doi.org/10.26434/chemrxiv.6300959.v1

Non-Equilibrium Crystallization Pathways of Manganese Oxides inAqueous SolutionWenhao Sun, Daniil A. Kitchaev, Denis Kramer, Gerbrand Ceder

Submitted date: 22/05/2018 • Posted date: 22/05/2018Licence: CC BY-NC-ND 4.0Citation information: Sun, Wenhao; Kitchaev, Daniil A.; Kramer, Denis; Ceder, Gerbrand (2018):Non-Equilibrium Crystallization Pathways of Manganese Oxides in Aqueous Solution. ChemRxiv. Fileset.

Aqueous precipitation of transition metal oxides often proceeds through non-equilibrium phases, whoseappearance cannot be anticipated from traditional phase diagrams. Without a precise understanding of whichmetastable phases form, or their lifetimes, targeted synthesis of specific metal oxides can become atrial-and-error process. Here, we derive a new thermodynamic potential for the free-energy of a metal oxide inwater, which reveals a hidden metastable energy landscape above the equilibrium Pourbaix diagram. Bycombining this ‘Pourbaix potential’ with classical nucleation theory, we interrogate how solution conditions caninfluence the multistage oxidation pathways of manganese oxides. We calculate that even within the samephase stability region of a Pourbaix diagram, subtle variations in pH and redox potential can redirect acrystallization pathway through different metastable phases. Our theoretical framework offers a predictiveplatform to navigate through the thermodynamic and kinetic energy landscape towards the rational synthesisof target metal oxide phases.

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1

Non-equilibrium crystallization pathways of manganese oxides in aqueous solution

Authors: Wenhao Sun1,2, Daniil Kitchaev2, Denis Kramer3, Gerbrand Ceder1,2,4

1Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

2Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 USA.

3Engineering Sciences, University of Southampton, SO17 1BJ, Southampton, UK

4Department of Materials Science and Engineering, University of California, Berkeley, CA 94720, USA

*Correspondence to: wenhaosun@lbl.gov, gceder@berkeley.edu

Abstract

Aqueous precipitation of transition metal oxides often proceeds through non-equilibrium phases,

whose appearance cannot be anticipated from traditional phase diagrams. Without a precise

understanding of which metastable phases form, or their lifetimes, targeted synthesis of specific metal

oxides can become a trial-and-error process. Here, we derive a new thermodynamic potential for the

free-energy of a metal oxide in water, which reveals a hidden metastable energy landscape above the

equilibrium Pourbaix diagram. By combining this ‘Pourbaix potential’ with classical nucleation theory,

we interrogate how solution conditions can influence the multistage oxidation pathways of manganese

oxides. We calculate that even within the same phase stability region of a Pourbaix diagram, subtle

variations in pH and redox potential can redirect a crystallization pathway through different metastable

phases. Our theoretical framework offers a predictive platform to navigate through the thermodynamic

and kinetic energy landscape towards the rational synthesis of target metal oxide phases.

2

Transition metal oxides drive the functionality of an enormous range of technological

materials; spanning battery cathodes, catalysts, fuel cells, magnetic media, and more. The breadth of

transition metal oxide applications largely stems from the diversity of their electronic, optical, and

magnetic properties, which can be tuned as a function of the crystal structure and metal oxidation state.1

Understanding how to rationally synthesize metal oxides in desired phases, with desired oxidation

states, is central towards unlocking the full potential of transition metal oxide design. The manganese

oxides are a remarkable example of structural and oxidation-state diversity, spanning more than 30

phases over oxidation states from Mn2+ to Mn7+.2 This broad structural diversity makes manganese

oxides relevant for a variety of applications; for example, the spinel λ-MnO2 phase is an important

lithium-ion battery cathode;3 ramsdellite-MnO2 is used in alkaline batteries;4 and Mn3+ containing

phases, such as Hausmannite Mn3O4 and bixbyite Mn2O3, are high-activity water-splitting catalysts.5,6,7

The precipitation and dissolution of various manganese (oxy)hydroxides also play important roles in

redox-active biogeochemical processes, such as mediating oceanic O2/H2S cycles, 8 microbial

metabolic cycles,9 and soil chemistry.10 Unfortunately, the structural diversity of the manganese oxides

also results in a myriad of possible crystallization pathways in solution, which often leads to poor

phase-control during crystal growth. Although synthesis recipes to specific manganese oxide phases

have been identified and catalogued,5,11 a comprehensive understanding of the thermodynamic and

kinetic processes that drive phase-selection during aqueous crystallization remains elusive.

Previously, we found that spectator ions can be important MnO2 structure-directing agents, as

intercalation of aqueous alkali cations such as Li+, Na+, K+, etc. can stabilize the metastable α-, δ-, and

λ-MnO2 polymorph frameworks at off-stoichiometric compositions. 12 However, precipitation of

manganese oxides often proceeds by Ostwald’s ‘Rule of Stages’,13 where a variety of metastable

manganese oxides and oxyhydroxides nucleate and grow prior to the formation of the equilibrium

phase. 14 , 15 These non-equilibrium crystallization pathways can occur both with 16 and without 17

impurity ions in solution. Further complicating the matter, small variations in precursor choice and

solution redox conditions can change which metastable phases are observed, as well as their lifetimes,

even when the final equilibrium product remains unchanged.18 Understanding how solution chemistry

influences structure-selection along a non-equilibrium crystallization pathway would enable the

rational design of synthesis routes; either towards desirable metastable phases, or away from long-

lived metastable byproducts and towards the synthesis of a desired equilibrium phase.19,20 Importantly,

a predictive understanding of hydrothermal synthesis developed on the manganese oxides could be

broadly generalized and applied to other transition metal oxide systems.

3

Classical nucleation theory dictates that a metastable phase can precipitate first from a

supersaturated solution if it has a lower surface energy, and thereby a lower nucleation barrier, than

the stable phase.21,22 This phenomenon has been validated for a number of polymorphic salts,23,24,25

where the supersaturation, σ, is defined as the ratio between the ion activity product of the precursors,

and the solubility product of the precipitate, e.g. + - MX

spM X /= K . However, two complications

arise when extending this definition of supersaturation to transition metal oxides. First, in metal oxide

precipitation, oxygen and hydrogen reactants originate from the H2O solvent, meaning an interpretation

of [O] and [H] activity based on solute concentration is ill-defined. Second, if the transition metal in

an aqueous ion precursor has a different oxidation state than in the solid precipitate (e.g., Mn2+(aq) vs

solid Mn4+O2), then supersaturation is not only a function of aqueous metal ion activity; redox reactions

involving electron transfer must also be specified. It is possible to map the equilibrium phases under

aqueous electrochemical conditions using Pourbaix diagrams,26 which have axes of pH and redox

potential, E. However, Pourbaix diagrams do not have an energy axis for determining the relative free-

energies between metastable and stable phases, and thus cannot be used to compute supersaturation,

or other thermodynamic driving forces for phase transformations.

In this work, we derive a unified thermodynamic and kinetic framework to evaluate the

multistage crystallization pathways of transition metal oxides in water. The backbone of our framework

is a new thermodynamic potential, which we name the Pourbaix potential, corresponding to the free-

energy of a phase in equilibrium with an external water reservoir at fixed pH and redox potential. The

Pourbaix potential adds a free-energy axis to Pourbaix diagrams, and reveals how changes in E, pH,

and even particle size, can influence the metastable energy landscape, altering the thermodynamic

driving forces between reactant and product phases. By combining the Pourbaix potential with classical

nucleation theory, we show that even when crystallization starts from the same precursor and ends with

the same equilibrium phase, minor variations in E and pH can qualitatively change which metastable

phases form on the crystallization pathway. Our theoretical framework offers a predictive platform to

map how experimental parameters influence non-equilibrium crystallization pathways, and represents

an important step towards a predictive theory of materials synthesis.

A thermodynamic potential for metal oxides in water

Thermodynamic analyses can often be simplified by a careful and deliberate choice of

boundary conditions.27 For example, the Gibbs thermodynamic potential is generally convenient for

analyzing chemical reactions in a laboratory setting, by bounding a thermodynamic system on a closed

4

reaction vessel with natural variables of temperature, pressure, and composition (Fig. 1, blue beaker).28

However, analyzing redox reactions in water with the Gibbs free-energy can be cumbersome, as the

composition natural variable results in numerous competing redox reactions involving exchange of

hydrogen, oxygen, and electrons, which can lead to large and complicated redox reaction networks. To

simplify the analysis, we can redefine the thermodynamic boundary conditions to not be around the

full aqueous system including precipitates, but to only be around the metal-containing phases in water

(Fig. 1, red MnOxHy). The resulting thermodynamic potential is no longer the Gibbs free-energy of a

closed reaction vessel, but rather, corresponds directly to the free-energy of an aqueous ion precursor

or metal oxide precipitate, being acted upon by an open external water reservoir at a given pH, redox

potential, and dissolved metal ion concentration. Under this thermodynamic grand potential, relative

free-energies between metal-containing phases of varying composition can be calculated directly,

without needing to explicitly enumerate redox reactions.

Figure 1. Thermodynamic boundary conditions for G, the Gibbs potential (blue beaker), and Ψ, the

Pourbaix potential (red MnOxHy). Evaluating redox reactions in aqueous solution with Gibbs free-

energy often results in complicated reaction networks. By reframing the boundary conditions, the

Pourbaix potential evaluates redox reactions implicitly, giving the free-energy of a metal oxide/ion in

equilibrium with an external water reservoir at a given pH and redox potential.

We derive this thermodynamic potential, Ψ, which we name the Pourbaix potential, by a

Legendre transformation of the Gibbs free energy with respect to µO, μH, and redox potential, under a

constraint of water-oxygen equilibrium.

5

H

H O

O

U U UG N Q N

N Q N

(1)

The partial derivative with respect to charge, Q, is the electrical potential, E; and the partial derivative

with respect to the number of oxygen atoms is the chemical potential of oxygen, µO. In solution, the

derivative with respect to the number of hydrogen atoms is the chemical potential of a proton µH+ at

the reference potential (E = 0 V vs. SHE) minus the electric work E required to bring the hydrogen

atom into the phase at E, where F is the Faraday constant. The thermodynamic potential can thus be

expressed as

( ) · · · .H O OHG µ E N E Q µ N (2)

In an aqueous system, µO and µH+ are constrained by the water-oxygen equilibrium

2 21H O 2 H O 2

2e (3)

which yields

+2O H O H

2 2E (4)

By our boundary conditions, the number of metal atoms are conserved between phase transformations.

Thus, by substituting Eq. 4 into Eq. 2 and normalizing Ψ by number of metal atoms, we obtain the

Pourbaix thermodynamic potential:

2

1( ) (2 ) (2 )O H O O H O HH

M

G N N N N N Q EN

(5)

The molar Gibbs free energy of a phase, G, is its chemical potential, μi= μio + RTln[ai], where

μio is given by the standard-state Gibbs formation free-energy, ΔGo

f. The activity of solids is ideally

one, and so the activity term is zero, but the chemical potential of metal ions ideally scales with the

natural log of the metal ion concentration in solution. The chemical potential of protons can be

transformed to pH by the relationship +Hln(10) pHRT .

6

A Pourbaix diagram is constructed as follows. Each phase is represented by a Pourbaix free-

energy surface, Ψ(E,pH); defined in Equation 5 by the molar Gibbs formation energy, G; the

composition, NM, NO and NH; and if the phase is an aqueous ion, the charge, Q, normalized by e- per

formula unit. The lowest-energy concave envelope formed by the intersection of all competing free-

energy surfaces defines the stable phases and their phase boundaries, as shown in Figure 2a. By

projecting these stability regions onto the E-pH plane, the conventional Pourbaix diagram is retrieved,

as shown in Figure 2b. Construction of Pourbaix diagrams using this approach is computationally

efficient, and circumvents the traditional procedure of calculating E-pH phase boundaries between

stability regions using the Nernst equation.29 Moreover, these Pourbaix free-energy planes extend into

E-pH regimes where they are metastable,30 in other words, where they are not on the lowest-energy

concave envelope. Comparing free-energy differences using the Pourbaix potential offers a more

elegant framework for evaluating electrochemical metastability than through a network redox

reactions, providing a simplified theoretical foundation for understanding the solid-aqueous

thermodynamics of transition metal oxides.

To apply this framework to the Mn-H2O system, we use the thermochemical dataset shown in

Table 1. Although it is possible to compute Gibbs free-energies for both aqueous ions and solid-state

phases using ab initio methods,31,32,33 bulk free-energies for most of the relevant aqueous and solid-

state Mn-O-H phases are known experimentally (S.I.1,). so we choose the experimental formation free-

energies to perform the thermodynamic analysis in this work. Missing experimental formation energies

for the bulk metastable phases β-MnOOH, R-MnO2 and γ-MnO2 are supplemented using DFT-SCAN

calculations,34 which we have previously shown to give an accurate description of the energetic

ordering and differences in bulk energies for manganese oxides. 35 These formation energies are

obtained by referencing the free-energy difference of the metastable polymorph against the ground-

state phase of the same composition. For Feitknechtite β-MnOOH, whose structure is not known, we

first performed an ab-initio structure prediction by hydrogenating various layered MnO2 phases,

(S.I.2), resulting in a structure with good agreement with experimental XRD patterns, and similar to

the recently resolved β-NiOOH phase.36 Example Pourbaix potentials for the manganese oxide system

can be found in S.I.3.

7

Figure 2. Construction of Mn-H2O Pourbaix diagrams using the Pourbaix thermodynamic potential

a.) Concave lowest-energy envelope of Pourbaix free-energy planes in system at [Mn]=10-2 M and

25°C. b.) Stability regions of equilibrium Mn-O-H phases as projected onto E-pH axis. Red dashed

lines correspond to redox stability window of water. c.) Pourbaix free-energy planes of metastable β-

MnOOH, γ-MnOOH, and R-MnO2, and full aqueous stability region of Mn3O4. d.) Projection of

aqueous metastability regions onto E-pH axis.

Table 1. Thermochemical Data for Mn-H2O solids

Phase ΔGof at 25°C

(eV/formula)

Source Surface Energy

(J/m2)

Source

Mn3O4 -13.300 Hem 1983 0.96 Birkner 2012

α-Mn2O3 -9.132 Hem 1978 1.36 This work

Mn(OH)2 -6.381 Hem 1983 0.47 This work

β-MnOOH -5.670 This work 0.53 This work

α-MnOOH -5.763 Fritsch 1997 0.65 This work

γ-MnOOH -5.780 Hem 1983 0.84 This work

R-MnO2 -4.767 Kitchaev 2015 1.33 This work

γ-MnO2 -4.787 Kitchaev 2015 1.44 This work

β-MnO2 -4.821 Hem 1983 1.55 This work

8

Metastable Pourbaix diagrams

Metastable phases do not typically appear on Pourbaix diagrams, because in Ψ-E-pH space

their free-energy planes lie above the concave envelope formed by the stable phases, as highlighted in

Figure 2c. However, the phase boundaries of metastable phases can still be constructed, by computing

the intersection of its free-energy plane with only the planes of the aqueous ions. This procedure can

also be performed for stable phases, thereby visualizing the full aqueous region where a compound is

supersaturated, even under E-pH conditions where another solid phase is more stable. In Figure 2d,

we outline phase boundaries for metastable β-MnOOH, γ-MnOOH, R-MnO2, and the full

supersaturation region for Mn3O4. This Pourbaix diagram shows numerous regions with overlapping

metastable phase boundaries, for example, at conditions corresponding to neutral aerated water (E ~

0.5 V, pH ~ 7)37. Precipitation of manganese oxides under these conditions would tread the bulk

stability regions of numerous thermodynamically-competitive phases.

Because all materials nucleate and grow through the nanoscale, where surface energies

dominate, mapping the influence of surface energies on nanoscale phase stability is crucial to

interpreting the initial precipitation of bulk metastable phases. Calorimetry experiments have found

that different surface energies between divalent (MO), trivalent (M2O3), and spinel (M3O4) metal

oxides can shift redox equilibria at the nanoscale by orders of magnitude in oxygen fugacity.38 Bulk

metastable phases of polymorphic oxides can also be stabilized at the nanoscale, if they have lower

surface energy than the stable polymorph.39 To investigate these effects, we generalize the Pourbaix

potential to include surface energy, by adding the thermodynamic conjugate variables γA as:

1( ) Bulkr

R

(6)

Where γ is the surface energy, R is an ‘effective’ particle radius—representing the specific surface area

in units of Area/Volume, η is the unitless shape factor (Area / Volume2/3) of the equilibrium particle

morphology, and ρ is the volume normalized per mole of metal.

9

We compute surface energies for all solid manganese oxide phases using DFT slab

calculations, prepared using the efficient creation and convergence scheme we developed in Reference

40, and computed using the SCAN metaGGA functional, which incorporates intermediate and long-

range van der Waals interactions.41 For each phase, we construct surface slabs for both low Miller

index surface orientations and for possible low-energy, high-index orientations, as screened by the

technique we developed in Reference 42. Morphology-averaged surface energies are obtained using

the Wulff construction, and are shown in Table 1, with details in S.I.4. Our computed surface energies

compare favorably with experimental hydrated surface energies from Birkner and Navrotsky.43

The generalized Pourbaix potential Ψ(E, pH, 1/R) exists in a four-dimensional thermodynamic

space, and can be projected onto the pH—1/R axes at fixed E, or the E—1/R axes at fixed pH, to

construct size-dependent Pourbaix diagrams. To highlight the nanoscale competition between

manganese oxide phases, Figure 3 shows two example Mn-H2O nanoscale Pourbaix diagrams; one

varying in redox potential at a fixed pH = 11, and one varying in pH at a fixed redox potential of E =

+0.5 V. We emphasize that these are not surface Pourbaix diagrams,44 which predict surface structure

as a function of E and pH; but are rather size-dependent Pourbaix diagrams, which emphasize crystal

structural phase stability as a function of size, E and pH.

Figure 3. Nanoscale Pourbaix diagrams a.) Size-dependent Pourbaix diagram with varying redox

potential, at fixed pH=11. b.) Size-dependent Pourbaix diagram with varying pH, at fixed redox

potential E = +0.5 V.

10

Surface energy contributions drive three major effects at the nanoscale. First, because surface

energy is always positive, the stability regions of all phases shrink relative to the aqueous ions as

particle size is decreased. Second, as measured by Birkner and Navrotsky, the surface energies of the

stable manganese oxide solids are ordered 3 4 2 3 2Mn O Mn O -ΜnO < < .43 As particle size radius is

reduced, our nanoscale Pourbaix diagrams show an enlargement of the Mn3O4 stability field and

reduction of the β-MnO2 stability field, effectively corresponding to shifts in oxidation-reduction

equilibria at the nanoscale. Third, as shown in Table 1, we calculate the surface energies of MnOOH

polymorphs to be ordered β-MnOOH α-MnOOH γ-MnOOH < < , and for the MnO2 polymorphs

2R-MnO -MnO2 β-MnO2. The bulk energies of these phases are ordered in the opposite direction,

which lead to the aforementioned polymorph stability crossovers at the nanoscale. The universality of

this inverse relationship between bulk energy and surface energy may originate from the fact that a

metastable structure has less cohesive energy than a stable phase, which implies a lower energy of

cleavage – e.g. a lower surface energy. We note that γ-MnO2, named ‘intergrowth’ due to having

structural motifs of both R- and β-MnO2, cannot be size-stabilized, suggesting it may be a kinetically-

limited transition state in a solid-state transformation between R-MnO2 and β-MnO2, or stabilized by

proton defect structures discussed in previous reports.12 These nanoscale Pourbaix diagrams show that

surface energy, E and pH, all operate on a similar energy scale of manganese oxide metastability,45

meaning that all of these thermodynamic handles are important drivers of structure-selection during

crystallization.

Crystallization pathways in redox-active systems

Multistage crystallization initiates from a metastable precursor, and cascades down in free-

energy to the equilibrium phase by a series of phase transformations. To compute a crystallization

pathway using the Gibbs free energy, one would evaluate the most favorable series of downhill

reactions through a complicated redox reaction network.46 A major advantage of the Pourbaix potential

is that at a given aqueous E, pH and ion concentration, redox reactions are evaluated implicitly,

meaning one can directly construct a one-dimensional Pourbaix free energy ordering between phases

of varying composition. By combining the Pourbaix potential with classical nucleation theory, we

arrive at a preliminary theoretical framework to evaluate transition metal oxide crystallization

pathways in aqueous solution. Using this framework, we demonstrate that subtle variations in E and

pH can modify which metastable phases occur on the multistage oxidation pathway of Mn2+(aq), even

when reactions occur within the same β-MnO2 stability region of the Pourbaix diagram.

11

Figure 4. Supersaturation of manganese oxides in solution for various pH at E = +0.5 V.

a.) Pourbaix free-energy differences between the Mn2+(aq) ion and the β-MnO2 phase, at varying

[Mn2+] concentrations (dashed lines). The projection of the lowest free-energy phases onto the pH-axis

marks the phase stability regions on the Pourbaix diagram. b.) Pourbaix free-energy differences

between various solid phases and the β-MnO2 phase, magnified in the energy axis.

Varying E and pH within a phase stability region on the Pourbaix diagram does not change the

equilibrium phase, but it can shift the metastable energy landscape, altering the thermodynamic driving

forces between precursors, intermediates and products. Figure 4 shows a ΔΨMnO2–pH slice of the free

energy planes from Figure 2a, at a fixed E = +0.5 V vs. SHE, which is representative of the redox

potential in aerated water.37 The dashed lines in Figure 4 show that ΨMn2+ increases linearly with

ln[Mn2+] concentration, consistent with traditional intuition regarding supersaturation. Higher [Mn2+]

activity enlarges the stability regions for Mn2O3 and MnO2, and also increases the supersaturation to

β-MnO2, for a given pH. However, Figure 4 also shows that the Mn2+(aq) supersaturation is strongly

dependent on pH, which is not obvious from a Pourbaix diagram or from ideal solution models.

Chemically, a high pH signifies a high concentration of OH– ions, which provides a thermodynamic

driving force for the oxidation of Mn2+(aq). A similar electrochemical effect is achievable through

12

positive redox potentials. Not only do E and pH affect the Pourbaix free-energies of aqueous ions,

Equation 5 shows that they also affect the relative Ψ between solids of different NO and NH, i.e. of

different compositions. In Figure 4b, the influence of pH on the free energy differences between

Mn3O4, Mn2O3, and the polymorphs of MnOOH and MnO2 is visualized. Overall, Figure 4 reveals a

dynamic metastable free-energy landscape over varying electrochemical conditions; a fact that is not

readily apparent in traditional Pourbaix diagrams.

This shifting free-energy landscape can lead to variations in multistage crystallization

pathways, even when starting with the same precursor and ending with the same equilibrium phase. In

Figure 5, we construct Pourbaix free-energy orderings of manganese (oxyhydr)oxide phases at three

conditions within the equilibrium β-MnO2 stability window; at pH = 8, 9.5, and 11, with E = +0.5 V

and [Mn2+] = 10-2 M. We compute the oxidation pathway of Mn2+(aq) under these conditions, using

the procedure we derived in Reference 47, described here briefly:

Starting from the metastable [Mn2+] precursor, we compute the steady-state nucleation rate, J,

to all lower free-energy phases, by

3

2exp

( )J

(7)

As shown earlier, many of the metastable manganese oxides and oxyhydroxides have lower surface

energies than the equilibrium phases. Because the nucleation barrier scales with γ3, a low surface

energy can compensate for a smaller thermodynamic driving force, ΔΨ, resulting in faster nucleation

rates. The induction time of a nucleation event is proportional to the inverse of the nucleation rate, τ ~

1 / J, meaning a fast-nucleating metastable phase can grow and consume Mn2+ ions prior to the

induction of more-stable phases. Even if the metastable phase completes crystal growth by consuming

Mn2+ to equilibrium, ΨMn2+ is still supersaturated with respect to the more stable phases. The next

lowest-barrier phase nucleates, and this process repeats by dissolution-reprecipitation in a recursive,

energetically-cascading series of metastable stages down to the equilibrium phase, β-MnO2.

13

Figure 5. Oxidation pathways of Mn2+(aq) at three pH conditions in the β-MnO2 stability

region. a) Induction time diagrams, with phases ordered vertically by the ΔΨ of a phase above β-

MnO2. From the Mn2+ precursor, the lowest-barrier phase nucleates and grows, persisting until the

induction of the next more-stable phase. The process then repeats. b) Schematic diagram of the three

crystallization pathways as a cascade through the metastable energy landscape; energy axis not

drawn to scale.

14

Figure 5a shows the computed Mn2+ oxidation pathways under the three considered pH

conditions. Near the β-MnO2 phase boundary at pH = 8, thermodynamic driving forces are small;

meaning nucleation barriers are high, induction times are long, and metastable intermediates will be

long-lived. From the balance of surface energies and bulk driving forces, we compute a crystallization

pathway of Mn2+(aq) Hausmannite Mn3O4 Groutite γ-MnOOH Bixbyite Mn2O3 Pyrolusite

β-MnO2. This progression is qualitatively comparable to the observed crystallization pathways in Ref

15 and 18, which proceeded in freshwater at 25°C over the course of eight months. At higher pH, the

increasingly stratified ΔΨ between metastable phases decreases the induction lifetimes of the transient

metastable phases, and qualitatively changes the crystallization pathways; forming β-MnOOH and

bypassing Mn2O3 at pH = 9.5, and at pH = 11, forming β-MnOOH and Ramsdellite MnO2. Overall,

these results indicate that hidden above the equilibrium Pourbaix diagram is a dynamic metastable

energy landscape, where free-energy differences between competing phases vary continuously with E

and pH. As summarized in Figure 5b, these variations can redirect a crystallization pathway down

through different metastable phases, even when crystallization initiates from the same precursor and

ends with the same equilibrium phase. These findings rationalize why non-equilibrium crystallization

pathways are so sensitive to solution conditions, and highlights the limitations of using an equilibrium

phase diagram to guide materials synthesis.48

Although our analysis overlooks many of the complicated solid-aqueous interactions relevant

to phase transformations in water, our results reveal novel qualitative insights for how oxidation-

reduction and surface energy drive polymorph-selection during metal oxide precipitation. Adding more

sophisticated solid-aqueous physics to our model; such as heterogeneous nucleation, surface energy

dependence on E and pH, solute transport, ion-desolvation, solid-state transformations, etc; can lead

to more accurate and quantitative predictions of crystallization pathways in solution. Coupling our

thermodynamic framework with accurate ab initio thermochemistry of solid-aqueous equilibria31,32,33

will pave the way to a predictive computational platform for guiding the targeted synthesis of

functional metal oxides.

15

Acknowledgements: This work was supported by the US Department of Energy, Office of Science, Basic

Energy Sciences, under Contract no. UGA-0-41029-16/ER392000 as a part of the DOE Energy Frontier

Research Center “Center for Next Generation of Materials by Design: Incorporating Metastability.” WS

used computing resources at the Argonne National Laboratory Center for Nanoscale Materials, an Office

of Science User Facility, which was supported by the U. S. Department of Energy, Office of Science, Office

of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. This research also used resources of

the Center for Functional Nanomaterials, which is a U.S. DOE Office of Science Facility, at Brookhaven

National Laboratory under Contract No. DE-SC0012704. WS thanks SYC for valuable insights. The

authors declare that they have no competing interests.

16

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Crystallization Pathways of Manganese Oxides from Aqueous Solution

Authors: Wenhao Sun1,2, Daniil Kitchaev2, Denis Kramer3, Gerbrand Ceder1,2,4

1Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

2Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 USA.

3Engineering Sciences, University of Southampton, SO17 1BJ, Southampton, UK

4Department of Materials Science and Engineering, University of California, Berkeley, CA 94720, USA

*Correspondence to: gceder@berkeley.edu

Supplementary Information

1. Formation Energies of Bulk Mn-O-H Phases

2. Ab initio structure prediction for metastable β-MnOOH

3. Example Generalized Pourbaix Potential

4. Surface energies of MnOxHy phases

5.

S.I.1. Bulk Formation Energies of Mn-O-H Phases

Formation Energies of Mn-O-H phases in eV/formula unit. For the ions and the lowest-energy phases, we choose the most recent experimental reference when available. For Fritsch and Navrotsky, and for Kitchaev et al, which provide relative energies between the metastable phases of MnOOH and MnO2 against the ground state, we reference the formation energies of the metastable phase against the experimental formation energy of Hem and Lind (1983). In this work, we disregard the α, δ, and λ polymorphs of MnO2, which we previously showed to be stabilized by intercalation of alkali impurity ions.1 For β-MnOOH, we use the bulk energy as calculated in this work, because the surface energies are calculatedfrom the same structure.

Phase Hem, Lind (1983)2

Hem (1978)3

Hem (1963)4

Fritsch, Navrotsky (1997)5

Kitchaev et al. (2015, 2017)1,6

Persson et al. (2012)7 Our selection

Mn2+ (aq) -2.363 -2.363 -2.359 -2.387 -2.363Mn3+ (aq) -0.850 -0.850 -0.850MnO4

- (aq) -4.658 -4.658MnO4

2- (aq) -5.221 -5.222 -5.222MnOH+ (aq) -4.198 -4.198 -4.198 -4.198Mn(OH)3

- (aq) -7.714 -7.714HMnO2

- (aq) -5.243 -5.243 -5.243 -5.243 -5.243

Mn 0 0 0 0MnO -3.762 -3.762Mn3O4 -13.300 -13.300 -13.263 -13.300Mn2O3 -9.132 -9.100 -9.132

Mn(OH)2 - amorphous -6.375 -6.375Mn(OH)2 - crystalline -6.381 -6.370 -6.381β-MnOOH -5.629 -5.670 -5.629α-MnOOH -5.763 -5.750 -5.763γ-MnOOH -5.780 -5.780 -5.780 -5.780 -5.780Mn(OH)3 -7.849 -7.849

R-MnO2 -4.765 -4.767 -4.767

γ-MnO2 -4.731 -4.787 -4.787β-MnO2 -4.821 -4.821 -4.826 -4.821 -4.821 -4.821

S.I.2. Ab initio structure prediction for metastable β-MnOOH

Feitknechtite, β-MnOOH, is a metastable manganese oxyhydroxide often observedduring aqueous precipitation. The crystal structure of β-MnOOH is not known, although itsXRD pattern has been resolved, and is catalogued as JCPDS card no. 00-018-0804. Becauseit is often an early precipitate during crystallization, nucleation theory would suggest that β-MnOOH has a low surface energy. However, without a crystal structure, we would be unableto construct surface slabs in DFT to compute the surface energy.

To produce a candidate structure for β-MnOOH, we perform an ab initio crystalstructure prediction, by sampling various known layered manganese oxide prototypeframeworks, enumerating potential hydrogen positions, and comparing candidate structuresuntil a good match with the known X-ray diffraction profile is attained. For layeredmanganese oxide prototype frameworks, we chose four general structural frameworks toinitialize the structural enumeration, as visualized in Fig. S1:

1.) The O1 stacking of δ-MnO2 based on pyrochroite Mn(OH)2, but enumerating half occupations ofthe hydrogen atoms, achieving an MnOOH stoichiometry

2.) The P2 stacking of Birnessite, δ-MnO2, which has the same layer structure but different layerstackings in the out-of-plane direction. We enumerated hydrogen arrangements in the inter-layer areabased on electrostatically-favorable vertices and midpoints of a Voronoi decomposition of thestructure, scaled to a 1 Å distance of the nearest oxygen. Note that the P3 stacking seen in, forexample, the β-NiOOH structure, was obtained as a relaxation of an initial O3 structure.

3.) The O3 stacking of δ-MnO2, following the same methodology as in 2.) to enumerate hydrogenpositions.

4.) The orthorhombic polymorph of LiMnO2, removing the Li atoms and adding hydrogen into theinterlayer region by analogy to the lepidocrocite FeOOH structure.

On these four generally layered MnO2 frameworks, we constructed 42 candidate structures with aMnOOH stoichiometry. All MnOOH candidate structures were then structurally relaxed in SCAN-DFT, considering a ferromagnetic and a representative antiferromagnetic magnetic ordering. Themost energetically favorable structures were those with the P2 framework, or a P3 frameworkobtained as a relaxation of the O3 initial structure, as seen in Figure S2. However, as the energy ofthe P2 and P3 structures are essentially identical (P3 being more stable by less than 1 meV/atom), werelied on the reference X-ray diffraction pattern to choose between the two structural candidates.Using the X-ray diffraction calculator in pymatgen, we computed XRD patterns for the candidatestructures (with simulated Cu-Kα source), and compared the resulting XRD patterns to the knownpattern in JCPDS card no. 00-018-0804.

Figure S1. Structural frameworks for candidate β-MnOOH structures, where a) O3-type δ-MnO2, b) O1-type δ-MnO2 derived from pyrochroite Mn(OH)2, c) P2-type δ-MnO2 and d) o-LiMnO2-type. The visualized structures in a),b) and c) are in the MnO2H2 stoichiometry, with all possible hydrogen positions for MnOOH visualized. Note thatthe P3 structure, seen in for example β-NiOOH, is obtained from a relaxation of the O3 structures in a), in the caseswhere it is energetically favorable.

Figure S2. Low energy structural candidates for the β-MnOOH structure, belonging to the P3 and P2 layeredstructure types.

Figure S3. Top) X-ray diffraction pattern for both the reference β-MnOOH entry from the JCPDS, and our predictedstructure in blue. Bottom) Computed X-ray diffraction patterns for all candidate β-MnOOH structures, with circlescentered on the 2θ of the computed peak, and the radius of each circle proportional to the intensity of each peak. Thereference XRD pattern is shown as black circles, with corresponding vertical black lines indicating their 2θ position.The color of each circle for the candidate structures is representative of their distance from the nearest referencepeak; blue means a reference peak is close by, whereas purple means the nearest reference peak is far away. Thehorizontal blue line marks the structure of our selected β-MnOOH structure.

JCPDS card no. 00-018-0804

Our selection: O3_0_1_s12_afm

Reference

Inte

nsi

ty

2 (Cu-K )

O1-type δ-MnO2

Layered LiMnO2

O3-type δ-MnO2

P2-type δ-MnO2

Figure S3 compares all the XRD patterns for the candidate structures. The LiMnO2

framework has a poor match for the 18° peak of the reference structure, indicating that thelayer-spacing is wrong and that this is not the proper framework. The other frameworks; O1-type δ-MnO2, P2 δ-MnO2, and O3-derived δ-MnO2 have the proper first peak position.However, both O1-type δ-MnO2 and P2 δ-MnO2 have poor fits on the second and third peaks,suggesting that the out-of-plane vector is at the wrong angle.

Of the four frameworks, P3 δ-MnO2 (derived as a relaxation of the O3 initialstructure) has the best fit on the first three peaks, meaning the β-MnOOH is most likely toexhibit the P3-type framework, with its corresponding out-of-plane vector angle. The Mn 3+

ions form an antiferromagnetic ordering, as shown in Figure S4. The structure is computed tohave an enthalpy of ΔH = 8.41 kJ/mol, relative the ground-state γ-MnOOH phase, withintypical error tolerance of the experimentally-measured ΔH = 14.6 kJ/mol. This structure issimilar to the β-NiOOH structure recently computed in Reference 8.

Figure S4. Crystal structure of β-MnOOH with best XRD fit with JCPDS no. 00-018-0804. Yellow and purple Mn3+ ions have alternating magnetic configurations.

S.I.4. Example Generalized Pourbaix Potential

Here we provide two example Pourbaix Potentials, for the MnO4-(aq) ion, and solid γ-MnOOH

The Pourbaix Potential is expressed with units of eV/Mn, as:

2

1( ) (2 ) (2 )O H O O H O HH

M

G N N N N N Q EN

We use 2H Oto be the experimental formation energy of water to be -2.4576 eV, as from Ref 8.

For the aqueous ion MnO4-, the Pourbaix potential is given as

4MnO1

-4.658 ln[Mn] (4)( 2.4576 eV) 2(4) 0 2(4) (0) ( 1)1 H

RT E

For the solid phase γ-MnOOH, the Pourbaix potential is given as

γ-MnOOH1

( 5.780 (2)( 2.4576 eV) (2(2) 1) (2(2) (1) (0))1 H

E

For nanoscale Pourbaix phase diagrams, the units of the surface energy term are expressed:

23

2 3

3 2

(2/ ) 33

1 eV 1 1 J eV nm m6.24 10

Mn nm m M

Å

n (m ) J

m

ÅR R � � � �� �� �� � � � � �� � � �״��� � �� � � � � � � �� � � � � � �� � � � � �� � � � � � � �� �

For the nucleation analyses, the classical nucleation barrier, *G , is given by:

32/3

2

4*

27G

where is the average surface energy of a nucleus, is a shape-factor (with units Area/Vol2/3), and ρis the volume per manganese atom, in units of Å3/Mn. Therefore, the numerator has units of eV3/Mn2,and the denominator has units of eV2/Mn2. ΔG* is divided by kBT in the total nucleation barrier, which is related to the steady-state nucleation rate by

*exp

B

GJ Z N

k T

� � � �� � 11\* MERGEFORMAT ()

where Z is the Zeldovich Factor, is the monomer attachment rate to a growing crystal, and N is the number of free monomers in solution. N will be the same between competing products, and the

differences in Z and between metal oxides of similar composition are usually much smaller than differences in the exponential term, which can vary by orders of magnitude. Therefore, analysis of nucleation rates between competing metal oxides can be approximated as having the same

exponential pre-factors.9 If the approximation is invalid, it is straightforward to include kinetic effectsin the analysis, by assigning a specific Z or β for each phase.

S.I.3 Surface energies of MnOxHy phases

Surface energies of MnOxHy phases are calculated in density functional theory, using surface slabs generated using the efficient creation and convergence scheme developed by Sun and Ceder.10 For each conventional bulk unit cell, low-index surfaces are enumerated, and surface energies are calculated withinthe SCAN metaGGA functional. Surface energy calculations were performed on surface slabs at least 15 Å thick and with 16 Å vacuum.

DFT calculations were performed using the Vienna Ab-Initio Software Package (VASP).11 We used the projector augmented wave (PAW)12 method with the strongly-constrained and appropriately-normed (SCAN)13 metaGGA (generalized-gradient approximation) functional. Plane-wave basis cutoff energies were set at 520 eV for all calculations. Brillouin Zones were sampled using Gaussian smearing, with at least 1000 k-points per reciprocal atom for bulk unit cells, and at least 700 k-points per reciprocal atom for surface slabs. Atoms were initially relaxed until forces were 1E-6 eV/Å. All structure preparations were performed using the Python Materials Genomic (Pymatgen) package.14

Surface energies were calculated with the equation

1

2 slab bulk i ii

E NE NA

� � � �� �

�

To compute hydrated surface energies, we attempted to model the first monolayer of strongly-bound water by adsorbing explicit water molecules onto the various surfaces. We previously used this technique to successfully model the hydrated surface energies in CaCO3 and FeS2. However, when we attempt this approach on the manganese oxides, the water molecule dissociates on many MnO2 surfaces, but not on MnOOH surfaces. The splitting of water into an H+ and OH- ion makes us unable to construct a self-consistent water chemical potential for computing a hydrated surface energy using the surface grand potential.

The thermodynamic effect of water hydration is to passivate broken bonds, resulting in a reduction ofsurface energy. The systematic underbinding of bonds in the generalized-gradient approximation oftenleads to surface energies being consistently under-predicted from experiment by 30%,15 which isapproximately the same amount as due to hydration. For this reason, we use the SCAN surface energiesof dry surfaces to approximate the experimental surface energies of hydrated surfaces. The dry DFT-calculated surface energies of bixbyite Mn2O3 and Pyrolusite β-MnO2 are found to be within the error barsof the hydrated surface energies, as measured by Birkner and Navrotsky.16 Therefore, we use the drysurface energies from SCAN to approximate the quantitative value of the hydrated surface energies.

We assume in this work that Δγ between manganese oxide phases does not vary significantly with E orpH, as chemical interactions between H+ or OH- ions and manganese oxide surfaces should be largelysimilar over changing surface structures. While in reality, H+ or OH- ions may adsorb preferentially ontospecific surfaces of specific polymorphs,17 identifying these relationships is enormously expensivecomputationally, and will be tackled in a future work. We emphasize that this work focuses primarily onthe contribution of the thermodynamic framework.

Table 2. Calculated surface energies, shape factors, and molar volumes of MnOxHy phases

CompositionSurface Energy

J/m2Shape FactorArea/Vol2/3

Volume/Metal

Å3/MnMn(OH)2 0.47 5.69 43.5

Mn3O4* 1.43 5.44 26.2

Mn2O3 1.36 5.84 26.0

β-MnOOH 0.56 6.40 37.1

α-MnOOH 0.65 7.00 34.7

γ-MnOOH 0.84 6.09 33.5

R-MnO2 1.33 5.78 29.8

γ-MnO2 1.44 6.11 28.9

β-MnO2 1.54 6.35 27.6

Equilibrium particle morphologies are computed using the Wulff construction. For the nucleation barrier, we use a surface energy that is averaged over the particle morphology, computed by the equation

Avg

hkl hklhkl

hklhkl

A

A

��

The shape factor, η, is unitless and size-invariant, and is computed from Area/Volume2/3 of the Wulff construction. For each structure, we also provide the surface energies of some facets that are slightly too high in energy to appear on the particle morphology, but could potentially be stabilized by adsorbates or variations in solution conditions.

Pyrolusite, β-MnO2

Average surface energy:

1.54 J/m2

Shape Factor

6.35

Volume/Mn

27.6 Å3/Mn

Miler Index Surface Energy (J/m2) Area Fraction

110 1.31 0.47

101 1.84 0.38

100 1.53 0.15

Miller Index Surface Energy (J/m2) Energy above Wulff(J/m2)

001 2.33 0.126

Intergrowth, γ-MnO2

Average SE:

1.44 J/m2

Shape Factor

6.22

Volume/Mn

28.9 Å3/Mn

Miler Index Surface Energy (J/m2) Area Fraction

001 1.00

100 1.61

110 2.06

010 2.17

Miller Index Surface Energy (J/m2) Energy above Wulff (J/m

111 2.35

Ramsdellite, R-MnO2

Average SE:

1.33 J/m2

Shape Factor

5.78

Volume/Mn

29.8 Å3/Mn

Miler Index Surface Energy (J/m2) Area Fraction

011 0.99 0.57

001 1.39 0.17

111 1.99 0.11

11-1 2.00 0.1

100 2.11 0.06

Miller Index Surface Energy (J/m2) Energy above Wulff (J/m

110 2.08 0.0146

γ-MnOOH, Manganite

Average SE:

0.84 J/m2

Shape Factor

6.09

Volume/Mn

33.5 Å3/Mn

Miler Index Surface Energy (J/m2)

010 0.55

100 1.03

001 1.15

10-1 1.23

Miller Index Surface Energy (J/m2) Energy above Wulff (J/m

10-2 1.40

101 1.5658α-MnOOH, Groutite

Average SE:

0.65 J/m2

Shape Factor

7.0

Volume/Mn

34.7 Å3/Mn

Miler Index Surface Energy (J/m2) Area Fraction

001 0.363 0.6

010 0.9239 0.24

100 1.32 0.16

β-MnOOH, Feitknechtite

Average SE:

0.53 J/m2

Shape Factor

6.40

Volume/Mn

37.1 Å3/Mn

Miler Index Surface Energy (J/m2) Area Fraction

111 0.41 0.48

010 0.49 0.26

1-1-1 0.93 0.14

01-1 0.78 0.11

001 1.20 0.006

Miller Index Surface Energy (J/m2) Energy above Wulff (J/m2)

110 1.26 0.29

1-10 1.28 0.3308

100 1.2260 0.3691

Hausmannite, Mn3O4

Average SE:

1.43 J/m2

Shape Factor

5.44

Volume/Mn

26.2 Å3/Mn

Miler Index Surface Energy (J/m2) Area Fraction

111 1.375 0.75

010 1.43 0.13

001 1.84 0.11

110 1.48 0.01

All surfaces of Hausmannite Mn3O4 are polar, and so surface slabs constructed in DFT are subject to theTasker electrostatic catastrophe,18 meaning a surface energy cannot be attained without reconstruction.Surface energies reported here are calculated using Tasker 3 to Tasker 2b reconstructions, by moving halfof the ions from one side of a slab to the other until the dipole is mitigated. However, such surfaces oftenresult in low-coordination numbers on the surface atoms. This undercoordination results in calculatedMn3O4 surface energies that are much higher than experiment, and moreover, do not agree with thegeneral observation that spinel surfaces have low surface energy. The real Hausmannite surface likelyexhibits other reconstructions, which may include passivation by the solvent or the electrical double layer,whose structure is beyond the scope of this work. For these reasons, we base the nucleation analyses inthis work on the experimentally-measured Hausmannite surface energy of 0.96 J/m2.

Tasker 2B-reconstructed Hausmannite (111) surface, with 2- and 3-fold coordinated surface Mn ions

Bixbyite, Mn2O3

Average SE:

1.36 J/m2

Shape Factor

5.84

Volume/Mn

26.0 Å3/Mn

Miler Index Surface Energy (J/m2) Area Fraction

001 1.81 0.18

011 1.77 0.13

110 1.17 0.69

101 2.43 .0001

Miller Index Surface Energy (J/m2) Energy above Wulff (J/m

100 1.81 0.157

Pyrochroite, Mn(OH)2

Average SE:

0.47 J/m2

Shape Factor

5.69

Volume/Mn

43.5 Å3/Mn

Miler Index Surface Energy (J/m2) Area Fraction

10-1 0.46 0.79

100 0.52 0.21

Miller Index Surface Energy (J/m2) Energy above Wulff (J/m

110 0.63 0.024

111 0.590 0.014

References

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2 Hem, John D., and Carol J. Lind. "Nonequilibrium models for predicting forms of precipitated manganese oxides." Geochimica et Cosmochimica Acta 47.11 (1983): 2037-2046.

3 Hem, John D. "Redox processes at surfaces of manganese oxide and their effects on aqueous metal ions." Chemical Geology 21.3-4(1978): 199-218.

4 Hem, John David. Chemical equilibria and rates of manganese oxidation. No. 1667-A. USGPO,, 1963.

5 Fritsch, Sophie, Jeffrey E. Post, and Alexandra Navrotsky. "Energetics of low-temperature polymorphs of manganese dioxide and oxyhydroxide." Geochimica et Cosmochimica Acta 61.13 (1997): 2613-2616.

6 Kitchaev, Daniil A., et al. "Energetics of MnO2 polymorphs in density functional theory." Physical Review B 93.4 (2016): 045132.

7 Persson, Kristin A., et al. "Prediction of solid-aqueous equilibria: Scheme to combine first-principles calculations of solids with experimental aqueous states." Physical Review B 85.23 (2012): 235438.

8 Tkalych, Alexander J., Kuang Yu, and Emily A. Carter. "Structural and electronic features of β-Ni (OH) 2 and β-NiOOH from first principles." The Journal of Physical Chemistry C 119.43 (2015): 24315-24322.

9 Sun, Wenhao, and Gerbrand Ceder. "Induction time of a polymorphic transformation." CrystEngComm 19.31 (2017): 4576-4585.

10 Sun, Wenhao, and Gerbrand Ceder. "Efficient creation and convergence of surface slabs." Surface Science 617 (2013): 53-59.

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12 Kresse, G., and D. Joubert. "From ultrasoft pseudopotentials to the projector augmented-wave method." Physical Review B 59.3 (1999): 1758.

13 Sun, Jianwei, Adrienn Ruzsinszky, and John P. Perdew. "Strongly constrained and appropriately normed semilocal density functional." Physical review letters 115.3 (2015): 036402.

14 Ong, Shyue Ping, et al. "Python Materials Genomics (pymatgen): A robust, open-source python library for materials analysis." Computational Materials Science 68 (2013): 314-319.

15 Goniakowski, J., et al. "Influence of gradient corrections on the bulk and surface properties of TiO 2 and SnO 2." Physical Review B 53.3 (1996): 957.

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17 Kitchaev, Daniil A., and Gerbrand Ceder. "Evaluating structure selection in the hydrothermal growth of FeS2 pyrite and marcasite." Nature Communications 7 (2016).

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