SUPPLEMENTARY INFORMATION

Transcription

1 SUPPLEENTARY INFORATION i: /nmat In situ NR Observatin f the Frmatin f etalli thium irstrutures in thium Batteries Rangeet Bhattaharyya a, Baris Key a, Hailng Chen a, Aam S. Best b, Anthny F. Hllenkam b, an Clare P. Grey a, a Chemistry Deartment, Stny Brk University, Stny Brk, NY USA b Cmmnwealth Sientifi an Inustrial Researh Organizatin, Divisin f Energy Tehnlgy, Bayview Ave, Claytn, Vitria 3168 Australia Chemistry Deartment, University f Cambrige, Lensfiel R, Cambrige CB2 1EW, UK nature materials 1

2 sulementary infrmatin i: /nmat Sulementary Infrmatin: Aenix: Thery Use t Quantify the NR Signals f etals. Fr rf fiel f strength ω 1, the fiel strength insie a metal (ω(x)), at a eth x frm surfae is given by, ω x) ω e. (1) ( 1 where, is the skin eth as efine in equatin 1. Fr iret exitatin NR exeriments, the NR signal intensity (S) eens n the rut f the strength f the alie rf (ω 1 ) an uratin f the rf ulse ( τ ), via, S ω 1 τ, where τ is hsen t satisfy ω 1τ π / 2 in rer t maximize the signal resnse. Sine, insie a metal, the rf strength ereases as a funtin f the eth, we relae ω 1 by ω(x) an write, x S sin( ω ( x) τ ) x with ω 0) ω. In the ase f a 0 ( 1 tyial metal eletre, the thikness f the metal () is far greater than the skin eth, an hene the uer limit f the integral an be set t infinity. The NR signal frm the entire vlume f the metal, S is, S s A sin( ω ( x) τ ) x s A 0 0 sin( ω( x) τ ) x (2) where A is the ttal surfae area f the metal blk an s is the signal er unit vlume f the metal. Fr ω ( 0) τ ω1τ π / 2 (i.e, when we use a π/2 ulse t exite the signal), an using equatin (1) we btain frm the abve integratin, S As (3) where, S is the NR signal frm a metal blk. Fr a metal blk f length a, with b, an thikness, A 2( ab + b + a) an the NR signal intensity an be written as, S {2ab + 2( a + b) } s (4) T further simlify alulatins we assume that the lithium metal eletre has nly tw tyes f mrhlgies, (i) metal having a thikness far greater than skin eth, (ii) mir- 2 nature ATERIALS

3 i: /nmat sulementary infrmatin strutures n the surfae f the eletre, with a thikness that is muh smaller than the skin eth (i.e., the rf enetratin f the enriti whiskers is ttal). We als assume that the metal eletre rir t eletrhemial yling has negligible mir-struture. If the ttal vlume f the lithium mir-struture is V, then the NR signal frm the mir-struture ( be written as S ) an an therefre, we an write frm equatin 4, S V ( s (5) S S m + V s s + ( Veff + V ) s ( A V ) (6) The mass f lithium esite at r strie frm ( ) the metal lithium eletre an reaily extrate frm the Eletrhemial ata: C m t 0 I t (7) where, m is the mass f a lithium atm, C is number f eletrns er Culmb, an I is the urrent at time t. We assume 100% Culmbi effiieny, i.e, the lss f lithium ue t the frmatin f a SEI r anther sie reatin is negligible. Nte that sine a tyial isharge ress results in striing f lithium ins frm the lithium eletre uner a negative value f urrent, the alulate mass ul be negative in sign; i.e., the negative sign iniates a lss f bservable mass frm the eletre. Susing that the ttal mass esite r strie frm the lithium eletre an be written as, + (8) where, is the mass f smthly esite r strie metal an is the mass f the mir-struture (mssy r enriti lithium). If smth esitin r striing results in a hange f thikness f the metal by an amunt, we an write, nature materials 3

4 sulementary infrmatin a b ρ an assuming the vlume f the mir-struture is V we an write, i: /nmat (9) ρ V (10) where, ρ is the ensity f the lithium metal. Thus we btain frm equatins 8,9 an 10, ρ a b + ρ V. Frm equatins 4 an 5, the ttal NR signal riginating frm the metal an the mir strutures an be written as (where the riginal thikness f the metal eletre, that is the thikness befre the striing r esitin, is, ), (11) S S + S {2ab + 2( a + b)( + )} s + V We ente the fratinal hange f NR signal intensity I as, s (12) S( S(0) 2( a + b) I S(0) A V A (13) where, A 2 ab + 2( a + b), is the area f the metal eletre befre eletrhemial yling. Fr marisn, we als alulate the imensinless arameter I fr tw extreme ases, (i) when we have a smth esitin r striing (I ) an (ii) when all esitin r striing results in mirstrutures (I ). Fr these tw ases, frm equatins 8, 9, 10 an 13, we btain, I 2( a + b) ( A ρ ab (14) an, ( I A ρ (15) We nte that the right han sies f equatins 15 an 16 are exresse in terms f knwn r exerimentally measure quantities. 4 nature ATERIALS

5 i: /nmat sulementary infrmatin Sine, all arameters exet an V in the equatins 12 an 13 are either knwn r an be measure exerimentally, ne an slve these tw equatins t alulate an V, an subsequently, by using equatins 8-10, the masses an an be alulate. Thus, the vlume V an the mass f the mir-strutures frme uring the eletrhemial yling an be estimate frm the fllwing exerimental arameters: the intensities f the metalli NR resnanes (i) riginating frm the mss an lithium metal eletre uring eletrhemial yling S, an (ii) at the beginning f the in-situ exeriments S (0), i.e., in the ristine state, assuming n mir-strutures have frme yet, (iii) the gemetry f the lithium metal eletre (length a, with b, an thikness ). Other 3 arameters suh as the skin eth () an the ensity f the lithium metal ( ρ 0.51gm ) are either knwn [15] r an be alulate as isusse earlier. It is imrtant t nte that the meth isusse abve es nt require the NR eaks riginating frm the f the lithium eletre an the mss t be well reslve. In rer t nfirm that the skin-eth must be taken int aunt, we have als erive arriate exressins uner the assumtin that there is n skin-eth rblem (in ther wrs the extent f rf enetratin is ttal fr bth the metal an the mir-strutures). We nw efine a imensinless arameter I vl, whih rresns t the NR signal intensity in a system where the signal is iretly rrtinal t the vlume (an thus mass) f the material; this an be alulate in a similar manner t equatins 12 r 13, I vl S( S(0) ( S(0) ρ ab. (16) The abve frmula an be mare with the exerimentally measure values f I ext. S far we have erive the relevant exressins f NR signal intensity riginating frm a single lithium metal eletre subjete t eletrhemial yling. Nw we shall als nsier a tye f ell where bth the eletres are lithium metal stris (a symmetri ell). Fr a symmetri ell net transfer f mass f lithium frm ne eletre t the ther at any given int f eletrhemial yling is zer, sine the lss f mass frm ne eletre results in an equal gain f mass by the ther eletre, that is, 0 (as befre, we assume that the lss f nature materials 5

6 sulementary infrmatin i: /nmat lithium in frming the SEI is negligible). Therefre, in the absene f the skin eth issues NR signal riginating frm a symmetri ell will remain nstant uring the eletrhemial yling. Als, smth esitin/striing resses at bth eletres will result in nstant NR signal sine the hange in thikness will be equal an site in sign fr bth the eletres. Hene we an write fr a symmetri ell, I I 0. Hwever equatins 8-13 an still be alie fr symmetri ells. Frm equatin 9 we btain, whih reresents the grwth f lithium mirstruture that urs at the exense f the lss f smthly esite lithium. Nte that the errrs intrue by any lss f metal ue t SEI frmatin r ther sie-reatins will lea t an unerestimatin f the extent f mirstruture frmatin, in systems with signifiant SEI frmatin. Hwever, SEI frmatin an be reaily mnitre in the in situ NR exeriment via the frmatin f iamagneti + seies with resnanes lse t 0 m. Thus, this effet an be easily rrete fr by mnitring the evlutin f the intensities f the lithium-nr signals f the iamagneti mnents, sine these are iretly relate t the mass f these seies. The ttal mass f lithium/ + remains nstant in the ell, an thus the sum, + SEI + eletr., where SEI an eletr. are the masses f lithium in the SEI an eletrlyte, resetively, remains unhange. vl (17) Analysis f the metal signal in a :Silin Cell Here the first hange invlves insertin f int silin, an the lss f frm the negative eletre [1]. Hwever, the metal signal remains essentially unhange n harging, nsistent with smth striing frm the stri (Figure S1). On harge, hwever, a signifiant inrease in metal signal urs, s that the aarent mass after ne yle has inrease ntieably, iniating that the eletre that is frme after n yle is nw mssy/enriti. There is a large irreversible aaity lss in the 1 st yle, hwever, this has n effet n the henmenn uner investigatin. The fllwing 2 n isharge (nt shwn) ntinues by remval f rimarily the mssy/enriti lithium. 6 nature ATERIALS

7 i: /nmat sulementary infrmatin Figure S1: (a) Setral snashts f the 7 metal signal. (b-) Current an vltage rfiles. () signal intensity (fratinal hange, I ext, nrmalize t the signal at the beginning). The intensity remains essentially nstant uring isharge ( striing). Sine unifrm striing leaves the eletre area unhange an the hange in thikness is negligible, the signal remains virtually nstant. The minr hanges in the signal intensity uring the 1 st isharge are mst likely ue t the frmatin f its whih will are smthe ut r remve as striing ntinues. Referenes: [1] Key, B., Bhattaharyya, R., rrette,., Sezne, V., Tarasn, J.-., Grey, C. P. Real- Time NR Investigatins f Strutural Changes in Silin Eletres fr thium-in Batteries. J. Am. Chem. S. 131, (2009). nature materials 7