Optimizing Proton Conductivity in Zirconates through Defect Engineering

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Optimizing proton conductivity in zirconates through defect engineering Andrew J. E. Rowberg, Leigh Weston, and Chris G. Van de Walle ACS Appl. Energy Mater., Just Accepted Manuscript • DOI: 10.1021/acsaem.8b02222 • Publication Date (Web): 12 Mar 2019 Downloaded from http://pubs.acs.org on March 17, 2019

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ACS Applied Energy Materials

Optimizing proton conductivity in zirconates through defect engineering †

Andrew J. E. Rowberg,

†Materials

Leigh Weston,

†,‡

and Chris G. Van de Walle

∗,†

Department, University of California, Santa Barbara, California 93106-5050, United States

‡Energy

Technologies Area, Lawrence Berkeley National Laboratory, 1 Cyclotron Rd, Berkeley, California 94720, United States

* E-mail: [email protected]

Abstract

Introduction

The alkaline-earth zirconates (CaZrO3 , SrZrO3 ,

Hydrogen is an attractive source of clean and

and BaZrO3 ) are under active investigation as

renewable energy. It is the most abundant el-

solid-state electrolytes in hydrogen fuel cells.

ement in the universe and oers roughly three

Their performance as proton conductors de-

times more chemical energy per mass than other

pends critically on the properties of accep-

chemical fuels, including natural gas, petrol,

tor

and coal.

dopants.

calculations and

point

Here, to

study

defects

in

we the

use role

rst-principles of

acceptors

incorporating

1,2

Electrochemical devices that use

hydrogen for energy applications require elec-

protons

trolytes with high hydrogen conductivity. For

through an oxygen-vacancy-mediated process.

high-temperature applications, it is necessary

For CaZrO3 , we nd that ZrCa antisites sup-

to use solid-state electrolytes, which are more

press formation of oxygen vacancies. Other in-

thermally stable than polymer electrolyte mem-

trinsic point defects are shown not to hinder

branes,;

performance.

ides are most promising.

Common unintentional impuri-

3

among these, proton-conducting ox-

46

The most widely

ties, such as N and C, are not good accep-

researched

tors but can incorporate in other congurations.

ABO3 perovskite crystal structure, which fa-

Our results show that the eectiveness of com-

cilitates fast proton hopping between nearby

mon dopants such as Sc and Y is limited by self-

O atoms.

compensation due to their incorporation on the

garded as the best proton-conducting oxide in

wrong cation site, where they act as donors.

terms of chemical stability and ionic conductiv-

We demonstrate that using alkali metal dopants

ity.

overcomes this problem, as the formation en-

(CaZrO3 ) and strontium zirconate (SrZrO3 ),

ergy of compensating donors is very high. Al-

also have attracted interest as proton conduc-

kali metal dopants also have low binding en-

tors,

ergies for protons, reducing their tendency to

commercial hydrogen gas sensors.

act as traps and hence enhancing proton conductivity.

7,8

of

these

materials

take

on

the

Barium zirconate (BaZrO3 ) is re-

Its related compounds, calcium zirconate

9

and CaZrO3 has been adopted for use in

6,10,11

Protons are incorporated into the zirconates

Our guidelines for choosing accep-

by creating oxygen vacancies during synthesis

tor dopants and optimizing synthesis conditions

and then exposing to water, leading to the re-

can greatly improve the ecacy of these proton-

action:

6

VO+2 + H2 O → 2H+ .

conducting oxides as solid-state electrolytes.

(1)

The as-grown material therefore needs to con-

ACS Paragon Plus Environment 1

ACS Applied Energy Materials 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 18

tain a high concentration of oxygen vacancies,

they would act as donors.

which is accomplished by doping with acceptor

ies have reported that K and Rb can enhance

impurities. Trivalent group-IIIB metals such as

proton conductivity in BaZrO3 ,

Y and Sc are most commonly used.

sults address the underlying reasons for this im-

6

When sub-

stituting on the tetravalent Zr site, these ele-

Some recent stud-

1316

and our re-

provement.

ments act as acceptors. However, there is some

We use rst-principles techniques based on

probability that they will incorporate on the

density functional theory (DFT) with a hybrid

divalent A site, where they act as donors, thus

functional to obtain a reliable description of

suppressing the intended formation of oxygen

atomic and electronic structure.

vacancies. We previously identied this wrong-

native point defects, including vacancies, cation

site incorporation as a problem in SrZrO3 ,

antisite defects, and self-interstitials. We then

12

We analyze

and one goal of the present study is to exam-

examine acceptor doping by studying substitu-

ine the degree to it also occurs in CaZrO3 and

tion on the A, B, and O lattice sites. For the

BaZrO3 .

alkali metals, and for C and N, we also consider

Another goal is to determine whether or not

incorporation on interstitial sites. We also ex-

oxygen vacancies are in fact the most prevalent

amine the tendency of the candidate dopants

donors in these systems. Other acceptors, such

to bind protons; strong binding causes the ac-

as cation antisite defects or self-interstitials,

ceptors to act as traps, thus reducing proton

could form as the dominant donor species and

conductivity.

in the process suppress the formation of oxygen

Previous rst-principles studies have exam-

vacancies. We nd that cation antisites (ZrCa )

ined some of the intrinsic and extrinsic defect

are low in energy in CaZrO3 .

properties of the alkaline-earth zirconates.

Under Zr-rich

conditions, they also form in SrZrO3 .

1521

Thus,

However, our report is the rst to apply hy-

doping CaZrO3 with acceptors will not lead to

brid density functionals to generate highly ac-

formation of oxygen vacancies; rather, ZrCa an-

curate results for the electronic properties and

tisites will form. In SrZrO3 , Sr-rich conditions

defect formation energies, to examine incorpo-

are necessary to preferentially create oxygen va-

ration of acceptors on wrong sites, and to do

cancies.

so for all three compounds. Our comprehensive

A third goal is to investigate other impurities

results allow us to assess how likely acceptor

that could be used as acceptor dopants while

dopants are to self-compensate and to provide

avoiding the self-compensation problem.

engineering solutions to avoid the formation of

On

the oxygen site, N and C are candidate accep-

unwanted defects.

tors; we will examine their eectiveness for gen-

dopants are superior to Sc and Y as promo-

erating oxygen vacancies. It is also important

tors of oxygen vacancies and have smaller pro-

to consider N and C because these elements are

ton binding energies, thus leading to higher pro-

commonly present during synthesis and device

ton conductivity. We also provide guidance for

operation; in particular, we identify a dicarbon

synthesis conditions that will optimize acceptor

complex that could lead to unintentional car-

incorporation.

bon incorporation in the crystal lattice. Impu-

Methodology

rities can also be incorporated on the A site, where monovalent elements such as the alkali metals should act as acceptors when substituting for the divalent Ca, Sr, or Ba.

We nd that alkali metal

Computational details

We nd

alkali metals to be superior to the trivalent ac-

We use DFT within the generalized Kohn-Sham

ceptors Y and Sc. We explicitly verify that in-

scheme,

corporation on the A site (as opposed to the Zr

initio

site) is preferred, and we also examine whether

22

as implemented in the Vienna

Simulation Package (VASP).

23

Ab

We use

the hybrid exchange-correlation functional of

compensation could occur due to incorporation

Heyd, Scuseria, and Ernzerhof (HSE),

of alkali metals as interstitials, in which case


24

with

Page 3 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


EF

25% mixing of short-range Hartree-Fock ex-

reservoir;

change.

erence to the valence-band maximum (VBM);

We apply projector augmented wave

(PAW) potentials

25,26

∆corr

is the Fermi level, which we ref-

28,29

with a plane-wave cuto 2 6 2 2 6 2 of 400 eV. The Ba 5s 5p 6s , Sr 4s 4p 5s , 2 6 2 2 2 6 Ca 3s 3p 4s , Zr 4d 5s , and O 2p electrons

and

are treated explicitly as valence.

ing synthesis. We express them in terms of the

is a nite-size correction term.

The chemical potentials

µi

are variables that

reect the abundance of various elements dur-

For the or-

thorhombic unit cells of CaZrO3 and SrZrO3 ,

deviations

which contain four formula units, a 4×4×3

∆µi

from the values for the elemen-

k-

tal references, i.e., the ground-state structures

point grid is used to integrate over the Brillouin

of the Ae metal, Zr metal, and an O atom in

zone; for BaZrO3 , which has a cubic unit cell

O2 . Assuming conditions close to equilibrium,

that contains one formula unit, we use a 6×6×6

the

k -point

grid.

∆µi

are related by

∆µAe + ∆µZr + 3∆µO = ∆H f (AeZrO3 ),

(3)

Defect calculations

where

To calculate defect properties, we construct su-

tion for AeZrO3 . Our calculated enthalpies of

2a × 2b × 2c,

listed in Table 1.

containing 8 unit

cells and 160 atoms in total; for cubic BaZrO3 , the supercells have dimensions

Table 1: Calculated and Reported Enthalpies of

3a × 3b × 3c,

containing 27 unit cells and 135 atoms.

Formation (in eV per Formula Unit) for Com-

For

pounds Pertinent to this Study.

the supercell calculations in each material, a 2×2×2

k -point

grid is used.

is the enthalpy of forma-

formation for the three AeZrO3 compounds are

percells: for CaZrO3 and SrZrO3 , the supercells have dimensions

∆H f (AeZrO3 )

We examine the

Compound

formation of alkaline-earth (VAe , Ae = {Ca, Sr,

∆H f

(eV) (calc)

∆H f

(eV) (exp)

Ba}), Zr (VZr ), and O vacancies (VO ), as well

CaZrO3

17.41

18.42

as cation antisite defects (AeZr and ZrAe ) and

SrZrO3

17.38

18.28

BaZrO3

17.29

18.28

CaO

6.14

6.58

a host atom, e.g., Na on a Ca site in CaZrO3

SrO

5.61

6.14

(NaCa ), Y on a Zr site (YZr ), or N on an O

BaO

5.09

5.68

CaCO3

11.92

12.52

N in interstitial positions (Nai , Ci , and Ni ). To

SrCO3

11.98

12.65

study the properties of protons, we also con-

BaCO3

11.91

12.58

sider interstitial hydrogen (Hi ). f q The formation energy E (D ) of a point de-

Ca(OH)2

9.84

10.21

Sr(OH)2

9.57

9.94

Ba(OH)2

9.30

9.79

ZrO2

10.99

11.41

Sc2 O3

18.98

19.79

Y 2 O3

19.05

19.75

Na2 O

3.76

4.29

K2 O

3.00

3.75

Rb2 O

2.62

3.51

Zr3 N4

11.19

10.16

self-interstitials (Aei , Zri , and Oi ).

To study

the eect of doping, we consider substitutional impurities, where an extrinsic element replaces

site (NO ). Additionally, we calculate the formation energy of alkali metals (e.g., Na), C, and

fect

D

in charge state

q

is calculated as

27

E f (Dq ) = E(Dq ) − Ebulk + X ni µi + qEF + ∆corr . q

E(D )

(2)

is the total energy of a supercell con-

q ; Ebulk is the total energy of a defect-free supercell; |ni | is the number of atoms of species i added (ni < 0) or removed (ni > 0) from the system; µi is the chemical potential of species i in an external taining defect

D

in charge state


30 31 31

32 32 32 32 32 32 32

32 32 32 32 32

32 32 32 33


While the

∆µi

are variable, they are subject

are imposed by an oxide phase Xa Ob :

to constraints imposed by formation of other

a∆µX + b∆µO ≤ ∆H f (Xa Ob ) .

compounds, namely,

∆µAe + ∆µO ≤ ∆H f (AeO)

∆µAe

The lack of dependence on

(4)

and

(6)

∆µZr

implies that our impurity chemical potentials

and

are the same under Ae-rich and Zr-rich condi-

f

∆µZr + 2∆µO ≤ ∆H (ZrO2 ) .

(5)

tions. The limiting phases were selected based on their likelihood of limiting the impurity solu-

The relevant enthalpies of formation are also f listed in Table 1. While these ∆H values are

bility under our chosen chemical potential conditions.

in reasonable agreement with experiment, some systematic deviations are evident. possible to include correction terms;

34

Project database as a reference.

however,

alently,

Changing

stitutional conguration CZr has no net chem-

bility region for AeZrO3 . We show this stability

ical potential dependence.

region graphically for each compound in Fig. 1.

the limiting phase;

For the purposes of presenting our results, we

mined by

will consider two particular chemical potential

∆µZr

For N, Zr3 N4 is

therefore,

∆µN

is deter-

and could, in principle, vary

between Ae-rich and Zr-rich extremes.

conditions; other conditions can always be ex-

ever, the magnitude of

amined by referring back to eq 2. For oxygen,

both cases that

eV, which cor-

of N2 (∆µN

responds to typical experimental conditions for ◦ 12,35 SrZrO3 sintered in air at 1650 C. These rel-

∆µN

∆µZr

How-

is large enough in

is bounded by formation

= 0) rather than Zr3 N4 .

For H, the

limiting phases are the alkaline-earth hydroxides, Ca(OH)2 , Sr(OH)2 , and Ba(OH)2 ; these

formation.

compounds provide a stronger limit on H in-

∆µO is chosen, eq 3 xes the sum of ∆µAe ∆µZr . To choose the Ae and Zr values,

Once

corporation than does water.

The calculated

enthalpies of formation for the limiting phases

we consider two extremes: Ae-rich and Zr-rich.

are also listed in Table 1.

Ae-rich conditions are determined by consider-

Results and Discussion

ing the bound expressed by eq 4, while Zr-rich conditions are determined by eq 5. These limits are labeled in Fig. 1. For the impurity species under consideration, we again dene the chemical potentials

∆µZr .

by the same amount, meaning that the sub-

elemental references, eqs 4 and 5 dene a sta-

VO

∆µAe , or equiv∆µZr changes ∆µC

pendent upon the choice of

per bounds imposed by the formation of the

atively O-poor conditions favor

For C, the

ates; thus, the chemical potential of C is de-

to establish limiting cases. Along with the up-

∆µO =−2.42

3638

limiting phases are the alkaline-earth carbon-

our present work, in which we use them merely

we choose a value

We investigated the pertinent binary

and ternary compounds, using the Materials

It may be

the calculated values suce for the purposes of

and

Page 4 of 18

Bulk Properties

∆µX

with respect to elemental references. An upper

The unit cells of CaZrO3 , SrZrO3 , and BaZrO3

bound is placed on these chemical potentials by

are shown in Figure 2; the depiction of BaZrO3

considering the formation of secondary phases,

in Figure 2(c) is expanded in order to directly

and for the purposes of presenting our results,

compare the structure with those of CaZrO3

we will set

∆µX to its value at that bound.

and SrZrO3 .

This

CaZrO3 and SrZrO3 crystallize

limit represents the most favorable condition

as distorted orthorhombic perovskites in the

for impurity incorporation (i.e., the solubility

space group

limit) and permits us to compare the likelihood

cells. The tilts of the BO6 octahedra are slightly

of various species to incorporate. For the ma-

more pronounced in CaZrO3 than in SrZrO3 ;

jority of impurities considered here, the bounds

these octahedra are also slightly anisotropic,

P bnm

with 20 atoms in their unit

such that we can identify two inequivalent O sites, one approximately in the


ab-plane,

which

Page 5 of 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a)

(b)

(c)

Figure 1: Stability regions for (a) CaZrO3 and (b) SrZrO3 , and (c) BaZrO3 , shaded in gray, in the

∆µZr -∆µO phase space. ∆µO = −2.42 eV.

The dashed line represents the choice of

c-axis,

which we label O(2).

BaZrO3 has

purities

higher symmetry and crystallizes as a cubic perovskite in the space group

P m3m;

used throughout this study,

Properties of Point Defects and Im-

we label O(1), and one linking Zr atoms along the

∆µO

The primary goal of materials synthesis is to

its unit cell

can be described by ve atoms. Calculated lat-

create high concentrations of

VO

tice parameters and band gaps are listed in Ta-

able proton uptake via eq 1.

The concentration

ble 2, along with experimental values. and

b

of

a

The

VO

is related to the defect formation energy

connect next-nearest-neighbor Zr atoms, while

the lattice vector in BaZrO3 connects nearest-

c(VO ) = Nsites exp

In order to directly com-

pare unit cell sizes, the lattice constant

√

BaZrO3 must be multiplied by

2,

a

in

where

yielding a

increase in lattice constants with increasing A-

,

(7)

is the Boltzmann constant and

Nsites

Calculated and Experimental Bulk

Native Point Defects

Properties for CaZrO3 , SrZrO3 , and BaZrO3 .

Our calculated formation energies for native

Band Material

Method

CaZrO3

HSE Exp

39,40

HSE Exp

BaZrO3

is decreased; thus, to promote VO formation, E f (VO ) should be as small as possible.

site cation size.

SrZrO3

kB

−E f (VO ) kB T

is the number of available sites in a unit cell. f Concentrations increase exponentially as E

value of 5.93 Å, which matches the monotonic

Table 2:

in order to en-

by a Boltzmann expression:

lattice vectors in CaZrO3 and SrZrO3

neighbor Zr atoms.

6

4143

HSE Exp

44

a

(Å)

b

(Å)

c

(Å)

point defects are shown in Figure 3.

Gap (eV)

5.60

5.80

8.05

5.4

5.59

5.77

8.02

5.7

5.81

5.87

8.24

5.2

5.80

5.82

8.21

5.2, 5.6

4.20

4.20

4.20

4.5

4.20

4.20

4.20

4.0

VO

in-

corporates with the lowest formation energy in +2 the +2 charge state. In order to form VO , a compensating negatively charged defect or impurity is needed to maintain overall charge neutrality in the system. The Fermi level will be pinned near the point where the formationenergy lines for the lowest-energy positively and negatively charged defects intersect. Forming VO+2 in high concentrations thus requires acceptor species with low formation energy. Among native defects, the most likely candidate accep−4 −2 −2 tors are VZr , VAe , and AeZr . However, as seen



(a)

Ca Sr Ba

Page 6 of 18

(b)

O(1)

O(1)

O(2)

O(2) 𝑐

ZrO6

𝑐

c

a

c b

(c)

𝑎

𝑏

𝑎 b

𝑎

𝑏

𝑎

𝑎

a

Figure 2: Unit cells of (a) CaZrO3 (b) SrZrO3 , and (c) BaZrO3 . For BaZrO3 , multiple cubic unit cells are shown to enable comparison with the lower-symmetry structures of CaZrO3 and SrZrO3 .

in Figure 3, these defects have relatively high

Table 3: Ionic Radii of Native Cations (Ca, Sr,

formation energies near the intersection point

Ba, and Zr) in Å. Values are Listed for 6-Fold

with

VO ,

(Zr-site) and 8-Fold (Ae-site) Ionic Coordina-

meaning that the resulting concentra-

tion Environments. (From Ref. 45).

tions will be low.

Extrinsic acceptor dopants +2 are needed to form VO at lower formation energies and in higher concentrations. +2 Interestingly, we nd that VO is not necessarily the primary native point defect that forms when acceptor doping is performed. In +2 CaZrO3 , the antisite defect ZrCa has a lower +2 formation energy than VO under both Ca-rich and Zr-rich conditions, irrespective of the oxy-

Host

Ionic Radius

Ionic Radius

Cation

6-fold Coordination

8-fold Coordination

Ca

1.00

1.12

Sr

1.18

1.26

Ba

1.35

1.42

Zr

0.72

0.84

gen chemical potential. Thus, the primary effect of doping CaZrO3 with acceptors will be +2 +2 to increase the concentration of ZrCa , not VO .

Y, which are trivalent and therefore act as acceptors when substituting for tetravalent Zr

It can readily be shown that the dierence in formation energy between ZrCa and

VO

on the B site.

does

However, there is a risk that

not depend on oxygen chemical potential; this

these dopants may also incorporate on the A

implies that more oxygen-rich conditions (as

site, where they replace divalent alkaline-earth

could, e.g., result from exposure to water) will

atoms and hence act as donors.

12

The pertinent formation energies are plotted

not aect the ZrCa concentration relative to VO . +2 +2 In SrZrO3 , ZrSr is also more stable than VO ,

in Figure 4. Using the example of Sc, we exam− ine the intersection of the ScZr formation-energy

but only under Zr-rich conditions; incorpora+2 tion of VO therefore requires Sr-rich growth +2 conditions. Only in BaZrO3 is VO the lowest-

line with that of the dominant donors.

energy native donor under all growth condi-

If the +2 formation energy at the intersection with VO is + +2 lower than at the intersection with ScAe or ZrAe ,

tions. These trends closely follow cation ionic

then formation of

radii (see Table 3):

formation of

among the alkaline-earth

VO

VO

will be favored; otherwise,

will be suppressed.

We note

cations, Ca is most similar in size to Zr, which

that our results on self-compensation are inde-

favors formation of antisite defects in CaZrO3 .

pendent of the choice of

∆µO :

it can be shown

that the formation energies at the intersection points are independent of

Group-IIIB Dopants

∆µO

(although the

Fermi-level value at which the crossing occurs The dopants most commonly used in the zir-

will change). Similarly, the formation energy at

conates are group-IIIB metals such as Sc and


𝑉Ca

6

CaZrO3, Ca-rich

O𝑖

4 2

𝑉Zr

Zr𝑖

Ca𝑖

ZrCa

0

1

2

CaZr 3

4

ZrSr

𝐸𝐹 (eV) 𝑉Ca

6

CaZrO3, Zr-rich

4

Ca𝑖

2

6

𝑉Zr

Zr𝑖

𝑉O 0

(d)

ZrCa 1

2

CaZr 3

𝐸𝐹 (eV)

4

-2

5

3

4

(e)

𝑉Zr

Zr𝑖

2

BaZr 𝑉Ba

SrZr

4

𝐸𝐹 (eV)

5

333

444

55

𝐸𝐹 (eV)

ZrBa

BaZrO3, Zr-rich

O𝑖 Zr𝑖

BaZr 𝑉Zr 𝑉Ba

00

𝑉O

-2 -2

3

222

Ba𝑖

22

ZrSr 1

11 1

66 44

𝑉O

O𝑖

(c)

O𝑖

0

00 0

5

SrZrO3, Zr-rich

𝑉Sr

Sr𝑖

BaZrO3, Ba-rich

𝑉O

-2 -2 -2

𝐸𝐹 (eV)

0

-2

SrZr 2

2

0

𝑉Zr

000

𝑉O

1

(b)

O𝑖

4

Zr𝑖 0

ZrBa

Ba𝑖 222 Zr𝑖

𝑉Zr

Sr𝑖

-2

5

666 444

0

𝑉O

SrZrO3, Sr-rich

O𝑖

2

0 -2

𝑉Sr

6 4

(a)

Formation Energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



Page 7 of 18

00

(f)

11

22

33

44

5

𝐸𝐹 (eV)

Figure 3: Formation energies of native defects as a function of Fermi level in CaZrO3 , SrZrO3 , and BaZrO3 (ac) under Ae-rich conditions and (df ) under Zr-rich conditions.



Page 8 of 18

− − the intersection point where ScZr or YZr com-

concentrations of

pensate with their corresponding A-site donors

factors to consider when identifying optimal

does not depend on

∆µZr or ∆µAe . VO+2 is not the

dopants; below, we will discuss the binding energies between protons and acceptor dopants,

Inspection of

which will provide an explanation for the superior characteristics of Y.

Figures 4(a) and (d) shows, however, that even +2 in the absence of ZrCa , Sc and Y would prefer to +2 self-compensate rather than generate VO . In +2 +2 SrZrO3 , Zr-rich conditions favor ZrSr over VO .

Group-IA Dopants We now examine the eectiveness of A-site

For Sr-rich conditions, Y will preferentially self-

alkali-metal dopants.

compensate, but Sc will be eective at gener+2 ating VO . Our values for VO in Figures 4(b) ous report;

tion from the perspective of material stability and proton mobility;

we attribute this discrepancy to a

dierent value of the

µO

15,16

however, those stud-

ies did not directly address the dierence with

reference. Finally, in

Y- or Sc-doped material, or how the improve-

BaZrO3 , no self-compensation occurs for both

ments are inuenced by growth conditions or by

Y and Sc due to the high formation energies of + + the ScBa and YBa donors.

wrong-site incorporation. Experimental studies

These trends can be explained by atomic size,

13,14

have also investigated alkali metal dop-

ing and shown that it increases the water up-

as shown in Table 4. The ionic radii of Sc and Y

take in BaZrO3 compared to Y doping,

are close to that of Zr, and they therefore read-

14

but

a microscopic explanation for this observation

ily incorporate on the Zr site. For incorporation

has not been provided.

on the A site, Sc and Y are closest in size to Ca,

All these issues are

comprehensively addressed here. We calculated

explaining why both dopants can readily incorporate on the Ca site in CaZrO3 .

Previous computational

studies have examined alkali-metal incorpora-

and (e) dier somewhat from those in a previ-

12

Clearly, there are other

lowest-

As already noted,

energy donor defect in CaZrO3 .

VO+2 .

the formation energies of Na, K, and Rb accep-

In SrZrO3 ,

tors on the A site in each material (Figure 4).

Y is closer in size to the Sr cation, while the

In CaZrO3 , Na incorporates most readily; in

smaller Sc ion is a worse t. Finally, in BaZrO3 ,

SrZrO3 , K is lowest in energy; and in BaZrO3 ,

both Sc and Y have a large size mismatch with

we nd that Rb is most favored.

Ba, and hence they will not incorporate on the

These spe-

cic dopants are indeed similar in size to their

A site.

host A-site cations, although, as can be seen in

Table 4:

Dierences (rDopant

− rHost )

in Ionic

Table 4, ionic size is not a perfect predictor of

Radii between Host Cations and Dopants in Å.

relative formation energies.

For Zr, a 6-Fold Coordination is Assumed; for

For alkali metals, wrong-site incorporation

the Alkaline-Earth Cations (Ca, Sr, Ba), an 8-

(i.e., incorporation on a Zr site) is expected to

Fold Coordination is Assumed. (From Ref. 45).

be less of a problem, because of the greater mismatch in both size and valence.

Host

Indeed, our

calculated formation energies for these congu-

Cation

Sc

Y

Na

K

Rb

Zr

0.03

0.18

0.30

0.66

0.80

Ca

0.25

0.10

0.06

0.39

0.49

Sr

0.39

0.24

0.08

0.25

0.35

stitials have high formation energies, and thus

Ba

0.55

0.40

0.34

0.09

0.19

self-compensation is not a problem.

rations are all very high. We also consider incorporation on interstitial sites, where the alkali metals act as donors.

Our results in Figure 4

show, however, that the Nai , Ki , and Rbi inter-

Figures 4(a) and (d) again show that, CaZrO3 ,

the experimental observation that, in BaZrO3 ,

SrZrO3 under Zr-rich conditions [Figure 4(e)];

Y is a signicantly superior dopant compared

6

VO

is suppressed due to preferential +2 formation of ZrCa . The same problem arises in

These arguments are not sucient to explain

to Sc.

in

however, at approximately 60% Zr-rich/40% Sr-

Our results show that Sc leads to higher


ZrSr CaZrO3, Ca-rich

4

NaCa

-2

ZrCa

YZr ScZr

ScSr

0 -2

K Sr ScZr

𝑉O

0

1

2

3

4

𝐸𝐹 (eV) CaZrO3, Zr-rich

4

YZr -2 -2

K𝑖 ScZr

YCa YZr

NaCa

-2

0

(d) Figure 4:

1

2

4

5

𝐸𝐹 (eV)

4

5

0

(e)

1

2

1 1

3

𝐸𝐹 (eV)

5

5

𝐸𝐹 (eV)

YBa

-2 -2

4

4 4

ZrBa

00

-4 -4

3 3

ScBa

22

YSr YZr

2 2

RbBa YZr ScZr

BaZrO3, Zr-rich

44

-4

3

0 0

Rb𝑖

ScZr K Sr

ZrSr

𝑉O

(c)

𝑉O

ScSr

0 -2

ZrCa

3

𝐸𝐹 (eV)

2

Na𝑖 ScCa

0

2

SrZrO3, Zr-rich

4

𝑉O

2

1

(b)

YBa

00

-4 -4

0

5

BaZrO3, Ba-rich

Rb ScBa 𝑖

22

YSr

-4

-4

-4

44

K𝑖

2

YCa

Na𝑖 ScCa

0

ZrBa

SrZrO3, Sr-rich

4

𝑉O

2

(a)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



Page 9 of 18

YZr ScZr RbBa

𝑉O 0

1

(f)

2

33

44

5

𝐸𝐹 (eV)

Formation energies of oxygen vacancies and dopant species in CaZrO3 , SrZrO3 , and

BaZrO3 (ac) under Ae-rich conditions and (df ) under Zr-rich conditions.



Page 10 of 18

+2 ZrSr be+2 comes more energetically favorable than VO .

ergies; it occurs in the neutral charge state over

Under Sr-rich conditions, ScZr is the lowest-

tent with C being isoelectronic with Zr. Mirror-

energy acceptor dopant in SrZrO3 [Figure 4(b)].

ing its behavior in ZrO2 ,

We observe, however, that KSr is only slightly

bon undergoes a large lattice relaxation away

higher in energy, and KSr becomes increasingly

from the Zr site, becoming threefold coordi-

favored over ScZr as the material becomes more

nated with a subset of the oxygen nearest neigh+4 bors in a similar fashion to Ci . +4 Both Ci and CZr are relatively stable cong-

rich conditions (independent of

∆µO ),

almost the entire range of Fermi levels, consis-

Zr-rich. At a point dened by 40% Zr-rich/60% Sr-rich, KSr becomes the lowest-energy accep+2 tor. BaZrO3 , nally, will see the highest VO

46,47

we nd that car-

urations, and the energy can further be lowered

concentrations when using RbBa as the accep-

by forming a complex, which we call (2C)Zr ,

tor and growing toward the Zr-rich limit. This

shown in Fig. 6(c); this conguration amounts

increase in

VO

concentration explains the ex-

to two C atoms replacing one Zr atom in the

perimental observation of improved water up-

lattice. Both C atoms adopt the same threefold

take with alkali-metal doping.

Overall, our

coordination with nearby O atoms as CZr , with

ndings suggest that alkali metals are excel-

the C atoms being located in oxygen triangles

lent choices to incorporate

VO

14

in SrZrO3 and

on opposite faces of the octahedron surrounding

BaZrO3 , and synthesis at intermediate condi-

the nominal Zr site. The formation energies of

tions for SrZrO3 and at the Zr-rich limit for

Ci and (2C)Zr can be low enough to potentially

BaZrO3 will maximize the

VO

concentration.

suppress the formation of oxygen vacancies; in addition, these congurations could provide a means for carbon incorporation, thus under-

Carbon and Nitrogen

mining the stability of the material. We remind

Finally, we consider incorporation of C and N.

the reader that our formation-energy plots as-

It was previously found that both species incorporate readily in ZrO2 .

46

sume that carbon is present at the solubility

Formation energies of

limit, i.e., a worst-case scenario in terms of un-

various congurations are plotted in Figure 5.

intentional carbon incorporation. Still, our re-

For NO , Ni , and CZr , these formation energies

sults highlight the importance of limiting expo-

do not vary between Ae-rich and Zr-rich conditions.

sure to carbon.

For NZr , we plot the formation ener-

The same general trends hold for N. NO can

gies at the Ae-rich limit, while for Ci , CO , and

incorporate with lower formation energies than

(2C)Zr , we plot the formation energies at the Zr-

CO but is still unfavorable. The formation en+5 ergy of NZr is also high. Ni is the most favored nitrogen conguration, forming most readily in

rich limit; in both cases the intent is to depict maximum incorporation. For reference, we also included the lowest-energy group-IA and group-

a threefold coordination environment with O +5 atoms. However, the formation energy of Ni is not low enough to play any role in acceptor

IIIB dopants for Ae-rich and Zr-rich conditions. We show the most favorable C congurations in BaZrO3 in Fig. 6; the congurations −2 in CaZrO3 and SrZrO3 are analogous. CO is

compensation, even at the solubility limit.

a candidate O-site acceptor; however, our cal-

Hydrogen

culations show its formation energy to be pro+4 hibitively large. We nd that Ci , shown in Fig. 6(a) adopts a threefold coordination with

In Figure 7 we show the calculated formation energies of hydrogen in both interstitial

neighboring O atoms; this conguration is also +4 46 very similar to that of Ci in ZrO2 . Struc-

and substitutional congurations (on O lattice

turally, this conguration mimics that of the −2 carbonate ion (CO3 ) in terms of CO bond ◦ lengths (∼1.29 Å) and bond angles (∼120 ).

urations at the Zr-rich limit, which represents

CZr , shown in Fig. 6(b), has lower formation en-

mation energies are between 0.1 eV and 0.6 eV

sites). We present energies of hydrogen congthe most energetically favorable limit for hydrogen incorporation. At the Ae-rich limit, for-


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



Page 11 of 18

8

NZr

CaZrO3 6 CO

CZr

4

-4

NO

𝑉O

-2

2C

C𝑖 0

1

N𝑖

ScZr

2

3

4

5

6

NO

𝑉O

-2

0

1

N𝑖

ScZr (Sr-rich)

2C

C𝑖

-4

2

K Sr Zr (Zr-rich) 3

4

N𝑖

CZr

2

NO

0

𝑉O

-2

𝐸𝐹 (eV)

(b)

CO

4

2

NZr

BaZrO3

NZr

CZr

0

(Ca-rich) NaCa Zr (Zr-rich)

𝐸𝐹 (eV)

(a)

SrZrO3 6 CO 4

2 0

8

8

-4 5

0

(Zr-rich)

(2C)Zr

C𝑖 1

RbBa

2

ScZr

(Ba-rich) 3

4

𝐸𝐹 (eV)

(c)

Figure 5: Formation energies of various congurations for C and N incorporation in (a) CaZrO3 , (b) SrZrO3 , and (c) BaZrO3 .

NZr is plotted under Ae-rich conditions, while Ci , CO , and (2C)Zr

are plotted at Zr-rich conditions. Values for the lowest-energy acceptors under Ae-rich and Zr-rich conditions and for

Ba

VO

are also included.

(a)

(b)

(c)

ZrO6 C

c

b a +4 Figure 6: Atomic congurations of C in BZO: (a) Ci , (b) CZr , and (c) (2C)Zr . In (b) and (c), the octahedra consisting of the nominal Zr site and its six surrounding O atoms are indicated by the transparent gray regions.



Table 5:

Binding Energies for Complexes be+ tween Hi and Acceptor Dopants in CaZrO3 , SrZrO3 , and BaZrO3 .

higher, which does not aect our conclusions. Hydrogen interstitials can be present either as − + acceptors (Hi ) or donors (Hi ). Given the applications of the zirconates, the interstitial pro+ ton, Hi , is most pertinent to our study. The + lowest-energy congurations for Hi in CaZrO3 ,

Ebind Acceptor

SrZrO3 , and BaZrO3 are shown in Figure 8.

21

Consistent with previous studies, we nd the + lowest-energy site for Hi to be coordinated closely with an O atom and in close proxim-

O(1); this dierence leads to the distinct con− gurations seen in Figures 8(a) and (b). Hi has fairly high formation energies and is unlikely to

(eV)

CaZrO3

SrZrO3

BaZrO3

− ScZr

0.31

0.39

0.36

−

YZr

ity to another O atom to which it can jump. In + CaZrO3 , the lowest-energy site has Hi bonded + to an O(2), while in SrZrO3 , Hi bonds to an

0.38

0.30

0.26

−

NaAe

0.40

0.32

0.49

− KAe

0.19

0.17

0.25

− RbAe

0.04

0.09

0.20

impediment to proton conductivity.

This ob-

servation helps to explain why Y is a superior

form.

dopant to Sc, as is observed experimentally.

Hydrogen on a substitutional oxygen site has

6

Our calculated binding energies are on the

48

been shown to be stable in oxides. We nd + that HO adopts a multicenter bonding congu-

same order as or even larger than reported proton migration barriers in the zirconates;

ration such that it is roughly equidistant from

18,19

therefore, proton mobility will be signicantly

nearby Zr cations. However, its formation en-

hindered in heavily doped systems.

ergy indicates that it less likely to incorporate

To this

end, doping BaZrO3 with Rb, which has a

than other donor species.

small proton binding energy, should provide improvements compared to doping with Y or

Dopant Interactions with Protons

Sc, which have higher binding energies.

energy among the elements considered here,

with respect to proton mobility in oxides. Pro-

which is consistent with other results on alkali

tons experience Coulombic attraction to nega-

metal doping.

tively charged acceptors; thus, while acceptor

15

For that reason, gains may be

achieved through doping SrZrO3 with either K,

dopants help to incorporate protons, they also

which has the lowest formation energy, or Rb,

hinder the mobility of protons during device operation. We calculate the binding energy + − of a proton Hi to an acceptor A as

In

general, Rb has the smallest proton binding

Trapping is another important consideration

− Ebind (H+ i −A ) = − f E f (H+ i ) + E (A )

Page 12 of 18

which has the lowest binding energy and only a

Ebind

slightly greater formation energy. For CaZrO3 , Rb has the lowest binding energy but also a prohibitively high formation energy; Sc incor-

− − E f (H+ i − A ).

porates more readily and has a low binding en-

(8)

ergy, but its propensity to self-compensate renders it a poor option compared to Na.

We list our calculated binding energies for all

Conclusions

the group-IA and group-IIIB dopants in Table 5. Our results indicate that,

in SrZrO3

and

BaZrO3 , our chosen alkali metal dopants have

Based on our results, we can oer engineering

the lowest proton binding energies.

It is also

recommendations to improve the performance

worth noting that YZr has a lower binding en-

of the alkaline-earth zirconate solid-state pro+2 ton conductors. In CaZrO3 the ZrCa antisite +2 defect is lower in energy than VO , making it

ergy than ScZr in SrZrO3 and BaZrO3 , consistent with other reports.

12,49

The lower binding

energy of Y indicates that it will be less of an

dicult to form useful concentrations of oxy-


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



Page 13 of 18

CaZrO3

4

H𝑖

2

HO

0

ScZr

4 4

SrZrO3

4

HO

0

ScZr

(Ca-rich)

NaCa

-2

𝑉O (a)

2

3

4

𝐸𝐹 (eV)

5

RbBa (Zr-rich)

-2 -2 -2

K Sr

𝑉O

(Zr-rich)

1

HO

0 0

0

(b)

𝑉O

ScZr

(Zr-rich)

(Ba-rich) -4

-4

0

H𝑖

(Sr-rich) -2

-4

2 2

H𝑖

2

BaZrO3

1

2

3

𝐸𝐹 (eV)

4

5

00

11

22

33

44

𝐸𝐹 (eV)

(c)

Figure 7: Formation energies of hydrogen congurations at the Zr-rich limit in (a) CaZrO3 , (b) SrZrO3 , and (c) BaZrO3 . Also included are the lowest-energy acceptors under Ae-rich and Zr-rich conditions, along with the oxygen vacancy and cation antisite formation energies.

(a)

Ca Sr Ba

(b)

(c)

c

c

ZrO6 H

b a

a

b

+ Figure 8: Atomic congurations of the lowest-energy positions for Hi in (a) CaZrO3 , (b) SrZrO3 , and (c) BaZrO3 .


5


Page 14 of 18

gen vacancies through doping. Acceptor dop+2 ing does increase VO concentrations in SrZrO3

mendations expressed in this material are those

and BaZrO3 , and we have focused on identi-

the views of the NSF. L.W. and C.G.V.d.W.

fying optimal dopants and growth conditions.

were supported by the Oce of Science of

Our results show that alkali metal doping is

the U.S. Department of Energy (DOE) (Grant

highly promising.

of the author(s) and do not necessarily reect

Alkali metal doping leads VO+2 , and it avoids

No. DE-FG02-07ER46434). Computational re-

to high concentrations of

sources were provided by the Center for Scien-

the self-compensation eects associated with Y

tic Computing at the California NanoSystems

doping in SrZrO3 . Alkali metal dopants also ex-

Institute and Materials Research Laboratory

hibit the smallest binding energies for protons

(an NSF MRSEC, Grant No.

DMR-1720256)

in SrZrO3 and BaZrO3 , thus reducing the im-

(NSF CNS-0960316), and by the National En-

pact of proton trapping. We have identied the

ergy Research Scientic Computing Center, a

lower proton binding energy of Y as a reason

DOE Oce of Science User Facility supported

for its demonstrated superiority over Sc; thus,

by the Oce of Science of the U.S. DOE under

it is signicant that the alkali-metal binding en-

Contract No. DE-AC02-05CH11231.

ergies are even lower. The incorporation of al-

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Graphical TOC Entry Formation Energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

4

YZr

𝑉O

2 0

-4

𝐒𝐫

YSr

-2

K Sr 0

1

2 3 𝑬𝑭 (eV)

4

𝐊

𝐇 5


Page 18 of 18

Optimizing Proton Conductivity in Zirconates through Defect Engineering

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