Classification
: Physical Sciences
:
Applied Physical Sciences
O
rigin of
low
sodium
capacity in
graphite
and
generally
weak
substrate
binding
of
Na and Mg among
alkali and alkaline
-
earth metal
s
Yuanyue Liu
,
*
1,2
Boris Merinov
1
and William A. Goddard III
*
1
1
Material
s and Process Simulation Center
2
the Resnick Sustainability Institute
California Institute of Technology, Pasadena, CA 91125, USA
*
Corresponden
ce to
:
yuanyue.liu.microman@gmail.com
and
wag@wag.caltech.edu
Keywords:
energy
storage; batteries
; quantum
-
mechanical
calculations
Abstract:
It is well known
that
graphite has a low capacity for Na but
a
high capacity for other
alkali
metals.
The growing interest in
alternative cation
batteries
beyond
Li
makes it
particularly
important to elucidate the origin of this behavior, which is
not
well
understood
.
In examining
this
question
, we find
a
quite
general
phenomenon
: among
the
alkali
and alkaline earth
metals,
Na
and Mg
generally
ha
ve
the weakest
chemical
binding
to
a given substrate
,
compared with
the
other
elements in the same
column of the periodic table
.
We demonstrate this
with
quantum
mechanics
calculations for a wide range of substrate materials (not limited to C)
c
overing a
variety of structures and
chemi
cal
compositions
.
Th
e
phenomenon
arises
from the competition
between
trends in the
ionization energy and
the
ion
-
substrate
coupling
, down the
columns of the
periodic table
.
Consequently, the
catho
dic voltage for Na and Mg is expected to be lower than
those for other metals in the same column.
Th
is
generality
provides
a
basis
for analyzing the
binding of alkali
and alkaline
-
earth
metal
atom
s
over
a broad range of systems.
Significance
:
The growing demand for energy storage urges the development of alternative
cation batteries, which calls for a systematic understanding of binding energetics. We discover a
general phenomenon for binding of alka
li and alkali
-
earth metal atoms with substrates,
which is
explained
in a unified picture of chemical bonding. This allows us to solve the long
-
standing
puzzle of low Na capacity in graphite,
predict the trends of battery voltages,
and also
forms
a
basis fo
r analyzing the binding of alkali and alkaline
-
earth metal atoms over a broad range of
systems.
\
body
Main text
:
Development of alternative cation
batteries beyond Li
could solve issues
related with
cost, stability, and
other
performance characteristics
(
1
-
3
)
.
Na is an obvious candidate, but
its
storage in
g
raphite
(the
commercial anode for Li
-
ion battery
)
is rather poor, with
a
n
electrochemical
capacity
<
~
35 mAh/
g
(
1
,
4
-
7
)
. Surprisingly,
other alkali metals have a high
capacity
(~ hundreds) in graph
ite
(
8
)
.
In order to form a basis
for improving
the
battery
performance
,
we s
eek
to understand t
he anomalously low
capacity
for Na
.
One
explanation
in
the
literature
for the
low
Na
capacity
is
:
Na intercalation expand
s
graphite from its favorable interlayer spacing,
by a greater amount than Li,
leading to a higher
strain energy for graphite and, therefore, a less favorable formation energy
for Na
-
graphite
compound compared to the Li analog
(
9
-
11
)
.
H
owever,
this explanation
would
sugge
st
that
graphite should have a low capacity for K, Rb and Cs
because of
their even larger size, which is
in
stark
contrast to the experimentally observed capacity
dramatically higher than
that
for Na
.
Th
is
inconsistency
calls for a revisit of
the
origin of the
low
Na
capacity in graphite
.
In this work,
we
us
e Quantum Mechanic
al
m
ethod
s
to show that the Na
anomaly
has
it
s
roots in
to
a
general
phenomenon
: among alkali
metals (denoted as M)
and alkaline
-
earth
metals
(denoted as EM)
,
Na
and Mg
generally
ha
ve
the weakest binding
to
a given substrate,
independent
of variation
s
in substrate structure and chemistry
!
This
phenomenon
results from the
competition between the ionization of the metal
atom
and the
ion
-
substrate
coupling, which have
opposi
te
trends
along
the
columns
.
The universality
of this phenomenon
provides
the basis
for
analyzing
trends in
binding of alkali
and alkaline
-
earth
met
als
over
a broad range of systems
,
and
offers
guidance for designing improved systems
.
Our
Density
functional theory (DFT) calculations us
ed
the
Vienna Ab
-
initio Simulation
Package
(VASP)
(
12
,
13
)
with projector augmented w
a
ve (PAW) pseudopotentials
(
14
,
15
)
.
The
Perdew
-
Burke
-
Ernzerhof (PBE) ex
change
-
correlation functional
(
16
)
including
van der Waals
corrections
(
DFT
-
D3
)
(
17
)
is employed
to model the graphite and its compounds
, while in other
cases where the van der Waals interaction is insignificant, we use PBE only
.
Th
e
plane
-
wave cut
-
off energy
is 400 eV, with sufficient Monkhorst
-
P
ack
sampled k
-
points
(
18
)
(for example
15x15x7 for graphite)
. A
ll structures are
fully
relaxed until the final fo
rce on each atom becomes
less than 0.01 eV/Å.
We
used
a single
M or EM atom with
6x6 unit cells of
each
substrate
material to model the binding with
graphene
,
its derivatives,
MoS
2
, SnS
2
,
and
TiS
2
,
while a 4x4
cell is applied
for V
2
O
5
.
F
or Pt
(111)
,
we use
d
a slab consisting of 6x6 surface cells, and
three
layers
,
with the bottom layer fixed in the same plane.
We
consider first
the case of graphite.
Fig. 1 shows the
calculated
formation energy (
E
f
)
of M
-
graphite
compounds
, where M = Li, Na, K, Rb, and Cs
.
The
E
f
is defined as:
E
f
=
[
E
(
tot
)
–
n
M
E
(bulk
M)
–
n
C
E
(graphite
) ] /
(
n
M
+
n
C
)
(1)
where
E
(tot) is the total energy of compound,
E
(bulk M) is the energy
per
M
atom
for
the bulk
metal,
E
(graphite) is the energy of C in graphite
,
n
M
and
n
C
are the
numb
er of
M
and C atoms in
the compound.
Here we focus on MC
6
and
MC
8
since
these stoichiometr
ies
are commonly found
in
non
-
Na
compounds
.
We find that
,
the
E
f
follows the order: Na > Li > K > Rb > Cs,
where
all
Ms
except Na
have negative
E
f
with graphite
,
a result
consistent with calculation
s
in
the
literature
which
us
e
different
method
(
19
)
.
Thus
Na
-
graphite compounds with high Na contents
are
not thermodynamically
stable
,
in contrast to
the
other
four
M
-
graphite compounds
, in
agreement with the
experimental
ly
observ
ed
low
-
Na
capacity
.
To understand
why
the
E
f
,
has a maximum at Na,
we
partition the
for
mation process
for
M
-
graphite
compound
s
into
three
steps, as
illustrated in Fig. 2
a
. First, the bulk metal is
evaporated to form isolated
atoms, with an energy cost of
E
d
(i.e., the cohesive energy)
. Second,
the
graphite
crystal
is strained to
the configuration
iden
tical to that of
the
M
-
intercalated
graphite,
with an energy cost of
E
s
. This
straining includes both interlayer expansion and
in
-
plane
stretching. Third the
M
atoms are
intercalated
into the strained
graphite, with an energy drop by
E
b
(
t
o be consistent with
the
other terms, we define
E
-
b
=
-
E
b
;
a stronger binding corresponds a
lower
E
-
b
)
. According to
Hess's law
:
E
f
=
E
d
+
E
s
+
E
-
b
(2)
This
analysis
helps
identify the dominating contribution.
Although some
terms
are difficult to
measure experimentally
(
such as
E
s
and
E
b
),
all are
calculated easily using DFT
.
As shown in Fig. 2b,
neither
E
d
,
E
s
, nor their combination has
a
trend
similar to
E
f
, which
suggests that they
do
not
embody the
origin
of
the
low
Na
capacity
.
F
or both MC
8
and MC
8
,
E
s
increases
monotonic
ally as M moves down
the periodic table
due to the
increasing
size of M
atom
s
,
while
E
d
decreases as a result of weakened cohesion
.
T
he combination of
E
s
and
E
d
shows
a monotonic drop
, indicating that the change of
E
d
overwhelms that of
E
s
.
Nevertheless, n
one of
them
explain
the maximum of
E
f
at Na.
On the other hand
,
E
-
b
exhibits a maximum at Na,
similar
to
that of
E
f
. This suggests that
the
low
Na
capacity
is
related directly to
E
-
b
.
In particular, c
ompared with Li, the Na binding is
so weak
that
it
exceeds
the
decrease
of
E
s
+
E
d
, making
E
f
higher for
Na
.
Th
is
weaker binding of Na compared with Li has been
reported
for other intercalation
compounds
,
which
has been proposed
to account for the observed lower cathodic voltage
(
20
)
.
Here
we
find
that
,
of
all
the 5 alkali
metals,
Na
always has the weakest binding
for any
given
substrate
.
We first
examine
dilute M adsorption on graphene
(Fig. 3a), which shows a maximum
of
E
-
b
at Na. Then we modify the adsorption sites by
incorporating
stru
ctural defects or foreign
atoms
.
Remarkably
, Na
always leads to
the weakest binding
(Fig. 3a)
. We contin
ue the test by
considering
other
two
-
dimensional
non
-
C
materials
that have been tested for
batteries
,
namely
MoS
2
, TiS
2
, SnS
2
, and V
2
O
5
(Fig. 3b)
.
We
then
extend
ed
th
is
test to the surface of
a typical
bulk
materials
Pt
(111) (
Fig. 3b
; a
s
common
ly found
in Pt
-
based catalysis in alkali
ne
solution
).
In all
cases,
Na has the weakest binding among
all five
alkali metals
,
independent
of the detailed
substrate
chemistry/structure
.
This general phenomenon
calls for a unified explanation.
E
-
b
is the energy change when
an
M atom moves from the vacuum to the
binding site
of
the substrate
.
We consider
t
his process to
first
involve ionization
of
M by
transferring
its
charge
to the substrate, with an energy
change
by
E
ion
. This is
followed by
the coupling
of the
cation
to
the substrate (negative
ly
charged
) with an energy decrease of
E
cp
(which includes the
electrostatic and other quantum
-
mechanical interactions),
as illustrated in Fig. 4a.
The
refore,
E
-
b
=
E
ion
+
E
cp
(3)
As M moves down the periodic table, the ionization potential decreases:
5.4 (Li)
,
5.1 (Na)
,
4.3
(K)
,
4.2 (Rb)
, and
3.9 (Cs),
which
favors the binding
and
results in a decrease of
E
ion
.
Note that
there is
a
n
abrupt drop in the
ionization
potential
between Na and K.
However, at the same time,
the distance between
cation
and the substrate becomes
larger,
which weakens the
ir
coupling
lead
ing
to
an
increase of
E
cp
.
T
o quantify this
competition
, Fig. 4b shows the
E
ion
and
E
cp
with
respect to those of Li
on the same substrate.
The
relative
E
ion
is
approximated
by
the difference
in
the
atomic
ionization
potential
(I
P
)
,
and the relative
E
cp
is
then
derived from Eq. (3).
Since
the
E
cp
increases smoothly from Li to Cs while the
E
ion
drops
dramatically
from Na to
K (in other
words,
the coupling
strength
increases smoothly from Cs to Li while the ionization cost
drop
s
dramatically from K to Na
)
, we
obtain
maximum of
E
-
b
for
Na
.
T
he
E
cp
is a general term which includes various kinds of interactions that are difficult to
separate
. However, for the cases of M adsorption on metal
(e.g. graphene and Pt (111))
, one
could expect the difference in
E
cp
of different Ms is dominated by the electro
static contribution,
wh
ich is
~
-
14.38/(2*
d
)
, where
d
is the distance
betwe
en the cation
and the substrate according to
the image charge method. Therefore in these cases:
∆
E
-
b
=
∆
E
ion
+
∆
E
cp
~
∆
[
-
14.38/(2*
d
)
]
+
∆
I
P
(
4
)
As shown in
Figure 4c
, the trend of
E
-
b
,
gi
v
en by
equation is similar to that calculated by using
DFT,
which
validates
that competition between
E
ion
and
E
cp
is
reason for
a maximum
of
E
-
b
at
Na
.
In
deed
, th
is
weak Na binding is also found in diatomic molecules M
-
X (where X=F, Cl, Br, I and
OH)
(
21
)
, which can be
explained similar
ly
.
It is interesting to
consider
whether the non
-
monotonic trend of the
E
-
b
is present
in other
columns
.
Based on
the
above explanation
s, we anticipate
that
this can be observed in
th
e
columns
where
E
ion
and
E
cp
have
a reverse trend when moving down the periodic table.
The
E
cp
perhaps always increases as the atomic siz
e gets larger; however,
E
ion
does not always decrease
,
giv
en
the fact that
the IP or electron affinity is non
-
monotonic for most groups
. In fact, only
the
first two
groups
have
a notably
decreasing
I
P
. Therefore, one may expect a similar
phenomenon
occurs for the EM group. Indeed, our calculations show that
among the EM element
s, Mg
generally has the weakest binding (Fig. 5)
with a given substrate
.
This
is consistent with the
experimental fact that Mg has a low capacity in graphite, similar to the case of Na
(
8
,
22
)
.
Note
that Be and Mg are o
nly physisorbed on pristine
or
nitrogen
-
doped graphene with
the
E
-
b
~
-
30
meV/
EM, significantly weaker than other EMs
. This is because
the work function of pristine or
nitrogen
-
doped
graphene
is too low to allow for a charge transfer from Be/Mg
, as sho
w
n
by the
band structures in the SI
. T
hese systems are perhaps not
practically
interesting
as the physisorbed
adatoms could easily detach or cluster.
I
t should also be noted that, Be tends to have a stron
ger
covalence than other EMs
, due to its high I
P
and sm
all size.
This might be the reason for the
significantly enhanced binding of Be with the mono
-
vacancy in graphene, in which case the
E
cp
contributes a large energy drop.
For
cathode
material
s
,
the
weak
binding
with
the metal
atoms
results in
a low cathodic
voltage. Therefore we anticipate
that
Na and Mg have a low cathod
ic
voltage compared with
other metals in the same columns. Indeed, the Na case has been verified by explicitly calculating
the cathodic voltage
for various
int
ercalation compo
unds
(
20
)
.
On the other hand, a weak binding
with
anode
is desired
to
enhance the voltage when connected with a
cathode
. However,
this
usually sacrifices capacity, as seen in the case of Na
in
graphite.
To improve the Na
capacity
,
it
is necessary to
reduce
E
f
. This can be
achieved
by
using a pre
-
strained graphite (i.e. reducing the
E
s
term in Eq. 2) with expanded interlayer spacing
through
intercalation
of some other species
,
as
has been demonstrated
experiment
ally
(
9
)
.
Our calculations show
that
the
optimum
E
f
for Na
-
graphite
is
reached
when the
graphite
interlayer distance
is
expand
ed
to 4.3
Å
, providing a target
value for experimental
design
.
Indeed
such an
expanded graphi
te
using organic pillars has been
shown
computationally
to provide very
promis
ing
hydrogen storage
of 6
.5
wt% at room
temperature
, meeting the DOE
requirement
(
23
)
. Alternatively, the
E
f
might
be reduced by
enhancing the binding
, which
might
be
achieved
through incorporati
ng
defects
(
24
,
25
)
.
In summary,
we use Quantum Mechanic
al
calculations,
to find
a general
phenomenon
—
among alkali
and alkaline
-
earth
metals,
Na
and Mg
generally
ha
ve
the weakest binding
for
a
given substrate
. We show that
this
results
from the com
petition between the ionization
of the
metal
atom
,
and the ion
-
substrate coupling
.
This finding elucidates the origin
of low Na capacity
in graphite,
predicts the voltage trends for
alkali and alkaline
-
earth metal ion
batteries
,
and
provides
a
basis
for analyzing the binding of alkali
and alkaline
-
earth
met
al
atom
s in a broad
range of systems
.
Acknowledgements
:
Y.L. thanks Drs. Brandon Wood, Suhuai Wei, and Jiayu Wan for helpful discussions and
Brandon Wood for providing access to the Lawre
nce Livermore National Laboratory
computational resources, which were used for some of the computations (supported under the
Laboratory Directed Research and Development Program). Most of the calculations were
performed on National Energy Research Scientif
ic Computing Center, a Department of Energy
(DOE) Office of Science User Facility supported by the Office of Science of the US DOE under
Contract DE
-
AC02
-
05CH11231. Y.L. acknowledges the support from Resnick Prize
Postdoctoral Fellowship at Caltech. This r
esearch was funded by the Bosch Energy Research
Ne
twork and by NSF (CBET 1512759)
.
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Liu Y, Wang YM, Yakobson BI, & Wood BC (2014) Assessing carbon
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based anodes for lithium
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1742.
Fig. 1
. Calculated formation energies (Eq. 1) of
alkali metal
(
M
)
-
graphite compounds. Note that
in contrast to other Ms, NaC
6
and NaC
8
have a positive formation energy.
Fig. 2
. (a)
Partition of
the formation process of M
-
graphite compound into separate steps. M:
pink; C: brown. (b) The energetics of each step, re
lative
to th
ose
of Li (see Eq. 2 and the related
text). ‘
-
binding’ means the reverse of binding energy, i.e.
E
-
b
in Eq. 2. Note that only
E
-
b
shows a
trend similar with
E
f
.
Fig. 3
.
E
-
b
(the negative of the binding energy) for alkali metals binding to various
substrate
materials, re
lative
to that of Li
(the absolute values can be found in the SI)
. (a) graphene
and its
derivatives
(
with defects or
substitutional
foreign
atoms)
;
(b) non
-
C
materials. Note that
Na
always has the weakest binding among
alkali
metals.