LETTERSPUBLISHED ONLINE: 5 SEPTEMBER 2016 | DOI: 10.1038/NMAT4739

Orientational order controls crystallineand amorphous thermal transport insuperatomic crystalsWee-Liat Ong1,2, Evan S. O’Brien1, Patrick S. M. Dougherty2, Daniel W. Paley1, C. Fred Higgs III2,3,Alan J. H. McGaughey2,4, Jonathan A. Malen2,4* and Xavier Roy1*

In the search for rationally assembled functional materials,superatomiccrystals (SACs)haverecentlyemergedasauniqueclass of compounds that combine programmable nanoscalebuilding blocks and atomic precision1–6. As such, they bridgetraditional semiconductors, molecular solids, and nanocrystalarrays by combining their most attractive features1–11. Here, wereport the first study of thermal transport in SACs, a criticalstep towards their deployment as electronic, thermoelectric,andphononicmaterials10–12. Using frequencydomain thermore-flectance (FDTR), we measure thermal conductivity in twoseries of SACs: the unary compounds Co6E8(PEt3)6 (E = S,Se, Te) and the binary compounds [Co6E8(PEt3)6][C60]2. Wefind that phonons that emerge from the periodicity of thesuperstructures contribute to thermal transport10,13,14. We alsodemonstrate a transformation from amorphous to crystallinethermal transport behaviour through manipulation of the vi-brational landscape and orientational order of the superatoms.The structural control of orientational order enabled by theatomic precision of SACs expands the conceptual design spacefor thermal science.

SACs are three-dimensional periodic arrays in which preformedsub-nanometre molecular clusters, which we term superatoms,emulate the role of atoms in traditional solid-state compounds4. Theready availability and tunability of superatoms present a promisingopportunity for creating newmaterials with multiple functionalitiesand emergent collective behaviours1–4,6,9. In this work, we explorethermal transport in two classes of SACs: unary compoundsin which the superatoms are held together by van der Waalsinteractions; and binary ionic solids assembled by inter-superatomcharge transfer2. This diversity of interaction produces a range ofphysical properties. For instance, the unary SACs are electricalinsulators while the binary SACs show thermally activated transportwith activation energies2 of 100–150meV. Herein, we show thatthe juxtaposition of structural control and diverse intra- and inter-superatombonding gives rise to complex vibrational landscapes andunexpected thermal transport behaviours.

In crystalline dielectrics, heat is primarily transported byquantized vibrations of the periodic lattice called phonons. Thevolumetric heat capacity Cv, group velocity v, and mean free path3 of phonons are strongly influenced by the electrical structureand bonding of the material. Kinetic theory approximates thermal

conductivity as a product of Cv and average values of v and3, k= Cvv̄3̄/3. Crystalline solids with strong covalent bonding(for example, Si and diamond) have room-temperature thermalconductivities greater than 100Wm−1 K−1, which increase withdecreasing temperature due to a reduction in phonon scatteringthat extends the mean free paths. Soft amorphous materials (forexample, polymers) conversely have room-temperature thermalconductivities below 1Wm−1 K−1, which decrease with decreasingtemperature due to the temperature dependence of the heat capacity.

In nanocrystal arrays, in which the fundamental building blocksare typically larger than 3 nm in diameter, thermal transport ismediated by disordered organic–inorganic interfaces and is welldescribed by effective medium approximations (EMAs)11,12,15. Incontrast, our superatoms are too small for bulk-like properties toemerge within individual clusters16,17, making the application ofEMAs unsuitable. In this study, we explore how the unique atomicdefinition of superatoms produces cooperative inter-superatomvibrations capable of transporting thermal energy. We report thefirst examination of thermal transport in SACs using thermalconductivity measurements complemented by first-principlescalculations of vibrational spectra and experimental measurementsof heat capacity, Young’s modulus, and thermal expansion.

We performed all measurements on single crystals (Fig. 1d).The synthesis of the superatoms Co6S8(PEt3)6, Co6Se8(PEt3)6 andCo6Te8(PEt3)6, and their crystallization into unary and binary SACsis described in the Methods. We label these materials by [Co6E8]and [Co6E8][C60]2 (Table 1). We determined the crystal structure ofeach SAC by single crystal X-ray diffraction (SCXRD). Figure 1b,cshows representative crystal structures of the unary and binary SACs[Co6Te8] and [Co6Te8][C60]2.

We measured the heat capacity of our SACs (Cv) usingdifferential scanning calorimetry (DSC) and compared the resultswith theoretical Cv values calculated from density functionaltheory (DFT) using vibrational spectra of isolated superatoms(see Methods). The molecular structure and the DFT-predictedvibrational spectra of the four superatoms are shown in Fig. 2a,b.The vibrational spectrum of each [Co6E8] spans two orders ofmagnitude, with numerous thermally active modes at 300K.Increasing the cluster core mass (that is, Co6S8 to Co6Se8 toCo6Te8) shifts the spectrum to lower frequencies. In contrast, thevibrational spectrum of an isolated C60 is narrower and has no

1Department of Chemistry, Columbia University, New York, New York 10027, USA. 2Department of Mechanical Engineering, Carnegie Mellon University,Pittsburgh, Pennsylvania 15213, USA. 3Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213,USA. 4Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA.*e-mail: jonmalen@andrew.cmu.edu; xr2114@columbia.edu

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LETTERS NATUREMATERIALS DOI: 10.1038/NMAT4739

a

a c

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Figure 1 | SAC structures and FDTR measurement. a, Schematic of the FDTR measurement on a gold-coated SAC. A pump laser (blue) heats the SACwhile a probe laser (green) measures the temperature-dependent reflectance of gold to determine the thermal conductivity. b, Crystal structure of[Co6Te8][C60]2 looking down the c-axis (left) and down the a-axis (right). c, Crystal structure of [Co6Te8] looking down the a-axis (left) and down theb-axis (right). In b,c, scale bar is 1 nm; C, black; P, orange; Co, blue; Te, red; hydrogen atoms are omitted for clarity. These structures were determined bySCXRD at 100 K. d, Optical microscopy image of a representative [Co6Te8][C60]2 crystal coated with a 60 nm Au transducer for FDTR measurement.Scale bar is 20 µm. e, Scanning electron microscopy (SEM) image of a nanoindented SAC surface. Scale bar is 1 µm.

Table 1 |Thermal and physical properties of SACs at room temperature.

SAC Type Superatom composition Densityρ (kgm−3)

Heat capacityCv (MJm−3 K−1)

Thermal conductivitykSAC (Wm−1 K−1)

Young’s modulusESAC (GPa)

[Co6S8] Unary Co6S8(PEt3)6 1,465 1.95 0.22± 0.05 4.0± 0.8[Co6Se8] Unary Co6Se8(PEt3)6 1,797 1.66 0.18± 0.04 2.3± 0.1[Co6Te8] Unary Co6Te8(PEt3)6 2,237 1.87 0.13± 0.03 0.62± 0.03[Co6Se8] [C60]2 Binary [Co6Se8(PEt3)6] [C60]2 1,902 1.74 0.25± 0.06 8.1± 0.5[Co6Te8] [C60]2 Binary [Co6Te8(PEt3)6] [C60]2 2,082 1.69 0.16± 0.04 1.5± 0.4The density is determined from SCXRD data. The uncertainty in kSAC is determined using the method described in ref. 21. The uncertainty in ESAC is the standard deviation obtained from sevennanoindentations. The crystal structures of [Co6S8] and [Co6Se8] contain one toluene molecule per cluster. We account for the included solvent molecule in all calculations and measurements. Noneof the other SACs are solvate crystals.

active modes at 300K due to the small atomic mass of carbonand the strong C-C covalent bonding18. We calculated the heatcapacity of each SAC as a function of temperature by summingover the vibrational spectra of the constituent superatoms accordingto Bose–Einstein occupancy (see Methods). The theoretical andexperimentalCv for [Co6Se8], [Co6Se8][C60]2, and experimental dataforC60 measured in ref. 19 are plotted in Fig. 2c. The predicted trendscapture the experimental behaviours: Cv decreases monotonicallywith decreasing temperature for all SACs except [Co6Se8][C60]2,which shows a peak at∼190K associatedwith a symmetry-loweringphase transition detected by SCXRD (as discussed later). Theslightly higher Cv of the binary crystal [Co6Se8][C60]2 relative tothe unary crystal [Co6Se8] results from an increase in the numberdensity of atoms. Similar trends were obtained for the other SACs(Supplementary Fig. 8).

Our heat capacity predictions, generated from the vibrationalspectra of isolated superatoms, are consistently 20–35% lower thanthe measured values. This under-prediction occurs because thecalculation does not capture the collective low-frequency, inter-superatom vibrational modes (that is, phonons) that emerge uponcrystallization. A similar discrepancy is observed between theexperimental and calculated heat capacities of C60. These low-frequency collectivemodes have been hypothesized to cause crystal-like thermal transport behaviour in single crystal C60, as evidencedby the temperature dependence of its thermal conductivity20. Howimportant are these inter-superatom phonons to thermal transportin SACs?

The single crystals produced using our synthetic approach havedimensions on the order of 100× 100× 100 µm3 (nl volume), mak-ing thermal conductivity measurements using conventional steady-state methods unviable. To overcome this challenge, we employedfrequency domain thermoreflectance (FDTR), a non-contact opticalpump–probe technique11,21. FDTR is amenable to the small size ofthe SACs as it uses a focused laser with a spot radius of 3.1± 0.1 µm.The thermal conductivities extracted from the fits, kSAC, range from0.13 to 0.25Wm−1 K−1 at room temperature. These results are listedin Table 1, along with the density (ρ), heat capacity and Young’smodulus (ESAC) of each compound, as calculated from SCXRDand nanoindentation data (Fig. 1d). From the density and Young’smodulus, we estimate the average sound speed (v̄ ∝

√ESAC/ρ) of

each SAC (see Supplementary Sections V and VI)22.The correlation between kSAC and v̄ for all five SACs at room

temperature is shown in Fig. 3. We observe that v̄ plays a predictiverole for thermal conductivity. The thermal conductivity scaleslinearly with v̄, a strong indication that thermal transport arisesfrom the acoustic phonons that emerge due to the collective inter-superatom vibrations, akin to so-called ‘coherent phonons’ in asuperlattice13,14. The non-zero extrapolation of the dashed line tov̄=0 suggests a parallel contribution from optical phonons (whichhave lower group velocities compared to acoustic phonons) or non-phonon-like vibrational transport by diffusons and locons23.

Two observations from our data are consistent with thisphonon description of thermal transport, that is, k = Cvv̄3̄/3.First, for the unary [Co6E8] and binary [Co6E8][C60]2 series, both

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Figure 2 | Experimental and theoretical heat capacities of SACs. a, Molecular structure of the superatoms [Co6E8] and C60. Hydrogens are omitted forclarity. C, black; P, orange; Co, S, Se, and Te colours are defined in the labels. b, DFT vibrational spectra of isolated [Co6E8] and C60. The vertical dotted linedenotes the frequency ω300K=kBT/}, with kB the Boltzmann constant, T the temperature (300 K), and } the reduced Planck constant. Vibrational modesnear and below this line are gradually activated at 300 K according to the Bose–Einstein distribution. c, Temperature dependence of the experimental(DSC) and calculated (DFT) heat capacities of [Co6Se8], C60 (ref. 19) and [Co6Se8][C60]2. The uncertainty bars in the measured heat capacity data comefrom the maximum variations over three separate runs.

v̄ and kSAC decrease as the density of the structure increaseswhen heavier chalcogen atoms are substituted for lighter ones.Second, v̄ and kSAC of the binary SACs are systematicallyhigher than those of the corresponding unary SACs. While theintroduction of C60 changes the heat capacity and density of thebinary SACs by less than 12%, our nanoindentation experimentsindicate that ESAC increases by more than 200% relative to thecorresponding unary crystals (Table 1). This enhancement isconsistent with the added contributions of inter-C60 and ionicinter-superatom interactions in the binary SACs, relative to theunary compounds.

To further interpret the measured kSAC, we note that the valuesare low and are similar in magnitude to those of polymers,suggesting short phonon mean free paths. To test this hypothesis,we consider the Cahill–Pohl minimum thermal conductivity model(see Supplementary Section VII)24, which sets a lower bound for thethermal conductivity (kmin) of amorphous solids and was used toapproximate the ultralow thermal conductivity of microcrystallinePCBM thin films25. The key assumption of this model, relative toconventional models for crystalline solids, is that all vibrationalmodes travel at the sound speed, yet have mean free paths equal tojust one-half of their wavelengths.

We bound contributions from inter- and intra-superatom vibra-tional modes by calculating the minimum thermal conductivity kminusing two approaches. When we calculate kmin as a first approxima-tion by defining n (the number density of participating oscillators)as the atomic number density of the SAC26, we severely overestimatethe measurements, as shown in Fig. 3 (labelled kmin-atomic). In doing

so, we are effectively unfolding the Brillouin zone and assumingthat optical phonons also propagate at the average sound speed. Inreality, optical phonons will propagate with reduced group velocitiesdue to bandgaps in the dispersion caused by mass and bondingdiversity within the SAC unit cell. To contrast the upper boundset by kmin-atomic, we calculate a lower bound by assuming that onlythe collective translational and rotational degrees of freedom of thesuperatoms contribute to kmin (refs 25,27) (that is, n is twice thesuperatom number density; see Supplementary Section VII). Theresults, plotted in Fig. 3 as kmin-super, are lower than kSAC. We suggesttwo possible explanations: intra-superatom modes contribute tothermal transport and inter-superatom modes with long mean freepaths transport energy.

To gain deeper insight, we performed temperature-dependentthermal conductivity measurements. The results are plotted inFig. 4a alongside reported experimental data for C60 (ref. 20).As the temperature decreases, C60 undergoes a sudden 0.4%contraction of its lattice parameter at 260K, resulting from astructural transition from a face-centred cubic (fcc) unit cell withfreely rotating C60 superatoms to a simple cubic (sc) structure witha basis of four orientationally ordered C60 superatoms (ref. 20).Yu et al. suggest that orientational disorder in the fcc phase stronglyscatters phonons, leading to temperature-independent thermalconductivity above 260K (ref. 20). Conversely, in the sc phasethe C60 superatoms are frozen in an ordered orientation, enablingcrystal-like thermal conductivity behaviour. Our measurements ofthe thermal conductivity of SACs as a function of temperature showsimilar unexpected and unusual features.

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Figure 3 | Thermal conductivity of SACs as a function of average soundspeed. kSAC is proportional to the average sound speed. All data werecollected at room temperature. For comparison we include the thermalconductivity20 and sound speed25,26,33 of crystalline C60. The dotted linethrough the experimental data is a guide to the eye. The Cahill–Pohlminimum thermal conductivity calculations using the full SAC atomicdensity (kmin-atomic) and the SAC superatom density (kmin-super) bound ourresults. The vertical uncertainty bar for the SAC data denotes theuncertainty in the thermal conductivity measurements21. The horizontaluncertainty bar in the SAC data comes from the range of sound speedsderived from the measured Young’s modulus (Table 1) using Poisson ratiosranging from 0.2 to 0.35 (see Supplementary Section VI for sound speedcalculation). For the C60 data, the horizontal uncertainty bar comes fromthe range of C60 sound speeds available in the literature25,26,33. The verticaluncertainty bars in the Cahill–Pohl predictions (that is, bar graphs) arecalculated using the upper and lower bounds of the SAC sound speeds.

The thermal conductivities of the unary SACs are temperature-independent for [Co6S8] and [Co6Se8], and decrease slightly for[Co6Te8]with decreasing temperature, a behaviour reported in otherlarge unit cell crystals (for example, single crystal MOF-5)28. Thistrend for the unary SACs is predicted by the Cahill–Pohl model,whose temperature dependence is related only to the occupancyof the heat-carrying modes24. Based on our discussion of Fig. 3,the modes that dominate heat transport in the SACs have lowfrequencies that will remain activated as the temperature decreases.

The binary series shows distinct behaviours. The thermalconductivity of [Co6Te8][C60]2 decreases modestly with decreasingtemperature, similar to [Co6Te8]. By contrast, [Co6Se8][C60]2shows a complex behaviour: between 300 and 200K, the thermalconductivity is temperature-independent; between 200 and 180K,the thermal conductivity increases abruptly by ∼25%; below180K, the behaviour resembles that of a crystalline material,where thermal conductivity, and hence phonon mean free paths,increase as temperature decreases. The solid lines fit to thelow-temperature [Co6Se8][C60]2 and C60 data are based on amodified Callaway model with the Born–von Karman dispersionproposed for thermal conductivity of crystalline solids (seeSupplementary Section VIII)29.

The distinct trends of [Co6Se8][C60]2 and [Co6Te8][C60]2 are re-markable given that these compounds are isostructural.We attributethis divergence to subtle differences in their crystal structures, anal-ogous to the behaviour of crystalline C60. Figure 4b,c shows the tem-perature dependence of the centroid-to-centroid distance betweenneighbouring C60 superatoms (r) and of the unit cell lattice parame-ters (a and c). In [Co6Se8][C60]2, r is comparable to that in crystallineC60 (ref. 30). Upon cooling, we observe an abrupt contraction ofr and a at ∼190K, together with an increase of c. This suddenstructural transformation is accompanied by a change in the crystalsymmetry (from P 3̄m1 to P 3̄), resulting from the ordering of thefullerenes and the PEt3 ligands below 190K. The ordering process isreflected in theDSCdata (Fig. 2c) and the thermal conductivity data.Below 190K, [Co6Se8][C60]2 is orientationally ordered and behaveslike a crystalline solid whose thermal conductivity increases withdecreasing temperature. Above 190K, the orientational disorderstrongly scatters phonons, leading to an amorphous behaviour. Bycontrast, substituting Te for Se in [Co6E8][C60]2 increases the sizeof the superatom, which results in a and r being ∼1.8 and ∼1.3%larger in [Co6Te8][C60]2 than in [Co6Se8][C60]2 at room temperature.Neighbouring C60 molecules in [Co6Te8][C60]2 thus never approachclosely enough to experience the short-range anisotropic interac-tions that lead to orientational ordering30,31. The unit cell contractscontinuously with decreasing temperature, r remains nearly con-stant, and the SAC exhibits an amorphous thermal conductivitybehaviour over the entire temperature range.

We have shown that thermal transport in SACs is mediatedby collective inter-superatom phonons whose mean free paths canbe modulated by the spacing and the strength of the interactionsbetween the superatoms. Our data suggest that as SACs transitionfrom an orientationally disordered structure to an ordered one,the phonon mean free paths, and hence the thermal conductivityof the material, will increase with decreasing temperature. Similardynamic disorder may also exist in emergent organic–inorganicperovskites, where molecular rotations at high temperatures are apotential origin of ‘ultralow’ thermal conductivity32. These resultschart a clear path to hierarchicalmaterials whose thermal propertiescan be tuned by modifying the size, structure and compositionof the superatom building blocks. Further thermal studies ofatomically precise SACs are thus essential for understandingand designing these materials for next-generation phononic andthermoelectric applications.

MethodsMethods and any associated references are available in the onlineversion of the paper.

Received 13 April 2016; accepted 21 July 2016;published online 5 September 2016

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AcknowledgementsFunding for this research was provided by the Center for Precision Assembly ofSuperstratic and Superatomic Solids, an NSF MRSEC (Award Number DMR-1420634).J.A.M. and W.-L.O. acknowledge support from the Army Research Office GrantW911NF-14-0350 and the National Science Foundation CAREER Award ENG-1149374.A.J.H.M. acknowledges support from NSF award DMR-1507325. X.R. and E.S.O’B. thankthe Air Force Office of Scientific Research (Award Number FA9550-14-1-0381). X-ray

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LETTERS NATUREMATERIALS DOI: 10.1038/NMAT4739

diffraction measurements were performed in the Shared Materials CharacterizationLaboratory at Columbia University. Use of the Shared Materials CharacterizationLaboratory was made possible by funding from Columbia University. We thank R. Hastiefor her help in making the illustrations. We also thank G. Elbaz and K. Lee for their helpwith sample preparation, and C. Nuckolls, M. Steigerwald, L. Campos, X. Zhu andC. Dean for the use of their instruments and for useful discussions.

Author contributionsW.-L.O. conducted the FDTR and DSC measurements on the SACs and first-principlescalculations. E.S.O’B. synthesized SACs and together with D.W.P. conducted SCXRDcharacterization. P.S.M.D. conducted the nanoindentations. W.-L.O. and E.S.O’B. wrote

the manuscript. J.A.M., X.R., A.J.H.M. and C.F.H.III edited the manuscript. All authorsdiscussed the data and commented on the manuscript.

Additional informationSupplementary information is available in the online version of the paper. Reprints andpermissions information is available online at www.nature.com/reprints.Correspondence and requests for materials should be addressed to J.A.M. or X.R.

Competing financial interestsThe authors declare no competing financial interests.

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NATUREMATERIALS DOI: 10.1038/NMAT4739 LETTERSMethodsThe superatoms Co6Se8(PEt3)6 and Co6Te8(PEt3)6 were synthesized by reactingPEt3, Se or Te, and Co2(CO)8 in refluxing toluene. Co6S8(PEt3)6 was obtained fromCo6S8(PPh3)6 via ligand substitution in tetrahydrofuran using a large excess ofPEt3. We prepared unary SACs by slow evaporation of a toluene solution ofCo6E8(PEt3)6, and collected black, shiny, rhombohedral crystals with side lengthson the order of 100 µm after 2–5 days. To prepare the binary SACs, we combinedCo6E8(PEt3)6 and two equivalents of C60 in toluene and obtained black, shinycrystals that were similar in shape and size to unary SACs after∼12 h. In the binarySACs, the constituent clusters remain unchanged, but charge is transferred betweenthem, forming ionic solids analogous to simple binary salts. We note that[Co6S8][C60]2 does not form using our approach, presumably because Co6S8(PEt3)6is too weak a reducing agent to transfer charge to C60. Further details andreferences for the synthesis are provided in the Supplementary Section I.

Single-crystal X-ray diffraction data were collected on an Agilent SuperNovadiffractometer using mirror-monochromated Mo Kα radiation. The crystals weremounted using a MiTeGen MicroMount and cooled to a set temperature with anOxford-Diffraction Cryojet system. By characterizing multiple samples of eachcompound, we confirmed that our synthetic approach reliably and consistentlyproduces single crystals. Details of data collection, integration, structure solutionand refinement are provided in the Supplementary Tables 1–5 andSupplementary Figs 4–7.

The Young’s modulus (ESAC) measurements of the SACs were done throughnanoindentation (MTS Nanoindenter XP). The average of at least seven indentswas taken to determine the elastic modulus, calculated by measuring theindentation load at a given penetration depth into the surface. This penetrationdepth was set at 1,000 nm to minimize the effect of the 60–70 nm gold coating oneach of the SACs, required for stability in air. This value is well beyond the 10%threshold established as a rule of thumb for minimizing substrate effects34. Eachindentation was then unloaded from its penetration depth, and ESAC was calculatedusing the slope of the unloading curve, as shown in Supplementary Fig. 9 (details inSupplementary Section V).

Differential scanning calorimetry (DSC) was performed using a TA InstrumentQ20 to measure the heat capacity. The scans were run with 5–15mg of SAC, whichwas loaded and sealed hermetically in Tzero aluminium pans inside a glove box.Heating and cooling DSC cycles were performed from 190 to 323K and repeated atrates ranging from 5 to 20Kmin−1 with an isothermal period of five minutesbetween heating and cooling runs. The measured heat capacity for a piece of 7.1mgreference Si crystal was within 3% of the published result over the entiretemperature range. Before each run, the DSC was carefully calibrated with the Sireference to minimize drift in the machine. Uncertainty in the heat capacity of theSAC samples comes from the maximum variation across different measurements,and is about 5%.

A first-principles-based harmonic vibrational analysis was performed toestimate the SAC heat capacity. The plane wave-based Vienna Ab-initio SimulationPackage (VASP) was used to perform density functional theory and densityfunctional perturbation theory calculations35. The Perdew–Burke–Ernzerhof (PBE)parameterized generalized gradient approximation (GGA) exchange–correlationswere used in all the calculations, which were converged to 1meV of the totalenergy. Ionic relaxation of the superatoms was performed until forces on each ionwere less than 0.1meVA−1. Isolated superatom vibrational analysis was performedto obtain the harmonic vibrational spectrum. Due to the large number of atoms persuperatom (at least 146) and the unknown suitability of the van der Waalscorrections in DFT for these SACs, we are unable to calculate the full Brillouinzone of inter-superatom modes. Each superatom was placed at the centre of a cubicsimulation cell. A vacuum space of at least 4 Å on all sides of the simulation cell anda minimum energy cutoff of 450 eV were found to be sufficient after the energyconvergence tests. We did not include spin-polarized or GGA+U corrections.

Using the isolated SAC vibrational spectra, we evaluate the analyticalexpression for the volumetric heat capacity,

Cv=kBV

∑j

xj2exj

[1−exj ]2, xj=

}ωj

kBT

where V is the average volume occupied by a superatom in a unit cell and j is themode index. For binary SACs co-crystallized with C60, the vibrational spectra of aC60 superatom and the relevant SAC were arithmetically added together based on

their stoichiometric composition for the heat capacity calculation. For the heatcapacity calculation of [Co6S8] and [Co6Se8], whose structures contain a toluenemolecule, the vibrational spectrum of a toluene molecule and that of thecorresponding superatom were arithmetically added together based on theirstoichiometric composition.

For thermal conductivity measurements, the SACs were either directly grownon or glued to a silicon wafer and coated with a thin gold transducer (60–70 nm) bymagnetron sputtering (Supplementary Figs 1–3). The thermal conductivities ofmore than ten different single crystals of each SAC, spanning multiple syntheses,were measured at room temperature using the FDTR technique. Our FDTRtechnique employs two continuous wave lasers (Coherent) to heat and probe agold-coated SAC sample for its unknown thermal conductivity11,21. Since thesegold-coated surfaces may not be parallel to the substrate surface, a goniometer anda rotating stage enable adjustments to make the crystal face normal to the laserbeam. The intensity of a 488 nm laser (the pump) was sinusoidally modulated from50 kHz to 5MHz to periodically heat the gold surface. The resulting thermalresponse is monitored by a 532 nm laser (the probe) through the thermoreflectanceof the gold surface. This probe signal was read by an amplified photodiode(Thorlabs, PDA 36A) and measured by a lock-in amplifier (Zurich Instrument,HF2LI), producing frequency-dependent phase data that depend on the thermalproperties of the sample. These data were fitted to an exact solution to the heatdiffusion equation (see Supplementary Table 6 for fitting parameters) to determinethe unknown thermal conductivity of the SAC sample36. We note that the binarySACs exhibit activated electrical conductivity, but we estimate that their electronicthermal conductivities are four orders of magnitude smaller than our measuredvalues (∼10−5 Wm−1 K−1) based on the Wiedemann–Franz law and the electricalconductivity of [Co6Se8][C60]2 (ref. 4).

Due to their low thermal conductivities, a steady-state temperature rise of30–40K occurs in the SACs during the FDTR measurements. An iterative fittingapproach is adopted to find a converged thermal conductivity value at the elevatedtemperature. An initial steady-state temperature is assumed to get a first estimate ofthe thermal conductivity. With this value, the resulting steady-state temperaturerise is calculated and the relevant properties at this new temperature are used todetermine a new thermal conductivity value. This process is repeated until aconverged thermal conductivity is obtained (that is, invariant up to the seconddecimal place). In all cases, two to four iterative loops were needed. More than tendifferent crystals were measured for experiments conducted at room temperaturefor each SAC, and their average thermal conductivity values are reported. Thedeviation between measurements is less than the uncertainty in a singleexperiment. For the temperature-dependent thermal conductivity trends, at leasttwo different crystals for most SACs (only one for [Co6Te8]) were measured in acryostat cooled with liquid nitrogen. The data in Fig. 4a for [Co6Te8][C60]2 areaverages of three different crystals; data for both [Co6S8] and [Co6Se8] are averagesof two different samples; data for [Co6Te8] comes from one sample.

The resulting thermal conductivity has an uncertainty of 20–28% due to thegoodness of fit of the model and input parameter uncertainties (thermalconductivity of the gold film, volumetric heat capacities, and thicknesses of thegold film and SACs)21. To minimize this uncertainty, we separately determined thegold film thickness using atomic force microscopy and its thermal conductivityusing the Wiedemann–Franz law. The electrical sheet resistance required in theWiedemann–Franz law was measured with a four-point probe performed on agold-coated dielectric substrate that was sputtered at the same time as the sample.The substrate properties are unimportant, as the heights of the SACs were typicallymore than 100 µm. Heat capacity values used in the fitting process were eitherexperimentally measured (for temperatures greater than 190K) or extrapolatedbelow 190K by adding a fixed percentage (20–35%) to the DFT values. Thispercentage is the average percentage difference between the DSC and the DFTvalues at T>200K.

References34. Tsui, T. Y. & Pharr, G. M. Substrate effects on nanoindentation mechanical

property measurement of soft films on hard substrates. J. Mater. Res. 14,292–301 (1999).

35. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energycalculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).

36. Cahill, D. G. Analysis of heat flow in layered structures for time-domainthermoreflectance. Rev. Sci. Instrum. 75, 5119–5122 (2004).

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