lengths (see also the projected density of states
in fig. S13).
To understand the effect of high (dis)charge
rate on pre-peak M in the Li-EELS spectra
(Fig. 2E), we also computed the Li-EELS spec-
tra of Li 5 Ti 5 O 12 and Li 6 Ti 5 O 12 configurations
with higher formation energies (which are
accessible at higher current rates or large
overpotential). Figure S10 shows that the
distortion of face-sharing Li(16c)and Li(8a)
polyhedra is affected by the presence of
neighboring Li(16d)or Ti(16d)( 22 ). The varying
local environment results in different inten-
sities and energy levels of pre-peak M [sec-
tion 7 in ( 22 )]. Face-sharing Li(16c)and Li(8a)
polyhedra in various Li4+xTi 5 O 12 with distor-
tion index [d; eq. S2 in ( 22 )] larger than ~0.06
result in the appearance of pre-peak M, whose
intensity tends to increase withd[Fig. 3D,
fig. S17, and section 7 in ( 22 )]. Such high
distortion levels reduce the effective coor-
dination number of Li(16c)and Li(8a).Onthe
basis of the coordination number weighting
scheme of ( 23 ), Li(16c)and Li(8a)withd~ 0.06
are found to be undercoordinated with effec-
tive coordination numbers of 4.7 and 3.6
(fig. S18), respectively, rather than the expected
6 and 4. Similar trends showing a more pro-
nounced pre-peak with undercoordinated
local environments are well established in
transition-metal K-edge x-ray absorption
near-edge structures ( 24 ). As observed in
Fig. 3E and fig. S19, highly distorted face-
sharing Li(16c)and Li(8a)polyhedra withd
higher than 0.06 appear more frequently
as the formation energy of the intermediate
Li 5 Ti 5 O 12 and Li 6 Ti 5 O 12 increases. This is con-
sistent with the presence of more face-sharing
Li(16c)and Li(8a)polyhedra in Li 5 Ti 5 O 12 config-
urations with higher formation energies, as
indicated by the points with different colors
in Fig. 3E. Highly distorted face-sharing Li(8a)
tetrahedra are observed much less often than
highly distorted Li(16c)octahedra in config-
urations with formation energy less than
100 meV/O 4 (Fig. 3E and fig. S19). Therefore,
the appearance of pre-peak M is mainly at-
tributed to face-sharing Li(16c)octahedra at low
current rates but to both face-sharing Li(16c)
and Li(8a)polyhedra at high current rates.
Phase transformation through a solid-solution
path is favorable for high-rate performance in
many electrodes, such as LiFePO 4 (LFP) ( 3 , 4 ).
However, LTO undergoes a first-order phase
transition ( 6 , 12 ) because the macroscopic
solid solution is largely inaccessible owing to
its high formation energy, in contrast to the
low formation energies of the metastable solid
solution in LFP [sections 5 and 8 in ( 22 )]. In-
stead, (de)lithiation proceeds by means of a
two-phase reaction, involving face-sharing
Li(8a)–Li(16c)local motifs at the boundaries
between the phase domains ( 12 , 13 ), which
are nanosized because of the low formationenergy of the interfaces [section 8 in ( 22 )].
Hence, whereas the origin of the fast rate in
LFP is the low energy of the metastable solid
solution, it is the low interfacial energy in
LTO that creates nanosized domains of each
phase and provides the interfacial pathways
for fast Li+-ion transport. Our results are gen-
erally consistent with the two-phase model
( 12 , 13 ), as we observed mainly interfacial-type
configurations at lower energy [sections 5 and
8in( 22 )]. However, our results further reveal a
large variety of face-sharing Li(8a)–Li(16c)local
motifs in the intermediate Li4+xTi 5 O 12 config-
urations. These local motifs, whose number
and distortion index display rate depen-
dence, may affect the kinetics in intermediate
compositions.
To obtain a mechanistic understanding of
fast Li diffusion in LTO, we performed nudged–
elastic-band ( 25 , 26 ) calculations that account
for distorted face-sharing Li polyhedra (Fig. 4
and figs. S23 and S24). The activation ener-
gies of Li+-ion migration in the lowest-energy
Li 4 Ti 5 O 12 and Li 5 Ti 5 O 12 (with an interstitial
Li+) and Li 7 Ti 5 O 12 (with a vacancy) config-
urations are ~343, ~216, and ~455 meV, re-
spectively (Fig. 4A). The low activation energy
of Li 5 Ti 5 O 12 is in line with the low migration
barriers previously obtained from NMR mea-
surements ( 10 ) and ab initio molecular dy-
namics ( 12 ). Our results indicate that facile
Li+migration occurs at the two-phase bound-
aries containing face-sharing Li polyhedra,
which is associated with lower activation bar-
riers compared with those in the end-members.
In general, the Li+-ion diffusion pathway in-
volves Li hopping from face-sharing tetrahedral
(octahedral) Li sites to octahedral (tetrahedral)
Li sites (Fig. 4B and fig. S23, B to H). Along this
path,althoughface-sharingLi+ions change
position, the number of face-sharing Li+ions
(three to four) remains nearly constant in the
Li 4 Ti 5 O 12 (always two) and Li 5 Ti 5 O 12 (from
threetofourtothree)pathways.Asaresult,
there is no abrupt increase of the energy of
the system. In the higher-energy pathway in
Li 7 Ti 5 O 12 , however, the number of face-sharing
Li+-ions changes substantially from zero to
two and back to zero (fig. S24, B to D). The
low migration barrier for Li+ions in the LTO
system can be attributed to two important
factors: (i) The number of face-sharing Li
polyhedra is smaller in the transition state
(when the migrating Li+ions are in the tri-
angular face in Fig. 4B) than in the initial and
final states within each step [for example,
there are three instances of face-sharing in
statesaandb(marked in Fig. 4) but only two
betweenaandbin Fig. 4B]. The reduction in
Li+–Li+repulsion in the transition state is
likely to lower the activation barrier. (ii) Be-
cause local distortion helps to reduce the
effective coordination number of Li (fig. S18),
the change in Li coordination is minimizedZhanget al.,Science 367 , 1030–1034 (2020) 28 February 2020 4of5
Fig. 4. Li+-ion migration pathways and the corresponding energy barriers in the intermediates.
(A) Energy profile of the pathways in Li4+dTi 5 O 12 (green), Li5+dTi 5 O 12 (red), and Li7-dTi 5 O 12 (blue) as a function
of distance along the paths. (B) Migration pathways involved for each step, from a to g, in one representative
intermediate, Li5+dTi 5 O 12 (movie S1 shows the trajectories of Li+-ion migration in Li5+dTi 5 O 12 ). The translucent
green spots mark the initial Li sites during each substepof migration. The black arrows indicate the migration
direction of each substep. The three-coordinated oxygen face through which the Li+ions migrate from a Li8a
tetrahedron to a Li16coctahedron is colored purple. The Li+-ion migration pathways in Li4+dTi 5 O 12 and Li7-dTi 5 O 12
are provided in movie S2 and figs. S23 and S24. btw., between.
RESEARCH | REPORT