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Thermodynamic analysis on energy densities of batteries†‡
Chen-Xi Zu
ab
and Hong Li*
a
Received 15th December 2010, Accepted 14th February 2011
DOI: 10.1039/c0ee00777c
The average increase in the rate of the energy density of secondary batteries has been about 3% in the
past 60 years. Obviously, a great breakthrough is needed in order to increase the energy density from
the current 210 Wh kg
1
of Li-ion batteries to the ambitious target of 500–700 Wh kg
1
to satisfy
application in electrical vehicles. A thermodynamic calculation on the theoretical energy densities of
1172 systems is performed and energy storage mechanisms are discussed, aiming to determine the
theoretical and practical limits of storing chemical energy and to screen possible systems. Among all
calculated systems, the Li/F
2
battery processes the highest energy density and the Li/O
2
battery ranks as
the second highest, theoretically about ten times higher than current Li-ion batteries. In this paper,
energy densities of Li-ion batteries and a comparison of Li, Na, Mg, Al, Zn-based batteries, Li-storage
capacities of the electrode materials and conversion reactions for energy storage, in addition to resource
and environmental concerns, are analyzed.
1. Introduction
Secondary batteries have become a core technology for sup-
porting the development of a sustainable and mobile society.
The demand for advanced batteries with high energy densities is
increasing continuously due to the rapid progress of wide
applications from advanced portable electronic devices to electric
vehicles (EVs) and smart grids.
1,2
The importance of the devel-
opment of secondary batteries has been recognized by govern-
ments, and clear targets and roadmaps have been set.
For example, the New Energy and Industrial Technology
Development Organization (NEDO) in Japan released their
project on Li-ion and advanced battery development in 2008.
Their targets are 500 Wh kg
1
before 2030 and 700 Wh kg
1
afterward to develop high-performance, low-cost rechargeable
batteries for accelerating the commercialization of new vehicles
such as EVs.
3,4
Can these ambitious targets be realized within the expected
duration and can Li-ion batteries take a continuous leading role?
An analysis of the battery development in term of energy density,
possible energy storage mechanisms and a theoretical thermo-
dynamic calculation on the energy densities of possible batteries
and related materials are performed to address these questions.
2. Progress of batteries in term of energy density
Fig. 1 and Fig. 2 present the roadmap of primary and secondary
batteries from 1900 to now, respectively. The Zn/MnO
2
(NH
4
Cl
or ZnCl
2
) type primary battery dominated almost the whole
a
Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China.
E-mail: hli@aphy.iphy.ac.cn; Fax: +0086-10-82649046; Tel: +0086-10-
82648067
b
School of Materials Science and Engineering, Beihang University, Beijing,
100191, China
† Electronic supplementary information (ESI) available. See DOI:
10.1039/c0ee00777c
‡ This article was submitted as part of a special collection of papers from
the Institute of Physics, Chinese Academy of Sciences (IoP-CAS).
Broader context
Greatly increasing energy densities of current rechargeable batteries has become urgently needed to progress from today’s hybrid
electric vehicles to plug-in hybrids to all-electric vehicles. This is also essential for many new technologies, such as advanced portable
electronic devices, robot and unmanned aerial vehicles. Some battery systems, such as Li-S and Li-air batteries, have been expected
to increase the energy densities 2–10 times greater than that of current Li-ion batteries. Are these targets realizable? Can we increase
the energy density of Li-ion batteries further? Which system is worthy of being investigated as next generation high energy density
battery? Thermodynamic calculation on 1172 material systems has been performed. The calculated energy densities and the voltage
of the batteries are reported in this paper. These results are helpful for clarifying above questions and determining the theoretical
limit of electrical energy storage in chemical power sources. In addition, concerns about lithium supply due to potential large scale
production of batteries for electric vehicles and smart grid are analyzed.
2614 | Energy Environ. Sci., 2011, 4, 2614–2624 This journal is ªThe Royal Society of Chemistry 2011
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www.rsc.org/ees ANALYSIS
market before the 1940s.
5
In the 1960s, the Zn/KOH/MnO
2
battery took the leading role, pulling the energy density level
from 40 Wh kg
1
to 100 Wh kg
1
. Due to the significant
advantage of its low cost, it has been developed continuously and
is used widely even today. Primary lithium batteries (Li/MnO
2
,
Li/(CF)
n
) and Zn-air batteries appeared around the 1970s. The
energy density was doubled to 200–250 Wh kg
1
. In the 1980s,
primary Li/SO
2
and Li/SOCl
2
batteries were applied in special
fields and the energy density reached over 380 Wh kg
1
. Actually,
lithium dry polymer electrolyte batteries have been developed
since 1980.
5
Their energy densities ranged from
220–280 Wh kg
1
. They have not been commercialized and are
still being developed as secondary batteries.
The rechargeable lead-acid battery has been commercialized
for more than 100 years. The energy density has increased
gradually from initial 25 Wh kg
1
to the current 55 Wh kg
1
.
Although the energy density is not very satisfactory, it is still the
main choice for starting, lighting and ignition (SLI) in
automobiles and backup battery due to the advantages of high
reliability, low cost, moderate power density, acceptable cycling
performance and good recycling feature. The nickel-cadmium
battery has also been widely used for many small portable elec-
tronic devices before the appearance of the nickel metal hydride
battery and lithium ion batteries in the 1990s, and because of its
environmental impact the market share decreased significantly
afterward. In the early 1980s, a rechargeable sodium-sulfur
battery was developed. It operates around 300 C with energy
density of 100–150 Wh kg
1
. Currently, the Na–S battery is one
of the choices as large-scale stationary battery for load-leveling
applications.
6
The nickel metal hydride battery appeared on the
market in 1989 with energy density of 50–80 Wh kg
1
.
7,8
Almost
two years later, the Li-ion battery was commercialized by the
Sony company.
9,10
The energy density has increased steadily
from 90 Wh kg
1
to the current 210 Wh kg
1
.
From 1950 to 2010, the energy density of commercial
secondary batteries increased by about 3 Wh kg
1
per year in
average as shown in the dashed line in Fig. 2. Following this
growth rate, the target energy densities of 500 Wh kg
1
and
700 Wh kg
1
will be realized in years of 2110 and 2177 respec-
tively from the current 210 Wh kg
1
. Actually, the annual growth
rate from 1990 to 2010 was accelerated to about 5.5 Wh kg
1
due
to the invention and development of Li-ion batteries, as shown
by the solid line in Fig. 2. Based on this, the targets of 500 Wh
kg
1
and 700 Wh kg
1
can be realized in years of 2064 and 2100,
respectively. However, it is still far behind the NEDO’s target. As
shown in Fig. 1 and 2, the growth rate of the energy densities of
the batteries is steady for 20–30 year periods until the appearance
of the next new technology.
It is essential to estimate the limit of energy densities of
possible battery systems for storage and converting chemical
energy into electric energy. The theoretical energy density of any
battery can be simply calculated from the thermodynamic data
once the positive and the negative electrode materials are
selected. In addition, the thermodynamic equilibrium voltage (or
so-called electronic motive force, in brief, emf) of the battery can
be also calculated, as shown below.
3. Calculation formulas
Any chemical reaction which contains two different reactants
and in which charge transfer occurs could be applied for elec-
trochemical energy storage.
Such a reaction can be written as:
aA+bB/gC+dD (1)
Here, the Gibbs free energy of the reaction under standard
condition (D
r
G
Q
) can be calculated from the sum of the forma-
tion energy of the reactants and products:
D
r
G
Q
¼gD
f
G
C
Q
+dD
f
G
D
Q
aD
f
G
A
Q
bD
f
G
B
Q
(2)
If the value of D
r
G
Q
is negative, the electrochemical reaction
along the direction defined in the eqn (1) could occur sponta-
neously and the reaction can be considered for electrochemical
energy storage. The maximum electrical work from this reaction
equals to D
r
G
Q
, as shown in the Nernst equation:
Fig. 2 History of development of secondary batteries in view of energy
density. Data is taken from literature.
4
Dash line shows the progress of
last 80 years and solid line represents the development of Li-ion batteries
in last 20 years.
Fig. 1 History of development of primary batteries in view of energy
density. Data is taken from literature.
5
This journal is ªThe Royal Society of Chemistry 2011 Energy Environ. Sci., 2011, 4, 2614–2624 | 2615
D
r
G
Q
¼nEF (3)
Here nrefers to the number of the charge transferred during the
reaction per mole reactant, Eis the thermodynamic equilibrium
voltage or the so-called electromotive force (emf) value and Fis
the Faraday constant.
Energy density is always expressed either by the gravimetric
energy density Wh kg
1
or the volumetric energy density
(WhL
1
). The gravimetric energy density of a battery can be
calculated as following:
3
M
¼D
r
G
Q
/SM(4)
SMis the sum of the formula mole weights of the two reactants.
The volumetric energy density (3
V
) of a battery can be calcu-
lated as following:
3
V
¼D
r
G
Q
/SV
M
(5)
SV
M
is the sum of the formula mole volume of the two reactants.
For a given electrode material, the specific energy storage
capacity can be calculated from the eqn (6):
Capacity ¼nF/3.6 M (mAh g
1
) (6)
Mrefers to the mole weight of the reactant (g mol
1
).
Accordingly to the eqn (1 to 5), the theoretical energy density
and theoretical voltage can be calculated when the values of the
Gibbs formation energy of the reactant and the density of the
reactant are known. These values can be found in the thermo-
dynamic data handbook.
11–13
If the Gibbs formation energy of
the reactant is not known, it can be obtained through first
principles calculations.
14
4. Reversible energy storage mechanisms
Before discussing the energy density of the battery, it is necessary
to summarize possible reaction mechanisms for energy storage.
Taking lithium-storage as an example, eight possible reversible
lithium storage mechanisms are listed in Fig. 3 and summarized
below.
4.1 Intercalation reaction mechanism
An intercalation reaction indicates that guest atoms are accom-
modated in the structure of the host compounds accompanied by
charge transfer:
15–17
xA
+
+xe
+H4A
x
H (7)
A layered structure is preferred for the host compounds, but
not limited to this. The ‘‘rocking chair concept’’ for rechargeable
lithium batteries, in which the intercalation compounds were
suggested to be used in both the positive and negative electrodes,
were firstly suggested by Armand in 1972
18
and commercialized
by SONY in 1990.
9,10
In current Li-ion batteries for portable
electronic devices, layered structure graphite (R-3mspace group)
and LiCoO
2
(R-3mspace group) are used as the negative and the
positive electrode material, respectively. Thus, the guest atoms
occupy the host lattice continuously and the chemical potential
of the host is modified gradually. The voltage profile of charging
and discharging within a single-phase intercalation regime nor-
mally shows a slope behavior and can be explained by the lattice
gas model.
19,20
The reversible lithium storage capacity is deter-
mined by the available vacancy sites for guest atoms, a trans-
ferrable charge number above 0.0 V vs. Li
+
/Li and the structure
stability of the host. Typically, the reversible lithium storage
capacity for the graphite negative electrode is 300–350 mAh g
1
(theoretical capacity is 372 mAh g
1
for forming LiC
6
) and is
around 135–145 mAh g
1
for the LiCoO
2
positive electrode (the
theoretical capacity is 274 mAh g
1
for extracting one mole of
lithium).
4.2 Phase transition mechanism
During discharging or charging, the reactant transforms directly
and continuously from the initial phase into another phase. For
example, LiFePO
4
converts into FePO
4
during charging (deli-
thiation)
21
and Li
4
Ti
5
O
12
anode converts into Li
7
Ti
5
O
12
during
discharging (lithiation).
22
In addition, it is also common that the
electrode material could undergo a series of phase transitions
during continuous lithium insertion or extraction. Taking the
alloy-type reaction as an example, Si can form a series of Li–Si
alloys during electrochemical lithiation at high temperatures and
show several voltage plateaus in the voltage profile.
23
The open circuit voltage profile of each phase transition
reaction will show one plateau when the Gibbs formation energy
of the reactants and products do not vary upon lithium insertion
and extraction within the phase transition regime.
4.3 Conversion reaction mechanism
The ‘‘conversion reaction’’ is a kind of phase transition mecha-
nism. The term is used here to define specifically the
Fig. 3 Scheme of reversible lithium storage mechanisms. See explanation in text part.
2616 | Energy Environ. Sci., 2011, 4, 2614–2624 This journal is ªThe Royal Society of Chemistry 2011
decomposition reaction from one parent compound into two or
more products after lithium insertion. Reversible heterogeneous
conversion reactions of transition metal oxides (TMO)
with lithium were reported for the first time on 2000 by
Poizot et al.:
24
2Li + TMO 4Li
2
O + TM (TM ¼Co, Fe, Ni, Cu) (8)
Later, reversible lithium storage has been observed in transi-
tion metal fluorides, sulfides, nitrides, phosphides and
hydrides.
25–29
Recently, the reversible conversion reaction is
also extended to other polyanion compounds, such as the
reaction (9):
30
xLi + Cu
2.33
V
4
O
11
4Li
x
V
4
O
11
+ 2.33Cu (9)
The lithium storage capacity through the conversion reaction
can be as high as 1480 mAh g
1
in the case of MgH
2
anode for Li
batteries (theoretical capacity is 2062 mAh g
1
for forming Mg
and 2LiH).
29
Many materials undergoing the conversion reaction
have been considered as positive or negative electrode materials.
In spite of their high capacity, most conversion reaction type
electrode materials suffer from high voltage polarization between
the charging and discharging, and the low initial Coulombic
efficiency.
31–33
A thermodynamic calculation on the emf value and the
Li-storage capacity of dozens of binary compounds was reported
in 2004 by Li et al.
34
In this paper, a more comprehensive
calculation is performed as shown in a later section.
4.4 Reversible chemical bonding
All types of chemical energy storage can be regarded as certain
type of reversible chemical bonding. Here this term is used
specifically for organic molecules containing carbonyl func-
tional groups, which has been developed recently by scientists
in Amiens.
35–38
The carbonyl groups can be utilized to bond
with lithium reversibly at room temperature with a reasonable
capacity and rate performance.
35–37
A typical compound is
dilithium rhodizonate, in which carbonyl groups can be used
for lithium storage with a theoretical capacity of 589 mAh g
1
at a voltage range of 1.5–3.0 V vs. Li
+
/Li. This concept has
been extended to ethoxycarbonyl-based organic compounds as
anode material with a capacity of 100–120 mAh g
1
at
a voltage range of 1.5–2.0 V. The voltage profiles are plateau
type since it is a kind of first-order phase transition reaction.
The voltage polarization is much lower than those observed in
conversion reactions.
38
Organic electrode materials and the
reversible chemical bonding mechanism remain many funda-
mental issues, such as ion transport, material design and
synthesis, stability, as well as technical challenges, such as low
volumetric energy density, moderate rate and cyclic perfor-
mances. However, they are important valuable candidates for
a sustainable development of future batteries since they could
be produced through biochemistry from abundant natural
products.
35–38
Li
2
C
6
O
6
+ 4Li 4Li
6
C
6
O
6
(10)
4.5 Surface charging mechanism
The surface charging mechanism refers to the storage of both
anions and cations from the electrolyte on the surface of the two
electrodes separately after applying an external electrical field,
charge balanced by the holes or electrons within the electrode.
Most of the supercapacitors operate based on both the surface
charging mechanism in addition to surface redox reactions
(pseudo-capacitors).
39–41
The surface charging is related to the
occupation of ions at the available surface sites on the surface of
the substrate electrode material. Therefore, the voltage profile is
a liner shape with a slope of Q/C in a certain voltage range.
42
The capacity of the surface charging is determined by the
capacitance, which is related to the surface area, thickness of the
double layer, dielectric constant and type of anion and cation in
the electrolyte. The supercapacitors have advantages of high
rate performance (1–10 kW kg
1
) and excellent cyclic perfor-
mance (100 000 cycles). Currently, combining the surface
charging mechanism and the redox reactions mentioned in 4.1–
4.3 has attracted much attention to increase the energy density
of supercapacitors.
41
4.6 Organic free radical mechanism
Organic radical molecules bear one (or multi) unpaired or open-
shell electron(s), and they are highly reactive by being converted
into closed-shell molecules through a dimer formation or a redox
reaction with other molecules, solvents, or molecular oxygen.
43
Radical polymers are aliphatic or non-conjugated polymers
which bear organic radicals as pendant groups repetitively in
each unit; the outer-sphere redox reactions of the radicals lead to
fast electron self-exchange reactions in electrolyte solutions. The
large heterogeneous electron-transfer rate of the redox centers
and the efficient mass-transfer process within the polymer layers
allow facile accommodation of the electrolyte ions to compensate
for charges generated from the neutral radicals, in which way the
radical polymers serve as ions storage materials, providing an
insight into the storage of lithium by forming the corresponding
charge pair within the electrode interface.
44
Since the first report
on organic radical batteries demonstrated by Nakahara et al.,
45
intensive studies have been focused on exploring cathode-active
and anode-active materials.
44,46
It was reported that the Li-ion
free-radical batteries are superior in safety, sustainability and
possess value in the configuration of flexible batteries,
47
however,
like organic electrode materials with reversible chemical bonding
mechanism, they face intrinsically lower volumetric energy
densities.
This journal is ªThe Royal Society of Chemistry 2011 Energy Environ. Sci., 2011, 4, 2614–2624 | 2617
4.7 Under potential deposition mechanism
It has been proposed that lithium can be stored within the
microporous or mesoporous materials just above the plating
voltage of lithium at 0.0 V vs. Li
+
/Li,
48–51
at a form of under
potential deposition (UPD). Previous TEM observation has
demonstrated the formation and disappearance of lithium clus-
ters within nanopores of carbon nanotubes during discharging
and charging.
52
This reaction occurs at lower voltage. Since the
formation energy of this reaction is mainly determined by
the adsorption energy of lithium on the substrate, related to the
occupation of surface sites, the observed voltage profiles are
slopes.
53
The kinetic property of lithium storage in microporous
materials is not very good.
53
In addition, the deposition voltage is
too closed to the plating voltage of lithium, leading to safety
concern. Therefore, the UPD mechanism in porous materials is
not suitable to be considered for applications in lithium batteries.
4.8 Interfacial charging mechanism
In the study of lithium storage in TiF
3
and VF
3
materials through
conversion reaction, it was found that extra lithium can be stored
reversibly in the LiF/M nanocomposites at a low voltage range of
0–1.2 V, showing sloped voltage profiles. Since the emf values of
the related conversion reactions are higher than 1.2 V vs. Li+/Li
and both LiF and Ti or V cannot accommodate lithium, it was
suggested that this reversible lithium storage mechanism is
caused by an interfacial interaction between lithium within the
M/LiF matrix, possibly leading to a distinct local charging.
54
A
clear physical picture on this phenomenon was given firstly by
Jamanik and Maier.
55,56
Further first principles calculation on
the lithium storage at the interface between Ti and Li
2
O
confirmed that this mechanism is thermodynamically favor-
able.
57
Some experimental evidence of the existence of this type of
mechanism has been provided recently.
58,59
The typical lithium
storage capacity of the interfacial charging is about 100–
300 mAh g
1
. The electrochemical potential of the interfacial
charging is not very high when a large amount of lithium is
inserted into the LiX/M nanocomposite. In view of capacity, Li-
storage through interfacial charging is not very competitive
compared to other mechanisms for storing lithium in the nega-
tive electrode. However, this mechanism should not be ignored
when the material has a nanostructure with abundant grain
boundaries.
5. Energy density of batteries
5.1 High energy density battery systems
According to the eqn (1 to 5), 1172 reactions have been calcu-
lated. The standard Gibbs free enthalpy data and the density
data at 25 C are taken from the literatures.
11–13
The detailed
calculated results are provided in the ESI (Table S1).† Fig. 4
displays 20 selected battery systems with higher gravimetric
energy densities among all systems. The graphite/LiCoO
2
type
Li-ion batteries is also included for comparison. Obviously, the
reactions show higher energy densities when the formation
energy values of the reactants are lower and those of the products
are higher. Among all calculated systems, the Li/F
2
battery holds
the highest record of 6294 Wh kg
1
. The Li/O
2
battery follows
closely with a gravimetric energy density of 5217 Wh kg
1
.
Besides the reactions of metal with fluorine and oxygen,
combustion reactions with oxygen and a few of conversion
reactions also show higher energy densities. It has to be
mentioned that the combustion reactions can be used to convert
chemical energy into the electrical energy directly through fuel
cells. The theoretical gravimetric energy densities of these reac-
tions shown in Fig. 4 are calculated for the isolated fuel cell
system with stoichiometrical fuel.
5.2 Comparison of batteries using different metal negative
electrodes
Fig. 5 shows gravimetric energy densities of selected battery
systems using Li, Na, Mg, Al, Zn as the negative electrode,
Fig. 4 Calculated energy densities of different battery systems according
to the Nernst equation. The formation energies of reactants and products
under standard conditions are taken from the literature.
12,13
The energy
density of the Li
2
C
6
O
6
/Li battery is calculated using data from the
literature.
35
Energy densities of the systems containing gas reactants are
calculated based on the reaction formula shown in the Figure.
Fig. 5 Comparison of the calculated gravimetric energy densities of
different battery systems using Li, Na, Mg, Al or Zn as anodes. The
corresponding reactions, emf values and volumetric energy densities are
listed in Table 1.
2618 | Energy Environ. Sci., 2011, 4, 2614–2624 This journal is ªThe Royal Society of Chemistry 2011
respectively. Theoretically, the reaction with fluorine inherits the
highest energy density. Since fluorine based batteries seem
impossible to be handled, the reactions with oxygen are
employed to represent the highest energy density level in each
group. Besides, several systems with high energy densities for
each metal are selected. For reactions in the same type, lithium
battery processes the higher gravimetric energy densities
compared to other metal negative electrode systems. However, in
terms of volumetric energy density, some Al and Mg systems
show certain advantages, as listed in Table 1. As we discussed in
the last section, if the production of lithium-based batteries
increases rapidly and the recycling technology of the lithium
batteries has not been developed very well, the available
resources of lithium could be a problem. If this happens, Na, Mg
and Al-based rechargeable batteries could be also considered
since their theoretical energy densities are comparable to or not
too much lower than those of lithium-based systems. Continuous
efforts on these batteries have been made.
60–68
5.3 Energy densities of rechargeable metal lithium batteries
Rechargeable metal lithium batteries have been developed for
over 50 years. The dendrite formation of lithium during the
charging process was regarded as inevitable. It causes practical
problems, such as poor safety characteristics, poor cyclability,
and the requirement for a long charging time.
10,69
Up to now,
rechargeable lithium batteries have not been commercialized
successfully. However, it is believed that those problems could be
solved by modifying the surface, replacing the electrolyte or
optimizing the electrode and battery structure. When metal
lithium is used as the negative electrode, the choice of the positive
electrode material can be extended widely from lithium-con-
taining compounds used in Li-ion batteries. The 20 systems with
higher energy densities among calculated systems are shown in
Fig. 6 for reference (see more results in the ESI: Table S3–S4†).
5.4 Energy densities of Li-ion batteries
Currently, at least three types of Li-ion batteries have been
developed for different applications. (1) High energy density
(150–210 Wh kg
1
): LiCoO
2
or LiNi
1/3
Co
1/3
Mn
1/3
O
2
is used in
Table 1 Calculated energy densities of different battery systems using Li, Na, Mg, Al or Zn as anodes. The volumetric energy densities of the batteries
containing gas components are not calculated
No. Electrochemical reaction DG/kJ mol
1
EMF/V Cathode capacity/mAh g
1
Energy density/Wh kg
1
Energy density/W h L
1
1 4Li + O
2
42Li
2
O1122 2.910 3350 5217 —
2 2Li + S 4Li
2
S439.0 2.275 1672 2654 2856
3 5Li + RuF
5
45LiF + Ru 2157 4.472 683.5 2597 5199
4 4Li + MnO
2
42Li
2
O+Mn 657.3 1.703 1233 1592 2642
5 CoO
2
+ LiC
6
4LiCoO
2
+C
6
347.4 3.600 273.8 567.8 1901
6 5Na + RuF
5
45NaF + Ru 1950 4.043 683.5 1742 3210
7 4Na + O
2
42Na
2
O751.0 1.950 3350 1683 —
8 NiCl
2
+ 2Na 4Ni + 2NaCl 509.2 2.640 413.6 805.6 1677
9 2Na + 3S 4Na
2
S
3
405.2 2.100 558.4 791.7 1179
10 4Na + MnO
2
42Na
2
O+Mn 285.9 0.741 1233 443.9 709.6
11 2Mg + O
2
42MgO 1139 2.950 3350 3924 —
12 5/2Mg + RuF
5
45/2MgF
2
+Ru 1896 3.931 683.5 2051 6181
13 Mg + S 4MgS 341.8 1.771 1672 1684 3221
14 2Mg + MnO
2
42MgO + Mn 673.5 1.745 1233 1380 4150
15 Mg + 2AgCl 4MgCl
2(aq)
+ 2Ag 497.5 2.580 186.8 444.4 2109
16 4/3Al + O
2
42/3Al
2
O
3
1055 2.733 3350 4311 —
17 5/3Al + RuF
5
45/3AlF
3
+Ru 1604 3.325 683.5 1848 6658
18 4/3Al + MnO
2
42/3Al
2
O
3
+Mn 589.8 1.528 1233 1333 5384
19 2/3Al + S 41/3Al
2
S
3
213.3 1.106 1672 1184 2676
20 2/3Al + AgO 41/3Al
2
O
3
+Ag 541.3 2.805 432.7 1060 6488
21 Zn + 1/2O
2
4ZnO 320.5 1.660 3350 1094 —
22 5/2Zn + RuF
5
45/2ZnF
2
+Ru 1002 2.077 683.5 776.0 3804
23 Zn + S 4ZnS(sphalerite) 201.3 1.043 1672 573.6 2162
24 Zn + 2MnO
2
4ZnO + Mn
2
O
3
271.4 1.410 308.3 315.1 1738
25 2NiOOH + 2H
2
O+Zn4
2Ni(OH)
2
+ Zn(OH)
2
273.0 1.410 292.3 266.2 891.8
Fig. 6 Comparison of the calculated energy densities of lithium battery
systems. Li-ion battery (LiCoO
2
/C) marked in red is also drawn for
comparison. The corresponding reactions are listed in Table S4.† Here
Li/MnO
2
(1) refers to conversion mechanism (Li
2
O/Mn as product) while
Li/MnO
2
(2) refers to intercalation mechanism (LiMnO
2
as product).
This journal is ªThe Royal Society of Chemistry 2011 Energy Environ. Sci., 2011, 4, 2614–2624 | 2619
the positive electrode and graphite is used in the negative elec-
trode. (2) High power density (1000–4000 Wkg
1
): LiMn
2
O
4
or
LiFePO
4
is used in the positive electrode and graphite or hard
carbon is used in the negative electrode. The energy density
ranges from 70–140 Wh kg
1
. (3) Long cycle life (3000–
10 000 cycles of 100% DOD): LiFePO
4
is used in the positive
electrode and Li
4
Ti
5
O
12
or graphite is used in the negative elec-
trode. In order to increase the energy density of Li-ion batteries,
high voltage positive electrode materials and high capacity
positive and negative materials are pursued. Many materials
have been investigated. It seems that Si and lithium-rich
compounds are quite competitive as the candidate for the nega-
tive and positive electrode respectively. Due to difficulty in
finding thermodynamic data of lithium-containing compounds,
the theoretical energy densities of Li-ion batteries could be
calculated based on the calculated open circuit voltage values
(OCV) from literatures and the highest transferable charge
number using the eqn (3). Taking the LiCoO
2
/C
6
as an example,
when the OCV is taken as 4.2 V, and charge is taken as one
electron. Then calculated value is 648.23 Wh kg
1
. However, in
the cases that the OCV of the batteries varies with the amount of
inserted/extracted lithium, taking average open circuit voltage
should be more reasonable. For example, if 3.6 V is taken as the
average open circuit voltage (AOCV) for the LiCoO
2
/C
6
battery,
the calculated value is 567.8 Wh kg
1
for extracting one lithium.
Actually, only 0.5 Li can be extracted. Accordingly, the
theoretical energy density of LiCoO
2
/C
6
battery should be
360 Wh kg
1
. It is difficult to calculate or measure average open
circuit voltage accurately, therefore, the calculated values of the
energy densities using AOCV could be overestimated or under-
estimated about 8–10% for the intercalation type Li-ion batteries
due to the deviation of the average open circuit voltage. In this
manuscript, the estimated theoretical energy densities of Li-ion
batteries are calculated using AOCV if not mentioned specifi-
cally. All calculated results and the parameters can be found in
the ESI (Tables S1 & S5).† A comparison of the calculated
theoretical gravimetric and volumetric energy density between
different materials is also shown in Fig. 7. Among them, the
highest value is 963.7 Wh kg
1
, which is 267% of the theoretical
value of current graphite/LiCoO
2
Li-ion batteries.
5.5 Real energy density of typical batteries
Since the weight or volume of the active material for storing
chemical energy is only a part of the total weight or volume of the
batteries, the real energy densities is always much lower than
calculated values. As seen in Table 2, the ratio of the real energy
density to calculated energy density (R) is 42–58% for Li-ion
batteries. Panasonic announced recently that their Li-ion
batteries using Ni-based positive electrode material and Si-based
negative electrode material could achieve an energy density of
251.9 Wh kg
1
(800 Wh L
1
), which is 41.9 Wh kg
1
higher than
the graphite/LiCoO
2
Li-ion batteries.
70
Taking the highet Rvalue of 58%, the estimated energy density
of the Li-ion battery using high capacity materials
(Si, Li
1.3
Ni
0.23
Co
0.23
Mn
0.54
O
2
), Li-air battery and Li–S battery is
approximately 497 Wh kg
1
, 3264 Wh kg
1
and 1541Wh kg
1
respectively. Obviously, it may be not possible for these new
batteries to achieve the same Rvalue of 58%. It has to be
mentioned that above consideration is suitable for the batteries
in which the positive and negative electrode materials are sealed
in the container. If the reactants are fed continuously from
external sources, as in the fuel cell, or the volume and weight
ratio of the reactants are very high, as in the redox flow batteries,
this Rratio may be higher, although current technologies show
still lower values as listed in Table 2. Typical energy densities of
portable fuel cell are claimed at a range of 120–800 Wh kg
1
and
110–380 Wh L
1
.
71
Rvalues are ranged from 3–23%.
6. Li-storage capacity of the electrode materials
As discussed in the Section 3, the calculated energy density of
a battery is determined by the formation energy of the reactants
and products. The real energy density equals roughly to the
product of the real lithium storage capacity and the average
working voltage. The working voltage of a battery is a voltage
difference between the electrode potentials of the positive and
negative electrode. For Li-ion batteries, in order to achieve high
energy density, the average lithium insertion potential of the
negative electrode should be as low as possible, just above the
lithium plating potential (50 mV–0 V vs. Li
+
/Li). This
requirement is not a problem for most of the high capacity
negative electrode materials. The average lithium insertion
potential of the positive electrode should be as high as possible,
but 0.5–1.0 V below the decomposition potential of nonaqueous
organic electrolytes (typically, 4.5–5.0 V vs. Li
+
/Li). The elec-
trode potential at equilibrium state is related to the Fermi level
(electrochemical potential) of the active electrode material. It can
be calculated simply from the thermodynamic data using the
Nernst equation for the phase transition reaction, conversion
reaction and chemical bonding reaction as mentioned above. For
the intercalation reaction, the estimation of the potential could
be obtained through the first principle simulation.
14,72
The theoretical lithium storage capacity is determined simply
by the number of transferable charges and number of extractable
or pluggable lithium ions. The real number of pluggable lithium
ions is sometimes limited by the structure stability, which is quite
difficult to be predicted accurately by theory. Actually, it is very
simple to estimate the maximum number of transferable charges.
Taking LiCoO
2
as an example, Co
3+
can be oxidized to Co
4+
.
Fig. 7 Comparison of the calculated gravimetric and volumetric energy
densities of selected Li-ion batteries. Solid short bar refers to estimated
practical energy densities, which are calculated from 1/3 theoretical
energy densities.
2620 | Energy Environ. Sci., 2011, 4, 2614–2624 This journal is ªThe Royal Society of Chemistry 2011
Therefore, the theoretical capacity can be calculated based on
one charge transfer since one mole of lithium is also available.
For conversion reaction, taking MnO as an example, Mn
2+
can
be reduced maximally to Mn
0
. Two electrons per mole can be
transferred. Obviously, multi-electron reaction materials are
interest for high capacity materials.
73
The charge transfer is considered mainly from the valence
variable transition metal cations. This is not necessary for all the
cases. Sometimes, anions could also take part into redox reac-
tions, such as S in Li–S battery and probably O in lithium-
enriched compounds [xLi
2
MnO
3
$(1 x)LiMO
2
].
74
Charge
transfer contributed from both transitional metal and anions
could lead to breakthrough of new high capacity cathode
materials for Li-ion batteries.
Lithium storage capacities of 448 kinds of materials have been
calculated. The detailed results can be found in the ESI
(Table S6–S9 and Figure S1–S3).† Apparently, materials
undergoing the conversion reaction show a high capacity for the
positive electrode materials and the materials undergoing an
alloy type reaction show a high capacity for the negative
electrode materials.
7. Storing energy through the conversion reaction
The conversion reaction mechanism was introduced in section
4.3. Actually, primary batteries operating through the conver-
sion reaction have been around for a long time, such as the
commercialized Li/CuO, Li/(CF)
n
, Li/SO
2
, Li/SOCl
2
, Li/FeS
2
batteries in the 1980s.
5
However, reversible conversion reactions
have attracted wide attention only after the report by P. Pozoit
et al. in 2000.
24
Conversion reactions show high voltage hysteresis between the
charging and discharging, which is related to both thermody-
namic and kinetic factors.
33
The initial Coulombic efficiency is
normally less than 75% except for RuO
2
.
75
As high capacity
negative electrode materials, the materials storing lithium
through conversion reactions are not competitive compared to
alloy-type materials, in term of high capacity, low voltage and
low voltage polarization.
The conversion reaction seems more attractive for exploring
the positive electrode materials. The emf values of the binary
transitional metal compounds for the same metal with the same
valence, have the following order for storing lithium: fluoride
> oxide > sulfide > nitride > phosphide. The materials with
higher oxidation state show higher emf values. For the same
material but inserted by different atoms, the emf values of the
conversion reactions for fluorides show the order of Li > Na >
Mg >Al. The insertion reactions of Na, Mg and Al are much less
studied than the lithium insertion reactions.
These tendencies can be seen clearly in Fig. 8, Fig. 9 and
Table S10–S11,† which could be also relevant and helpful to
understand the tendency for the materials storing chemical
energy through the intercalation or phase transition mechanisms.
A comprehensive calculation result can be found in the ESI
(Table S1, Figure S4–S11)† for reference.
Two points are worth mentioning. (1) The reversible conver-
sion reaction is a reminder that disordered nanostructured or
nanocomposite materials could be also considered as electrode
materials, instead of just highly ordered crystalline materials. (2)
It is known that the materials cannot be inserted with lithium to
complete the conversion reaction if their emf values are less than
0.5–1.0 V vs. Li
+
/Li due to the high overpotential.
34
This infor-
mation is helpful for searching solid electrolytes and solid sealant
materials for solid state lithium batteries.
8. Resource and environmental issue
Due to the large scale applications and the potential markets for
high energy density and high power density batteries for electric
Table 2 Real energy density of typical batteries
Battery type Electrochemical reaction Cal. energy density/Wh kg
1
Real energy density/Wh kg
1
Real/Cal. (%)
Pb-acid Pb + PbO
2
+2H
2
SO
4
42PbSO
4
+2H
2
O 171 25–55 15–32
Na–S 2Na + 3S4Na
2
S
3
792 80–150 10–19
Ni-MxH 1/5LaNi
5
(1/2H
2
)+NiOOH ¼Ni(OH)
2
+ LaNi
5
240 50–70 20–29
Li-ion 2Li
0.5
CoO
2
+ LiC
6
42LiCoO
2
+C
6
360 150–210 42–58
Li–S Li + 2S4Li
2
S 2654 250–350 9–13
Li-MnO
2
2Li + 2MnO
2
4Li
2
O+Mn
2
O
3
970 100–220 10–23
Zn–O
2
Zn + 1/2O
2
/ZnO 1094 150–200 14–18
Li-(CF)
n
Li+(CF)
n
/LiF + C 2189 200–300 9–13
Li–O
2
2Li + O
2
/2Li
2
O 5217 — —
Li–F
2
2Li + F
2
/2LiF 6294 — —
H
2
–O
2
H
2
+ 1/2O
2
/H
2
O 3525 120–800 3–23
Fig. 8 Calculated EMF values (V) of conversion reactions between
selected binary transition metal compounds and lithium.
This journal is ªThe Royal Society of Chemistry 2011 Energy Environ. Sci., 2011, 4, 2614–2624 | 2621
vehicles and long life stationary batteries for smart grid and
dispersed renewable energy systems, concerns about the natural
resources for the sustainable development of lithium batteries are
increasing continuously. The abundance of lithium in earth
accounts for only 0.002% among all constituting elements
(Figure S12†),
76–78
and only few of countries, such as Argentina,
Chile, China, and the United States, are the leading producers of
lithium carbonate.
79
According to data from the US
Geological Survey (USGS) and Meridian International Research
(MIR),
79–82
the resources of lithium are identified as a total of
25.5 million tons 2010, in which the reserve base accounts for
approximately 11 million tons and the reserve 4 million tons.
Lithium consumption increased by 6% on average per year from
2000 to 2008,
80
from this point it slowed down to less than 4%
growth rate owing to the economic crisis.
83
In that time the total
world lithium consumption was about 21 280 tons, so the exist-
ing resources of lithium could be sustained for approximately 65
years from now on taking an average 5% growth per year as an
estimate. (Data of the lithium reserve base are used for estima-
tion and the ever increasing demand from the EV market is not
considered at this moment.)
However, the potential market for electrical vehicles could
accelerate the demanding for lithium resource to a large scale.
Currently, global lithium end-use markets are estimated as
follows: ceramics and glass, 31%; batteries, 23%; lubricating
greases, 10%; air treatment, 5%; continuous casting, 4%; primary
aluminium production, 3%; and other uses, 24%.
80
Lithium use in
batteries expanded notably in recent years (20% average
growth),
79
and electric vehicle batteries could be projected to
dominate the long-term lithium demand. Today, some 60 M
light-duty vehicles are produced each year in the world, and in
2050 the number is estimated to be 175 M following a linear
growth model.
84
Assuming that around 60% of them might have
electric drives and among which EV sales account approximately
22% (an optimistic market penetration scenario is chosen), then
if one EV vehicle is equipped with a 50 kWh battery the total
lithium request in this aspect alone could be 570 000 t. (existing
LiIon/LiMP ‘‘Energy Batteries’’ for EVs require about 0.3 g of
lithium metal equivalent per kWh, in the form of lithium
carbonate),
81
more than 20 times the current lithium annual
world production level of 25 000 t. In terms of the remaining
68 M plug-in hybrid electric vehicle (PHEV) sales, if they were all
PHEV 20s with a small 5 kWh battery, the total amount of
lithium metals required would therefore be 102 000 t. Actually,
according to this model, given that all the lithium reserves were
used to satisfy the EV and HEV markets, it would be approxi-
mately 36 years before we run out of lithium. In practice, the
demand for lithium varies greatly for different types of battery
chemistry and the difference could be 5 to 8 times the present
energy density level of Li-ion batteries.
World demand for lithium resources, especially in the electric
vehicle market is difficult to estimate due to the complex
scenarios considering many possible compromises between cost
and performance. However, it is safe to say that the new and
increasing demand on the lithium supply could be reduced by
developing recycling technologies, although currently this
contribution is negligible according to the survey from USGS.
80
Since Scrosati et al. reported a preliminary laboratory-scale
lithium battery recycling process in 1999,
85,86
many endeavors
have been made. However, lithium recycling is currently not
profitable for small lithium batteries. Obviously, a breakthrough
is needed to maximize recovery with minimum impact and
decrease the cost. Recently, the ionothermal synthesis method
and hydrometallurgical leaching process may possess some value
regarding this issue.
87,88
It could be more cost-effective for the
recycling of large size battery. It has been estimated that
switching from virgin resource supply to recycling for cobalt and
nickel for Li-ion battery cathode material results in a 51%
natural resource saving.
89
Table S12 (ESI†) gives toxicity information on major elements
that are used in battery assembly. It has been analyzed that the
mean cobalt level of the battery electrode is about 45 times the
toxicity threshold limit concentration for cobalt while the mean
nickel result is about 38 times the toxicity threshold limit
concentration. Spent portable rechargeable lithium batteries
should be handled as toxic materials that require special treat-
ment. Implementation of a well-coordinated management
strategy for spent batteries is urgently required to check the
dissipation of large doses of toxic heavy metals into the envi-
ronment.
90
It should be also mentioned that although chromium
and vanadium containing battery systems could deliver higher
energy densities, they should not be applied in term of environ-
mental protection due to their high toxicity.
Due to superior recycling technologies, sustainability and
green chemistry concepts, organic electrode materials have been
studied over the years. The feasibility of using active Li
x
C
6
O
6
organic molecules that could be prepared from natural sugars
common to living systems is currently under investigation.
35
Although organic materials have several disadvantages in terms
of their limited thermal stability, low specific gravity and poor
solubility in electrolytes, the search for electroactive organic
molecules synthesized from biomass may pave the way for
sustainable development of next generation batteries.
1
9. Summary and outlook
In the past 60 years, the energy density of rechargeable batteries
has increased from 25 Wh kg
1
to the current value of
Fig. 9 Calculated EMF (V) of conversion reactions between selected
binary transitonal metal fluorides and Li, Na, Mg or Al.
2622 | Energy Environ. Sci., 2011, 4, 2614–2624 This journal is ªThe Royal Society of Chemistry 2011
210 Wh kg
1
. According to this growth speed, it is not possible to
realize the target of 500 Wh kg
1
for the application of electric
vehicles before the year 2030. A breakthrough is needed urgently.
The thermodynamic calculations are helpful for checking the
theoretical limitation, predicting and searching possible energy
storage systems. It is found that the energy density of the Li/F
2
battery is the highest among calculated 1172 systems. The Li/O
2
battery ranks as No. 2 with a theoretical energy density of 5216.9
Wh kg
1
. Currently, the highest ratio of the real energy density to
the theoretical energy density is 58%, achieved by the LiCoO
2
/C
6
Li-ion batteries. If this Rvalue could be hold for many new
batteries as calculated in this manuscript, it is really possible to
realize the ambitious target of 500–700 Wh kg
1
.
Due to the great demand for applications of electric vehicles
and stationary batteries for load-leveling and dispersed renew-
able energy systems, increasing the energy densities and cyclic
performance of the batteries, improving the recycling technolo-
gies for rechargeable lithium batteries, and developing Na, Mg
and Al-based batteries, in addition to organic rechargeable
batteries, should be important strategies for sustainable devel-
opment of secondary batteries. However, many scientific and
technological barriers need to be overcome.
Acknowledgements
Financial support from CAS (KJCX2-YW-W26), NSFC
(50730005), ‘‘863’’ project (2009AA033101) and ‘‘973’’ project
(2007CB936501) is acknowledged.
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2624 | Energy Environ. Sci., 2011, 4, 2614–2624 This journal is ªThe Royal Society of Chemistry 2011
Supplemental document
Thermodynamic analysis on energy densities of batteries
Chen-Xi Zu1, 2, Hong Li 1, *
1 Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
2 School of Materials Science and Engineering, Beihang University, Beijing
100191, China
Corresponding author: hli@aphy.iphy.ac.cn
Supplementary data caption:
Table S1. All chemical reactions calculated.
Table S2. Thermodynamic data of typical battery systems. The volumetric
energy densities of the batteries containing gas components are not
calculated.
Table S3. Thermodynamic data of selected typical lithium battery systems.
Table S4. Thermodynamic data of all lithium battery systems calculated.
Table S5. Thermodynamic data of lithium-ion battery systems with high
gravimetric energy densities.
Table S6. Capacity values of typical lithium-free cathodes.
Table S7. Capacity values of lithium-contained cathodes.
Table S8. Capacity values of typical anodes.
Table S9. Capacity values calculated in all.
Table S10. Calculated EMF values (V) of conversion reactions between binary
transition mental compounds and lithium.
Table S11. Calculated EMF (V) of conversion reactions between fluorides and
Supplementary Material (ESI) for Energy & Environmental Science
This journal is © Royal Society of Chemistry 2011
Li, Na, Mg or Al.
Table S12. Key elements in the battery assembling and the toxicity.
Figure S1. Capacity values of typical lithium-free cathodes.
Figure S2. Capacity values of lithium-contained cathodes.
Figure S3. Capacity values of typical anodes.
Figure S4. Calculated EMF values (V) of conversion reactions between
transition mental salts and lithium.
Figure S5. Calculated EMF values (V) of conversion reactions between binary
transition mental compounds and sodium.
Figure S6. Calculated EMF values (V) of conversion reactions between binary
transition mental compounds and magnesium.
Figure S7. Calculated EMF values (V) of conversion reactions between binary
transition mental compounds and aluminum.
Figure S8. Calculated EMF (V) of conversion reactions between oxides and Li,
Na, Mg or Al.
Figure S9. Calculated EMF (V) of conversion reactions between sulphides and
Li, Na, Mg or Al.
Figure S10. Calculated EMF (V) of conversion reactions between nitrides and
Li, Na, Mg or Al.
Figure S11. Calculated EMF (V) of conversion reactions between fluorides and
Li, Na, Mg or Al.
Figure S12. Elements abundance in the earth.
Supplementary Material (ESI) for Energy & Environmental Science
This journal is © Royal Society of Chemistry 2011
Table S1. All chemical reactions calculated.
Li
MaXb n
∆rG
(kJ mol-1)
EMF
(V)
Capacity
(m A h g-1)
Cal.
Energy
density
(W h kg-1)
Cal.
Energy
density
(W h L-1)
F
BeF2 2.00 -196.0 1.016 1140.3 894.1 1125.3
NaF 1.00 -41.4 0.429 638.3 235.0 409.2
MgF2 2.00 -104.3 0.540 860.4 380.3 632.8
AlF3 3.00 -332.0 1.147 957.5 880.0 1395.5
KF 1.00 -49.9 0.517 461.3 213.1 380.5
CaF2 2.00 0.2 -0.001 686.6 -0.6 -1.1
ScF3 3.00 -223.3 0.771 788.7 505.1 775.8
TiF3 3.00 -401.1 1.386 766.8 886.5 1501.9
TiF4 4.00 -791.8 2.052 865.5 1450.6 2284.9
VF3 3.00 -536.4 1.853 744.9 1157.3 2096.1
CrF3 3.00 -659.7 2.279 737.7 1411.5 2707.6
MnF2 2.00 -368.3 1.909 576.8 957.8 2073.2
MnF3 3.00 -763.3 2.637 718.3 1597.1 3002.6
FeF2 2.00 -506.8 2.626 571.2 1306.8 2876.5
FeF3 3.00 -791.1 2.733 712.5 1644.1 3224.4
CoF2 2.00 -528.2 2.737 553.0 1324.1 3074.0
CoF3 3.00 -1044.1 3.607 693.6 2120.8 4211.1
NiF2 2.00 -571.3 2.961 554.4 1435.2 3407.8
CuF 1.00 -327.7 3.396 324.7 1017.2 3696.7
CuF2 2.00 -683.4 3.541 527.9 1644.7 3796.5
ZnF2 2.00 -462.1 2.395 518.5 1094.6 2725.5
GaF3 3.00 -677.8 2.342 634.5 1276.1 2795.8
RbF 1.00 -59.2 0.613 256.6 147.5 388.0
YF3 3.00 -118.4 0.409 551.1 197.3 435.8
ZrF2 2.00 -262.4 1.360 414.8 509.3 -
ZrF3 3.00 -437.5 1.512 542.5 719.0 1647.2
ZrF4 4.00 -540.9 1.402 641.1 770.6 1674.3
Supplementary Material (ESI) for Energy & Environmental Science
This journal is © Royal Society of Chemistry 2011
NbF5 5.00 -1239.5 2.569 713.2 1546.7 2558.3
RuF3 3.00 - - 508.7 - -
RuF5 5.00 -2157.2 4.472 683.5 2596.7 5198.8
AgF 1.00 -400.7 4.153 211.3 831.8 3209.8
SnF2 2.00 -573.9 2.974 342.1 934.6 2644.5
LaF3 3.00 -139.3 0.481 410.4 178.6 536.0
CeF3 3.00 -207.1 0.715 407.9 264.0 810.2
O
BeO-α 2.00 18.9 -0.098 2143.1 -135.0 -153.0
B2O3 3.00 -244.7 0.845 2309.7 1221.5 1290.9
Na2O 1.00 -92.9 0.962 864.9 680.0 967.8
MgO
microcrystal 2.00 8.1 -0.042 1329.9 -41.5 -61.0
Al2O3 3.00 -50.7 0.175 1577.2 196.0 271.7
SiO2 quartz 4.00 -266.1 0.689 1784.3 841.4 983.1
SiO2 high
cristobalite 4.00 -268.8 0.696 1784.3 850.0 960.5
P4O10 5.00 -722.2 1.497 1888.2 1898.3 2040.5
K2O 1.00 -119.6 1.239 569.1 614.5 1005.1
CaO 2.00 42.1 -0.218 955.9 -167.2 -273.3
Sc2O3 3.00 67.9 -0.235 1166.0 -210.1 -331.8
TiO 2.00 -66.2 0.343 839.3 236.5 472.7
Ti2O3 3.00 -124.7 0.431 1118.8 373.7 629.6
Ti3O5 3.33 -162.9 0.506 1198.6 463.2 742.8
TiO2-R 4.00 -233.3 0.605 1342.3 602.2 911.1
TiO2 4.00 -233.6 0.605 1342.3 602.9 912.1
TiO2-A 4.00 -239.5 0.621 1342.3 618.1 917.9
VO 2.00 -157.0 0.814 800.7 539.6 1259.5
V2O3 3.00 -272.2 0.940 1072.9 789.4 1390.1
VO2 4.00 196.1 -0.508 1292.6 -492.0 -765.9
V3O5 3.33 -334.3 1.040 1151.2 921.8 -
V2O5 5.00 -693.3 1.437 1473.6 1532.6 2090.0
CrO2 4.00 -577.5 1.496 1276.3 1435.4 2319.2
Cr2O3 3.00 -312.8 1.080 1058.0 897.3 1622.2
Cr3O4 (Δ
H=-1513 kJ
mol-1) 2.67 -237.9 0.925 974.7 719.7 1415.8
Supplementary Material (ESI) for Energy & Environmental Science
This journal is © Royal Society of Chemistry 2011
CrO3 6.00 -1171.0 2.023 1608.2 2296.6 2828.0
MnO2 4.00 -657.3 1.703 1233.1 1591.8 2642.1
Mn2O3 3.00 -401.3 1.386 1018.6 1117.3 2034.6
MnO 2.00 -198.3 1.028 755.6 649.4 1405.0
Mn3O4 2.67 -320.5 1.246 937.1 939.4 1765.9
FeO 2.00 -309.8 1.605 746.1 1003.8 2266.4
Fe2O3
hematite 3.00 -470.7 1.626 1007.0 1298.8 2412.2
Fe3O4
magnetite 2.67 -409.8 1.593 926.1 1189.6 2295.5
CoO 2.00 -347.0 1.798 715.3 1085.3 2561.4
Co3O4 2.67 -490.3 1.905 890.4 1378.7 2849.2
NiO 2.00 -349.5 1.811 717.6 1096.1 2695.1
Ni2O3 3.00 - - 972.3 - -
CuO 2.00 -431.5 2.236 673.9 1282.9 3105.0
Cu2O 1.00 -207.6 2.152 374.6 734.7 2313.8
ZnO 2.00 -240.7 1.247 658.6 701.8 1649.7
Ga2O3 3.00 -342.7 1.184 857.9 830.9 1742.8
GeO 2.00 -324.0 1.679 604.7 877.9 -
GeO2 4.00 -601.0 1.557 1024.5 1260.9 2179.1
As4O6
octahedral 3.00 -553.7 1.913 812.8 1284.4 2365.2
As2O5 5.00 -1011.9 2.097 1166.1 1878.5 3068.7
SeO2 4.00 -950.9 2.464 966.2 1904.1 3298.4
Y2O3 3.00 66.5 -0.230 712.1 -138.2 -300.8
ZrO2 4.00 -79.6 0.206 870.0 146.4 300.1
NbO 2.00 -169.3 0.877 492.2 382.9 1149.1
NbO2 4.00 -381.9 0.990 858.3 694.9 1450.0
Nb2O5 5.00 -520.1 1.078 1008.3 862.0 1525.2
MoO2 4.00 -589.4 1.527 837.9 1051.5 2281.3
MoO3 6.00 -1015.6 1.754 1117.2 1520.1 2597.4
RuO2 4.00 -842.4 2.183 805.6 1454.9 3301.9
RuO4 8.00 -2092.6 2.711 1298.9 2635.0 3770.7
AgO 2.00 -575.0 2.980 432.7 1159.6 3757.3
Ag2O 1.00 -275.0 2.850 231.3 622.0 2625.8
Ag2O3 3.00 -902.5 3.118 609.7 1641.9 -
La2O3 3.00 11.1 -0.038 493.6 -16.8 -48.2
Supplementary Material (ESI) for Energy & Environmental Science
This journal is © Royal Society of Chemistry 2011
CeO2 4.00 -97.8 0.253 622.9 135.9 358.2
Ce2O3 3.00 11.3 -0.039 489.9 -17.0 -47.9
WO2 4.00 -588.5 1.525 496.7 671.1 2271.2
WO3 6.00 -919.6 1.589 693.6 934.0 2318.3
Na2O2 1.00 -61.6 0.639 687.4 372.7 636.4
K2O2 1.00 -72.9 0.756 486.4 326.5 522.9
Ag2O2 1.00 -299.3 3.102 216.4 635.5 2804.1
NaO2 1.00 - - 487.4 - -
KO2 1.00 - - 377.0 - -
CaO2 1.00 - - 371.8 - -
S
BeS 2.00 -206.0 1.068 1304.9 1041.2 1318.4
B2S3 3.00 -534.7 1.847 1364.8 1862.8 2016.7
Na2S 1.00 -44.6 0.462 686.8 269.5 364.1
MgS 2.00 -97.2 0.504 950.9 384.3 574.1
Al2S3 3.00 -338.5 1.169 1070.9 980.4 1234.6
SiS2 4.00 -665.4 1.724 1162.5 1540.5 1901.6
P4S3 1.50 -289.5 2.000 730.6 1229.0 1725.6
P4S7 3.50 -693.5 2.054 1077.1 1729.4 2259.3
P2S5 5.00 -1027.9 2.131 1205.8 1957.7 2384.6
K2S 1.00 -37.5 0.389 486.1 167.8 233.1
CaS 2.00 38.4 -0.199 743.0 -124.0 -198.1
Sc2S3 3.00 - - 864.1 - -
TiS2 4.00 -475.8 1.233 957.2 945.7 1550.8
TiS 2.00 -168.9 0.875 670.6 500.2 1003.6
Ti2S3 3.00 - - 837.8 - -
VS 2.00 - - 645.8 - -
V2S3 3.00 - - 811.8 - -
VS2 4.00 - - 931.6 - -
V2S5 5.00 - - 1022.1 - -
CrS 2.00 -264.6 1.371 637.7 750.3 -
Cr2S3 3.00 -574.6 1.985 803.3 1319.9 2435.0
MnS 2.00 -220.6 1.143 616.1 607.4 1210.5
MnS2 4.00 -653.0 1.692 900.4 1235.4 -
FeS 2.00 -338.6 1.755 609.7 924.0 2104.1
FeS2(marcasite 4.00 -721.9 1.870 893.6 1357.3 2642.3
Supplementary Material (ESI) for Energy & Environmental Science
This journal is © Royal Society of Chemistry 2011
)
FeS2(pyrite) 4.00 -711.1 1.843 893.6 1337.0 2602.7
CoS 2.00 - - 589.0 - -
Co2S3 3.00 - - 751.2 - -
CoS2 4.00 -732.4 1.898 871.1 1348.7 2523.6
Co3S4 2.67 -423.0 1.644 702.8 977.6 -
NiS 2.00 -359.5 1.863 590.6 954.3 2349.8
Ni3S4 2.67 -488.0 1.897 704.5 1130.1 2423.8
Ni3S2 1.33 -222.7 1.731 446.3 692.4 -
NiS2 4.00 -753.3 1.952 872.8 1389.5 -
CuS 2.00 -385.4 1.997 560.6 977.7 2323.1
Cu2S 1.00 -176.4 1.828 336.8 566.3 1800.9
ZnS 2.00 -237.7 1.232 550.0 593.0 1321.3
Ga2S3 3.00 -405.6 1.401 682.4 812.7 1590.7
GaS 2.00 -234.3 1.214 526.6 562.7 1242.9
GeS 2.00 -367.5 1.904 511.9 860.8 1980.9
GeS2 4.00 -723.4 1.874 783.8 1221.3 2062.4
As2S3 3.00 -574.2 1.984 653.6 1108.8 2139.5
Se2S6 6.00 - - 918.1 - -
Se4S4 2.00 - - 482.8 - -
RuS2 4.00 - - 648.9 - -
Y2S3 3.00 - - 586.9 - -
ZrS2 4.00 -308.0 0.798 690.1 467.2 928.5
NbS2 4.00 - - 690.1 - -
MoS2 4.00 -652.1 1.690 669.7 964.3 2166.0
Mo2S3 3.00 -519.2 1.794 558.2 874.8 2276.0
Ag2S(argent
ite) 1.00 -199.2 2.064 216.3 422.8 1835.8
LaS 2.00 12.5 -0.065 313.5 -18.8 -61.5
La2S3 3.00 -54.3 0.188 430.0 72.6 195.6
CeS 2.00 12.5 -0.065 311.3 -18.7 -62.9
WS2 4.00 -628.1 1.627 432.3 632.8 2061.9
Na2S2 1.00 - - 486.8 - -
N
Be3N2 2.00 91.9 -0.476 2921.1 -792.0 -779.1
BN 3.00 99.8 -0.345 3239.7 -607.4 -550.3
(CN) 3.00 - - 3090.4 - -
Supplementary Material (ESI) for Energy & Environmental Science
This journal is © Royal Society of Chemistry 2011
Na3N 1.00 - - 969.0 - -
Mg3N2 2.00 47.9 -0.248 1593.3 -280.0 -346.4
AlN 3.00 158.4 -0.547 1961.6 -711.8 -852.9
Si3N4 4.00 42.7 -0.111 2292.6 -159.3 -177.9
K3N 1.00 - - 612.4 - -
Ca3N2 2.00 36.9 -0.191 1084.7 -162.1 -230.5
ScN 3.00 155.2 -0.536 1363.6 -540.2 -
TiN 3.00 115.2 -0.398 1299.5 -387.0 -629.1
VN 3.00 62.5 -0.216 1238.0 -202.3 -350.0
CrN 3.00 -35.6 0.123 1218.2 113.9 197.1
Cr2N 1.50 -13.2 0.091 681.4 52.8 130.2
Mn4N 0.75 -5.9 0.082 344.0 25.8 -
Mn5N2 1.20 -20.4 0.177 531.2 82.4 -
Fe2N 1.50 - - 639.7 - -
Fe4N 0.75 -31.2 0.431 338.7 134.3 -
Co3N 1.00 -31.4 0.326 421.4 123.7 380.4
NiN 3.00 - - 1106.0 - -
Cu3N 1.00 - - 392.9 - -
Zn3N2 2.00 -98.8 0.512 717.3 309.9 722.3
GaN 3.00 -50.9 0.176 960.3 135.1 268.0
Ge3N4 4.00 - - 1174.0 - -
As3N5 5.00 - - 1363.7 - -
SeN2 6.00 - - 1503.3 - -
YN 3.00 140.0 -0.484 781.3 -314.2 -677.7
ZrN 3.00 208.1 -0.719 764.1 -458.6 -1073.7
NbN 3.00 77.3 -0.267 752.1 -168.1 -416.0
MoN 3.00 - - 731.3 - -
RuN 3.00 - - 698.7 - -
Ag3N 1.00 - - 238.2 - -
LaN 3.00 142.4 -0.492 525.8 -227.7 -641.1
CeN 3.00 166.4 -0.575 521.7 -264.1 -789.5
WN2 6.00 - - 759.1 - -
NaN3 1.00 - - 179.8 - -
KN3 1.00 - - 162.3 - -
AgN3 1.00 - - 114.6 - -
P -
Be3P2 2.00 - - 1807.2 - -
Supplementary Material (ESI) for Energy & Environmental Science
This journal is © Royal Society of Chemistry 2011
BP 3.00 - - 1924.2 - -
Na3P 1.00 - - 804.5 - -
Mg3P2 2.00 - - 1192.4 - -
AlP 3.00 - - 1387.3 - -
Si3P4 4.00 - - 1545.1 - -
K3P 1.00 - - 542.3 - -
Ca3P2 2.00 - - 882.7 - -
ScP 3.00 - - 1058.9 - -
TiP 3.00 - - 1019.8 - -
(VP) 3.00 - - 981.6 - -
CrP 3.00 - - 969.1 - -
MnP 3.00 - - 935.9 - -
Mn2P 1.50 - - 570.9 - -
FeP 3.00 - - 926.1 - -
Fe2P 1.50 - - 563.6 - -
Fe3P 1.00 - - 405.0 - -
Co2P 1.50 - - 540.2 - -
Ni2P 1.50 - - 542.0 - -
Ni3P 1.00 - - 388.3 - -
Ni5P2 1.20 - - 452.5 - -
CuP2 6.00 - - 1281.4 - -
Cu3P 1.00 - - 362.8 - -
Zn3P2 2.00 - - 623.0 - -
GaP 3.00 - - 798.5 - -
GeP 3.00 - - 776.0 - -
Ge3P4 4.00 - - 940.9 - -
As3P5 5.00 - - 1059.0 - -
Se(P)2 6.00 - - 1141.2 - -
YP 3.00 - - 670.7 - -
ZrP2 6.00 - - 1049.9 - -
NbP 3.00 - - 649.0 - -
MoP 3.00 - - 633.5 - -
RuP 3.00 - - 608.9 - -
AgP2 6.00 - - 947.0 - -
AgP3 9.00 - - 1201.3 - -
LaP 3.00 - - 473.3 - -
Ce3P4 4.00 - - 590.9 - -
Supplementary Material (ESI) for Energy & Environmental Science
This journal is © Royal Society of Chemistry 2011
WP2 6.00 - - 654.3 - -
Cl
BeCl2 2.00 -323.2 1.675 670.7 957.1 1319.1
PCl5 5.00 -1617.1 3.352 643.5 1849.0 2736.5
NaCl 1.00 -0.3 0.003 458.6 1.3 2.1
MgCl2 2.00 -177.0 0.917 563.0 450.7 734.4
AlCl3 3.00 -524.4 1.812 603.0 944.9 1570.3
KCl 1.00 24.1 -0.250 359.5 -82.1 -132.6
CaCl2 2.00 -20.0 0.104 483.0 44.5 71.6
ScCl3 3.00 -327.3 1.131 531.4 528.2 891.0
TiCl2 2.00 -304.4 1.577 451.3 637.4 1322.4
TiCl3 3.00 -499.7 1.726 521.3 793.0 1424.9
VCl2 2.00 -362.8 1.880 439.9 742.5 1581.6
VCl3 3.00 -641.9 2.218 511.2 1001.0 1950.2
CrCl2 2.00 -412.8 2.139 436.1 838.3 1669.8
CrCl3 3.00 -667.1 2.305 507.7 1034.2 1922.9
MnCl2 2.00 -328.3 1.701 425.9 652.7 1335.8
FeCl2 2.00 -466.5 2.417 422.9 921.4 1964.0
FeCl3 3.00 -819.2 2.830 495.7 1243.3 2397.2
CoCl2 2.00 -499.0 2.586 412.8 964.4 2144.4
NiCl2 2.00 -509.8 2.642 413.6 987.0 2250.7
CuCl 1.00 -264.5 2.741 270.7 693.5 1990.5
CuCl2 2.00 -593.1 3.074 398.7 1110.7 2513.7
ZnCl2 2.00 -399.4 2.070 393.3 738.8 1522.3
GaCl3 3.00 -698.4 2.413 456.6 985.2 1759.1
AsCl5 5.00 - - 531.4 - -
SeCl4 4.00 - - 485.6 - -
YCl3 3.00 -225.5 0.779 411.8 289.8 550.3
ZrCl2 2.00 -382.8 1.984 330.6 604.1 1375.5
ZrCl3 3.00 -507.2 1.752 406.9 645.1 1357.6
ZrCl4 4.00 -647.7 1.678 460.0 689.9 1330.6
NbCl5 5.00 -1238.8 2.568 496.0 1128.7 2121.9
NbCl4 4.00 -932.1 2.415 456.7 986.4 2065.6
MoCl4 4.00 -1135.6 2.942 450.9 1188.0 -
MoCl5 5.00 -1499.0 3.107 490.5 1352.3 2631.5
Supplementary Material (ESI) for Energy & Environmental Science
This journal is © Royal Society of Chemistry 2011
MoCl6 6.00 -1915.4 3.309 521.0 1518.8 -
RuCl3 3.00 -993.5 3.432 387.6 1209.0 2605.8
AgCl 1.00 -274.6 2.846 187.0 507.6 1967.2
SnCl2 2.00 -482.6 2.501 282.7 658.7 1811.5
LaCl3 3.00 - - 327.8 - -
CeCl3 3.00 -168.4 0.582 326.2 175.0 462.8
WCl2 2.00 -548.8 2.844 210.4 567.5 2093.4
WCl4 4.00 -1177.6 3.051 329.2 925.6 2670.7
WCl5 5.00 -1520.0 3.151 371.1 1066.7 2671.3
WCl6 6.00 -1850.4 3.196 405.5 1173.0 2696.1
BO2-
NaBO2 1.00 -56.7 0.588 407.3 216.6 396.8
Mg(BO2)2 2.00 - - 487.6 - -
Al (BO2)3 3.00 - - 517.4 - -
KBO2 1.00 -39.5 0.409 327.2 123.4 -
Sc(BO2)3 3.00 - - 463.7 - -
Ti (BO2)4 4.00 - - 489.3 - -
V(BO2)5 5.00 - - 505.7 - -
Cr(BO2)6 6.00 - - 520.6 - -
Mn (BO2)3 3.00 - - 438.5 - -
Fe (BO2)2 2.00 - - 378.9 - -
Co (BO2)3 3.00 - - 429.1 - -
Ni(BO2)2 2.00 - - 371.4 - -
Cu(BO2)2 2.00 - - 359.3 - -
Zn(BO2)2 2.00 - - 355.0 - -
Ga(BO2)3 3.00 - - 405.8 - -
Ge(BO2)4 4.00 - - 439.6 - -
Y (BO2)3 3.00 - - 369.9 - -
Zr (BO2)4 4.00 - - 408.5 - -
Nb BO2 1.00 - - 197.5 - -
MoBO2 1.00 - - 193.2 - -
Ru(BO2)2 2.00 - - 287.1 - -
Ag BO2 1.00 - - 177.9 - -
La (BO2)3 3.00 - - 300.8 - -
Ce(BO2)4 4.00 - - 344.3 - -
Supplementary Material (ESI) for Energy & Environmental Science
This journal is © Royal Society of Chemistry 2011
W (BO2)6 6.00 - - 364.9 - -
Be3(BO3)2 2.00 - - 1111.7 - -
Ca3(BO3)2 2.00 - - 676.1 - -
CO32-
Be CO3 2.00 - - 776.6 - -
B