High Thermoelectric Performance of Ag9GaSe6 Enabled by ...

Article

High Thermoelectric Performance ofAg9GaSe6 Enabled by Low Cutoff Frequencyof Acoustic Phonons

Siqi Lin, Wen Li, Shasha Li, ...,

Yidong Xu, Yue Chen, Yanzhong

Pei

[email protected]

HIGHLIGHTS

Ag9GaSe6 shows a promising

thermoelectric figure of merit

(zT � 1.5)

It has an extremely low lattice

thermal conductivity (kL� 0.15 W/m K)

Its low cutoff frequency of acoustic

phonons contributes to the low kL

The principle guides the design of

materials with expected kL

Acoustic phonons contribute most to lattice thermal conductivity (kL), due to their

high velocities. The cutoff frequency of acoustic phonons (um) indicates not only

the population but also the velocity and therefore guides the discovery of

semiconducting Ag9GaSe6 with an extremely low kL through a low um stemming

from both its large primitive cell and weakly bonded Ag. This opens new

possibilities for high-performance thermoelectrics, illustrated by the high

thermoelectric figure of merit (zT = 1.5) in this material.

Lin et al., Joule 1, 816–830

December 20, 2017 ª 2017 Elsevier Inc.

http://dx.doi.org/10.1016/j.joule.2017.09.006

Article

High Thermoelectric Performanceof Ag9GaSe6 Enabled by Low CutoffFrequency of Acoustic PhononsSiqi Lin,1 Wen Li,1 Shasha Li,2 Xinyue Zhang,1 Zhiwei Chen,1 Yidong Xu,1 Yue Chen,2

and Yanzhong Pei1,3,*

Context & Scale

Heat flow drives the charge

carriers in a material to flow along

the same direction, enabling

direct conversion from heat to

electricity, known as

thermoelectric technology. In

order to work efficiently, the

materials should be thermal

insulators to minimize heat loss.

Lattice vibrations, with long

wavelengths and high

propagation speeds (acoustic

SUMMARY

When the number of atoms in a primitive cell (N) increases, the first Brillouin

zone shrinks and folds back the high-frequency portion of acoustic vibrations

as optical ones with reduced velocities near zone boundaries. Soft bonds lead

to flattened phonon dispersion and thus a low sound velocity. This work shows

the cutoff frequency of acoustic phonons (um) as an important parameter to

include both effects on the lattice thermal conductivity (kL). A low um of

�0.5 THz in Ag9GaSe6 due to its large N and weakly bonded Ag atoms leads

this material to be one of the least thermally conductive dense solids (kL� 0.15 W/m K). This contributes to the peak thermoelectric figure of merit,

zT, as high as 1.5. The principle used here not only leads to the exploration of

Ag9GaSe6 as a promising thermoelectric but also enables a measurable param-

eter for designing materials with expected kL.

phonons), dominate heat

conduction in most thermoelectric

materials.

The cutoff frequency of acoustic

phonons (um), characterizing both

the population and the velocity, is

therefore a key measure of lattice

thermal conductivity (kL). Here, an

extremely low um in Ag9GaSe6 is

realized due to its large primitive

cell and weak chemical bonds for

both a small population and

velocity of acoustic phonons. The

resulting extremely low kL

contributes to the superior

thermoelectric figure of merit, zT,

of 1.5. The principle here guides

the design of materials with

expected kL for many potential

applications of heat, including

thermoelectrics.

INTRODUCTION

Thermoelectrics, directly converting heat into electricity, has long been considered

as a potential technology for solving the energy crisis.1 The performance of a

thermoelectric material is determined by the figure of merit zT = sS2T/(kE+kL), where

s, S, T, kE, and kL are the electrical conductivity, the Seebeck coefficient, the absolute

temperature, and the electronic and the lattice components of the thermal conduc-

tivity, respectively.

Because S, s, and kE strongly couple with each other, it is difficult to achieve a high zTby

a simple improvement of one of these parameters. Decoupling these parameters for

enhancing zT via band convergence or nestification has been demonstrated to be

successful in various materials such as IV-VI compounds,2–8 Mg2Si,9 half-Heusler,10,11

and Te.12,13 Alternatively, reducing the only independent material property, lattice

thermal conductivity kL, has also been demonstrated to effectively enhance zT. Typical

approaches include point defects,14–20 dislocations,21–23 and nanostructures.24–27

Recently, numerous efforts have been made to develop new thermoelectric

materials with superior performance. A variety of new materials with high zT, such

as b-Zn4Sb3,28 Cu2Se,

29,30 SnSe,31 and MgAgSb32–34 have been reported to be

promising for thermoelectric applications. These high zT materials have intrinsically

low lattice thermal conductivity, due to various mechanisms, including crystal

structure complexity,28 liquid-like ions,29 and lattice anharmonicity.35 This works

indicates the importance of an intrinsic low lattice thermal conductivity for exploring

new thermoelectrics.

816 Joule 1, 816–830, December 20, 2017 ª 2017 Elsevier Inc.

1Interdisciplinary Materials Research Center,School of Materials Science and Engineering,Tongji University, 4800 Caoan Road, Shanghai201804, China

2Department of Mechanical Engineering, TheUniversity of Hong Kong, Pokfulam Road, HongKong SAR, China

3Lead Contact

*Correspondence: [email protected]

http://dx.doi.org/10.1016/j.joule.2017.09.006

Intrinsically low lattice thermal conductivity usually happens in materials with a large

primitive cell. This is fundamentally associated with the reduced population of

acoustic phonons, which have a high velocity and therefore contribute dominantly

to the lattice thermal conductivity. In more detail, when the number of atoms in a

primitive cell increases, the lattice parameter increases, resulting in a reduced

volume of the first Brillouin zone. This leads the high-frequency portion of acoustic

vibration modes to be folded back into the first Brillouin zone as optical modes,

but with significantly reduced velocities near zone boundaries. Optical phonons

usually have extremely low velocities, leading to a negligible contribution to the lat-

tice thermal conductivity.36,37 In the case of a large primitive cell, the population of

acoustic phonons that dominate the lattice thermal conductivity is significantly

reduced.

Another key parameter determining the lattice thermal conductivity is the propaga-

tion of phonons (i.e., sound velocity, v). When the medium varies from a gas to a

liquid and then to a solid, sound waves travel faster and faster, roughly indicating

that a weakly bonded medium reduces the velocity. In a crystalline solid, weakly

bonded heavy constituent elements usually lead to a flattening in phonon disper-

sion. This essentially results in a low lattice thermal conductivity.

Although the above strategies are indeed effective for exploring materials

with a low lattice thermal conductivity (kL), the individual effectiveness on kL is

by definition still not well quantified. Since both a large primitive cell and soft

bonds lead to a small frequency of acoustic phonons at the boundary of the

first Brillouin zone, this work uses such a frequency as an important parameter

determining the kL of a material. This frequency is exactly the cutoff frequency of

acoustic phonons (um), which can be determined by measuring the sound velocity

(v) and the crystal structure parameters (the number of atoms in the primitive cell

[N] and the atomic volume [V ]) via um = 2pv � ðNVÞ�1=3 according to Debye

approximation.

Guided by the above concept of a low cutoff frequency for low lattice thermal

conductivities, this work focuses on a semiconducting material, Ag9GaSe6, for its

potential in thermoelectrics. The primitive cell includes a large number of atoms,

more than half of which are weakly bonded Ag+ cations. Therefore, Ag9GaSe6 is

assumed to have a low lattice thermal conductivity due to its low um for potential

thermoelectric applications. It should be noted that the weakly bonded Ag+ cations

further induce an order-disorder phase transition from b-Ag9GaSe6 to a-Ag9GaSe6at 281 K.38–40

The thermoelectric transport properties of Ag9GaSe6 above room temperature are

investigated in this work. While most of the semiconductors, including thermoelec-

tric materials, have a cutoff frequency of 1–3 THz for acoustic phonons, Ag9GaSe6shows an extremely low cutoff frequency (only �0.5 THz) of acoustic phonons.

This material successfully shows a kL as low as�0.15W/m K in the entire temperature

range, being one of the least thermally conductive crystalline solids. This work may

shed light on the origin of the extremely low lattice thermal conductivities observed

in other high-performance thermoelectrics41–48 as well. Although the thermoelectric

power factor of Ag9GaSe6 is much lower than those of conventional thermoelectrics,

a peak thermoelectric figure of merit, zT � 1.5, can be achieved in Ag9GaSe6 alloys,

of which the transport properties can be well understood by a single parabolic band

model. This work opens new possibilities of thermoelectric advancements through a

low cutoff frequency of acoustic phonons.

Joule 1, 816–830, December 20, 2017 817

Figure 1. Phase Characterization

(A–D) Crystal structure of Ag9GaSe6 in the high temperature (>281 K) phase (A). Powder X-ray

diffraction patterns (B), the lattice parameter (C), and room temperature Hall carrier concentration

(D) for Ag9Ga(Se1�xTex)6, indicating formation of a solid solution.

RESULTS AND DISCUSSION

Ag9GaSe6 shows a phase transition between b-Ag9GaSe6 (space group P213) and

a-Ag9GaSe6 (space group F43m) at 281 K.38–40 The cubic crystal structure of the

low-temperature b-Ag9GaSe6 is formed by a [GaSe4]5� and Se2� anion framework

and ordered Ag+ fully occupying its lattice sites. Above 281 K, the anion framework

becomes more symmetrical in an F43m lattice, while Ag atoms get highly disordered

with an occupancy of only 12.5% and 25%, respectively, on the 96i and 48h sites

(Figure 1A). It is interesting to note that the order-disorder transition does not induce

a change in the lattice parameter. Moreover, the disordered phase stabilizes at room

temperature or higher. Compared with previously reported materials with complex

crystal structures involving phase transitions,29,34,35,41,47,48 these features can be

advantages for thermoelectric applications.

The powder X-ray diffraction patterns (XRD) for the samples are shown in Figure 1B.

All the peaks can be indexed to the corresponding F43m structure.With increasing x,

the lattice parameter (Figure 1C) increases linearly while the carrier concentration

decreases (Figure 1D). The lattice expansion can be understood by the larger

size of Te compared with that of Se. A broad range of Hall carrier concentration

(3 � 10 3 1018 cm�3) at room temperature is achieved (Figure 1D). Other dopants

such as Cr, Cd, Zn, Ge, and S were also used to tune the carrier concentration, yet

they all seem to be not as effective (Table S1).

Scanning electron microscopy (SEM) observations and energy dispersive

spectrometer (EDS) composition mapping of Ag, Se, and Ga for Ag9GaSe6 (Figure 2)

and Ag9Ga(Se0.9Te0.1)6 (Figure S1) were carried out to further confirm the purity and

homogeneity. The optical measurements49 enabled estimation of the band gap

818 Joule 1, 816–830, December 20, 2017

Figure 2. Microstructures of Ag9GaSe6(A–D) SEM image (A) and the corresponding EDS composition mapping of Ag (B), Se (C), Ga (D) for

Ag9GaSe6.

(�0.56 eV) for Ag9GaSe6. It is shown that the band gap of Ag9Ga(Se1�xTex)6decreased from 0.56 eV for x = 0 to 0.46 eV for x = 0.17 (Figure 3). The XRD results

and the optical and transport properties for Ag9GaSe6 with other dopants

mentioned above are included in Figures S2 and S3.

Ab initio molecular dynamics simulations were performed to understand the

atomic vibrations at elevated temperatures for the low-temperature phase (Fig-

ure 4A). It is seen that all atoms vibrate in the vicinity of their equilibrium positions

at 300 K (Figure 4B), whereas the Ag atoms exhibit a diffusive behavior at 500 K

(Figure 4C). This indicates that Ag atoms are loosely bonded to the neighboring

atoms. The simulation results should rationalize the experimentally observed Ag

partial occupancy in the high-temperature phase. It should be noted that, due

to the partial occupancy of Ag in the high-temperature phase, the simulation

can be carried out on the low-temperature phase only. However, it is reasonable

to assume that Ag atoms get more diffusive in the high-temperature phase

because of the existence of unoccupied vacancies. Further considering the un-

changed lattice parameters for both low- and high-temperature cubic phases,

the main difference relies on the occupancy of Ag atoms. Therefore, it is believed

that Ag atoms are also weakly bonded (if not weaker) in the high-temperature

phase.

Further electron density distribution and Bader charges are carried out to confirm

the soft bonding in Ag9GaSe6. Directional electron density distribution between

Ga and Se atoms is seen from Figure 5, indicating strong covalent bonds. However,

the electron density distribution surrounding the Ag atoms is nearly spherical,

suggesting weak chemical bonds to neighboring atoms. Bader charge analysis

shows that each Ag and Ga atom loses 0.26 and 0.97 electrons, respectively, while

each Se atom receives 0.56 electrons. This again indicates that Ag atoms are weakly

bonded due to ionic interactions. Such bonding characteristics provide an insight in

Joule 1, 816–830, December 20, 2017 819

Figure 3. Optical Absorption

The normalized optical absorption versus photon energy at room temperature for

Ag9Ga(Se1�xTex)6.

understanding why the lattice dynamics shows a diffusive behavior of Ag atoms

(Figure 4).

It is known that soft bonding usually leads to a flattened phonon dispersion,

which is shown in Figure 6A. By projecting the phonon density of states (DOS) of

Ag9GaSe6 onto different atomic species (Figure 6B), it is found that the majority

of the low-frequency phonon modes below 3 THz are contributed by the Ag atoms.

This is consistent with the feature that Ag atoms are weakly bonded. Therefore, it

is seen that most of the optical phonon modes are nearly non-dispersive,

ensuring a negligible contribution to the lattice thermal conductivity.37

Further, due to the soft bonding, both the transverse (vt = 1,200 m/s) and longitu-

dinal (vl = 2,900 m/s) sound velocities calculated from phonon dispersions are

extremely low for Ag9GaSe6, which is well confirmed by the measurements

(vt = 1,167 m/s, vl = 2,917 m/s) at room temperature. Besides the soft bonds

emphasized in this work, other mechanisms50,51 are found to be effective for a

low sound velocity.

Because there are many atoms (high N) in the crystal cell of Ag9GaSe6, the small

volume of the first Brillouin zone and the softly bonded Ag atoms (low v) lead the

cutoff frequency of acoustic phonons to be as low as �0.5 THz (Figure 5). This cutoff

frequency of acoustic phonons is significantly lower than those of typical semi-

conductors, including thermoelectrics. The room temperature lattice thermal con-

ductivity as a function of cutoff frequency for acoustic phonons is shown in Figure 7

for semiconductors with potential as thermoelectrics (more details are given in

Table S2). It is seen that a low cutoff frequency of acoustic phonons is indeed helpful

for a low lattice thermal conductivity.

The theoretical basis relies on the fact that the cutoff frequency of acoustic

phonons, um = 2pv � ðNVÞ�1=3, defines the upper limit of the integral of the lattice

820 Joule 1, 816–830, December 20, 2017

Figure 4. Molecular Dynamics Simulations

(A–C) Crystal structure of Ag9GaSe6 in the low-temperature phase projected onto the (100) plane

(A) and the corresponding atomic trajectories at (B) 300 K and (C) 500 K, with Ag in blue, Ga in red,

and Se in green.

thermal conductivity. Equation 1 shows the expression of kL for Umklapp scat-

tering, according to a Debye phonon dispersion and exclusion of optical

phonons:36,37

kL =

ffiffiffiffiffiffiffiffi6p23

p

4p2

R

kBMV

2=3Z um

0

v2

g2T

0B@� Zu

kBT

�2

,eðZu=kBTÞ

ðeðZu=kBTÞ � 1Þ2

1CAdu; (Equation 1)

Joule 1, 816–830, December 20, 2017 821

Figure 5. Electron Density Distribution

(A and B) Electron density isosurface of 0.4 e/A3 in Ag9GaSe6 (A) and the electron density

distribution in an atomic plane crossing the Se-Ga-Se bonds (B).

where R is the gas constant, kB is the Boltzmann constant, M is the average atomic

mass, v is the average sound speed, g is the Gruneisen parameter, and �h is the

reduced Planck constant. It should be noted that a more accurate determination

on phonon dispersion such as by density functional theory (DFT) calculations50,51

would lead to a more accurate estimation of kL.

Therefore, use of the number of atoms in the primitive cell (N) for measuring the

crystal complexity and the sound velocity (v) for characterizing the bonding stiffness

in this work, a product of 2pvðNVÞ�1=3, which is essentially the cutoff frequency of

acoustic phonons according to Debye approximation, successfully includes both

effects in the lattice thermal conductivity. The cutoff frequency of acoustic phonons

um physically means the frequency of acoustic phonons at the boundary of the

Brillouin zone. In the case of a given sound velocity, the volume of the first Brillouin

zone is proportional to um.3 Therefore, this work reveals a high lattice thermal

conductivity when the volume of the first Brillouin zone is large, at a given sound

velocity (Figure 7).

According to the above discussion, a um as low as �0.5 THz in Ag9GaSe6 (Figure 6)

would lead to an expectation of extremely low lattice thermal conductivity. The

temperature-dependent total thermal conductivity (k) and its lattice component

(kL) for Ag9Ga(Se1�xTex)6 (0 % x % 0.17) are shown in Figure 8. It is found that

k for all samples is as low as 0.5W/m K over the entire temperature range. The lattice

thermal conductivity (kL) is estimated by subtracting the electronic thermal

conductivity (ke) via the Wiedemann-Franz law (ke = LT/r) from the total thermal

conductivity, where L is the Lorenz factor determined by the single parabolic

band (SPB) model with acoustic scattering (Figure S4). The observed kL of

�0.15 W m�1 K�1, over the entire temperature range, is indeed one of the

lowest among known thermoelectrics. The much lower lattice thermal conductivity

in Ag9GaSe6 (kL � 0.15 W/m K) than in Ga2Se3 with high concentration intrinsic

vacancies (kL � 0.6 W/m K52) or in GaSe (kL � 2.1 and�16 W/m K along and perpen-

dicular to the c axis at room temperature, respectively53) suggests that the loosely

bonded Ag atoms contribute to the low lattice thermal conductivity of Ag9GaSe6.

It should be noted that the total thermal conductivity (k) is as low as�0.4 W/m K and

largely (�50%) comes from its electronic component; a combination of multiple

measurement uncertainties can mathematically affect the absolute values of kL.

822 Joule 1, 816–830, December 20, 2017

Figure 6. Phonon Dispersion

(A and B) Calculated phonon dispersions (A) and the projected phonon density of states (B) for

Ag9GaSe6.

A statistical measurement on kL yields an average of 0.15 W/m K for all samples with

an SD of 0.058W/m K (Figure 8). Nevertheless, we are able to draw a safe conclusion

that an extremely low kL is achieved in Ag9GaSe6 with a low um, which supports our

main conclusion. In addition, the measured kL very weakly depends on temperature,

which is a strong indication of Ag9GaSe6 as a phonon glass by nature. This

may explain that further introduction of atomic scale defects does not enable a

clear additional reduction in kL (Figure 8), which can easily fall within the range of

its measurement uncertainty, even if additional reduction indeed exists.

The measured room temperature longitudinal (vl), transverse (vt), and mean (v)

sound velocities for all the Ag9Ga(Se1�xTex)6 samples are listed in Table 1. The

change in v does not exceed 5%, which is within the measurement uncertainty.

Importantly, it is found that the mean sound velocity v � 1,350 m/s is one of the

lowest among known thermoelectric semiconductors.41 Table 1 also lists the bulk

(B) and shear (G) modulus, Gruneisen parameter, and Debye temperature (QD)

calculated from the sound velocities.54 The Gruneisen parameter, characterizing

the anharmonicity of the lattice vibrations, is high (�2.6), which is presumably

due to the loosely bonded Ag atoms. The Debye temperature is estimated to be

�143 K with an error of <3% for Ag9Ga(Se1�xTex)6. All these features support the

low lattice thermal conductivity observed in this work.

Providing a low kL ensured by the low um in Ag9GaSe6, a generic guideline for

realizing high zT will be a synergy with electronic performance enhancement

Joule 1, 816–830, December 20, 2017 823

Figure 7. Survey of um versus kLRoom temperature lattice thermal

conductivity versus the cutoff

frequency of acoustic phonons for

semiconductors.

through first optimizing the carrier concentration and then manipulating the band

structures at an optimized carrier concentration. This gives a band structure

calculation for the low-temperature phase (Figure 9) to reveal the electronic trans-

port properties of Ag9GaSe6-based materials. The conduction band maximal was

found at the G point, therefore, the band degeneracy (Nv) in n-type is 1. This is

significantly lower than that of conventional thermoelectrics, which usually have Nv

of 4 or higher.6,7,11,55,56 For this reason, all the samples here showing an n-type

conduction are not expected to have a high thermoelectric power factor. It should

be noted that the optical measurement suggests a direct band gap in Ag9GaSe6,

which is consistent with the DFT calculations.

The modified Becke-Johnson (mBJ) exchange potential is used in our DFT calcula-

tions. The mBJ exchange potential can significantly improve the theoretical band

gap, with a similar accuracy to the hybrid functional or the GW method. As a result,

the DFT band gap obtained is in good agreement with optimal measurements. In

addition, the calculated band structure shows a single band conduction behavior

in n-type, which is confirmed by the transport property measurements. Therefore,

the currently calculated band structure is reasonably reliable for evaluating the trans-

port properties in the absence of strong bipolar conduction as is the case in the cur-

rent study.

Substituting Se by Te in Ag9GaSe6 enables effective tuning of the carrier concen-

trations in a broad range, enabling a reliable evaluation of the thermoelectric

transport properties. Hall mobility (mH) decreases with increasing temperature via

mH � T�1.5 (Figure 10A) for all the samples in the entire temperature range, indi-

cating an overall dominant charge carrier scattering by acoustic phonons.57,58

This enables a SPB model59 to understand the electronic transport properties.

Assuming the conduction band is isotropic, the estimated density-of-state effec-

tive mass (m*) and deformation potential coefficient60 (Edef) are shown in Fig-

ure 10B. Both Edef and m* show a weak dependence on temperature and carrier

concentration. The SPB model-predicted Seebeck coefficient (Figure 10C) and

Hall mobility (Figure 10D), as a function of the Hall carrier concentration, agree

well with the measurements at different temperatures. All these indicate a rigid

band behavior for this material. Moreover, Edef of �24 eV and m* of 0.16 me

(me is the free electron mass) are within the typical range for thermoelectric

semiconductors.61–64

824 Joule 1, 816–830, December 20, 2017

Figure 8. Thermal Properties

Temperature-dependent total

thermal conductivity and lattice

thermal conductivity for

Ag9Ga(Se1�xTex)6, compared with

the lattice thermal conductivity of

Ga2Se3 with intrinsic vacancies.52

The temperature-dependent Seebeck coefficient, resistivity, and zT are shown in Fig-

ure 11 for Ag9Ga(Se1�xTex)6. A negative Seebeck coefficient indicates an n-type

conduction for all the samples, which is consistent with the Hall measurements.

The majority of the samples obtained in this work show a typical degenerate semi-

conducting behavior, meaning a continuous increase in the Seebeck coefficient

and resistivity as the temperature rises. The decrease in r and S at high temperatures

for low carrier concentration samples can be ascribed to the existence of minority

carriers.

A peak zT of �1.5 is achieved at 850 K, which mainly relies on the extremely low

lattice thermal conductivity due to the low cutoff frequency of acoustic phonons.

Using an average lattice thermal conductivity of 0.15 W m�1 K�1 (Figure 8), the

SPB model enables a prediction on zT versus Hall carrier concentration, which is

shown in Figure 11D. It is found that a peak zT as high as 1.6 can be expected

when the Hall carrier concentration is reduced to about 3 3 1018 cm�3 at 800 K.

This suggests that Ag9GaSe6 is a promising thermoelectric material.

Note here that zT in n-type Ag9GaSe6 seems to have not enough scope for further

enhancement through engineering the band, due to the simplicity of the conduction

band (Figure 9). However, an even higher zT could be expected through further band

engineering, probably in p-type conduction, because of the multiple valence band

structure (Figure 9). This can be the playground for this compound as a thermoelec-

tric material. The possibility of engineering valence bands as desired can be realized

in principle by the richness in the composition of the IB9IIIVI6 compound family,

Table 1. Elastic Properties

Composition vt (m/s) vl (m/s) V (m/s) B (GPa) G (GPa) g QD (K)

x = 0 1,167 2,917 1,322 48.8 10.0 2.7 141

x = 0.05 1,222 2,916 1,382 47.5 10.9 2.6 147

x = 0.08 1195 2,953 1,353 49.8 10.4 2.6 144

x = 0.10 1177 2,948 1,333 49.9 10.1 2.7 142

x = 0.12 1,195 2,975 1,353 50.7 10.4 2.7 144

x = 0.15 1,195 2,941 1,352 49.2 10.4 2.6 143

x = 0.17 1,197 2,955 1,355 49.8 10.5 2.6 143

Room temperature transverse (vt), longitudinal (vl), and mean (v) sound velocities, bulk (B) and shear (G)

modules, Gruneisen parameter (g) as well as Debye temperature (QD) for Ag9Ga(Se1�xTex)6.

Joule 1, 816–830, December 20, 2017 825

Figure 9. Band Structure

DFT band structure of Ag9GaSe6 in P213 phase.

where IB, III, and VI can be Ag/Cu, Al/Ga/In, and S/Se/Te, respectively. Achieving

possibly higher zT is further enabled by the fact that all these materials have similarly

complex crystal structures and partial occupancy on the IB sites, thus all are likely to

show an ultra-low intrinsic lattice thermal conductivity. Furthermore, a Cu-based

analog or heavy substitution of Ag by Cu can be an effective approach to address

the issue due to the scarcity of Ag and to reduce the cost of the material.

This work shows the cutoff frequency of acoustic phonons, as an important

parameter integrating effects on the lattice thermal conductivity due to crystal struc-

ture complexity and soft bonding. This enables not only effective guidance for

Figure 10. Electronic Transport Properties

(A–D) Temperature-dependent Hall mobility, mH (A), density-of-state effective mass, m* and

deformation potential coefficient, Edef (B), Hall carrier concentration-dependent Seebeck

coefficient (C), and Hall mobility (D) at 300, 500, and 800 K for Ag9GaSe6. The solid curves in (C) and

(D) show the SPB model predictions.

826 Joule 1, 816–830, December 20, 2017

Figure 11. Thermoelectric Transport Properties

(A–C) Temperature-dependent Seebeck coefficient (A), resistivity (B), and figure of merit, zT (C) for

Ag9Ga(Se1�xTex)6.

(D) The model-predicted zT versus carrier concentration at 300, 500, and 800 K for Ag9GaSe6.

designing materials with expected lattice thermal conductivity but also effective

exploration of new thermoelectrics such as Ag9GaSe6 of zT � 1.5. The scope for

follow-up studies on IB9IIIVI6 compounds relies on the richness in the composition,

which allows sufficient degrees of freedom for electronic structure manipulation for

performance enhancements.

EXPERIMENTAL PROCEDURES

Polycrystalline Ag9Ga(Se1�xTex)6 (x % 0.1) and Ag9Ga1�xMx(Se1�ySy)6 (M = Cr, Cd,

Zn, Ge; x% 0.06; y% 0.10) samples were synthesized by melting the stoichiometric

amount of high-purity elements (>99.99%) at 1,227 K for 6 hr, quenching in cold

water, and annealing at 900 K for 3 days. The resulting ingots were hand ground

into fine powder for X-ray diffraction (XRD) and hot press. Pellet samples were

obtained by an induction heating hot press system65 at 900 K for 1 hr under a uniaxial

pressure of�60 MPa. The dense samples obtained (>98% of the theoretical density)

were about 12 mm in diameter and �1.5 mm in thickness.

The electrical transport properties, including resistivity, Seebeck coefficient, and

Hall coefficient, were measured simultaneously on the pellet samples under helium.

The Seebeck coefficient was obtained from the slope of the thermopower versus

temperature difference within 0–5 K.66 The resistivity and Hall coefficient (RH) were

measured using the van der Pauw technique under a reversible magnetic field of

1.5 T. Thermal diffusivity (D) was measured using the laser flash technique with the

Netzsch LFA457 system. The thermal conductivity was calculated via k = dCpD,

where d is the density measured using the mass and geometric volume of the pellet

and Cp is the heat capacity determined by the Dulong-Petit limit. All the transport

Joule 1, 816–830, December 20, 2017 827

property measurements were carried out in the temperature range of 300–850 K.

Hysteresis on the transport properties was initially observed but disappeared

after a few thermal cycles or annealing. The measurement uncertainty for each

transport property (S, r, and k) is about 5%. The microstructure was characterized

by SEM equipped with EDS. The sound velocity was measured using an ultrasonic

pulse receiver (Olympus-NDT) equipped with an oscilloscope (Keysight). Optical

diffusive reflectance was measured by infrared Fourier transform spectroscopy

(Bruker Tensor II).

Phonon dispersions and projected phonon DOS of Ag9GaSe6 were calculated using

the small displacement method with a 2 3 2 3 2 supercell containing 512 atoms

with Phonopy.67 The force constants were calculated based on DFT using VASP68

with an energy tolerance of 10�8 eV. The electron-ion interactions were treated

using the projector augmented wave method.69 The exchange-correlation interac-

tions were taken into account with the Perdew-Burke-Ernzerhof functional.70 The

valence electronic states were expanded in plane-wave basis sets with an energy

cutoff of 400 eV. The Brillouin zone integrations were performed with a 1 3 1 3 1

Monkhorst-Pack grid71 for the supercell containing 512 atoms. A 23 23 2 supercell

was also used for ab initiomolecular dynamics simulations in the canonical ensemble

(NVT) at 300 K and 500 K. Ab initiomolecular dynamics simulations were performed

for 4 ps with a time step of 1 fs; atomic trajectories were collected from 0.5 ps.

The mBJ method72 was applied to obtain a more realistic electronic band gap

from DFT.

SUPPLEMENTAL INFORMATION

Supplemental Information includes four figures and two tables and can be found

with this article online at http://dx.doi.org/10.1016/j.joule.2017.09.006.

AUTHOR CONTRIBUTIONS

Conceptualization, Y.P.; DFT Calculations, S. Li and Y.C.; Experiments, S. Lin, W.L.,

and Y.X.; Discussions, S. Lin, W.L., S. Li, X.Z., Z.C., Y.X., Y.C., and Y.P.; Writing, S. Lin,

W.L., and Y.P.

ACKNOWLEDGMENTS

This work is supported by the National Natural Science Foundation of China (grant

nos. 51422208, 11474219, 51772215), the National Recruitment Program of Global

Youth Experts (1000 Plan). S. Li and Y.C. are grateful for financial support from the

Early Career Scheme of RGC under Project No. 27202516 and the research

computing facilities offered by ITS, HKU.

Received: April 25, 2017

Revised: June 30, 2017

Accepted: September 8, 2017

Published: October 4, 2017

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828 Joule 1, 816–830, December 20, 2017

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JOUL, Volume 1

Supplemental Information

High Thermoelectric Performance

of Ag9GaSe6 Enabled by Low Cutoff

Frequency of Acoustic Phonons

Siqi Lin, Wen Li, Shasha Li, Xinyue Zhang, Zhiwei Chen, Yidong Xu, YueChen, and Yanzhong Pei

Table S1. Elastic properties for Ag9Ga1-xMx(Se1-ySy)6. Room temperature Hall carrier concentration

(nH), transverse (vt), longitudinal (vl) and mean (v) sound velocities, bulk (B) and shear (G) modules,

Gruneisen parameter (γ) and Debye temperature (D) for Ag9GaSe6 with various dopants.

Compounds nH

(cm-3)

vt

(m/s)

vl

(m/s)

v

(m/s)

B

(GPa)

G

(GPa) γ

D

(K)

Ag9GaSe6 7.0e18 1168 2899 1323 48.1 10.0 2.7 142

Ag9Ga0.98Cr0.02Se6 7.6e18 1147 2920 1300 49.4 9.6 2.7 139

Ag9Ga0.96Cr0.04Se6 7.1e18 1206 2857 1364 45.4 10.6 2.5 146

Ag9Ga0.94Cr0.06Se6 6.3e18 1185 2800 1340 43.6 10.3 2.5 143

Ag9Ga0.94Cd0.06Se6 1.1e19 1140 2757 1290 42.8 9.5 2.6 138

Ag9Ga0.94Zn0.06Se6 9.1e18 1145 2851 1297 46.6 9.6 2.7 138

Ag9Ga0.94Ge0.06Se6 9.0e18 1173 2890 1328 47.6 10.0 2.6 142

Ag9Ga(Se0.95S0.05)6 9.0e18 1179 2913 1335 48.4 10.1 2.6 143

Ag9Ga(Se0.90S0.10)6 8.9e18 1230 3097 1394 55.2 11.0 2.7 150

Table S2. Relationship between cut-off frequency and lattice thermal conductivity. Cut-off

frequency for transverse (TA1,TA2) and longitudinal (LA) acoustic phonon branches, the mean

cut-off frequency (m) and the room temperature lattice thermal conductivity(L) for semiconductors.

Compounds TA1 TA2 LA m L Refs.

Argyrodite

semiconductors

Ag9GaSe6 0.51 0.51 0.64 0.54 0.2 This work

Ag8SnSe6 0.44 0.44 0.56 0.47 0.2 1

Cu8GeSe6 0.42 0.42 0.67 0.46 0.3 2

Elemental

semiconductors

Diamond 24.50 24.50 36.40 26.75 2000.0 3, 4

Si 4.41 4.41 12.26 5.01 156.0 4, 5

Ge 2.40 2.40 7.29 2.73 60.0 4, 5

SiC 11.19 11.19 19.20 12.41 490.0 4, 6

Se 1.81 2.16 2.16 2.01 4.5 7, 8

Te 1.04 1.47 1.47 1.25 2.3 8

III-V

semiconductors

BN 9.17 21.55 31.04 12.81 391.0 9, 10

BP 9.59 9.59 16.14 10.61 360.0 11, 12

BAs 5.93 5.93 9.72 6.55 210.0 11, 12

AlN 10.23 10.23 17.78 11.36 319.0 13, 14

AlP 3.98 3.98 10.58 4.52 90.0 11, 15

AlAs 2.80 2.80 6.40 3.16 91.0 5, 16

AlSb 2.19 2.19 4.64 2.47 56.0 5, 14

GaN 5.84 5.84 10.72 6.51 130.0 17, 18

GaP 3.11 3.11 7.65 3.52 100.0 19, 20

GaAs 2.46 2.46 6.83 2.80 44.0 5, 21

GaSb 1.71 1.71 5.00 1.95 33.0 5, 22

II-VI

semiconductors

ZnS 2.66 2.66 6.47 3.01 27.0 23, 24

ZnSe 2.07 2.07 5.59 2.35 19.0 24, 25

ZnTe 1.71 1.71 4.15 1.94 18.0 24, 26

CdSe 1.34 1.34 4.57 1.52 9.0 27, 28

CdTe 1.18 1.18 3.79 1.34 7.5 24, 26

I-III-VI2

semiconductors

CuInSe2 1.53 1.53 1.80 1.60 3.7 29, 30

AgGaSe2 1.02 1.02 1.57 1.12 1.0 31, 32

CdGeAs2 1.99 1.99 2.66 2.14 4.0 30, 33

I2-IV-VI3

&I3-V-VI4

semiconductors

Cu3SbS4 0.76 0.76 0.94 1.74 4.1 34

Cu3SbSe3 1.64 1.77 1.83 0.80 0.5 35

Cu3SbSe4 1.31 1.38 1.42 1.37 2.9 34

IIx-IVy

semiconductors

Mg2Ge 2.27 2.27 3.63 2.50 6.6 36, 37

Mg2Sn 2.25 2.25 3.73 2.49 13.0 30, 38

IVx-VIy

semiconductors

GeSe 0.45 0.45 0.76 1.35 2.0 28, 39

PbS 1.23 1.23 1.63 1.32 2.5 28, 39

PbSe 0.97 0.97 1.49 1.06 1.6 40, 41

PbTe 0.73 0.73 0.96 0.78 2.0 41, 42

SnTe 1.49 1.49 1.03 1.26 2.8 43, 44

GeTe 1.52 1.67 2.04 1.69 3.0 45, 46

Typical

thermoelctrics

MgAgSb 0.73 0.92 1.10 0.87 0.6 47

CaAgSb 0.99 0.99 1.44 1.08 1.7 47, 48

CoSb3 1.57 1.57 2.62 1.74 10.0 49, 50

Ba8Ga16Ge30 1.06 1.06 1.44 1.14 1.6 51, 52

Bi2Te3 0.50 0.50 0.79 0.55 1.3 53

The mean cut-off frequency (m) for acoustic phonons is obtained by:

𝜔𝑚 = 1

3 1

𝜔𝑇𝐴13 +

1

𝜔𝑇𝐴23 +

1

𝜔𝐿𝐴3

−13

Ag10 mm Ga

Se Te

10 mm

10 mm10 mm

10 mm

(a) (b) (c)

(d) (e)

Ag9Ga(Se0.9Te0.1)6

Ag: Ga: Se: Te53.79: 7.60: 35.41: 3.19

(f)

Figure S1. Microstructure of Ag9Ga(Se0.9Te0.1)6. SEM image (a), EDS composition mapping of Ag

(b), Ga (c), Se (d), Te(e) and the energy spectrum (f) for Ag9Ga(Se0.9Te0.1)6.

0.5 0.6 0.7 0.8

x=0, y=0

x=0.02, y=0 Cr

x=0.04, y=0 Cr

x=0.06, y=0 Cr

x=0.06, y=0 Cd

x=0.06, y=0 Zn

x=0.06, y=0 Ge

x=0, y=0.05

x=0, y=0.10

Ag9Ga

1-xM

x(Se

1-yS

y)6 (M=Cr,Cd,Zn,Ge)

A

bso

rpti

on

(N

orm

alize

d)

hv (eV)

Eg=0.56ev

20 30 40 50 60 70 80 90

x=0, y=0.10

Ag9Ga

1-xM

x(Se

1-yS

y)6 (M=Cr,Cd,Zn,Ge)

x=0, y=0.05

x=0.06, y=0Ge

x=0.06, y=0Zn

x=0.06, y=0Cd

x=0.06, y=0Cr

x=0.04, y=0Cr

x=0.02, y=0Cr

Inte

ns

ity

(a

.u.)

2 (deg.)

x=0, y=0

ICSD #15252

(a) (b)

Figure S2. XRD and optical measurements for Ag9Ga1-xMx(Se1-ySy)6. Powder X-ray diffraction

patterns (a) and the normalized optical absorption versus photon energy at room temperature (b) for

Ag9Ga1-xMx(Se1-ySy)6. All the peaks can be well indexed to the corresponding F43m structure,

indicating the high phase purity. The optical measurements shows that the band gap remains nearly

unchanged for various doping/alloying for Ag9GaSe6.

1017

1018

1019

0

1

2

3

4

5

6

7

8; ; ; Prediction

; ; ; Exp. Ag9Ga(Se

1-xTe

x)

; ; ; Exp. other doping&alloys

n

H (cm

-3)

PF

(m

W/c

m-K

2)

300K

500K

800K

m* ~ 0.16me

Edef ~ 24eV

300 400 500 600 700 800 900

-150

-100

-50

Ag9Ga

1-xM

x(Se

1-yS

y)

6 (M=Cr,Cd,Zn,Ge)

S (m

V/K

)

T (K)300 400 500 600 700 800 900

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5Ag

9Ga

1-xM

x(Se

1-yS

y)

6 (M=Cr,Cd,Zn,Ge)

x=0, y=0

x=0.02, y=0 Cr x=0.04, y=0 Cr

x=0.06, y=0 Cr x=0.06, y=0 Cd

x=0.06, y=0 Zn x=0.06, y=0 Ge

x=0, y=0.05 x=0, y=0.10

(

m

cm

)

T (K)

300 400 500 600 700 800 9000.0

0.2

0.4

0.6

0.8

1.0

1.2

Ag9Ga

1-xM

x(Se

1-yS

y)6 (M=Cr,Cd,Zn,Ge)

x=0, y=0

x=0.02, y=0 Cr

x=0.04, y=0 Cr

x=0.06, y=0 Cr

x=0.06, y=0 Cd

x=0.06, y=0 Zn

x=0.06, y=0 Ge

x=0, y=0.05

x=0, y=0.10

zT

T (K)300 400 500 600 700 800 900

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

L~0.15W/m-K

Standard deviation ~ 0.058 W/m-K

,

L (

W/m

-K)

T (K)

(a) (b)

(c) (d)

(e) (f)

300 400 500 600 700 8000

10

20

30

m*

(me)

Ed

ef (

ev)

T (K)

0.0

0.2

0.4

0.6

0.8

Figure S3. Transport properties for Ag9Ga1-xMx(Se1-ySy)6. Temperature dependent Seebeck

coefficient (a), resistivity (b)，density of state effective mass, m* and deformation potential coefficient,

Edef (c) for Ag9Ga1-xMx(Se1-ySy)6. The comparison between the measurements and prediction on power

factor versus Hall carrier concentration (d). Temperature dependent total thermal conductivity, lattice

thermal conductivity (e) and figure of merit (zT) for Ag9Ga1-xMx(Se1-ySy)6.

300 400 500 600 700 800 9001.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3 x=0 1.2E19

x=0.05 8.5E18

x=0.08 6.6E18

x=0.10 3.1E18

x=0.12 4.1E18

x=0.15 4.0E18

x=0.17 2.3E18

Ag9Ga(Se

1-xTe

x)6

T (K)

L ×

10

8 (

V2/K

2)

Figure S4. Lorenz factor for Ag9Ga(Se1-xTex)6. Temperature dependent Lorenz factor for

Ag9Ga(Se1-xTex)6.

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