Synthesis, crystal and electronic structure of CaNi₂Al₈

2.1 Synthesis

Calcium pieces (ChemPur, 99.5%), nickel pieces (Unichema, 99.9+%) and aluminum pellets (Onyxmet, 99.99%) were used as starting materials for all syntheses reported herein. In the first attempt, the elements were weighed in an elemental ratio of 1:2:9 and placed into open niobium crucibles, which were subsequently put in a quartz glass ampoule and evacuated. The ampoule was transferred to an induction furnace (Trumpf Hüttinger, Truheat 5010) and the crucible was placed in the center of the coil. The power output was increased until a red glow, indicating a temperature of about 1100 K, was observed. The temperature was kept for 10 min followed by cooling, achieved by reducing the power output and finally by switching off the power supply. Afterwards, the sample was removed from the crucible. As CaNi₂Al₈ and CaNiAl₉ were observed as the main products, attempts were made to synthesize the pure compounds using the same reactants as before, however, with a 1:2:8 and 1:1:9 ratio. Again, the elements were placed in the refractory metal crucible, which was placed in a quartz ampoule that was evacuated. As before, the ampoules were centered in the coil of the induction furnace. The temperature was increased, held for 10 min followed by cooling. Large crystals were observed in the nominal CaNiAl₉ attempt (Figure 2). In a final attempt, the elements were again weighed in a 1:2:8 ratio, however, pressed into pellets (ø = 6 mm, 100 bar) in air. The pellet was transferred into a Nb crucible, which was placed in a quartz ampoule to be evacuated and heated using an induction furnace and the same temperature protocol stated before. All samples are silvery with metallic luster and stable in air over several months.

2.2 X-ray diffraction

Powder X-ray diffraction (PXRD) patterns of the pulverized samples were recorded at room temperature on a D8-A25-Advance diffractometer (Bruker, Karlsruhe, Germany) in Bragg-Brentano θ-θ-geometry (goniometer radius 280 mm) with CuK _α-radiation (λ = 154.0596 pm). A 12 µm Ni foil working as K _β filter and a variable divergence slit were mounted at the primary beam side. A LYNXEYE detector with 192 channels was used at the secondary beam side. Experiments were carried out in a 2θ range of 7–120° with a step size of 0.013° and a total scan time of 1 h. The recorded data was evaluated using the Bruker Topas 5.0 software [26].

From the crushed samples, single crystals were isolated and investigated at T = 130 K on a Bruker X8 APEX2 Nonius κ-CCD diffractometer, operating with graphite monochromated MoK _α radiation (λ = 0.71073 Å). A numerical absorption correction using the Bruker Sadabs data package [27] was applied to the data set. The structure was solved and refined using Superflip [28] and Jana2006 [29, 30] (vide infra).

CSD 2093897 contains the supplementary crystallographic data for this paper. The data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/structures.

2.3 Quantum-chemical calculations

The first-principles calculations were carried out with Quantum ESPRESSO [31, 32] for the structural relaxation of CaNi₂Al₈ using PAW pseudopotentials [33] from the PSLibrary version 1.0.0 [34]. The kinetic energy cut-off for the plane waves was set to 100 Ry, while the cut-off for the charge density and potential was set to 400 Ry. The structural relaxation stopped when a total energy convergence of 10⁻⁶ Ry and a force convergence of 10⁻⁵ Ry a ₀ ⁻¹ was reached. The Marzari-Vanderbilt cold smearing [35] and a Gaussian spreading of 0.01 Ry were chosen to account for the Brillouin-zone integration. The k-mesh was divided by 4 × 4 × 16 using the Monkhorst-Pack algorithm [36]. Exchange and correlation in this density functional theory (DFT) based method were treated with the generalized gradient approximation (GGA) functional as parameterized by Perdew, Burke and Ernzerhof (PBE-GGA) [37]. Quantum ESPRESSO was also used to generate the all-electron and valence electron densities, which were then used to calculate the Bader charges according to the methods described by Henkelman et al. [38], [39], [40] and Yu and Trinkle [41] with the Critic2 program [42, 43]. The chemical bonding analysis was carried out using the tight-binding, linear muffin-tin orbitals with the atomic spheres approximation (TB-LMTO-ASA) [44, 45] as implemented in the program TB-LMTO 4.7 [46]. Exchange and correlation were treated with the GGA functional as parameterized by Perdew et al. [47]. The k-mesh was 8 × 6 × 22, which leads to 240 k-points in the irreducible Brillouin zone (IBZ). The radii of the automatically generated Wigner-Seitz cells for Ca, Ni and Al were 2.02, 1.37–1.39 and 1.41–1.67 Å, respectively. No empty spheres were needed for the LMTO calculations. The bonding analysis was carried out by calculation of the density-of-states (DOS) and the crystal orbital Hamilton population (COHP) [48] and its integrals (ICOHP). The ICOHP can be seen as a semi-quantitative bonding energy which measures covalent contributions in solids. Because –COHP values are plotted, negative –COHP values are antibonding states, positive ones are bonding states and non-bonding states have –COHP values of zero. The Fermi level was set to 0 eV as reference.

3.1 Powder X-ray diffraction

All samples were investigated by powder X-ray diffraction experiments. The samples are not phase pure, however, CaNi₂Al₈ is the main phase in all three cases. Besides CaNi₂Al₈ (CaFe₂Al₈ type, space group Pbam, a = 1253.2, b = 1450.0, c = 397.5 pm [11]) also CaNiAl₉ (own type, space group P6₃/mmc, a = 760.02, c = 794.57 pm [9, 10]) along with binary Ni₂Al₃ (own type, space group P 3 ‾ m1, a = 402.82, c = 489.06 pm [49]) and unreacted elemental Al (Cu type, space group Fm 3 ‾ m, a = 405.0 pm [50]) could be identified from the diffraction data. The diffraction patterns are shown in Figure 1, the obtained lattice parameters and phase contributions are summarized in Table 1. Unidentified phases are indicated by asterisks in the diffraction patterns and have been treated by single-line fits. The phase composition changed significantly with increasing amounts of CaNi₂Al₈; however, phase-pure samples have not been obtained with the available setup.

Figure 1:

X-ray powder diffraction patterns of the three synthetic attempts. (Top) Synthesis with a nominal composition of CaNi₂Al₉; (middle) synthesis with a nominal composition of CaNi₂Al₈ (bottom) synthesis with a nominal composition of CaNi₂Al₈, but the reactants were pressed to a pellet (see Experimental Section for more details). The green dashes indicate the Bragg positions of CaNi₂Al₈, Ni₂Al₃, CaNiAl₉, and Al (from top to bottom).

Figure 2:

Microscopic image from crystallites of CaNi₂Al₈.

3.2 Single-crystal X-ray diffraction and structure refinement

Rod-shaped single crystals (Figure 2) were isolated from the bulk and mounted onto a Bruker X8 APEX2 diffractometer. Careful analysis of the obtained single-crystal X-ray diffraction data revealed an orthorhombic lattice, and space group Pbam was found to be correct. Isotypism with the CaFe₂Al₈-type structure was already evident from the powder diffraction patterns. The structure was solved using the charge flipping algorithm of Superflip [28] and a least-squares refinement on F ² using the program Jana2006 [29, 30] was carried out. All atomic positions were refined with anisotropic displacement parameters, and as a check for the correct compositions, the occupancy parameters were refined in a separate series of least-square cycles. All sites were fully occupied within three standard deviations; final difference Fourier syntheses were contourless. Details of the structure determination, atomic parameters and interatomic distances can be found in Tables 2 –4.

3.3 Crystal chemistry

The crystal structure of CaNi₂Al₈ has been refined previously from powder X-ray diffraction data (a = 1253.2, b = 1450.0, c = 397.5 pm) [11], however, no single-crystal X-ray diffraction data was available so far. The title compound shows isotypism with the orthorhombic CaFe₂Al₈-type structure (space group Pbam; Z = 4) with lattice parameters of a = 1252.30(6), b = 1443.73(7) and c = 395.78(2) pm (single-crystal data). The crystal structure can be described as a polyanionic network of Ni and Al atoms according to [Ni₂Al₈] ^δ– (Figure 3, left) with the calcium cations residing in pentagonal prismatic cavities (Ca@Al₁₀) of said framework (Figure 4, top left). The Ca–Al distances range between 312 and 317 pm, which is slightly longer than the sum of the covalent radii (Ca + Al: 174 + 125 pm [51]), indicating at least partial covalent interactions. The Ni–Al distances in the polyanion range from 234 to 261 pm, underlining the bonding character of these interactions, since the shortest interactions are well in line with the sum of the covalent radii (Al + Ni: 125 + 115 = 240 pm [51]; see quantum chemical calculations). These interactions are observed between the Ni1 and Al7 atoms, which align opposite to the single homoatomic Ni interactions (Ni1–Ni1: 285 pm) in the structure. The Ni1–Ni1 distance is significantly longer compared to the ones found in fcc-Ni (249 pm; Cu type, Fm 3 ‾ m [50]) or the sum of the covalent radii (230 pm [51]), however, ICOHP values suggest that this interaction is rather weak (vide infra). It is interesting to note that although the Al content of CaNi₂Al₈ exceeds 70 at.%, still short homoatomic transition metal interactions can be observed. In M _x T _y Al _z compounds with high Al content (>70 at.%) usually an isolation of the M and T atoms occurs. Besides the other aluminum-containing MT ₂Al₈ compounds (CeFe₂Al₈ type, M = Ca, La–Nd, Sm, Eu, Yb, T = Fe, Co, Ni [11], [12], [13], [14], [15], [16], [17], [18, 52], [53], [54], [55], [56], [57]), only the ThCr₂Si₂-type (space group I4/mmm [58]) representatives BaCu_0.2Al_3.8, BaAg_0.3Al_3.7 and CaZn_0.5Al_3.5 [59] as well as CaMn_2.1Al_9.9 [60] (CeMn₄Al₈ [61]/ThMn₁₂ type [62]; space group I4/mmm) have been reported with short (240–290 pm) T–T distances. The Al–Al distances finally range between 265 and 314 pm, which is longer compared to the sum of the covalent radii (250 pm [51]) but near the value for elemental Al (286 pm; fcc, Cu type, space group Fm 3 ‾ m [50]), indicating different degrees of Al–Al bonding (vide infra).

Figure 3:

Crystal structure of CaNi₂Al₈ depicted along [001]: (left) Emphasis on the [Ni₂Al₈] ^δ– polyanion; (right) emphasis on the respective colored coordination polyhedra. Ca atoms are depicted in blue, Ni atoms in black and Al as open circles; atom labels are given with numbers. For the color-coding see Figure 4.

Figure 4:

Coordination polyhedra in the crystal structure of CaNi₂Al₈ surrounding the atoms Ca (top left), Ni1 (top middle), Ni2 (top right), Al1 (bottom left), Al6 (bottom middle), and Al7 (bottom right). Ca atoms are depicted in blue, Ni atoms in black and Al as open circles. The atom labels, Wyckoff positions and the site symmetries are given.

Alternatively, the structure can be described based on different coordination polyhedra and their respective connection. As stated before, the Ca atoms reside in pentagonal prismatic cavities (Figure 4, top left). The Ni1 atoms are surrounded by nine Al atoms in the shape of a three-fold capped trigonal prism plus the additional short Ni contact. Two of these prisms are condensed via a common Al2–Al2 edge to form double units (Figure 4, top middle). The Ni2 atoms exhibit a similar coordination environment (Figure 4, top right), but in contrast to the Ni1 atoms, no Ni–Ni contacts are observed, hence isolated polyhedra are present. These trigonal prisms (Ni1 in dark gray, Ni2 in light gray) are separated by the Al1, Al6 and Al7 polyhedra shown in orange, red and green in Figure 3, right. The Al1 and Al7 atoms are surrounded by eight other Al atoms in the shape of a distorted cube, while the Al6 atoms are surrounded in a pentagonal prismatic fashion (Figure 4, bottom left to right). The Ni2 prisms are connected via a rectangular face to the Al1 polyhedron followed by another Ni2 prism. The Ni1 double entity is surrounded by two Al6 and two Al7 prisms. These building blocks are arranged in a herringbone pattern in the ab plane, and the remaining spaces are filled by the Ca polyhedra. All atoms centered in the respective polyhedra (Ca, Ni1, Ni2, Al1, Al6 and Al7) are located on z = 0, while the atoms forming the top and bottom faces are found on z = 1/2.

3.4 Quantum-chemical calculations

The results of the structural optimization by the DFT calculation are discussed first. The lattice parameters after the relaxation using the experimental data of the single crystal as a starting point for the DFT calculation are a _theo = 1258.07 pm, b _theo = 1451.23 pm and c _theo = 396.86 pm and are therefore in very good agreement with the experimental PXRD results (Table 1). The bond lengths after the structural relaxation can be found in Table 5. In general, the bond lengths are slightly larger than those found in the experiment, but still in good agreement. The absolute Pearson electronegativity of Ca, Ni and Al is 2.20, 4.40 and 3.23 eV, respectively, and hence one would expect a relatively high positive charge on Ca to balance the negative charge of the polyanionic [Ni₂Al₈] network. To check this hypothesis, Bader charges were calculated. For Ca, Ni and Al the Bader charges according to the Henkelman et al. and the Yu and Trinkle methods are +1.20/+1.20, −3.13/−3.06 to −3.46/−3.38 and +0.25/+0.24 to +1.29/+1.28, respectively (Table 6). Al2 and Al6 are the only Al atoms with Bader charges larger than 1 (+1.29/+1.28 and +1.10/+1.07). The high positive charges of Al2 and Al6 are due to their position right between the negatively charged Ni1 and between the Ni1 and Ni2 atoms (Figure 3), respectively. However, the picture of a purely ionic compound is too crude. The density-of-states reveals that CaNi₂Al₈ is a metal in analogy to LaFe₂Al₈ [45], because of the non-vanishing states at the Fermi level (Figure 5, left). The presence of pseudogaps near the Fermi level from −1.25 to +0.6 eV with no maximum of the DOS at the Fermi level indicates an electronically stable compound with both ionic and covalent interactions [63, 64]. Ca contributes very little to the DOS, while Al contributes mostly in the area of −11 to −4 and −2 eV and above. The Ni states dominate the DOS from −4 to −2 eV. Therefore, Ni is mainly involved in ionic and covalent bonding as its states are localized in a certain energy area, while Al contributes significantly to the metallic bonding in this compound. The DOS also shows similar shapes of the Ni and Al DOS in the area from −4.5 to at least +6 eV, which is also an indicator of a covalently bonded Ni–Al network. A more quantitative measure of covalent bonding is the integrated crystal orbital Hamilton population (ICOHP, Table 5). The ICOHPs of the Ni–Al bonds are in the range from −1.07 to −1.81 eV, suggesting covalent interactions, and therefore the picture of a Ni–Al network is valid. The strongest covalent interactions, however, can be found between the Al5 and Al8 atoms within the Al layer showing an ICOHP of −1.94 eV. Also, quite strong is the intralayer covalent bond Al3–Al4 with an ICOHP of −1.80 eV. The other intralayer covalent bonds between the Al atoms are weaker as the ICOHPS are between −0.69 and −1.25 eV. Less covalent are the interlayer Al–Al bonds found between the Al central atoms and the Al atoms on the vertices of the polyhedron (−0.55 to −1.10 eV). Only weak covalent bonding can be found between Ca and Al as the ICOHPs are in the range from −0.29 to −0.53 eV. Similar to the Ca–Al bonds, the Ni1–Ni1 bonds are weak with an ICOHP of −0.49 eV, although the bond length is quite short (288 pm). The reason for the weak Ni1–Ni1 covalent bond can be found in the −COHP plots (Figure 5, center). From −3 eV to the Fermi level there are antibonding states, which considerably weaken the Ni1–Ni1 bond. The Ca–Al bonds, e.g. Ca–Al5, and the Al–Al bonds, e.g. Al5–Al8, show no occupied antibonding states. The Ni–Al bonds show either only few antibonding states near the Fermi level (Ni1–Al7) or hardly any antibonding states at all (Ni2–Al6; Figure 5 right).

Figure 5:

(Left) Density of states (DOS) of CaNi₂Al₈; (middle) –COHP plots for the Ca–Al5, Ni1–Ni1 and Al5–Al8 bonds (center); (right) –COHP plots of the Ni1–Al7 and Ni2–Al6 bonds.