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Acta Materialia 55 (2007) 2671–2681

Thin-film solid-state reactions of solid BaCO3 and BaO vaporwith (100) rutile substrates

Andriy Lotnyk *, Stephan Senz, Dietrich Hesse

Max Planck Institute of Microstructure Physics, Department 2, Weinberg 2, D-06120 Halle (Saale), Germany

Received 26 September 2006; received in revised form 28 November 2006; accepted 1 December 2006Available online 26 February 2007

Abstract

Thin-film solid-state reactions in the BaCO3–TiO2 and BaO–TiO2 systems have been experimentally studied in air and in vacuum,respectively, on (100) TiO2 substrates. The solid–solid reactions in vacuum and in air showed that different processes occur duringBaTiO3 formation: an intermediate Ba2TiO4 compound is always observed in vacuum but not in air. The crystallographic orientationsbetween the reaction products and the TiO2 substrate were investigated by X-ray diffractometry and transmission electron microscopy.One orientation relationship has been found for BaTiO3 after a solid–solid reaction, whereas different orientation relationships forBaTiO3 have been identified after a vapor–solid reaction. At high temperatures, Ti-rich polytitanates were grown in both types ofsolid-state reactions but with quite different textures. The crystallographic relationships and their origins are analyzed.� 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Solid-state reactions; Thin film; Barium titanate; Rutile single crystals; Transmission electron microscopy (TEM)

1. Introduction

Compounds in the BaCO3–TiO2 system are of interestbecause many ternary barium polytitanates are used aselectronic materials for capacitative and microwavedevices. One of the most important compounds is BaTiO3.Ferroelectric ceramics based on BaTiO3 are widely used inmultilayer capacitors and thermoresistors [1].

The common way to produce BaTiO3 ceramics is thesolid-state reaction synthesis of BaCO3–TiO2 raw materials[2–8]. To optimize the properties of the final ceramic mate-rials, advanced knowledge of the formation mechanism ofBaTiO3 is necessary. At the beginning of the 1990s thismechanism was elucidated by Niepce and Thomas [8],who proposed a mechanistic model based on sphericalTiO2 particles surrounded by BaCO3. It was concludedthat some BaTiO3 forms first, followed by the formationof Ba2TiO4. Finally, the orthotitanate Ba2TiO4 combines

1359-6454/$30.00 � 2007 Acta Materialia Inc. Published by Elsevier Ltd. All

doi:10.1016/j.actamat.2006.12.022

* Corresponding author. Tel.: +49 345 5582; fax: +49 345 5511223.E-mail address: lotnyk@mpi-halle.de (A. Lotnyk).

with the remaining TiO2 to form BaTiO3. The effect of boththe particle size of the initial reactants and the pressure onthe solid-state synthesis of BaTiO3 was reported by Hen-nings et al. [9] and by Buscaglia et al. [10], respectively.Hennings et al. found that the formation of Ba2TiO4 inair can be suppressed in a reaction between submicrometerBaCO3 and fine TiO2. Buscaglia et al. reported that the cal-cination of nanocrystalline BaCO3 and TiO2 powders per-formed in flowing air at 1 bar (100 kPa) completelysuppresses the formation of the Ba2TiO4 secondary phase.However, a decrease of pressure down to 40 mbar inducedthe formation of Ba2TiO4 at a reaction temperature of740 �C. A different phase sequence was observed in core-shell powders by Rossel et al. [11]. In this work, duringthe process leading to the formation of BaTiO3, not onlywas the Ba2TiO4 phase observed during heating, but alsoa number of Ti-rich intermediates.

Model experiments should provide a better understand-ing of such complex reaction mechanisms. In our previouswork we investigated the formation of BaTiO3 thin filmsfrom (110) TiO2 single crystals and a solid BaCO3 filmby solid-state reactions in vacuum [12]. We found that a

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2672 A. Lotnyk et al. / Acta Materialia 55 (2007) 2671–2681

Ba2TiO4 intermediate phase forms first by direct reactionbetween BaCO3 and (110) TiO2, followed by the formationof BaTiO3. Different orientation relations have been foundfor the reaction products grown on (110) TiO2 dependingon the reaction conditions, all of which imply, however, acommon [001] TiO2 tilt axis.

Reactions between BaO (vapor) and TiO2 (rutile) singlecrystals with different surface orientations had been inves-tigated by Graff et al. [13] at temperatures between 700and 900 �C in a vacuum of about 10�2 Pa. The authorsconcluded that BaTiO3 was formed as the first product inthe reaction between BaO and TiO2. No intermediatephases such as Ba2TiO4 were mentioned in that work.

In the present paper we extend our model experimentsusing (100) TiO2 single crystals. The phase formationsequences and orientation relationships during BaTiO3

growth from the reaction between BaCO3 (solid) or BaO(vapor), respectively, and (100) TiO2 in vacuum and inair are studied. In this way the work also permits a compar-ison of phase formation during solid–solid reactions in vac-uum and in air.

2. Experimental

The details of sample preparation have been reportedelsewhere [12]. Briefly, polished (10 0) surfaces of commer-cial TiO2 (rutile) single crystals (CrysTec GmbH, Berlin,Germany) were subjected to a BaCO3 vapor that was pro-duced by electron-beam evaporation of a BaCO3 powdertarget in a high-vacuum system with a base pressure of1–2 · 10�3 Pa. During the deposition pure oxygen wasintroduced to establish a pressure of 1 ·10�2 Pa. The depo-sition rate (�0.08 nm s�1) and the thickness of the thinfilm (�50 nm) were monitored in situ by a quartz micro-balance. During deposition, the substrates were heated ina tube furnace at 500 �C directly by thermal irradiation,followed by solid–solid reaction at temperatures from600 to 1000 �C between BaCO3 and TiO2 for 30 min invacuum or in air. For the vapor–solid reaction, the sub-strates were heated from 600 to 1100 �C directly by ther-mal irradiation during deposition. In view of the highvolatility (low sticking coefficient) of CO2 at such hightemperatures, the vapor reacting with the rutile substrateconsists of BaO [12].

The phases present in the thin films after reaction andtheir orientation relationships were investigated by X-raydiffraction (XRD, X’pert MRD, Philips, Eindhoven, TheNetherlands) with Cu Ka radiation. Pole figure measure-ments (center: w = 0�, rim: w = 90�) were performed todetermine the crystallographic orientation of the formedphases relative to the (100) rutile single crystals. Themicrostructure of the reacted interface was investigatedby cross-sectional transmission electron microscopy(TEM). The samples for TEM were made by standardmethods. TEM investigations were carried out in a PhilipsCM 20 T operated at 200 kV and a JEOL 4010 operated at400 kV.

3. Results

3.1. Phase formation

3.1.1. Solid-state reactions in vacuum (10�2 Pa)

The phase sequences during solid-state reactions of bothtypes (solid–solid and vapor–solid) on (100) rutile sub-strates at temperatures between 600 and 900 �C indicate aprocess that is similar to the reaction on (110) TiO2. Itcan be summarized as follows:

� At a substrate temperature of 500 �C a single BaCO3

phase is present, as detected by XRD.� The formation of BaTiO3 is always preceded by an inter-

mediate Ba2TiO4 compound at temperatures between600 and 700 �C. At 800 �C only BaTiO3 was detectedin solid–solid reactions whereas the vapor–solid reactionat 700 and 800 �C resulted in the simultaneous forma-tion of two phases (Ba2TiO4 and BaTiO3). Ba2TiO4

can exist in monoclinic (a low-temperature modifica-tion) and orthorhombic (a high-temperature form)structures [14–16]. We observed the orthorhombic orth-otitanate only. The Ba2TiO4 phase was found to be avery unstable compound and decomposed when exposedto air, most probably by reaction with H2O and CO2.Our observations are in good agreement with the dataobtained in [17,18].� After solid-state reactions at high temperatures (900–

1100 �C) Ti-rich phases were found by XRD and TEMinvestigations in both types of the solid-state reactions.BaTi4O9 was formed after solid-state reaction at1000 �C, whereas Ba6Ti17O40 and Ba4Ti13O30 wereobserved after vapor–solid reaction at 900–1000 �Cand 1100 �C, respectively.

3.1.2. Solid-state reaction in air

The results of the solid–solid reaction of BaCO3 with the(10 0) TiO2 surface in air are different from those of thereaction in vacuum. BaTiO3 and non-reacted BaCO3 weredetected by XRD measurements after the solid–solid reac-tion in air at temperatures between 600 and 700 �C for30 min. This is in contrast to the observations in vacuum.The reaction at 800 �C resulted in the formation of onlyBaTiO3, without any evidence of remaining BaCO3. Afterreaction at 900 �C, some BaTiO3 grains and a Ti-rich phasewere observed as the reaction products. At 1000 �C, theBa4Ti13O30 phase was formed.

A summary of the phase sequences is given in Table 1.

3.2. Orientation relationships

In order to facilitate a better understanding of theresults of TEM investigations given in this part of thepaper, the crystal data of the investigated phases are listedin Table 2. It should be noted that the perovskite BaTiO3 isknown to have several temperature-dependent phase tran-

Table 1Overview of the observed phase sequence

A. Lotnyk et al. / Acta Materialia 55 (2007) 2671–2681 2673

sitions. At temperatures above 120 �C (Tc for bulk),BaTiO3 has a simple cubic structure. Below Tc, the crystalis tetragonally distorted and ferroelectric. As shown below,the reaction experiments on TiO2 surfaces were performedat temperatures higher than 600 �C, where the BaTiO3 iscubic. After cooling down to room temperature, a transfor-mation of the cubic form of BaTiO3 to its tetragonal phasemay occur and ferroelectric domains can form. We havenot considered the questions of phase transition anddomain formation in this work. Consequently, we willuse the pseudocubic indexing for BaTiO3.

3.2.1. Orientation of BaCO3

The barium carbonate (BC) formed with a defined ori-entation to the substrate as indicated by XRD h–2h and

Table 2Crystal data of the TiO2 (rutile), BaCO3, Ba2TiO4, BaTiO3, Ba6Ti17O40, Ba4T

Phase Crystal system Space group

TiO2 (rutile) Tetragonal P42/mnm (13

BaCO3 Orthorhombic Pnma (62)

Ba2TiO4 Orthorhombic Pnam (62)

BaTiO3 Cubic Pm�3m (221)

Ba6Ti17O40 Monoclinic C2/c (15)

Ba4Ti13O30 Orthorhombic Cmca (64)

BaTi4O9 Orthorhombic Pmmn (59)

texture measurements. A XRD h–2h scan indicated thatthe (10 0) plane of BaCO3 (2h = 27.7�) is parallel to the(100) substrate surface (T). A pole figure recorded at2h = 23.9� of the sample prepared at a substrate tempera-ture of 500 �C is shown in Fig. 1. This figure displays ratherbroad reflections of BaCO3 in both the u and w directions.The X-ray intensity of this phase is rather low. In addition,some weak peaks were observed in a 2h scan, indicatingthat the film contains unoriented parts. The mean orienta-tion relationship of most of the BaCO3 grains determinedby pole figure measurements and a u scan of the TiO2

(110) reflection (w = 45�, 2h = 27.45�) was derived as:

ð100ÞBCkð100ÞT;½0 31�BCk½001�T:The u positions corresponding to the (001) and ð00�1Þ sub-strate planes are denoted ‘‘A’’ and ‘‘B’’, respectively, inFig. 1.

3.2.2. Orientation of Ba2TiO4

Fig. 2a gives the pole figure taken at 2h = 29.24� of thesample prepared after solid–solid reaction at a temperatureof 700 �C. The orientation relationship of Ba2TiO4 (B2T)to the (10 0) rutile surface was found as follows:

ð100ÞB2Tkð1 00ÞT;½00 1�B2Tk½001�T:This orientation relationship was also observed for thesample prepared after solid–solid reaction at a temperatureof 600 �C and after vapor–solid reaction at temperaturesbetween 600 and 800 �C.

3.2.3. Orientation of BaTiO3

The BaTiO3 (BT) grains are crystallographically well-oriented. To identify the orientation relationship betweenthis phase and the substrate, a series of pole figures were

i13O30 and BaTi4O9 phases

Lattice parameters JCPDS number

6) a = b = 0.459 nm 21–1276c = 0.295 nm

a = 0.643 nm 45–1471b = 0.531 nmc = 0.89 nm

a = 0.765 nm 38–1481b = 1.055 nmc = 0.61 nm

a = 0.401 nm 89–2475

a = 0.988 nm 77–1566b = 1.709 nmc = 1.891 nmb = 98.72�

a = 1.706 nm 84–2213b = 0.986 nmc = 1.405 nm

a = 1.452 nm 77–1565b = 0.379 nmc = 0.629 nm

Fig. 1. BaCO3 (111) (2h = 23.9�) pole figure of a sample prepared at a substrate temperature of 500 �C. The peaks are situated at w = 55�. The positionsof marks A and B in all pole figures correspond to the u values of the (001) and ð00�1Þ substrate planes, respectively.

2674 A. Lotnyk et al. / Acta Materialia 55 (2007) 2671–2681

recorded with different 2h values. Fig. 2b gives the pole fig-ure taken at 2h = 31.4� of the sample prepared after solid–solid reaction at a temperature of 700 �C. A first orienta-tion relationship of BaTiO3 grains was found as:

ð111ÞBTkð100ÞT;½1�10�BTk½001�T:

Such an orientation relationship was also observed for thesamples after solid–solid reaction at temperatures between600 and 900 �C in vacuum and in air, as well as after va-por–solid reaction at 700 �C. Noticeably, the (111) BT(2h = 38.8�) reflection could not be detected in XRD h–2h scans containing the TiO2 (200) peak because it is com-pletely hidden by the strong TiO2 (200) peak (2h = 39.2�).Therefore, pole figures are more suitable to detect thisphase and to analyze its crystallographic orientation.

Fig. 3 shows a high–resolution TEM (HRTEM) imageof the interface region between a BaTiO3 thin film and a(100) rutile single crystal substrate of a sample preparedat a substrate temperature of 700 �C. In Fig. 3b, the aboveorientation relationship of BaTiO3 grown after vapor–solidreaction is easily confirmed; the direction of the electronbeam is [001] for the substrate and ½1�10� for the BaTiO3.The interface between the thin film and the substrate isnot flat. Large and small (11 0) and ð1�10Þ rutile facets areclearly visible in Figs. 3a and b. The large (11 0) facets werealso observed by Graff et al. [13]. In addition, ð11�1Þ twinswere found within BaTiO3 grains.

A XRD h–2h scan of the sample made after vapor–solidreaction at a substrate temperature of 800 �C showed theappearance of the characteristic reflection of (112) BaTiO3

(2h = 56.2�) beside the substrate reflections (not shown),

which means that the (112) plane of BaTiO3 is parallelto the (100) substrate plane. Fig. 4a shows a cross-sec-tional bright-field TEM image of a reaction layer preparedby vapor–solid reaction at 800 �C. The interface betweenthe thin film and the substrate is rough. Well-orientedBaTiO3 grains were formed after the reaction. This wasconfirmed by selected area electron diffraction (Fig. 4b)as well as by XRD texture measurements (not shown).Two orientation relationships for BaTiO3 were found atthis temperature as follows:

main : ð112ÞBTkð100ÞT;½1�10�BTk½001�T;

minor : ð111ÞBTkð100ÞT;½1�10�BTk½001�T:The main orientation relationship is in good agreementwith that reported by Graff et al. [13]. The main (112) ori-entation of BaTiO3 deviates from the minor (111) one by atilt of 19.5� around the ½1�10� BaTiO3i[001] TiO2 tilt axis.

Fig. 5 shows a HRTEM image of the interface regionafter the reaction between BaO vapor and the (10 0) rutilesingle crystal of a sample prepared at a substrate tempera-ture of 900 �C. The reaction layer consists of BaTiO3 andTi-rich grains. The latter were observed between the TiO2

substrate and the BaTiO3 phase. In Fig. 5b the (200) and(00 2) interplanar distances of the Ti-rich phase are�0.938 nm and �0.488 nm (respectively) with an angle of�98.8� in between them. This Ti-rich grain was identifiedas Ba6Ti17O40, and this phase was also found in other partsof the sample. Planar defects such as stacking faults lyingalong (001) planes were observed within the Ba6Ti17O40

grains. These defects are typical of Ti-rich phases grownby solid-state reactions [13,19,20]. The crystallographic ori-

Fig. 2. X-ray pole figure of a sample prepared after solid-state reaction at 700 �C: (a) measured with 2h = 29.24� (Ba2TiO4 {031}/{002} family). All peakssituated at w = 90� correspond to a (100) orientation of Ba2TiO4; (b) measured with 2h = 31.4� (BaTiO3 {101} family). The peaks are situated at w = 35�and 90� and thus correspond to a (111) orientation of BaTiO3.

A. Lotnyk et al. / Acta Materialia 55 (2007) 2671–2681 2675

entation relationship found by HRTEM between theBaTiO3 and Ba6Ti17O40 (6–17) grains is:

ð001Þ6–17kð111ÞBT; ½010�6–17k½1�10�BT:

This orientation relationship indicates a topotaxial reactionbetween BaTiO3 and Ba6Ti17O40 which was previously ob-served and explained by Krasevec et al. [21].

The BaTiO3 grains have also a well-defined orientationto the rutile substrate. Different orientations of the BaTiO3

phase were found by XRD texture measurements andHRTEM investigations at 900 �C: (223) BaTiO3i(100)TiO2 (grain A in Fig. 5), (33 5) BaTiO3i(100) TiO2 (grainB in Fig. 5), (225) BaTiO3i(100) TiO2 and (111)BaTiO3i(100) TiO2. The in-plane orientation relationshipis found to be ½1�10� BaTiO3 i [00 1] TiO2 for all these orien-tations. The (223) BaTiO3i(100) TiO2 and (335)BaTiO3i(100) TiO2 orientations can be understood as aresult of a systematic tilt around the ½1�10� BaTiO3 i[001]

Fig. 3. High-resolution TEM micrographs of samples made after vapor–solid reaction at a substrate temperature of 700 �C. (a) Thin film–substrateinterface. Large (110) and ð1�10Þ TiO2 facets were formed after thereaction. (b) Lattice plane images of BaTiO3 in the ½1�10� viewing directionand substrate in the [001] viewing direction (magnified section of image(a)). Small (110) TiO2 facets (marked by black lines) and ð11�1Þ twins inBaTiO3 were also observed.

Fig. 4. (a) Bright-field TEM micrograph of a reaction layer formed aftervapor–solid reaction on the (100) rutile surface at a substrate temperatureof 800 �C. (b) Electron diffraction pattern taken from the surface regionbetween the rutile substrate (T) and the reaction layer. Well-orientedBaTiO3 (BT) grains were found in the thin film. Viewing direction is ½11�1�BaTiO3i[010] TiO2.

2676 A. Lotnyk et al. / Acta Materialia 55 (2007) 2671–2681

T tilt axis starting from the low-index orientation (111)BaTiO3i(100) TiO2: \BaTiO3 (111);(223) = 11.4�, \BaTiO3

(111);(335) = 14.4�, \BaTiO3 (111);(225) = 25.2�.

3.2.4. Orientation of the Ti-rich phasesTi-rich phases grew during both types of solid-state

reaction at high reaction temperatures in vacuum and inair but with quite different textures. At 1000 �C, a polycrys-talline BaTi4O9 phase was formed after the solid–solidreaction in vacuum. In air, at 1000 �C a polycrystallineBa4Ti13O30 phase with a fibrous texture was identified.The XRD pattern (not shown) showed all the reflectionsof the Ba4Ti13O30 phase as found in the powder diffracto-gram but the intensity relations of the peaks were changeddue to a preferred orientation of the Ba4Ti13O30 phase.

Unlike the solid–solid reaction, a vapor–solid reactionat 900 and 1000 �C produced well-oriented Ti-rich phases.An example for 900 �C is shown in Fig. 5. The Ti-richgrains were found between the BaTiO3 phase and the(10 0) TiO2 substrate (Fig. 5a). The Ba6Ti17O40 grains wereformed with a well-defined orientation to the (100) rutilesubstrate. The crystallographic orientation relationshipfound by HRTEM between the TiO2 substrate and theBa6Ti17O40 (6–17) grains can be written as:

ð0 01Þ6–17kð010ÞT; ½010�6–17k½001�T;which is, however, not exactly fulfilled. By analyzing manyHRTEM images, it was found that the (001) plane ofBa6Ti17O40 can form an angle between 0� and �9� withthe (010) plane of the substrate. Thus, a deviation from0� to �9� around the [01 0] Ba6Ti17O40 i[001] TiO2 tilt axisis possible for Ba6Ti17O40 grains in the above orientation.

A vapor–solid reaction at 1100 �C produced well-ori-ented Ba4Ti13O30 (4–13) grains as indicated by a XRD h–2h scan and texture measurements. A XRD h–2h scan indi-cates that the (010) plane of Ba4Ti13O30 is parallel to the(10 0) substrate plane (not shown). Pole figure measure-ments taken at 2h = 28.3� show a splitting of the {131}/

Fig. 5. High-resolution TEM cross-sectional images of reaction products grown between BaO vapor and (100) TiO2 at 900 �C: (a) thin film–substrateinterface; lattice plane images of (b) BaTiO3 and Ba6Ti17O40 grains and (c) the rutile substrate. The long white lines in (b) mark the (001) Ba6Ti17O40i(111)BaTiO3 lattice planes. Viewing direction is [010] Ba6Ti17O40i½1�10� BaTiO3i[001] TiO2.

A. Lotnyk et al. / Acta Materialia 55 (2007) 2671–2681 2677

{42 1} Ba4Ti13O30 peaks, which means that the thin filmconsists of several kinds of tilted grains with a common tiltaxis. The mean orientation relationship of most of theBa4Ti13O30 grains obtained from pole figure analysis andhigh-resolution TEM (Figs. 6a and b) is:

ð010Þ4–13kð100ÞT; ½001�4–13k½010�T:In Fig. 6b the (200) plane of Ba4Ti13O30 is not exactlyparallel to (002) TiO2. Thus the common tilt axis ofBa4Ti13O30 grains derived by pole figure and HRTEM is[001] Ba4Ti13O30i[010] TiO2. Because of the tetragonalityof the TiO2 unit cell, either the [100] TiO2 or the [01 0]TiO2 axis is a tilt axis for the Ba4Ti13O30 grains.

All the determined orientation relationships between theproduct phases and the substrate for the solid–solid reac-tion (ss) and the vapor–solid reaction (vs) are listed inTable 3. The misfits were calculated by using the equationadopted in the near-coincidence site lattice theory (NCSL):F = 2(n Æ a � m Æ b)/(n Æ a + m Æ b), where a and b are latticeparameters of two materials, e.g. BaTiO3 (a) and TiO2 (b),and n and m are integers [22,23].

3.3. Initial stage of the reaction between BaO vapor and

(100) TiO2

This part of the work was performed to specify whichphase is nucleated first during a vapor–solid reaction athigh reaction temperature. A very small amount of BaOwas deposited on the hot (100) TiO2 substrate at 900 �C.The nominal thickness of BaO was �1 nm; the reaction

time was �2 min. Fig. 7 shows HRTEM images of thereaction products that formed on the (100) rutile sub-strate during the initial stage of the reaction betweenBaO vapor and the (100) TiO2 substrate at 900 �C.BaTiO3 and Ti-rich grains were found on the substratesurface after the reaction. The Ti-rich islands have anaverage size of about 10 nm in height and 25 nm in width.The Ba6Ti17O40 Ti-rich phase was identified by fast Fou-rier transformation (FFT) of the corresponding HRTEMimages (Figs. 7b and c). The orientation of the small Ti-rich islands is identical to the large ones presented earlierin this text. BaTiO3 grains were also formed, well-ori-ented with respect to the rutile substrate (Fig. 7e). Theygrew with a (111) orientation. However, their densitywas much lower than the density of the Ti-rich grains.Mainly, the (100) rutile surface was covered by Ti-richislands.

4. Discussion

4.1. Phase formation

The solid–solid reactions in vacuum and in air showedthat different processes occur during BaTiO3 formation.The Ba2TiO4 phase is observed always after reaction invacuum. However, this compound is not detected aftersolid-state reaction in air.

In the classical theory of nucleation, the rate of nucle-ation of a new nucleus q* is given by:

Fig. 6. High-resolution TEM cross-sectional image of a sample after thereaction between a BaO vapor and the (100) rutile substrate at 1100 �C:(a) thin film–substrate interface; (b) FFT of image (a). Viewing direction is[001] Ba4Ti13O30 (4–13)i[010] TiO2 (T).

Tab

le3

Ori

enta

tio

nre

lati

on

ship

san

dm

isfi

tva

lues

bet

wee

np

rod

uct

ph

ases

and

the

(10

0)T

iO2

sub

stra

te

Ph

ase

T(�

C)

Ori

enta

tio

nre

lati

on

ship

Mis

fit

Pla

ne

Dir

ecti

on

In-p

lan

eIn

-pla

ne

rota

ted

by

90�

BaC

O3

500

(10

0)B

Ci(

10

0)T

[03

1]B

Ci[0

01]

T2ð

2dð0

� 11Þ

BC�

3dð0

01Þ

TÞ=ð2

dð0

� 11Þ

BCþ

3dð0

01Þ

T޼�

3%2(

7d(0

13)B

C�

4dT

(01

0))

/(7d

(01

3)B

C+

4d(0

10)T

)=�

1.3%

Ba 2

TiO

4ss

600–

700

and

vs60

0–80

0

(10

0)B

2Ti(

10

0)T

[00

1]B

2Ti[0

01]

T2(

2d(0

01)B

2T�

d(0

01)T

)/(2

d(0

01)B

2T

+d

(00

1)T

)=

+3.

3%2(

3d(0

10)B

2T�

7d(0

10)T

)/(3

d(0

10)B

2T+

7d(0

10)T

)=�

1.5%

BaT

iO3

ssan

dvs

600–

900

(11

1)B

Ti(

10

0)T

½1� 10�B

Ti[0

01]

T2ð

dð1

� 10Þ

BT�

dð0

01Þ

TÞ=ðdð1

� 10Þ

BTþ

dð0

01Þ

T޼�

4:1%

2ð3dð1

1� 2Þ

BT�

dð0

10Þ

TÞ=ð3

dð1

1� 2Þ

BTþ

dð0

10Þ

TÞ¼þ

6:9%

vs80

0(1

12)

BT

i(1

00)

T2ð

2dð1

1� 1Þ

BT�

dð0

10Þ

TÞ=ð2

dð1

1� 1Þ

BTþ

dð0

10Þ

TÞ¼þ

0:7%

vs90

0(2

23)

BT

i(1

00)

T2ð

7dð3

3� 4Þ

BT�

dð0

10Þ

TÞ=ð7

dð3

3� 4Þ

BTþ

dð0

10Þ

TÞ¼þ

4:7%

(33

5)B

Ti(

10

0)T

2ð10

dð5

5� 6Þ

BT�

dð0

10Þ

TÞ=ð1

0dð5

5� 6Þ

BTþ

dð0

10Þ

T޼�

6%(2

25)

BT

i(1

00)

T2ð

9dð5

5� 4Þ

BT�

dð0

10Þ

TÞ=ð9

dð5

5� 4Þ

BTþ

dð0

10Þ

T޼�

3:6%

Ba 6

Ti 1

7O

40

vs90

0–10

00(0

01)

6–17

i(0

10)

T[0

10]

6�17

i[00

1]T

2(d

(01

0)6�

17�

6d(0

01)T

)/(d

(01

0)6�

17+

6d(0

10)T

)=�

3.5%

2ð3dð� 1

013Þ

6�17�

dð0

10Þ

TÞ=ð3

dð� 1

013Þ

6�17þ

dð0

01Þ

T޼�

5%

Ba 4

Ti 1

3O

30

vs11

00(0

10)

4–13

i(1

00)

T[0

01]

4–13

i[01

0]T

2(d

(00

1)4�

13�

3d(0

10)T

)/(d

(00

1)4�

13

+3

d(0

10)T

)=

+2%

2(d

(10

0)4�

13�

6d(0

01)T

)/(d

(10

0)4�

13

+6d

(00

1)T

)=�

3.7%

2678 A. Lotnyk et al. / Acta Materialia 55 (2007) 2671–2681

q� � expð�r3=DG2kT Þ expð�Q=kT Þ;where r is the specific interfacial energy, DG is the Gibbsfree energy of formation, k is the Boltzmann constant, T

is the temperature and Q is the mean activation energy ofthe diffusion term [24]. Thus, the rate of nucleation isproportional to a term of the form exp(–r3/DG2kT)and, therefore, the nucleation of a new phase will occurrapidly for compounds with high (more negative) valuesof DG.

Fig. 7. High-resolution TEM cross-sectional image of a sample after the reaction of a BaO vapor with a (100) TiO2 substrate at a substrate temperature of900 �C. The nominal thickness of BaO was �1 nm. (a) The reaction between BaO and the rutile substrate results in the formation of Ti-rich islands.(b) FFT image of a Ba6Ti17O40 (6–17) Ti-rich grain. (c) FFT image of the rutile substrate (T). Viewing direction is [010] Ba6Ti17O40i[001] TiO2.(d) Oriented BaTiO3 grains were also found at the interface. (e) Computer-processed lattice plane images of BaTiO3 and the rutile substrate (magnifiedsection of image (d)). The arrow in image (e) marks a (111) twin boundary in BaTiO3. Viewing direction is ½1�10� BaTiO3i[001] TiO2.

A. Lotnyk et al. / Acta Materialia 55 (2007) 2671–2681 2679

We have calculated DG values for the formation ofBa2TiO4 and BaTiO3 by the reaction between BaCO3 andTiO2 in vacuum and in air, where DG values for these reac-tions are strongly dependent on the partial pressure of CO2

(in vacuum P CO2is 10�5 mbar while in air P CO2

is 0.3 mbar).The DG� (standard Gibbs energy) values were taken fromRef. [25]. In vacuum, the DG values for the formation ofBa2TiO4 (�229.4 kJ mol�1 at 600 �C) and BaTiO3

(�165.3 kJ mol�1 at 600 �C) are distinctly different, witha higher (more negative) value for Ba2TiO4 (see also Table2 in Ref. [12]). Thus, Ba2TiO4 will always form as the firstphase in vacuum. In air, the DG value for BaTiO3 forma-tion at 600 �C (DG � � 90.5 kJ mol�1) is more negativethan for Ba2TiO4 formation at 600 �C (DG �� 79.7 kJ mol�1), while at temperatures higher than�657 �C the DG values for Ba2TiO4 formation becomemore negative than for BaTiO3 formation. Consequently,BaTiO3 can be nucleated during heating at 600 �C as thefirst phase in air. The formation of the Ba2TiO4 compoundby direct reaction of BaCO3 with TiO2 substrates in air attemperatures higher than 657 �C may be suppressed due toa diffusion barrier induced by BaTiO3 grains which arenucleated during ramping up (�10 K min�1) to the reac-tion temperatures.

The formation of Ba2TiO4 in air is, however, consideredpossible by a reaction between BaCO3 and already-formedBaTiO3 at its expense at temperatures above 800 �C [7,8].In our case, Ba2TiO4 was not observed to form via the

reaction between BaCO3 and BaTiO3 after heating in airat temperatures between 600 and 700 �C (see Table 1).From a thermodynamic point of view, the formation ofBa2TiO4 via a reaction between BaCO3 with BaTiO3 attemperatures up to 644 �C is hindered by the positive val-ues of DG. We used only a thin layer of BaCO3 (50 nm),and at a temperature of 800 �C this layer reacted rapidlywith BaTiO3.

After solid-state reaction at high reaction temperatures,Ti-rich barium polytitanates were identified. In the bulkphase diagram of the BaO–TiO2 system, the compoundsBaTi4O9, Ba6Ti17O40 and Ba4Ti13O30 exist between temper-atures of about 900 and 1400 �C [2]. The Ti-rich com-pounds were observed in our experiments after reactionsat temperatures between 900 and 1100 �C.

4.2. Orientation relationships

4.2.1. Orientation of BaTiO3

The BaTiO3 grains grew oriented with respect to thesubstrate in both types of solid-state reactions. One orien-tation relation of BaTiO3 on (100) TiO2 was found aftersolid-state reactions in vacuum and in air. On the otherhand, different orientation relations between the BaTiO3

grains and the rutile substrates were observed after vapor–solid reaction. This difference may be due to a number ofreasons.

2680 A. Lotnyk et al. / Acta Materialia 55 (2007) 2671–2681

It has been well established that the growth of films withpreferred orientation on a substrate is closely related tosurface free energy, film/substrate interface energy as wellas misfit strain energy [26–30]. However, during solid-statereactions, nucleation and diffusion take place so that thesystem cannot immediately reach thermodynamic equilib-rium. Thus, the kinetic effect of nucleation of thin filmswith preferred orientation should also be taken intoaccount. The two different solid-state reaction geometriesused in the present study may lead to two different nucle-ation conditions.

As was shown in Ref. [12], the orientation of the BaTiO3

grains after the solid–solid reaction with (110) rutile doesnot depend on the orientation of BaCO3. Thus, in the caseof the solid–solid reaction, the nucleation of BaTiO3 mighthave mainly occurred by diffusion of Ba ions into the TiO2

lattice. It is reasonable to expect the nucleation of BaTiO3

grains with their low-index (111) plane on the (100) rutilesurface, which is also facilitated by a certain crystallo-graphic similarity between the (111) BaTiO3 and (100)TiO2 planes. Fig. 8a and b show a schematic view downthe (100) plane of TiO2 and the (111) plane of BaTiO3.A similarity in the arrangements of the oxygen atomsaround the Ti atoms in the (100) plane of TiO2 and inthe (111) plane of BaTiO3 (marked by dashed lines inFig. 8a and b) is obvious.

On the other hand, in the case of vapor–solid reaction,the orientations of the product phases are a complex func-tion of the reaction conditions such as substrate tempera-ture and deposition rate. Surface diffusion may bedominant in the vapor–solid reaction, and a direct nucle-ation of BaTiO3 grains on the TiO2 surface may occur.Recently, the rutile surfaces have received considerableattention in surface science. It was found that the (10 0)

Fig. 8. Schematic diagram of the projection of (a) the (100) plane of TiO2

(rutile) and (b) the (111) plane of BaTiO3. To show all atoms in theBaTiO3 unit cell, the radius of Ba atoms is reduced from their original sizein (b), while the radius of Ti atoms is increased in (b).

TiO2 surface shows three distinct surface structures, i.e.(1 · 3), (1 · 5) and (1 · 7), which appear by annealing atthe temperatures of 600, 800 and 1200 �C, respectively[31]. The nucleation kinetics on these surface structurescan be different. The growth of (111)-oriented BaTiO3

grains at a substrate temperature of 700 �C seems to haveoccurred for the crystallographic reasons given above.However, with increasing substrate temperature up to800 �C, the morphology of the rutile surface is changedwhich will lead to other nucleation conditions than at asubstrate temperature of 700 �C. As a consequence, thenucleation of (112)-oriented BaTiO3 grains at a substratetemperature of 800 �C has occurred. This observation isalso supported by NCSL calculations applied for (112)BaTiO3 on (100) rutile. In this theory, the smaller the mis-fit and the higher the periodicity (low m, n), the lower is theinterfacial energy [23,22]. A computer program written inthe Free Pascal programming language was used to calcu-late NCSL misfit values for all index combinations(�9 6 (h,k, l) 6 +9) as in Ref. [12]. The (112) orientationwas found on the first position in the calculated list, i.e.as the best solution. Thus, the (112) orientation of BaTiO3

is most favorable out of a large set of misfit solutions.After vapor–solid reaction at a substrate temperature of

900 �C, BaTiO3 of several different orientations wasobserved on top of the Ba6Ti17O40 phase. Investigation ofthe initial stage of the vapor–solid reaction of a 1 nm thickBaO layer with the (100) TiO2 substrate at this tempera-ture showed that both BaTiO3 and Ba6Ti17O40 phasesnucleate during the initial stage of the reaction. However,the density of the Ti-rich grains was much higher than thatof the (111)-oriented BaTiO3 grains. Thus, with increasingreaction time (increasing amount of BaO), BaTiO3 grainswill nucleate on the as-formed Ba6Ti17O40 grains, whichnow play the role of a substrate for BaTiO3 growth. Thus,the orientations of BaTiO3 are mainly given by the orienta-tion of Ba6Ti17O40 grains. The topotaxial relationship ofBaTiO3 with respect to Ba6Ti17O40 results in the orienta-tion (111) BaTiO3i(111) Ba6Ti17O40. The tilt of the (001)Ba6Ti17O40 plane can be calculated from the tilt of the(10 0) Ba6Ti17O40 plane using the angle b = 98.7� betweenthem. The result of this calculation is a tilt of the (001)Ba6Ti17O40 plane around the [010] Ba6Ti17O40i[001]TiO2 axis by 8.7� to 17.7�. Corresponding tilts of BaTiO3

grains were indeed observed, confirming the abovediscussion.

4.2.2. Orientation of Ti-rich phases

Ti-rich phases were grown in both types of solid-statereaction at high reaction temperatures, but with quite dif-ferent textures. Oriented Ba6Ti17O40 and Ba4Ti13O30

phases were formed after vapor–solid reaction at substratetemperatures between 900 and 1100 �C. Unlike to thevapor–solid reaction, polycrystalline BaTi4O9 andBa4Ti13O30 (with fibrous texture) phases were found afterthe solid–solid reaction at 1000 �C in vacuum and in air,respectively. These differences are caused by the reaction

A. Lotnyk et al. / Acta Materialia 55 (2007) 2671–2681 2681

conditions changing with increasing temperature. In thevapor–solid reaction, the BaO vapor directly reacts withthe (100) TiO2 surface. In this case, the orientations ofthe reaction products are determined only by the orienta-tion of the substrate. Thus, nucleation directly on the rutilesingle crystal surface results in well-oriented Ti-rich grains.The initial reaction during solid–solid experiments seems tobe dominated by Ti out-diffusion. At low reaction temper-ature, Ba2TiO4 with an orientation influenced by the orien-tation of BaCO3 was observed [12]. If this behavior isextrapolated to high temperatures, we can expect a morerapid Ti out-diffusion, resulting in a high Ti concentrationat BaCO3 grain boundaries and on top of the BaCO3 layer.The nucleation of Ti-rich phases now occurs without adirect interface to the substrate surface and thus resultsin a random orientation of the Ti-rich phases.

5. Conclusions

The formation of BaTiO3 thin films from BaCO3 and(100) rutile single crystals by solid-state reactions has beenstudied experimentally under vacuum and in air. The inter-mediate Ba2TiO4 compound was formed in vacuum butnot in air. We assume that the formation of Ba2TiO4 inair is suppressed due to a BaTiO3 nucleation barrier.

Well-defined orientation relationships are foundbetween Ba2TiO4, BaTiO3, Ba6Ti17O40, Ba4Ti13O30 andthe (10 0) TiO2 substrate, as well as between BaTiO3 andBa6Ti17O40. One definite orientation relationship has beenfound for BaTiO3 on (100) TiO2 after solid–solid reaction,whereas different orientation relationships between BaTiO3

and (100) rutile substrates have been observed after vapor–solid reaction depending on the substrate temperature.These differences are explained in terms of the differentnucleation conditions. At high reaction temperatures, Ti-rich phases were grown in both types of solid-state reac-tions but with quite different texture. PolycrystallineBaTi4O9 and Ba4Ti13O30 phases are produced by solid–solid reaction in vacuum and in air, respectively, while ori-ented Ba6Ti17O40 and Ba4Ti13O30 phases are formed afterthe vapor–solid reaction. These differences are most prob-ably caused by the reaction conditions changing withincreasing reaction temperature.

Acknowledgements

Work supported by Deutsche Forschungsgemeinschaft(DFG) via SFB 418 at Martin-Luther-Universitat Halle,Wittenberg. The authors are thankful to Ms. S. Swatekfor TEM sample preparation.

References

[1] Kirby KW, Wechsler BA. J Am Ceram Soc 1991;74(8):1841.[2] Ritter JJ, Roth RS, Blendel JE. J Am Ceram Soc 1986;69:155.[3] Cournil M, Soustelle M, Thomas M. Oxidation of Metals 1979;13:77.[4] Cournil M, Soustelle M, Thomas M. Oxid Met 1979;13:89.[5] Mutin JC, Niepce JC. Mater Sci Lett 1984;3:591.[6] Beauger A, Mutin JC, Niepce JC. J Mater Sci 1983;18:3041.[7] Beauger A, Mutin JC, Niepce JC. J Mater Sci 1983;18:3543.[8] Niepce JC, Thomas G. Solid State Ionics 1990;43:69.[9] Hennings DFK, Schreinemacher BS, Schreinemacher H. J Am Ceram

Soc 2001;84:2777.[10] Buscaglia MT, Bassoli M, Buscaglia V. J Am Ceram Soc

2005;88:2374.[11] Rossel M, Gablenz M, Muller T, Roder A, Abicht H-P. Anal Bioanal

Chem 2003;375:310.[12] Lotnyk A, Senz S, Hesse D. Solid State Ionics 2006;177:429.[13] Gaff A, Senz S, Voltzke D, Abicht H-P, Hesse D. J Eur Ceram Soc

2005;25:2201.[14] Bland JA. Acta Cryst 1961;14:875.[15] Gunter JR, Jameson GB. Acta Cryst 1984;C40:207.[16] Pfaff G. J Mater Sci Lett 1991;10:1059.[17] Felgner K-H, Muller T, Langhammer HT, Abicht H-P. Mater Lett

2004;58:1943.[18] Lee SJ, Biegalski MD, Kriven WM. J Mater Res 1999;14:3001.[19] Hesse D, Graff A, Senz S, Zakharov ND. Mater Sci Forum 1999;294–

296:597.[20] Graff A. PhD thesis, Marthin-Luther Universitat Halle, Wittenberg;

1999.[21] Krasevec V, Drofenik M, Kolar D. J Am Ceram Soc

1987;70:C193.[22] Grimmer H, Bollmann W, Warrington DH. Acta Crystallogr

1974;A30:197.[23] Sayle TXT, Catlow CRA, Sayle DC, Parker SC, Harding JH. Philos

Mag 1993;A68:565.[24] d’Heurle FM. J Mater Res 1988;3:167.[25] Barin I. Thermochemical data of pure substances. Weinheim: VCH

Verlagsgesellschaft; 1995.[26] Berbenni V, Marini A, Bruni G. Thermochim Acta 2001;374:151.[27] Thompson CV. J Appl Phys 1985;58:763.[28] Thompson CV. Annu Rev Mater Sci 1990;20:245.[29] Carel R, Thompson CV, Frost HJ. Acta Mater 1996;44:2479.[30] Oh UC, Je JH. J Appl Phys 1993;74:1692.[31] Chung YW, Lo WJ, Somorjai GA. Surf Sci 1977;64:588.