Structure of Cubic Al 73.8 Pd 13.6 Fe 12.6 Phase with High Al Content

: A cubic ternary phase Al 73.8 Pd 13.6 Fe 12.6 (designated C (cid:48) phase), with very high Al content (Al / TM = 2.82, TM denotes transition metal) was prepared by spark plasma sintering (SPS). Its crystal structure was determined by combing single-crystal X-ray di ﬀ raction (SXRD) and scanning electron microscope (SEM) equipped with energy dispersive X-ray spectroscopy (EDS) measurements. The crystal structure of the new phase can be described with a small unit cell ( a = 7.6403(2) Å; space group Pm 3, No. 200) as that of Al 2.63 Rh ( a = 7.6692(1) Å; space group P23 , No. 195) while di ﬀ erent from those of the reported Al 39 Pd 21 Fe 2 ( a = 15.515(1) Å; space group Fm 3, No. 202) and Al 69 Pd 17 Fe 14 ( a = 15.3982(2) Å; space group Im 3, No. 204) compounds, which both adopt a double length unit cell in the Al–Pd–Fe system. The mechanism of distributing more Al atoms in the new phase was compared with that of the Al 2.63 Rh phase by analyzing their site symmetry and the corresponding site of occupancies (SOF). Furthermore, relations of the C (cid:48) phase to the reported Al 69 Pd 17 Fe 14 (designated C1 phase) and Al 39 Pd 21 Fe 2 (designated C2 phase) phases were investigated by analyzing their building units with the “nanocluster” method in the ToposPro package.

Both the quasicrystals and their approximants in the Al-Pd-Fe alloys have been the subject of extensive research for their similarity and diversity of phases with those in the Al-Cu-Fe and Al-Pd-Mn alloys [8,[27][28][29].During the past thirty years, several stable 2D and 1D quasicrystals and metastable 3D quasicrystals, as well as some quasicrystal approximants in the Al-Pd-Fe alloy, have been reported [5,[30][31][32][33][34][35].For clarity, most known phases with their stoichiometry range in the ternary diagram of Al-Pd-Fe described by Balanetskyy et al. are reproduced and shown in Figure 1 [34].A stable cubic approximant phase with nominal composition, Al 70 Pd 10 Fe 20 was found to coexist with a decagonal phase and an icosahedral phase in the melt-quenched Al-Pd-Fe alloys [5].A few years later, it was confirmed that the metastable icosahedral phase was first formed by rapid quenching (obtained by melt spinning with a 20 cm diameter copper roller rotating at 6000 rpm) in the liquid Crystals 2019, 9, 526 2 of 11 with nominal composition Al 70 Pd 10 Fe 20 and then transformed to the cubic phase with a period of about 20.5 Å (obtained by slow cooling and full annealing) [30].In another work, the crystal structure of Al 39 Pd 21 Fe 2 (the C2 phase) has been solved and refined with a large unit cell (space group Fm3; a = 15.515Å.) [32].An untrivial ordering scheme was observed by analyzing its relationships with other Al-TM compounds, and consequently a plausible geometrical model was derived for static disorder concerning certain Al sites.The structures of two other cubic approximants Al 63.6 Pd 30.2 Fe 6.2 and Al 68.9 Pd 17.1 Fe 13.9 with space groups Fm3 and Im3, respectively, have been found by single-crystal X-ray diffraction measurements [22].However, the structure of Al 68.9 Pd 17.1 Fe 13.9 (designated C1 phase, with a concise formula Al 69 Pd 17 Fe 14 ) was updated with space group Im3 in another work [31].Note that the Al concentration in the Al 63.6 Pd 30.2 Fe 6.2 and Al 68.9 Pd 17.1 Fe 13.9 phase is quite close to that of the Al 39 Pd 21 Fe 2 and Al 70 Pd 10 Fe 20 phase, respectively.
These approximants to the icosahedral phase in the Al-Pd-Fe system have been summarized as the C phase with formula Al72.8Pd14.3Fe12.9(Pm3 ̅ , a = 7.655 Å ), the C1 phase with formula Al68.2Pd21.4Fe10.4(Im3 ̅ , a = 15.389Å ), and the C2 phase with formula Al64.3Pd30.3Fe5.4(Fm3 ̅ , a = 15.515Å ) in comprehensive work by Balanetskyy et al.In this work, scanning and transmission electron microscopy with electron-probe microanalysis was combined with X-ray structure analysis and used to study their mutual transformations and orientation relationships [33].Despite the aforementioned extensive efforts, the crystal structure of the C phase has not been determined.

Materials and Methods
Pure elements (Al 99.8%, Pd 99.95%, Fe 99.8%) were mixed in the stoichiometric ratio 75:15:10, ground and homogenized in an agate mortar.The blended powders were then packed with graphite paper and filled into a graphite die, which was placed between the upper and lower conductive plates of the SPS machine.The graphite die was then set to the pressure value of ~50 MPa, with a sintering temperature of 1100 °C and a high vacuum of 6 × 10 −3 Pa in Ar atmosphere.These conditions were maintained for 10 minutes and then cooled rapidly to room temperature by shutting off the power.Finally, the sintered block was removed from the graphite die and broken into small pieces.
The SPS specimens were cut to a size 12 mm × 10 mm × 4 mm, then wrapped in phenolic powders and heated to 140 °C for 10 minutes.After cooling in water, the specimens were ground with 400 to 2000 grit silicon carbide paper and polished with W2.5 artificial diamond paste.Next, the specimens were treated by surface erosion with a self-prepared erosion agent (HF: 2 mL; HCl: 3 mL; HNO3: 5 mL; and H2O: 190 mL), followed by cleaning and drying with distilled water and ethanol.A scanning In this work, scanning and transmission electron microscopy with electron-probe microanalysis was combined with X-ray structure analysis and used to study their mutual transformations and orientation relationships [33].Despite the aforementioned extensive efforts, the crystal structure of the C phase has not been determined.
In the present work, we report the detailed crystal structure analysis of a cubic ternary Al 73.9 Fe 13.7 Pd 12.4 phase (designated C phase as its composition is slightly different than that of the C phase) with very high Al content.The sample was prepared using the spark plasma sintering (SPS) approach when revisiting the Al 75 Pd 15 Fe 10 2D quasicrystals and its cubic approximants [34,35].Furthermore, its similarity and difference with the reported C1, C2 phases and Al 2.63 Rh are discussed.

Materials and Methods
Pure elements (Al 99.8%, Pd 99.95%, Fe 99.8%) were mixed in the stoichiometric ratio 75:15:10, ground and homogenized in an agate mortar.The blended powders were then packed with graphite paper and filled into a graphite die, which was placed between the upper and lower conductive plates of the SPS machine.The graphite die was then set to the pressure value of ~50 MPa, with a sintering temperature of 1100 • C and a high vacuum of 6 × 10 −3 Pa in Ar atmosphere.These conditions were maintained for 10 minutes and then cooled rapidly to room temperature by shutting off the power.Finally, the sintered block was removed from the graphite die and broken into small pieces.
The SPS specimens were cut to a size 12 mm × 10 mm × 4 mm, then wrapped in phenolic powders and heated to 140 • C for 10 minutes.After cooling in water, the specimens were ground with 400 to Crystals 2019, 9, 526 3 of 11 2000 grit silicon carbide paper and polished with W2.5 artificial diamond paste.Next, the specimens were treated by surface erosion with a self-prepared erosion agent (HF: 2 mL; HCl: 3 mL; HNO 3 : 5 mL; and H 2 O: 190 mL), followed by cleaning and drying with distilled water and ethanol.A scanning electron microscope (SEM, Hitachi S-3400N type, Hitachi, Tokyo, Japan) equipped with EDS (EDAX Inc., Mahwah, NJ, USA) at a cathode voltage of 20 kV and a current of 80 mA was used to characterize the morphology and chemical composition.The chemical compositions of each element were analyzed by comparing the integrated net intensities with corresponding data collected automatically by the EDAX Inc.Two standard samples (pure aluminum and copper) were adopted to calibrate the peak positions from time to time.A fragment of single crystal with dimensions 105 × 75 × 40 µm 3 was selected by a polarizing microscope (LEICA DM4 M) for diffraction measurements with a four-circle single-crystal X-ray diffractometer (Bruker D8 venture, Bruker AXS GmbH, Karlsruhe, Germany).All data processing was performed with the APEX3 program suit, including data reduction by SAINT, absorption correction by SADABS, structural solving and refinement by SHELXT and SHELXL [36][37][38], respectively.The topological features of the discovered C phase with the available C1 and C2 phases were analyzed by the nanocluster approach implanted in the ToposPro package [39][40][41][42].

Microstructure
The microstructure of the SPS sample after polishing and etching is shown by the SEM images in Figure 2a-c.From Figure 2a one can observe that some parts of the surface were scratched off during polishing and plenty of gear-shaped single-crystal pillars showed up at these sites.There were four common regions (denoted as A, B, C, E) and one special region where the gear-shaped single crystal was located (denoted as D), as illustrated by the different contrast images in Figure 2b,c, which was further confirmed by the EDS analysis results listed in Table 1. Figure 2d shows the morphology of the selected specimen fragment after the single-crystal XRD measurements, and the chemical composition in region F was used as a reference during the following structural refinement of the discovered C phase.The recovered phases should not be chemical equilibrium phases and the possible phases for each region are shown in Table 1.Concerning the chemical composition uncertainties for each phase (especially for the element iron), with some regions like region C and D it is difficult to distinguish between the 19, 9, 526 3 of 11 microscope (SEM, Hitachi S-3400N type, Hitachi, Tokyo, Japan) equipped with EDS (EDAX wah, NJ, USA) at a cathode voltage of 20 kV and a current of 80 mA was used to characterize phology and chemical composition.The chemical compositions of each element were by comparing the integrated net intensities with corresponding data collected automatically AX Inc.Two standard samples (pure aluminum and copper) were adopted to calibrate the itions from time to time.A fragment of single crystal with dimensions 105 × 75 × 40 μm 3 was by a polarizing microscope (LEICA DM4 M) for diffraction measurements with a four-circle ystal X-ray diffractometer (Bruker D8 venture, Bruker AXS GmbH, Karlsruhe, Germany).processing was performed with the APEX3 program suit, including data reduction by absorption correction by SADABS, structural solving and refinement by SHELXT and [36][37][38], respectively.The topological features of the discovered C′ phase with the available 2 phases were analyzed by the nanocluster approach implanted in the ToposPro package s and Discussion ostructure microstructure of the SPS sample after polishing and etching is shown by the SEM images e 2a-c.From Figure 2a one can observe that some parts of the surface were scratched off olishing and plenty of gear-shaped single-crystal pillars showed up at these sites.There were mon regions (denoted as A, B, C, E) and one special region where the gear-shaped single as located (denoted as D), as illustrated by the different contrast images in Figure 2b,c, which her confirmed by the EDS analysis results listed in Table 1. Figure 2d shows the morphology lected specimen fragment after the single-crystal XRD measurements, and the chemical tion in region F was used as a reference during the following structural refinement of the ed C′ phase.The recovered phases should not be chemical equilibrium phases and the phases for each region are shown in Table 1.Concerning the chemical composition ties for each phase (especially for the element iron), with some regions like region C and D cult to distinguish between the ꜫ phase and QCs phase.chemical composition of the gear-shaped single-crystal (Region D) was found to scatter with entration of the quasicrystal phase, although ten-fold X-ray diffraction patterns suggested ation of quasicrystals (see Figures S1 and S2 in the Supplementary Materials to compare the diffraction patterns of the quasicrystals and the cubic C′ phase discussed here).However, yond the scope of the present study.Concerning the selected fragment of the single-crystal EDS analysis was carried out on three areas (Region F) which provided an average chemical tion of Al74.0Pd12.1Fe13.9.This fits well with the refined model with the measured single-crystal fraction data sets.
phase and QCs phase.were taken with back-scattered electron (BSE).EDS analysis was performed on different sites of the denoted regions A-F and results are listed in Table 1.   1.  [36][37][38], respectively.The topological features of the discovered C′ phase with t C1 and C2 phases were analyzed by the nanocluster approach implanted in the Topos [39][40][41][42].

Microstructure
The microstructure of the SPS sample after polishing and etching is shown by the in Figure 2a-c.From Figure 2a one can observe that some parts of the surface were s during polishing and plenty of gear-shaped single-crystal pillars showed up at these sites four common regions (denoted as A, B, C, E) and one special region where the gear-sh crystal was located (denoted as D), as illustrated by the different contrast images in Figure was further confirmed by the EDS analysis results listed in Table 1. Figure 2d shows the of the selected specimen fragment after the single-crystal XRD measurements, and t composition in region F was used as a reference during the following structural refine discovered C′ phase.The recovered phases should not be chemical equilibrium pha possible phases for each region are shown in Table 1.Concerning the chemical uncertainties for each phase (especially for the element iron), with some regions like reg it is difficult to distinguish between the ꜫ phase and QCs phase.
The chemical composition of the gear-shaped single-crystal (Region D) was found to the concentration of the quasicrystal phase, although ten-fold X-ray diffraction pattern the formation of quasicrystals (see Figures S1 and S2 in the Supplementary Materials to projected diffraction patterns of the quasicrystals and the cubic C′ phase discussed here this is beyond the scope of the present study.Concerning the selected fragment of the s sample, EDS analysis was carried out on three areas (Region F) which provided an avera composition of Al74.0Pd12.1Fe13.9.This fits well with the refined model with the measured s X-ray diffraction data sets.

Microstructure
The microstructure of the SPS sample after polishing and etching is show in Figure 2a-c.From Figure 2a one can observe that some parts of the surfac during polishing and plenty of gear-shaped single-crystal pillars showed up at t four common regions (denoted as A, B, C, E) and one special region where th crystal was located (denoted as D), as illustrated by the different contrast images was further confirmed by the EDS analysis results listed in Table 1. Figure 2d sh of the selected specimen fragment after the single-crystal XRD measuremen composition in region F was used as a reference during the following structu discovered C′ phase.The recovered phases should not be chemical equilibr possible phases for each region are shown in Table 1.Concerning the c uncertainties for each phase (especially for the element iron), with some region it is difficult to distinguish between the ꜫ phase and QCs phase.
The chemical composition of the gear-shaped single-crystal (Region D) was the concentration of the quasicrystal phase, although ten-fold X-ray diffractio the formation of quasicrystals (see Figures S1 and S2 in the Supplementary Ma projected diffraction patterns of the quasicrystals and the cubic C′ phase discu this is beyond the scope of the present study.Concerning the selected fragmen sample, EDS analysis was carried out on three areas (Region F) which provided composition of Al74.0Pd12.1Fe13.9.This fits well with the refined model with the me X-ray diffraction data sets.
- 12.1 (± 3.2) 13.9 (± 3.8) C -phase 1 C -phase is slightly different from the C-phase mentioned in [43]. 2 Chemical composition range fits that of the 3 of 11 pe (SEM, Hitachi S-3400N type, Hitachi, Tokyo, Japan) equipped with EDS (EDAX , USA) at a cathode voltage of 20 kV and a current of 80 mA was used to characterize and chemical composition.The chemical compositions of each element were aring the integrated net intensities with corresponding data collected automatically Two standard samples (pure aluminum and copper) were adopted to calibrate the m time to time.A fragment of single crystal with dimensions 105 × 75 × 40 μm 3 was rizing microscope (LEICA DM4 M) for diffraction measurements with a four-circle ay diffractometer (Bruker D8 venture, Bruker AXS GmbH, Karlsruhe, Germany).ing was performed with the APEX3 program suit, including data reduction by n correction by SADABS, structural solving and refinement by SHELXT and respectively.The topological features of the discovered C′ phase with the available s were analyzed by the nanocluster approach implanted in the ToposPro package scussion e ucture of the SPS sample after polishing and etching is shown by the SEM images rom Figure 2a one can observe that some parts of the surface were scratched off and plenty of gear-shaped single-crystal pillars showed up at these sites.There were ions (denoted as A, B, C, E) and one special region where the gear-shaped single d (denoted as D), as illustrated by the different contrast images in Figure 2b,c, which rmed by the EDS analysis results listed in Table 1. Figure 2d shows the morphology pecimen fragment after the single-crystal XRD measurements, and the chemical gion F was used as a reference during the following structural refinement of the ase.The recovered phases should not be chemical equilibrium phases and the for each region are shown in Table 1.Concerning the chemical composition each phase (especially for the element iron), with some regions like region C and D stinguish between the ꜫ phase and QCs phase.l composition of the gear-shaped single-crystal (Region D) was found to scatter with of the quasicrystal phase, although ten-fold X-ray diffraction patterns suggested uasicrystals (see Figures S1 and S2 in the Supplementary Materials to compare the ion patterns of the quasicrystals and the cubic C′ phase discussed here).However, scope of the present study.Concerning the selected fragment of the single-crystal ysis was carried out on three areas (Region F) which provided an average chemical l74.0Pd12.1Fe13.9.This fits well with the refined model with the measured single-crystal data sets.
-phase [34,44]. 3Chemical composition range disagrees with that of reported decagonal quasicrystal.However, ten-fold X-ray diffraction patterns were observed and will be discussed elsewhere (see Figure S1 in the Supplementary Materials). 4 The Fe-rich phase has been described as O-Al 3 Fe in [45], as well as O-Al 13 (Pd, Fe) 4 in [34].
The chemical composition of the gear-shaped single-crystal (Region D) was found to scatter with the concentration of the quasicrystal phase, although ten-fold X-ray diffraction patterns suggested the formation of quasicrystals (see Figures S1 and S2 in the Supplementary Materials to compare the projected diffraction patterns of the quasicrystals and the cubic C phase discussed here).However, this is beyond the scope of the present study.Concerning the selected fragment of the single-crystal sample, EDS analysis was carried out on three areas (Region F) which provided an average chemical composition of Al 74.0 Pd 12.1 Fe 13.9 .This fits well with the refined model with the measured single-crystal X-ray diffraction data sets.

Crystal Structure Determination
The structure model was solved with space group Pm3 (No. 200) by direct method.The crystal data, data collection, and structure refinement details are summarized in Table 2.The crystal was refined with PART and EADP commands for TM2 atoms (Pd/Fe co-occupied position, see Table 3).The site occupancy factor (SOF) of Pd2 was refined to be 0.473(84).The detailed crystal structure information of the present phase was accepted by the Cambridge Crystallographic Data Centre (CCDC) with deposition number 1897801.All data sets collected by a four-circle single-crystal X-ray diffractometer (Bruker D8 Venture, Bruker AXS GmbH, Karlsruhe, Germany) have been published at the public repository Mendeley Data: https://data.mendeley.com/datasets/538y46cpmh/1.
Note that the P23 space group was also applied to solve and refine the new phase (see Table S1 of the Supplementary Materials).However, it was not adopted, as the refinement indicators (e.g., R 1 , ωR 2 and ∆ρ max , ∆ρ min ) became much worse.The disorder discussed in the present work mainly concerns the vacancies/co-occupied positions and positional disorder as reflected by site occupancy factors and unreasonable short length bonds.Stream-like diffuse scattering features (see Figure S2d-f   For the convenience of the following discussion, bond lengths for the C -phase are listed in Table S2 of the Supplementary Materials.The coordination polyhedra formed around Fe1 and Pd1 atoms are illustrated in Figure S3 of the Supplementary Materials where the distances to the vertices are also listed.The detailed crystallographic information of C1, C2, and C phases are attached in Table S3 of the Supplementary Materials in the study of the group-subgroup relationship through the construction of the Bärnighausen tree approach for interested readers [46,47].
There are five Al and three TM determined sites in the refined structural model, as shown in Table 3 and Figure 3a.One TM site is occupied by a mixture of Fe and Pd atoms and the remaining two are fully occupied by Fe and Pd, respectively.Only one Al (Al1) site is fully occupied and the rest are partially occupied.Among these partially occupied Al sites, the SOF of Al2 is 0.629( 14) but those of Al3, Al4, and Al5 sites are all lower than 0.5.The last three sites are quite close to each other and have quite abnormal anisotropic parameters.The atomic displacement parameters (ADPs) of these partially occupied Al sites are all very large, especially those of Al3 site atoms refined to be 0.072 (7), implying disorder should exist at these positions.Note that the ADPs of the Al5 site have to be isotropic, otherwise the crystal structure would collapse.Considering the short distance between these three sites (Al3-Al4 = 1.40(3)Å, Al3-Al5 = 1.34(4)Å, Al4-Al5 = 1.17(3)Å), one can deduce that all of these should be divided from the same atomic position.ωR2 (all data) 0.0888 ∆ρmax, ∆ρmin (e Å -3 ) 0.847, -0.992There are five Al and three TM determined sites in the refined structural model, as shown in Table 3 and Figure 3a.One TM site is occupied by a mixture of Fe and Pd atoms and the remaining two are fully occupied by Fe and Pd, respectively.Only one Al (Al1) site is fully occupied and the rest are partially occupied.Among these partially occupied Al sites, the SOF of Al2 is 0.629( 14) but those of Al3, Al4, and Al5 sites are all lower than 0.5.The last three sites are quite close to each other and have quite abnormal anisotropic parameters.The atomic displacement parameters (ADPs) of these partially occupied Al sites are all very large, especially those of Al3 site atoms refined to be 0.072 (7), implying disorder should exist at these positions.Note that the ADPs of the Al5 site have to be isotropic, otherwise the crystal structure would collapse.Considering the short distance between these three sites (Al3-Al4 = 1.40(3)Å , Al3-Al5 = 1.34(4)Å , Al4-Al5 = 1.17(3)Å ), one can deduce that all of these should be divided from the same atomic position.Table 3.The atomic positions of the C′-phase (in gray) compared to those of the Al2.63Rh phase (Occ. indicates the site occupancy factor).It was found that the C -phase was still an isotype of the typical Al 2.63 Rh phase, as shown in Figure 3b, and both had an identical framework, mainly composed of TM atoms [49].The crystal structure of the Al 2.63 Rh phase was refined in the non-centrosymmetric P23 space group and also adopted small unit cells as the C -phase.There were five fully occupied (Rh1, Rh2, Rh3, Al1, and Al2) atoms and three partially occupied (Al3, Al4, and Al5) atoms in the Al 2.63 Rh structure (refer to Table 3).From Table 3, it can be seen that Pd1 (Rh1), Fe1 (Rh2), and TM2 (Rh3) occupied the same Wyckoff position, which were located at the center, corner and face of the unit cell of the C -phase (Al 2.63 Rh), respectively.

Label
Contrary to the nearly identical TM atoms, there were some differences between the light atoms, except for the Al1 atoms of the C -phase and the Al 2.63 Rh phase which resulted in a higher concentration of Al in the former phase.Firstly, different site symmetry of Al2 atoms contributed to more light atoms in the C -phase, although its SOF was much lower than that of the Al 2.63 Rh phase.Secondly, Al3 and Al4 atoms had the same site symmetry in both phases but had larger SOF in the C -phase than that of the Al 2.63 Rh phase, which contributed to more light atoms.Finally, the Al5 atoms contributed to slightly fewer light atoms in the C -phase than that of the Al 2.63 Rh phase.To summarize, there were more Al atoms in the unit cell of the C -phase which resulted in a higher Al content (Al/TM = 2.82) than that of the Al 2.63 Rh phase.This Al/TM ratio value of 2.82 is the highest among the Al-Pd-Fe system, although it is still not comparable to those in the Al-Cu-Fe system (e.g., an Al/TM ratio value of 3.17 in a recently discovered λ-Al 13 Fe 4 -type intermetallic (Al,Cu) 13 (Fe,Cu) 4 compound [50]).

Topological Features
Relations of the C -phase to the reported C1 (Al 69 Pd 17 Fe 14 ) and C2 (Al 39 Pd 21 Fe 2 ) phases were investigated by analyzing their building units with the "nanocluster" method integrated in the ToposPro package [39].It was found that the arrangement of atomic clusters in all aforementioned three phases could simply be described as an icosahedra cluster centered at a Pd atom plus eight identical (C ) or different (C1 and C2) polyhedron clusters, as illustrated in Figures 4 and 5.
For the C -phase, the first building unit is an icosahedra cluster composed of a centered Pd (Pd1) atom located at Wyckoff position 1b ( 12 , 1 2 , 1 2 ) and 12 Al (Al1) atoms occupying the 12k Wyckoff position forming an icosahedron as shown in Figure 4a.The atomic distance between Al1 and Pd1 atoms equals 2.711 Å.The second building unit is a complex double-shell cluster centered at the Fe (Fe1) atom.The first shell (inner-shell) is composed of 32-coordinated atoms (Al2, Al4, and Al5), forming an irregular polyhedron as shown in Figure 4b.The atomic distance between the centering Fe1 and Al2, Al4, and Al5 equals 2.433 Å, 2.358 Å, and 2.437 Å, respectively.The second shell (outer-shell) is composed of 48-coordinated atoms including 12 Al3 atoms, 24 Al1 atoms, and 12 Pd2 atoms as shown in Figure 4c.Note that all the Al1 atoms are shared with the surrounding first building units as shown in Figure 4d.The two building units are closely connected to form the global crystal structure of the C -phase as shown in Figure 4e.
For the C1 (Al 69 Pd 17 Fe 14 ) and C2 (Al 39 Pd 21 Fe 2 ) phases, both are described by the supercell of the basic Al 2.63 Rh phase and have lower Al element content and a higher degree of disorder than the present C -phase.It was also found that both of the C1 and C2 phases have three building units by the "nanocluster" method [39].Both of them had an icosahedron cluster centered at the Pd atom (1st building unit, Figure 5a,a * ) and a complicated double-shell cluster centered Al/Fe atom (second building unit, Figure 5e).The double-shell cluster is composed of a 14-coordinated (8 Pd atoms and 6 Al atoms) first shell (inner-shell) and a 48-coordinated (36 Al atoms plus 12 Pd atoms) second shell (outer-shell) as shown in Figure 5d,e.The third building unit of the C1 and C2 phases is an 18-coordinated spindle-shaped cluster centered at the Fe atom (Figure 5c), and a 20-coordinated dodecahedron cluster centered at the Fe/Pd atom (Figure 5b), respectively.There are six spindle-shaped clusters plus two double-shell clusters in the C1 phase, while there are four dodecahedron clusters plus four double-shell clusters in the C2 phase surrounding their centered icosahedron cluster.It can be deduced that the different Al content (Al/TM) in the C1 and C2 phases is mainly caused by the eight different clusters surrounding the icosahedron cluster, although both have similar topological features.One can easily conclude that all three of the aforementioned phases can be simply described as an icosahedron cluster centered at a Pd atom plus eight identical (C′) or different (C1 and C2) polyhedron clusters.In other words, the C′, C1, and C2 phases are mainly distinguished from their second and third building units.The C1 and C2 phases have a different second building unit and additional third building unit from those of the C′ phase.There are 2(4) second building and 6(4) third building units to total eight clusters surrounding the first building unit for the C1 (C2) phase.It is the different type and number of second and third building units, as well as the site of occupancy, that decides the different content of Al elements in these three phases.One can easily conclude that all three of the aforementioned phases can be simply described as an icosahedron cluster centered at a Pd atom plus eight identical (C ) or different (C1 and C2) polyhedron clusters.In other words, the C , C1, and C2 phases are mainly distinguished from their second and third building units.The C1 and C2 phases have a different second building unit and additional third building unit from those of the C phase.There are 2(4) second building and 6(4) third building units to total eight clusters surrounding the first building unit for the C1 (C2) phase.It is the different type and number of second and third building units, as well as the site of occupancy, that decides the different content of Al elements in these three phases.

Conclusions
In summary, the crystal structure of a cubic ternary phase Al 73.8 Pd 13.6 Fe 12.6 (designated C phase) synthesized by SPS approach with very high Al content (Al/TM = 2.82) was solved and refined by combing SXRD and SEM/EDS measurements.The crystal structure of the C phase can be described by a small unit cell (a = 7.6403(2) Å) with space group Pm3 (No. 200).It is deduced that a higher Al content in the C -phase than that of the Al 2.63 Rh phase can be mainly attributed to the different site symmetry and SOF of Al atoms located at the 8i Wyckoff position.Furthermore, it was found that the C phase, the C1 (Al 69 Pd 17 Fe 14 ), and C2 (Al 39 Pd 21 Fe 2 ) phases have an identical icosahedron building unit centered at a Pd atom with different configurations of surrounding eight building units, resulting in different aluminum element content in these three phases.As an important quasicrystal approximant phase, the discovery and study of the C phase would stimulate more experimental or theoretical efforts focusing on the intermetallic compounds and phase diagram of the Al-Pd-Fe ternary system.

Figure 1 .
Figure 1.Overall compositions of the high-Al Al-Pd-Fe phases between 1020 • C and 900 • C; Region of the ε-phases is given for 750 • C. (M: monoclinic M-Al 13 Fe 4 ; O: orthorhombic O-Al 13 (Fe,Pd) 4 ; δ: Al 3 Pd 2 ; β: Al(Pd,Fe); ε: Al 3 PdFex (the x component is between 0% and 10%); C-phase: in a compositional range of 1-2 at.% around Al 71.5 Pd 15.0 Fe 13.5 ; C 1 -phase: in a compositional range between Al 69.5 Pd 14.8 Fe 15.7 and Al 68.5 Pd 22.2 Fe 9.3 ; C 2 -phase: in a compositional range around Al 67.0 Pd 24.5 Fe 8.5 ).These approximants to the icosahedral phase in the Al-Pd-Fe system have been summarized as the C phase with formula Al 72.8 Pd 14.3 Fe 12.9 (Pm3, a = 7.655 Å), the C1 phase with formula Al 68.2 Pd 21.4 Fe 10.4 (Im3, a = 15.389Å), and the C2 phase with formula Al 64.3 Pd 30.3 Fe 5.4 (Fm3, a = 15.515Å) in comprehensive work by Balanetskyy et al.In this work, scanning and transmission electron microscopy with electron-probe microanalysis was combined with X-ray structure analysis and used to study their mutual transformations and orientation relationships[33].Despite the aforementioned extensive efforts, the crystal structure of the C phase has not been determined.In the present work, we report the detailed crystal structure analysis of a cubic ternary Al 73.9 Fe 13.7 Pd 12.4 phase (designated C phase as its composition is slightly different than that of the C phase) with very high Al content.The sample was prepared using the spark plasma sintering (SPS) approach when revisiting the Al 75 Pd 15 Fe 10 2D quasicrystals and its cubic approximants[34,35].Furthermore, its similarity and difference with the reported C1, C2 phases and Al 2.63 Rh are discussed.

Crystals 2019, 9 , 526 4 of 11 Figure 2 .
Figure 2. Scanning electron microscope (SEM) micrographs and energy dispersive X-ray spectroscopy (EDS) analysis of Al-Pd-Fe samples prepared by SPS.(a-c) reveal the as-cast state and (d) the fragment of measured single crystal.(a) and (d) were taken with secondary electron (SE), (b) and (c)were taken with back-scattered electron (BSE).EDS analysis was performed on different sites of the denoted regions A-F and results are listed in Table1.

Figure 2 .
Figure 2. Scanning electron microscope (SEM) micrographs and energy dispersive X-ray spectroscopy (EDS) analysis of Al-Pd-Fe samples prepared by SPS.(a-c) reveal the as-cast state and (d) the fragment of measured single crystal.(a) and (d) were taken with secondary electron (SE), (b) and (c) were taken with back-scattered electron (BSE).EDS analysis was performed on different sites of the denoted regions A-F and results are listed in Table1.
are ignored when processing the single-crystal X-ray diffraction datasets by the APEX3 suit program.

Figure 3 .
Figure 3.The crystal structure of the C -phase (a) and the Al 2.63 Rh phase (b) projected along the [001] direction.(Graphs prepared by DIAMOND [48]).
eight different clusters surrounding the icosahedron cluster, although both have similar topological features.

Figure 4 .
Figure 4. Building units and their packing around high symmetric positions in the C′-phase.(a): the first building unit which is an icosahedra cluster; the inner-shell of the second building unit; (c) the outer-shell of the second building unit; (d) packing pattern of one first building unit and four inner-shells; e) packing pattern of one first building unit and four second building units.

Figure 4 .
Figure 4. Building units and their packing around high symmetric positions in the C -phase.(a): the first building unit which is an icosahedra cluster; (b) the inner-shell of the second building unit; (c) the outer-shell of the second building unit; (d) packing pattern of one first building unit and four inner-shells; (e) packing pattern of one first building unit and four second building units.

Figure 4 .
Figure 4. Building units and their packing around high symmetric positions in the C′-phase.(a): the first building unit which is an icosahedra cluster; (b) the inner-shell of the second building unit; (c) the outer-shell of the second building unit; (d) packing pattern of one first building unit and four inner-shells; e) packing pattern of one first building unit and four second building units.

Figure 5 .
Figure 5. Building units and their packing around high symmetric positions in the C1 and C2 phases.(a) and (a*): the first building unit which is an icosahedra cluster; (b) the third building unit of the C2 phase; (c) the third building unit of the C1 phase; (d) the inner-shell of the second building unit; (e) the outer-shell of the second building unit; (f) packing pattern of the C2 phase; (g) packing pattern of the C1 phase.

Figure 5 .
Figure 5. Building units and their packing around high symmetric positions in the C1 and C2 phases.(a) and (a*): the first building unit which is an icosahedra cluster; (b) the third building unit of the C2 phase; (c) the third building unit of the C1 phase; (d) the inner-shell of the second building unit; (e) the outer-shell of the second building unit; (f) packing pattern of the C2 phase; (g) packing pattern of the C1 phase.

Table 1 .
The chemical compositions of a piece of educts and a fragment of single crystal from the spark plasma sintering samples analyzed by the EDS (bold numbers indicate the mean values of different measured chemical compositions in the same region).Regions A-F are denoted in Figure2.by the EDAX Inc.Two standard samples (pure aluminum and copper) were adopted to peak positions from time to time.A fragment of single crystal with dimensions 105 × 75 × selected by a polarizing microscope (LEICA DM4 M) for diffraction measurements with single-crystal X-ray diffractometer (Bruker D8 venture, Bruker AXS GmbH, Karlsruhe All data processing was performed with the APEX3 program suit, including data r SAINT, absorption correction by SADABS, structural solving and refinement by SH SHELXL or QCs3SEM, Hitachi S-3400N type, Hitachi, Tokyo, Japan) equip Inc., Mahwah, NJ, USA) at a cathode voltage of 20 kV and a current of 80 mA wa the morphology and chemical composition.The chemical compositions of analyzed by comparing the integrated net intensities with corresponding data co by the EDAX Inc.Two standard samples (pure aluminum and copper) were ad peak positions from time to time.A fragment of single crystal with dimensions selected by a polarizing microscope (LEICA DM4 M) for diffraction measureme single-crystal X-ray diffractometer (Bruker D8 venture, Bruker AXS GmbH, K All data processing was performed with the APEX3 program suit, includin SAINT, absorption correction by SADABS, structural solving and refineme SHELXL phase2

Table 2 .
The crystallographic data of the C -phase.

Table 3 .
The atomic positions of the C -phase (in gray) compared to those of the Al 2.63 Rh phase (Occ.indicates the site occupancy factor).