. 2017 Jun 14;8:15830. doi: 10.1038/ncomms15830

Table 1. Proton–phonon coupling constant u obtained from least square fit to the lattice-assisted proton transfer model after Samgin, respectively, for the Ce–O stretching and O-H stretching mode¹⁵.

Method	Assist phonon wavenumber (cm⁻¹)	Factor A (cm ps⁻¹)	Proton-phonon coupling constant u	Activation energy E_a (eV)
EIS	355 (Ce–O stretching)	1.49 × 10¹²	5.29	0.64±0.03
QENS	355 (Ce–O stretching)	0.041	3.87	0.326±0.001
QENS	3,560 (O–H stretching)	7.6 × 10³	3.23 (>700 K)	1.29±0.21
QENS	3,560 (O–H stretching)	2.83 × 10⁸	4.00 (<700 K)	1.98±0.35

EIS, electrochemical impedance spectroscopy; QENS, quasi-elastic neutron scattering.

The activation energy E_a is calculated according to ref. 30.

Table 1. Proton–phonon coupling constant u obtained from least square fit to the lattice-assisted proton transfer model after Samgin, respectively, for the Ce–O stretching and O-H stretching mode15.