[1] Laboratory for Thin Films and Photovoltaics, Empa - Swiss Federal Laboratories for

Transcription

1 Supporting Information The Effect of Gallium Substitution on Lithium Ion Conductivity and Phase Evolution in Sputtered Li 7-3x Ga x La 3 Zr 2 O 12 Thin Films: Supporting Information M. Rawlence 1,2, A. N. Filippin 1, A. Wäckerlin 1, T.-Y. Lin 1, E. Cuervo-Reyes 3, A. Remhof 3, C. Battaglia 3, J.L.M. Rupp 2, 4, S. Buecheler* 1 [1] Laboratory for Thin Films and Photovoltaics, Empa - Swiss Federal Laboratories for Material Science and Technology, Überlandstr. 129, CH-8600 Dübendorf, Switzerland [2] Electrochemical Materials, ETH Zurich, CH-8093 Zurich, Switzerland [3] Laboratory Materials for Energy Conversion, Empa - Swiss Federal Laboratories for Material Science and Technology, Überlandstr. 129, CH-8600 Dübendorf, Switzerland [4] Electrochemical Materials, Massachusetts Institute of Technology (MIT) Cambridge, MA, 02139, USA * Corresponding author: stephan.buecheler@empa.ch S-1

2 Figure S1) Grazing incidence XRD of typical as-deposited thin films of LLZO and LLZO co-sputtered with Li 2 O. Incidence angle ω = 1. A broad reflection is observed between 2θ of for both films. S-2

3 Figure S2) XRD LLZO + Li 2 O co-sputtered film at 300 C. Two possible matches are Zr 3 O and Li 4 Zr 3 O 8 however the measured pattern is not fully explained. S-3

4 Intensity / a.u. splitting/broadening 700 C 0h Li5GaO4 600 C 1h 500 C 1h c-llzo t-llzo θ / Figure S3) XRD segments from intensity contour plot of film with 0.20 Ga showing the development of the LLZO phase over the course of the in-situ annealing. The splitting and broadening seen at 600 C are clear indications of tetragonal LLZO. S-4

5 Figure S4) top view and cross-section SEM of the films xga = a) 0.2 b) 0.81 c) 0.16 d) Cross-sections are obtained from freshly cleaved edges. S-5

6 Figure S5) Depth profile of respective peak intensities for x Ga = films for each element from XPS measurements. Due to the low yield of Li1s signal, the intensity has been increased by factor x10 for clearer observation. The dotted lines indicate at which point the detailed XPS analyses and quantification was carried out. S-6

7 Figure S6) XPS spectra of La3d, O1s and Zr3d orbitals for gallium doped samples. The bonding environments do not change significantly for these elements as the gallium concentration is altered. The La 3d peak was fitted by 3 doublets with fixed FWHM and distance. However intensities of components were left free, as they vary depending on the hybridization of the orbitals and chemical composition of the La compound. The energy position of the first La3d doublet is ev. Zr3d was fit with the doublet, peak at lower BE is at ev S-7

8 Figure S7) Trends in atomic percent of 2 chemical states (violet - lower BE, blue - higher BE) of Li1s and Ga2p across 4 samples. A correlation is observed between both lower BE states and both higher BE states allowing these states to be assigned to the same phases. S-8

9 Figure S8) Conductivity measurements for film with 0.18 Ga over the course of three heating and cooling cycles. Conductivities were calculated via. R-CPE circuit fitting. Such differences in measured conductivity between the first and second cycles could be related to the contact between the gold electrode and the film. An improved contact 1 with the gold electrode could be established after the first heating due to the alloying of lithium with gold, which is a known phenomenon. 1 S-9

10 Conductivity Calculations based on Electric Modulus Ionic conductivity can be generaly calculated as = /, where is the lattice electric permitivity (i.e., the permitivity at frequencies well above those where polarization effects due to mobile ions take place) and is the average conductivity relaxation time. The latter is estimated as the inverse of the frequency at the maximum. Taking into account the electrodynamic definition for ε* : = from where the the real and imaginary components of M* can then be expressed as: = +( ) = +( ) one finds that at high frequencies the term σ/ε 0 ω tends to 0 and therefore the function reduces to M intercept = 1/ε s. S-10

11 Figure S9) Kramers-Kronig test for all temperatures measured of the x Ga = 0.18 film. Some data ranges were deleted as the measured impedance appeared to remain constant as frequency was changed. S-11

12 Figure S10) Arrhenius plot of x Ga = 0.18 film ionic conductivity from impedance and electric modulus analysis presented in Fig. 6. S-12

13 Arrhenius Plot Fitting Methods The general expression for the conductivity = / ( ), (1) he relaxation function ( ) for the model with two activation energies is taken as a statistical average of two independent relaxation processes ( )= exp +(1 )exp [ ]. The relaxation times are =ω exp and =ω exp ( ), where (and 1 ) are the statistical weights proportional to the multiplicity of the site, or volume fraction, with the corresponding activation energy. and are the jump-attempt frequencies and must be both of the order of the lattice vibrations (normally ~10 15 Hz). is the lattice relative permitivity. The fit for the composition with 0.14 Ga gives us activation energies =0.66(3) and =0.38(3) but the ratio ( ) =1.2(8) 10 would result in an impossibly large value, far above the logical range of 1 order of magnitude difference. One can also verify that the temperature dependence of the two relaxation times does not agree with that of the impedance or electric modulus plot. Such inconsistencies have been discussed in the past and may be resolved if one takes ion-ion correlations into account. Therefore we fit our data with a model which takes ion ion correlation into account. The relaxation function takes a simple exponential form for < with a decay time =ω exp ( / ) and after the characteristic correlation time,, ( ) becomes a streched exponential ( )=exp ( ), with 0 <1. The effective activation energy resulting from the evaluation of equation (1) with ( ) exhibits a crossover from its high- S-13

14 temperature value,, determined by the lattice energy barriers to a larger low-temperature value, /(1 ). This dependence reduces to a standard Arrhenius behavior when the correlation exponents vanishes =0 and its universality, and accuracy, has been demostrated in the past via cross testing with experiments that do not involve impedance analysis. 2 4 The model which takes ion ion correlation into account gives = ev and a correlation exponent = For ionic conductors has been generally found between 0.27 and The temperature dependence of the effective activation energy is shown in Fig. S10. The reamining important parameter from the fit, the product of the jumpattempt frquency and the correlation time, is 10, also consistent with literature data for the correlation time of several picoseconds. Figure S11) T-dependence of the effective activation energy, = ( )/ (1/ ), calculated from the fit with Eq.1 for the film with 0.14 Ga. The plot has been extrapolated to low (50 K) and high (666 K) temperatures. The inset shows the range accessed in our measurements. The high temperature limit of = =0.35 is reached at about 530 K. The dotted line shows the apparent activation energy with the choice of y-axis in S-14 Figure 7.

15 References 1. Taillades, G., Benjelloun, N., Sarradin, J., Ribes, M. Metal-based very thin film anodes for lithium ion microbatteries. Solid State Ion , (2002). 2. Macdonald, J.R., The Ngai coupling model of relaxation: Generalizations, alternatives, and their use in the analysis of non-arrhenius conductivity in glassy, fast-ionic materials. J. Appl. Phys. 84, (1998). 3. Cramer, C., Funke, K., Buscher, M., Happe, A., Saatkamp, T., Wilmer, D., Ion Dynamics in Glass-Forming Systems: II. Conductivity Spectra Above the Glass Transformation Temperature. Philos. Mag. B, 71, (1995). 4. Cuervo-Reyes, E. Why the dipolar response in dielectrics and spin-glasses is unavoidably universal. Sci. Rep. 6, (2016). 5. Ngai, K. L., Greaves, G. N., Moynihan, C. T. Correlation between the Activation Energies for Ionic Conductivity for Short and Long Time Scales and the Kohlrausch Stretching Parameter beta for Ionically Conducting Solids and Melts. Phys Rev Lett 80, (1998). S-15