Hidden Two-Step Phase Transition and Competing

Transcription

1 Suppoting Infomation fo Hien Two-Step Phase Tansition an Competing Reaction Pathways in LiFePO 4 Yukinoi Koyama, Takeshi Uyama, Yuki Oikasa, Takahio Naka, Hieyuki Komatsu, Keiji Shimoa, Hauno Muayama, Katsutoshi Fukua, Hajime Aai, Eiichio Matsubaa, Yoshihau Uchimoto, an Zempachi Ogumi Office of Society-Acaemia Collaboation fo Innovation, Kyoto Univesity, Gokasho, Uji, Kyoto , Japan Gauate School of Human an Envionmental Stuies, Kyoto Univesity, Yoshia-Nihonmatsu, Sakyo, Kyoto , Japan Depatment of Mateials Science an Engineeing, Kyoto Univesity, Yoshia-Honmachi, Sakyo, Kyoto , Japan S1

2 Note S1 Metho fo simulation of phase-tansition kinetics base on two-step moel Phase-tansition behavio of LiFePO 4 is quantifie by a macoscopic an phenomenological moel consieing two consecutive electochemical pocesses, ie tansition between an (step ) an between an L (step ), an ecomposition of metastable The last involves ispopotionation to the themoynamically stable phases of L an, as illustate in Scheme S1 The pesent moel eals with factions of L,, an (c L, c, an c ; c L + c + c = 1) aveage in electoes A single lithium composition is assume fo (x; expeimentally evaluate as 076) Fist-oe eactions an negligible evese eactions ae assume fo both the two electochemical pocesses an the ispopotionation of Then, we may epesent the eaction ates of the two electochemical pocesses fo chaging ( an L fo steps an, espectively) an the ispopotionation of ( ) as follows: L k α k c β k c c L, whee k, k an k ae eaction-ate paametes fo step, step an the ispopotionation, espectively The entie electochemical eaction ate ( e ) is xl x e 1 The time eivatives of the phase factions ae obtaine as c t c t c t L L L x 1 x The eaction-ate paametes ae usually consiee to be constant at fixe conitions in tems of intensive vaiables In galvanostatic chaging, howeve, the ate paametes fo the electochemical pocesses (k an k ) ae vaiable, which is analogous to contolling ovepotential in expeiments to maintain a given cuent, ie constant e The ate paamete fo the ispopotionation k is constant at a given tempeatue an inepenent fom the electochemical eaction ate, an it becomes smalle at lowe tempeatues Time is nomalize in tems of the entie electochemical eaction ate Thus, the kinetic equations can be efomatte as follows: cl c c c 1 L c c L xc c c 1 xc L xc 1 x c, whee is nomalize time ( e t), is the atio of the ate paametes fo the two electochemical pocesses (k /k ), is the nomalize ate paamete fo step (k / e ), an is the elative chaging ate to the ispopotionation ate paamete ( e /k ) Hee, is assume to be constant egaless of chaging o ischaging, values of k an k, an S2

3 tempeatue Une given paametes an, an initial conitions c L ( = 0) = 1, c ( = 0) = 0, an c ( = 0) = 0, c X (X = L,, an ) an ae numeically solve as functions of nomalize time by Doman Pince explicit metho Fo ischaging, the evese lithium insetion is consiee Hence, the kinetic equations ae L c t c t c t e L k k k c c c 1 x L L L x x 1 x The equations fo ischaging can be efomulate with the nomalize time as cl c c 1 c c c xc c 1 xc xc 1 x c c The opeano XRD measuements in this stuy suggest that metastable isappeas in 05 1 h at 25 C (k 1 2 h 1 ), an the lifetime is estimate to be ca 40 h at 5 C (k 0025 h 1 ; see Figue S5 an ef 16) Hence, 1 C ate at 25 an 5 C coespons to 05 1 an ~40, espectively In this stuy, is set at (low ates an high tempeatues) to 500 (high ates an low tempeatues) The expeimental evience of ischaging ening at single at 5 C an 10 C ates, an at 5 C (Figue 2a) suggests that step is slowe than step ; thus, > 1 As the specific value of is unknown, we set it to 2 10 in this stuy The epote atio of the eaction ate constants fo the two-step phase tansitions of Li x Ni 05 Mn 15 O 4 via potential-step chaging is 40 [ef 21] Figue S6 shows vaiation of phase factions with nomalize time uing chaging an ischaging at vaious values of (2, 5, an 10) an (00005, 0005, 005, 05, 5, 50, an 500) The faction of inceases at highe an lowe uing chaging, an at highe an highe uing ischaging, wheeas the epenence of the phase faction on is insignificant To quantify contibutions of the thee pocesses in chaging an ischaging, the following atios of the eaction ates wee evaluate as functions of nomalize time: S3

4 f f f α β x e 1 x xc L e x c L fo chaging, an f f f α β x e 1 x L xc L e x c fo ischaging The quantities of f an f ae espectively the contibutions of steps an with espect to the entie electochemical eaction (f + f = 1) The quantity of f is the faction of that ecomposes though the ispopotionation; hence (1 f ) is the faction consume by the electochemical pocesses Scheme S1 Pocesses in (a) chaging an (b) ischaging base on the two-step phase tansition moel with eaction-ate paametes in the phase-tansition simulation: two electochemical pocesses in the tansition between an (step ) an between an L (step ), an ispopotionation of metastable to the themoynamically stable phases of L an S4

5 Table S1 Diffaction peak positions of Li x FePO 4, LiFePO 4, an FePO 4 Values of 2 an obtaine by wie-ange XRD measuements with coesponing inices assuming olivine stuctues Diffaction peaks enote by cosshatch (#) an agge ( ) symbols wee unable to be sepaate fom iffaction peaks oiginating fom cell components an X-ay winows, an fom ajacent iffaction peaks, espectively; they wee not use to estimate lattice constants Mille inices Li x FePO 4 LiFePO 4 FePO 4 h k l 2 / egee / Å 2 / egee / Å 2 / egee / Å # 5104 # Weak intensity Weak intensity Weak intensity # # # # Weak intensity Weak intensity Weak intensity Weak intensity Weak intensity # Weak intensity # # # # # # Weak intensity # Weak intensity Weak intensity # Weak intensity Weak intensity S5

6 a) XRD patten b) SEM image Figue S1 (a) XRD patten with inices of an olivine stuctue an (b) SEM image of the pistine LiFePO 4 sample synthesize by a hyothemal metho S6

7 Figue S2 Opeano XRD pattens uing (a, c, e, g) the fist chaging an (b,, f, h) the fist ischaging (a, b) at a ate of 1 C (170 ma g 1 ) an a tempeatue of 25 C, (c, ) at 10 C (1700 ma g 1 ) an 25 C, (e, f) at 1 C an 5 C, an (g, h) at 10 C an 5 C Colos epesent states of chage (SOCs) of the cells Black lines enote the pattens at the beginning of the chaging o at the en of the ischaging; e lines enote the pattens at the en of the chaging S7

8 Figue S3 (top) Potential pofiles an (bottom) chage an ischage capacities of each cycle in opeano XRD measuements (a) at a ate of 1 C (170 ma g 1 ) an a tempeatue of 25 C, (b) at 10 C (1700 ma g 1 ) an 25 C, (c) at 1 C an 5 C, an () at 10 C an 5 C Insets show magnifie potential pofiles The lithium compositions on the uppe hoizontal axes ae estimate fom the cumulative capacities S8

9 Figue S4 (top) Opeano XRD pattens at a tempeatue of 25 C an ates of (a) 10 C (1700 ma g 1 ) an (b) 30 C (5100 ma g 1 ) fo a LiFePO 4 sample synthesize by a soli-state eaction metho with 60 nm paticle size (bottom) XRD pattens enote by the blue aows on the top panels Boken lines enote the positions of the L 211/020, 211, 020, an 020 iffactions as eye-guies S9

10 Figue S5 Time epenence of nomalize intensities of 211 an 020 iffaction peaks fom metastable in (a) linea an (b) logaithmic scales The measuements wee conucte une open-cicuit conitions afte five chage ischage cycles at a ate of 10 C (1700 ma g 1 ) an tempeatues of 25, 5, an 5 C S10

11 Figue S6 Vaiation of phase factions of L,, an (c X ) fo the two-step phase tansition moel with nomalize time () uing (a, c, e) chaging an (b,, f) ischaging Ratio of ate paametes fo step to step () is set to (a, b) 2, (c, ) 5, an (e, f) 10; elative chaging an ischaging ate to ispopotionation ate paamete () is set to 00005, 0005, 005, 05, 5, 50, an 500 S11