ApplPhysLett_94_203109

Improved thermoelectric properties of Mg2SixGeySn1xy nanoparticle-in-alloy materials

S. Wang and N. Mingo

Citation: Appl. Phys. Lett. 94, 203109 (2009); doi: 10.1063/1.3139785

View online: https://www.sodocs.net/doc/4b4701978.html,/10.1063/1.3139785

View Table of Contents: https://www.sodocs.net/doc/4b4701978.html,/resource/1/APPLAB/v94/i20

Published by the American Institute of Physics.

Related Articles

Manipulating the spin of single-molecule magnet by thermal spin-transfer torque

Appl. Phys. Lett. 99, 133110 (2011)

Improvement of thermoelectric properties for half-Heusler TiNiSn by interstitial Ni defects

J. Appl. Phys. 110, 063710 (2011)

The texture related anisotropy of thermoelectric properties in bismuth telluride based polycrystalline alloys Appl. Phys. Lett. 99, 124102 (2011)

Thermoelectric properties for single crystal bismuth nanowires using a mean free path limitation model

J. Appl. Phys. 110, 053702 (2011)

Thermopower and thermal conductivity of Kondo lattice CeCu4Al

J. Appl. Phys. 110, 043709 (2011)

Additional information on Appl. Phys. Lett.

Journal Homepage: https://www.sodocs.net/doc/4b4701978.html,/

Journal Information: https://www.sodocs.net/doc/4b4701978.html,/about/about_the_journal

Top downloads: https://www.sodocs.net/doc/4b4701978.html,/features/most_downloaded

Information for Authors: https://www.sodocs.net/doc/4b4701978.html,/authors

Improved thermoelectric properties of Mg2Si x Ge y Sn1?x?y nanoparticle-in-alloy materials

S.Wang1,a?and N.Mingo2

1LETI/DIHS/LCRF,CEA-Grenoble,17rue des Martyrs,38000Grenoble,France

2LITEN,CEA-Grenoble,17rue des Martyrs,38000Grenoble,France

?Received6April2009;accepted30April2009;published online21May2009?

We theoretically?nd that introducing nanoparticles into Mg2Si x Ge y Sn1?x?y alloys considerably improves their thermoelectric?gure of merit?ZT?.We have computed the thermal conductivity versus nanoparticle size of this class of nanocomposites for nine different material types at various temperatures.We provide validity ranges of nanoparticle concentration that will not reduce the thermoelectric power factor,but will considerably decrease the thermal conductivity.ZT enhancements of two times the alloy values are within reach.In particular,n-type Mg2Si0.4Sn0.6with Mg2Si or Mg2Ge nanoparticles stand out as one of the best materials for intermediate temperature ?800K?applications,providing a good nontoxic alternative to PbTe.?2009American Institute of Physics.?DOI:10.1063/1.3139785?

The nanoparticle embedded in alloy thermoelectric ?NEAT?material approach to improved thermoelectric per-formance has been investigated in several recent publications.1–6By including nanoparticles lattice matched with the alloy,the?gure of merit?ZT?can be greatly en-hanced.It has been demonstrated experimentally that ErAs nanoparticles in InGaAs matrix led to a50%reduction in thermal conductivity and a100%increase in ZT.2,5The ma-jor contribution of the nanoparticles is to decrease the ther-mal conductivity below that of the simple alloy by ef?ciently scattering phonons.It has been pointed out that the reduction is very large and is not very sensitive to the particle size in NEAT materials.6This is very advantageous for producing NEAT materials as the accurate control of the particle size is not essential to obtain high ZTs.

Mg2Si x Ge y Sn1?x?y alloys should be especially well suited to produce NEAT materials because they share a com-mon?uorite type structure with little variation between their lattice constants.The alloys Mg2Si and Mg2Ge have almost the same lattice constants??0.639nm?and Mg2Sn has a lattice constant of?0.677nm.7This allows one to conceive embedded nanoparticles seamlessly integrated in the matrix lattice,and completely dislocation free.The lack of disloca-tions has been identi?ed as an essential aspect of the NEAT approach,since only then one can have electronic transport unaffected while at the same time increasing pho-non scattering.2,3,6Magnesium silicide/germanide/stannide alloys are already excellent thermoelectric materials in bulk form.7,8They are being seriously considered as an improved alternative to PbTe,which is an undesirable source of toxic waste.Thus,it is very important to address whether Mg2Si x Ge y Sn1?x?y NEAT materials may have higher ZTs than the simple alloys,and how much improvement can be expected.

In order to assess the thermoelectric performance of Mg2Si x Ge y Sn1?x?y based NEAT composites,we have com-puted their thermal conductivity,and also estimated“safe”concentration limits within which the thermoelectric power factor is not expected to be reduced by the presence of nano-particles.The thermal conductivities of NEAT materials can be calculated by the method used in Ref.6.In contrast with that paper,which averaged together the three acoustic branches,in this letter we explicitly consider the three acous-tic phonon branches.9By using the frequency dependent re-laxation time approximation,the thermal conductivity of the alloy can be expressed as

??T?=?0?T?????2?df B dT d?,?1?

with f B?T?=1/?e??/k B T?1?.The function T???is related to the phonon dispersions and life times as10

T???=

?2

2?

?

i=1

3?

i

???

v i

?????i c?,?2?

where?is the step function and?i c are the branch cutoff frequencies taking the values of the maximum frequencies in the two transverse acoustic?TA?and one longitudinal acous-tic?LA?branches,respectively.10We make the linear ap-proximation for the acoustic phonon dispersions with branch sound speeds v TA and v LA,respectively.The values of the cutoff frequencies were extracted from Ref.11and the mea-sured sound velocities in Refs.12and13are used.Those values are given in Table I.

The total relaxation time contains the contributions of the anharmonic?a?,alloy disorder?d?,and nanoparticle?np?scatterings,

a?Electronic mail:shidong.wang@cea.fr.

TABLE I.Sound speeds?v?,cutoff frequencies??c?,and anharmonic scat-

tering parameters?B and C?of TA and LA phonons in different alloys.

v TA/v LA

?km/s?

?TA c/?LA c

?THz?a

B

?10?18Ks?

C

?K?

Mg2Si 4.9/7.7b29.7/52.3 2.147.0

Mg2Ge 3.9/6.2c27.2/40.5 2.835.6

Mg2Sn 3.0/4.9b13.9/22.4 2.037.0

a Reference11.

b Reference12.

c Reference13.

APPLIED PHYSICS LETTERS94,203109?2009?

0003-6951/2009/94?20?/203109/3/$25.00?2009American Institute of Physics

94,203109-1

??1=?a?1+?d?1+?np?1.?3?The anharmonic contribution is described by10

?a?1=B T?2e?C/T.?4?We obtained parameters B and C for alloys Mg2B?B

=Si,Ge,Sn?by?tting the calculated thermal conductivities

to their experimental values.7,11The?tted values are given in Table I.For Mg2A x B1?x?A,B=Si,Ge,Sn?alloys,we use the weighted average parameters:B=x B A+?1?x?B B and simi-

larly for C.The alloy disorder contribution is accounted for by using the effective medium approach14

?d?1=x?1?x?A?4,?5?where A AB=???M A?M B?/M AB?2+2??K A?K B?/K AB?2??3/?4?v3?with the atomic weight M,the force constant K, the sound velocity v,and?equal0.44times the lattice parameter in the anti?uorite structure case.This gives

A Mg

2SiGe

=2.38?10?41s3,A Mg

2

GeSn

=5.9?10?41s3,

A Mg

2SiSn

=1.0?10?40s3,which yield bulk alloy thermal

conductivities in good agreement with the experimental ones.7,15The nanoparticle contribution is

?np?1=v??s?1+?l?1??1?,?6?where?is the concentration of nanoparticles per unit vol-ume,v is the sound speed,and?s,l are the short and long wavelength cross sections,respectively,given by3,6,16,17?s=2?R2,?7?

?l=4?R 2

9??R v ?4???D D?2+3??K K?2?,?8?

where R is the nanoparticle radius,?D??K?is the difference between the densities?force constants?of the nanoparticles

and the matrix material,and D?K?is the matrix density ?force constant?.The force constants of Mg2B’s are estimated by K?v2D and we use the weighted values for the force

constants of Mg2A x B1?x’s,namely,K AB=xK A+?1?x?K B.

We have investigated nine different NEAT systems.

Three of them consist of the three binary matrices,with em-

bedded nanoparticles of the third remaining material:Mg2Sn

in Mg2Si0.4Ge0.6,Mg2Si in Mg2Ge0.4Sn0.6,and Mg2Ge in

Mg2Si0.4Sn0.6.The matrix alloy ratio x was chosen as the one

used in the experiments.7,8,15,18The other six combinations

studied are Mg2Si/Ge in Mg2Si0.4Ge0.6,Mg2Ge/Sn in

Mg2Ge0.4Sn0.6,and Mg2Si/Sn in Mg2Si0.4Sn0.6,correspond-

ing to nanoparticles of each of the two constituting pure

phases embedded into the alloys.

Nanoparticles in these materials strongly reduce the

composite’s thermal conductivities.As shown in Fig.1a

3.4%volume fraction of the nanoparticles may result in

about50%reduction below the matrices’thermal conductivi-

ties at300K.The relative reductions in the thermal conduc-

tivities in the nine composites are given in Table II.The

optimal nanoparticle diameters,minimizing the thermal con-

ductivities,depend on the involved materials but they are

always of the order of a few nanometers.The minimum?’s shown do not change appreciably if a different value of the bulk alloy thermal conductivity is used as a starting point, via a different A?c.f.Eq.?5??.This implies that the results remain robust without any need for a precise measurement of the bulk alloy?.It is indeed possible that the reduced?reported in Refs.19and20may have been caused by nucle-

ation of nanoparticles upon introduction of Sb atoms.How-

ever,even if this were the case,our results show that much

smaller?can be still achieved at rather low nanoparticle volume fractions.

We now give an upper bound estimation of the effect of

nanoparticles on the electron mobilities.We assume that no

dislocations or defects are introduced in the composites.The

effect of nanoparticles is negligible if their contribution to

the inverse mean free path is much smaller than the intrinsic

inverse mean free path of the pure alloy matrix.This is the

case when the nanoparticle volume fraction is smaller than ??R/3?matrix,where?matrix is the electron mean free path in the matrix,and R is the nanoparticle radius.6The estimated

screening length due to the electrons is about1nm at the

optimal carrier concentration,1019–1020cm?3given in Ref.

8.Therefore,the Coulomb scattering due to the charged

nanoparticles is effectively screened and is not taken into

account here.?matrix can be estimated from the experimental

electron mobility.As we have not found any systematic in-

vestigation of the electron mobility in Mg2A x B1?x alloys,we

use the weighted mobility?a=x?A+?1?x??B as an upper limit for the alloy mobility.The actual mobility and elec-tronic mean free path in the alloys are expected to be even smaller than these estimates.The values of Mg2B single crystal mobilities are given in Ref.8.At300K,the alloy electron mobilities?I?286cm2/Vs,?II?397cm2/Vs, and?III?333cm2/Vs,yielding the electron mean

free FIG.1.?Color online?Calculated thermal conductivities???of different Mg2Si x Ge y Sn1?x?y NEAT materials as a function of particle diameters at300 K and800K with3.4%nanoparticle volume fraction.The horizontal lines denote calculated?of??a?and?d??Mg2Si0.4Ge0.6,??b?and?e??Mg2Ge0.4Sn0.6,??c?and?f??and Mg2Si0.4Sn0.6matrices for comparison.

paths?I?13nm,?II?16nm,and?III?29nm.The indi-ces I,II,and III stand for Mg2Si0.4Ge0.6,Mg2Ge0.4Sn0.6,and Mg2Si0.4Sn0.6matrices,respectively.Thus for the3.4%vol-ume fraction used in calculations,the effect of nanoparticles larger than1.6nm?Mg2Si0.4Ge0.6and Mg2Si0.4Sn0.6?and2.8 nm?Mg2Ge0.4Sn0.6?are negligible.The optimal particle sizes in all nine NEAT materials are much larger than these values ?see Table II?.Therefore,we can safely neglect the effect of the nanoparticles on the electron mobility for the3.4%vol-ume fractions considered here.

As the nanoparticles have negligible effects on the elec-tron mobilities,an increased ZT is expected due to the re-duction in thermal conductivity.The estimated maximum ZTs in n-type materials at both300and800K are shown in Table II.The increases of ZTs in NEAT materials are about 150%at300K and73%at800K.For n-type Mg2Si0.4Sn0.6 with electron concentration of?1020cm?3,Ref.8reported a value of ZT?1.1at800K.This makes one expect ZT ?1.9for a composite with3.4%Mg2Si or Mg2Ge nanopar-ticle concentration.For p-type bulk materials,a value of ZT?0.14at450K for Mg2Ge0.4Sn0.6has been obtained,18 indicating that a ZT?0.27is possible with a Mg2Si or Mg2Ge in Mg2Ge0.4Sn0.6NEAT compound.Although pre-dicted values for some silicide nanoparticles in SiGe are slightly higher,the magnesium based NEAT compounds might be easier to grow in a dislocation free fashion,due to their aforementioned shared lattice structure.At least for Mg2Sn x Si1?x,a solubility gap up to x=0.9exists in the phase diagram21implying that nearly pure Mg2Si nanoparticles could be stable inside the alloy matrix.However,solubility of the particles into the matrix may be a concern in other cases with small or inexistent solubility gaps,particularly if using sintering approaches.For small device applications,an alternative growth route via deposition techniques,such as chemical vapor deposition,can grow nanodots inside mate-rials even for fully soluble systems,and could circumvent the problem above.

In conclusion,we have calculated the thermoelectric properties of different types of Mg2Si x Ge y Sn1?x?y NEAT ma-terials.A small concentration of3.4%nanoparticles can lead to reductions in thermal conductivities of?60%at300K and?40%at800K with the optimal particle size of a few nanometers.Moreover,the minimum of the thermal conduc-tivity is not very sensitive to the particle size.A best value of ZT?1.9at800K is obtained for Mg2Si or Mg2Ge nanopar-ticles in Mg2Si x Sn1?x,considerably higher than the best re-ported value for the alloys of1.1.Magnesium based NEAT composites are a promising nontoxic substitute for PbTe in intermediate temperature thermoelectric applications.

We are grateful to M.Plissonnier for bringing this prob-lem to our attention,and C.Navone, D.A.Broido,N.P. Kobayashi,A.Shakouri,and D.A.Stewart for discussions. S.W.acknowledges support from the Chimtronique program. 1K.F.Hsu,S.Loo,F.Guo,W.Chen,J.S.Dyck,C.Uher,T.Hogan,E.K. Polychroniadis,and M.G.Kanatzidis,Science303,818?2004?.

2W.Kim,J.Zide,A.Gossard,D.Klenov,S.Stemmer,A.Shakouri,and A. Majumdar,Phys.Rev.Lett.96,045901?2006?.

3W.Kim and A.Majumdar,J.Appl.Phys.99,084306?2006?.

4L.D.Chen,X.Y.Huang,M.Zhou,X.Shi,and W.B.Zhang,J.Appl. Phys.99,064305?2006?.

5Y.K.Koh,S.L.Singer,W.Kim,J.M.O.Zide,H.Lu,D.G.Cahill,A. Majumdar,and A.C.Gossard,J.Appl.Phys.105,054303?2009?.

6N.Mingo,D.Hauser,N.P.Kobayashi,M.Plissonnier,and A.Shakouri, Nano Lett.9,711?2009?.

7V.K.Zaitsev,M.I.Fedorov,I.S.Eremin,and E.A.Gurieva,in Thermo-electrics Handbook:Macro to Nano,edited by D.M.Rowe?CRC,Cleve-land,2006?,Chap.29.

8V.K.Zaitsev,M.I.Fedorov,E.A.Gurieva,I.S.Eremin,P.P.Konstan-tinov,A.Y.Samunin,and M.V.Vedernikov,Phys.Rev.B74,045207?2006?.

9D.T.Morelli,J.P.Heremans,and G.A.Slack,Phys.Rev.B66,195304?2002?.

10N.Mingo,Phys.Rev.B68,113308?2003?.

11J.J.Martin,J.Phys.Chem.Solids33,1139?1972?.

12Landolt-B?rnstein database,URL https://www.sodocs.net/doc/4b4701978.html,/laboe?SGWID ?0-10113-0-0-0.

13P.Chung,W.Whitten,and G.Danielson,J.Phys.Chem.Solids26,1753?1965?.

14B.Abeles,Phys.Rev.131,1906?1963?.

https://www.sodocs.net/doc/4b4701978.html,Botz,D.R.Mason,and D.F.O’Kane,J.Electrochem.Soc.110, 127?1963?.

16P.G.Klemens,Proc.Phys.Soc.A68,1113?1955?.

17J.M.Ziman,Electrons and Phonons?Oxford University Press,New York, 2001?.

18M.Fedorov,V.Zaitsev,I.Eremin,E.Gurieva,A.Burkov,P.Konstanti-nov,M.Vedernikov,A.Samunin,G.Isachenko,and A.Shabaldin,Phys. Solid State48,1486?2006?.

19Q.Zhang,J.He,T.J.Zhu,S.N.Zhang,X.B.Zhao,and T.M.Tritt,Appl. Phys.Lett.93,102109?2008?.

20Q.Zhang,H.Yin,X.B.Zhao,J.He,X.H.Ji,T.J.Zhu,and T.M.Tritt, Phys.Status Solidi A205,1657?2008?.

21I.Jung,D.Kang,W.Park,N.J.Kim,and S.Ahn,Calphad31,192?2007?.

TABLE II.Calculated matrix thermal conductivity??matrix?,maximum relative reduction in thermal conductivity,optimal particle diameter?a0?,and estimated ZTs in different n-type NEAT materials with3.4%nanoparticle volume fraction at300K.The values in brackets are at800K.

Matrix Mg2Si0.4Ge0.6Mg2Ge0.4Sn0.6Mg2Si0.4Sn0.6

Nanoparticle Mg2Si Mg2Ge Mg2Sn Mg2Si Mg2Ge Mg2Sn Mg2Si Mg2Ge Mg2Sn ?matrix?W/mK? 2.86?1.43? 2.38?1.18? 1.97?1.03?

?min NEAT/?matrix?%?60?78?63?81?50?69?44?63?43?62?46?65?40?59?39?58?43?62?

a0?nm?9.2?8.7?11.9?11.4? 4.2?3.7? 5.9?5.2? 5.7?5.1?7.3?6.5?7.6?6.6?7.0?6.0?9.6?8.4?ZT matrix0.2a0.1b,c0.2?1.10?c

ZT NEAT0.330.320.400.230.230.220.49?1.86?0.51?1.90?0.46?1.76?

a Reference15.

b Reference7.

c Reference8.