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.

From: Experimental neutron scattering evidence for proton polaron in hydrated metal oxide proton conductors

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

  1. EIS, electrochemical impedance spectroscopy; QENS, quasi-elastic neutron scattering.
  2. The activation energy Ea is calculated according to ref. 30.
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