Computer Modeling of Lithium Phosphate and Thiophosphate Electrolyte Materials

Transcription

1 Computer Modeling of thium hosphte nd Thiophosphte Eletrolyte Mterils N. A. W. Holzwrth, Nihols Lepley nd Yojun A. Du Deprtment of hysis, Wke Forest University, Winston-lem, NC, UA Current ddress: ICAM, Ruhr-Universität, 4478 Bohum, Germny Introdution thium phosphorous oxynitride (N) films were developed t k Ridge Ntionl Lortory s very promising solid stte eletrolytes for use in rehrgele tteries nd other pplitions. The films hve ompositions lose to tht of rystlline 3 4 nd ioni ondutivities of 6 /m. In previous work, 2 we investigted detiled mehnisms for ion migrtion in idelized models of N sed on 3 4 nd relted phosphonitrides. In those mterils we found tht ions n diffuse y vny nd interstitil mehnisms with migrtion energies of.3-.7 ev. In the present work, we report preliminry results for extending this modeling study to lithium thiophosphte mterils whih hve reently reeived ttention s promising ndidtes for solid-stte eletrolytes 3 where inresed ioni ondutivity s lrge s 3 /m hs een reported. Clultionl Methods The omputtionl methods used in this work were the sme s those used in our previous studies of eletrolytes relted to N. In Ref. [2], the hoie of lultionl prmeters nd the vlidtion of the lultionl methods re presented. Briefly, we used density funtionl theory 4 to tret the eletroni sttes nd the Born-ppenheimer pproximtion to tret the tomi positions {R }, resulting in determintion of the totl energy E({R }) of the system. The lol density pproximtion (LDA) 5 ws used for the exhnge-orreltion funtionl. Most of the omputtions were rried out using the Wsf pkge; 6 while few lultions were performed using the init 7 nd pwpw 8 pkges s well. Visuliztions were onstruted using the pendx 9 nd XCryDEN softwre pkges. In this work, severl lithium phosphte nd thiophosphte mterils re modeled to determine their optimized lttie strutures, their totl energies, nd their eletroni strutures. Inluded in this study re mterils hrterized y isolted phosphte nd thiophosphte groups 3 4 nd 3 4 nd mterils hrterized y phosphte nd thiophosphte dimers nd nd nd In ddition, the superioni onduting mteril 7 3 is lso modeled s re reently disovered rystlline rgyrodite mterils 7 6 nd 6 5 Cl. A omprison of ion vny migrtion in nd shows tht the migrtion energy rrier to e smller (less thn one-hlf) in the thiophosphte mteril thn in the phosphte mteril. trting from experimentl informtion for eh mteril or relted mteril, restrited optimiztion of the totl energy E({R }) with respet to the tomi positions {R } nd unit ell prmeters, llows us to model stle nd met-stle strutures nd to estimte the het of formtion ( H). For eh met-stle struture, qulittive piture of the vlene stte distriution n e determined from the verged prtil densities of sttes N (E). In ddition, migrtion energies (E m ) for ion migrtion were estimted using the nudged elsti nd method.

2 3 4 nd nd 3 4 re hrterized y isolted phosphte or thiophosphte groups. 3 4 hs een reported in two different orthorhomi rystlline forms the β form 2 hs symmetry mn2 (#3) nd the γ form 3 hs symmetry nm (#62). In our previous work we found tht the β form is more stle y.3 ev per formul unit, while more experimentl results re reported for the γ form. The rystl struture of 3 4 ws reported y Merier et l. 4 to hve n orthorhomi symmetry nm (#62) whih differs from γ- 3 4 struture euse of different site oupnies, some of whih re frtionl. We determined optimized totl energies for 3 4 in severl pproximtions to the Merier struture nd in the β nd γ strutures of 3 4, nd found the lowest energy struture to e tht of β ur results indite this struture to e more stle thn the most stle pproximtion to the Merier struture y. ev per formul unit nd more stle thn the γ- 3 4 struture y.2 ev per formul unit. The omprison of 3 4 nd 3 4 in the β- 3 4 is illustrted in Fig.. The lttie prmeters of 3 4 re found to e roughly 25% lrger thn those of 3 4 nd the frtionl oordintes re quite similr for the two strutures FIG. Bll nd stik digrms for 3 4 nd 3 4 in the mn2 struture (β- 3 4 ). <N (E)> sttes/ev/sphere.5.5 β- 3 4 β E (ev) FIG.2 rtil densities of sttes for 3 4 nd 3 4. In Fig. 2 the prtil densities of sttes of 3 4 nd 3 4 re ompred. The 3p vlene nds of 3 4 over wider rnge of energies thn does the 2p vlene nds of 3 4. As noted in our erlier work the two lower nds hve pσ hrter with signifint hyridiztion with the 3s nd 3p sttes, while the top of the vlene nd is hs pπ hrter. It is interesting to note tht the mgnitudes of the ontriutions to N (E) the prtil densities of sttes re generlly lrger thn those of, inditing tht the hrge of the 2p sttes is more onfined within the nlysis sphere thn is the hrge of the 3p sttes. While the lulted nd gps within density funtionl theory re systemtilly underestimted, it is ler tht the gp in 3 4 is less thn hlf of tht in 3 4.

3 7 6 nd 5 5 Cl There hs een numer of reent studies of lithium thiophosphte mterils with dditionl sulfur nd lithium ions in struture ssoited with the minerl rgyrodite. 5 The high ion ondutivity oserved 6 in these mterils is ssoited with high-temperture rystlline forms hving multiple frtionl oupny sites. However, these mterils lso hve ordered low-temperture strutures whih we hve modeled in this work. The low temperture struture of 7 6 hs een found to e n2 (#33). The low temperture struture of 6 5 Cl hs not een reported, ut it is resonle to ssume tht it is similr to tht reported for 6 5 I whih forms monolini struture with C (#9) symmetry. The lultions optimized the 7 6 nd 6 5 Cl strutures nd the results re illustrted in Fig. 4. For 7 6 there re two unounded ions ssoited with eh thiophosphte group nd for 6 5 Cl there is one unounded ion nd one unounded Cl ion for eh thiophosphte group Cl FIG. 3 Bll nd stik digrms for 7 6 in the n2 struture (left) nd 6 5 Cl in the C struture (right). Cl <N (E)> sttes/ev/sphere.5.5 (u) Cl (u) 6 5 Cl E (ev) FIG.4 rtil densities of sttes for 7 6 nd 6 5 Cl. Contriutions from unounded sites re indited with (u). Next we onsider the prtil densities of sttes of the rgyrodite strutured thiophosphtes, ompring the prtil densities of sttes of 7 6 nd 6 5 Cl in Fig. 4. For 7 6, the isolted ions re found to ontriute reltively nrrow nds ner the top of the vlene nd. For 6 5 Cl, the isolted Cl ion on triutions re t lower energy thn those of the isolted ions.

4 4 2 6 nd The rystl struture of ws desried y Merier 7 s hexgonl 6 3 /mm (#93) with hlf oupny of the (4e) sites. ur eletroni struture lultions of the 6 possile onfigurtions of this unit ell find the lowest energy struture to e desried y the 3m (#62) struture whih is sugroup of the originl spe group. In this hexgonl group, the ions re loted t 2 (/3, 2/3, ) nd 2d (/3, 2/3, /2) sites, the ions re loted t 2e (,, z ) sites, nd the ions re loted t 6k (x,, z ) sites. We were lso le to simulte met-stle phosphte mteril with the sme struturer. In onstrst to the other phosphtes nd thiophosphtes, n interesting hrteristi of the optimized nd strutures is the presene of diret ond etween two ions. In the - ond length is 2.24 Å whih is % longer thn the - ond length, while in the - ond length is 2. Å whih is 4% longer thn the - ond length. This is illustrted in Fig. 5. <N (E)> sttes/ev/sphere E (ev) FIG.6 rtil densities of sttes for nd rtil densities of sttes for nd re ompred. In ddition to the nds orresponding to 3p sttes, one dditionl vlene nd is present due to the filled 3sσ ond, whose ontriution is onentrted ner the ottom of the spetrum FIG. 5 Bll nd stik digrms for unit ells of (left) nd (right) in the 3m struture.

5 4 2 7 nd While to the est of our knowledge, the rystl struture of is unknown, ws found to rystllize 8 in the struture (#2). ur simultions onfirm this struture nd simultions for the orresponding thiophosphte show tht it hs t lest met-stle stte in the sme struture FIG. 7 Bll nd stik digrms for unit ells of (left) nd (right) in the struture. <N (E)> sttes/ev/sphere () () E (ev) FIG.8 rtil densities of sttes for nd Contriutions from ridging or sites re indited with (). rtil densities of sttes for nd re ompred. For these mterils, while sttes with ontriutions from the site ontriute throughout the vlene nd, there is no dditionl vlene stte due to filled sttes s in the se of nd n the other hnd there re two types of () sttes. In ddition to the norml tetrhedrl () site ontriutions, the ridging () site ontriutions re shown seprtely on the plot. In prtiulr, there is nd t the ottom of the vlene nd sttes whih orresponds to sttes hrterized primrily y 2pσ or 3pσ ontriutions for nd 4 2 7, respetively.

6 Hets of Formtion In order to ssess the hemil stility of the mterils, we estimted the hets of formtion reltive to their deomposition to elementl mterils in their stndrd sttes s defined in the CRC Hndook, 9 using the methods desried in our erlier work. In order to extend the nlysis to sulfur ontining mterils we needed to estimte the equilirium energy of the stndrd stte of elementl, whih is the orthorhomi form (α- 8 ) 2 hving the struture F ddd (#7). In order to extend the nlysis to Cl-ontining mterils, we needed to estimte the energy of the stndrd stte of elementl Cl, whih is moleulr Cl 2. Insted of evluting this energy diretly, we estimted it from the totl energies of Cl in the rokslt struture, Cl 4 in the nm (#62) struture, 2 nd Cl 5 in the 4/n (#85) struture 22 nd the het of formtion dt vlues for these mterils given in the CRC Hndook. From these results, we n mke some omments on reltive stilities of these mterils. For exmple, the lultions suggest tht is more stle thn in the sense tht in their stndrd sttes: H( ) + H() = H( ).84 ev. In ft there re literture reports of glssy 4 2 7, ut we know of no reports of rystlline By onstrst, for the nlogous phosphte mterils, we find H( ) + 2 H( 2) = H( ) ev, suggesting tht is signifintly unstle reltive to In ft we know of no literture reports of oservtions of rystls. For the rgyrodite mteril, the lultions lso suggest tht 7 6 is unstle reltive to deomposition into 3 4 nd 2 in the sense tht H( 7 6 ) = H( 3 4 ) + 2 H( 2 ) +.32 ev. In this estimte, we used the β- 3 4 struture to evlute H( 3 4 ) nd the result is within our expeted lultion error. The mteril with hlorine is lso mrginlly unstle reltive to deomposition into 3 4, 2, nd Cl s shown in the H( 6 5 Cl) = H( 3 4 ) + H( 2 ) + H(Cl) +.38 ev. TABLE I Hets of formtion per formul unit lulted for the listed referene nd lithium phosphte nd thiophosphte mterils. The struture is desried in terms of the spe group using the nottion of The Interntionl Tle of Crystllogrph. When ville, experimentl vlues of H from The CRC Hndook 9 re lso listed. Mteril truture H l (ev) H exp (ev) 2 F m 3m (#225) β- 3 4 mn2 (#3) -2.3 γ- 3 4 nm (#62) (#2) m (#62) F m 3m (#225) β- 3 4 mn2 (#3) γ- 3 4 nm (#62) n2 (#33) (#2) m (#62) (#2) Cl F m 3m (#225) Cl 4 nm (#62) Cl 5 4/n (#85) Cl C (#9) -6. The lultions lso suggest tht 7 3 is mrginlly stle with respet to deomposition into 3 4 nd in the sense tht H( 7 3 ) = H( 3 4 ) + H( ).6 ev. Agin, this is within the expeted lultionl error.

7 Ion Migrtion Energies An importnt question out these mterils is how the ion migrtion differs in the phosphte nd thiophosphte mterils. A mesure of the ioni ondutivity σ s funtion temperture T is expeted to follow the Arrehenius reltion: σ T = K n e E m/kt, where k is the Boltzmnn onstnt, K is mteril-dependent prmeter, n is the numer of moile ions or ion vnies, nd E m is the migrtion energy E pth (ev) E m In this initil study, we fous on the migrtion energy E m for ion vny migrtion in idelized rystls of nd These two mterils form similr stle nd met-stle rystls with symmetry. For the simultions, we onstruted 2 2 superells nd studied the migrtion of ion vny etween 6 sites seprted y roughly 3. Å nd 3.6 Å for nd 4 2 7, respetively. The sites do not spn omplete pth within the superell ut do over representtive rnge of rystl environments. The 6 sites re illustrted in Fig. 9 for the superell. A orresponding geometry ws used for the superell. The nd oupnies of the superell sttes were djusted in order to pproximte n insulting environment for ion migrtion, nd the exess hrge ws ompensted y dding uniform hrge of the opposite sign. The 6 optimized onfigurtions for ion vny were used s the end points for the NEB lultion in whih 7 intermedite imges were used to pproximte the minimum energy pth. The energy pth digrm is shown in Fig. 9, ompring the results for nd E m th FIG. 9 Left: ion vny sites used in migrtion energy study in imilr sites were used for Right: Energy pth digrm for ion vny migrtion in nd The integer lels on the the horizontl xis orrespond to the 6 vny sites indited in the struturl digrm. Between eh pir of optimized vny onfigurtions re 7 NEB imge onfigurtions long the minimum energy pth. The ontinuous line is onstruted with spline interpoltion etween the imge energies. As is evident from the energy pth digrm shown in Fig. 9, the energy lndspe for this system is omplited. However, the results indite ler qulittive result tht the migrtion energy rriers for ion vny migrtion in is less thn hlf tht in For the prtiulr migrtion pth hosen, we find the migrtion energy energy rriers to e E m =.3 ev for nd E m =.8 ev for

8 ummry nd Conlusions This study hs found some interesting similrities nd differenes etween the phosphte nd thiophosphte mterils. ur struturl optimiztions were generlly in good greement with the experimentl strutures, lthough there re some differenes. For exmple, our lultions for 3 4 indited tht the most stle struture is tht of β- 3 4, while the experiment 4 indited struture similr to γ- 3 4 with prtil oupnies of some of the sites. A similr disrepny ws found for the struture of These differenes re undoutedly relted to rel temperture effets whih re not onsidered in the simultions. In generl, greter vriety in the onding onfigurtions of the thiophosphtes is oserved ompred with those of the phosphtes. The rgyrodite strutures 5 with unounded nd Cl groups within the rystl nd inresed onentrtions of ions re very intriguing. In ddition to our nlysis of the optimized strutures nd their stilities, we hve presented some preliminry results pertining to ion vny migrtion within representtive set of mterils. We find tht the energy rriers for ion vny migrtion in to e less thn hlf tht for This result is onsistent with the experimentl oservtion of inresed ioni ondutivity in the thiophosphte mterils ompred with those of the phosphtes. ur nlysis suggests tht one ftor ontriuting to the lowered potentil rriers in the thiophosphtes is the more diffuse vlene hrge distriution ner the sites ompred with the ompt vlene hrge distriution ner the sites. Aknowledgements This work ws supported y NF grnts DMR nd nd y the Wke Forest University DEAC omputer luster. We would like to thnk Dr. F. tdler for informing us out the rgyrodite mterils. Biliogrphy [] J. B. Btes, et l., olid tte Ionis 5356, 647 (992); N. J. Dudney, Interfe 7 (3), 44 (28). [2] Y. A. Du, N. A. W. Holzwrth, Journl of the Eletrohemil oiety 54, A999 (27); Y. A. Du, N. A. W. Holzwrth, hys. Rev. B 8, 846 (5pp) (2). [3] F. Mizuno, A. Hyshi, K. Tdng, M. Ttsumisgo, Eletrohemil nd olid- tte Letters 8, A63 (25); K. Minmi, A. Hyshi, M. Ttsumisgo, olid tte Ionis 79, 282 (28); A. Hyshi, K. Minmi, M. Ttsumisgo, Journl of Non-rystlline olids 355, 99 (29); J. Trevey, J.. Jng, Y. W. Jung, C. R. toldt,.-h. Lee, Eletrohemistry Communitions, 83 (29). [4]. Hohenerg, W. Kohn, hysil Review 36, B864 (964); W. Kohn, L. J. hm, hysil Review 4, A33 (965). [5] J.. erdew, Y. Wng, hys. Rev. B 45, 3244 (992). [6]. Ginnozzi, et l., J. hys.: Condens. Mtter 2, (9pp) (29). Aville from the wesite [7] X. Gonze, et l., Zeit. Kristllogr. 22, 558 (25). Aville from the wesite http: // [8] A. R. Tkett, N. A. W. Holzwrth, G. E. Mtthews, Computer hysis Communitions 35, 348 (2). Aville from the wesite [9] pendx The pen oure oftwre rojet Bsed on IBMs Visuliztion Dt Explorer is ville from the we site [] A. Koklj, Journl of Moleulr Grphis nd Modelling 7, 76 (999). [] H. Jónsson, G. Mills, K. W. Josen, Clssil nd Quntum Dynmis in Condensed hse imultions, B. J. Berne, G. Ciotti, D. F. Coker, eds. (World ientifi, ingpore, 998), pp ; G. Henkelmn, B.. Uerug, H. Jónsson, J. Chem. hys. 3, 99 (2); G. Henkelmn, H. Jónsson, J. Chem. hys. 3, 9978 (2). [2] C. Keffer, A. Mighell, F. Muer, H. wnson,. Blok, Inorgni Chemistry 6, 9 (967). [3]. V. Ykuovih, V.. Urusov, Crystllogrphy Reports 42, 26 (997). [4] R. Merier, J.-. Mlugni, B. Fhyst, G. Roert, At Cryst. B 38, 887 (982). [5]. T. Kong, et l., Chem. Eur. J. 6, 538 (2);. T. Kong, et l., Chem. Eur. J. 6, 298 (2); H.-J. Deiseroth, et l., Angew. Chem. Int. Ed. 47, 755 (28). [6] F. tdler, C. Fietzek, EC Trns. 25, 77 (2). [7] R. Merier, J.. Mlugni, B. Fys, J. Douglde, G. Roert, Journl of olid tte Chemistry 43, 5 (982). [8] A. Didouh, M. L. Veig, C. io, M. Mrtinez-Ripoll, At Cryst. C 53, 67 (997). [9] D. R. de, ed., CRC Hndook of Chemistry nd hysis, 9th Edition (CRC ress, Tylor & Frnis Group, 29). IBN 3: [2]. J. Rettig, J. Trotter, At Cryst. C 43, 226 (987). [2] K. D. M. Hrris, M. Tremyne, Chem. Mter. 8, 2554 (996). [22] D. Clrk, H. M. owell, A. F.Wells, Journl of the Chemil oiety 34, 642 (942).