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Article

Crystal and Electronic Structure of Ternary Bismuthides BaTM1.8Bi2 (TM = Au, Ag) with a New Variation of the BaAu2Sb2 Structure Type

by
Andrey I. Shilov
1,
Evgeny O. Rakhmanov
1,
Konstantin A. Lyssenko
1,2,
Alexey N. Kuznetsov
1,3,
Igor V. Morozov
1 and
Andrei V. Shevelkov
1,*
1
Department of Chemistry, Lomonosov Moscow State University, Moscow 119991, Russia
2
Faculty of Chemistry, National University Higher School of Economics, Moscow 109028, Russia
3
Kurnakov Institute of General and Inorganic Chemistry of RAS, Moscow 119991, Russia
*
Author to whom correspondence should be addressed.
Crystals 2024, 14(2), 155; https://doi.org/10.3390/cryst14020155
Submission received: 21 December 2023 / Revised: 27 January 2024 / Accepted: 29 January 2024 / Published: 31 January 2024
(This article belongs to the Section Crystalline Metals and Alloys)
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Abstract

:
Recently discovered bismuthides with the BaAu2Sb2 structure type demonstrate interesting properties and electronic structures. Here, we report successful crystal growth, crystal structure, band structure calculations, and DOS for BaAg1.8Bi2 and BaAu1.8Bi2. Grown crystals were characterized by a combination of single crystal X-ray diffraction and EDX spectroscopy. Both compounds crystallized in a new variation of BaAu2Sb2 structure type and demonstrated metallic properties according to our DFT calculations.

1. Introduction

Complex pnictides of d-metals have long been the focus of researcher’s attention due to the diversity of their structures combined with interesting physical properties [1,2,3,4,5,6]. The discovery of superconductors based on layered ferroarsenides in 2008 caused great interest in the scientific community and stimulated the search for analogues of these compounds. Among them is a parent superconducting compound BaFe2As2 and related arsenides that crystallize in the ThCr2Si2 structure type. Recently, the pronounced spin–orbit interaction in bismuth-containing analogs has attracted attention since additional topologically determined properties are expected. In this regard, ternary bismuthides with crystal structures related to the so-called 122 family of iron-containing superconductors have become intriguing objects of investigation. However, it turned out that, whereas phosphides, arsenides, and antimonides of the 122 family are numerous, isostructural bismuthide analogues of this family are quite rare [7].
The first bismuthide with the ThCr2Si2 type of structure, BaMn2Bi2, was reported only in 2013. It displays antiferromagnetic and thermoelectric properties, and, with the partial substitution of barium for potassium, it demonstrates a transition to a superconducting state [1,8,9]. Recently, we have presented several compounds of the ATM2Bi2 (A = K, Rb, Cs, TM = Zn, Cd) series crystallizing in the ThCr2Si2 structure type, in which a certain electron deficiency and the presence of Bi···Bi interaction between neighboring layers were observed [10]. These features of new compounds are in line with the earlier discussion of the variety of the bonding pattern in 122 compounds [11] (Figure 1a).
Other bismuthides of the ATM2Bi2 series (TM = d-metal, A = alkali, alkali-earth, or rare-earth metal) are also known, but they belong to different structure types; in particular, when TM belongs to elements of groups 10 or 11 of the periodic table (TM = Pd, Pt, Ag), 122 compounds crystallize in the CaBe2Ge2 type (sp. gr. P4/nmm) and its derivatives (Figure 1b). In contrast to the above-described compounds with the ThCr2Si2 structure, they are built of antifluorite-like layers [TMBi], made of edge-sharing [TMBi4] tetrahedra that alternate with inverted fluorite-like layers [BiTM] of the same composition and structure, in which Bi and TM atoms swap places. Bi atoms form a regular square grid with a Bi−Bi distance of about 3.45 Å, above and below which T atoms are placed to form tetrahedral polyhedra [BiTM4] connected by common edges. Alternating [BiTM] and [TMBi] layers are combined into a three-dimensional framework with the help of Bi−TM bonds. Finally, A-cations are placed in the resulting voids [12,13,14]. For a number of bismuthides and antimonides, a monoclinic distortion (sp. gr. P21/m) was detected, associated with a certain displacement of the layers with respect to each other, which made it possible to distinguish a separate structure type of BaAu2Sb2. Low-temperature superconductivity has recently been discovered for SrPd2Bi2 (P4/nmm) and BaPt2Bi2 (P21/m) compounds with the critical temperature of 1.9 and 2.0 K, respectively [13,14].
The compound BaAg1.8Bi2 was first reported in 2007 [12]. It crystallizes in the CaBe2Ge2 structure type and features partial occupation of the positions of one of the silver atoms and disordering of the bismuth atom. It should be noted that 122 pnictides containing group 11 metals (Cu, Ag, Au) are often characterized by non-stoichiometry of the d-metal in the position of the fluorite-like layer [PnTM] [12,14]. Despite the existence of the bismuthide BaAg1.8Bi2, as well as gold-containing antimonide BaAu2Sb2, barium/gold bismuthide BaAu1.8Bi2 remained unknown until now.
In this paper, we describe the crystal growth of large, up to 4 mm in linear dimensions, crystals of bismuthides BaAg1.8Bi2 and, for the first time, synthesized BaAu1.8Bi2. The study of the crystal structure by X-ray single crystal diffraction showed that, despite their close relation to the BaAu2Sb2 type, these compounds exhibit certain structural features and crystallize in a monoclinic space group C2/m that has not been previously encountered for this family of structures. We present a detailed discussion of their crystal structures, paying special attention to minor yet important differences between silver- and gold-containing compounds. We also report key features of their electronic structure and compare them to related compounds of the 122 and 112 families of bismuthides.

2. Materials and Methods

2.1. Crystal Growth and Sample Characterization

Single crystals of BaTM1,8Bi2 (TM = Ag (1) or Au (2)) were obtained by the self-flux method. All operations with the starting materials and products were performed in a dry argon glovebox with a volume fraction of water and oxygen vapors not higher than 0.1 ppm. Elemental barium, bismuth, silver, and gold were used as starting materials. Reagents were taken in the ratio Ba:TM:Bi = 1:2:7, placed in an alumina crucible, which was welded by electric arc into a niobium container in an argon atmosphere, and then isolated in a vacuumed and sealed quartz ampule. The ampule was heated to a temperature of 1050 °C, annealed for 24 h, cooled down to 450 °C at a rate of 3 °C/h, kept at this temperature for 24 h, after which the furnace was turned off. The crucible was removed and carefully cut, the grown crystals were separated from the excess bismuth by centrifugation and then mechanically under a Levenhuk DTX 700 digital microscope (Prague, Czech Republic) installed inside the glovebox. As a result, BaTM1,8Bi2 single crystals were obtained in the form of plates with sizes up to 4 × 4 × 0.5 mm3 (Figure 2). When exposed to air, these crystals gradually break down, so their storage and sample preparation were carried out in a dry argon glovebox.
The crystal structure of both compounds was established by single-crystal X-ray diffraction analysis using a Bruker D8 Quest diffractometer, Mo-Kα, equipped with a CCD Photon III detector. The solution and refinement of the crystal structures were performed using the SHELXT-2018 v.2 and SHELXL-2018 v.3 software packages [15,16]; the absorption correction was applied numerically with the aid of a crystal-shape model using the SADABS software package [17]. Crystal structures of 1 and 2 were deposited in the CSD structural database, 2312786 (1) and 2312785 (2). Crystal data and details of experiments, crystal structure refinement, and selected interatomic distances are given in Table 1 and Table 2.
To confirm the chemical composition of both compounds, the crystals were examined using a scanning electron microscope JSM JEOL 6490-LV (Tokyo, Japan) (accelerating voltage 30 kV, secondary electron emission detector) equipped with an INCA x-Sight energy dispersive X-ray spectroscopy system (EDXS, Tokyo, Japan).

2.2. Computational Details

Calculations of the electronic structures of BaTM2Bi2 (TM = Ag, Au, Pd) and BaZnBi2 were performed on the Density Functional Theory (DFT) level using the projector augmented wave method (PAW) as implemented in the Vienna Ab initio Simulation Package (VASP) [18,19]. Fully ordered models with full site occupancies were used in the calculations. Experimental structure parameters were used for the calculations and transformed to the P1 group; in all cases, atomic coordinates were allowed to relax to eliminate stresses in the structure. The r2SCAN exchange-correlation functional of the meta-GGA type was used for the calculations [20,21]. The number of k-points in the first Brillouin zone was chosen so as to provide a step between k-points of no more than 0.02 Å−1. Energy cutoff was set to 550 eV, and the energy convergence criterion was at 10−5 eV. Charge density analysis was performed employing PAW augmentation using the Bader 1.04 package from Henkelman group [22,23,24,25]. DOS and band plots were produced using sumo 2.3.7 package [26]. Direct-space COHP (Crystal Orbital Hamilton Population) analysis was performed based on the VASP calculations using LOBSTER 5.0.0 package [27,28,29,30,31]. COHP plots were produced using wxDragon package [32].

3. Results and Discussion

3.1. Synthesis and Crystal Structure

Crystals of compounds 1 and 2 were grown by the self-flux method using molten bismuth as a reactive solvent. The self-flux method is frequently used for growing various pnictides of the 122 series [33]. Also, this approach was employed to obtain bismuthides of the composition 111 [34] and, during the attempt to synthesize the BaAgBi compound, BaAg1.83Bi2 single crystals were obtained for the first time [12]. In our experiments, the ratio of components and the temperature profile were optimized, which made it possible to reproducibly obtain single crystals of compounds 1 and 2 of acceptable size and quality. Figure 2 shows optical and electronic photographs of the samples obtained. Their chemical composition probed by EDX spectroscopy was found to be Ba1.06(3)Ag1.81(2)Bi2.13(4) for 1 and Ba0.97(5)Au1.80(6)Bi2.23(5) for 2, which corresponds well to the crystal data discussed below.
The bismuthides 1 and 2 are isostructural. They crystallize with a new structure type, which is very similar to that of BaAu2Sb2, in that both types demonstrate a monoclinic distortion of the CaBe2Ge2 structure type. However, compounds 1 and 2 crystallize in the space group C2/m (Table 1), whereas BaAu2Sb2 exhibits a smaller unit cell volume and the space group P21/m. A specific feature of the crystal structure of 1 and 2, never previously described for compounds crystallizing in the structure type of CaBe2Ge2 and its derivatives, consists in the presence of a local disordering of d-metal atoms in the antifluorite-like layer [TMBi], which is caused by the partial occupation of the TM1 position in the fluorite-like layer.
In the crystal structures of 1 and 2, [BiTM0.8] and [TMBi] layers run parallel to the ab plane (Figure 3). We will further discuss the entire structure as consisting of layers at z = 0 and z = 0.5 and barium atoms occupying large voids.
At a height of z = 0.5, there is a fluorite-like layer [Bi(1)TM(1)0.8], in which Bi(1) atoms form a slightly distorted flat square grid, the average Bi···Bi distances being 3.453 and 3.464 Å in 1 and 2, respectively. Above or below the centers of the squares of this grid, TM(1) atoms are staggered, binding simultaneously four Bi(1) atoms from this layer at distances of 2.900 (1) and 2.902 Å (2). In addition, the TM(1) atom forms another TM–Bi bond with a length of 2.759 Å in 1 and 2.744 Å in 2, directed along the c axis towards the Bi(2) atom from the neighboring layer. Thus, the coordination polyhedron of the TM(1) atom is a tetragonal pyramid [TMBi5] (Figure 4a, Table 2). At the same time, a tetrahedral environment of TM atoms is formed around the bismuth atoms (Figure 4b). The [BiTM4] tetrahedra are noticeably compressed along the c axis, the TM−Bi−TM angles at the edges of the tetrahedron perpendicular to the c axis are 114.7 deg. for 1 and 115.2 deg. for 2. It should be noted that the observed interatomic distances correspond well to those calculated using covalent radii from [35]. Thus, the calculated bond lengths of Ag−Bi and Au−Bi are 2.93 and 2.84 Å in 1 and 2, respectively (Table 2). We also note that the geometric characteristics describing the [BiTM0.8] layer are very close in both structures (Table 2).
It should be taken into account that about 20% of TM(1) positions are vacant; the occupancy of the Ag(1) and Au(1) positions is 0.794 and 0.814, respectively. This means that a number of the [BiTM4] tetrahedra have vertices missing. Indeed, in the absence of one TM(1) atom, there are four [BiTM4] tetrahedra at once that are missing this atom. Figure S1 shows a view of the [BiAu0.8] layer, in which 20% of Au(1) vacancies are distributed uniformly in an ordered manner, by analogy with the well-known crystal structure of K2Fe4Se5 (the so-called “245” phase), in which 20% of vacancies are placed in an ordered square iron grid [36]. It can be seen that, with such a vacancy distribution, the amount of Bi(1) atoms with a full tetrahedral environment is exactly 20%, whereas all other Bi(1) atoms (80%) have only 3 Au1 atoms in their environment. Apparently, despite the shortage of d-metal atoms, the [BiTM0.8] layer is stabilized due to a certain chemical interaction between Bi atoms directly in the square bismuth grid. This phenomenon will be given special attention further in this paper.
At z = 0, there is an antifluorite-like layer of the composition [TMBi] inverted relative to the [BiTM0.8] layer, such that TM atoms form a square grid, above and below which there are either Bi(2) atoms with the occupancy of about 0.8, or more distant Bi(2′) atoms with the occupancy of about 0.2. The peculiarity of the structure of the [TMBi] layer is that there is a splitting of the TM(2) position relative to the geometric center (idealized position, indicated by Au3 in Figure 3 and Figure 5c), which corresponds to the Wyckoff position 4g. The difference between the crystal structures of 1 and 2 is that in the former, the Ag position is split into two equally populated positions located at a distance of 0.38 Å from each other, whereas in the latter structure, the Au position is split into 4 equally populated positions (2 × Au2 and 2 × Au2′), the distance between which is 0.6−0.7 Å. A comparison of possible Au−Bi distances (Figure S2) allows us to uniquely determine the geometry of the [Au2Bi4] and [Au2′Bi4] tetrahedra (Figure 5a,b). It can be seen that, in each case, the tetrahedra include three Bi2 atoms and one Bi2′ atom. Indeed, each of the four positions of gold, Au2 or Au2′, is shifted relative to the local center towards one of the four possible positions Bi2′, forming a bond with it of acceptable length (about 3 Å). The situation when the Bi2 atom is placed at this vertex instead of the Bi2′ atom is impossible, since the corresponding Au2−Bi2 distance would be too small (2.352 Å). This consideration also shows that for the seemingly highly probable case when four Bi2 atoms are located at the vertices of the [Au(2)Bi4] tetrahedron, one of the Au−Bi distances turns out to be unacceptably short. Thus, the relative number of tetrahedra of the type [Au(2)Bi(2)4] in the [AuBi] layer should be small, and the [Au(2)Bi(2)3Bi(2′)1] tetrahedra should prevail.
We note that the split of the TM2 (TM = Ag) position was not observed in the previous study [12]. The reason that this structural feature was not detected in the earlier work may be that the X-ray diffraction study was performed at room temperature (297 K), at which thermal vibrations of atoms make it difficult to detect local splitting of the atomic positions of Ag. In this work, the experiment was carried out at a temperature of 116(2)K, which significantly affected the magnitude of the thermal displacement parameters and allowed us to clarify the disordering of the silver atom. In general, the solution of the BaAg1.8Bi2 structure presented earlier [12] has a number of disadvantages, such as large values of the residual electron density as well as a significant increase in the Ag−Bi bond length (up to 0.3 Å) when the bismuth atom is shifted to a position with a minor population. The solution proposed in this paper is free of such issues.
As a result of the structural features discussed above, the [TMBi4] tetrahedra in the [TMBi] layer are quite distorted compared to [BiTM4] tetrahedra in the [BiTM0.8] layer (Figure 5a,b, Table 2). The Au−Bi distances vary from 2.843 to 3.035 Å, whereas the average distance in each tetrahedron is 2.931 Å, which correlates well with the literature data on the covalent radii (2.84 Å [35]). The situation is similar with the tetrahedron [Ag(1)Bi(2)3Bi(2′)1] in 1.
Similar to the TM(1) atom surrounded by five Bi atoms, the Bi(2) atom is surrounded by five Au atoms forming a [BiAu5] tetragonal pyramid (Figure 5c). The base of the pyramid is four Au(2)/Au(2′) atoms from the [AuBi] layer and the vertex is the Au(1) atom from the neighboring [BiTM0.8] layer. In the absence of the Au(1) atom, the bismuth atom is displaced along the c axis from the [AuBi] layer towards the [BiAu0.8] layer, which is, from the Bi(2) position to the Bi(2′) position (Figure 3 and Figure 5c,d). This displacement allows bismuth to form stronger bonds with four Ba atoms, compensating for the departure of the Au(1) atom from its coordination sphere. Indeed, the Bi(2′)−Ba distances of 3.48 Å correspond to the formation of a strong chemical bond between these atoms; this estimation is based on covalent radii of Bi and Ba atoms taken from [35] or effective ionic radii Bi3− from [5] and Ba2+ (CN8) from [37]. Both estimations give practically the same value of 3.63 or 3.64 Å, respectively.
Alternating [BiTM0.8] and [TMBi] layers are combined into a three-dimensional framework with the help of interlayer Bi−TM bonds. Ba2+ cations fill the centers of the resulting 17-vertex polyhedra, which can be described as two interpenetrating polyhedra, a TM8 Archimedean antiprism, and a Bi9 mono-capped Archimedean antiprism (Figure 6). The calculated Malliken charge of the Ba2+ cation in BaAg1.83Bi2 is +1.93 [12], which indicates the ionic nature of the bonding between the barium cation with its environment. The long Ba−Bi distances, 3.70–3.90 Å, not counting the shorter distance 3.48 Å to the Bi(2) atom with a minor population, allow us to consider the interaction of the electropositive cation Ba2+ and the anionic three-dimensional framework [TM1.8Bi2]2− as characteristic of “guest-host” clathrate-like compounds, which can also mean that these compounds have promising thermoelectric properties [38].
Vacancies in the Au1 positions and Bi2′ atoms are located on the c axis in pairs in the interlayer space. Consequently, any distribution of Au(1) vacancies in the [BiAu] layer inevitably leads to the same time of distribution of Bi(2′) atoms across the [AuBi] layer; therefore, an ordered distribution of Au1 vacancies presented in Figure S2 will correspond to the same ordered distribution of Bi2′ atoms in the [AuBi] layer (Figure S3). At the same time, the [AuBi(2)3Bi(2′)] tetrahedra will prevail (their share will be 80%), which corresponds well to the nature of the splitting of gold atoms in the [AuBi] layer. The analysis shows that the observed local structural features of 1 and 2 may indicate the possibility of the existence of a partial or complete ordering of TM(1) vacancies, which may lead to the formation of a superstructure. This was not observed in our X-ray crystal structure experiments, and it is possible that its detection requires the use of high-resolution electron microscopy methods.
The Bi···Bi distances in the fluorite-like [BiTM] layers are 3.466 Å in 1 and 3.453 Å in 2, which are weaker than the single Bi−Bi bond of 3.05 Å but are significantly shorter than Bi···Bi nonbonding distances exceeding 4 Å in square grids observed in other bismuthides [39]. The interatomic distance undoubtedly corresponds to the presence of a certain interaction. The calculation of the bond strength by analyzing the overlap populations, performed for BaAg1.83Bi2 [10], yielded a value of 0.17, which points at a weak interaction between bismuth atoms. It is interesting to note that the [Bi]− layer in the form of a regular square grid with almost the same Bi···Bi distance (3.3−3.5 Å) is characteristic of the 112 family of bismuthides, for example, BaZnBi2 [40]. This is also reported for binary compounds, for example, EuBi2 [41]; moreover, in these compounds, such layers are not decorated with some other atoms and experience only electrostatic interaction with Ba2+ or Eu2+ cations. The explanation of the nature of the chemical interaction in such layers was given in the review by Papoian and Hoffmann [42], according to which the Bi atoms in such a flat grid are connected to each other due to the hypervalent interaction of p-orbitals lying in the plane. The formal oxidation state of bismuth in such a layer is −1. In the case of compounds 1 and 2 with the structure derived from CaBe2Ge2, the Bi(1) atoms forming the [Bi]− layer, in addition to hypervalent bonds, also form covalent bonds with TM = Ag, Au atoms within the [Bi(TM)4] tetrahedra. Thus, it can be assumed that the formal oxidation state of Bi(1) is −1 and −3 for Bi(2). Then, in the stoichiometric compound BaTM2Bi2, the formal oxidation state of the d-element will be +1, which corresponds well to the observed TM−Bi bond lengths. The incomplete population of d-metal atoms in the TM(1) position complicates such a formal consideration; however, the presence of metallic conductivity predicted in the literature [12] for 1 implies a partial generalization of electrons in a negatively charged core [TM1.8Bi2]2−, which removes the requirement for the quantitative fulfillment of the Zintl rule.

3.2. Electronic Structure and Bonding

DFT calculations on the idealized ordered BaAg2Bi2 and BaAu2Bi2 structures were performed to establish main features of their electronic structures and evaluate bonding patterns. For the sake of comparison, we also performed DFT calculations on the BaPd2Bi2 and BaZnBi2 phases. Total and projected densities of states (DOS) near the Fermi level are shown in Figure 7, with the enlarged area around the Fermi level shown in Figure S4 in the Supplementary information section.
As seen from the plots, all the 122-type compounds share the same essential features. The region below the Fermi level is dominated by the contributions from transition metal d-states, which are practically filled, that are mixed with bismuth p-states and transition metal s-states. Ba s-states are essentially vacant and reside above the Fermi level, while Bi s-states reside significantly below the Fermi energy and do not contribute to the DOS around it. Qualitatively, this picture has similarities with what is observed for BaZnBi2; however, there are significant differences: Zn d-states appear to be significantly more localized, and their mixing with Zn s-states and Bi p-states is far less pronounced. According to rather low, yet non-zero, DOS at the Fermi level, all the compounds are metallic conductors, which was experimentally confirmed for BaZnBi2 in the literature [43]. Figure 8 displays energy dispersion curves along the high symmetry points (band structure) for the 122-type compounds. It confirms the metallic nature of the compounds and the main contributions around the Fermi level arising from transition metal d- and s-states and bismuth p-states. The pictures with SOC and spin polarization taken into account and those without it are rather similar, with minor differences, of which, perhaps, the most notable is the opening of the gap at the A and B points for BaAg2Bi2 and BaAu2Bi2 upon “switching” SOC on; however, this does not change the 3D metallic nature of these compounds.
To characterize interactions in the structures of bismuthides, we have performed a Crystal Orbital Hamilton Population (COHP) analysis. Partial COHP for Bi−TM, Bi−Bi, and TM−TM interactions are shown in Figure 9. As seen from the plots, in the 122-type compounds, the first one is the most prominent, at the same time, it is the least optimized, featuring occupied antibonding states at and below the Fermi level. Homoatomic Bi−Bi and TM−TM interactions are better optimized, as there is only minor occupancy of antibonding states; however, they contribute significantly less to the total bond energy of the respective compounds. In contrast, in the structure of BaZnBi2, Bi−Zn and Bi−Bi interactions are two major and almost equal contributions to the bond energy, and they appear to be equally optimized near the Fermi level with only minor differences.
This picture is complemented by analyzing calculated partial COHP values, integrated up to the Fermi level (IpCOHP), which can be taken as relative bond strengths (see Table 3). According to the data, Bi−TM are, indeed, the strongest interactions energy-wise in the 122-type compounds. Their averaged relative energies per bond are from ca. 1.5 (BaAg2Bi2, BaPd2Bi2) to ca. 2 (BaAu2Bi2) times larger than those of the next strongest bonds, Bi−Bi. When compared to these two interactions, TM−TM appears to be minor. On the contrary, in BaZnBi2 Bi−Bi interactions are on par and even ca. 20% stronger than Bi−Zn ones [43]. This analysis shows that, in the 122-type compounds in question, the structure is primarily stabilized by the Bi−TM interactions, where extra transition metal is important, and in the BaZnBi2, lacking extra Zn, Bi−Bi interactions come to the forefront. Also, it must be noted that, considering the notable antibonding character of the Bi−TM interactions, depleting these states of electrons below the Fermi level might act as a stabilizing factor as well, thus the transition metal vacancies and related disorder in the structures of Ag- and Au-containing 122-type compounds (vide supra) can be rationalized based on the COHP data.
Calculated Bader atomic charges (Table 4) show that the charge is strongly transferred from Ba atoms towards TM (the strongest charge density acceptor in 122) and Bi (accumulates the most negative charge in BaZnBi2). Atomic charges of the TM and Bi atoms in the 122-type compounds are less radical, implying mostly covalent polar heterometallic and covalent homometallic interactions, which is consistent with the DOS and COHP analysis.

4. Conclusions

We have developed a self-flux technique for growing crystals of ternary bismuthides BaAg1.8Bi2 and BaAu1.8Bi2 from the reactive bismuth flux. The latter compound was prepared for the first time, whereas the former was already known from the literature. Their crystal structure is viewed as yet another variant of the monoclinic distortion of the CaBe2Ge2 type of structure and resembles that of the BaAu2Sb2 crystal structure. The crystal structure features the alternation of fluorite-like [BiTM] and antifluorite-like [TMBi] layers along the c-axis, with Ba2+ cations residing in large 17-vertex voids formed between the layers. An important feature of the crystal structure is the disordering of the TM atoms in the antifluorite-like layer such that two (Ag) or four (Au) equally occupied alternating positions form. Another important feature is the partial population of the TM position in the fluorite-like layer. This not only distinguishes the BaTM1.8Bi2 compounds from other phases of the 122 family, but also leads to significant features in their electronic structure, which was analyzed based on the DFT calculations. Considering rather weak Bi···Bi bonding with Bi−Bi distances of about 3.45 Å, the dominant contribution of d-states of silver or gold to the bands near the Fermi level, and strong and non-optimized TM−Bi interactions, depleting the d-states right below the Fermi level might act as a stabilizing factor. Moreover, almost identical population of the respective site by Ag and Au atoms in the title structures and the dominance of Bi−Bi interactions in BaZnBi2 compound lacking an extra Zn atom might be another indication of the primary importance of the electronic factor. The noticeable similarity of the crystal and electronic structure of BaTM2Bi2 and 122 superconductors calls for the exploration of the properties of the title compound at low temperatures, which will be the topic of a separate study.

Supplementary Materials

The following supporting information can be downloaded at https://www.mdpi.com/article/10.3390/cryst14020155/s1: Figure S1: Variant of the ordered distribution of 20% vacancies of gold atoms in the [Bi1Au1] layer; Figure S2: Variation of the coordination environment for split positions of Au2 and Au2′ atoms in 2 and Ag2 atoms in 1; Figure S3: [Au(2,2′)Bi] layer with an ordered distribution of Bi2′ atoms; Figure S4: Enlarged DOS plot around the Fermi level for BaAg2Bi2, BaAu2Bi2, BaPd2Bi2, and BaZnBi2.

Author Contributions

Conceptualization A.I.S. and I.V.M., methodology I.V.M. and A.I.S., synthesis A.I.S. and E.O.R., investigation A.I.S., E.O.R., K.A.L. and A.N.K., data curation I.V.M. and A.N.K., writing—original draft preparation, I.V.M., A.N.K. and A.I.S., writing—review and editing A.V.S. and I.V.M., visualization A.I.S. and I.V.M., supervision A.V.S., project administration A.V.S. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported in part by the Ministry for Science and Higher Education of Russian Federation, grant No. 075-15-2021-1353.

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors on request.

Acknowledgments

X-ray diffraction studies were carried out using an X-ray diffractometer for the analysis of single crystals Bruker D8 QUEST purchased under the Development Program of Lomonosov Moscow State University.

Conflicts of Interest

The authors declare no conflicts of interest.

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Crystals 14 00155 g001
Figure 1. ThCr2Si2 structure type represented by RbCd2Bi2 (a) and CaBe2Ge2 structure types (b).
Figure 1. ThCr2Si2 structure type represented by RbCd2Bi2 (a) and CaBe2Ge2 structure types (b).
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Figure 2. Optical and electronic images of BaAu1.8Bi2 (a,c) and BaAg1.8Bi2 (b,d) crystals.
Figure 2. Optical and electronic images of BaAu1.8Bi2 (a,c) and BaAg1.8Bi2 (b,d) crystals.
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Crystals 14 00155 g003
Figure 3. Crystal structure of BaAu1.8Bi2. Au3 occupies the ideal 4g position instead of locally split positions Au2 and Au2′. One of the Au1 atoms is removed; this leads to the replacement of the Bi2 atom with a Bi2’ atom.
Figure 3. Crystal structure of BaAu1.8Bi2. Au3 occupies the ideal 4g position instead of locally split positions Au2 and Au2′. One of the Au1 atoms is removed; this leads to the replacement of the Bi2 atom with a Bi2’ atom.
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Figure 4. Coordination polyhedra of Au1 (a) and Bi1 (b), which form the [BiAu0.8] layer at a height of z = 0.5 of the unit cell (see Figure 3). Bond lengths are displayed in Å.
Figure 4. Coordination polyhedra of Au1 (a) and Bi1 (b), which form the [BiAu0.8] layer at a height of z = 0.5 of the unit cell (see Figure 3). Bond lengths are displayed in Å.
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Crystals 14 00155 g005
Figure 5. Coordination polyhedra of atoms forming the [TMBi] layer at a height of z = 0 of the unit cell (see Figure 3): (a) coordination polyhedron for Au2; (b) coordination polyhedron for Ag2; (c) coordination polyhedron for Bi2 atom (instead of disordered Au2 and Au2′ atoms, idealized Au3 are given); (d) coordination polyhedron for Bi2′. All bond lengths are displayed in Å.
Figure 5. Coordination polyhedra of atoms forming the [TMBi] layer at a height of z = 0 of the unit cell (see Figure 3): (a) coordination polyhedron for Au2; (b) coordination polyhedron for Ag2; (c) coordination polyhedron for Bi2 atom (instead of disordered Au2 and Au2′ atoms, idealized Au3 are given); (d) coordination polyhedron for Bi2′. All bond lengths are displayed in Å.
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Figure 6. Environment of the Ba1 atom in the structure of 2 (see Figure 3). Bi2′ atoms with minor occupancies are not shown; see text for details.
Figure 6. Environment of the Ba1 atom in the structure of 2 (see Figure 3). Bi2′ atoms with minor occupancies are not shown; see text for details.
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Figure 7. Calculated total and projected DOS near the Fermi level (marked by dotted line) for BaAg2Bi2 (a), BaAu2Bi2 (b), BaPd2Bi2 (c), and BaZnBi2 (d).
Figure 7. Calculated total and projected DOS near the Fermi level (marked by dotted line) for BaAg2Bi2 (a), BaAu2Bi2 (b), BaPd2Bi2 (c), and BaZnBi2 (d).
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Figure 8. Calculated band structure near the Fermi level (marked by dotted line) for BaAg2Bi2 (top row), BaAu2Bi2 (middle row), and BaPd2Bi2 (bottom row). Left column shows the results of the calculations without spin–orbit coupling (SOC), right column—with SOC and spin polarization taken into account. The thickness of the bands is proportional to their contribution.
Figure 8. Calculated band structure near the Fermi level (marked by dotted line) for BaAg2Bi2 (top row), BaAu2Bi2 (middle row), and BaPd2Bi2 (bottom row). Left column shows the results of the calculations without spin–orbit coupling (SOC), right column—with SOC and spin polarization taken into account. The thickness of the bands is proportional to their contribution.
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Crystals 14 00155 g009
Figure 9. Calculated COHP plots for BaTM2Bi2 (TM = Ag, Au, Pd) and BaZnBi2. Red line corresponds to TM−Bi interactions, blue—Bi−Bi, green—TM−TM.
Figure 9. Calculated COHP plots for BaTM2Bi2 (TM = Ag, Au, Pd) and BaZnBi2. Red line corresponds to TM−Bi interactions, blue—Bi−Bi, green—TM−TM.
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Table 1. Crystal data collection and refinement parameters for BaTM1.8Bi2.
Table 1. Crystal data collection and refinement parameters for BaTM1.8Bi2.
EDX CompositionBa1.06(3)Ag1.81(2)Bi2.13(4)Ba0.97(5)Au1.80(6)Bi2.23(5)
Chemical formulaBaAg1.79Bi2BaAu1.79Bi2
Mr749.93894.57
Crystal system, space groupMonoclinic, C2/m
a, Å6.9058(7)6.9298(5)
b, Å6.9047(7)6.9340(5)
c, Å11.5384(12)11.1159(8)
β, deg.90.010(5)90.020(4)
V, Å3550.18(10)534.13(7)
Z44
Radiation typeMo Kα1
Temperature116(2)116(2)
µ (mm−1)76.916119,911
DiffractometerBruker Quest D8
Absorption correctionSADABS
Tmin, Tmax0.034, 0.1990.022, 0.119
No. of measured, independent,
and observed [I > 2σ(I)] reflections		3988, 792, 7132486, 756, 649
Rint0.12480.0631
R, wR, GooF0.0463, 0.1088, 1.1330.0392, 0.0891, 1.104
No. of parameters4141
Largest difference in peak/hole (e/Å3)−2.638/3.397−3.470/3.621
CCDC23127862312785
Table 2. Selected bond lengths (Å) for BaTM1.8Bi2.
Table 2. Selected bond lengths (Å) for BaTM1.8Bi2.
PolyhedronBond1 (TM = Ag)2 (TM = Au)
Bi square netBi1−Bi13.4529(4) × 23.4649(3) × 2
3.4460(16)3.462(3)
3.4587(16)3.472(2)
[Bi1(TM1)4]Bi1−TM12.8986(19) × 22.9001(13) × 2
2.9012(14) × 22.9042(11) × 2
TM1−Bi22.758(2)2.7438(13)
[TM2(Bi2)3(Bi2′)]TM2−Bi22.955(7)2.843(12)
2.956(7)2.855(12)
2.735(8)3.024(13)
TM2−Bi2′3.110(8)3.002(6)
[TM2′(Bi2)3(Bi2′)]TM2′−Bi22.955(7)2.853(12)
2.957(7)2.855(12)
2.720(7)3.035(13)
TM2′−Bi2′3.120(9)2.984(5)
Table 3. Calculated averaged IpCOHP values for atom pairs (eV/bond) for BaTM2Bi2 (TM = Ag, Au, Pd) and BaZnBi2.
Table 3. Calculated averaged IpCOHP values for atom pairs (eV/bond) for BaTM2Bi2 (TM = Ag, Au, Pd) and BaZnBi2.
Compound Bond
Bi−TMBi−BiTM−TM
BaAg2Bi2−1.27−0.82−0.20
BaAu2Bi2−1.36−0.67−0.28
BaPd2Bi2−1.51−0.90−0.18
BaZnBi2−1.04−1.24−0.03
Table 4. Calculated Bader charges for BaTM2Bi2 (TM = Ag, Au, Pd) and BaZnBi2.
Table 4. Calculated Bader charges for BaTM2Bi2 (TM = Ag, Au, Pd) and BaZnBi2.
Compound Atom
BaTMBi
BaAg2Bi2+1.24−0.29−0.33
BaAu2Bi2+1.37−0.72+0.03
BaPd2Bi2+1.28−0.57−0.07
BaZnBi2+1.25+0.15−0.70
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Shilov, A.I.; Rakhmanov, E.O.; Lyssenko, K.A.; Kuznetsov, A.N.; Morozov, I.V.; Shevelkov, A.V. Crystal and Electronic Structure of Ternary Bismuthides BaTM1.8Bi2 (TM = Au, Ag) with a New Variation of the BaAu2Sb2 Structure Type. Crystals 2024, 14, 155. https://doi.org/10.3390/cryst14020155

AMA Style

Shilov AI, Rakhmanov EO, Lyssenko KA, Kuznetsov AN, Morozov IV, Shevelkov AV. Crystal and Electronic Structure of Ternary Bismuthides BaTM1.8Bi2 (TM = Au, Ag) with a New Variation of the BaAu2Sb2 Structure Type. Crystals. 2024; 14(2):155. https://doi.org/10.3390/cryst14020155

Chicago/Turabian Style

Shilov, Andrey I., Evgeny O. Rakhmanov, Konstantin A. Lyssenko, Alexey N. Kuznetsov, Igor V. Morozov, and Andrei V. Shevelkov. 2024. "Crystal and Electronic Structure of Ternary Bismuthides BaTM1.8Bi2 (TM = Au, Ag) with a New Variation of the BaAu2Sb2 Structure Type" Crystals 14, no. 2: 155. https://doi.org/10.3390/cryst14020155

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