This paper is published as part of a PCCP Themed Issue on: Physical chemistry of solids – the science behind materials engineering Guest Editors: Jürgen Janek, Manfred Martin and Klaus Dieter Becker

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Physical chemistry of solids—the science behind materials engineering Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b905911n

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Micro-ionics: next generation power sources Harry L. Tuller, Scott J. Litzelman and WooChul Jung, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b901906e

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Direct calorimetric measurement of grain boundary and surface enthalpies in yttria-stabilized zirconia Shushu Chen, Hugo J. Avila-Paredes, Sangtae Kim, Jinfeng Zhao, Zuhair A. Munir and Alexandra Navrotsky, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b819740g

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In situ investigation of coloration processes in LiNbO3 : MgO during reducing/oxidizing high-temperature treatments Dmytro Sugak, Yaroslav Zhydachevskii, Yuriy Sugak, Oleg Buryy, Sergii Ubizskii, Ivan Solskii, Alexander Börger and Klaus-Dieter Becker, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b822631h

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Ultrathin oxide films and heterojunctions: CaO layers on BaO and SrO Chris E. Mohn, Neil L. Allan and John H. Harding, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b822588e

Formation entropies of intrinsic point defects in cubic In2O3 from first-principles density functional theory calculations Péter Ágoston and Karsten Albe, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b900280d

Hydrogen adsorption on Pd-containing Au(111) bimetallic surfaces Sudha Venkatachalam and Timo Jacob, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b900250b

Interdiffusion and surface-sandwich ordering in initial Ni-core–Pd-shell nanoparticle Alexander V. Evteev, Elena V. Levchenko, Irina V. Belova and Graeme E. Murch, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b822112j

First-principles study on defect chemistry and migration of oxide ions in ceria doped with rare-earth cations Masanobu Nakayama and Manfred Martin, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b900162jAn electrochemical study of lithium insertion into Cr5-yTiySe8 (y = 1, 2, 3, 4, 4.5) beyond the intercalation limit Sylvio Indris, Joseph Wontcheu and Wolfgang Bensch, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b822397a

Mixed LiCo0.6M0.4PO4 (M = Mn, Fe, Ni) phosphates: cycling mechanism and thermal stability Natalia N. Bramnik, Dmytro M. Trots, Heiko J. Hofmann and Helmut Ehrenberg, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b901319a

Changes in the crystal and electronic structure of LiCoO2 and LiNiO2 upon Li intercalation and de-intercalation Sonja Laubach, Stefan Laubach, Peter C. Schmidt, David Ensling, Stefan Schmid, Wolfram Jaegermann, Andreas Thißen, Kristian Nikolowski and Helmut Ehrenberg, Phys. Chem. Chem. Phys., 2009 DOI: 10.1039/b901200a

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Ultrathin oxide films and heterojunctions: CaO layers on BaO and SrO

Chris E. Mohn,abc

Neil L. Allan*aand John H. Harding

d

Received 17th December 2008, Accepted 17th February 2009

First published as an Advance Article on the web 17th March 2009

DOI: 10.1039/b822588e

We examine the form of the islands formed by CaO on BaO and SrO substrates using both

periodic density functional theory and atomistic simulation techniques. (100) edges dominate the

island morphology and we examine how the CaO adjusts to the substrate in small and medium

sized islands and at much larger coverages. There is no direct overlay of CaO ion pairs over OBa

or OSr pairs in the top substrate layer. Rather, island bond lengths are all much shorter than

those even in bulk CaO, even in the interior of the islands, and more similar to those in CaO

clusters and isolated thin films. Corner atoms are associated with particularly short Ca–O bond

lengths and the low coordination numbers at such positions. The islands show a marked

deviation from planarity which can be broadly rationalized in terms of different preferential bond

lengths for Ca and O with substrate O and Ba (Sr), respectively. The marked preferences for

particular bond lengths lead to the formation of loops or gaps in non-square islands, areas where

islands interact and along the mid-edges of large islands. Exchange with the much larger cations

in the substrate is surprisingly facile. Our results indicate the difficulties of preparing sharp,

ordered thin oxide films even at low temperatures.

Introduction

Nanostructure fabrication requires 2-D control of interfaces

and the assembly of objects on the nanometre scale remains a

primary objective in several fields.1 The manufacture of

devices often demands the ability to exercise precise control

over the growth of thin films on a host substrate. Indeed,

atomic level definition may be required for applications such

as supported superconductors, magnetic, optical and electronic

devices. Using techniques such as molecular beam epitaxy

(MBE), chemical vapour deposition (CVD) and pulsed laser

deposition (PLD), it is possible to produce phases that are very

different from those found in the bulk,2 leading to new

nanoscale materials. One recent example is the prediction of

a new planar graphene form3 of ZnO, subsequently confirmed

experimentally.4 Here, where there may be little guidance from

analogies with bulk materials, computer simulation plays a

vital role both in interpreting the experimental data (such as

RHEED, GIXRD, TEM) and in predicting the structures that

can arise.

There have been innumerable publications devoted to the

bulk properties of the alkaline earth oxides and their surfaces,

using both classical and quantum mechanical methods, and,

more recently, to the rich, surface-dominated chemistry of gas-

phase clusters of, e.g., MgO and CaO.5 In this paper we turn

our attention to the structure of some ultra thin oxide films.

Such films are of interest in diverse fields ranging from

catalysis to the development of new oxide gate dielectrics.6

Here we concentrate on alkaline earth oxides which have a

dielectric constant high enough to be of use as a gate dielectric

and in particular on the structure of monolayer islands of CaO

grown on SrO and BaO, which relates directly to MBE studies

of growth of these oxides.6 We examine islands of CaO of this

type on the (100) surfaces of BaO and SrO and BaO–SrO

mixtures. There is a large size mismatch between the sizes of

Ca2+, Sr2+ and Ba2+ (six-fold coordinate radii 1.00, 1.18 and

1.35 A, respectively7) and the bulk lattice parameters of CaO,

SrO and BaO are 4.81, 5.16 and 5.53 A, respectively. Thus this

system is particularly suitable for investigating interesting

questions regarding the nature of any epitaxial matching in

ultrathin films and how islands on the surface accommodate

the strain. These are crucial issues when considering the

complex processes involved in film growth over larger length

and time scales.w We investigate how the structures of small

islands of CaO relate to the structure of a complete film and

compare the form of the islands when the substrate is SrO or

BaO with those lying over a mixture of these two end

members.

There have been several studies8 of overlayers formed by the

heavier alkaline earth oxides on MgO. BaO on MgO is an

extreme (and interesting) example, previously considered both

experimentally (XPS) and theoretically.9 There is a mismatch

of only 10% between the lattice parameter of BaO andffiffiffi

2p� aðMgOÞ (=5.96 A). Thus, at 50% BaO coverage, a

BaO overlayer forms on top of the MgO with a 2D lattice

parameter close to 5.96 A and the overlayer rotates by

a School of Chemistry, University of Bristol, Cantock’s Close, Bristol,UK BS8 1TS. E-mail: N.L.Allan@bristol.ac.uk;Fax: +44 (0)117 925 0612; Tel: +44 (0)117 928 8308

b Laboratoire des Colloıdes, Verres et Nanomateriaux, UMR 5587,Universite Montpelier II-CNRS, 34095, Montpellier, France

cDepartment of Chemistry and Centre for Materials Science andNanotechnology, University of Oslo, Postbox 1033, Blindern,N-0315, Oslo, Norway

dDepartment of Engineering Materials, University of Sheffield,Sir Robert Hadfield Building, Mappin Street, Sheffield, UK S1 3JD

w For example, Kinetic Monte Carlo methods require that allprocesses involved and their rates are known in advance.

This journal is �c the Owner Societies 2009 Phys. Chem. Chem. Phys., 2009, 11, 3217–3225 | 3217

PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics

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451 relative to the substrate. In this structure alternate ions in

the overlayer along a 2D lattice vector occupy positions

directly above ions of the same charge and there are equal

numbers of nearest neighbour attractive and repulsive

Coulombic interactions.9 Here, we are examining the reverse

case; deposition of a lighter oxide on a heavier.

The energy minimisation techniques we use to examine the

local minima in the potential energy landscape for particular

islands are broadly similar to those of Shluger et al.10 in a

study of (NaCl)n clusters at the (100) surface of MgO. We have

also been motivated by results from previous studies11–14 of

diffusion of cation–anion pairs over oxide surfaces which

indicate that barriers to diffusion for single ion pairs (one

formula unit) are a few tenths of an eV, and kinetic Monte

Carlo simulations suggest that islands, once formed, remain

essentially intact even at high temperatures (41000 K) even

though outer layers may rearrange (for example to eliminate

edges). Ion pairs aggregate to form islands which rapidly

equilibrate. While ion pairs may exchange one or both

members of a pair with the corresponding surface ion, this is

negligible for the ions once inside an island due to the larger

number of bonds that need to be broken. Energy minimisation

of possible island morphologies as a function of surface

coverage is thus an appropriate tool for examining the

structures that may form under some MBE deposition

conditions, or other low temperature atomic beam

deposition techniques15). In our calculations we mimic slow

deposition processes consistent with our previous oxide

work11–14 where each step in the growth process involves

the attachment of a new ion pair to an already optimised

(energy-minimised) island. We start with a small island

(4 atoms). We place a new pair at possible edge-positions

followed by full relaxation of each new 6-atom island.

Subsequently a new pair is attached at different possible

edge-positions of the 6-atom islands and the resulting 8-ion

islands are fully relaxed and so forth. As the island size

increases, only low energy islands are used for subsequent

growth. A rather different methodology, less applicable for

our present purposes, is that of Sayle and coworkers,16–18 who

were primarily interested in high temperature processes. This

involves short molecular dynamics runs at 1200 K followed by

quenching and energy minimisation. In the MBE experiment

the actual surface temperature is modest (o500 K).

Methods

All calculations involve energy minimisation19–21 in the static

limit. Many of these used two-body interionic potentials to

represent the non-Coulombic interactions between the ions,

where we employed the well-established Lewis–Catlow set of

empirical potentials.22 Long range interactions were evaluated

using a 2-D Parry summation.23 Slabs of BaO or SrO, containing

5 layers, each comprising 200 ions and periodically repeating in

two dimensions, were set up. Calcium and oxide ions were added

on top of the slab as appropriate. Only ions in the top 3 layers of

the substrate were allowed to relax during the geometry

optimisations, so formally the methodology resembles the two-

region approach of the MIDAS code.24 Test runs in which an

extra layer was included in the optimisation yielded no significant

differences.

Ab initio density functional theory (DFT) calculations

were carried out with the VASP code25–28 using the

Perdew–Burke–Ernzerhof generalized-gradient approximation

(GGA) density functional.29 A plane wave basis set with an energy

cutoff of 250 eV, appropriate for the projector-augmented

wave (PAW) pseudo-potentials,27,30 was used. A gamma point

sampling of the Brillouin zone was found to be sufficient. The

extra computational expense of these calculations limits

them to a smaller number of ions than the potential-based

minimisations. In these first principles calculations the surface

was represented by a slab of ions, periodically repeated in

three dimensions, with a gap of E10 A between slabs in the

stacking direction to prevent inter-slab interactions. Each slab

contained 4 layers of substrate, each containing 50 ions

(200 ions in total), and only the top two layers were allowed

to relax.

Results and discussion

Small islands

Both pair potential and ab initio calculations show that small

islands of CaO on both BaO and on SrO form almost

exclusively with (100) edges. (100) edges have also been

observed11 for BaO islands on BaO, where of course there is no

cation mismatch, during kinetic Monte Carlo runs with input

activation energies determined using temperature accelerated

dynamics and are also evident in the high-temperature simula-

tions of Sayle.16 Representative examples of both ab initio and

pair potential calculations are shown for small islands of CaO

on BaO in Fig. 1, which also demonstrates the extent of the

matching of the islands with the substrate layer. For 8, 12 or

16 atom islands, the lowest-energy is at the bottom and islands

are shown from bottom to top in order of increasing energy.

For a given size island, the higher the perimeter the less

negative is the binding energy per ion pair. Islands which

terminate with (110) edges do not correspond to local minima

on the potential energy surface (in either type of calculation)

and relax to (100)-edged islands on minimisation. The same

qualitative picture and relative energy orderings emerge from

both the ab initio and the pair potential runs.

In free oxide clusters lower coordinated Ca ions have shorter

bond lengths,31 and the bond lengths in all the islands are

shorter than those in bulk CaO (ab initio 2.413 A) where the Ca

is six-coordinate to oxygen. In the square 16-ion island on BaO

(Fig. 1), the lowest in energy of all the 16-ion islands examined,

the ab initio O3–Ca3 distances in the central ring of four atoms

are 2.38 A. The O2–Ca distances, where O2 lies on an island

edge, are 2.35 A (to the inner ring Ca3), 2.39 A (to the edge

Ca1) and 2.19 A (to the corner Ca2). The Ca1–O1 (a corner

oxygen) distance is 2.20 A. All these distances are less than the

calculated ab initio bulk Ca–O separation of 2.413 A. So it is

clear that there is no expansion of any bond length above a

bulk-like CaO value (2.413 A) to a value closer to the Ba–O

substrate separation to try to achieve some type of epitaxial

matching in which ions of opposite charge are directly overlaid.

Rather the Ca–O bond lengths remain close to those for a 2-D

3218 | Phys. Chem. Chem. Phys., 2009, 11, 3217–3225 This journal is �c the Owner Societies 2009

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CaO island in the absence of a substrate—for a gas-phase

16-ion island all calculated Ca–O separations are in the range

2.3–2.4 A except at corners (E2.1 A). A full set of bond lengths

for islands on both BaO and SrO substrates, including a

comparison between ab initio and potential-based results, is

given in Table 1. The potential-based results are, in general, in

good agreement with the ab initio as is also clear from Fig. 1.

For the distances Ca1–O1 and O2–Ca2 there is qualitative

agreement, although the shortening relative to the bulk

and the interior of the island is somewhat exaggerated by

the potential-based techniques. Both methods suggest

particularly striking small internuclear separations involving

atoms at the corners accompanying coordination numbers as

low as three.

As well as these short corner intralayer distances, both types

of calculation show that the islands pucker at the edges,

involving also a pronounced upward shift of the ions in the

outermost substrate layer as is clear from Fig. 2 which shows

sideways views of the BaO slab, looking along two different

directions. The (DFT) rumpling (deviation from planarity) of

the island is as much as E0.5 A while that of the top substrate

layer is as large as E1.1 A. In broad terms, the driving forces

for these distortions from planarity are readily understood in

terms of the island–substrate bond lengths listed in Table 1

and the variations in coordination of different atoms. Ab initio

(DFT) Ba(substrate)-O(island) distances are in the range

2.47 A (to corner island O1)–2.62 A (to both edge and interior

island O) (cf. the Ba–O separation in bulk BaO of 2.76 A)

while Ca(island)-O(substrate) distances are maintained at

shorter values (2.36, 2.41 and 2.27 A for island interior, edge

and corner O, respectively), consistent with the variation in

Ca–O distances within the island itself. Relaxations of all

substrate layers other than the surface layer itself are much

smaller.

Fig. 1 CaO islands and underlying BaO substrate. (a) top views of the lowest-energy 4-, 6-, 8- (�2) and 12-ion (�2) islands and three different

16-ion islands, optimized using interatomic potentials (b) for comparison, top views of the same three 16-ion islands shown in (a) but optimized

using DFT. For a given number of ions, the lowest energy island is that shown at the bottom. For the 16-ion islands A is lowest in energy and the

next two lowest are B and C in turn. a and b denote directions of substrate surface lattice vectors; c lies perpendicular to the surface. In all plots

Ca2+, Ba2+ and O2� are black, grey and red, respectively.

Table 1 Nearest neighbour distances (A) in square 16-atom islands ofCaO on SrO and on BaO (using a surface unit cell such that the surfacecoverage is 30%) calculated using DFT and pair potentials. Atomlabels are shown in Fig. 1

Intra-island distanceSrO

PotentialBaO

PotentialDFT DFT

O1–Ca1 2.17 2.13 2.20 2.14O2–Ca2 2.18 2.13 2.19 2.14Ca1–O2 2.38 2.24 2.39 2.25O2–Ca3 2.32 2.30 2.35 2.33Ca1–O3 2.29 2.29 2.31 2.30O3–Ca3 2.35 2.23 2.38 2.25Island–substrate distanceCa1–O 2.42 2.45 2.41 2.47Ca2–O 2.30 2.18 2.27 2.19Ca3–O 2.38 2.38 2.36 2.41O1–Sr/Ba 2.37 2.35 2.47 2.52O2–Sr/Ba 2.49 2.57 2.62 2.71O3–Sr/Ba 2.49 2.47 2.62 2.58

This journal is �c the Owner Societies 2009 Phys. Chem. Chem. Phys., 2009, 11, 3217–3225 | 3219

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Islands of CaO on SrO are very similar and so we do not

give a further set of plots. Ca–O1, Ca–O2 and Ca–O3

distances are all in the same ranges as on BaO (Table 1), while

the O(island)-substrate separation reflects the smaller size of

Sr2+ relative to Ba2+.

For the 16-atoms islands (for example) we see that when

islands are not square or rectangular, the smaller

optimum cation–anion separations at the corners give rise to

characteristic features such as the ‘loops’ or ‘gaps’ for some of

the higher energy islands; we return to these features again

below. All such islands are higher in energy than the square

arrangement, with the energies increasing with increasing

island perimeter.

Large islands

Fig. 3 gives top and side views of some successively larger

islands (64 (8 � 8), 72 (9 � 8) and 90 ions (10 � 9)) on

BaO from pair potential calculations (only). As for smaller

islands, only those with (100) edges are stable. The detailed

structure of the islands shows that arguments based on simple

epitaxial matching are misleading. In the interior of the islands

the Ca–O bond lengths are very similar to those in the inner

ring of the small islands considered above. Bond lengths

involving ions at the outermost edges and corners of the

islands are similar to those at the edges of the small island

with the corner O–Ca separations again being particularly

short at o2.2 A.

Fig. 2 Side views (from two different directions) of the optimized square (4 � 4) 16-ion CaO island shown in Fig. 1. (a) pair potential (b) DFT

results.

Fig. 3 Top and side views of some larger islands-64 (8 � 8), 72 (9 � 8) and 90 ions (10 � 9)-of CaO on BaO, optimized using pair potential

calculations.

3220 | Phys. Chem. Chem. Phys., 2009, 11, 3217–3225 This journal is �c the Owner Societies 2009

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In a square 8 � 8 (64-atom) island, the Ca–O bond lengths

increase markedly as one passes from a corner along an edge

and are largest at mid-edge. Again, like small islands, larger

islands are far from flat, with a pronounced puckering as can

be seen by comparing the side-views in Fig. 2 and Fig. 3. Since

the Ca–O distances are all so much shorter than Ba–O it is

clear that, when close to the centre of an island, ions lie not too

far from a substrate layer ion of the opposite charge. This

cannot be maintained, even with puckering, for the outer

regions of islands which exceed a certain size. The effects of

this can be seen strikingly in Fig. 3b and 3c. In Fig. 3b a

rectangular 9 � 8 (72-ion) island is clearly breaking apart at

the mid-edges and in Fig. 3c we see how a rectangular island

(10 � 9) is almost torn apart at the mid-edges with the

accompanying formation of large gaps.

Once again, islands of CaO on SrO show similar qualitative

behaviour. Since the mismatch between substrate and adsor-

bate is smaller, larger islands than in the BaO case are needed

to see the pronounced gaps and separations of the type shown

in Fig. 3b and 3c.

From the optimised energies of the substrate (ES) and island

plus substrate (EIS) it is straightforward to calculate the

average binding energy per ion pair for each island and, for

the potential-based results, this is plotted as a function of total

island size in Fig. 4. The plot includes the energies for the

islands shown in Fig. 1. For comparison the binding energy of

a single (isolated) CaO ion pair on BaO is �22.15 eV. The

binding energy decreases with increasing island coverage by

just over 50% from the single ion pair value to E�34.8 eV,

but the variation is irregular with dips for islands containing

even number of ion pairs. For a given size island, the longer

the perimeter the less negative is the binding energy per ion

pair. Comparing potential and DFT based results the binding

energy of the second lowest island (labelled B in Fig. 1) is

0.5 eV per ion pair higher (less negative) than for the lowest

energy island (A) from both sets of calculations. There

can be larger differences in relative energies for higher energy

islands such as C (Fig. 1), where the binding energy per

ion pair (ab initio) is less negative than for A by 1.0 eV

(DFT) and by 0.6 eV (potentials) respectively, but we stress

that the order of energies of the islands is the same from both

methods.

Island aggregation and larger coverages

When two islands meet there can be substantial distortions

broadly similar to those already noted for small non-square

islands. Once again approximately elliptical loops or gaps are

formed. Typical dimensions of these loops are in the range

3.5–5 A. For example Fig. 5 shows optimized square 4 � 4

(16-ion), and 6� 6 (36-ion) islands separated by (approximately)

the BaO lattice parameter and the dramatic structural

effects of depositing two additional pairs between the

islands so that the two now meet. The resulting 56-ion island

is E�3.6 eV more stable than two separate isolated 4 � 5 and

6 � 6 islands.

We show in Fig. 6 an example which corresponds to 100%

coverage. Results are presented from both DFT and pair

potential calculations. When examining this figure, it is

important to remember that periodic boundary conditions in

the plane of the surface have been used in the calculations.

Both computational methods show that smaller islands form

with marked gaps between adjacent islands and marked

distortions at the edges. Ion pairs were deposited in turn until

the coverage reached 100% with optimization after every

deposition, thus mimicking a slow deposition process. The

predominance of (100) edges, consistent with the shapes of the

islands at lower coverage, is striking as is the distortion

accompanying the elliptical gaps, which are comparable in

size to those noted in Fig. 5. Considerably more distorted,

higher energy structures (not shown here), with many more

elliptical gaps, emerge if the 100% coverage optimization is

started from an initial configuration in which every ion in

the CaO layer overlies an ion of the opposite charge in the top

BaO layer in the slab (thus mimicking fast deposition as in

ref. 16). Large coverages can thus be considered to a

good approximation as a set of interacting small islands. While

our calculations are in the low-temperature (static) limit,

these features are markedly reminiscent of those obtained

for high coverages at high temperatures obtained by Sayle

(e.g., Fig. 7e of ref. 16, Fig. 5 of ref. 17, Fig. 7 and 8 of ref. 18).

Overall, our results lend support to the concept of ‘‘critical

areas’’ proposed in ref. 17 and 18. This suggests that a

dislocation evolves when the area of a nanoparticle in contact

with a substrate exceeds a critical value, which is governed by

the misfit between substrate and overlayer. The value of this

area for a monolayer CaO on BaO from Fig. 3c, 5 and 6

appears to be as low as that associated with an island

3 (ion pairs) � 3 (ion-pairs) (200–300 A2).

Fig. 6 also shows a side view which shows that the marked

deviation from planarity is maintained for these large

coverages and indeed results also in very large distortions of

the top BaO layer. We return to consider high coverages for

bilayers below.

Fig. 4 Binding energies (potential-based) on BaO (eV per CaO ion

pair) as a function of island size. Npairs is the number of ion pairs in the

island and for almost all island sizes results are plotted for several

islands with different shapes (the lowest energies are those shown

in Fig. 1). For a given size island the longer the perimeter the

less negative is the binding energy per ion pair. For comparison

the binding energy of a single (isolated) CaO ion pair on BaO is

�22.15 eV.

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SrO–BaO substrates

Here we consider briefly the effect of a mixed substrate on the

form of the islands. In a BaO–SrO slab there will be

pronounced segregation of the much larger Ba2+ ion to the

surface32 and at the surface the Ba2+ ions will cluster

together.33 Nevertheless a larger enthalpy of absorption of

CaO over SrO would lead to preferential adsorption over SrO

regions. We have carried out a small number of simulations of

CaO on a substrate where the top layer comprises 50% BaO

and 50% SrO (and thus refers to an overall bulk composition

with a much smaller BaO content). There is little mismatch

between the CaO islands grown above BaO regions and above

SrO regions. The intra-island bond lengths and the orientation

of the islands, which are dominated by the stronger and stiffer

Ca–O bonds, are virtually the same in both regions. The major

difference lies in the height of the islands above the substrate

reflecting the different O(island)-Sr and O(island)-Ba bond

lengths.

Cation exchange

Our previous work has highlighted the possibility of exchange

between absorbed cations and cations in the outermost surface

layer and concluded that this is most likely when the adsorbate

cation is comparable in size or smaller than that in the

substrate.11–13 Exchange is clearly related to the possible

extent of Ca penetration into the substrate, and for the

Fig. 5 Top views of optimized (pair potential) square 4 � 4 (16-ion), and 6 � 6 (36-ion) CaO islands on BaO separated by (approximately) the

BaO lattice parameter (left) and (right) the results from depositing two additional ion pairs between the islands so that the two are now (formally)

joined.

Fig. 6 Top and side views of optimized 100% coverage structure (‘‘slow deposition’’ scenario) (a) pair potential results (b) DFT optimized.

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16-ion square islands shown in Fig. 7 we have carried out

calculations in which a Ca ion in an island and a Ba or Sr ion

in the top layer of the substrate are interchanged. The energy

of this substitution is exothermic, and the calculated energies

are similar from both potential-based and ab initio

calculations. The (DFT) energy for swapping an island corner

Ca and a substrate Sr as shown in Fig. 7b is as low asE0.2 eV,

and even for a Ca and Ba interchange is only E0.6 eV. The

energy for the analogous swap involving an edge Ca (Fig. 7a)

is less than 0.1 eV higher in both cases—substitution at the two

sites is almost equienergetic. If the Ca–O bond length did not

vary with coordination (i.e., in the absence of relaxation) this

would be unexpected, as marked segregation of the larger ion

to the site with the lowest coordination would be predicted to

be the most favoured on bond energy grounds. The close

substitution energies at the two sites reflect the different bond

lengths at edges and corners and the resulting variation in

Ca–O and Ba–O bond strengths. The much larger Ba2+ and

Sr2+ ions cannot relax inwards as much as the smaller Ca2+

(recall the very short distances involving corner atoms in

Fig. 1) and so there is an extra electrostatic penalty to

pay for substitution at a corner site compared to edge

locations. Indeed edge rather than corner substitution in cubic

nanoclusters has been noted recently for a Ca2+ substitutional

trace element in cubic MgO nanoparticles,34 where in contrast

both potential and ab initio (DFT) results show that for the

Ca2+ the edge position (4-coordinated) is favoured over

the corner (3-coordinated) by E0.4 eV. Marked effects

that variations in coordination number can have on bulk

substitution and thus on solution energies have been described

previously.35

Multilayers and pillars

In practice, under some conditions such as larger deposition

rates,36 exclusive monolayer formation is unlikely, even

though kinetic Monte Carlo simulations11–13 suggest that

islands, once formed, remain essentially intact even at high

temperatures. We have also described how the deposition of

ion pairs on top of steps can lead to step collapse under certain

conditions as ions in the step edge are pushed out and fall

down into the resulting space, thus favouring monolayer

formation.13

There are an enormous number of possibilities here but we

restrict ourselves to a short consideration of islands two layers

thick. Starting with the square 16-ion island (A) in Fig. 1, we

removed one O1–Ca1 pair and placed these two ions on top of

a Ca1–O3 pair in the now 14-ion first layer. This did not

correspond to any local minimum on the energy surface (using

pair potentials), simply relaxing back to the original 16-ion

single-layer island (cf. the step collapse we have seen

previously13 in high temperature molecular dynamics

simulations). Placing this O1–Ca1 pair in the centre of the

island does correspond to a local minimum but one much

higher in energy (by 0.64 eV in pair potential calculations)

than even the monolayer high-energy island C (Fig. 1).

Forming a double layer island with 8-ions in each layer

(i.e., a double layer of the 8-ion island in Fig. 1a) is still higher

in energy by 0.14 eV per ion pair than the square 16-ion island

A. Only for larger islands are bilayers thermodynamically

stable with respect to the corresponding monolayer island.

For example, a bilayer comprising two 4 � 4 16-ion layers is

lower in energy by 0.3 eV per ion pair than a 8 � 4 rectangular

32-ion monolayer island and here we note also that no low

energy square monolayer island is possible for 32-ions.

Overall, these results lend strong support to the applicability

of our energy minimisation of monolayer islands in a relatively

low temperature, low-flux regime.

Fig. 8 shows a two layer island of CaO on BaO (DFT

results), where each layer contains 16-ions. The patterns in the

interatomic distances in the bottom layer are the same as in the

single layer islands, with the magnitude of the variations

reduced. Distances involving atoms along edges are effectively

unchanged from their single layer values while those in the

interior increase slightly. More significant changes take place

with corner atoms, where separations increase, consistent with

the increase in coordination number. For example, the corner

O1–Ca1 separation increases by E0.2 A. The rumpling is

much smaller in the second layer, consistent with the argument

presented in an earlier section.

We have also carried out a brief study of higher energy

two-layer islands containing loops (not shown in Fig. 8) and it

is clear that these persist into the upper layer. In addition

Fig. 9a shows a square 64-ion island (cf. Fig. 3a) on top of a

full CaO monolayer (Fig. 6a), and Fig. 9b) shows a full double

layer of CaO. The characteristic gaps and loops we have noted

are very evident, and essentially the same in form, even though

the ‘dislocation gap’ in the middle of the central island in

Fig. 8 Side view of a two-layer island of CaO on BaO (optimised with

DFT), where each layer in the island contains 16-ions.

Fig. 7 16-ion islands showing the exchange of (a) a corner or (b) an

edge Ca2+ ion (black) and substrate cation (grey).

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Fig. 3a disappears, consistent with an increase in ‘critical area’

for bilayers relative to monolayers. If this is a more general

phenomenon at ionic heterojunctions it is tempting to

associate such gaps and loops with such features as the well

established enhanced ionic conductivity.

Conclusions

Islands formed by CaO on BaO have been examined using

both pair potential and periodic ab initio techniques. (100)

edges dominate the island morphology and we have seen how

the CaO adjusts to the substrate in small and medium sized

islands and at much larger coverages. There is no direct

overlay of CaO ion pairs over OBa pairs in the top substrate

layer. Rather the bond lengths in the islands are all much

shorter than those even in bulk CaO, even at the centre of the

islands, and more similar to those in CaO clusters and isolated

thin films. Corner atoms are associated with particularly short

Ca–O bond lengths. There is a marked deviation from

planarity, which can be broadly rationalized in terms of

different preferential bond lengths for Ca and O with substrate

O and Ba, respectively. The marked preferences for particular

bond lengths lead to the formation of loops or gaps in

non-square islands, in regions where islands interact and along

the mid-edges of large islands. Larger islands effectively break

up to form a set of strongly interacting smaller islands. We

stress that all the structures we have examined in this paper are

minima in the potential energy surface even in the static limit

to which we have limited this study. Exchange with the much

larger cations in the substrate is surprisingly facile. Addition of

a second layer to the islands has only a relatively small effect

on the first layer, chiefly confined to corner atoms which

change their coordination. Our results indicate the difficulties

of preparing sharp, ordered thin oxide films even at low

temperatures, given the spontaneous formation of this type

of structure.

Acknowledgements

We are grateful to Rodney McKee (Oak Ridge) for suggesting

this problem to us and his generous hospitality in visits of

N.L.A. and J.H.H. to Tennessee and Oak Ridge. Computa-

tional resources were provided by the Mott2 Machine at

Rutherford as part of the ‘‘Simulation on the edge’’ consor-

tium, and through a grant of computing time for the

Programme for Supercomputing, Norway. C.E.M. is funded

by the Norges Forskningsrad. J.H.H. acknowledges support

from EPSRC grants EP/F010834/1 and GR/R85969/01, and

N.L.A. GR/R85952/01.

References

1 B. S. Guiton and P. K. Davies, Nat. Mater., 2007, 6, 586.2 E.g., P. X. Gao, Y. Ding, W. Mai, W. L. Hughes, C. Lao andZ. L. Wang, Science, 2005, 309, 1700.

3 C. L. Freeman, F. Claeyssens, N. L. Allan and J. H. Harding,Phys. Rev. Lett., 2006, 96, 066012.

4 C. Tusche, H. L. Meyerheim and J. Kirschner, Phys. Rev. Lett.,2007, 99, 026102.

5 C. Roberts and R. L. Johnston, Phys. Chem., Phys. Chem., 2001, 3,5024.

6 E.g., M. B. Nardelli, F. J. Walker and R. A. McKee, Phys. StatusSolidi., 2004, 241, 2279; R. McKee, F. J. Walker andM. F. Chisholm, Science, 2001, 293, 468; R. McKee,F. J. Walker and M. F. Chisholm, Phys. Rev. Lett., 1998, 81, 3014.

7 R. D. Shannon, Acta Crystallogr., Sect. A, 1976, 32, 751.8 E.g., L. L. Cao, R. G. Egdell, W. R. Flavell, K. F. Mok andW. C. Mackrodt, J. Mater. Chem., 1991, 1, 785 and referencestherein.

9 M. Cotter, S. Campbell, L. L. Cao, R. G. Egdell andW. C. Mackrodt, Surf. Sci., 1989, 208, 267.

Fig. 9 Top and side views of (a) a square 64-ion CaO island (cf. Fig. 3a) on top of a 100% CaO monolayer (as Fig. 6a) (b) a 100% double layer of

CaO. Pair-potential results only are shown.

3224 | Phys. Chem. Chem. Phys., 2009, 11, 3217–3225 This journal is �c the Owner Societies 2009

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ishe

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17

Mar

ch 2

009.

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ded

by U

nive

rsity

of

Illin

ois

at C

hica

go o

n 21

/10/

2014

19:

29:3

7.

View Article Online

10 A. L. Shluger, A. L. Rohl and D. H. Gay, Phys. Rev. B, 1995, 51,13631.

11 D. J. Harris, J. H. Harding, M. Yu. Lavrentiev, N. L. Allan andJ. A. Purton, J. Phys.: Condens. Matter, 2004, 16, L187.

12 M. Yu. Lavrentiev, D. J. Harris, J. H. Harding, N. L. Allan andJ. A. Purton, Dalton Trans., 2004, 3071.

13 D. J. Harris, T. S. Farrow, J. H. Harding, M. Yu. Lavrentiev,N. L. Allan, W. Smith and J. A. Purton, Phys. Chem. Chem. Phys.,2005, 7, 1839.

14 G. Henkelman, B. P. Uberuaga, D. J. Harris, J. H. Harding andN. L. Allan, Phys. Rev. B, 2005, 72, 115437.

15 For example, D. Fischer and M. Jansen, Z. Anorg. Allg. Chem.,2004, 630, 2697.

16 D. C. Sayle, J. Mater. Chem, 1998, 8, 2025.17 D. C. Sayle, J. A. Doig, S. A. Maicaneanu and G. W. Watson,

Phys. Rev. B, 2002, 65, 245414.18 D. C. Sayle and G. W.Watson, J. Phys. Chem. B, 2002, 106, 10793.19 M. B. Taylor, G. D. Barrera, N. L. Allan, T. H. K. Barron and

W. C. Mackrodt, Comput. Phys. Commun., 1998, 109, 135.20 M. B. Taylor, G. D. Barrera, N. L. Allan and T. H. K. Barron,

Phys. Rev. B, 1997, 56, 14380.21 J. D. Gale and A. L. Rohl, Mol. Simul., 2003, 29, 291.

22 G. V. Lewis and C. R. A. Catlow, J. Phys. C, 1985, 18, 1149.23 E.g., M. B. Taylor, C. E. Sims, G. D. Barrera, N. L. Allan and

W. C. Mackrodt, Phys. Rev. B, 1999, 59, 6742.24 P. A. Tasker, Phil. Mag. A, 1979, 39, 119.25 G. Kresse and J. Hafner, Phys. Rev. B, 1993, 47, 558.26 G. Kresse and J. Hafner, Phys. Rev. B, 1994, 49, 14251.27 G. Kresse and J. Furthmuller, Comput. Mater. Sci., 1996, 6, 16.28 G. Kresse and J. Furthmuller, Phys. Rev. B, 1996, 54, 11169.29 J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996,

77, 3865.30 P. E. Blochl, Phys. Rev. B, 1994, 50, 17953.31 F. Bawa and I. Panas, Phys. Chem., Chem, Phys., 2001, 3, 3042.32 J. A. Purton, M. Yu. Lavrentiev, N. L. Allan and I. T. Todorov,

Phys. Chem., Chem. Phys, 2005, 7, 3601; J. A. Purton andN. L. Allan, J. Cryst. Growth, 2006, 294, 130.

33 C. E. Mohn, M. Yu. Lavrentiev, N. L. Allan, E. Bakken andS. Stølen, Phys. Chem. Chem. Phys., 2005, 7, 1127.

34 K. McKenna, private communication.35 W. van Westrenen, N. L. Allan, J. D. Blundy, M. Yu. Lavrentiev,

B. R. Lucas and J. A. Purton, Chem. Commun., 2003, 786.36 O. Nilsen, C. E. Mohn, A. Kjekshus and H. Fjellvag, J. Appl.

Phys., 2007, 102, 024906.

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