647 & + 0 . 18977683 \\ - 0 . 08002272 & + 0 . 23016517 & - 0 . 97011617 \\ - 0 . 93585766 & + 0 . 31718914 & + 0 . 15245238 \end{pmatrix}```
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
Informed Consent Statement
Not applicable.
Data Availability Statement
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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