A new clathrate solid solution Ba8Cu16 − xAuxP30 (x = 4, 8, 12) was synthesized by a high-temperature solid-state annealing method. The crystal structures of Ba8Cu16 − xAuxP30 were determined by single crystal x-ray diffraction. This clathrate solid solution crystallizes in the orthorhombic superstructure of clathrate-I type with 23 crystallographically independent framework sites, eight of them are occupied by Au/Cu and 15 are exclusively occupied by P atoms. The distribution of Au and Cu atoms over these eight framework sites is not random with a clear preference for Au to occupy the largest (Au/Cu)P4 tetrahedra in the framework. The thermal stability and thermoelectric properties of the Ba8Cu16 − xAuxP30 solid solution were evaluated. Low thermal conductivity was achieved for Ba8Cu16 − xAuxP30 due to the combination of the host–guest crystal structure with rattling Ba atoms with the presence of heavy Au atoms and substitutional Cu/Au disorder in the clathrate framework.

Thermoelectric materials have attracted significant attention due to their capability to directly convert heat into electrical power and vice versa.1–4 The performance of a thermoelectric material is evaluated through the dimensionless figure-of-merit zT = S2T/ρκ, where S is the Seebeck thermopower, T is the absolute temperature, ρ is the electrical resistivity, and κ is the thermal conductivity. Achieving highly efficient thermoelectric properties requires the combination of excellent charge transport performance and as low as possible thermal conductivity in crystalline solid materials.5–7 Understanding the thermal transport in solids is not only important for thermoelectrics1–7 but also for other disciplines such as phononic8,9 and heat shield materials.10 Many strategies to optimize thermal conductivity of a material have been studied, including static and dynamic disorder,11,12 strong bonding anharmonicity,13–15 crystal structure complexity enhancement,16–18 and nanostructure engineering.19–27 

Systems with intrinsically low thermal conductivity play an important role in thermoelectric research. Inorganic clathrates are promising systems due to their host–guest structure and possible rattling of guest atoms inside framework cages.28–32 The covalent three-dimensional framework in clathrate compounds provides routes for electrical conductivity coupled with rattling atoms in the framework cages and complex structure of framework, resulting in an efficient phonon scattering reducing thermal conductivity. This has been demonstrated in tetrel-based (Si, Ge, Sn) clathrates.30,31 Many research efforts have been focused on understating the interplay between framework and guest atoms.31,33–35 We have shown that transition metal–phosphorus clathrates are viable thermoelectric materials.32,36–38 Ba8Au16P30 was demonstrated to exhibit ultralow thermal conductivity (<0.6 W m–1 K–1 at 300 K) due to the complex crystal structure and twinned microstructures.16 The isostructural analog Ba8Cu16P30 was discovered earlier39 but with higher thermal conductivity (>1 W m–1 K–1 at 300 K),36,37,40 which points out on the importance of the heavy elements in the framework to achieve ultralow thermal conductivity. At room temperatures, the thermal conductivity of few other pnictide clathrates with {Cu,Zn,Ge}-P frameworks were reported to be 0.6 W m–1 K–1 (Ba8Cu14Zn2P30),38 0.7 W m–1 K–1 (Ba8Cu14Ge6P26),36 1.7 W m–1 K–1 (Ba8Cu13Zn11P29),41 and 1.1 W m–1 K–1 (La1.6Ba6.4Cu16P30).37 This demonstrates that low thermal conductivity may depend on the bonding features of the crystal structure in addition to the weight of the elements forming the framework. To investigate this question, we studied the Ba8Cu16 − xAuxP30 (x = 4, 8, 12) solid solution.

All preparation and handling of samples were performed in an Ar-filled glovebox with the O2 level below 1 ppm. All starting materials were of commercial grade and used as received: Ba dendritic pieces (Sigma-Aldrich, 99.9%), Cu powder (Sigma-Aldrich, 99.9%), Au powder (Alfa Aesar, 99.96%), and red P powder (Alfa Aesar, 99%).

About 0.7 g of single-phase polycrystalline samples of Ba8Cu16 − xAuxP30 were obtained via solid-state reaction of elements. The elements in a stoichiometric ratio (Ba:Cu:Au:P = 8:16–x:x:30; x = 4, 8, 12) were loaded into a carbonized silica ampoules, which were evacuated and flame-sealed (inner diameter 9 mm, outer diameter 11 mm, sealed length 6 cm). The ampoules were heated from room temperature to 1123 K over 17 h , annealed at this temperature for 144 h, and cooled in the turned-off furnace. The samples were finely ground in the mortar and reloaded into new carbonized silica ampoules in the glovebox, resealed, and reheated using the same temperature profile as the first annealing. This procedure was repeated for a third time. After three annealings, fine polycrystalline black powders of Ba8Cu16 − xAuxP30 (x = 4, 8, 12) were obtained (Figs. S1–S3 in the supplementary material). The lab and advanced synchrotron PXRD, all confirmed the high purity nature of Ba8Cu16 − xAuxP30 (x = 4, 8, 12) samples as shown in Fig. 1 and Figs. S1–S3 and S8 in the supplementary material.

FIG. 1.

Experimental synchrotron (black) and calculated (blue) powder diffraction patterns for the Ba8Cu8Au8P30 sample. Inset: (a) crystal structure of Ba8Cu16 − xAuxP30, pentagonal dodecahedra: gray and blue; tetrakaidecahedra: red, black, and orange. (b): Connectivity of polyhedrons in Ba8Cu16P30.

FIG. 1.

Experimental synchrotron (black) and calculated (blue) powder diffraction patterns for the Ba8Cu8Au8P30 sample. Inset: (a) crystal structure of Ba8Cu16 − xAuxP30, pentagonal dodecahedra: gray and blue; tetrakaidecahedra: red, black, and orange. (b): Connectivity of polyhedrons in Ba8Cu16P30.

Close modal

The samples were characterized by laboratory powder x-ray diffraction (XRD) using a Rigaku Miniflex 600 diffractometer employing Cu-Kα radiation with a Ni-Kβ filter. High-resolution synchrotron powder x-ray diffraction data were collected at beamline 11-BM (λ = 0.413685 Å) at the Advanced Photon Source (APS) at Argonne National Laboratory (ANL).

Single crystal x-ray diffraction experiments were collected at 90 K using a Bruker AXS SMART diffractometer with an APEX-II CCD detector with Mo-Kα radiation. The datasets were recorded as ω-scans with a 0.4° step width and integrated with the Bruker SAINT software package.42 Multiscan absorption corrections were applied.42 The solution and refinement of the crystal structures were carried out using the SHELX suite of programs.43 After locating positions for all atoms, the site occupancy of all framework atoms was refined. The refined occupancies for 15 P sites were not different from unity within one e.s.d. and was fixed to unity for the final refinements. For the metal sites, each site was set as jointly occupied by Au and Cu atoms with the constrains of the equivalent atomic positions, atomic displacement parameters, and total occupancy of 100%. The final refinements were performed using anisotropic atomic displacement parameters for all atoms. A summary of pertinent information relating to data collection and refinement parameters is provided in Table I, and the atomic parameters and interatomic distances are provided in Tables S2 and S3 in the supplementary material. Further details of the crystal structure determination may be found through Cambridge Crystallographic Data Centre by using CCDC-1955842 (Ba8Cu13.3Au2.7(1)P30), CCDC-1955841 (Ba8Cu8.6Au7.4(1)P30), CCDC-1955840 (Ba8Cu4.4Au11.6(1)P30), and CCDC-1955839 (Ba8Cu4.2Au11.8(1)P30).

TABLE I.

Selected crystal data and structure refinement parameters for Ba8Cu16 − xAuxP30. R1 = ∑||Fo| – |Fc||/∑|Fo|; wR2 = [∑[w(Fo2 – Fc2)2]/∑[w(Fo2)2]]1/2, and w = 1/[σ2Fo2 + (A⋅P)2 + B⋅P], P = (Fo2 + 2Fc2)/3; A and B are weight coefficients.

FormulaBa8Cu13.3Au2.7(1)P30Ba8Cu8.6Au7.4(1)P30Ba8Cu4.4Au11.6(1)P30Ba8Cu4.2Au11.8(1)P30
CCDC No. 1955842 1955841 1955840 1955839 
Temperature 90(2) K 
Wavelength Mo-Kα, 0.71073 Å 
Space group Orthorhombic Pbcn (No. 60) 
a, Å 14.200(1) 14.354(3) 14.480(2) 14.487(1) 
b, Å 10.137(1) 10.229(2) 10.320(1) 10.332(1) 
c, Å 28.153(3) 28.437(5) 28.684(3) 28.694(2) 
Volume, Å3 4052.5(6) 4175.3(1) 4286.2(9)3 4294.7(6) 
Z 
Density, g/cm3 5.59 6.42 7.11 7.14 
μ, mm–1 25.53 38.78 49.91 50.45 
Data/parameter 6219/255 7520/255 6586/255 8032/255 
G-o-F 1.03 1.05 1.00 1.03 
Final R
[I > 2σ(I)] 
R1 = 0.029
wR2 = 0.088 
R1 = 0.046
wR2 = 0.091 
R1 = 0.026
wR2 = 0.061 
R1 = 0.029
wR2 = 0.049 
Final R
(all data) 
R1 = 0.049
wR2 = 0.114 
R1 = 0.088
wR2 = 0.105 
R1 = 0.033
wR2 = 0.064 
R1 = 0.048
wR2 = 0.054 
Largest diff. peaks, e/Å3 1.80/−1.38 2.75/−2.89 1.95/−2.40 2.34/−2.10 
FormulaBa8Cu13.3Au2.7(1)P30Ba8Cu8.6Au7.4(1)P30Ba8Cu4.4Au11.6(1)P30Ba8Cu4.2Au11.8(1)P30
CCDC No. 1955842 1955841 1955840 1955839 
Temperature 90(2) K 
Wavelength Mo-Kα, 0.71073 Å 
Space group Orthorhombic Pbcn (No. 60) 
a, Å 14.200(1) 14.354(3) 14.480(2) 14.487(1) 
b, Å 10.137(1) 10.229(2) 10.320(1) 10.332(1) 
c, Å 28.153(3) 28.437(5) 28.684(3) 28.694(2) 
Volume, Å3 4052.5(6) 4175.3(1) 4286.2(9)3 4294.7(6) 
Z 
Density, g/cm3 5.59 6.42 7.11 7.14 
μ, mm–1 25.53 38.78 49.91 50.45 
Data/parameter 6219/255 7520/255 6586/255 8032/255 
G-o-F 1.03 1.05 1.00 1.03 
Final R
[I > 2σ(I)] 
R1 = 0.029
wR2 = 0.088 
R1 = 0.046
wR2 = 0.091 
R1 = 0.026
wR2 = 0.061 
R1 = 0.029
wR2 = 0.049 
Final R
(all data) 
R1 = 0.049
wR2 = 0.114 
R1 = 0.088
wR2 = 0.105 
R1 = 0.033
wR2 = 0.064 
R1 = 0.048
wR2 = 0.054 
Largest diff. peaks, e/Å3 1.80/−1.38 2.75/−2.89 1.95/−2.40 2.34/−2.10 

The polycrystalline samples of Ba8Cu16 − xAuxP30 (x = 4, 8, 12) were carefully ground into fine powder in the glovebox and then loaded into a graphite die with WC plungers, sintered at 798 K (Ba8Cu4Au12P30), 823 K (Ba8Cu8Au8P30), and 873 K (Ba8Cu12Au4P30) through spark plasma sintering (SPS 1050: Sumitomo Coal Mining Co, Ltd.) for 10 min with a uniaxial pressure of 156 MPa to form a pellet with a dimension of 5 mm Ø and a thickness of ∼2.5 mm. The geometrical densities of all pellets were comparable and fall into a small interval of 91%–94% of the theoretical x-ray density. Graphite and possible surface contaminations were removed by polishing in the glovebox. No sample decomposition of the sample after SPS was detected by powder x-ray diffraction.

Differential scanning calorimetry (DSC) was conducted using a Netzsch differential 114 scanning calorimeter. The powder samples of Ba8Cu4Au12P30 (40 mg), Ba8Cu8Au8P30 (70 mg), and Ba8Cu12Au4P30 (70 mg) were sealed inside an evacuated silica DSC ampoule (diameter 5 mm) and heated to 1273 K with a heating/cooling rate of 10 K/min.

Transport properties in the temperature range of 2–300 K were studied using the commercial Physical Properties Measurement System (PPMS, Quantum Design). The Seebeck thermopower and thermal conductivity were measured using the Thermal Transport Option. The electrical resistivity was measured by a standard four-point alternating-current technique to exclude the resistance of the leads.

The Ba8Cu16 − xAuxP30 (x = 4, 8, 12) solid solutions adopt the same crystal structure as their parent compounds Ba8Cu16P30 and Ba8Au16P30. They crystallize in clathrate-I superstructure in orthorhombic Pbcn space group (the inset in Fig. 1, Table I, and Fig. S7 in the supplementary material). In the clathrate framework, every Cu/Au site is surrounded by 4P atoms. Such (Au/Cu)P4 tetrahedra are joint into a 3D framework by means of sharing vertices and forming P–P bonds. The Au/Cu–P framework contains five types of polyhedral cages, two pentagonal dodecahedra (gray and blue in Fig. 1), and three tetrakaidecahedra (red, black, and orange in Fig. 1). The Ba cations are located inside both types of cages. A detailed plot of the connections between polyhedrons in Ba8Cu16P30 is presented in Fig. 1(b) and Fig. S7 in the supplementary material. The constituent Ba1–Ba5 polyhedrons are also shown in Fig. S7 in the supplementary material.

Single-phase samples of Ba8Cu16 − xAuxP30 (x = 4, 8, 12) solid solutions were obtained, which was demonstrated by synchrotron powder x-ray diffraction (Fig. 1 and Figs. S1–S3 in the supplementary material). Based on variable-temperature synchrotron powder x-ray diffraction, there is no phase transition from 100 K to 300 K (Figs. S1–S3 in the supplementary material). No significant segregation into Cu-rich and Au-rich phases was detected, but the diffraction peaks are somewhat wider than those for synchrotron x-ray diffraction patterns of the parent compounds, Ba8Cu16P30 and Ba8Au16P30, measured in the identical conditions. This indicates that the solid solution samples might have small variability in the Cu/Au content across the sample. The single crystal x-ray diffraction results confirmed the existence of small phase width in Ba8Cu16 − xAuxP30 solid solution as summarized in Table I. For clarity of discussion, the nominalized chemical formulas Ba8Cu4Au12P30, Ba8Cu8Au8P30, and Ba8Cu12Au4P30 are used for general discussion, while the experimentally determined chemical formulas from single crystal x-ray diffraction are also used to refer to specific samples.

Au has a larger metallic radius (1.44 Å) than Cu (1.28 Å).44 In the crystal structure of the parent compound, Ba8Cu16P30, there are eight independent Cu positions, resulting in eight CuP4 tetrahedra with different volume as shown by the blue curve in Fig. 2. The Au distribution in the crystal structures of Ba8Cu16 − xAuxP30 is not stochastic, Au atoms prefer to occupy tetrahedra with the largest volume (green curves in Fig. 2). For the composition with the lowest Au content, x = 2.7, 17% of the framework atoms are Au, there is a clear preference for Au to occupy Cu4 and Cu7 sites with the largest volume of (Cu/Au)P4 tetrahedra, while sites with the smallest volume, Cu1 and Cu2, contain no Au atoms. For the composition with higher overall Au content, the Au content in those sites is still below the average (Fig. 2).

FIG. 2.

A plot showing correlation between CuP4 tetrahedron volume in the crystal structure of Ba8Cu16P30 (blue curve and circles, left axis) and the relative Au content in each metal site in Ba8Cu16 − xAuxP30 (green curves, right axis), x = 2.7 (squares), 7.4 (triangles), 11.8 (stars). Numerical data are presented in Table S1 in the supplementary material.

FIG. 2.

A plot showing correlation between CuP4 tetrahedron volume in the crystal structure of Ba8Cu16P30 (blue curve and circles, left axis) and the relative Au content in each metal site in Ba8Cu16 − xAuxP30 (green curves, right axis), x = 2.7 (squares), 7.4 (triangles), 11.8 (stars). Numerical data are presented in Table S1 in the supplementary material.

Close modal

In the clathrate framework, the metal–phosphorus interactions are elongated with Au/Cu substitution. For Ba8Cu16P30, the Cu–P interactions fall into the range of 2.26–2.48 Å, while Au–P interactions in Ba8Au16P30 are longer, 2.32–2.58 Å. The (Cu/Au)-P distances in Ba8Cu16 − xAuxP30 increase with the overall Au content and the Au content in the specific site (Table S3 in the supplementary material). Besides typical covalent P–P interactions, 2.16–2.30 Å, there is one elongated P15–P15 distance in Ba8Cu16P30, 2.52 Å.39 This distance gets significantly longer in Ba8Au16P30, 2.72 Å.16 The typical P–P bonds interaction in Ba8Cu16 − xAuxP30 solid solutions are comparable to those in the parent structure, 2.16–2.31 Å (Table S3 in the supplementary material). The P15–P15 distances in Ba8Cu16 − xAuxP30 follow the Vegard behavior except for the composition with x close to 8. For Ba8Cu8.6Au7.4P30, the P15–P15 distance is on a par with the same distance in the compositions with x close to 12 (Fig. 3 and Table S3 in the supplementary material). P15 site is connected to two other P atoms and (Cu/Au)3 metal site. (Cu/Au)3–P15 distances also change nonlinearly with the increasing Au content, indicating that a redistribution of the electron density has taken place around this site.

FIG. 3.

P15–P15 interatomic distance in Ba8Cu16 − xAuxP3. The dashed line is drawn to guide the eye.

FIG. 3.

P15–P15 interatomic distance in Ba8Cu16 − xAuxP3. The dashed line is drawn to guide the eye.

Close modal

The thermal stabilities of Ba8Cu16 − xAuxP30 were measured by DSC (Fig. 4). All Ba8Cu16 − xAuxP30 samples melt congruently. Ba8Cu16P30 has the highest thermal stability, melting at 1140(3) K, while Ba8Au16P30 exhibits the lowest melting temperature of 982(3) K. Upon mixing Cu and Au atoms, the thermal stability of Ba8Cu16 − xAuxP30 decreases with increasing Au content.

FIG. 4.

Thermal stability of Ba8Cu16 − xAuxP30 obtained by DSC measurements, end points with x = 0 and 16 are taken from Refs. 16 and 45. The lines are drawn to guide the eye.

FIG. 4.

Thermal stability of Ba8Cu16 − xAuxP30 obtained by DSC measurements, end points with x = 0 and 16 are taken from Refs. 16 and 45. The lines are drawn to guide the eye.

Close modal

Thermoelectric properties of Ba8Cu16 − xAuxP30 (x = 4, 8, 12) solid solutions were measured on high density pellets. For the purpose of comparison, the thermoelectric properties of the parent compounds, Ba8Cu16P30 and Ba8Au16P30, were extracted from our previous reports.16,36,38

Ba8Cu16P30 was studied in detail with respect to heat capacity, band structure, and electrical conductivity, showing p-type metallic properties.36,38,46,47 Replacement of Cu with Au introduces 5d orbitals. Au is known to exhibit different bonding modes, including aurophilic interactions.48 However, in the case of the studied solid solution, all Au atoms are surrounded by 4P atoms and shortest Au–Au distance is over 4 Å. Thus, we hypothesized that Cu/Au substitution should lead to minimal changes in the electronic structure, while the presence of the atomic disorder should impact thermal transport properties.

At room temperature Ba8Cu16P30 and Ba8Au16P30 exhibit comparable positive values of Seebeck coefficients of 12 μV K–1 and 15 μV K–1, respectively, in accordance with their metallic electron-deficient nature. Temperature dependences of the Seebeck thermopowers for studied solid solution are provided in Fig. S4 in the supplementary material. For quaternary compositions, the isovalent Cu/Au substitution has no drastic effect on the carrier concentration, resulting in the similar thermopower values of 10–16 μV K–1 at room temperature.

Ba8Cu16 − xAuxP30 samples exhibit metal-like behavior with the resistivities increasing with temperature (Fig. 5). For the ternary compounds, Ba8Cu16P30 has lower electrical resistivity than Ba8Au16P30. Upon mixing Cu and Au in the clathrate framework, quaternary samples exhibit higher resistivity than the two parent compounds (Fig. 5). Similar Seebeck coefficients, which are sensitive to carrier concentration, indicate that the carrier concentrations are similar for all studied Ba8Cu16 − xAuxP30. The enhancement of electrical resistivity for quaternary compositions can be explained by the suppression of hole mobility due to the introduction of atomic disorder in the clathrate framework and compositional disorder due to variation in the Au/Cu content within the samples. Among three mixed Au–Cu-containing samples, the resistivity follows the trend observed for ternary phases: samples with higher Cu content manifest lower resistivity (Fig. 5).

FIG. 5.

Temperature dependences of the electrical resistivity for Ba8Cu16 − xAuxP30.

FIG. 5.

Temperature dependences of the electrical resistivity for Ba8Cu16 − xAuxP30.

Close modal

The studied clathrates inherit low thermal conductivity observed for regular clathrate-I compounds, which is additionally suppressed due to the complex orthorhombic superstructure [Fig. 6(a)]. An effect of the introduction of the heavy element in the framework can be deduced by comparison of the thermal conductivities for parent compounds. Thermal conductivity of 1.0 W m–1 K–1 at 200 K Ba8Cu16P30 is reduced by a factor of 2 when Cu is completely replaced with Au. The total thermal conductivity of Ba8Cu16 − xAuxP30 (x = 4, 8, 12) solid solution falls in between those two values, with the lowest thermal conductivity observed for sample with the highest Au content. The total thermal conductivity of Ba8Cu4Au12P30 sample is close to that of the Au-containing end member, Ba8Au16P30, while the samples with lower Au content have thermal conductivities more similar to those of Ba8Cu16P30. The extremely low thermal conductivity of Ba8Cu4Au12P30 can be explained by a complex crystal structure coupled with atomic disorder of Cu mixing with Au in the clathrate framework.

FIG. 6.

(a) Temperature dependences of total thermal conductivities for Ba8Cu16 − xAuxP30. (b): Lattice thermal conductivities values at 200 K. The dashed line is drawn to guide the eye.

FIG. 6.

(a) Temperature dependences of total thermal conductivities for Ba8Cu16 − xAuxP30. (b): Lattice thermal conductivities values at 200 K. The dashed line is drawn to guide the eye.

Close modal

The total thermal conductivity, κtotal, of crystalline solid can be expressed as a sum of charge carrier thermal conductivity, κE, and lattice thermal conductivity, κL. The carrier thermal conductivity can be estimated by applying Wiedemann–Franz law, κE = LT/ρ, where L is the Lorenz number, ρ stands for the electrical resistivity, and T is the absolute temperature. The lattice thermal conductivity can be obtained by subtracting carrier thermal conductivity from total thermal conductivity, κL = κtotal – κE. The carrier and lattice thermal conductivities Ba8Cu16 − xAuxP30 are presented in Figs. S5 and S6 in the supplementary material. The charge carrier contribution to the electronic conductivity is similar for all three Au/Cu solid solution compositions (Fig. S5 in the supplementary material). As mentioned above, the charge carrier lattice thermal conductivity is proportional to the electrical conductivity, which is determined by carrier concentration and carrier mobility. When the isovalent Au replaces Cu, the carrier concentration is expected to remain unchanged, which is supported by the comparable Seebeck coefficients of Ba8Cu16 − xAuxP30. The slight change of electrical conductivity is due to the presence of structural disorder, which will reduce the carrier mobility. Thermal conductivity is the sum of contributions from carriers and phonons. Phonon can be efficiently scattered by atomic disorder, where the carrier is less affected due to the longer mean free path.6 This explains why there is no significant change of the electrical conductivity upon mixing Cu with Au, while the thermal conductivity exhibits apparent difference. The 200 K values of the lattice thermal conductivity are provided in Fig. 6(b). One can see that at 200 K, the lattice thermal conductivities are similar for samples with x = 0, 4, and 8, which agrees with the trend observed for the total thermal conductivity. The increase of the Au content over eight resulted in a significant reduction of lattice thermal conductivity [Fig. 6(b)]. The lattice thermal conductivity of Ba8Cu16 − xAuxP30 (x = 0, 4, 8, 12, 16) solid solution falls into the range of 0.25–0.65 W m–1 K–1 at 200 K, which are comparable to many state-of-art thermoelectric materials such as β-Zn8Sb7,11 Ca1 − xRexAg1 − ySb,12 Gd117Co56Sn112,17 and Ag9TlTe5.18 The low lattice thermal conductivity in Ba8Cu16 − xAuxP30 (x = 4, 8, 12) solid solutions is due to a combination of complex host–guest crystal structure and the presence of atomic level disorder in the metal sublattice.

The clathrate solid solution Ba8Cu16 − xAuxP30 was synthesized via the high-temperature solid-state synthesis technique. According to single crystal x-ray diffraction, Au preferably occupied metal sites located inside the largest (Cu/Au)P4 tetrahedra in the clathrate framework. The Ba8Cu16 − xAuxP30 solid solution melts congruently, following the trend of increasing melting temperature with higher Cu content. Thermoelectric properties confirmed that all members of Ba8Cu16 − xAuxP30 solid solution are p-type metallic conductors. The thermal conductivities of Ba8Cu16 − xAuxP30 samples remain at a very low level due to atomic disorder involving heavy atoms, Au, in the complex clathrate crystal structure.

See the supplementary material for the details of the synchrotron powder x-ray diffraction data, the atomic parameters and interatomic distances, the Seebeck coefficients, the carrier thermal conductivity, the lattice thermal conductivity, and EDS analyses of Ba8Cu16 − xAuxP30 (x = 4, 8, 12) solid solution. The average atomic distances and polyhedron volumes of [CuP4] tetrahedra in Ba8Cu16P30 and Au occupancy of metal sites in the crystal structures of Ba8Cu16 − xAuxP30 (x = 4, 8, 12) are shown. Detailed connection of polyhedrons in Ba8Cu16P30 (bottom right) with individual Ba1–Ba5 polyhedra are also presented. Refined PXRD of Ba8Cu8Au8P30.

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

The authors are thankful to Dr. S. Lapidus and Dr. Juli-Anna Dolyniuk-Johnson for collecting synchrotron XRD patterns. This research was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering under Award No. DE-SC0008931. Use of the Advanced Photon Source at Argonne National Laboratory was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-06CH11357.

The authors declare no competing financial interest.

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