Anionic Doping and Cationic Site Preference in CaYb4Al2Sb6–xGex

Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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Anionic Doping and Cationic Site Preference in CaYb4Al2Sb6−xGex (x = 0.2, 0.5, 0.7): Origin of the Enhanced Seebeck Coefficient and the Structural Transformation Sung-Ji Lim,† Gnu Nam,† Seungeun Shin,† Kyunghan Ahn,‡ Yunho Lee,§ and Tae-Soo You*,†

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†

Department of Chemistry and BK21Plus Research Team, Chungbuk National University, Cheongju, Chungbuk 28644, Republic of Korea ‡ Department of Applied Physics, Kyung Hee University, Yong-in 17104, Republic of Korea § Department of Chemistry, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea S Supporting Information *

ABSTRACT: Three Zintl phase compounds belonging to the CaYb4Al2Sb6−xGex (x = 0.2, 0.5, 0.7; nominal compositions) system with various Ge-doping contents were successfully synthesized by arc-melting and were initially crystallized in the Ba5Al2Bi6-type phase (space group Pbam, Pearson codes oP26). However, after post-heat treatment at an elevated temperature, the originally obtained crystal structure was transformed into the homeotypic Ca5Ga2Sb6-type structure according to powder and single-crystal X-ray diffraction analyses. Two types of crystal structures share some isotypic structural moieties, such as the one-dimensional anionic chains formed by 1∞[Al2Sb8] and the void-filling Ca2+/Yb2+ mixed cations, but the slightly different spatial arrangements in each unit cell make these two structural types distinguishable. This series of title compounds is originally investigated to examine whether anionic p-type doping using Ge can successfully enhance thermoelectric (TE) properties of the Yb-rich CaYb4Al2Sb6−xGex series even after the phase transition from the Ba5Al2Bi6-type to the Ca5Ga2Sb6-type phase. More interestingly, we also reveal that the given structural transformation is triggered by the particularly different site-preference of Ca2+ and Yb2+ among three available cationic sites in each structure type, which is significantly affected by thermodynamic conditions of this system. Band structure and density of states analyses calculated by density functional theory using the tightbinding linear muffin-tin orbital method also prove that the Ge-doping actually increases band degeneracies and the number of resonant peaks near the Fermi level resulting in the improvement of Seebeck coefficients. Electron localization function analyses for the (0 1 0) sliced-plane and the 3D isosurface nicely illustrates the distortion of the paired-electron densities due to the introduction of Ge. The systematic TE property measurements imply that the attempted anionic p-type doping is indeed effective to improve the TE characteristics of the title CaYb4Al2Sb6−yGey system.

1. INTRODUCTION Thermoelectric (TE) materials have been received great attention from worldwide researchers since they can be considered as one of the most promising green energy sources because of their capability for converting wasted heat into electricity.1−4 In a group of various candidates, the Zintl phase is relatively new for TE material application, and at the same time, it is considered as an intrinsically suitable candidate given its complex crystal structure and electron transport characteristic based on the combination of the space-filling cationic elements and the covalently bonded (poly)anionic frameworks.5 The efficiency of TE material can be expressed by the dimensionless figure-of-merit ZT = σS2T/κ (σ, electrical conductivity; S, Seebeck coefficient; κ, the thermal conductivity; T, absolute temperature).6 Therefore, high σ and S values, as well as low κ values, are essential for the maximum ZT. © XXXX American Chemical Society

In the last 5 years, we have tried to understand the correlation among structure-composition-property of various Zintl phase TE materials. Some of the compounds contain the Ca11‑xYbxSb10‑yGey (0 ≤ x ≤ 9; 0 ≤ y ≤ 3; 0 ≤ z ≤ 3),7 Eu11‑xKxBi10‑ySny (x = 0, 0.26; y = 0.86, 1.93),8 RELixCu2−yP2 (RE = La, Pr, Nd, Gd, Er; 0.82 ≤ x ≤ 1; 1.19 ≤ y ≤ 1.54),9 and Yb14‑xCaxAlSb11 (4.81 ≤ x ≤ 10.57) systems.10 In particular, we recently reported a quaternary Ca5−xYbxAl2Sb6 (1.0 ≤ x ≤ 5.0)11 system, which underwent the single-crystal-to-singlecrystal structural transformation from the arc-melted Ba5Al2Bi6-type12 to the Ca5Ga2Sb6-type13 phase after the post-heat treatment. This structural transformation also caused the transition of electrical transport property from metallic to semiconducting character, which eventually resulted in someReceived: January 22, 2019

A

DOI: 10.1021/acs.inorgchem.9b00181 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

crystals were picked up for further data collection using Bruker’s APEX217 program. Data reduction, integration, and unit cell parameter refinements were conducted using the SAINT program,18 and SADABS was used to perform semiempirical absorption corrections based on equivalents.19 The entire sets of reflections of the two selected compounds were well matched with the orthorhombic crystal system, and the space group Pbam was assigned for both of the Ba5Al2Bi6-type and Ca5Ga2Sb6-type phases. Detailed crystal structures were solved by direct methods and refined to convergence by full matrix least-squares methods on F2. The refined parameters include the scale factor, the atomic positions with anisotropic displacement parameters (ADPs), extinction coefficients, and occupancy factors of the Ca/Yb and Sb/Ge mixed-sites. During the last stage of a refinement cycle, atomic positions were standardized using STRUCTURE TIDY.20 Important crystallographic data, atomic positions with ADPs, and selected interatomic distances are shown in Tables 1−3. Refinement results of each crystal structure

what enhancing TE properties of the title compounds without introducing any dopant. There were several reports about introducing p-type cationic elements for this systems to improve ZT even further,14−16 but there was no report of using an anionic element like Ge for Sb. In this report, we discussed our comprehensive results of experimental and theoretical studies for the quinary CaYb4Al2Sb6−xGex (x = 0.2, 0.5, 0.7; nominal compositions) system, where small amounts of p-type Ge substitutions for Sb successfully enhanced ZT. In particular, during our thorough theoretical investigations, we also revealed for the first time that the observed structural transformation between two structure types was actually triggered by the particularly different site-preference of Ca2+ and Yb2+ among three available cationic sites in each structure type based on the Q values (QVAL) analysis. The enhanced Seebeck coefficient S as a result of Ge-doping was also nicely elucidated by the increased degeneracies of band extrema and resonant peaks near the Fermi level (EF) based on the band structure analysis by using density functional theory (DFT) calculations. Density of states (DOS) curves and electron localization function (ELF) diagrams were also studied by DFT using the tightbinding linear muffin-tin orbital (TB-LMTO) method to understand the overall electronic structure and the localization of paired-electron density. TE properties of the two title compounds before and after the structural transformation were measured and compared with those of our two previously reported isotypic Zintl TE materials Ca1.58(2)Yb3.42Al2Sb6 (Ba5Al2Bi6-type) and Ca1.55(1)Yb3.45Al2Sb6 (Ca5Ga2Sb6-type).11

Table 1. SXRD Data and Structure Refinement Results for Ca1.11(2)Yb3.89Al2Sb5.77(2)Ge0.23 and Ca0.99(3)Yb4.01Al2Sb5.84(2)Ge0.16 empirical formula structure type crystal system space group unit cell dimensions (Å)

volume (Å3) dcalcd (g/cm3) data/restraints/parameters R indicesa (I > 2σ(I))

2. EXPERIMENTAL SECTION 2.1. Synthesis. All sample preparation processes were conducted inside an Ar-filled glovebox with O2 and H2O contents below 0.1 ppm or under vacuum. The used reactant elements were purchased from Alfa Aesar, and the list is as follows: Ca (shot, 99.5%), Yb (ingot, 99.9%), Al (piece, 99.9%), Sb (shot, 99.9%), and Ge (piece, 99.9%). The slightly tanned surfaces of Yb and Ca were cleaned by scraping with a scalpel or a metal brush in a glovebox before loaded for reactions. Since we originally planned to investigate the Ge-doping effect for the quaternary Ca5−xYbxAl2Sb6 (1.0 ≤ x ≤ 5.0) system, which was expected to undergo the structural transformation, we initially attempted to synthesize several Yb-rich compounds with Ca:Yb:Al:Sb:Ge ratios of 1:4:2:5.8:0.2, 1:4:2:5.5:0.5, and 1:4:2:5.3:0.7 by arc-melting. After that, those products were annealed at 1023 K for 1 week, and the solid-state structural transformation from the Ba5Al2Bi6-type to Ca5Ga2Sb6-type phase was successfully observed according to the powder X-ray diffraction (PXRD) patterns shown in the Supporting Information, Figure S1. All products were air- and moisture-stable for at least up to 2 weeks. 2.2. X-ray Diffraction. The three title compounds belonging to the quinary solid-solution CaYb4Al2Sb6−xGex (x = 0.2, 0.5, 0.7; nominal compositions) system were characterized by both PXRD and single-crystal X-ray diffraction (SXRD) measurements. PXRD patterns were obtained at room temperature using a Bruker D8 diffractometer equipped with an area detector and monochromatic Cu Kα1 radiation (λ = 1.54059 Å). The collection step size was set at 0.05° in the range 15° ≤ 2θ ≤ 85° with a total exposure time of 1 h. The phase purities of the title compounds were checked by comparing the collected powder patterns with the simulated patterns previously reported for our two compounds, Ca 1.58(2) Yb 3.42 Al 2 Sb 6 and Ca1.55(1)Yb3.45Al2Sb6,11 respectively, adopting the Ba5Al2Bi6-type12 and Ca5Ga2Sb6-type13 phases. SXRD data were collected using a Bruker SMART APEX CCD-based diffractometer equipped with Mo Kα1 radiation (λ = 0.71073 Å). Some cubic/bar-shaped silvery singlecrystals were chosen from each batch of products, and the crystal qualities were briefly checked by a rapid scan. After that, the best

R indicesa (all data) goodness of fit on F2 largest diff. peak/hole (e/Å3)

Ca1.11(2)Yb3.89Al2Sb 5.77(2)Ge0.23

Ca0.99(3)Yb4.01Al2Sb 5.84(2)Ge0.16

Ba5Al2Bi6 orthorhombic Pbam (no. 55) a = 7.319(2) b = 22.930(2) c = 4.406(1) 739.53(9) 6.695 861/0/45 R1 = 0.0233 wR2 = 0.0525 R1 = 0.0281 wR2 = 0.0550 1.079 2.352/−1.481

Ca5Ga2Sb6 orthorhombic Pbam (no. 55) a = 11.999(2) b = 13.977(2) c = 4.420(2) 741.3(2) 6.765 865/0/45 R1 = 0.0305 wR2 = 0.0618 R1 = 0.0425 wR2 = 0.0654 1.051 1.604/−1.884

R1 = ∑||Fo| − |Fc||/∑|Fo|; wR2 = {∑[w(Fo2 − Fc2]/∑[w(Fo2)2]}]1/2, where w = 1/[σ2Fo2 + (A − P)2 + B − P], in which P = (Fo2 + 2Fc2)/3 and A and B are weight coefficients. a

have been deposited at the Cambridge Crystallographic Data Centre with reference CCDC 1889076 for Ca1.11Yb3.89Al2Sb5.77Ge0.23 and 1889077 for Ca0.99Yb4.01Al2Sb5.84Ge0.16. 2.3. Electronic Structure Calculations. A series of comprehensive theoretical calculations were conducted by using TB-LMTO method with atomic sphere approximation (ASA)21−25 to understand the cationic site-preference,10,26,27 QVAL analyses,28 and overall electronic structure of the title compounds. In particular, to study the cationic site-preference, we designed three hypothetical Ca5Ge2Sb6type models with an idealized composition of CaYb4Al2Sb5.5Ge0.5 and assigned Ca at a different cationic site in each model. However, Ge was allocated only at the Sb1 site, where the Ge content was experimentally refined in both structure types. To apply this particular composition, the symmetry of these models were lowered from the refined Pbam to its subgroup Pm. Detailed information about these crystal structures including lattice parameters and atomic positions were extracted from SXRD data of Ca1.11(2)Yb3.89Al2Sb5.77(2)Ge0.23 for the Ba5Al2Bi6-type phase and Ca0.99(3)Yb4.01Al2Sb5.84(2)Ge0.16 for the Ca5Ga2Sb6-type phase. The following DOS, band structure and ELF were thoroughly examined using a model showing the lowest electronic energy, where Ca is located at the M3 site. For 3D visualization of ELF, the Visualization for Electronic and Structural Analysis program29 was exploited. During the TB-LMTO-ASA calculations, the local density approxB

DOI: 10.1021/acs.inorgchem.9b00181 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Table 2. Atomic Coordinates and Equivalent Isotropic Displacement Parameters (Ueqa) from SXRD Refinements for Ca1.11(2)Yb3.89Al2Sb5.77(2)Ge0.23 and Ca0.99(3)Yb4.01Al2Sb5.84(2)Ge0.16 atom

Wyckoff site

M1b M2b M3b Al Sb1/Ge Sb2 Sb3

4g 4g 2a 4h 4h 4h 4g

M1b M2b M3b Al Sb1/Ge Sb2 Sb3

4g 4g 2a 4h 4h 4h 4g

occupation (Ca2+/Yb2+)

x

Ca1.11(2)Yb3.89Al2Sb5.77(2)Ge0.23 (Ba5Al2Bi6-type) 0.23(1)/0.77 0.0507(2) 0.24(1)/0.76 0.2337(2) 0.17(2)/0.83 0 1 0.1852(5) 0.88(1)/0.12 0.3008(1) 1 0.4870(1) 1 0.4762(1) Ca0.99(3)Yb4.01Al2Sb5.84(2)Ge0.16 (Ca5Ga2Sb6-type) 0.18(2)/0.82 0.0905(2) 0.17(2)/0.83 0.3274(2) 0.28(2)/0.72 0 1 0.3312(4) 0.92(1)/0.08 0.0241(2) 1 0.1558(2) 1 0.3379(2)

y

z

Ueqa (Å2)

0.4112(1) 0.2477(1) 0 0.1218(2) 0.0054(1) 0.1879(1) 0.3643(1)

0 0 0 1 /2 1 /2 1 /2 0

0.0078(2) 0.0074(2) 0.0077(3) 0.0092(7) 0.0076(3) 0.0072(2) 0.0072(2)

0.2483(2) 0.0142(2) 0 0.2117(3) 0.4005(2) 0.0943(2) 0.3222(2)

0 0 0 1 /2 1 /2 1 /2 0

0.0090(2) 0.0096(3) 0.0081(4) 0.0118(9) 0.0087(3) 0.0077(3) 0.0081(3)

a

Ueq is defined as one-third of the trace of the orthogonalized Uij tensor. bM = Ca2+/Yb2+ mixed site. the self-consistent charge density was obtained using 360 irreducible k-points in the Brillouin zone for the structural models. 2.4. Electrical Transport Properties. Each arc-molten ingot of Ca1.11(2)Yb3.89Al2Sb5.77(2)Ge0.23 (Ba5Al2Bi6-type) and Ca0.99(3)Yb4.01Al2Sb5.84(2)Ge0.16 (Ca5Ga2Sb6-type) was directly cut and polished into a rectangular shape (3 mm × 3 mm × 10 mm) for the electrical transport properties measurements. 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 room temperature to ca. 700 K using a ULVACRIKO ZEM-3 instrument system. The densities of both prepared samples were higher than 95% of their theoretical densities according to the geometric density measurements. 2.5. Thermal Conductivities. Two disk-shaped samples of Ca1.11(2)Yb3.89Al2Sb5.77(2)Ge0.23 and Ca0.99(3)Yb4.01Al2Sb5.84(2)Ge0.16 were also directly prepared from the ingots synthesized by arc melting. Thermal diffusivity (D) was directly measured using these samples under the Ar atmosphere from room temperature to ca. 700 K by a flash diffusivity method using a Netzsch LFA 457 MicroFlash instrument. In the flash diffusivity method, the front face of a diskshaped sample is irradiated by a short laser burst, and the resultant temperature increase on the rear face is recorded and analyzed by an IR detector. The thermal conductivity (κ) was calculated from the equation κ = DCpρ, where ρ and Cp are the density and heat capacity of the sample, respectively. In this work, the Dulong−Petit value (3R/ atom, where R is the gas constant) was used for Cp. The total thermal conductivity κtot was assumed to be the sum of the lattice (κlatt) and electronic (κelec) thermal conductivities. κelec was expressed using the Wiedemann−Franz law (κelec = LσT), where L is the temperaturedependent Lorenz number. The L value was estimated using the single parabolic band (SPB) model with acoustic phonon scattering from the temperature-dependent Seebeck coefficient (see Supporting Information, Table S1).34 Finally, κlatt was calculated from the relationship κlatt = κtot − κelec.

Table 3. Selected Bond Distances for Ca1.11(2)Yb3.89Al2Sb5.77(2)Ge0.23 and Ca0.99(3)Yb4.01Al2Sb5.84(2)Ge0.16 bond distance (Å)

structure type Ca5Ga2Sb6 and Ba5Al2Bi6

Ca5Ga2Sb6

Ba5Al2Bi6

Ca1.11(2) Yb3.89Al2Sb 5.77(2)Ge0.23

Ca0.99(3) Yb4.01Al2Sb 5.84(2)Ge0.16

Al−Sb1/Ge

2.799(4)

2.796(5)

Al−Sb2 Al−Sb3 (×2) Sb1/Ge−Sb1/Ge M1−Sb1/Ge (×2) M1−Sb2 (×2) M2−Sb1/Ge (×2) M2−Sb3 M3−Sb2 (×4) M3−Sb3 (×2) M2−Sb2 (×2) M2−Sb2 (×2) M1−Sb1/Ge (×2) M1−Sb3 M3−Sb1/Ge (×4) M3−Sb3 (×2)

2.679(4) 2.701(2) 2.926(1) − − − − − − 3.210(2) 3.189(2) 3.443(2) 3.295(1) 3.117(2) 3.117(2)

2.669(5) 2.697(3) 2.840(1) 3.170(2) 3.183(2) 3.446(1) 3.337(1) 3.180(2) 3.156(2) − − − − − −

atomic pair

imation was used for exchange and correlation, and all relativistic effects were taken into account using a scalar relativistic approximation except spin−orbit coupling. The symmetry of the potential is considered spherical inside each of the Wigner−Seitz (WS) atomic spheres,21−25 and a combined correction is used to take into account the overlapping part. The WS radius for each atomic sphere was calculated by requiring that the overlapping potential be the best possible approximation to the full potential and was determined by an automatic procedure.30 The WS radii used for the structure type are listed here: Ca = 3.98−3.99 Å, Yb = 3.93−4.21 Å, Al = 2.92−2.93 Å, Ge = 3.17 Å, and Sb = 3.25−3.41 Å. The basis sets included 4s, 4p, and 3d orbitals for Ca; 6s, 6p, and 5d orbitals for Yb; 3s, 3p, and 3d orbitals for Al; 5s, 5p, 5d, and 4f orbitals for Sb; and 4s, 4p, and 4d orbitals for Ge. The Ca 4p, Yb 6p, Al 3d, Sb 5d and 4f, and Ge 4d orbitals were treated by the Löwdin downfolding technique.31 The 4f wave functions of Yb were treated as core functions.32 The kspace integrations were conducted by the tetrahedron method,33 and

3. RESULTS AND DISCUSSION 3.1. Crystal Structure. Three Zintl phase compounds belonging to the quinary CaYb4Al2Sb6−xGex system with x = 0.2, 0.5, 0.7 (nominal compositions) were successfully synthesized by arc-melting and characterized by both PXRD and SXRD analyses. The title compounds originally adopted the orthorhombic Pbam with Pearson codes oP26 (Ba5Al2Bi6type, Z = 2) and contained seven crystallographically C

DOI: 10.1021/acs.inorgchem.9b00181 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 1. Crystal structures of (a) Ca1.11(2)Yb3.89Al2Sb5.77(2)Ge0.23 (Ba5Al2Bi6-type) and (b) Ca0.99(3)Yb4.01Al2Sb5.84(2)Ge0.16 (Ca5Ga2Sb6-type) viewed along the c-axis direction. The [AlSb4] tetrahedron and the Sb1/Ge−Sb1/Ge bonds are emphasized as a blue polyhedron and a green dumbbell, respectively. Color codes: M, gray; Al, light gray; Sb, yellow; Sb1/Ge mixed-sites, green.

independent atomic sites: three Ca2+/Yb2+ mixed-sites, one Al site, one Sb/Ge mixed-site, and two Sb sites (see Tables 1 and 2). Since the Sb1 site includes small amounts of the p-type Gedopants, the title compounds can be regarded as quinary derivatives of the previously reported quaternary Ca5−xYbxAl2Sb6 (1.0 ≤ x ≤ 5.0) system.11 In our earlier report about this particular isotypic quaternary system, we claimed that the phase transitions of some Yb-rich compounds from their originally crystallized Ba5Al2Bi6-type phase12 to the Ca5Ga2Sb6-type phase13 were activated by the post-heat treatment after the initial synthesis, and it resulted in improving TE properties. Therefore, in this work, we planned to investigate whether the addition of p-type Ge-dopant in the Yb-rich Ca5−xYbxAl2Sb6 system would successfully introduce a p-type carrier and eventually further improve TE properties after the phase transition to the Ca5Ga2Sb6-type phase. Therefore, we targeted the particular Ca:Yb ratio of 1:4, which was already proven to take the structural transformation after annealing in the quaternary system, and we introduced three different amounts of Ge-dopants for Sb, resulting in producing the title quinary CaYb4Al2Sb6−xGex (x = 0.2, 0.5, 0.7) system. Just like its predecessor Ca5−xYbxAl2Sb6 system, the three title compounds with Ge-doping initially crystallized in the Ba5Al2Bi6-type structure (Figure 1a) via arc-melting. However, after the annealing procedure at 1023 K for 1 week, the original Ba5Al2Bi6-type phase12 was successfully transformed to the Ca5Ga2Sb6-type phase13 (Figure 1b). The Ca5Ga2Sb6-type phase also adopted the same space group Pbam and included three mixed-cationic sites and four anionic sites, just like the Ba5Al2Bi6-type phase12 (see Tables 1 and 2). Two structure types commonly contain two isotypic structural building blocks: (1) the one-dimensional (1D) 1 ∞ [Al 2 (Sb/Ge) 2 Sb 2 Sb 4/2 ] double chains formed by two dimerized Al(Sb/Ge)4 tetrahedra35,36 and (2) the mixedcations of Ca2+/Yb2+ allocated between these 1D anionic chains. However, the method of assembling these building blocks in each structure type and the local coordinate geometries consisting of the 1∞[Al2(Sb/Ge)6] moiety make these two structure types distinguishable. In particular, the Sb1/Ge−Sb1/Ge bond distance bridging two neighboring Al(Sb/Ge)4 tetrahedra, which is also closely related to the shift of electrical transport property from metallic to semiconducting behavior, was shortened from 2.92 Å in Ca1.11(2)Yb3.89Al2Sb5.77(2)Ge0.23 (Ba5Al2Bi6-type) to 2.84 Å in

Ca0.99(3)Yb4.01Al2Sb5.84(2)Ge0.16 (Ca5Ga2Sb6-type) as provided in Figure 2. Since the coordinate environments surrounding

1 Figure 2. Coordination geometry of the localized ∞ [Al2(Sb/ Ge) 2 Sb 2 Sb 4/2 ] moiety in (a) Ca 1.11(2) Yb 3.89 Al 2 Sb 5.77(2) Ge 0.23 (Ba5Al2Bi6-type) and (b) Ca0.99(3)Yb4.01Al2Sb5.84(2)Ge0.16 (Ca5Ga2Sb6type). Atomic labels and Sb1/Ge−Sb1/Ge bond distances are also displayed. Color codes for atoms: Al, light gray; Sb, yellow; Sb1/Ge mixed-sites, green.

each cationic site in two structure types are isotypic, we exploit three cationic sites observed in Ca0.99(3)Yb4.01Al2Sb5.84(2)Ge0.16 (Ca5Ga2Sb6-type) to discuss the detail local coordination geometries. As shown in Figure 3, both of the M1 and M3 sites adopted the octahedral geometry encapsulated by a total of six Sb or the Sb1/Ge mixed-sites. On the other hand, the M2 site is located in the two-edge capped square pyramid built by seven anionic elements. Quite interestingly, two title phases clearly display two distinctive site-preference of Ca2+ and Yb2+ at the three cationic sites, respectively, as can be seen in Table 2. Normally, any particular site-preference26,27 of an atom should be elucidated either by the size-factor based on the size match between a site volume and a central atom37 or by the electronic-factor based on the correlation between an electronegativity of an atom and the QVAL at the site.28 In our title compounds, a cationic site-preference observed in Ca0.99(3)Yb4.01Al2Sb5.84(2)Ge0.16 (Ca5Ga2Sb6-type) can be explained by both of the sizes- and the electronic-factor criteria, whereas those observed in Ca1.11(2)Yb3.89Al2Sb5.77(2)Ge0.23 (Ba5Al2Bi6-type) can hardly be. More interestingly, during the thorough studies to understand two different cationic sitepreferences, for the first time in the A5M2Sb6 (A = Ca, Sr, Eu; D

DOI: 10.1021/acs.inorgchem.9b00181 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 3. Three cationic sites surrounded by anionic elements in Ca0.99(3)Yb4.01Al2Sb5.84(2)Ge0.16 (Ca5Ga2Sb6-type). Detailed atomic labels and interatomic distances are displayed. Color codes: M, gray; Sb, yellow; Sb1/Ge mixed-sites, green.

Table 4. QVAL of CaYb4Al2Sb6 in the Ba5Al2Bi6-Type and Ca5Ga2Sb6-Type Structures QVAL

site

M1

M2

M3

Al

Sb1

Sb2

Sb3

Ba5Al2Bi6-type Ca5Ga2Sb6-type

2.630 2.574

2.740 2.757

2.409 2.528

2.622 2.717

4.416 4.549

4.631 4.411

4.759 4.727

M = Al, Ga, In) series,11,13,35,36,38−40 we revealed a significant influence of the cationic site-preference to the observed structural transformation and eventually to the electrical transport property of each structure type. We will further discuss this topic in the subsequent section. 3.2. Cationic Site-Preference and Structural Transformation. As shown in Table 2, in the Ca0.99(3)Yb4.01Al2Sb5.84(2)Ge0.16 (Ca5Ga2Sb6-type), the largest Ca2+ occupation of 28% is observed at the 6-coordinate M3 site, whereas the 6-coordinate M1 and even the 7-coordinate M2 sites contain the relatively smaller Ca2+ contents. First, this type of site-preference can be elucidated by the size-factor criterion.37 The M1 and M3 sites show quite similar coordination environments, where six Sb or the Sb1/Ge mixed-sites form the distorted octahedra as shown in Figure 3. However, according to the bond distances between M and Sb(Sb1/Ge) as well as the inner angles of ∠Sb−M−Sb, the M3 site can provide a relatively more symmetric coordinate environment than the M1 site. Therefore, the relatively smaller Ca2+ prefers the M3 site. In addition, the M2 site surrounded by seven anions forming a two-edge capped square pyramid provides the largest site volume, and therefore it rather prefers to contain more Yb2+ contents than Ca2+. Second, the electronic-factor based on the QVAL of each site can also nicely explain this type of cationic site-preference.28 Generally, we can evaluate the QVAL of an atomic site using the integrated electron densities of the WS sphere. Therefore, on the basis of this QVAL criterion, an atom having a relatively higher electronegativity should prefer the site having the higher electron density, which is indicated by the larger QVAL.28 According to our QVAL evaluation by DFT calculations (Table 4), the M3 site has the smallest value, whereas the M2 site has the largest one in both structure types. Therefore, the largest (smallest) Ca2+ content found at the M3 (M2) site in the Ca5Ga2Sb6-type compound is nicely elucidated by the QVAL evaluation as well. On the contrary, in Ca 1.11(2) Yb 3.89 Al 2 Sb 5.77(2) Ge 0.23 (Ba5Al2Bi6-type), neither the size-factor nor the electronicfactor can elucidate the refined site-preference of Ca2+ and Yb2+. For instance, the M3 site having the smallest QVAL as well as site volume actually contains the largest Yb2+ content.

Therefore, based on these comprehensive investigations, we claim that the driving force for the phase transition of a Yb-rich compound from the Ba5Al2Bi6-type to Ca5Ga2Sb6-type phase should be attributed to the specific site-preference of Ca2+ and Yb2+. During the original arc-melting, the kinetically more favored Ca2+ and Yb2+ arrangement resulted in the Ba5Al2Bi6type phase. However, the post-heat treatment process provided the large enough activation energy to migrate cations to the more thermodynamically favored sites with respect to both of the size-factor as well as the electronic-factor criteria, just like what was observed in the Ca5Ga2Sb6-type phase, and it eventually triggered the observed structural transformation. Interestingly, the same pattern of such distinctive cationic sitepreferences in two structure types is also observed in the previously reported Ca5−xYbxAl2Sb6 (1.0 ≤ x ≤ 5.0) system.11 3.3. Electronic Structures and Chemical Bonding. In our previous report about the Ca5−xYbxAl2Sb6 (1.0 ≤ x ≤ 5.0) system, we mentioned that the Ca5Al2Sb6-type phase was thermodynamically more favorable than the Ba5Al2Bi6-type phase on the basis of the total electronic energy difference 0.66 eV/formula unit between two structure types.11 In this current report, since we claimed that the migration of cations during the annealing process should be a driving force of this particular structural transformation, first, we designed three different coloring patterns (see Supporting Information, Table S2)41 in which each contains a different Ca site, respectively, and we compared their total electronic energies with each other to confirm the most favorable Ca site in the Ca5Ga2Sb6type phase. In addition, to further understand the origin of the energy difference among three coloring patterns, we thoroughly investigated the site- and bond-energies37 consisting of the total electronic energy of each pattern (see Table 5). According to the detailed theoretical analyses, the total electronic energy and band energy of model 3 having Ca at the M3 site are relatively smaller than those of models 1 and 2, respectively, having Ca at the M1 and the M2 sites. As Ca occupies one of the cationic sites, the site-energy of the Ca occupying site in the corresponding model becomes smaller than that of the same site occupied by Yb in two other models. This site-energy difference is the largest as Ca occupies the M3 E

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Inorganic Chemistry Table 5. Site-Energy and Bond-Energy Comparison among Three CaYb4Al2Sb5.5Ge0.5 Models with Different Ca Positions model 1 (Ca at M1) ETOTa (eV) EBanda (eV) site energies (eV) M1 M2 M3 Al Sb1/Ge Sb2 Sb3 total relative total bond energies (eV) Sb1/Ge−Sb1/Ge (dimer) Al−Sb1/Ge Al−Sb2 Al−Sb3 (×2) M1−Sb1/Ge (×2) M1−Sb2 (×2) M2−Sb1/Ge (×2) M2−Sb3 M3−Sb2 (×4) M3−Sb3 (×2) total relative total site + bond energies (eV) relative total

model 2 (Ca at M2)

model 3 (Ca at M3)

0.073 0.507

0.657 0.672

0 0

8.896 5.753 7.034 −32.991 −119.690 −121.376 −129.646 −382.019 0.336

10.527 4.265 7.019 −32.942 −119.935 −121.222 −129.003 −381.291 1.064

10.447 5.608 5.185 −32.429 −118.912 −122.37 −129.880 −382.355 0

−1.896 −2.110 −2.723 −5.687 −1.959 −2.152 −1.264 −1.024 −4.040 −1.947 −24.804 0.039 −406.823 0.375

−1.894 −2.106 −2.700 −5.675 −1.996 −2.181 −1.225 −0.964 −4.017 −1.992 −24.750 0.092 −406.041 1.157

−1.900 −2.109 −2.695 −5.678 −1.994 −2.216 −1.274 −1.030 −3.994 −1.951 −24.842 0 −407.197 0

Figure 4. (a) DOS curves and (b) band structures of CaYb4Al2Sb5.5Ge0.5 (Ca5Ga2Sb6-type). EF corresponding to 45.5 VEC (dashed line) is the energy reference (0 eV), and two additional lines corresponding to 45.84 VEC (Ca0.99(3)Yb4.01Al2Sb5.84(2)Ge0.16, dotted line) and 46.0 VEC (CaYb4Al2Sb6, dash-dotted line) are also indicated. Color codes: total DOS (bold black outline), Yb PDOS (gray region), Ca PDOS (orange region), Sb PDOS (yellow region), Ge PDOS (green region), and Al PDOS (purple region).

state near EF can also be attributed to increasing Seebeck coefficient of the title phase, just like in several other known compounds including Sn1‑x‑yInxCdyTe, PbSe:Alx, InxSn1−xTe, and SnTe-AgInTe2.44−47 DOS curves and band structures of CaYb4Al2Sb6 (Ca5Ga2Sb6-type) without Ge-doping are provided in the Supporting Information, Figure S2, for comparison. Last, ELF analyses48 were also conducted for the Ca5Ga2Sb6type phase to see the influence of Ge-doping for locations and distributions of paired-electron densities on the anionic frameworks. For this purpose, we compared ELF diagrams of CaYb4Al2Sb5.5Ge0.5 to those of CaYb4Al2Sb6 as shown in Figure 5. As Ge substitutes Sb1 at the Wyckoff 4h site, due to the slightly lower electronegativity of Ge than Sb, the electron density of bonding-pair between Ge and Al in the [Al(Sb/ Ge)4] tetrahedron looks like more diffused toward Al as illustrated in the 2D contour map of the (0 1 0) sliced-plane (Figure 5, parts a and b). This phenomenon is even more noticeable in the 3D ELF isosurfaces. The disk-shaped attractor representing the bonding-pairs between Ge and Al becomes relatively thicker and is located closer to Al with a more distorted disk-shape due to the Ge-doping. In addition, the size of a large umbrella-shaped isosurface representing lone-pairs on Sb1 (Figure 5c) becomes shrunken and eventually results in a small mushroom-shape isosurface as Ge substitutes Sb1 (Figure 5d). 3.4. Thermoelectric Properties. Thermoelectric properties were measured for two Ge-doped title compounds and compared with two previously reported isotypic compounds in Figures 6 and 7. Temperature-dependent electrical conductivities σ are shown for Ca1.58(2)Yb3.42Al2Sb6,11 Ca 1.11(2) Yb 3.89 Al 2 Sb 5.77(2) Ge 0.23 (both Ba 5 Al 2 Bi 6 -type), Ca1.55(1)Yb3.45Al2Sb6,11 and Ca0.99(3)Yb4.01Al2Sb5.84(2)Ge0.16 (both Ca5Ga2Sb6-type) in Figure 6a. Two Ba5Al2Bi6-type compounds show metallic conduction behaviors indicating a decreasing trend of σ as temperature increases except for an uprising σ at T > 500 K for Ca1.11(2)Yb3.89Al2Sb5.77(2)Ge0.23 (Ba5Al2Bi6-type) which may be related to thermal excitation of

a

ETOT and EBand of models 1 and 2 are indicative of the relative energy differences compared to model 3.

site in model 3. These theoretical consequences are nicely agreed with the experimental observation in the Ca5Ga2Sb6type compounds, where Ca prefers M3, M1, and M2 in order. Moreover, the site-energy difference is more significant than the bond-energy difference between the three models. Therefore, it is clear that the site-energy is the more important decision factor for the total electronic energy of each coloring pattern. Second, to understand the Ge-doping effect for the transport properties of the Ca5 Ga2Sb6-type phase, we conducted DOS and band structure analyses using model 3 by the TB-LMTO method. 21−25 In Figure 4a, three Fermi levels (E F ) corresponding to valence electron counts (VEC) of 46, 45.84, and 45.5 for CaYb 4 Al 2 Sb 6 , Ca 0 . 9 9 ( 3 ) Yb 4 . 0 1 Al2Sb5.84(2)Ge0.16, and CaYb4Al2Sb5.5Ge0.5, respectively, are displayed. As Ge-dopants are introduced, the degeneracy of band extrema, representing the number of the peak in the valence band, increases at the X point due to the additional bands from Ge (Figure 4b). Moreover, the doubly degenerated band is also observed at the region between the Γ and Z points. Thus, the increased degeneracy of band extrema should influence the effective mass of Ca0.99(3)Yb4.01Al2Sb5.84(2)Ge0.16 and results in an increasing Seebeck coefficient.42,43 In addition, a small peak at ca. 0.25 eV near the top of the valence band is also observed in the DOS curves. This peak should be generated by the increased energy in the upper valence band region, and therefore, this resonant F

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Figure 5. Electron localization function (ELF) diagrams of CaYb4Al2Sb6 (a and c) and CaYb4Al2Sb5.5Ge0.5 (b and d) illustrated as the 2D contour map for the (0 1 0) sliced-plane and the 3D isosurface for the [Al2Sb8] moiety. In parts a and b, the color scheme from blue to red corresponds to ELF between 0.0 and 1.0. The ELF value higher than 0.5 indicates the region exceeding the ELF value of free-electron. In parts c and d, yellow isosurfaces show the areas having ELF values higher than 0.65.

Figure 6. Temperature-dependent (a) electrical conductivities σ and (b) Seebeck coefficients S of Ca1.11(2)Yb3.89Al2Sb5.77(2)Ge0.23 (Ba5Al2Bi6-type) and Ca0.99(3)Yb4.01Al2Sb5.84(2)Ge0.16 (Ca5Ga2Sb6-type) measured between 300 and 700 K. The σ and S values of Ca1.58(2)Yb3.42Al2Sb6 (Ba5Al2Bi6type) and Ca1.55(1)Yb3.45Al2Sb6 (Ca5Ga2Sb6-type) from the literature are also displayed in parts a and b.

Ca1.58(2)Yb3.42Al2Sb6, Ca1.11(2)Yb3.89Al2Sb5.77(2)Ge0.23 (both Ba5Al2Bi6-type), Ca1.55(1)Yb3.45Al2Sb6, and Ca0.99(3)Yb4.01Al2Sb5.84(2)Ge0.16 (both Ca5Ga2Sb6-type), respectively. These largely different S values depending on the structure type nicely represent the Ba5 Al2 Bi 6 -type-toCa5Ga2Sb6-type structural transformation regardless of the Ge-doping, which eventually results in the metal-to-semiconductor transition. Recently, we revealed that the Ge-doping for Sb in the Ca11‑xYbxSb10‑yGez (0 ≤ x ≤ 9; 0 ≤ y ≤ 3; 0 ≤ z ≤ 3) system6 successfully generated extra hole carriers, which effectively weakened the compensation effects of electrons and holes. Therefore, we claimed that the Ge-doping eventually

minority carriers during heating. In addition, the Ge-doping reduces the room temperature σ of the Ba5Al2Bi6-type phase: 296.01(1) S cm−1 for Ca1.58(2)Yb3.42Al2Sb6 vs 213.99(1) S cm−1 for Ca1.11(2)Yb3.89Al2Sb5.77(2)Ge0.23. On the contrary, two Ca5Ga2Sb6-type compounds display semiconducting behaviors where σ increases with increasing temperature. In particular, the room temperature σ of two Ca5Ga2Sb6-type phases, Ca1.55(1)Yb3.45Al2Sb6 and Ca0.99(3)Yb4.02Al2Sb5.84(2)Ge0.16, are 2.21(1) and 6.33(2) S cm−1, respectively. Figure 6b shows Seebeck coefficients S of four compounds as a function of temperature, and the room temperature S values are 19.56(2), 33.98(2), 119.55(1), and 180.04(2) μV K − 1 for G

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Figure 7. Temperature-dependent (a) total thermal conductivities κtot and (b) figure of merits ZT of Ca1.11(2)Yb3.89Al2Sb5.77(2)Ge0.23 (Ba5Al2Bi6type) and Ca0.99(3)Yb4.01Al2Sb5.84(2)Ge0.16 (Ca5Ga2Sb6-type) measured between 300 and 700 K. The κtot and ZT values of Ca1.58(2)Yb3.42Al2Sb6 (Ba5Al2Bi6-type) and Ca1.55(1)Yb3.45Al2Sb6 (Ca5Ga2Sb6-type) from the literature are also displayed in parts a and b.

various p-type Ge contents. The crystal structure of all three compounds crystallized in the Ba5Al2Bi6-type phase after the initially arc-meting, but during the post-heat treatment at an elevated temperature, the original structure was successfully transformed to the Ca5Ga2Sb6-type phase. Despite several structural similarities, two types of cations: Ca2+ and Yb2+ showed a distinctive site-preference in each structure type, and we claimed that the driving force for this phase transition of the Yb-rich compounds should be attributed to the specific site-preference of Ca2+ and Yb2+. The large activation energy through the annealing process made two types of cations to migrate to the more thermodynamically favored sites, which were observed in the Ca5Ga2Sb6-type phase, and this migration of cations eventually triggered the observed structural transformation. In addition, the series of comprehensive DFT calculations proved that the total electronic energy difference between two structure types was mainly originated from the site-energy of the M3 site rather than various bondenergies. DOS and band structure analyses also indicated that the increased degeneracy of band extrema and the addition of resonant states near EF by the Ge doping for Sb should be attributed to the increase of Seebeck coefficients of the title compound. ELF sliced-planes and 3D isosurfaces indicated that the Ge-doping also caused the distortion of a disk-shaped bonding-pair between Ge and Al in the [Al(Sb/Ge)4] tetrahedral unit and the shrinkage of an umbrella-shaped lone-pair on the bridging Ge as well.

improved S by restraining bipolar conduction. In this regard, the Ge-doping for Sb in the title CaYb5Al2Sb6−xGex system also successfully enhanced the room temperature S value by 50%, especially for the Ca5Ga2Sb6-type phase. Temperature-dependent thermal conductivities κ are provided in Figure 7a. To obtain the lattice thermal conductivity κlatt, the electrical thermal conductivity κelec should first be evaluated by the Wiedemann−Franz law κelec = LσT (L: the Lorenz number from an SPB model with acoustic phonon scattering),34 and then the relationship of κtot = κelec + κlatt can be exploited. The room temperature L of the two title compounds Ca1.11(2)Yb3.89Al2Sb5.77(2)Ge0.23 and Ca0.99(3)Yb4.01Al2Sb5.84(2)Ge0.16 are 2.19(1) and 1.26(2), respectively. It is noted that the contribution of κelec to κtot is almost negligible for the Ca5Ga2Sb6-type compounds so that the κlatt is approximately the same as κtot. Therefore, the room temperature κ l a t t values of Ca 1 . 5 8 ( 2 ) Yb 3 . 4 2 Al 2 Sb 6 , 1 1 Ca 1.11(2) Yb 3.89 Al 2 Sb 5.77(2) Ge 0.23 (both Ba 5 Al 2 Bi 6 -type), Ca1.55(1)Yb3.45Al2Sb6,11 and Ca0.99(3)Yb4.01Al2Sb5.84(2)Ge0.16 (both Ca5Ga2Sb6-type) can be considered as 3.78(1), 2.19(1), 1.08(1), and 1.26(2) W m−1 K−1, respectively (Supporting Information, Figure S3). This indicates that the semiconducting Ca5Ga2Sb6-type compounds should be less phonon conducting than the metallic Ba5Al2Bi6-type compounds. Last, Figure 7b shows the comparison for ZT of these four compounds. All of the four compounds show the increasing trends of ZT with increasing temperature. Interestingly, ZT of the Ge-doped Ca0.99(3)Yb4.01Al2Sb5.84(2)Ge0.16 at 660 K is more than doubled comparing to that of Ca1.55(1)Yb3.45Al2Sb6. This result successfully demonstrates that the Ge-doping along with the structural transformation via the post-heat treatment for the Yb-rich compound can significantly help to enhance TE properties of the title CaYb5Al2Sb6−xGex system. The further improvement of TE performance of the title system can possibly be achieved by more sophisticated band engineering,43 such as the particular effective doping for increasing charge carrier density.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.9b00181. PXRD patterns of the three title compounds, DOS and band structures of CaYb4Al2Sb6 (Ca5Ga2Sb6-type), and temperature-dependent lattice thermal conductivity κlatt of Ca1.11(2)Yb3.89Al2Sb5.77(2)Ge0.23 (Ba5Al2Bi6-type) and Ca0.99(3)Yb4.01Al2Sb5.84(2)Ge0.16 (Ca5Ga2Sb6-type) (PDF) Accession Codes

4. CONCLUSION Three quinary Zintl phase compounds belonging to the CaYb5Al2Sb6−xGex system were successfully synthesized with

CCDC 1889076−1889077 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by H

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emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

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AUTHOR INFORMATION

Corresponding Author

*(T-S.Y.) E-mail: [email protected]. Telephone: +82 (43) 261-2282. Fax: +82 (43) 267-2289. ORCID

Kyunghan Ahn: 0000-0002-7806-8043 Yunho Lee: 0000-0002-9113-9491 Tae-Soo You: 0000-0001-9710-2166 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research is supported by Basic Science Research Program through National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (NRF2018R1D1A1B07049249).

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DOI: 10.1021/acs.inorgchem.9b00181 Inorg. Chem. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.inorgchem.9b00181 Inorg. Chem. XXXX, XXX, XXX−XXX