Synthesis, Crystal and Electronic Structure of the New Ternary Compound Ca₃InAs₃

Abstract

Crystals of a new ternary compound in the Ca-In-As family, Ca₃InAs₃, have been successfully synthesized via flux growth techniques. This is only the third known compound between the respective elements. As elucidated by single-crystal X-ray diffraction measurements, Ca₃InAs₃ crystallizes in the orthorhombic space group Pnma (No. 62, Pearson symbol oP28) with unit cell parameters a = 12.296(2) Å, b = 4.2553(7) Å, and c = 13.735(2) Å. The smallest building motifs of the structure are InAs₄ tetrahedra, which are connected to one another by shared As corners, forming infinite [InAs₂As_2/2] chains. The latter propagate along the crystallographic b-axis. The As-In-As bond angles within the InAs₄ tetrahedra deviate from the ideal 109.5° value and range from 98.12(2)° to 116.53(2)°, attesting to a small distortion from the regular tetrahedral geometry. Electronic structure calculations indicate the opening of a bandgap, consistent with the expected (Ca²⁺)₃(In³⁺)(As^3–)₃ formula breakdown based on conventional oxidation numbers. The calculations also show that the Ca–As interactions are an intermediate between covalent and ionic, while providing evidence of strong covalent features of the In–As interactions. Weak s-p hybridization of In states was observed, supporting the experimentally found deviation of the InAs₄ moiety from the ideal tetrahedral symmetry.

1. Introduction

Pnictogen-based (pnictogen, i.e., the group 15 elements P, As, Sb and Bi; abbreviated as Pn hereafter) compounds with a formula of A₃MPn₃ are reported to crystallize in several distinct structures, where A is an alkaline-earth or divalent rare-earth metal, M is a triel, i.e., a group 13 element [1]. The different structure types are originating from the way the MP₄ tetrahedra are interconnected and arranged.

For example, Ca₃AlAs₃ [2], Sr₃InP₃ [3], Ca₃InP₃ [4], Ca₃GaAs₃ [4], Ca₃AlSb₃ [5], Eu₃InAs₃ [6], and Yb₃AlSb₃ [7] all crystallize in the orthorhombic Pnma space group (No. 62. Pearson symbol oP28). The MPn₄ tetrahedra in the structures of the above-mentioned compounds are connected to one another with shared Pn corners, forming an infinite straight chain along the crystallographic b-axis. Surveying the published structures suggests that the In-containing A₃MPn₃ compounds tend to crystallize in the Pnma structure described above, although this is a requisite for the realization of infinite chains as a structural motif.

One should also note that there are A₃MPn₃ structures with corner-sharing tetrahedra crystallizing in different space groups. The Sr₃GaSb₃ compound [3] is a relevant example here since the GaSb₄ tetrahedra in the structure are also connected via corner-sharing, but the resultant chains are not straight, but rather zigzagging. This difference results in an amplified structural complexity in Sr₃GaSb₃, evident from the increased number of repeating units per unit cell and the lowered symmetry; the latter compound crystallizes with the monoclinic space group P2₁/n (No. 14; Pearson symbol mP56) [3].

In addition to corner-sharing, the tetrahedra in an A₃MPn₃ compound can also be connected via edge-sharing. Such connections are observed in Ba₃GaSb₃ (space group: Pnma) [4], Ba₃AlSb₃ [2] (space group: Cmce), and Eu₃AlAs₃ (space group: P2₁/c) [8], in which the tetrahedra are connected via Pn–Pn edge-sharing, forming [M₂Pn₆]¹²⁻ dimers (diborane-like units of dual tetrahedra). The different space groups of the above compounds reflect the different arrangements and orientations of the [M₂Pn₆]¹²⁻ dimers within the unit cell.

In the present study, we synthesized a previously unknown compound in the A₃MPn₃ family, Ca₃InAs₃. We determined the crystal structure of Ca₃InAs₃ via single-crystal X-ray diffraction methods. Electronic structure calculations show that the bonding between Ca–As has an admixture of covalent and ionic character, while evidence of strong covalent features of the In–As interactions is observed.

2. Materials and Methods

2.1. Synthesis

Single crystals of Ca₃InAs₃ were synthesized by using indium as molten flux. Ca, In, and As were purchased from Alfa Aesar with stated purity of 99.9 wt % or higher, and were used as received. Manipulations were carried out in an argon-filled glovebox. A starting composition of Ca:In:As of 1:30:1 was used. Excessive In was used as the medium for the crystal growth. The corresponding amounts of elements were loaded into 2 mL alumina crucibles, which were then put inside fused silica ampoules. A piece of quartz wool was placed on top of the crucible without touching the elements inside. The ampoule was sealed under a vacuum level of ca. 30 millitorrs.

All samples in this study were heated in standard muffle furnaces with a temperature profile as follows: 100 °C → 200 °C/h to 1000 °C → hold at 1000 °C for 15.5 h → 5 °C/h to 650 °C. At this point of the crystal growth, the sealed tube was taken out from the furnace, flipped, and the molten metallic flux was separated from the grown crystals by centrifugation. The sealed ampoule was break-opened in the glovebox afterwards. Inspection of the specimen under an optical microscope revealed the presence of many small crystallites, the majority of which were CaIn₂As₂ [9] with only a minor fraction of crystals of Ca₃InAs₃.

The crystals were brittle and had a metallic luster; they were found to degrade in ambient air within about ten minutes. During the brief exposure, the crystals’ surface becomes tarnished; after several hours in air the material becomes amorphous.

2.2. Single-Crystal X-ray Diffraction (SC-XRD)

Single-crystal X-ray diffraction (SC-XRD) was performed on single crystals using a Bruker APEX II CCD diffractometer, equipped with Mo Kα radiation. Single-crystal morphologies for Ca₃InAs₃ were typically thin rod-like, but were cut (under a microscope in dry Paratone-N oil) to block shape, with each side smaller than 100 µm in length. The measurements were conducted at a temperature of 200 K under a N₂ atmosphere to achieve optimal data quality and avoid decomposition of the sample during the measurement. Data integration and semiempirical absorption correction were performed with the Bruker-supplied software [10]. The crystal structure was solved with ShelXT [11] using the intrinsic phasing method. Structure refinements were carried out using the ShelXL software, which employs full-matrix least-squares minimization on F² [12]. Olex2 software was used as a graphical interface [13]. Atomic coordinates of all compounds reported in this paper were standardized with the Structure Tidy program [14]. All sites were refined with anisotropic displacement parameters. The site occupation factors (SOF) were checked by freeing an individual SOF, while other variables were kept fixed. No statistically significant deviations were observed for the SOF on any of the atomic sites. Final difference Fourier map was flat and featureless. Selected crystallographic data are summarized in

Table 1. Selected crystal data and structure refinement parameters for Ca₃InAs₃.

Formula	Ca3InAs3
Formula weight (g·mol−1)	459.82
Radiation, λ	Mo Kα, 0.71073 Å
Temperature (°C)	–70(2)
Crystal system	orthorhombic
Space group	Pnma (No. 62)
Z	4
a (Å)	12.296(2)
b (Å)	4.2553(7)
c (Å)	13.735(2)
V (Å3)	718.7(2)
ρcalc (g·cm−3)	4.25
µMoKα (cm−1)	190.1
Reflections: parameters	1151: 44
R1 [I > 2σ(I)] a	0.0222
R1 (all data) a	0.0330
wR2 [I > 2σ(I)] a	0.0463
wR2 (all data) a	0.0496
Largest peak; deepest hole (e/Å−3)	0.83; –1.05

[a] R₁ = ∑||F_o| – |F_c||/∑|F_o|; wR₂ = [∑[w(F_o² – F_c²)²]/∑[w(F_o²)²]]^1/2, where w = 1/[σ²F_o² + (0.0213·P)² + (0.301·P)], and P = (F_o² + 2F_c²)/3.

.

2.3. Powder X-ray Diffraction

X-ray powder diffraction patterns were collected at room temperature on a Rigaku MiniFlex powder diffractometer, using filtered Cu Kα radiation. Because Ca₃InAs₃ was the minor phase, and because the experiment was carried out at ambient conditions, there was a very high background. The just a few experimentally observed peaks matched mostly with the calculated positions for CaIn₂As₂ [9] (major phase) and elemental In (left over flux).

2.4. Electronic Structure Calculations

To investigate the chemical bonding of all compositions, electronic structure calculations were performed within the local density approximation (density functional theory) using the TB-LMTO-ASA program [15]. Experimental unit cell parameters and atomic coordinates from Table 1 and

Table 2. Atomic coordinates and equivalent isotropic displacement parameters (U_eq) for Ca₃InAs₃.

Atom	Wyckoff Symbol	Site Symmetry	x	y	z	Ueq (Å2) a
As1	4c	.m	0.04891(4)	1/4	0.36528(4)	0.0103(1)
As2	4c	.m	0.25779(4)	1/4	0.62613(4)	0.0086(1)
As3	4c	.m	0.60837(4)	1/4	0.61098(4)	0.0085(1)
In	4c	.m	0.05554(3)	1/4	0.69988(3)	0.0103(2)
Ca1	4c	.m	0.06164(7)	1/4	0.10532(8)	0.0104(2)
Ca2	4c	.m	0.26873(7)	1/4	0.28697(8)	0.0092(2)
Ca3	4c	.m	0.34436(8)	1/4	0.00296(8)	0.0104(2)

[a] U_eq is defined as one third of the trace of the orthogonalized U_ij tensor.

were used as input parameters in the calculations. In order to satisfy the atomic sphere approximation (ASA), we employed the von-Barth-Hedin functional [16] and introduced empty spheres. The Brillouin zone was sampled by a 1000 k-point grid. Electronic density of states (DOS), atom-projected electronic density of states (PDOS), and crystal orbital Hamilton population (COHP) were calculated with modules in the LMTO program [17].

3. Results and Discussion

3.1. Crystal Structure

To date, only two compounds have been structurally characterized for the Ca-In-As ternary phase diagram, namely CaIn₂As₂ [9] and Ca₃In₂As₄ [18]. The Ca₃InAs₃ reported in the present study is a previously unknown phase and is described in the following paragraphs for the first time.

Ca₃InAs₃ crystallizes in the orthorhombic Pnma space group (No. 62. Pearson symbol oP28) with the Ca₃InP₃ structure type (also referred to as Ca₃AlAs₃ structure type) [19]. The unit cell parameters are a = 12.296(2) Å, b = 4.2553(7) Å and c = 13.735(2) Å. Other relevant crystallographic parameters are tabulated in Table 1. The factional coordinates of the seven crystallographically unique atomic positions are tabulated in Table 2. All positions are of the same symmetry, m, with the same Wyckoff position 4c.

A view of the crystal structure of Ca₃InAs₃ is shown in Figure 1. As shown there, we prefer to visualize the structure as Ca²⁺ cations and In–As polyanionic sub-lattice. The InAs₄ tetrahedra are connected to one another with shared As corners, forming an infinite straight chain along the crystallographic b-axis.

Selected interatomic distances obtained from the single-crystal refinements can be found listed in

Table 3. Selected interatomic distances (Å) in Ca₃InAs₃. Contacts longer than 3.9 Å are not shown.

Atoms	Distance (Å)	Atoms	Distance (Å)
In–As1 (×2)	2.6415(5)	As2–In	2.6853(7)
In–As2	2.6853(7)	As2–Ca1 (×2)	3.0885(8)
In–As3	2.6779(7)	As2–Ca2 (×2)	3.0845(9)
In–Ca1 (×2)	3.710(1)	As2–Ca3 (×2)	2.9945(8)
In–Ca2 (×2)	3.2600(8)	As3–In	2.6779(7)
In–Ca3 (×2)	3.655(1)	As3–Ca1 (×2)	2.984(8)
In–Ca3	3.809(1)	As3–Ca1	3.026(1)
As1–In (×2)	2.6415(5)	As3–Ca2 (×2)	2.9623(8)
As1–Ca1	3.574(1)	As3–Ca3	3.297(1)
As1–Ca2	2.9091(1)	Ca1–Ca2	3.565(1)
As1–Ca3	3.099(1)	Ca1–Ca3	3.750(1)
As1–Ca3 (×2)	3.1345(9)

. The In–As distances range from 2.642 to 2.685 Å. These values match very well the metrics reported for another ternary arsenides such as Eu₃InAs₃ [6], Ba₃InAs₃ [20], CaIn₂As₂ [9], Ca₃In₂As₄ [18] and Sr₃In₂As₄ [21], among others. It should also be noted the experimentally observed bond length values are comparable to the sum of the respective single-bonded covalent radii (r_In and r_As are 1.42 Å and 1.21 Å, respectively, yielding a summation value of 2.63 Å [22], which is an indication of the strong covalent bonding nature of the In–As interactions. One may also notice that there are some Ca–As distances that are shorter than 3.0 Å; this also points at substantial covalency of these interactions since the single-bonded covalent radius of Ca is 1.74 Å [22]. Further evidence of this supposition can be found in the DOS and COHP discussions in Section 3.2.

In addition, it is observed that the As-In-As bond angles within the InAs₄ tetrahedra deviate from the 109.5° value expected for a regular tetrahedron. Similar tetrahedral distortions are also reported for other “3-1-3” compounds [6,9,20,21].

Lastly, considering the lack of any homoatomic bonding, we can rationalize the structure and the bonding in this new ternary arsenide as a typical valence-precise compound, i.e., a Zintl phase. There are two complimentary ways to understand the electronic charge balance of Ca₃InAs₃. The first way is to simply exaggerate the ionicity of the bonding and view the formula as [Ca²⁺]₃[In³⁺][As³⁻]₃. Considering the close electronegativities of In (χ_P 1.7) and As (χ_P 2.0) [22], assigning an oxidation number of +3 for In and –3 for As may be hard to justify. Therefore, the other way may be preferred. From the point of view of the Zintl formalism [23], the formal charge of an In atom, covalently bonded to four As atoms will be 1–. In the [InAs₂As_2/2] tetrahedral chain, formally [InAs₃]⁶⁻, two of the As atoms at the shared-corner positions have two bonds (2b) and their formal charge is also 1–. The other two As atoms (terminal ones) only have one covalent bond (1b), and need two more valence electrons to satisfy their octets; the formal charge of 1b-As is thus 2–. Therefore, the formula Ca₃InAs₃ could be expressed as (Ca²⁺)₃[(In¹⁻)(1b-As²⁻)₂(2b-As¹⁻)].

Either the fully ionic or the bonding picture within the Zintl formalism capture the essence of the valance electron count in Ca₃InAs₃, which is expected to be an intrinsic semiconductor. The notion of semiconducting behavior is confirmed by the electronic structure calculations, presented next.

3.2. Electronic Structure

The bonding characteristics of Ca₃InAs₃ were investigated via electronic structure calculations using the LMTO program [15]. We evaluated the electronic properties of the new material with calculations employing the experimental data listed in Table 1 and Table 2.

The stacked atom-projected electronic density of states (DOS) curves for Ca₃InAs₃ are shown in Figure 2a, in which a calculated bandgap of approx. 0.46 eV can be observed. This value is reconcilable with those of other ternaty indium arsenides, such as Eu₃InAs₃ and CaIn₂As₂ which have calculated bandgaps on the order of 0.2 and 0.5 eV [6,9]. The existence of a bandgap is in agreement with the formal electron count as discussed in the previous section. Knowing that DFT methods typically underestimate the bandgap, the actual bandgap of Ca₃InAs₃ is speculated to be larger.

The majority of the states in the conduction band are dominated by Ca d orbitals, with minor As and In contributions. The states close to the valence band maximum are contributed mainly by the As p orbitals with minor Sr and In contributions. Specifically, in the region of −1 < E − E_F < 0 eV, the contribution of the As p orbitals is most considerable. The minor overlap of Ca and As states suggest that there are some covalent features between Ca and As. Therefore, due to the incomplete electron transfer of the cation, strictly speaking, Ca₃InAs₃ does not exhibit the textbook characteristics of a Zintl phase.

A few insights can be observed for the bonding of the InAs₄ tetrahedra. In-p and As-p states showed extensive overlapping in the range of between −4.1 < E − E_F < −2 eV (Figure 2c,d). This means the existence of a strong covalent feature of the In–As interactions. In addition, the In atoms show a clear separation between the s and p orbitals, indicating a weak s-p hybridization. This insight agrees well with the InAs₄ tetrahedra distortion given by the crystal refinements.

Figure 3 shows the electronic band structure of Ca₃InAs₃ in momentum space. As evident from the plot, there are no bands crossing from the valence band to the conduction band. The lowest energy separation between the top of the valence band and the bottom of the conduction band occurs at the Γ-point. This observation is suggestive of a direct bandgap semiconductor.

The crystal orbital Hamilton population curves (COHP) for the averaged selected interactions of Ca₃InAs₃ are plotted in Figure 4. Both the In–As and Ca–As interactions are optimized at the Fermi level. For the Ca–As interactions, some bonding features can still be observed above the Fermi level when 0.5 < E − E_F < 2 eV. This indicates the possibility of electron doping on the Ca site. In contrast, In–As interactions only show antibonding features above the Fermi level.

4. Conclusions

With this study, we reported on the discovery of the new compound, Ca₃InAs₃, extending the knowledge in the Ca-In-As compositional space, and expanding the variety of compounds that crystallize with this quasi 1D-structure. The bonding characteristics of Ca₃InAs₃ were studied both experimentally and computationally. We found that Ca₃InAs₃ is an intrinsic semiconductor, where the InAs₄ tetrahedral building units are lightly distorted. A possibility of doping on the Ca site is also suggested.

This materials system can providee promising thermoelectric material candidates and/or topological insulators, but for quality property measurements, the synthetic challenges making a phase-pure bulk sample must be resolved.