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Journal of Physics and Chemistry of Solids 68 (2007) 570–575

www.elsevier.com/locate/jpcs

Ab initio structural and energetic study ofLaMO3 (M ¼ Al, Ga) perovskites

Bo Wua,b,�, Matvei Zinkevicha, Fritz Aldingera, Wenqing Zhangc

aMax-Planck-Institut fur Metallforschung und Institut fur Nichtmetallische Anorganische Materialien der Universitat Stuttgart,

Heisenbergstrasse 3, 70569 Stuttgart, GermanybCollege of Materials Science and Engineering, Fuzhou University, 350108 Shangjie, Minhou, Fuzhou, PR China

cShanghai Institute of Ceramics, Chinese Academy of Sciences, 200050 Shanghai, PR China

Received 13 July 2006; received in revised form 18 January 2007; accepted 18 January 2007

Abstract

The equilibrium crystal structure parameters and the total energies of the polymorphous LaMO3 perovskites (M ¼ Al, Ga) and their

constituent binary oxides A-La2O3, a-Al2O3 and b-Ga2O3 were calculated with ab initio method based on density function theory (DFT)

and projector augmented wave method (PAW) using both local density approximation (LDA) and generalized gradient approximation

(GGA). The relative lattice stabilities of the various configurations with respect to the ground state and the enthalpies of formation of the

stable perovskites from the constituent binary oxides were obtained. The enthalpies of formation at 298.15K calculated within LDA,

�67:19 and �49:99kJmol�1 for the stable configurations of LaAlO3 and LaGaO3, respectively, agree well with the available

experimental data, while the enthalpies calculated within GGA are much less negative. It was the first time that recurred the experimental

enthalpies of formation at 298.15K for the stable configurations of LaAlO3 and LaGaO3 from a fundamental ab initio calculation.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: A. Ceramics; A. Inorganic compounds; C. Ab initio calculations; D. Crystal structure; D. Thermodynamic properties

1. Introduction

Perovskite-type compounds with the general formulaABO3 have numerous technological applications due totheir wide range of attractive properties, e.g., piezoelectric,ferroelectric, dielectric, ion-conducting, etc. In particular,LaAlO3 and LaGaO3 perovskites have received consider-able attention as the substrates of the high-temperaturesuperconductors [1] and the parent materials of theelectrolytes in solid oxide fuel cells [2]. To design and usesuch materials, the crystal structures and thermodynamicproperties are of great significance.

The ideal perovskite-type lattice is cubic (C-LaMO3),while the structures of compounds with M ¼ Al or Ga

front matter r 2007 Elsevier Ltd. All rights reserved.

s.2007.01.031

ng author. College of Materials Science and Engineering,

ity, 350108 Shangjie, Minhou, Fuzhou, PR China.

07 1272; fax: +86 591 2286 6537.

sses: drwubo@hotmail.com (B. Wu),

pg.de (M. Zinkevich), aldinger@mf.mpg.de

qzhang@mail.sic.ac.cn (W. Zhang).

typically show rhombohedral (R-LaMO3) or orthorhombic(O-LaMO3) distortions, depending on the temperature andpressure. The thermodynamic data of LaMO3 werereviewed by Cheng and Navrotsky [3]. The recommendedvalue of the enthalpy of formation of R-LaAlO3 fromLa2O3 and Al2O3 at 298K is �69:61� 3:23, and that forO-LaGaO3 from La2O3 and Ga2O3 is �52:39�1:99 kJmol�1, respectively. Almost identical value forO-LaGaO3, � 54:3� 1:5 kJmol�1, was obtained in a recentcalorimetric study [4]. The corresponding enthalpies offormation from elements are then �1803:26� 3:32(R-LaAlO3) and �1492:74� 2:10 kJmol�1 (O-LaGaO3).The enthalpy of the O! R phase transition in LaGaO3 at414K was reported as 355 Jmol�1 [5], 170 Jmol�1 [3],and 305 Jmol�1 [6], and the R! C phase transition inLaAlO3 around 800K was considered to be of a secondorder [7] though a very small heat effect of 70 Jmol�1 wasmeasured [3].With the availability of the powerful computers, reliable

models, and efficient algorithms, nowadays, the ab initio

ARTICLE IN PRESSB. Wu et al. / Journal of Physics and Chemistry of Solids 68 (2007) 570–575 571

calculations are important for a fundamental understand-ing of the materials. And the development of the densityfunctional theory (DFT) [8] has reached a level where it ispossible, from the ‘‘parameter-free’’ quantum mechanicalcalculations to obtain the total energies, atomic forces,vibration frequencies, magnetic moments, mechanical,optical properties, etc. Thanks to its universal and high-throughput characters, the ab initio calculation has becomea cost-effective tool in solid-state physics and materialsscience [9]. When starting an ab initio calculation, oneneeds only to specify the atomic numbers of the constituentelements and the information about the arrangement inspace, i.e., the primitive vectors and atomic positions of thespecies in the unit cell of the structure. Although the mostaccurate techniques are the full-potential methods [9], theprojector augmented wave potentials (PAW) methods[10,11] are the state of the art in the current ab initio

calculations because of the limited computer resources.Both the local density approximation (LDA) [12] and thegeneralized gradient approximation (GGA) [13–15] havebeen used extensively.

Results of the previous ab initio calculations of theenthalpies of formation of LaGaO3 in different structures[4,16] are summarized in Table 1. In both works, theVienna ab initio simulation package (VASP) [17–19] andGGA were employed. The enthalpies of formation fromelements and binary oxides were calculated as thedifferences of the total energies between LaGaO3 andmetallic La, metallic Ga and O2 gas or La2O3 and Ga2O3,respectively. However, only the enthalpies of formationfrom elements calculated by the present authors [4] are

Table 1

Results of the previous ab initio calculations of the enthalpy of formation

of LaGaO3 at 0K ðkJmol�1Þ

Structurea D�f H (from

elements)

D�f ;oxH (from

binary oxides)

Reference

O �1332:28 �19:29 [16]

O �1490:35 �20:40 [4]

R �1329:39 �16:40 [16]

R �1488:04 �18:08 [4]

C �1302:38 þ10:61 [16]

aO—orthorhombic, R—rhombohedral, C—cubic.

Table 2

Crystallographic information of compounds

Compound Prototype Pearson symbol

A-La2O3 La2O3 hP5

a-Al2O3 a-Al2O3 hR10

b-Ga2O3 Dy2Ni3 mS20

O-LaMO3 GdFeO3 oP20

R-LaMO3 CaTiO3 hR10

C-LaMO3 CaTiO3 cP5

close to the experimental data, while the enthalpies offormation from oxides show large deviations. For LaAlO3,the enthalpies of formation from ab initio calculation have,to our knowledge, not been reported so far.In the present paper, the ab initio calculations within

both the LDA and the GGA were employed to study thecrystal structure parameters and the energetics of phasetransformation and phase formation in LaAlO3 andLaGaO3 perovskites.

2. Computational method

The crystallographic information of the compoundsinvolved in present study is given in Table 2. Allcalculations were carried out using the VASP code. Theresults correspond to the state at the absolute zerotemperature, zero pressure and without zero-point motion.For the GGA exchange-correlation energy, the Perdew–Burke–Ernzerhof parameterization (PAW–PBE) [14,15]was used. The eigenstates were expanded in the plane-wave basis functions, and the ion cores were representedusing the PAW potentials [10,11]. The La 5s25p65d16s2, Al3s23p1, Ga 4s24p1, and O 2s22p4 states were treated as fullyrelaxed energy bands. The following Monkhorst–Packmeshes [20] were used to sample the Brillouin zone: a 5�5� 5 for the rhombohedral compounds (including a-Al2O3), a 6� 6� 6 for the orthorhombic compounds andmonoclinic b-Ga2O3, and an 11� 11� 11 for the cubicperovskites. For the hexagonal La2O3, an 8� 8� 6 gammacentered grids method [21] was employed. The kineticenergy cutoff was set at 520 eV. The computationalparameters were carefully checked and a stable calculatedresult was obtained. The total energies converged to a valuegreater than o1meV per atom. The atomic geometrieswere optimized using Hellman–Feynman forces and theconjugate gradients [22]. The total energies, Etot, wereminimized with respect to the volumes (volume relaxation),the shapes of the unit cells (cell external relaxation), andthe positions of the atoms within the cell (cell internalrelaxation) fully.

3. Results and discussion

The parameters of equilibrium crystal structure andthe total energies of the compounds are summarized in

Space group Number Strukturbericht

designation

P3m1 164 D52

R3c 167 D51

C2=m 12 D52

Pbnm 62 E21

R3c 167 D51

Pm3m 221 E21

ARTICLE IN PRESS

Table 3

The equilibrium crystal structure parameters and the total energies of the

compounds

Compound Parameter Method

LDA GGA Experimentala Reference

a-Al2O3 a 4.735 4.809 4.757(1) [23]

c 12.899 13.118 12.9877(1)

V 250.46 262.75 254.52

Etot �41.566 �37.403

b-Ga2O3 a 12.229 12.517 12.214(3) [24]

b 3.037 3.098 3.0371(9)

c 5.800 5.915 5.7981(9)

b ð�Þ 103.780 103.845 103.83(2)

V 209.18 222.73 208.85

Etot �34.3416 �30.0598

A-La2O3 a 3.884 3.938 3.9381(3) [25]

c 5.950 6.173 6.1361(6)

V 77.74 82.90 82.41

Etot �45.8834 �41.9079

O-LaAlO3 a 5.309 5.411

b 5.295 5.395

c 7.470 7.639

V 210.01 223.03

Etot �44.4046 �40.0673

R-LaAlO3 a 5.306 5.417 5.3647(1) [26]

c 12.931 13.189 13.1114(3)

V 315.29 334.85 326.79

Etot �44.4176 �40.0709

C-LaAlO3 a 3.739 3.810 3.8106(1) [26]

V 52.29 55.29 55.33

Etot �44.4021 �40.0476

O-LaGaO3 a 5.477 5.612 5.52432(2) [27]

b 5.463 5.557 5.49249(2)

c 7.735 7.892 7.77435(3)

V 231.42 246.15 235.89

Etot �40.6342 �36.2610

R-LaGaO3 a 5.496 5.608 5.5429(1) [28]

c 13.172 13.488 13.4328(2)

V 344.61 367.32 357.41

Etot �40.610 �36.226

C-LaGaO3 a 3.850 3.928 3.886

V 57.07 60.70 58.68 [29]

Etot �40.3458 �35.8961

The lattice parameters ða; b; cÞ are given in A, the unit cell volume ðV Þ in

A3, and the total energies (EtotÞ in eV per formula unit.aThe numbers in parentheses are the estimated errors or the standard

errors, in units of the last decimal.

Table 4

The calculated atomic coordinates [30] of the compounds in comparison

with selected experimental data

Compound Variable LDA GGA Experimentala Reference

a-Al2O3 zAl;12c 0.354 0.354 0.35220(1) [23]

xO1;18e 0.306 0.306 0.30634(7)

b-Ga2O3 xGa1;4i 0.091 0.091 0.09050(2) [24]

zGa1;4i 0.796 0.795 0.79460(5)

xGa2;4i 0.160 0.159 0.15866(2)

zGa2;4i 0.317 0.316 0.31402(5)

xO1;4i 0.168 0.166 0.1645(2)

zO1;4i 0.111 0.111 0.1098(3)

xO2;4i 0.173 0.174 0.1733(2)

zO2;4i 0.560 0.561 0.5632(4)

xO3;4i �0.003 �0.003 �0.0041(2)

zO3;4i 0.256 0.257 0.2566(3)

A-La2O3 zLa1;2d 0.244 0.247 0.2467(2) [25]

zO1;2d 0.646 0.645 0.6470(2)

O-LaAlO3 xLa1;4c �0.001 �0.002

yLa1;4c �0.003 �0.010

xO1;4c 0.038 0.044

yO1;4c 0.497 0.497

xO2;8d 0.757 0.735

yO2;8d 0.243 0.265

zO2;8d 0.017 0.023

R-LaAlO3 xO1;18e 0.533 0.541 0.5281(1) [26]

O-LaGaO3 xLa1;4c �0.007 �0.009 �0.0037(1) [27]

yLa1;4c �0.022 �0.038 �0.0168(1)

xO1;4c 0.075 0.078 0.0668(1)

yO1;4c 0.505 0.482 0.5068(2)

xO2;8d 0.774 0.714 0.7701(1)

yO2;8d 0.225 0.287 0.2290(1)

zO2;8d 0.039 0.042 0.0358(1)

R-LaGaO3 xO1;18e 0.567 0.571 0.5548(2) [28]

aThe numbers in parentheses are the estimated errors or the standard

errors, in units of the last decimal.

B. Wu et al. / Journal of Physics and Chemistry of Solids 68 (2007) 570–575572

Table 3. For the sake of brevity, only variable latticeparameters are presented. The calculated variable atomiccoordinates [30] of the compounds as well as the selectedexperimental data are compiled in Table 4. It should benoted that the calculated lattice parameters and the unitcell volume refer to the absolute zero temperature and thus,they are expected to be smaller than the experimentallymeasured values, due to some thermal expansion between0K and room temperature.

From Table 3, it is seen that for the a-Al2O3 andb-Ga2O3 which consist of p-elements, the lattice constantsand volumes of unit cell calculated within LDA agree wellwith the experimental results, while they are severelyoverestimated by GGA. For the A-type La2O3, however,the volume calculated within GGA agrees well with theexperimental data, but it is underestimated by LDA. Forthe LaMO3 perovskites, the experimental lattice para-meters and unit cell volume lie, in general, in between thevalues calculated within GGA and LDA. One should bearin mind that C-LaAlO3 and R-LaGaO3 phases cannot bequenched and thus, the reported crystal structure para-meters [26,28] correspond to high temperatures. Referringto Table 4 one can state that both the LDA and the GGAresult in similar positional parameters, which are also closeto the experimental values.The calculated enthalpies of transformation with respect

to the transitions from the rhombohedral structures to the

ARTICLE IN PRESSB. Wu et al. / Journal of Physics and Chemistry of Solids 68 (2007) 570–575 573

orthorhombic and cubic polymorphs are listed in Table 5.The results show that the rhombohedral LaAlO3 and theorthorhombic LaGaO3 are the most stable structures, inboth calculations within LDA and GGA at 0K, which areconsistent with the experimental observations [31,32]. Thecalculated enthalpies of the O! R phase transition inLaGaO3 and of the R! C phase transition in LaAlO3 areof the same order of magnitude as the measured values (seeabove). However, the direct comparison is not possible,since the low-temperature heat capacity data for C-LaAlO3

and R-LaGaO3 are not available. The calculated datapresented in Tables 3 and 5 show that O-LaAlO3, C-LaAlO3, R-LaGaO3 and C-LaGaO3 are metastable struc-tures at ambient conditions, while they can, in principle, beobtained at sufficiently high pressure because the changesof volume from their stable structures of groundstate arenegative.

The enthalpies of formation of the perovskites fromtheir constituent binary oxides, D�f ;oxH, were calculatedaccording to

D�f ;oxH ¼ EtotðLaMO3Þ � 0:5EtotðLa2O3Þ � 0:5EtotðM2O3Þ.

(1)

Using the heat content data in the temperature range of0–298.15K, which are summarized in Table 6, the

Table 5

The calculated enthalpy of O- and C-LaMO3 perovskites relative to the

rhombohedral structure

Perovskite DH ðkJmol�1Þ

LDA GGA

O-LaAlO3 þ1:25 þ0:35O-LaGaO3 �2:30 �3:34C-LaAlO3 þ1:50 þ2:25C-LaGaO3 þ25:53 þ31:87

Table 6

The heat contents of the compounds in the temperature range 0–298.15K

ðkJmol�1Þ

Compound a-Al2O3 b-Ga2O3 A-La2O3 R-LaAlO3 O-LaGaO3

H298:15–H0 10.014 14.510 19.842 14.570 17.521

Reference [33] [34] [35] [32] [6]

Table 7

The enthalpies of formation of stable LaMO3 perovskites from the constituen

Perovskite Calculated at 0K Extrapolated to 298

LDA GGA LDA

R-LaAlO3 �66.84 �40.04 �67.20

O-LaGaO3 �50.34 �26.74 �49.99

enthalpies of formation at 0K were extrapolated to298.15K. Generally, the heat content difference for thesynthesis reaction of the LaMO3 perovskites between 0 and298.15K is smaller than 1:0 kJmol�1. The enthalpies offormation of the perovskites are summarized in Table 7.The results show that the values calculated within LDAagree quite well with the available experimental data, whilethose calculated within GGA are much less negative forboth perovskites.At present, there is no consensus in the literature, which

approximation, i.e., LDA or GGA gives better results. Theresults of the ab initio calculations depend on the softwarepackages and approximations to be employed. In theworks on oxides [36–39], the structural parameters of HfO2

[36] and BaTiO3 [37] calculated within LDA were found tocompare better with experiments than those calculatedwithin GGA, while the opposite is true in the case ofPbZrO3 [38], PbTiO3 [38,39], and BaTiO3 [39]. Althoughthe LDA fails to describe the exchange-correlation hole inall its details, in some case, it does describe the integratedaverage value exactly, and this was proven to be essentialfor the accurate predictions of materials properties [40].Further improvements in theory and methodology aredefinitely necessary for the accurate predictions of theproperties of perovskites.

4. Summary and conclusions

Ab initio calculations were successfully employed tostudy the polymorphous LaMO3 perovskites (M ¼ Al, Ga)as well as the constituent binary oxides based on densityfunctional theory (DFT) and projector augmented wavemethod (PAW) using both the LDA and GGA. The bestagreement with experimental data concerning the latticeparameters and the volume of the unit cell of a-Al2O3 andb-Ga2O3, which consist of p-elements, was obtained withinLDA, whereas GGA works better for La2O3. Theexperimental crystal structure data for LaMO3 perovskiteswere found to lie in between the values calculated withinGGA and LDA. The calculations correctly predicted therhombohedral LaAlO3 and the orthorhombic LaGaO3 tobe ground state configurations at the absolute zerotemperature and zero pressure, and the calculated enthal-pies of the O! R phase transition in LaGaO3 and of theR! C phase transition in LaAlO3 are consistent withexperimental data. The crystallographic parameters and

t binary oxides ðkJmol�1Þ

.15K Experimental data at 298K Reference

GGA

�40.40 69.61 73.23 [3]

�26.39 �52.39 71.99 [3]

�54.3 71.5 [4]

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the relative lattice stabilities of the metastable orthorhom-bic LaAlO3 and cubic LaGaO3 were calculated. Theenthalpies of formation of the perovskites from theconstituent binary oxides at 298.15K calculated withinLDA, �67:19 and �49:99 kJmol�1 for the stable config-urations of LaAlO3 and LaGaO3, respectively, agree wellwith the available experimental data, while the enthalpiescalculated within GGA are much less negative. It was thefirst time that recurred the experimental enthalpies offormation at 298.15K for the stable configurations ofLaAlO3 and LaGaO3 from a fundamental ab initio

calculation.

Acknowledgments

The authors thank Dr. Chong Wang for helpfuldiscussions. One of the authors, Dr. Bo Wu, gratefullyacknowledges the scholarship provided by Max-Planck-Gesellschaft.

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