Hydrogen Diffusion in Hybrid Perovskites from Exchange NMR

Ion migration is an important phenomenon affecting the performance of hybrid perovskite solar cells. It is particularly challenging, however, to disentangle the contribution of H+ diffusion from that of other ions, and the atomic-scale mechanism remains unclear. Here, we use 2H exchange NMR to prove that 2H+ ions exchange between MA+ cations on the time scale of seconds for both MAPbI3 and FA0.7MA0.3PbI3 perovskites. We do this by exploiting 15N-enriched MA+ to label the cations by their 15N spin state. The exchange rates and activation energy are then calculated by performing experiments as functions of mixing time and temperature. By comparing the measured exchange rates to previously measured bulk H+ diffusivities, we demonstrate that, after dissociating, H+ ions travel through the lattice before associating to another cation rather than hopping between adjacent cations.

Figure S4: Fitted 2 H exchange rates from variable-mixing-time EXSY spectra of N-deuterated 15 N-MAPbI3 as a function of temperature, for different deuteration levels.For low deuteration and higher MAS rate, the exchange is dominated by physical exchange, which increases with increasing temperature.For high deuteration and lower MAS rate, the exchange is dominated by spin diffusion, which decreases with increasing temperature, indicating narrowing of the zeroquantum linewidth.
Figure S5: a) Fitted 2 H exchange rates from variable-mixing-time EXSY spectra of N-deuterated 15 N-MAPbI3 as a function of MAS rate at 319 K for different levels of deuteration.The contribution of spin diffusion to the exchange rate was determined by assuming that the physical diffusion rate is the same for both samples at all MAS rates (fitted as 0.082 s -1 ), and that the spin diffusion rates of the two samples are related by the same multiplicative factor at each MAS rate (fitted as 6.49, similar to the ratio of the deuteration levels).b) The fitted spin diffusion rates as a function of the inverse square of the MAS rate, showing a linear dependence for both samples.This is ascribed to narrowing of the 2 H resonances (Figure S6), and hence of the zero-quantum linewidth. 36,37Table S1: 2 H-2 H exchange data for 15% N-deuterated 15 N-MAPbI3.

Figure
Figure S6: 2 H NMR spectra of a) 15% and b) 90% N-deuterated 15 N-MAPbI3 as a function of MAS rate at 319 K.With increasing MAS rate, the resonances narrow, resulting in reduced overlap and suppressed spin diffusion.

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Figure S7: a,b) Build-up of the cross/diagonal peak intensity ratio in the 2 H EXSY spectra of 15% N-deuterated 15 N-MAPbI3 as a function of mixing time for different temperatures and (a) 20 kHz MAS, (b) 10 kHz MAS, as well as fits to a stretched tanh function (solid lines).c) The average exchange rate, 〈 ex 〉, as a function of temperature for the fits in (a,b).

Figure S8 :
Figure S8: Build-up of the cross/diagonal peak intensity ratio of the 15 N-coupled MA + peaks in the 2 H EXSY spectra of FA0.7( 15 N-MA)0.3PbI3at 20 kHz MAS as a function of mixing time for different temperatures, as well as fits to a tanh function (solid lines).

Figure
Figure S9: X-ray diffraction pattern of a mechanosynthesised sample of natural abundance MAPbI3 recorded with Cu Kα radiation.The red lines are the calculated reflections for MAPbI3 based on ICSD entry 124919.

Table S2 :
Fitted 2 H-2 H exchange rate for MA + in FA0.7MA0.3PbI3and the calculated physical exchange rate between MA + cations.

Table S3 :
Fitted Arrhenius behaviours for the physical exchange of 2 H + between 15 Nα-MA + and 15 Nβ-MA + ,  phys =  0 exp(− a / B ), where  B is Boltzmann's constant.Note that the exchange rate of 2 H + between any cations, regardless of spin state, has double the value of  0 .