Complex Structure, Chemical Bonding, and Electrical Transport Properties of a La-Doped Zintl Phase

Abstract

The La-doped ternary Zintl phase Ca_10.43(3)La_0.57Sb_9.69(1) was successfully synthesized by arc melting, and the title compound adopted the Ho₁₁Ge₁₀-type structure with a tetragonal I4/mmm space group (Z = 4, Pearson code tI84). The complex crystal structure is composed of (1) the four different kinds of cationic Ca or Ca/La mixed sites surrounded by seven or nine Sb atoms and (2) the 3-dimensional cage-shaped anionic frameworks built by the other two types of Sb atoms. In particular, the La dopants preferred to occupy the Ca4 and Ca1 sites, and this specific cationic-site preference can be rationalized by both electronic and size-factor criteria. Moreover, the ca. 16% occupational deficiency observed at the Sb3 site was attributed to the energetically unfavorable antibonding character of the Sb3–Sb3 bond in the [Sb3]₄ tetramers, according to a series of DFT calculations. A crystal Hamilton overlap population curve analysis also proved that the title compound Ca_10.43(3)La_0.57Sb_9.69(1) tried to keep the valence electron count below 71.02 to remain energetically stable in the Ho₁₁Ge₁₀-type phase. Measurements of temperature-dependent electrical transport properties revealed that the La doping indeed enhanced the electrical conductivity of Ca_10.43(3)La_0.57Sb_9.69(1) compared to the un-doped Ca₁₁Sb₁₀. However, unlike other rare earth metal (RE)-doped compounds in the Ca_11−xRE_xSb₁₀ (RE = Nd and Sm) system that display semiconducting behavior, the La-doped title compound showed poor metallic electrical properties. The positive values of Seebeck coefficients indicated the p-type character of the title compound despite the successful n-type La doping, and this should be attributed to Sb deficiency.

1. Introduction

The global energy crisis and increasing environmental concerns have intensified the search for sustainable energy solutions [1]. Thermoelectric (TE) materials, capable of directly converting waste heat into electricity, have been considered as one of the most effective solutions to address these challenges [2]. The efficiency of TE materials is quantified by the dimensionless figure of merit, ZT = σS²T/κ (σ: electrical conductivity, S: Seebeck coefficient, T: absolute temperature, and κ: thermal conductivity) [3]. The pursuit of high-performance TE materials has led researchers to explore various candidate material systems, including skutterudites, half-Heusler alloys, clathrates, and chalcogenides [4,5,6,7]. Among these candidates, Zintl phases have gained significant attention in recent years due to their particularly complex crystal structures and electron transport characteristics, which make Zintl phases an intrinsically excellent candidate for the application of TE materials. Our exploration to search for new TE materials led us to conduct comprehensive investigations on the Zintl phase A₁₁M₁₀ (A = alkali/alkaline earth/rare earth metals; M = tetrels, pnictogens) series, adopting the Ho₁₁Ge₁₀-type phase. At the early stage, our study focused on applying p-type dopants in this series, which resulted in producing the Ca_11−xYb_xSb_10−yGe_z [8] and Ca_11−xA_xSb_10−yGe_z (A = Na, Li) [9] systems. To further explore the compositional tunability of the A₁₁M₁₀ series, we expanded our study for the n-type dopant application using trivalent rare earth metals (RE³⁺), which resulted in producing the ternary Ca_11−xRE_xSb_10−y system [10,11].

In this study, the crystal structure of the newly synthesized La-doped Ca_10.43(3)La_0.57Sb_9.69(1) was thoroughly studied based on both powder and single-crystal X-ray diffraction (PXRD and SXRD) analyses, and the particular site preference of La for the Ca4 site was rationalized by the electronic factor as well as size-factor criteria. We also observed a certain amount of Sb vacancies at the Sb3 site, which is consistent with previous reports on isotypic systems. A series of density functional theory (DFT) calculations was performed to study the effects of cationic doping and anionic vacancy on its electronic structure, and the density of states (DOSs) and crystal orbital Hamilton population (COHP) curves were carefully analyzed. Electrical transport properties of Ca_10.43(3)La_0.57Sb_9.69(1) were also measured, and its electrical conductivity (σ) and Seebeck coefficients (S) were compared with those of the binary reference compound Ca₁₁Sb₁₀ as well as two ternary compounds with n-type dopants: Ca_10.75(3)Nd_0.25Sb_9.82(1) and Ca_10.82(4)Sm_0.18Sb_9.86(1) [10].

2. Results and Discussion

2.1. Crystal Structure Analysis

The ternary Zintl phase compound Ca_10.43(3)La_0.57Sb_9.69(1) was initially synthesized by arc melting, and its crystal structure was successfully characterized by both PXRD and SXRD analyses. Interestingly, large amounts of square-shaped single crystals were obtained on the surface of a product ingot, as shown in Figure 1. This title compound adopted the Ho₁₁Ge₁₀-type phase, having a tetragonal space group of I4/mmm (Z = 4, Pearson code tI84) with a total of nine crystallographically independent atomic sites: four cationic sites (two Ca sites and two Ca/La mixed sites) and five Sb sites, as provided in the Supplementary Materials, Table S1.

The initial phase purity of the product was checked by indexing the collected PXRD pattern using the simulated PXRD based on the SXRD data of Ca_10.43(3)La_0.57Sb_9.69(1). After that, the lattice parameters of a unit cell were checked by the Le Bail fit method, as shown in Figure 2. The results indicate that the lattice parameters were a = 12.04(1) Å and c = 17.47(3) Å, which is in good agreement with the SXRD refinement results provided in Table 1.

Further detailed refinement for this structure, including lattice parameters, atomic coordinates, and bond distances, was conducted using the collected SXRD analysis. Since the overall crystal structure of several isotypic compounds in the Ca_11−xRE_xSb_10−y (RE = rare earth metals) [10,11] system is already discussed in other previous reports, the structural explanation will be brief in this article. As illustrated in Figure 3a, the overall crystal structure is quite complex, but it can be simplified by categorizing five anionic Sb atoms into two groups: (1) three types of “isolated Sb atoms”, including Sb2, Sb4, and Sb5, and (2) two types of “connecting Sb atoms” involving Sb1 and Sb3. More specifically, three types of isolated Sb atoms are, respectively, surrounded by eight or nine Ca or Ca/La mixed sites, forming the particular polyhedra (see Figure 3b–d). The geometry of each polyhedron can be described as follows: (1) Sb2 site (Wyckoff 8j): a trigonal prism that has two mono-capped rectangular faces, (2) Sb4 site (Wyckoff 4e): an anti-square prism that has one mono-capped square face, and (3) Sb5 site (Wyckoff 4d): a dodecahedron. Furthermore, these polyhedra share their triangular or rectangular faces with adjacent polyhedra and fill the void within the 3-dimensional (3D) cage-shaped anionic frameworks formed by two types of “connecting Sb atoms”. The cage-shaped 3D anionic framework is built by the assembly of dumbbell-shaped Sb1 dimers (Wyckoff 16m) and square-ring-shaped Sb3 tetramers (Wyckoff 8h), which are bridged via the relatively longer Sb1–Sb3 interaction, as shown in Figure 3e,f.

This type of crystal structure can also be alternately viewed as an assembly of four types of distinctive cation-centered polyhedra formed by seven or nine surrounding Sb atoms, as displayed in Figure 4a–d. These cationic sites can be described as follows: (1) the Ca1 and Ca3 sites are distorted pentagonal bipyramids, (2) the Ca2 site is a square pyramid that has two mono-capped edges, and (3) the Ca4 site is a square pyramid that has two bi-capped edges. Quite interestingly, the trivalent La³⁺ cation showed a specific site preference for the Ca1 and Ca4 sites as they substituted the Ca²⁺ cation among four available sites. Moreover, the amount of the La³⁺ dopant is about five times higher at the Ca4 site than at the Ca1 site, as shown in the Supplementary Materials, Table S1. A similar type of cationic site preference was previously reported in the Ce³⁺-doped Ca_10.59(2)Ce_0.41Sb_9.67(1) analog [10], where the Ce dopant showed a ca. 6% occupancy at Ca1 and ca. 15% at the Ca4 site. More interestingly, as the total amount of the La dopant increased from 3.91% in the previously reported Ca_10.57(2)La_0.43Sb_9.59(1) [10] to 5.18% in the current work for Ca_10.43(3)La_0.57Sb_9.69(1), the La occupancy at the Ca1 site remained nearly the same (ca. 6%), while the occupancy at the Ca4 site increased by nearly two-fold from ca. 17% to 32%, as plotted in Figure 4e. This type of particular atomic site preference can be attributed to either (1) the electronic-factor criterion based on the Q value (QVAL) or (2) the size-factor criterion based on the size of a substituting cation. In this work, the observed site preference of the La dopant satisfied both criteria, as observed in the Ce-doped Ca_10.59(2)Ce_0.41Sb_9.67(1) compound [10]. Further details about this site preference will be discussed in the subsequent Electronic Structure Calculation Section.

Lastly, the SXRD refinement revealed that the Sb3 site contained ca. 16% vacancy, resulting in the chemical composition of Ca_10.43(3)La_0.57Sb_9.69(1), and a corresponding valence electron count (VEC) of 71.02. This type of Sb vacancy occurrence should be attributed to nature’s choices of removing some electrons from the energetically unfavorable Sb3–Sb3 antibonding states to maintain the overall stability of the crystal structure. A detailed discussion about the correlation between the Sb3–Sb3 antibonding states and structural stability will be discussed in the subsequent Electronic Structure Calculation Section as well.

2.2. Electronic Structure and Chemical Bonding

To investigate the influence of n-type doping using the trivalent La³⁺ for the divalent Ca²⁺ on the overall electronic structure of the title compound Ca_10.43(3)La_0.57Sb_9.69(1), we performed a series of DFT calculations by using the TB-LMTO-ASA method. For practical reasons, we designed a hypothetical structural model with an idealized composition of Ca_10.5La_0.5Sb₁₀, and the symmetry of this model was lowered from the experimentally refined space group I4/mmm (No. 139) to its subspace group I4 (No.79). The lattice parameters and the atomic sites were extracted from the SXRD refinement result of Ca_10.43(3)La_0.57Sb_9.69(1). All detailed structural information on this model is provided in the Supplementary Materials, Table S2.

As shown in Figure 5a, the overall TDOS curve can be divided into two regions below the Fermi level (E_F): (1) the s-orbital states of Sb mostly contribute the lower region between ca. −11 eV and −7.5 eV and (2) the p-orbital states of Sb largely contribute the upper region between ca. −4.5 eV and 0 eV, with some states from Ca. Since the trivalent La³⁺ substituted ca. 4.5% of the divalent Ca²⁺ overall cationic sites in the Ca_10.5La_0.5Sb₁₀ model, the original E_F corresponding to 72.5 VEC is located in the middle of a DOS peak near the bottom of the conduction band, which implies a poor metallic property of this model. However, the adjusted E_F corresponding to 71.02 VEC from the refined composition of Ca_10.43(3)La_0.57Sb_9.69(1) is located on the edge of a DOS peak at −0.22 eV. Thus, we believe that although we successfully introduced some additional electrons using the trivalent La³⁺ dopants to the title system to make the n-type analog, due to the energetically unfavorably high TDOS level, nature spontaneously chose to remove some electrons from the anionic Sb by forming vacancies. As a result, the high TDOS level at the original E_F lowered at the adjusted E_F, and the title compound Ca_10.43(3)La_0.57Sb_9.69(1) remained energetically stable with the poor metallic character.

Figure 5b illustrates the four types of crystal orbital Hamilton population (COHP) curves, corresponding to the interatomic interactions between cationic and anionic elements or among different anionic elements. As mentioned earlier, the original E_F with 72.5 eV is located at the strong antibonding state of the Sb3–Sb3 curve, but the adjusted E_F with 71.02 eV migrated down to the bottom of the conduction band, resulting in removing electrons from the antibonding states.

Therefore, we can conclude that the title compound tried to remain energetically stable by keeping the VEC below a certain level. According to a previous report, the ternary analog Ca_10.57(3)La_0.43Sb_9.59(1) [10] showed an even smaller VEC of 70.38, where the corresponding E_F is now moved even further down to the nearly non-bonding state, as displayed in Figure 5b. These observations strongly suggest that the range of VEC values allowing for an energetically stable compound formation lies at least between 70.38 and 71.02, and the flexibility in electronic structure and vacancy formation related to this VEC range provides the compositional range and stability of these compounds.

In addition, the observed site preference of cationic elements in the title compound can be rationalized by both (1) the electronic-structure-factor criterion based on the Q value (QVAL) or (2) the size-factor criterion based on the size of a substituting cation [10]. Since the calculated QVAL of the Ca4 site is the largest (see Table 2), and the electronegativity of La is higher than Ca (La = 1.10, Ca = 1.00 in Pauling scale) [12], the observed site preference can be rationalized by the electronic-factor criterion. In addition, the site volume of the Ca4 site is the largest among the four cationic sites with 9 coordinates, as provided in Table 2. Therefore, the relatively larger La (r(La³⁺) = 1.22 Å, r(Ca²⁺) = 1.18 Å) [13] occupying the Ca4 site also satisfies the size-factor criterion. Therefore, we can conclude that the site preference of La dopants for the Ca4 site and Ca1 site nicely follows the two given criteria.

2.3. Electrical Transport Properties

Figure 6a illustrates the temperature-dependent σ of the title compound Ca_10.43(3)La_0.57Sb_9.69(1) compared to Ca₁₁Sb₁₀, Ca_10.75(3)Nd_0.25Sb_9.82(1), and Ca_10.82(4)Sm_0.18Sb_9.86(1) [8,10]. The observed maximum σ values for these compounds are 17, 175, 131, and 258 S/cm, respectively. The La-doped compound, like the Nd- and Sm-doped variants, exhibited enhanced σ values compared to Ca₁₁Sb₁₀, consistent with the theoretical predictions placing E_F at the bottom of the conduction band region. In particular, the correlation between the amounts of RE dopants and σ values is not directly linear, which should be attributed to the varying concentrations of Sb vacancies among these compounds, according to previous reports. Moreover, the temperature dependence of σ values varies as follows: the Nd- and Sm-doped compounds show slightly increasing σ values with an increasing temperature, indicative of semiconducting behavior. On the other hand, the title La-doped compound exhibits a small decreasing trend as the temperature rises, displaying a metallic-like characteristic. This kind of distinct behavior of the La-doped compound suggests a unique electronic structure as well as carrier transport mechanism compared to its analogs with heavier RE dopants.

The temperature-dependent S is presented in Figure 6b. The La-doped compound showed lower S values than Ca₁₁Sb₁₀, similar to those of the Nd- and Sm-doped analogs. Consistent with other thermoelectric materials, an inversely proportional relationship between S and σ is observed for the title compound like other n-dopant added analogs. The observed maximum S values are 17, 7, 8, and 4 μV/K for Ca₁₁Sb₁₀, Ca_10.43(3)La_0.57Sb_9.69(1), Ca_10.75(3)Nd_0.25Sb_9.82(1), and Ca_10.82(4)Sm_0.18Sb_9.86(1), respectively [8,10]. Despite the successful introduction of an n-type dopant, all three ternary compounds displayed positive S values, indicating persistent p-type electrical behaviors. This phenomenon should be attributed to the occurrence of the Sb3 vacancies, which induced an increase in hole carrier concentration and eventually resulted in effectively compromising the n-type doping effect. In addition, we can assume that among the analogs having the relatively lighter RE³⁺ cations, the amounts of RE dopants in the Ca_11−xRE_xSb_10−y system can be expected to be proportional to the Sb vacancy concentration, and therefore, this could lead to a predictable correlation with the carrier concentration. The resultant power factor PF (PF = σS²) was also evaluated, as shown in the Supplementary Materials, Figure S1. The PF of Ca_10.43(3)La_0.57Sb_9.69(1) exhibits higher values compared to Ca₁₁Sb₁₀ and Ca_10.82(4)Sm_0.18Sb_9.86(1). However, Ca_10.75(3)Nd_0.25Sb_9.82(1) exhibits a higher PF than Ca_10.43(3)La_0.57Sb_9.69(1), above 623 K. This result can be attributed to the inversely proportional relationship between S and σ, which may cause Ca_10.43(3)La_0.57Sb_9.69(1) to have lower individual values.

Therefore, despite the successful introduction of n-type dopants, the La-, Nd-, and Sm-containing compounds still exhibited p-type electrical behavior, which limited their thermoelectric performance. To address this challenge and further enhance the material’s properties, we propose exploring the co-doping strategy with other rare earth metals. According to our previous studies on the Ca_11−xRE_xSb_10−y (RE = Tb, Dy, Ho, Er, and Tm) [11] system, the “heavy” rare earth metals exhibited a specific site preference, predominantly doping the Ca2 and Ca3 sites. By co-doping with La and Tm, it was anticipated that La would target the Ca1 and Ca4 sites, while Tm would target the Ca2 and Ca3 sites, enabling a higher overall doping level. This strategy is expected to facilitate the synthesis of n-type Zintl thermoelectric compounds with an optimized carrier concentration. Future experimental validation of this approach will be crucial to fully realize its potential.

3. Materials and Methods

3.1. Synthesis

The sample preparation process was performed inside an Ar-filled glovebox with O₂ and H₂O contents below 0.1 ppm or inside an arc-melting furnace under vacuum conditions. The reactant elements were purchased from Alfa Aesar: Ca (shot, 99.5%); La (pieces, 99.9%); and Sb (piece, 99.999%). The lightly tanned surfaces of La and Ca were cleaned by scraping them off using a scalpel or a metal brush inside a glovebox before use. The title compound was synthesized by arc melting using reactant mixtures with a Ca/La/Sb ratio of 10:1:10. As we used a larger amount of La for the synthesis, impurity phases, including CaSb₂, were observed. Therefore, a ratio of 10:1:10 was selected to successfully synthesize the target compound as a single-phase product. To ensure homogeneity, the product ingot was re-melted at least five times, as fewer repetitions led to impurities and inhomogeneity, while additional repetitions showed no further improvements. Interestingly, large amounts of square-shaped single crystals were obtained on the surface of a product ingot, as shown in Figure 1. The product was air and moisture stable for at least up to 3 weeks.

3.2. X-Ray Crystallographic Analysis

The phase purity and crystal structure of the title compound were characterized using both PXRD and SXRD analyses. The PXRD pattern was collected at room temperature using a Miniflex 600 diffractometer (Rigaku Co., Tokyo, Japan) equipped with an area detector and Cu Kα₁ radiation (λ = 1.54059 Å). The collection step size was set to 0.02° in the 15° ≤ 2θ ≤ 85° range with a total exposure time of 30 min. The phase purity was initially checked by indexing a collected PXRD pattern with a simulated pattern, and then, the lattice parameters were examined by using the Le Bail fit method, as shown in Figure 2 [14]. The SXRD data of Ca_10.43(3)La_0.57Sb_9.69(1) was collected at room temperature using a SMART BREEZE CCD-based diffractometer equipped (Bruker AXS Inc., Madison, WI, USA) with Mo Kα₁ radiation (λ = 0.71073 Å). After a quick quality check of several metallic lustrous single crystals from the product batch, a square-shaped crystal with well-defined edges and smooth surfaces (as shown in Figure 1) was carefully selected for full data collection using Bruker’s APEX2 program [15]. Data reduction, integration, and unit cell parameter refinements were executed using the SAINT program [16], and SADABS [17] was used to perform semiempirical absorption corrections based on equivalents. The entire set of reflections was in good agreement with the tetragonal crystal system, and finally, a space group I4/mmm (No. 139) was chosen for the title compound. The detailed crystal structure was solved by a direct method and refined to convergence by the full-matrix least-squares method on F². The refined parameters include the scale factor; atomic positions, including anisotropic displacement parameters (ADPs); extinction coefficients; and the occupancy factors at the two Ca/La mixed sites and the Sb3 site with some vacancies. In the last stage of the refinement cycle, atomic positions were standardized using STRUCTURE TIDY [18]. Important crystallographic data, atomic positions with ADPs, and several selected interatomic distances are provided in Table 1 and the Supplementary Materials, Tables S2 and S3. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif. The depository number is CCDC–2393367 for Ca_10.43(3)La_0.57Sb_9.69(1).

3.3. Electronic Structure Calculation

To investigate the impact of n-type trivalent La³⁺ doping for divalent Ca²⁺ on the electronic structures and chemical bonding of Ca_10.43(3)La_0.57Sb_9.69(1), we performed a series of theoretical calculations using a structural model with an idealized composition of Ca_10.5La_0.5Sb₁₀. The calculations were performed using the Stuttgart TB-LMTO software (version 4.7), applying the atomic sphere approximation (ASA) [19,20,21,22]. In order to apply the idealized composition, its symmetry was lowered from the experimentally determined tetragonal space group I4/mmm (No. 139) to the subgroup I4 (No. 79). This modification ensured compatibility with the composition while maintaining energetically favorable atomic configurations. The lattice parameters and atomic coordinates were derived from SXRD data of Ca_10.43(3)La_0.57Sb_9.69(1). Comprehensive details about the hypothetical model are provided in the Supplementary Materials, Table S2.

The ASA method involves filling the space with overlapping Wigner–Seitz (WS) atomic spheres. Exchange and correlation effects were managed using the local density approximation. A scalar relativistic approximation was applied to account for relativistic effects, excluding spin–orbit coupling. Within each WS sphere, the potential was treated as spherically symmetric, and a correction was applied to take into account the overlapping part [23]. The WS sphere radii were calculated automatically to ensure the overlapping potential closely approximated the full potential. The overlap was minimized to reduce errors in kinetic energy, which increased with the fourth power of the relative overlap. The WS radii used were Ca = 1.780–2.385 Å, La = 2.385 Å, and Sb = 1.816–1.982 Å. The basis sets included the 4s, 4p, and 3d orbitals for Ca; 6s, 6p, and 5d orbitals for La; and 5s, 5p, 5d, and 4d orbitals for Sb. In addition, the Löwdin downfolding technique [24] was employed to handle the Ca 4p, La 6p, and Sb 5d and 4f orbitals. k-space integration was executed using the tetrahedron method [25], with 448 irreducible k-points in the Brillouin zone used to achieve a self-consistent charge density.

3.4. Thermal Gravimetric Analysis (TGA)

The thermal stability of the compound was verified by TGA using a Instruments SDT2960 thermal analyzer (TA Instruments, New Castle, DE, USA). A total of 10 mg of the pulverized sample was placed on an alumina pan and heated to 1100 K at a rate of 10 K/min under a continuous Ar flow condition. After that, the sample was naturally cooled down to room temperature. The TGA analysis proved that the compound was thermally stable up to ca. 950 K, as shown in the Supplementary Materials, Figure S1.

3.5. Electrical Transport Properties Measurement

The arc-melted ingot of the title compound was cut and polished into bar shapes (3 mm × 3 mm × 10 mm) for the electrical transport property measurements. The density of the sample measured by the geometric method was higher than 95%. The longer direction coincides with the direction in which the electrical conductivity was measured. The electrical conductivity (σ) and the Seebeck coefficient (S) were measured simultaneously under a helium atmosphere from 372 to 661 K using a ZEM-3 instrument system (ULVAC-RIKO Inc., Yokohama, Japan).

4. Conclusions

A ternary Zintl phase compound Ca_10.43(3)La_0.57Sb_9.69(1) was successfully synthesized by arc melting, and PXRD and SXRD analyses revealed that the title compound crystallized in the tetragonal Ho₁₁Ge₁₀-type structure. The successfully introduced n-type La dopant not only preferentially substituted Ca at the Ca4 site with a minor substitution at the Ca1 site, but it triggered ca. 16% of Sb vacancies at the Sb3 site. The observed cationic site preference was nicely elucidated by both electronic-factor as well as size-factor criteria. DFT calculations also proved that the Sb vacancies at the Sb3 site can be rationalized by the energetically unfavorable antibonding character of the Sb3–Sb3 bond, which seemed to keep a certain range of VECs for the energetically favorable states.

Temperature-dependent σ measurements revealed that La doping enhanced the σ values compared to the undoped binary Ca₁₁Sb₁₀ and exhibited metallic-like behavior, contrasting with the semiconducting characteristics observed in the Nd- and Sm-doped analogs. Despite the successful n-type La doping, the title compound still showed positive S values, indicating p-type electrical behavior due to the occurrence of Sb3 vacancies. These anionic vacancies eventually induced an increase in the hole carrier concentration and resulted in compromising the n-type doping effect. According to our comprehensive investigation of the Ca_11−xRE_xSb_10−y system, we believe that the amounts of RE dopants should be proportional to the Sb vacancy concentration; thus, this result can lead us to predict its correlation with the carrier concentration. Future studies should focus on employing co-doping strategies with La and other “heavy” rare earth metals to achieve n-type behaviors, optimize carrier concentrations, and further enhance the thermoelectric performance of the material.

Author Contributions

Conceptualization, J.L. and T.-S.Y.; methodology, J.L.; software, J.L. and Y.L.; formal analysis, M.-H.C.; investigation, J.L.; resources, K.M.O. and T.-S.Y.; data curation, J.L., Y.L. and M.-H.C.; writing—original draft preparation, J.L.; writing—review and editing, T.-S.Y.; visualization, J.L. and Y.L.; supervision, T.-S.Y.; project administration, T.-S.Y.; funding acquisition, T.-S.Y. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data are contained within the article.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

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Figures and Tables

Figure 1. SEM image of the surface of the title compound Ca10.43(3)La0.57Sb9.69(1). A scale bar is provided.

Figure 2. Le Bail fit results using the collected PXRD pattern of Ca10.43(3)La0.57Sb9.69(1). The reliability factors are Rwp = 8.24%, RP = 5.82%, and GoF = 2.43.

Figure 3. (a) Overall crystal structure of Ca10.43(3)La0.57Sb9.69(1) shown by ball-and-stick and polyhedral representations. (b–d) Three kinds of cationic polyhedra enclosing three types of isolated Sb atoms (Sb2, Sb3, and Sb5), (e) the tetramer of [Sb3]4, and (f) the dumbbell-shaped [Sb1]2. A unit cell outline (black box) is provided. Color codes: Ca, gray; Ca/La, dark gray; Sb, yellow; Sb1, green; Sb3, blue.

Figure 4. (a–d) Four types of cationic sites surrounded by seven or nine neighboring Sb atoms in Ca10.43(3)La0.57Sb9.69(1). All local geometry is illustrated in ball-and-stick and coordination polyhedra representations. Color codes: Ca, gray; Ca/La, dark gray; Sb, yellow; Sb1, green; Sb3, blue. (e) Mixed occupancy of the RE metals at the four cationic sites in the Ca11−xRExSb10−y (RE = La and Ce) system.

Figure 5. (a) TDOS, PDOS, and (b) COHP curves for Ca10.5La0.5Sb10. In the COHP diagram, the “+” and “−” regions indicate bonding and antibonding interactions, respectively. The vertical straight line, the dashed line, and the dash-dotted line correspond to EF and the refined compositions of Ca10.57(2)La0.43Sb9.59(1) and Ca10.43(3)La0.57Sb9.69(1), respectively. The VEC of the refined compositions is also provided. Color codes: TDOS, bold black outline; Ca PDOS, gray region; Ho PDOS, dark gray region; Sb PDOS, yellow region.

Figure 6. Temperature-dependent (a) electrical conductivity σ and (b) Seebeck coefficient S of Ca10.43(3)La0.57Sb9.69(1) measured over the temperature range of 373–674 K. The results of the three reference compounds (Ca11Sb10, Ca10.75(3)Nd0.25Sb9.82(1), and Ca10.82(4)Sm0.18Sb9.86(1)) [8,10] are also plotted for comparison purposes. Reprinted with permission from reference [8,10]. Copyright 2017 and 2019 American Chemical Society.

Table 1

SXRD data and structure refinement results for Ca_10.43(3)La_0.57Sb_9.69(1).

Formula weight (g/mol)	1676.164
Space group; Z	I4/mmm (No. 139); 4
Unit cell dimensions (Å)	a = 12.0258(2)
	c = 17.4202(4)
Volume (Å3)	2519.3(1)
Data/restraints/parameters	712/0/42
R indices a (I > 2σ(I))	R1 = 0.0279
	wR2 = 0.0645
R indices a (all data)	R1 = 0.0333
	wR2 = 0.0669
Goodness of fit on F2	1.118
Largest diff. peak/hole (e/Å3)	2.460/−2.129

^a R₁ = Σ||F_o| − |F_c||/Σ|F_o|; wR₂ = {Σ[w(F_o² − F_c²)/Σ[w(F_o²)²]}^1/2, where w = 1/[σ²F_o²+(A − P)²+B − P], in which P = (F_o² + 2F_c²)/3, and A and B are weight coefficients.

Table 2

Site volume and QVAL values for each atomic site of Ca_10.5La_0.5Sb₁₀.

Atom	Ca1	Ca2	Ca3	Ca4/La	Sb1	Sb2	Sb3	Sb4	Sb5
Wyckoff site	16n	16n	8h	4e	16m	8j	8h	4e	4d
QVAL	1.677	2.072	1.553	3.278	4.999	5.254	4.808	5.565	5.438
Volume (Å3)	58.27	49.24	61.34	77.10	88.26	66.67	90.02	80.76	58.32

Supplementary Materials

The following are available online at https://www.mdpi.com/article/10.3390/inorganics12120333/s1, Table S1: Atomic coordinates and equivalent isotropic displacement parameters (U_eq^a) from the SXRD refinements for Ca_10.43(3)La_0.57Sb_9.69(1); Table S2: Detailed structural information of the structure model of Ca_10.5La_0.5Sb₁₀; Table S3: Selected bond distances for Ca_10.43(3)La_0.57Sb_9.69(1); Figure S1. Temperature-dependent power factor PF of Ca_10.43(3)La_0.57Sb_9.69(1), measured over the temperature range of 373–674 K. The results of the three reference compounds (Ca₁₁Sb₁₀, Ca_10.75(3)Nd_0.25Sb_9.82(1), and Ca_10.82(4)Sm_0.18Sb_9.86(1)) [8,10] are also plotted for comparison purposes; Figure S2: TGA results for Ca_10.43(3)La_0.57Sb_9.69(1) over a temperature range of 300 K to 1100 K. The CIF and the checkCIF output files are included in the Supplementary Materials.

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