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Liquid Metal Batteries: Past, Present, and Future

Hojong Kim, Dane A. Boysen, Jocelyn M. Newhouse, Brian L. Spatocco, Brice Chung, Paul J. Burke,

David J. Bradwell, Kai Jiang, Alina A. Tomaszowska, Kangli Wang, Weifeng Wei, Luis A. Ortiz,

Salvador A. Barriga, Sophie M. Poizeau, and Donald R. Sadoway*

Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge,

Massachusetts 02139-4307, United States

4.3.1. Compressive Seals Q

4.3.2. Adhesive Seals Q

4.4. Thermal Management Q

5. Conclusions R

Author Information R

Corresponding Author R

Notes R

Biographies R

Acknowledgments V

Glossary V

Symbols V

Acronyms V

References V

CONTENTS

1. INTRODUCTION

1. Introduction A

1.1. Description B The evolution of the liquid metal battery is a story of a novel

1.2. Advantages and Disadvantages B technology originally conceived in a di erent economic and

1.3. Applications C political climate to provide exibility in addressing the

2. Past Work C constraints of a society just entering the nuclear age and with

2.1. Hoopes Cells D aspirations to electrify the everyday experience. Ironically, it is

2.2. Thermally Regenerative Batteries D these same massive research projects that receded into

2.3. Bimetallic Cells E obscurity that can now be resurrected and reinvented as an

2.3.1. General Motors Corporation E exciting opportunity for addressing society s ambitions for both

2.3.2. Atomics International E sustainable and environmentally benign energy. In contrast to

3.3.3. Argonne National Laboratory E the public s demand for the constant improvement of high-

3. Present Work G performance lithium-ion batteries for portable electronics,1

3.1. Electrodes G liquid metal batteries are instead the story of a society catching

3.1.1. Thermodynamics H up with a technology far ahead of its time.

3.1.2. Economics I The story of the all-liquid electrochemical cell begins nearly a

3.1.3. Alloying J century ago with advances in the electrolytic production of

3.2. Electrolyte K ultrahigh-purity aluminum. Building upon those early advances

3.3. Cell Performance M in classical electrometallurgy, four decades later the U.S.

3.3.1. Na Bi Cells M government began to fund pioneering work at a few of the

3.3.2. Mg Sb Cells N nation s top industrial and national laboratories to develop all-

3.3.3. Li Pb Sb Cells N liquid cells for energy storage applications. Motivated by the

4. Future Work O Cold War battle for technological supremacy, intensive research

4.1. New Chemistries O on these thermally and electrically rechargeable all-liquid

4.1.1. Lithium O energy storage cells continued in the U.S. throughout the

4.1.2. Sodium O next decade, only to be abandoned as e orts shifted toward

4.1.3. Calcium P higher-energy-density rechargeable cells with immobilized

4.1.4. Barium P components better suited for automotive applications. After a

4.1.5. Strontium P nearly 40-year hiatus, the rapid deployment of renewable

4.2. Corrosion P energy technologies, such as wind and solar power, has

4.2.1. Negative Current Collector P hastened the demand for low-cost, long-life, large-scale energy

4.2.2. Positive Current Collector Q

4.2.3. Electrical Insulator Q

Received: May 22, 2012

4.3. Seals Q

A dx.doi.org/10.1021/cr300205k Chem. Rev. XXXX, XXX, XXX XXX

XXXX American Chemical Society

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storage and renewed interest in the rechargeable three-liquid-

layer galvanic cell the liquid metal battery.

1.1. Description

A liquid metal battery comprises two liquid metal electrodes

separated by a molten salt electrolyte that self-segregate into

three layers based upon density and immiscibility (Figure 1).

Figure 3. Deposition potentials versus the standard hydrogen

electrode (SHE) in aqueous electrolytes of candidate electrode

Figure 1. Schematic diagram of a liquid metal battery upon (a)

species, from which candidate negative (orange) and positive

discharging and (b) charging.

(green) liquid metal battery electrode materials are selected.2

strong electron donor with a strong electron acceptor while

avoiding nonmetals in the choice of the latter.

The strong interaction between metals A and B provides the

thermodynamic driving force (cell voltage) for the liquid metal

battery cell. Upon discharge the negative electrode layer

reduces in thickness, as metal A is electrochemically oxidized (A

Az+ + ze ), and the cations are conducted across the molten

salt electrolyte to the positive electrode as electrons are released

to an external circuit, Figure 1a. Simultaneously, the positive

electrode layer grows in thickness, as the cations are

electrochemically reduced to form a liquid A B alloy [Az+ +

ze A(in B)]. This process is reversed upon charging, Figure

Figure 2. Negative (orange) and positive (green) electrode material

1b.

candidates for liquid metal batteries.

1.2. Advantages and Disadvantages

Liquidity endows liquid metal batteries with superior kinetics

and transport properties. The operating voltage of any

The compositions of the liquid metal electrodes, highlighted in

electrochemical cell, Ecell, deviates from the equilibrium cell

the periodic table presented in Figure 2, are constrained

potential, Ecell,eq, based upon current density, j, dependent

according to the following three requirements:

losses or voltage ine ciencies, (j), such that Ecell(j) = Ecell,eq

(1) liquid at practical temperatures, that is, the melting i i(j). Typical voltage ine ciencies include (1) charge

temperature should be less than 1000 C and the boiling transfer losses, ct, resulting from sluggish electrode kinetics,

point greater than 25 C (Tb > 25 C, Tm

(2) electrically conductive, with a minimum electronic the cell electrolyte, electrodes, and current collectors, and (3)

mass transport, mt, losses caused by slow di usion of reactants

conductivity greater than the ionic conductivity of a

typical molten salt electrolyte ( > 1 S cm 1) to and products away from the electrode electrolyte inter-

face.3,4 Liquid metal batteries boast ultrafast electrode charge-

(3) nonradioactive, that is, available in the form of a naturally

transfer kinetics due to liquid liquid electrode electrolyte

occurring, stable isotope

Candidate electrode materials are preliminarily sorted into interfaces, high rate capability, and low ohmic losses enabled by

highly conductive molten salt electrolytes (up to 3 S cm 1), and

either positive or negative electrodes by the deposition

potential of the candidate electrode material from aqueous rapid mass transport of reactants and products to and from the

solution2 (Figure 3); however, since liquid metal batteries use electrode electrolyte interface by liquid-state di usion. In

molten salt electrolytes, these deposition potentials are not combination, these properties allow liquid metal batteries to

strictly comparable. Electrode materials with a deposition operate with relatively high voltage e ciencies at high current

potential more negative than 2.0 V are negative electrodes (A densities.

metals) and those with potential more positive than 1.0 V are Liquid metal batteries also have the potential of being low-

positive electrodes (B metals), with aluminum being unique in cost because many of the candidate electrode materials are

that it could be either. Alternately, one can sort elements based earth-abundant and inexpensive. Moreover, the natural self-

upon their electronegativity: the more electropositive metals segregation of the active liquid components allows simpler,

being candidates for the negative electrode and the more lower-cost cell fabrication compared with that of conventional

electronegative metals (including the semimetals) being batteries. Finally, perhaps the most attractive feature of these

candidates for the positive electrode. The idea is to pair a batteries is the continuous creation and annihilation of the

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liquid metal electrodes upon charge discharge cycling. This

feature grants liquid metal batteries the potential for

unprecedented cycle life by rendering them immune to

microstructural electrode degradation mechanisms that limit

the cycle life of a conventional battery.5,6 When taken together,

low cost of materials, simple assembly, and the potential for

long lifetimes position liquid metal batteries particularly well for

competition in the grid-storage market.

Despite these advantages, liquid metal batteries possess some

disadvantages, which make them unsuitable for use in portable

applications. These include elevated operating temperatures

(generally >200 C), low theoretical speci c energy density

(typically 99.97 mass %) top electrode; separated by a

molten salt electrolyte, as shown in Figure 6.12 14 Immediately

Figure 7. (a) Schematic drawing of Yeager s original 1958 concept of a

thermally regenerative battery.17 (b) Schematic diagram from Argonne

National Laboratory of a thermally regenerative bimetallic cell.

describes a three-liquid-layer electrolytic cell for the puri cation of National Laboratory.

aluminum.12 Adapted from Alcoa patent, US Patent No. 1,534,315.

apparent is the physical similarity of the Hoopes cell to a liquid

produce compound AB and electricity (A + B AB +

metal battery (Figure 1), except that in a Hoopes cell high-

electricity), but use thermal energy to recharge by thermo-

purity aluminum is produced only upon charging and then

chemically dissociating compound AB back into cell reactants A

siphoned o . In theory, the cell could be operated as a

and B (AB + heat A + B). Unlike a purely electrochemical

rechargeable battery, albeit a poor one with an equilibrium cell

cell, the thermally regenerative cell is subject to Carnot cycle

voltage of under 30 mV.15 Hoopes cells are still in operation

e ciency limitations, such that the maximum e ciency is

today and have logged more than 20 years of continuous

Carnot = ( T 1 T 2 )/ T 1, where T 1 and T 2 are the

operation without retro tting.16

thermochemical regenerator and electrochemical cell operating

2.2. Thermally Regenerative Batteries temperatures, respectively.

It was not until the 1960s that the three-liquid-layer In a decade of massive investments in nuclear energy and

electrochemical cell became of interest for energy storage and growing interest in solar energy (thermal energy sources), the

conversion applications. In 1958, Yeager proposed the concept capability of thermally regenerative cells to convert low-grade

of a thermally regenerative closed cycle battery that could thermal energy into high-grade electrical energy on demand at

reasonable theoretical e ciencies ( > 15%) and with no

convert heat into chemically stored energy, which in turn could

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moving parts quickly gained widespread appeal and spawned

research and development programs across the United States.

Over the next decade, two general types of thermally

regenerative batteries emerged: (1) metal hydride or metal

halide cells and (2) bimetallic cells. For metal hydride or halide

cells, hydrogen or halogen gases (X2 = H2, F2, Cl2, Br2, I2) are

electrochemically reacted with a liquid metal A to form a metal

hydride or halide discharge product (AX) that is solvated in a

molten salt electrolyte and subsequently thermochemically

regenerated (dissociated) back into a hydrogen or halide gas

and liquid metal. By contrast, in bimetallic cells an electro-

positive liquid metal A is reacted with an electronegative liquid

metal B to form a molten metal alloy AB that is then thermally

regenerated (distilled) through the preferential evaporation of

reactant gas A from AB liquid product, as depicted in Figure 7b.

Of this body of work, only bimetallic cells exhibit the three-

liquid-layer self-segregating structure relevant to this review.

For a more comprehensive review of thermally regenerative

cells that includes both cell types see Crouthamel and Recht

(1967).18 In the United States, large-scale research and

development e orts were undertaken in the 1960s to develop

bimetallic thermally regenerative cells at the General Motors

Corporation, Argonne National Laboratory, and Atomics

International (a division of North American Aviation).

2.3. Bimetallic Cells

2.3.1. General Motors Corporation. In 1960, Agruss at Figure 8. A K KOH KBr KI Hg di erential density liquid metal cell

General Motors led the rst patent on thermally regenerative developed at the General Motors Corporation: (a) schematic diagram

and (b) plot of cell voltage versus time upon charge and discharge at

bimetallic cells, in which he describes essentially a liquid metal

87 mA cm 2 and 300 C with an 11.5 cm2 electrode area and 1.5 cm

battery that is thermally recharged .19 General Motors began

electrolyte thickness. Reprinted with permission from ref 22.

their research on Na Sn liquid metal cells with a NaCl NaI

molten salt electrolyte, which they demonstrated electro-

chemical charge discharge for over a month at 700 C,

achieving current densities up to 0.7 A cm 2 and Coulombic General Motors fell into anonymity, going for decades without

e ciencies of 95% at modest cell voltages of 0.33 0.43 V.20 22 citation in the annals of contemporary scienti c literature.

Later, they redirected the program toward the development of 3.3.3. Argonne National Laboratory. From 1961 to

K Hg thermally regenerative cells with KOH KBr KI molten 1967, Argonne National Laboratory carried out perhaps the

salt electrolytes because the kinetics of separating K Hg were most comprehensive work on bimetallic cells. The initial

felt to be far superior to the earlier Na Sn system. 22 Using a program focused primarily on the development of bimetallic

cell as depicted in Figure 8a, General Motors reversibly cells for thermally regenerative batteries; however, the high

charged discharged a K Hg cell at a current density of 87 mA electrical charge and discharge rate capability of these cells led

cm 2 and achieved Coulombic e ciencies of 90 95%. A researchers to believe that bimetallic cells were also attractive

sample charge discharge plot is reproduced in Figure 8b. candidates for secondary cell applications.27 38 Early work was

Using a three-cell K Hg battery in conjunction with a thermal devoted to Na and Li negative electrodes with Pb, Sb, and Bi

regenerative system, Agruss and Karas reported 60 h of positive electrodes, but later work moved toward the

successful operation at a power density of 48 mW cm 2 and development of chalcogenide (S, Se, Te) positive electrodes.

thermal to electric energy conversion e ciency of 3%.22,23 The research program at Argonne was extensive, spanning

Results of General Motors thermally and electrically fundamental thermodynamic investigations of electrode

rechargeable bimetallic cells are summarized in Tables 1 and couples, to the measurement of molten salt electrolyte

2, respectively. properties, to the study of cell component corrosion, and to

2.3.2. Atomics International. Within the same decade, the design and testing of practical cells. Given the breadth of

Atomics International undertook the development of Na Hg work carried out at Argonne, only some of the highlights are

bimetallic cells for application in a space power plant to convert reviewed here; further details can be found in the

literature.31 60

heat from a compact nuclear reactor into electricity. The initial

static cell tests (no owing electrodes) at 510 C were carried For sodium-based bimetallic cells, Argonne selected the

lowest known melting point (530 C) all-sodium ion ternary

out using cells very similar to those used by General Motors

eutectic molten salt electrolyte (15:32:53 mol % NaF NaCl

(Figure 8a), only the ternary sodium halide molten salt

NaI), which has an ionic conductivity of 2.2 S cm 1 at 550 C.

electrolyte was immobilized within a solid ceramic matrix. The

cell was then operated in conjunction with a thermal Lead was selected over Bi and Sn for thermally regenerative

regenerator at 670 690 C for nearly 1200 h; however, cells because of simpler thermal distillation of the discharge

product. A 28 Ah Na Pb (30 mol % Na) thermally

mercury corrosion ultimately led to system failure, these results

are summarized in Table 1.24 26 Despite these profound regenerative cell was successfully constructed and operated

research e orts, both the work at Atomics International and for a total of 45 h, while discharging continuously for several

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Table 1. Performance Results of Thermally Regenerative Bimetallic Cells

Na Hg24 26

Na Sn22 K Hg22 Na Pb37

unit

NaCl NaI KOH KBr KI Na halides ceramic ller NaF NaCl NaI

electrolyte chemistry

625 650

operating temperature 325 490 575

670 690

regeneration temperature 1000 875

1a 1a

cm2

electrode area 45

interelectrode distance cm 1.9

charge discharge current 0.05 0.10

A 0.1 5

theoretical capacity Ah 28

discharge capacity Ah 0.025

0.05 0.10

power output W 35

0.33 0.43 0.70 0.84 0.30 0.80 0.3 0.5

open-circuit voltage V

average discharge voltage V 0.3 0.17

estimated e ciency % 16 7 300

organizationb GM GM ANL ANL

Unknown electrode area normalized to one. bResults obtained at General Motors (GM) and Argonne National Laboratory (ANL).

hours at 110 mA cm 2 and 170 mV at cell and regenerator mol %) which melts at 341 C was preferred. In general, it was

temperatures of 575 C and 875 C (930 Pa), respectively.37 found that lithium halides melt about 200 C lower than their

For secondary cells, Na Bi was preferred because of a higher sodium halide homologues. This is important because it allows

theoretical cell voltage. Several Na Bi 15 Ah secondary cells lithium-based cells to operate at lower temperatures, provides

were constructed using a design that featured an externally for lower solubility of the electrode materials in the electrolyte,

cooled silicone rubber seal and frozen electrolyte side-wall, as and signi cantly reduces cell self-discharge. Initial lithium-based

illustrated in Figure 9a. One of these cells was continuously cells were tested with Zn, Cd, Pb, Bi, Sn, and Te positive

operated for more than 17 months with no appreciable electrodes, and all were capable of operating at current densities

in excess of 0.3 A cm 2. Based upon thermodynamic

degradation in performance. Cells achieved charge discharge

current densities as high as 1.1 A cm 2 at 535 650 C with a investigations of the Li Sn system, Argonne predicted that

0.4 cm thick electrolyte; however, high current densities excellent separation of lithium from tin could be achieved with

a galvanic cell at 327 C and regenerator at 1023 C with a

prevented the cell from achieving its theoretical cell capacity

upon discharge as a result of electrode di usion limitations system e ciency of nearly 30%. These predictions remain

unveri ed because Li Sn thermally regenerative systems were

concomitant with the formation of intermetallic species at the

never constructed.37

electrode electrolyte interface, Figure 9b. A relatively large

Of the initial candidate couples tested, Li Te exhibited the

self-discharge rate was observed in all sodium-based cells due to

highest cell voltages (1.7 1.8 V) and was therefore deemed the

sodium solubility in the molten salt electrolyte, requiring charge

rates greater than 110 mA cm 2 and limiting Coulombic most promising secondary cell electrode couple. Lithium

e ciencies to less than 80% at 665 mA cm 2 and 565 C.37 tellurium secondary cells were constructed in accordance with a

design similar to that used for the Na Bi cells (Figure 9a),

Ultimately, the issue of sodium solubility in molten salt

operated at 480 C, charged discharged at massive current

electrolytes that results in high self-discharge rates drove a shift

densities of up to 7 A cm 2 (Figure 10a), and displayed no

toward the solid-state electrolyte sodium -alumina after its

discovery at Ford Motor Company in 1966.61 64 signs of degradation after 300 h of operation. In contrast to the

Na Bi cells, the Li Te cells exhibited consistent voltage

For lithium-based bimetallic cells, Argonne investigated

discharge pro les even at current densities as high as 3 A cm 2,

several binary and ternary lithium halide molten salt electro-

Figure 10b.37,42

lytes, but the LiF LiCl LiI eutectic composition (12:29:59

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Figure 9. A Na NaF NaCl NaI Bi bimetallic secondary cell

developed at Argonne National Laboratory: (a) schematic of a 20

Ah nominal capacity cell with externally cooled seal and (b) plot of cell

voltage versus capacity at various constant-current discharge rates of a

cell at 580 C with a 45 cm2 electrode area and 0.4 cm interelectrode

Figure 10. A Li LiF LiCl LiI Te bimetallic secondary cell developed

Argonne National Laboratory.

at Argonne National Laboratory: (a) plot of cell voltage as a function

of steady-state current density at 470 C, where circles represent

data for a cell with 9.6 Ah capacity, 3.9 cm2 negative electrode area, 10

cm2 positive electrode area, and 0.5 cm interelectrode distance and

By the end of the 1960s, Argonne had almost exclusively

triangles are for a cell with 1.6 Ah capacity, 10 cm2 negative

redirected their research toward high speci c energy density

electrode area, 10 cm2 positive electrode area, and 0.5 cm

lithium chalcogenide cells for use in electric ve-

hicles.43 46,48,49,51 53,65 Not long after this, Argonne shifted interelectrode distance; (b) plot of cell voltage versus capacity at

various constant-current discharge rates and 480 C with a 10 cm2

direction again, this time toward Li FeS cells, after the

electrode area and 0.5 cm interelectrode distance. Reprinted with

Li S cells in iron containers, which led to greatly enhanced cell

cyclability.66 As a result, the low speci c energy density of

3.1. Electrodes

bimetallic galvanic cells made them comparatively unattractive

for portable applications and much of the aforementioned Implicit in the design of any new battery system is the selection

research fell into obscurity for the next few decades. of which electrode chemistry to investigate in order to

maximize performance and provide quanti able bene ts over

3. PRESENT WORK existing technologies. Traditionally, metrics such as energy

This section aims to reintroduce liquid metal battery e ciency, energy density, and power density are employed to

technology, provide insight into research challenges, and give compare the relative strengths and weaknesses of electro-

perspective on where new opportunities lie. We endeavor to chemical energy storage systems for a particular application. By

present researchers with a thorough introduction to the basic contrast, grid-scale energy storage technologies are stationary,

thermodynamics, economics, and unique properties of liquid and therefore generally unconstrained by the need for high

metal battery systems. energy and power densities. Despite the presence of fewer

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Table 3. Equilibrium Cell Voltages from Full-Charge to Full-Discharge (V) of A B Electrode Couplesa

B Li Na K Mg Ca Ba

0.31 0.07125 0.21 0.0874,83 0.44 0.1776,87

0.56 0.37140b 0.22 0.0281,114 0.21 0.0971

0.67 0.1375,82,84,103 0.72 0.0722,67

0.30 0.3092b 0.20 0.0777 0.44 0.41105 0.53 0.15122

0.59 0.57101b 0.20 0.0193,127 0.25 0.1473,79,94

0.55 0.5097 0.30 0.06108,114 0.24 0.02123,136 0.24 0.1173,79 0.62 0.3488

0.42 0.1198 0.44 0.0769 0.23 0.1272

0.70 0.5799,100 0.45 0.2278,90,108,109,114 0.35 0.1985,112 0.77 0.5195 1.08 0.7195

0.68 0.42137 0.47 0.2086,111 0.51 0.1570,117 0.21 0.1379,112 0.69 0.5095 1.02 0.6695

0.92 0.9291 0.86 0.6180,116,128 1.01 0.54121,129 0.51 0.3985,112 1.04 0.9495 1.40 1.1595

0.86 0.7791 0.74 0.4737,113,116,126 0.90 0.45116,120 0.38 0.2785,112 0.90 0.7989,95,96 1.30 0.9795

1.76 1.7042,134 1.75 1.44110 2.10 1.47119

Equilibrium cell voltages as function of mole fraction, Ecell,eq(xA), are estimated from full-charge, Ec(0.10, 0.05), to full-discharge, Ed(0.50, 0.33), as

discussed in the text. bDeviations from this calculation method: (1) Li Al cells, Ed(0.47); (2) Li Ga cells, Ed(0.45); (3) Li Cd, Ec(0.11) and

Ed(0.45).

GA(in B) = GA(l) + RT ln aA(in B)

constraints, stationary energy storage solutions must provide

signi cant levels of energy or power, depending on the

GA(l) = GA(l) + RT ln aA(l) (aA(l) = 1)

application, at particularly stringent price points. Thus, in (5)

identifying candidate systems, the complementary metrics of

where ai is the activity, G the standard chemical potential, R

voltage (impacting rate capability and energy e ciency) and A(l)

the gas constant, and T temperature. From the Nernst equation

electrode material cost per unit of energy storage capacity

($ kWh 1) are used to evaluate candidate electrode chemistries. Gcell = zFEcell,eq

(6)

In addition to metrics that directly quantify the cost and

performance of the cell, electrode alloying is identi ed as a and eqs 4 and 5, the cell equilibrium voltage is related to the

promising path forward to lower system-level costs by change in partial molar Gibbs free energy

depressing the melting point and thus operating temperature

Ecell,eq = Gcell /(zF ) = (RT /(zF ))ln aA(in B)

(7)

of the battery.

3.1.1. Thermodynamics. The theoretical voltage of any where F is the Faraday constant and z the number of electrons.

electrochemical cell is dete rmined by the fundamental Conceptually, the thermodynamic driving force for cell

thermodynamics of the negative and positive electrode discharge can be interpreted as emanating from a strong

materials. For liquid metal battery systems, there are over interaction of metal A with metal B, in which the activity of A

100 possible binary alloy electrode combinations, each carrying can be extremely low (aA(in B) can be as low as 10 10). This is

with it a unique voltage discharge pro le. The evaluation of the manifest in the form of a high equilibrium cell voltage.

thermodynamic properties of binary alloy systems enables the Experimental measurements of enthalpies of reaction,

identi cation of chemistries with higher cell voltages, which electromotive force, vapor pressure, and chemical equilibrium

facilitate greater cell e ciencies at faster charge discharge have been made to determine the thermodynamic activities of

rates. most binary alloys as a function of mole fraction and

The generic liquid metal battery electrochemical cell can be temperature [aA = f(xA,T)] and are readily available in the

written as literature.22,37,67 141 These data can be used to calculate the

A(l) AX z(l) A(in B) theoretical cell discharge pro le of an electrode couple;

(1)

however, a detailed comparison of the multitude of possible

where A is the negative electrode metal, B is the positive liquid metal battery electrode couples is impractical due to the

electrode metal, and AXz is an alkali or alkaline-earth molten wide variety of phase behavior exhibited in binary alloy systems.

salt electrolyte. For this cell, the generic negative and positive To address this issue, an imprecise, but e ective method for

half-cell reactions are estimating cell voltages for binary alloy electrode couples is

constructed here. From literature data, the equilibrium cell

A(l) = Az + + ze

negative

voltages in Table 3 were calculated at two di erent mole

Az + + ze = A(in B) fractions, xA, corresponding roughly to the cell voltage at full-

positive (2)

charge, Ec, and discharge, Ed. In order to avoid the steep rise in

and the overall cell reaction is voltage as the positive electrode approaches in nite dilution

(xA 0), Ec is approximated from the theoretical voltage at

A(l) = A(in B)

cell (3)

full-charge mole fractions, xA,c = 0.10 and 0.05 for alkali and

The thermodynamic driving force is the change in partial molar alkaline-earth systems, respectively. The full-discharge voltage,

Gibbs free energy, Ed, is obtained from the theoretical cell voltage at discharge

mole fractions, xA,d = 0.50 and 0.33 for alkali and alkaline-earth

Gcell = GA(in B) GA(l)

(4)

systems, respectively, selected such that both systems have

where the partial molar Gibbs energy G i for each component i equivalent negative electrode molar capacities [i.e., znA = nB,

is given by where for alkali systems z = 1, alkaline-earth systems z = 2, and

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xA,d = nA/(nA + nB)]. In most cases, the equilibrium cell voltages is reported in order to quantify the recent volatility of the metal

were estimated at temperatures slightly above the melting point according to

of the higher melting electrode; however, it should be noted m

(m 1) 1 (Pi, j Pi )2 100%

i = Pi

that the temperature dependence of the cell potential tends to

be small (typically less than 0.02 V/100 C) over a wide j (9)

range of concentrations.

Cest,

The complexity of estimating a full theoretical discharge The estimated cost of energy for electrode couples, on a

molten salt electrolyte, which they demonstrated electro-

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