REVIEWS. Engineering half-heusler thermoelectric materials using Zintl chemistry

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1 Engineering hlf-heusler thermoeletri mterils using Zintl hemistry Wolfgng G. Zeier 1, Jennifer Shmit, Geoffroy Hutier 3, Umut Aydemir 1, Zhry M. Gis 4, Cludi Felser 5 nd G. Jeffrey Snyder 1 Astrt Hlf-Heusler ompounds sed on XNiSn nd XCoS (X = Ti, Zr or Hf) hve rpidly eome importnt thermoeletri mterils for onverting wste het into eletriity. In this Review, we provide n overview on the eletroni properties of hlf-heusler ompounds in n ttempt to understnd their si struturl hemistry nd physil properties, nd to guide their further development. Hlf-Heusler ompounds n exhiit semionduting trnsport ehviour even though they re desried s intermetlli ompounds. Therefore, it is most useful to onsider these systems s rigid-nd semiondutors within the frmework of Zintl (or vlene-preise) ompounds. These onsidertions id our understnding of their properties, suh s the ndgp nd low hole moility euse of interstitil Ni defets in XNiSn. Understnding the struturl nd onding hrteristis, inluding the presene of defets, will help to develop different strtegies to improve nd design etter hlf-heusler thermoeletri mterils. 1 Deprtment of Mterils Siene nd Engineering, Northwestern University, Evnston, Illinois 60208, USA. 2 Institut für Anorgnishe und Anlytishe Chemie, Johnnes Gutenerg Universität, Studingerweg 9, Minz, Germny. 3 Institute of Condensed Mtter nd Nnosienes (IMCN), Université tholique de Louvin, 1348 Louvinl Neuve, Belgium. 4 Division of Chemistry nd Chemil Engineering, Cliforni Institute of Tehnology, Psden, Cliforni 91125, USA. 5 Mx-Plnk-Institut für Chemishe Physik fester Stoffe, Nöthnitzer Strße 40, Dresden, Germny. Correspondene to G.J.S. jeff.snyder@northwestern.edu Artile numer: doi: /ntrevmts Pulished online 17 My 2016 The inresing demnd for lterntive energy tehnologies hs sprked renewed interest in thermoeletri mterils, whih diretly onvert wste het into eletriity. As solid-stte energy onverters, thermoeletris offer simpliity ompred with onventionl systems tht rely on vpour-ompression yle. Thermoeletri genertors hve een suessfully used in spe missions using rdioisotope het soures, whih lst more thn 30 yers 1. In nother exmple, the utomotive industry is investigting thermoeletri mterils for reovering wste het from exhust systems 2, in whih ost, reliility nd sfety, s well s effiieny, re importnt onsidertions. Unfortuntely, the thermoeletri onversion effiieny of these devies is generlly low euse, like ny thermodynmi het engine, it is limited y the Crnot effiieny (tht is, the mximum thermodynmilly possile effiieny of het engine) nd lso y the effiieny of the thermoeletri mteril itself, hrterized y the figure of merit (termed zt). The sis of thermoeletri trnsport nd the different pprohes to improve zt re explined in BOX 1. Strtegies to develop more effiient thermoeletris inlude the investigtion of mterils suh s skutterudites 3,4, lthrthes 5 8, hlopyrites 9 11 nd other Zintl ompounds 12 16, or the engineering of existing thermoeletri mterils Mny of these mterils hve promising thermoeletri properties euse of their omplex rystl nd eletroni strutures. More speifilly, most of these mterils n e onsidered s Zintl ompounds, whih omprise eletropositive tions tht donte their vlene eletrons to form n nioni frmework nd losed vlene shell onfigurtion hieved y omining forml hrge trnsfer with ovlent onding (BOX 2). As onsequene of the omplex nion frmework tht ontriutes to low lttie therml ondutivity, Zintl ompounds n hve lrge unit ells 26. Zintl phses n e lloyed to ontrol their rrier onentrtion nd to influene the eletron nd phonon trnsport. In ddition, simple vlene rules n e used to find new ompositions 13 16, Hlf-Heusler ompounds with the omposition XNiSn nd XCoS (X = Ti, Zr or Hf) hve eome importnt thermoeletri mterils for use in wste het reovery pplitions. This is euse of their high thermoeletri performne, low toxiity, reltively inexpensive elementl omposition nd roust mehnil properties. As onsequene of their high lttie therml ondutivity, muh prior work hs foused on the redution of the therml ondutivity y vrying the hemistry, proessing nd mirostruture of the ompounds 31,32. There re mny ompounds nd lloys (tht is, solid solutions nd mixtures with other hlf-heusler phses or smll quntities of other struturl types) with the hlf-heusler struture displying rih hemistry tht re studied for vrious different physil properties (for exmple, mgnetism nd hlf-metlliity) 32 38, leding to greter interest in the understnding of the eletroni struture nd the predition of new phses NATURE REVIEWS MATERIALS ADVANCE ONLINE PUBLICATION 1

2 Hlf-Heusler ompounds re generlly onsidered to e simple intermetlli ompounds nd re therefore regrded s very different kind of thermoeletri (typilly semionduting) mteril. Although hlf-heusler ompounds re not often onsidered s Zintl ompounds 42, mny of the sme onding nd doping priniples developed for Zintl ompounds re helpful in explining nd understnding the struture nd onding in hlf-heusler ompounds, s well s improving nd prediting new mterils. This knowledge ould led to n improvement in the thermoeletri properties of these mterils. In this Review, we use pulished dt of n type XNiSn (X = Ti, Zr or Hf) hlf-heusler ompounds to expnd our understnding of their hemistry nd eletroni properties. We provide simplified model for the eletroni nd trnsport properties of hlf-heusler mterils, hopefully leding to etter understnding of possile strtegies nd limittions in optimizing the thermoeletri effiieny. Box 1 Strtegies for improving the thermoeletri effiieny The effiieny of thermoeletri mteril is governed y its figure of merit, termed zt. This depends on the Seeek oeffiient (thermopower), α, eletril ondutivity, σ, therml ondutivity, κ, nd the temperture of opertion, T. The therml ondutivity itself is sum of its therml nd eletroni ontriution, κ L nd κ el, respetively. Although mny of these prmeters re hevily interdependent 49 for exmple, lrge α usully results in low σ, or lrge σ inreses κ there re wys to optimize or deouple these different prmeters. For exmple, optimiztion n e hieved y ontrolling the rrier onentrtion of mteril (pnel ), euse eh of these prmeters is dependent on the mount of moile rriers 14,49. A low therml ondutivity (pnels, nd d) n e hieved y inhiiting the trnsport of het through lttie virtions lled phonons. A ommon pproh is to introdue oundries from nnometre-sle mirostrutures (pnel ) tht stter phonons t interfes 19, Low verge phonon veloity n e hieved with very omplex rystl strutures (pnel ) of different onding environments nd lrge unit ells 14,15,26. Superioni mterils exhiit high disorder sttering nd liquid-like phonon ehviour 120,121 (pnel d). Simultneously, high thermopower nd high eletril ondutivity n e otined y multiple degenerte vlleys in the nd struture (pnel e) tht is enhned y nd onvergene 17,18,122,123. Crrier onentrtion zt zt α σ α 2 σ κ el κ L e High vlley degenery Energy (ev) E F Crrier onentrtion (m 3 ) Density of sttes Optimize rrier onentrtion zt = α 2 σt κ Lower therml ondutivity Improve thermopower Sttering of phonons Complex strutures d Phonon liquids 2 ADVANCE ONLINE PUBLICATION

3 Box 2 Struturl motifs in Zintl ompounds Zintl phses or ompounds re solids omprising very eletropositive tions (suh s group 1 nd 2 elements) nd the more eletronegtive, non-metlli elements of group 13 to 16. In Zintl phses, suh s NTl, FeS 2 or CSi, the most eletropositive omponent dontes ll vlene eletrons to the nion. Aording to the Zintl Klemm onep3 25, the nion forms ovlently onded sustruture in whih the resulting Zintl frmework forms ording to its vlene eletron ount in similr mnner to simpler strutures 22. For exmple, the Zintl nion Tl in NTl exhiits four vlene eletrons nd forms (following the otet rule) dimond struture 23 with N + s the ounter ion. Other exmples re pyrite (FeS 2 ), in whih S 2 2 pirs form, nd CSi, in whih Si 2 form ontinuous silion hins ording to the vlene eletron ount of elementl sulfur. C 3 AlS 3 nd C 14 AlS 11 re prominent exmples for good thermoeletri Zintl phses with infinite tetrhedrl (AlS 4 ) n hins 15,28,29,124,125, nd AlS 4 9 tetrhedr nd S 3 7 dumells, respetively These ovlently onded Zintl frmeworks provide n idel sffold for thermoeletri optimiztion y mens of doping 12 14,16,26,49,129. NTI FeS 2 CSi C 3 AIS 3 C 14 AIS 11 Furthermore, onsistent piture for XNiSn is only rehed y inluding disordered, interstitil Ni with out 5% oupny on the full-heusler site, whih is nominlly vnt in the hlf-heusler struture. Also, in this se, Zintl hemistry n help to explin why Ni on this site does not led to eletroni doping, ut insted signifintly hnges the vlene nd struture. The vlene nd produed y the interstitil Ni is very nrrow, produing hevy, low moility holes. Zintl hemistry in hlf-heuslers Hlf-Heusler ompounds re often desried s intermetllis with 1:1:1 stoihiometry of three interpenetrting fe-entred ui (f) sultties 33. In this Review, we use the generl formul XYZ for thermoeletri hlf- Heusler ompounds in whih, unless designted otherwise, X (Ti, Zr or Hf), Y (Ni or Co) nd Z (Sn or S) re loted t the Wykoff positions: X oupies 4 (0, 0, 0), Y oupies 4 (1/4, 1/4, 1/4) nd Z oupies 4 (1/2, 1/2, 1/2). The Wykoff position 4d (3/4, 3/4, 3/4) mkes n unoupied fourth f sulttie, whih would result in the full-heusler XY 2 Z struture if filled with more Y toms. In the hlf-heusler struture, position 4 is unique, eing qurter of ell (tetrhedrlly oordinted, nlogous to ZnS) wy from oth other sultties, whih re hlf ell (othedrlly oordinted, nlogous to NCl) shifted from eh other. Swithing ll of the X nd Z elements on the 4 nd 4 positions results in the sme, ut inverted, struture, ut swithing X or Z with the Y element would mke different mteril. Thus, there ould, in priniple, e three distint vrints for the elements XYZ with hlf-heusler strutures depending on whih element is in the tetrhedrl (4) site 46. However, s result of the hemistry, only one vrint is stle. In some ses, different site is ssigned to e vnt, resulting in different lltetrhedrl site 46. For exmple, 4 n e vnt nd 4d n e filled, whih mkes 4 the ll-tetrhedrl site 47. A initio lultions onfirm tht the differenes re signifint 33, nd, s result, it is importnt to relize tht some dtses (for exmple, the Inorgni Crystl Struture Dtse (ICSD)) hve the positions of the elements ssigned inorretly. Hlf-Heusler ompounds hve sustruture similr to dimond-like ZnS lttie (FIG. 1). This sustruture is formed y the elements with the smllest differene in eletronegtivity, usully Y s Ni or Co nd Z s Sn or S. Typilly, the most eletronegtive element Z (Sn or S) NATURE REVIEWS MATERIALS ADVANCE ONLINE PUBLICATION 3

4 Figure 1 Shemti representtion of the hlf-heusler struture. Hlf-Heusler ompounds hve the omposition XYZ, onsisting of ovlent, dimond-like (or ZnS) sustruture of the (YZ) n Zintl hemistry frmework (purple tetrhedr) formed y the tetrhedrl oordintion of Y toms (purple) nd Z toms (lue). The eletropositive X n+ (red) fills the othedrl voids round the tetrhedrl frmework. nd the most eletropositive element X (often Ti, Zr or Hf), whih hve the most ioni intertion, form the NCl sulttie (4 nd 4) with othedrl oordintion, leving the ll-tetrhedrl site to the intermedite eletronegtive element Y (Ni or Co). This is not lwys the se; for exmple, MgAgAs is n exeption, whih is notle euse it is often onsidered to e the struturl prototype 33. In the MgAgAs struture, the most eletronegtive element, As, is on the ll-tetrhedrl site rther thn the intermedite eletronegtive element, Ag. If the nming of the ompound is to mth those of other hlf-heusler ompounds, the formul should e given s MgAsAg. Hlf-Heusler ompounds n exhiit semionduting trnsport ehviour even though they re desried s intermetlli ompounds. In this Review, however, we define true intermetlli ompounds s metls tht hve well-defined rystl strutures in whih the eletroni onfigurtion my not e desried y simple losed-shell pproh (tht is, using Zintl hemistry desription). Indeed, y pplying the onepts of Zintl ompounds to hlf-heusler ompounds, s proposed y Whngo nd o-workers 48, we n simplify the disussion nd understnding of these mterils, similr to how our understnding of other omplex semiondutors hs een ided y the sme pproh 14,49. The numer of eletrons in mny simple semiondutors n generlly e explined with simple vlene ounting rules tht ount for the numer of eletrons required to fill the vlene nd (often onding) oritls seprted y ndgp with the empty ondution nd (often ntionding) oritls. The semionduting hlf-heusler ompounds re frequently ssoited with n 18 eletron rule (or sometimes 8 eletron rule, s in LiAlSi (REF. 33)), whih suggests tht it my e helpful to desrie hlf-heusler ompounds in the sme wy tht we desrie omplex semiondutors 34,48,50. Zintl ompounds typilly ontin metlli elements tht form onds nd eletroni strutures reminisent of non-metls 23. In Zintl (s opposed to intermetlli) ompounds, the struture nd onding strongly orrelte to the vlene eletron ount (VEC) tht drives stility nd eletroni struture. A orreltion etween the struturl pttern nd the vlene eletron numer is therefore neessry for the desription of ompound s Zintl phse 24. The vlene eletron rule for XYZ hlf-heusler ompounds n e rtionlized in the Zintl Klemm onep5, in whih the most eletropositive element X dontes ll of its vlene eletrons to the more eletronegtive elements Y nd Z. As result, hlf-heusler ompounds n e desried s X n+ (YZ) n. Y nd Z form ovlent tetrhedrlly onded sulttie, ting s Zintl-nion frmework kone (purple tetrhedr in FIG. 1), with similr eletroni struture to the ovlently onded struture of ZnS or Si with the zin lende (or dimond) struture (see the NTl struture in BOX 2). In the se of LiAlSi, the (AlSi) nion hs the sme eletroni onfigurtion s Si with Li + in the othedrl holes to lne the hrge 33. As onsequene of the trnsfer of eletrons, eh of the elements rehes losed-shell onfigurtion, leding to n 8 eletron onfigurtion for LiAlSi nd n 18 eletron onfigurtion for XYZ, in whih Y is d 10 trnsition metl. The struture, onding nd stility reltionship in Zintl ompounds n e filitted y eletron ounting using Zintl vlene onept. In generl, Zintl ompounds re thought to omprise ovlently onded network of omplex nions in whih the hrge is lned y simple tions tht donte their vlene eletrons to reh nole gs onfigurtion. Trditionlly, the VEC nd otet rule ( = 8 VEC, where is the numer of onds) were used to predit onding in Zintl phses 51. Now, Zintl hemistry vlene onept is more useful euse the onds n e esily oserved from the struturl refinements, nd we need to understnd the eletroni struture in terms of doped or metlli Zintl ompounds 52. Here, we define the vlene of n tom (following the otet 8 N rule, where N is the numer of onds) 53 s the numer of exess eletrons n tom rings to the struture reltive to the numer of eletron oritls it is dding to the vlene nd: V = e (1) V = e + 8 (2) For eh tom (where denotes tions nd denotes nions), V is the vlene, e is the numer of vlene eletrons nd is the numer of onds 14. For exmple, in LiAlSi, Li is Li + euse it dontes one eletron to form (AlSi), ut Li does not ontriute to the numer of oritls in the vlene nd. Eh of the four-onded Al (with e = 3) nd Si (e = 4) sites require four ( = 4) eletrons per tom for the onding, giving Al 1 vlene of 1 nd Si 0 vlene of 0. The stoihiometri sum of the vlenes in LiAlSi is 0, nd, s result, Zintl semiondutor n e expeted from the eletroni struture. It should e noted tht the vlene of ovlent tom my not well 4 ADVANCE ONLINE PUBLICATION

5 d e Ni 0 Y Sn 4 Z p x p y p z s d xy d xz d yz d z 2 d x 2 y 2 (NiSn) 4 (YZ) n ZrNiSn XYZ Zr 4+ X n+ * * * 1 * 1 e g g e p x p y p z s d z 2 d x 2 y 2 d xy d xz d yz f Energy E g (YZ) n s p oritls (ntionding) X n+ d oritls Y d oritls Y nd X d oritls (non-onding) g Energy E F (ev) Ni Sn Zr p x p y p z s 1 e 1 X n+ d nd (YZ) n s p oritls (onding) Density of sttes Density of sttes Figure 2 Density of sttes evolution vi moleulr oritls. Colour-oded tomi oritls of tetrhedrlly oordinted Ni in zero vlene (d 10 ) onfigurtion (pnel ) nd the more eletronegtive (tht is, tomi oritls re lower in energy) Sn 4 (pnel ). The resulting moleulr oritls of (NiSn) 4 with the onding nd ntionding s or p oritls re shown in pnel ; the filled Ni d oritls re non-onding. Moleulr oritls of ZrNiSn nd the tomi oritls of Zr 4+ re depited in pnel d nd e. The intertion of the Ni nd Zr d oritls leds to ndgp nd forms the vlene nd ondution nds, nd results in vlene nd edge with Zr d hrter (pnel d). Pnel f is the shemti formtion of the density of sttes in X n+ (YZ) n. The s p onding oritls of the tetrhedrlly (sp 3 hyridized) oordinted Zintl-nion frmework form the lower energy vlene nd (lue) with the X n+ tion ontriution in the vlene nd edge (ornge), euse of the X n+ d oritl intertion with the YZ n frmework. The lolized, non-onding d oritls of Y form flt nd hevy vlene nd (purple). Pnel g depits the lulted prtil density of sttes of ZrNiSn, showing the different elementl ontriutions (Supplementry informtion S1 (ox)). E F, Fermi energy. represent its hrge, s demonstrted y Al 1 ; it would e more urte to lulte the hrge from the eletron density 50. Alterntively, ll of the (AlSi) onding oritls n e ssigned to Si rther thn eqully shred with Al, mking Al tion nd resulting in vlenes Al 3+ nd Si 4 tht mth the expeted isolted ioni hrge. Regrdless of the proedure used to ssign vlene (for exmple, Al 1 or Al 3+ ove), (AlSi) hs the orret numer of vlene oritls to e semiondutor. Zintl ompounds tht ontin trnsition metls n e derived from inry ompounds in the sme wy tht other Zintl ompounds n, s long s the d eletrons re ounted for in the vlene ount 51. Hlf-Heusler ompounds ontining trnsition metls n e understood y nlogy. To this end, the onding environment in hlf-heusler ompounds nd the evolution of the moleulr oritls 33 re given in FIG. 2 e. The tomi oritls nd moleulr oritls hve een olour oded to depit different elementl ontriutions. In the se of ZrNiSn, the nion network of (NiSn) 4 is four-onded dimond-like sustruture tht forms onding nd ntionding moleulr oritls of the forml nion sttes (YZ) n. Beuse this is tetrhedrl onding environment, these onding nd ntionding moleulr oritls normlly omprise Ni nd Sn s nd p tomi oritls 33. There will, however, e some intertion etween the Ni d oritls of the sme symmetry nd the Sn 4 s nd p oritls, leding to slight inrese in the 1 * nd * moleulr oritl energies nd derese in the e nd moleulr oritl energies 45. The intertion of the Ni d tomi oritls in the (NiSn) 4 moleulr oritl (FIG. 2) with the more eletropositive Zr 4+ d tomi oritls in its othedrl rystl field environment results in splitting (onding intertion) of the Ni nd Zr 4+ d oritls. This intertion leds to the ndgp in hlf-heusler ompounds omprising two trnsition metls 33,45. Furthermore, mixing or intertion of the p-onding oritls of (NiSn) 4 n e expeted with Zr 4+ d oritls tht hve pproprite symmetry in the othedrl Sn oordintion environment (indited in FIG. 2d,e ut omitting full othedrl moleulr oritl digrm). The intertion of Zr 4+ d oritls with the onding p oritls of the nioni frmework introdues vlene nd edge with Zr 4+ d oritl hrter. The moleulr oritl pproh n e trnslted into density of sttes 54, enling simplified shemti of the density of sttes of ZrNiSn (FIG. 2f). The tomi oritls of Zr 4+ re higher in energy euse of the higher eletropositive hrter, nd therefore the oritl ontriutions to the ondution nd re from the intertion etween Zr 4+ d oritls nd Ni d oritls. The filled d oritls will hve mostly Ni like hrter. However, it should not e forgotten tht there is mixing of the Zr 4+ nd Ni d oritls, whih n e seen in the lulted prtil density of sttes (FIG. 2g), in whih there is some Zr 4+ ontriution, lthough less thn Ni, to the flt d nd. The flt Ni d oritls re not t the vlene nd edge euse of lrger overlp of the onding s nd p oritls. This leds to wider nd dispersion, s well s the intertion etween Ni d nd Sn s p oritls, whih move the Ni d oritls further downwrds in energy. Density funtionl theory (DFT) NATURE REVIEWS MATERIALS ADVANCE ONLINE PUBLICATION 5

6 lultions onfirm this generl piture for the eletroni struture in FIG. 2g, in whih mostly X element d-oritl hrter n e found t the vlene nd edge s onsequene of the intertion with the (YZ) n onding oritls 43,55. The lulted oritl projeted prtil density of sttes nd full nd struture n e found in Supplementry informtion S2 S4 (figures). These energeti onfigurtions n hnge depending on the omposition of the mteril. A stronger Y nd Z onding intertion will inrese the energy seprtion of the onding nd ntionding moleulr oritls ( 1, nd 1 *, *), resulting in n s or p vlene nd t lower energies nd Y d oritls t the vlene nd edge. By ontrst, the sustitution of X (for exmple, Zr) with n element of higher eletronegtivity (lower in energy) will ultimtely inrese the influene of X on the hevy Y d oritls, leding to hnges in eletroni trnsport. Ni hs full d 10 eletron onfigurtion tht overlps with the s p onding oritls of (NiSn) 4 (FIG. 2). This hs een onfirmed y DFT lultions, whih show tht ll of the flt nd hevy d nds re well elow the Fermi level 48. These lolized non-onding d oritls require ten eletrons for eh Ni tom or ll ten vlene eletrons tht Ni tom ontriutes. Vlene nd sttes for holes, hving some influene from the Ni d nd, re hevy nd therefore exhiit low rrier moility. This is in ontrst to the reltively light ondution nd, whih leds to the etter n type performne ompred with the p type performne in ZrNiSn (REFS 56,57). The size of the ndgp tht is formed depends on the hyridiztion etween the d oritls of X nd Y, s well s the ond strength etween Y nd Z, in this se Ni nd Sn, nd more speifilly their s p-oritl intertion 33. For X = Ti, Zr or Hf, the ndgp is essentilly the sme for the different tions 43, euse their eletronegtivity is similr. Therefore, solid solutions or even omposites with these tions should hve reltively little effet on the ndgp nd other eletroni properties, whih is indeed the se 43. However, hemilly different tions, suh s N, hve lredy een shown to inrese the ndgp nd the density-of sttes effetive mss in the ondution nd 58. The ndgp of XCoS is found to e lrger thn the ndgp in XNiSn (REF. 59), euse the ovlent (YZ) n network hnges signifintly etween the lloys (Co oritls re higher in energy thn Ni oritls) 60, nd the energeti seprtion of the onding nd ntionding oritls is lso lrger. This lrge ndgp suppresses the onset of ipolr ondution ompred with the XNiSn system, llowing good thermoeletri performne in p type XCoS t tempertures higher thn 1,000 K (REF. 61). Chnges or sustitutions of the Y or Z elements n e expeted to engineer the ndgp nd effetive mss, m*, depending on eletronegtivity nd ond strength. A similr eletroni struture to XNiSn is oserved in ternry ompounds desried with vlene (X 4+ ) 3 (Y 0 ) 3 (S 3 ) 4 with X = Zr or Hf nd Y = Ni or Pt (REF. 42). Desriing the onding nd eletroni intertions using Zintl onept is vlid nd provides good understnding of how the different onding intertions in hlf-heusler ompounds influene the eletroni density of sttes. Using qulittive sheme of moleulr oritls leves us with good explntion for the lulted prtil density of sttes (FIG. 2). Hlf-Heusler defet hemistry The Zintl Klemm onept for onding nd vlene n lso e used to understnd defets in hlf-heusler mterils. Point defets, suh s tomi vnies, tomi impurities nd interstitil toms, pper to ontrol the therml nd eletril trnsport properties in hlf-heusler mterils in even more wys thn in typil semiondutor. For exmple, in Zr 4+ NiSn 4, the vlene eletrons of the X n+, in this se Zr 4+, re needed to fill the (NiSn) 4 onding oritls tht mke up the vlene nd, similr to LiAlSi. Aliovlent sustitution of Zr 4+ with n element of different vlene (for exmple, S 3+ ) should lter the eletron ount in n esily preditle wy (resulting in p type mteril with S sustitution) ; however, isovlent sustitution of Zr (for exmple, with Ti or Hf) should hve little effet. For n type mterils, the sustitution of elements with elementl neighours in the periodi tle ontining dditionl eletrons, suh s S on Sn sites, is effetive nd esily explined within Zintl hemistry vlene onept. Similrly, tion doping for p type mterils nd nion doping for n type mt erils is expeted to e most effetive nd lest disruptive to eletron trnsport 65,66. Vnies n lso e understood within the Zintl onding onept. Ctions, suh s Zr 4+, donte eletrons, dding oritls to the ondution nd, ut not to the vlene nd; euse the numer of vlene nd oritls is unltered, tion vnies led to eletron defiieny or p type eletroni trnsport 12,16. Anion vnies led to exess eletrons in ioni mterils euse of the removl of vlene oritls, ut in ovlent strutures the vlene oritls re still needed for onding (or n e interpreted s dditionl lone pir oritls in, for exmple, BGe 5 nd B 8 Ge 43 ) For Ni vnies in Zr 4+ NiSn 4, this mens tht the lolized d oritls re removed from the system, ut the four dditionl eletrons needed per (NiSn) 4 re required for sp 3 tetrhedrl onding. Ultimtely, Ni vnies or exess Ni (with d 10 onfigurtion) should e lrgely eletron neutrl (effetively Ni 0 y ssigning onding (NiSn) 4 oritls to Sn s Sn 4 ) suh tht non-stoihiometry in the form of ZrNi 1+ x Sn n e expeted to not move the Fermi level outside the ndgp (tht is, not t s n effiient dopnt). However, nti-site defets (for exmple, Ni on Sn sites) re expeted to e muh higher in energy euse the Zintl desription gives eh element very different funtion nd vlene. Indeed, no nti-site defets ut signifint nonstoihiometry in ZrNi 1± x Sn with x = ~0.05 hve een oserved 47,70 72 in nominlly stoihiometri ZrNiSn, in whih t lest 5% of the Ni is on the interstitil 4d site, whih is fully oupied in the full-heusler struture 70, Suh lrge mount of exess Ni in undoped ZrNiSn (typilly displying intrinsi ut slightly n type ehviour) implies tht the extr Ni is primrily unhrged, requiring liovlent sustitution (for exmple, S on Sn sites) for extrinsi semionduting properties. 6 ADVANCE ONLINE PUBLICATION

7 Energy Oservle ndgp E g Interstitil Ni in-gp sttes E F Density of sttes Although interstitil Ni should not e strong dopnt, signifint effets on the eletroni nd struture re expeted if x is lrge in ZrNi 1+ x Sn y dding filled d oritls to the eletroni struture. The experimentl ndgp, E g (round 0.15eV) 64,76, of ZrNiSn is muh smller thn expeted y DFT (0.5 ev) 42,43,77. This is highly unexpeted euse DFT usully underestimtes, not overestimtes, the ndgp 78. Exess Ni on interstitil sites re expeted to produe filled (eh Ni interstitil site ontriutes ten eletrons with its d oritls) in gp sttes 79 81, shown shemtilly in FIG. 3. The interstitil Ni d oritls re filled nd, hene, the Fermi level is not expeted to e pinned in the impurity sttes. Interstitil d oritls hve poorer onding with Z toms thn with the norml Y toms nd re therefore higher in energy. Considering the moleulr oritls (FIG. 2d), it is esily understndle tht non-interting d oritls will led to dditionl sttes in the ndgp. These interstitil sttes hve een lulted 72,79 to e ner the ondution nd edge in ZrNi 1+ x Sn (FIG. 3). The presene of these sttes nd of disordered toms re needed to explin the therml nd eletroni trnsport properties of ZrNiSn, suh s the predominne of disorder sttering similr to n lloy for oth eletrons nd phonons even in unlloyed ZrNiSn 64,76,81,82, nd hve een oserved diretly y X ry photoeletron spetrosopy 71,83. Despite drstilly redued ndgp s result of the Ni interstitil nd, n type XNiSn is not overwhelmed y ipolr ondution euse the holes hve very low moility 84. Normlly, when the ndgp is smll reltive to the therml energy, k B T, minority rriers of the opposite sign will e thermlly exited. These minority rriers will redue the thermopower, α, ut only if they hve ppreile moility, μ (REF. 85). This is euse the totl thermopower, α totl, for multiple rriers is given y the sum of individul α, weighted y the individul eletril ondutivity, σ (REF. 86): α totl = (α n σ n + α p σ p )/(σ n + σ p ) (3) Energy (ev) Figure 3 In gp sttes formtion vi d oritls from interstitil Ni. Shemti digrm of the density of sttes in Xn+(YZ)n showing the in gp Ni sttes (purple) resulting from intrinsi defets. These extr sttes in the ndgp led to smller oserved optil ndgp, Eg (REF. 64). Clulted nd struture showing the nd within the energy gp ner the ondution nd edge 79. EF, Fermi energy. R Γ X M Γ The flt Ni interstitil nds hve high m* nd therefore low μ nd low σ (σ = neμ). This impurity vlene nd hs suh low moility tht its ility to redue the thermo power is suppressed until higher tempertures re rehed. The effetive ndgp in n type XNiSn is 0.3 ev insted of the tul 0.15 ev gp 64. The soluility of exess Ni my lso e relted to mirostruture nd therefore to strtegies tht redue therml ondutivity y forming omposites 87. For exmple, the disorder of Ni defets in XNi 1+ x Sn dds entropy tht enhnes the temperture dependene of the Ni soluility. This should led to solid-stte nnoprtile preipittion mehnisms 88, whih my explin full-heusler endotxil nnoprtile formtion in hlf-heusler ompositions 89,90. Suh nnoprtile omposites hve not only een studied for their ility to redue lttie therml ondutivity ut lso for their possile effets on the eletroni struture 32, In the se of XCoS, X dontes four vlene eletrons forming CoS 4 suunit, in whih Co exhiits nominl vlene of 1 to form the d 10 onfigurtion. A Co vny will not e eletron neutrl unless it forms lolized d 9 onfigurtion, whih is unlikely. Thus, XCoS is expeted to remin stoihiometri, s hs een oserved experimentlly 91, in ontrst to XNi 1+ x Sn. Empiril trnsport model in hlf-heuslers The predition of the semionduting trnsport properties of Zintl phses using m* hs proved to e powerful tool to understnd nd optimize these mterils 10,15,16,28,29,92. Models using m* impliitly fit trnsport dt to proli nd model, in whih devitions from the model n e used to identify multi-nd or nonproli nd effets 93,94. In this Review, we ttempt to understnd hlf-heusler ompounds using m* to onfirm the piture of Zintl ompound semi ondutor. Reders re referred to My et l. 92 for detiled informtion on the methods used. Even though it would e of interest to understnd the properties of hlf-heusler ompounds t high tempertures, t whih the zt is highest, the model used is most urte t low tempertures in the region of single rrier type. Furthermore, there is signifint lk of Hll-effet dt t higher tempertures. As result, we nlyse the pulished Seeek oeffiient, α, s funtion of Hll rrier onentrtion, n H, for vrious n type XNiSn lloys 82, t 300 K (FIG. 4). A tle of the hemil ompositions of these hlf-heulser ompounds nd their orresponding trnsport dt (Seeek oeffiient nd rrier onentrtion) n e found in Supplementry informtion S5 (tle). FIGURE 4 ompres trnsport dt with modelled Pisrenko reltion (α s funtion of n H ) using the prmeters for m*, nd drift moility, μ 0, otined y Zhu nd ollegues 82. Unfortuntely, similr nlysis for p type XNiSn is not possile euse of lk of good Hll dt, possily s result of the low moility of the holes. The dt in FIG. 4 generlly follow the trend of semiondutor, orroorting the Zintl hemistry formlism nd the onlusion of semiondutor-type nd ehviour in the hlf-heusler ompound, XNiSn. However, there is sustntil stter in the dt, whih my e NATURE REVIEWS MATERIALS ADVANCE ONLINE PUBLICATION 7

8 α (μv K 1 ) XNiSn XCoS 1 x Sn x n H (m 3 ) Figure 4 A Pisrenko plot of hlf-heusler ompounds. The Seeek oeffiient, α, s funtion of the Hll rrier onentrtion, n H, for vrious n type XNiSn (REFS 82,95 105) nd p-type XCoS (REF. 114) hlf-heusler ompounds t 300 K. For n type XNiSn, the dt otined using the prmeters of Xie et l. 82 revel n effetive mss, m*, of 2.9 m e nd drift moility, μ 0, of 30 m 2 Vs 1, nd show tht semionduting nd model desries the trend for XNiSn hlf-heusler ompounds. There is sustntil stter in the m* of literture dt tht my e onsequene of impurities nd ompositionl vritions. For p type XCoS, lrger m* (10 m e ) nd smller μ 0 (3.6 m 2 Vs 1 ) 114 is shown. relted to impurity phses nd multiple omponents in lloys. Multiphse ehviour n led to signifint devitions from the single m* model euse of in homogeneous rrier onentrtions or nd struture 106. It is well known tht hlf-heusler ompounds re prone to the formtion of impurities, influened y the omposition nd synthesis proedure 38. For exmple, the XNiSn phse ppers to require syntheti Ni exess 73,82 with the exess Ni in the empty fourth sulttie, resulting in the forementioned in gp sttes. At lrge vlues of x metlli full-heusler inlusions n nulete 31, , strongly influening the eletril ondutivity nd pprent rrier onentrtion even efore suh prtiles form peroltion pth 106. Furthermore, it hs een shown tht even smples tht seem to e phse pure n e omposed of multiple hlf-heusler phses with only slight vritions in lttie prmeters nd therefore smll differenes in stoihiometry nd rrier onentrtion 112. The stter in the reported vlues nd the possile inrese of m* with n H ould e onsequenes of the omplex nd ehviour. This influene of hnging m* my our s result of light-to-hevy nd trnsition t inresing rrier onentrtion, s seen in L 3 x Te 4, possily euse of the hnge to more Zr oritls or the (NiSn) 4 oritls t higher energies 113. In this se, redued onding intertion etween Y nd Z in n type mterils is expeted to led to n inresed ontriution of the (YZ) n ntionding nds to the trnsport t lower rrier onentrtions s these shift to lower energies. This would imply the possiility of hieving nd onvergene in hlf-heusler mterils, potentilly leding to etter thermoeletri performnes. As onsequene of this strong tendeny of im purity formtion, it ws not possile to nlyse the Pisrenko reltion of mny pulished XCoS ompounds. Mgneti seondry phses tht n e formed (for exmple, in full-heusler ompounds or elementl Co) 111 my use the unrelile Hll dt in the literture. Nevertheless, it hs een shown tht systems with p type XCoS 1 x Sn x n e desried with single m*, when there re no mgneti impurities present 114 (results re shown in FIG. 4). For referene purposes only (s the true mss will depend on the sttering), m* = 10 m e (ousti phonon sttering) nd μ 0 = 3.6 m 2 Vs 1 show good greement with pulished dt, gin orroorting semionduting ehviour in hlf-heusler ompounds 81. This higher density-of-sttes effetive mss t higher rrier onentrtions my indite Fermi-level lotion deeper in the vlene nd, in whih the Co d oritls re minly ontriuting to the high density of sttes. In nother p type system (N/V)FeS, the vlidity nd utility of n m* model hve een shown. More speifilly, inresing the rtio of V results in n inrese in the m* of the vlene nd 115,116. In the Zintl formlism, tht n e understood euse of the lower eletronegtivity differene etween V nd the Fe S frmework, V will ontriute more to the ovlent onding, nd more V oritls will mix with the vlene nd edge, explining the inrese in m*. Conlusions Hlf-Heusler ompounds n e understood using Zintl hemistry, in whih the different onding intertions of ovlently onded sulttie nd the more ioni intertion to the most eletronegtive tion explin the existing eletroni strutures. Rther thn thinking of these mterils s intermetlli ompounds, we insted use Zintl hemistry to explin the preise vlene eletron ount nd the resulting lrge ndgp tht n e used to predit new Hlf-Heusler ompounds. In ddition, the growing evidene for exess interstitil Ni in XNiSn n explin the unexpetedly smll ndgp nd unusully low hole moility tht llow good thermoeletri performne of the n type mteril. Ultimtely, understnding the onding intertions nd their influene on the eletroni struture my led to strtegies tht n optimize the hemistry of hlf-heusler ompounds nd possily engineer defets for improving their eletroni properties. An evlution of the literture dt suggests tht to first order it my e possile to desrie the n type XNiSn nd some p type XCoS hlf-heuslers s rigidnd semiondutors with n effetive mss. The tendeny of hlf-heuslers with mixed X toms to form impurity phses ppers to led to omposites with devitions in trnsport properties. Nevertheless, suh model n e used to dedue the effet of nd engineering the moility, μ, nd effetive mss, m*, using hemil doping strtegies within Zintl hemistry onept. Although multiphse mterils my ultimtely e superior for thermoeletri pplitions, there is still muh to lern out the omplex eletroni struture in these mterils from theoretil nd experimentl investigtions of model, single-phse ompositions. 8 ADVANCE ONLINE PUBLICATION

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Zintl phses s thermoeletri mterils: tuned trnsport properties of the ompounds C x Y 1 x Zn 2 S 2. Adv. Funt. Mter. 15, (2005). Aknowledgements The uthors thnk A. Zunger nd Y. Yu for helpful disussions. W.G.Z. nd G.J.S. knowledge the EFRC Solid-Stte Solr- Therml Energy Conversion Center (S3TEC) wrd numer DE SC nd funding from the Bosh-BERN progrm. J.S. nd C.F. knowledge the Germn BMBF joint projet TEG The nd struture nd prtil density of sttes lultions for this projet were performed under the Mterils Projet work, supported y the Deprtment of Energy Bsi Energy Sienes progrm under Grnt No. EDCBEE, DOE Contrt DE AC02 05CH Competing interests sttement The uthors delre no ompeting interests. SUPPLEMENTARY INFORMATION See online rtile: S1 (ox) S2 (figure) S3 (figure) S4 (figure) S5 (tle) ALL LINKS ARE ACTIVE IN THE ONLINE PDF 10 ADVANCE ONLINE PUBLICATION