The new barium compound Ba₄Al_7+x: formation and crystal structure

3.1 Synthesis

Samples obtained directly after arc melting contained mostly two- or three-phases, even if stoichiometric amounts of the starting components were used for the preparation of the known binary phase. This is due to the fact that all intermediate phases in the investigated system form peritectically with the exception of BaAl₄, which forms congruently. Homogenization of the samples was performed at temperatures slightly below their formation points. For thermal treatment, as-cast samples were powdered and subsequently enclosed in tantalum containers. The phases that appeared in these samples after annealing were those expected at the nominal composition, e.g. by using this approach the synthesis procedure was controlled best. Both compact and powdered Ba–Al samples are very sensitive to air and moisture.

3.2 High-temperature powder diffraction and lattice parameters

High-temperature powder diffraction was performed on a sample with the nominal composition Ba₄₄Al₅₆, i.e. containing exclusively the barium-richest phase Ba₄Al₅. Up to ~720°C only diffraction reflections of the initial phase Ba₄Al₅ were observed and the lattice parameters followed the expected positive expansion. At temperatures of 720 and 740°C diffraction lines of the barium-poorer phases Ba₇Al₁₀ and Ba₃Al₅ appeared, respectively, confirming the peritectic character of the formation of these phases. Above 750°C, diffraction lines of the binary barium silicide BaSi [18] were detected, due to the reaction of the randomly distributed barium with the walls of the quartz capillary. In the powder diffraction patterns collected between 820 and 850°C, a hitherto unknown phase was observed which decomposes peritectically into liquid and Ba₇Al₁₃. The latter phase remained stable up to 900°C, the highest temperature in this experiment.

3.3 Crystal structure determination of Ba₄Al_7+x (x = 0.17)

The new barium aluminide was initially detected in the high-temperature diffraction patterns obtained at the synchrotron source. The diffraction reflections were automatically indexed [19] yielding a hexagonal (trigonal) primitive unit cell with the lattice parameters a ≈ 6.14 and c ≈ 39.30 Å. This finding agrees well with the regularities observed in the Ba–Al system: all known phases in this binary system with the exception of BaAl₄ adopt hexagonal (trigonal) symmetry, similar lattice parameters a of about 6.1 Å and different parameters c, which result from the different sequences of the related building blocks. Even the cubic high-pressure phase BaAl₂ (MgCu₂ type, space group Fd3̅m, a(cub) = 8.702 Å) [4, 5] could be represented in the rhombohedral setting (hexagonal axes) in a similar way: a(rh) = a(cub)/2= 6.15 Å and c(rh) = a(cub) ×3 = 15.07 Å. The crystal structures of such intermetallic compounds can be frequently understood by applying the intergrowth approach [20, 21]. Using this crystal chemical trend, a tentative model of the new barium aluminide with 4 Ba and 5 Al crystallographic sites and the composition Ba₄Al₇ was developed in space group P6₃/mmc. The simulated X-ray powder diffraction pattern showed a good agreement with the experimental data obtained in situ at elevated temperatures, with the exception of the two strongest reflections 110 and 116, which were practically absent on the experimental pattern. This discrepancy was caused by the preferred orientation of the crystallites (texture), due to the pronounced {110} atomic layers in the structure. The tentative information about the composition and the formation temperature of the new compound was used for the optimization of the synthesis routine, yielding an almost single-phase and well crystallized bulk material (Fig. 1).

Fig. 1:

High-resolution powder diffraction pattern of Ba₄Al_7+x recorded with the synchrotron radiation (ID31 beamline at ESRF). The bars below the pattern correspond to the calculated positions of the reflections of Ba₄Al_7+x (upper row, majority phase) and Ba₇Al₁₃ (lower row, minority phase). The refinement resulted in the phase ratio of 0.953(8):0.047. The difference curve indicates a good agreement between theoretical and experimental patterns.

Single crystal for X-ray diffraction data was extracted from the sample with the nominal composition Ba_35.9Al_64.1. Atomic parameters of the developed model with 4 Ba and 5 Al atomic sites (space group P6₃/mmc) were used as initial values for the crystal structure refinement. The refinement converged to residuals R = 0.082 and wR2 = 0.148. Whereas atomic displacement parameters of all Ba and of a part of the Al positions showed physically reasonable values between 0.0122(3) and 0.0266(5) Ų, those for the Al4a and Al5a sites were significantly increased to 0.039(2) and 0.057(5) Ų, respectively. Moreover, two pronounced peaks were located in the difference Fourier map in this part of the structure: 10.08 e Å^–3 at 1.33 Å from Al5a and 6.99 e Å^–3 at 0.64 Å from Al4a (Fig. 2). In the next steps, the latter were included into the refinement procedure (designated respectively as Al5b and Al4b) and their occupancies as well as the occupancies of the Al4a and Al5a sites were refined as free variables. The residuals dropped to R = 0.052 and wR2 = 0.080, and the refined occupancies resulted in the values of 0.734(8) for Al4a and 0.25(1) for Al4b, 0.66(3) for Al5a and 0.34(1) for Al5b. The latter numbers indicate that the sum of the occupancies of corresponding split positions practically do not deviate from unity. Thus, in the last refinement cycles the occupancies of Al4a and Al4b, and of Al5a and Al5b sites were constrained. The final refinement was performed with the anisotropic approximation for atomic displacement parameters for all Ba and Al1–Al3 positions, while those for the split positions (Al4a and Al4b, Al5a and Al5b) were kept isotropic. The refinement led to the residuals R = 0.039 and wR2 = 0.059. The final difference Fourier synthesis did not reveal pronounced features with the largest difference values amounting to 1.85 and –0.97 e Å^–3, respectively.

Fig. 2:

The difference Fourier maps obtained after refinement of the “ideal” structure of Ba₄Al₇ (left part) and those obtained after implementation of the additional atomic positions in the model Ba₄Al_7+x (right part). Isolines are drawn with the step of 1 e Å^–3.

The refined occupancies of ~2/3 and ~1/3 for the Al4a (Al5a) and Al4b (Al5b) atomic sites, respectively (Table 2), may suggest the formation of an ordered superstructure for the investigated phase, e.g. with hexagonal metric and a(superstr.) = 3a(subcell). However, a careful examination of both powder and single diffraction data did not yield evidence for the existence of such a superstructure.

Additionally, the following checks were done in separate cycles. The increased value of the atomic displacement parameter for Ba3 (approx. 2× larger as compared with those for the reminder Ba sites, Table 2) indicated a possible partial occupancy for this position. Nevertheless, the refinement of the occupancy of the Ba3 site resulted in the value of 1.001(8), thus showing a full occupancy solely by Ba species. The enlarged interatomic distances around the Al5a position (d(Al5a–Al4a) = 2.95 Å, d(Al5a–Ba1) = 3.57 Å) may indicate a possible presence of Ba atoms in this site. The refinement of the occupancy of the Al5a position by using the scattering factors of Ba resulted in the Al5a:Al4a ratio of ~1:30. This model was ruled out from crystal chemical considerations (if Al atoms occupy the Al5a site, this ratio is ca. 1:6, s. Structure Description). On the other hand, such increased Al–Al distances of 3.077 Å were observed in the high pressure phase BaAl₂ (MgCu₂ type) [4, 5]. Thus, the structure model listed in Tables 1 and 2 is considered to be the final result of the refinement.

Further details of the crystal structure investigation may be obtained from Fachinformationszentrum Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (fax: +49-7247-808-666; e-mail: crysdata@fiz-karlsruhe.de, http://www.fiz-karlsruhe.de/request_for_deposited_data.html) on quoting the deposition number CSD-431104.

4.1 Description of the crystal structure of Ba₄Al_7+x (x = 0.17)

Analysis of the Pearson Data Base [22] reveals that the crystal structure of Ba₄Al_7+x (Fig. 3) represents a new structure type. As a conference contribution [23], a ternary Ba₈Al_9+xGa_6−x phase with similar lattice parameters and composition (hexagonal, a = 6.033, c = 38.775 Å) was reported. Nevertheless, an absence of further crystallographic information in the literature did not allow to attribute this phase as isostructural to Ba₄Al_7+x. The crystal structure of Ba₄Al_7+x is described by 4 Ba, 3 fully occupied Al positions and 4 partially occupied Al sites. The occupancies were constrained pairwise with the ratio of the occupancy factors close to 2:1 in both cases (Table 2). Topologically, the crystal structure of Ba₄Al_7+x is a derivative of a Laves phase of the MgZn₂ type [24], where building fragments of the latter are separated by barium atoms. The arrangement of the building blocks in the structure of Ba₄Al_7+x can be described by the sequence (AABAB)₂, where A and B designate fragments of the MgZn₂ [24] and Ni₂In [25] types. The latter structure type is realized, e.g. in Zr₂Al [26] and Sc₂Al [27]. There are two kinds of building blocks consisting of Laves phase fragments in the structure: singular (A) and doubled (AA). Singular blocks contain only fully occupied Al positions, whereas doubled blocks are partially disordered. The arrangement of the Al atoms in the singular block can be described as an almost planar Kagomé net, where each triangle is capped above and below by additional Al atoms, yielding trigonal bipyramids. The analysis of the interatomic distances shows that Al–Al contacts within the bipyramid are significantly shorter (2.823 and 2.733 Å between equatorial-equatorial and equatorial-axial atoms, respectively) than the interatomic distances of 3.268 Å between neighboring bipyramids. Thus, the arrangement of the Al atoms within isolated trigonal bipyramids in the discussed fragment is a rather zero-dimensional one. This description based on a Kagomé net has only formal character and is far away from the real situation in the structure of Ba₄Al_7+x. But, from a topological point of view, the description of this part of the structure as containing Kagomé layers stacked parallel to (001) is more convenient for the structure visualization.

Fig. 3:

Projection of the crystal structure of Ba₄Al_7+x along [110]. The digits within large circles correspond to atomic designation of Ba positions. Those for the Al sites are marked as digits adjacent to small atoms. In the right-hand part of the Figure, the ordering sequence of the building blocks in the structure is designated. The solid line shows the projection of the unit cell.

In the double Laves phase blocks (AA), the situation is slightly different. Two models of the ordering of Al atoms within these blocks are possible. In the first model, there are two different kinds of arrangements, which are realized in the separate Laves phase blocks. In the first kind only the singular Al positions at the inversion center (Al5a and supplemented Al4a sites) are realized (Fig. 4a), and in the other kind only Al–Al pairs (Al5b and supplemented Al4b sites) are present (Fig. 4b). The first case is very similar to the situation just discussed above for the singular Laves phase blocks (A). The interatomic Al–Al distances realized here are: 2.943, 2.951 (2.661) and 3.149 Å between equatorial-equatorial, equatorial-axial and bipyramid-bipyramid atoms, respectively (Fig. 4a, fragment I). In the second kind of arrangements, the distances are quite different: 2.672 Å for Al–Al pairs, 3.911 and 2.641 (2.845 Å) between equatorial-equatorial and equatorial-axial atoms, respectively (Fig. 4b, fragment II). However, an unreasonable distance of 2.18 Å occurs between neighboring bipyramids, ruling out this model. The second model visualizes the presence of both fragments I and II within one block. Taking into account the refined occupancies ~2/3 and ~1/3, one can suggest an arrangement of this block in which fragments I and II are distributed in an ordered manner (Fig. 4c). In the model just discussed, distances within fragments I and II are kept, but the unreasonable contact of 2.18 Å observed in the first model for the layers containing only fragments II is no longer present. The distance of 2.697 Å which is realized between the neighboring fragments I and II, is in excellent agreement with the closest Al–Al contacts of 2.863 Å observed in the elemental aluminum [28]. This interaction can explain probably also the slightly elongated equatorial-equatorial and equatorial-axial distances of 2.933 and 2.945 Å, observed in the fragment I. Taking into account this model, we can assume a 2D character of the Al arrangement in this block. The latter model agrees very well with the occupancies of the Al5a (Al5b) and Al4a (Al4b) sites and provides reasonable Al–Al distances. This kind of ordering requires an increase of the unit cell, which should be reflected in the appearance of superstructure reflections. In both our powder and single-crystal diffraction experiments, these reflections are not observed, revealing an absence of long range order of the Al substructure. The shortest Al–Al distance of 4.89 Å between atoms located in adjacent Laves-phase blocks evidences the complete absence of the interaction between aluminum atoms of neighboring blocks.

Fig. 4:

Possible arrangements of Al atoms within double Laves phase blocks: (a) Al5a and Al4a positions, described in the ideal B₄Al₇ model, form fragment I; (b) Al5b and Al4b positions form fragment II; (c) proposed ordering of fragments I and II, taking into account an occupancy ratio of 2:1.

The arrangement of the Ba atoms in the crystal structure of Ba₄Al_7+x can be described as an abc–cba–ab–bac–cab–b sequence of hexagonal layers. Most of the barium positions (Ba1, B2 and Ba4) are tetrahedrally coordinated by Ba atoms. Only the Ba3 site, located in the Ni₂In-type block (B), has an octahedral coordination. Consequently, the shortest homonuclear contacts d(Ba4–Ba4) = 3.710 and d(Ba1–Ba2) = 3.723 Å, occur between Ba atoms within MgZn₂-like blocks. The corresponding distances around the Ba3 atom are slightly longer: d(Ba3–Ba2) = 3.893 Å (3×) and d(Ba3–Ba4) = 4.032 Å (3×). All these values are definitely shorter than the Ba–Ba contacts of 4.350 Å observed in bcc barium [28], indicating some cationic character of the Ba atoms in the structure of Ba₄Al_7+x. The Ba–Al distances cover the relatively narrow range 3.483–3.590 Å for the Ba sites with the tetrahedral homonuclear environment (Ba1, Ba2 and Ba4). The Al atoms around the Ba3 site which are located within the Ba₆ octahedron are displaced slightly away from the central atom at 3.802–3.974 Å. All atoms in the structure are located in {110} planes. This fact is reflected in the pronounced preferred orientation observed during the HT measurements.

4.2 Structural relationship

The building fragments of the crystal structure of Ba₄Al_7+x match very well with the regularities in the structure description used for other phases in the Ba–Al system (with the exception of BaAl₄) as well as for the related aluminide Sr₅Al₉ [29]. In Fig. 5, these structures are shown to be in agreement with an increased content of alkaline-earth metal. All these structures are described by a hexagonal metric with a similar lattice parameter a = ≈6.1 Å and different parameters c, caused by the different sequence of the building blocks. The basic blocks of this series are atomic arrangements typical for Laves phases (designated as D for MgCu₂ and A for MgZn₂ fragments). In BaAl₂ only blocks of type D are realized. In the next structures of the series they are separated initially by mono- and later by double-layers of Ba atoms. Formally, these fragments can be described as Ni₂In- (B) [26] and Na₃As-type (C) blocks [30], respectively. The following sequences are realized in the Ba–Al compounds: (D)₃ for BaAl₂, (ADAB) for Ba₇Al₁₃, (AAB)₃ for Sr₅Al₉, (AABAB)₂ for Ba₄Al_7+x, (AB)₂ for Ba₃Al₅, (ABAC)₃ for Ba₇Al₁₀, (AC)₂ for Ba₄Al₅. In both structures with double Laves phase blocks (the initial Ba₇Al₁₃ model [7] and the structure of Ba₄Al_7+x now reported), partial disorder is observed. The precise investigation of the Ba₇Al₁₃ structure revealed an additional position for Al requiring an increase of the hexagonal unit cell (a(new) = 3a(old)) and a slightly modified composition of Ba₂₁Al₄₀ [6]. The introduction of the additional atomic site and the reduction of the symmetry reflect the deformation of the ideal Al substructure in the Laves phase blocks. A similar situation is observed in Ba₄Al_7+x, where one of the ordered models is also characterized by the corrugation of the Al net. It seems that the size ratio of Ba and Al is not optimal for building the ideal double Laves-phase blocks. For this reason the pure Laves phase BaAl₂ is metastable and can be synthesized only at high pressure [4, 5].

Fig. 5:

Stacking of the building blocks in the Ba–Al structures as well as in the related Sr₅Al₉ structure. A, B, C and D are segments of the structure types MgZn₂, Ni₂In, Na₃As and MgCu₂, respectively.

4.3 Updated binary Ba–Al phase diagram

The first report of a Ba–Al phase diagram was published by Alberti in 1934 [31], who presented the aluminum-rich part of the system (up to 11 at% Ba). The complete concentration interval was provided in the early fifties [32]. Nevertheless, this report contains solely BaAl₄ as an intermediate phase. The phase diagram published by Bruzzone and Merlo [11] included the phases Ba₂₁Al₄₀ (Ba₇Al₁₃) and Ba₄Al₅, which had been discovered in the meantime. Nevertheless, in that report they are denoted as BaAl₂ and BaAl. In a later overview [33], the Ba–Al phase diagram was updated with the Ba₃Al₅ phase [8, 9]. Thus, before the start of the present study, the experimental phase diagram was about 40 years old and the Ba₇Al₁₀ phase [8, 9] was absent. The examination of the thermal analysis experiments (Fig. 6) have now resulted in an updated Ba–Al phase diagram (Fig. 7). All intermediate binary phases in this system (with the exception of BaAl₄) are formed peritectically from the melt and the corresponding neighboring phases with larger content of Al. The synthesis of Ba₄Al_7+x from the melt is feasible in the relatively narrow temperature interval of 826–841°C only. This may be the reason why this phase was not observed in previous studies.

Fig. 6:

Difference scanning calorimetry (DSC) curves obtained from single-phase samples in the Ba–Al system. For each phase, the onset temperature of the corresponding peritectic decomposition is noted.

Fig. 7:

Updated binary Ba–Al phase diagram between 30 and 50 at% of Ba.