Orthorhombic to trigonal phase transition of perovskite-type (Ndx,Sm1−x)AlO3

Journal of Alloys and Compounds 266 (1998) 104–110

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Orthorhombic to trigonal phase transition of perovskite-type (Nd x ,Sm 12x )AlO 3 1 ,a a a, b b Akira Yoshikawa , Akihiro Saitow , Hiroyuki Horiuchi *, Toetsu Shishido , Tsuguo Fukuda a

Mineralogical Institute, Graduate School of Science, University of Tokyo, Hongo, Bunkyo, Tokyo 113, Japan b Institute for Materials Research, Tohoku University, Katahira, Aoba, Sendai, 980, Japan Received 21 June 1997

Abstract Phase transition of solid solution phases of (Nd x ,Sm 12x )AlO 3 was investigated by powder X-ray diffraction technique. The transition temperature T c from orthorhombic to trigonal structure is linearly related to x in (Nd x ,Sm 12x )AlO 3 with the relation of T c (8C)52 1043.4x1785.8 as an approximation at ambient pressure. This transition is reversible against the change of temperature. At room temperature, the structural change from orthorhombic to trigonal system takes place at around x50.73 when x varies from 0.0 to 1.0 in (Nd x ,Sm 12x )AlO 3 . Thus, the average ionic radius of R31 plays an important role to decide the structure of RAlO 3 , and an appropriate selection of ionic radius r R for R will function so as to control temperature and / or pressure for the structural change. As a result, structural diagram of RAlO 3 given by temperature condition and atomic number of R, which implies a phase diagram under pressure and temperature conditions, was proposed. Change of molar volume of a series of RAlO 3 was also discussed based on both effects of temperature and ionic radius R31 .  1998 Elsevier Science S.A. Keywords: Structure of (Nd x ,Sm 12x )AlO 3 ; Phase transition; Phase diagram of RAlO 3 ; X-ray diffraction

1. Introduction Perovskite-type structures of a chemical formula ABO 3 have widely been studying from the interests of ferroelectric magnetic properties and so on. Among them, rare-earth orthoaluminates RAlO 3 are also one of potential candidate materials as a substrate on which oxide thin film with perovskite-related structures is made. Perovskite-type RAlO 3 shows various structural behaviours which involve phase transition caused by a slight deformation from its ideal cubic structure, and these behaviours are governed by kinds of R cations as well as by temperature and / or pressure conditions. Therefore, basic knowledge of the relationship among the effects of ionic radii of R31 , temperature and pressure conditions on their structural characteristics will be indispensable for better understanding their physical properties and for their advanced applications. Lattice constants of a series of RAlO 3 systematically *Corresponding author. 1 Current address: Institute for Materials Research, Tohoku University, Katahira, Aoba, Sendai, 980, Japan. 0925-8388 / 98 / $19.00  1998 Elsevier Science S.A. All rights reserved. PII S0925-8388( 97 )00449-0

change depending on the ionic radius of R31 , furthermore, the phases with larger ions of R5La|Nd except Ce crystallize in trigonal structures with rhombohedral lattice and those with smaller ions of R5Sm|Lu are orthorhombic [1,2]. CeAlO 3 is exceptional and it crystallizes in pseudotetragonal structure [3]. Most of these phases could be synthesized by solid state reaction at 16008C and at atmospheric pressure by Shishido et al. [4], however, the phases such as YbAlO 3 and LuAlO 3 which contain smaller R31 are not stable in such a high temperature but they could be synthesized only at lower temperature and / or higher pressure compared with other RAlO 3 phases. For example, they were synthesized at 32.5 Kbar and 12008C using NaOH flux by Dernier and Maines [2], and also at relatively low temperature of 9608C using KF flux by Shishido et al. [4] at atmospheric pressure. It is of interests to note the structural change which takes place by an appropriate selection of R31 ion. This selection is effective for changing ionic radius of R31 in the structure and it may imply a structural change caused by apparently changing temperature and / or pressure. In particular, the intermediate phases between SmAlO 3 (orthorhombic) and NdAlO 3 (trigonal) are interest-

A. Yoshikawa et al. / Journal of Alloys and Compounds 266 (1998) 104 – 110

ing objects in order to explicate the relationship of both effects of ionic radii of R31 and temperatures on the crystal structures. In fact, Yoshikawa et al. [5] synthesized solid solution phases of (Nd x , Sm 12x )AlO 3 in the range of x50.0|1.0 with interval of 0.2, and a change from orthorhombic to trigonal structure was found at the value of x between 0.6 and 0.8. Orthorhombic to trigonal phase transition was also observed by O’Bryan et al. for SmAlO 3 [6], and that of trigonal to cubic structure was observed by Geller and Raccah [7] for the solid solution of (La 12x , Pr x )AlO 3 and NdAlO 3 . All phases of (La 12x , Pr x )AlO 3 and NdAlO 3 belong to trigonal structure at room temperature, and phase transitions from trigonal to cubic structures were confirmed at high temperatures for all of LaAlO 3 , PrAlO 3 and NdAlO 3 . As a result, phase boundary between cubic and trigonal structures was decided by Geller and Raccah [7] as a function of temperature against species R, however, the boundary between trigonal and orthorhombic phases is still unknown. In this paper, structural change from orthorhombic to trigonal system by substitution of Nd for Sm for the solid solution of (Nd x , Sm 12x )AlO 3 was studied in detail at room temperature, and furthermore, phase transitions from orthorhombic to trigonal structure of (Nd x , Sm 12x )AlO 3 were investigated for the phases of x50.0, x50.4 and 0.6 by means of high-temperature powder X-ray diffraction technique. As a result, the phase boundary between trigonal and orthorhombic structures was decided as a function of temperature against an average atomic number of R, which intimates a change of ionic radius of R31 . In addition, both change rates of molar volume of RAlO 3

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against temperature increase and against the substitution of larger R31 for smaller ones were estimated, and their relationship was discussed.

2. Experiments

2.1. Samples Eight kinds of phases (Nd x , Sm 12x )AlO 3 with x50.0, 0.2, 0.4, 0.6, 0.73, 0.76, 0.8 and 1.0 were prepared in order to observe the structural change by the substitution of Nd for Sm. In addition, three orthorhombic phases of above specimens with x50.0, 0.4 and 0.6 were used for hightemperature powder X-ray diffraction experiments. These samples were prepared by a solid state reaction using mixtures of commercial reagents (High Purity Chemicals Co Ltd.) of Nd 2 O 3 (purity; 99.99%) and Sm 2 O 3 (purity; 99.99%) and Al 2 O 3 (purity; 99.999%). The reaction was performed using a graphite crucible in He gas atmosphere, and reaction temperature and time are 16008C and 2 h, respectively. The crystalline particle sizes of products were less than 3 mm. The lattice constants of these phases which we previously reported were summarized in Table 1 for the later discussion.

2.2. Structural change of ( Nd x , Sm12 x ) AlO3 by substitution of Nd for Sm Parts of powder X-ray diffraction patterns of (Nd x , Sm 12x )AlO 3 for various x, which were observed at room temperature of 238C, were shown in Fig. 1. The weak

Table 1 Lattice constants of RAlO 3 (R5La–Lu) and (Nd x , Sm 12x )AlO 3 NA

R

57 La 58 Ce 59 Pr 60 Nd 0.8Nd10.2Sm 0.6Nd10.4Sm 0.4Nd10.6Sm 0.2Nd10.8Sm 62 Sm 63 Eu 64 Gd 65 Tb 66 Dy 67 Ho 68 Er 69 Tm 70 Yb 71 Lu

˚ a/A

˚ b/A

˚ c/A

a/8

Z

Molar ˚3 vol. / A

Structure

5.353(2) 3.763(1) 5.308(1) 5.290(3) 5.287(2) 5.311(1) 5.303(1) 5.296(1) 5.288(1) 5.269(1) 5.253(1) 5.226(1) 5.206(1) 5.183(1) 5.163(1) 5.145(1) 5.123(1) 5.107(5)

– – – – – 5.294(1) 5.292(1) 5.291(1) 5.284(1) 5.291(1) 5.299(1) 5.304(1) 5.318(1) 5.318(2) 5.328(1) 5.323(3) 5.327(2) 5.330(5)

– 3.792(1) – – – 7.486(5) 7.471(3) 7.478(5) 7.469(2) 7.456(1) 7.441(1) 7.417(1) 7.392(1) 7.370(3) 7.354(1) 7.325(3) 7.303(2) 7.298(7)

60.12(2) – 60.29(1) 60.39(4) 60.41(2) – – – – – – – – – – – – –

2 1 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4

54.40 53.69 53.20 52.80 52.75 52.60 52.40 52.37 52.18 51.97 51.78 51.40 51.17 50.80 50.58 50.15 49.83 49.66

Trig. Tetra. Trig. Trig. Trig. Ortho. Ortho. Ortho. Ortho. Ortho. Ortho. Ortho. Ortho. Ortho. Ortho. Ortho. Ortho. Ortho.

NA ; atomic number; Trig.; Trigonal structures with rhombohedral lattices (La–Lu), Tetra.; Pseudotetragonal structure(Ce), Ortho.; Orthorhombic structures (Sm–Lu). Z; Number of molecular unit of RAlO 3 in the unit cell. Data were summarized from Tanaka et al. [3], Shishido et al. [4], and Yoshikawa et al. [5].

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Fig. 1. Powder X-ray diffraction patterns which show structural change against chemical composition of x of (Nd x , Sm 12x )AlO 3 . The pattern with x50.73 is trigonal but a very small amount of orthorhombic phase seems still remaining.

reflections of 311 and 131 observed at 2u 5568|578 are characterized only by an orthorhombic phase, and larger ¯ peak separations of 200 and 222 at 2u 5418|428 and 211 and 321 at 2u 5548|558 are more remarkable in rhombohedral phases than orthorhombic phases. Thus, the reflections for the phases of x#0.6 can be indexed on the basis of an orthorhombic lattice and those for x$0.76, by a rhombohedral lattice. The phase of x50.73 is also clearly trigonal but it seems a very small amount of orthorhombic phase coexists because very weak 311 and 131 reflections still remain if these peak positions are scrutinized. Therefore, as an approximation, it will be assumed that the crystal structure of (Nd x , Sm 12x )AlO 3 changes from orthorhombic to trigonal at the chemical composition of around x50.73 at room temperature (around 238C) by substitution of Nd for Sm.

2.3. High-temperature powder X-ray diffraction Experiments of high-temperature powder X-ray diffraction were performed using CuKa radiation with condition of 40 kV and 40 mA (Model; JDX-3530 / DX-GOHV1, JEOL Ltd., Japan). Pyrolytic graphite was used as an analyzer monochromator. The samples were filled in a Pt?Rh10% sample holder with depth of 0.5 mm and the experiments were performed in air. Divergence and scattering slits used were 1 degree in their apertures, and receiving slit was 0.2 mm in the width. The u –2u scan method was applied with step width of 0.02 degrees for 2u angle and counting time was 10 sec at each step. Temperatures were monitored and controlled by a Pt–Pt?Rh13% thermocouple. The temperature gradient in the sample area is less than 18C up to the temperature around 10008C. The temperature intervals in the process of increasing and decreasing temperatures were 58C at the temperature near phase transition.

2.3.1. SmAlO3 O’Bryan et al. [6] observed the orthorhombic to trigonal phase transition by combination of powder X-ray diffraction, thermal analysis and the dilatometric thermal expan-

sion. As a result, they reported that the phase transition temperature of SmAlO 3 was 7858C. We also reconfirmed above results. Powder X-ray diffraction patterns at the temperatures of 7808C and 8008C were shown in Fig. 2 for 2u range between 528 and 588. Their reflections can be explained on the basis of the orthorhombic and trigonal lattice constants, respectively. The weak reflections of 311 and 131 at 7808C, which are characterized only by an orthorhombic structure, are not observed at 8008C, and the overlapped stronger peaks of 310, 130, 222 and 114 of orthorhombic phase at 7808C are more separated at 8008C ¯ and 321 on the basis of a and they are indexed as 211 rhombohedral lattice. Thus, the phase transition temperature of 7858C reported by O’Bryan et al. [6] was confirmed also in this experiment.

2.3.2. ( Nd0.4 , Sm0.6 ) AlO3 and ( Nd0.6 , Sm0.4 ) AlO3 High-temperature powder X-ray diffraction experiments were performed at the temperature ranges of 258C|4208C, and 258C|2008C, for (Nd 0.4 , Sm 0.6 )AlO 3 and (Nd 0.6 , Sm 0.4 )AlO 3 , respectively. The diffraction profiles which were observed in the 2u ranges of 418|438 and 548|568 were shown in Fig. 3a and b, respectively. The changes of profiles which are due to the phase transition from orthorhombic to trigonal structure were observed at around 3708C and 1608C, respectively. Reflection indices of Fig. 3a and b for lower and higher temperature phases were assigned on the basis of the orthorhombic and rhombohedral lattice constants, respectively, as described in the phase transition of SmAlO 3 . It seems that both orthorhombic and trigonal phases coexist at around phase transition temperatures within a width of about 658C. This will be discussed later again. There were some difficulties for peak decomposition of overlapped peaks at near phase transition temperatures because of the coexistence of two phases. Therefore, the 2u

Fig. 2. Powder X-ray diffraction patterns of SmAlO 3 at 7808C and 8008C. 7808C; Orthorhombic structure, 8008C; trigonal structure. The peak near 58.58 is from the Pt sample holder.

A. Yoshikawa et al. / Journal of Alloys and Compounds 266 (1998) 104 – 110

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Fig. 3. Powder X-ray diffraction patterns at increasing temperatures; (a) (Nd 0.4 , Sm 0.6 )AlO 3 , (b) (Nd 0.6 , Sm 0.4 )AlO 3 . Structure changes from orthorhombic to trigonal system at around 3708C and 1608C, in (a) and (b), respectively.

value of each reflection was carefully analyzed with aid of a peak decomposition program, PROFIT by Toraya [8], and the lattice constants were obtained by least-squares method.

2.3.3. Reproducibility of the phase transition The phase transition phenomena were repeatedly observed by increasing and decreasing temperatures. One of examples was shown in Fig. 4 for the 2u range of 538 and 578 for the case of (Nd 0.4 , Sm 0.6 )AlO 3 . In this experiment, the temperature was repeatedly changed in the temperature range between 3458C and 4108C at interval of 58C. The rate of increasing or decreasing temperatures is 108C min 21 , and 2 min were spent at each temperature before measurement. Thus, the phase transition reversibly take places against increasing and decreasing temperatures.

3. Results and discussion

3.1. Phase diagram of ( Nd x , Sm12 x ) AlO3 The phase transition temperatures, T c , from orthorhombic to trigonal structures of (Nd x , Sm 12x )AlO 3 for x50.0,

Fig. 4. X-ray powder diffraction pattern of (Nd 0.4 , Sm 0.6 )AlO 3 at the condition of repetition of increasing and decreasing temperatures. Structural changes are reversible against temperature changes.

0.4 and 0.6 were around 7858C, 3708C and 1608C, respectively, at high temperatures. In addition, structural change of (Nd x , Sm 12x )AlO 3 from orthorhombic to trigonal by substitution of Nd for Sm takes place at x50.73 at room temperature (238C). A set of these data, (x, T c ), were plotted, using solid circles as a boundary between trigonal and orthorhombic phases in Fig. 5. As a first approximation, the relationship between x and T c will be assumed to be linear. Their relationship was decided by leastsquares fitting and the result was given in Table 2. As a result, structural boundary between trigonal and orthorhombic phases of (Nd x , Sm 12x )AlO 3 was decided as shown by a solid line in Fig. 5. In this figure, the structural boundary between trigonal and cubic structures was also given based on the results by Geller and Raccah [7]. Thus, structural boundaries among cubic, trigonal and orthorhombic phases of RAlO 3 against atomic numbers of R are summarized in Fig. 5. It is of interest to note that the diffraction patterns showing structural changes of (Nd x , Sm 12x )AlO 3 shown in

A. Yoshikawa et al. / Journal of Alloys and Compounds 266 (1998) 104 – 110

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Fig. 5. Structural diagram of temperature against atomic number of R. In the phases for x50.4 and 0.6 in (Nd x , Sm 12x )AlO 3 , atomic numbers are the values given by 60x162(12x).

Fig. 1 is apparently analogous to those observed by temperature increase given in Fig. 3. Since ionic radius of R31 approximately linearly increases against the decrease of the atomic number of R, polyhedral volume RO 12 in the RAlO 3 structure also increases accompanied with the same change as above. The similar volume expansion will be achieved also in the structures by temperature increase, in which thermal vibrations of lattices are yielded. On the other hand, in solid solution of (Nd x , Sm 12x )AlO 3 in which Sm 31 is partially substituted by Nd 31 , a statistical fluctuation of the size of RO 12 polyhedra will be occurred in the structure. Thus, what are happening in both struc-

tures at elevated temperatures and of solid solution at room temperature are physically different, however, it will be considered that the time-averaged and space-averaged structures of above both structures are analogous. This will be one of essential reasons why structural behaviours in Fig. 1 and Fig. 3 resemble to each other. Ionic radii r R for R31 calculated by r R 5x?r(Nd 31 )1(12x)?r(Sm 31 ) are given in Table 2, where, r(Nd 31 ) and r(Sm 31 ) are 1.12 ˚ respectively [9]. and 1.09 A, As the same discussion as above, phenomena of the decrease of unit cell volume of RAlO 3 against the increase of atomic number of R will be considered to be analogous to the compression of volume by pressure. Therefore, the horizontal axis in Fig. 5 may be regarded as a change of pressure. As a result, the structural diagram of Fig. 5 will imply phase diagram of RAlO 3 under various temperature and pressure conditions. There were some difficulties in order to decide a clear phase transition temperature T c for (Nd x , Sm 12x )AlO 3 . This is because both reflections from low and high temperature phases were observed in the powder X-ray diffraction pattern, showing temperature width of about 658C at each T c . These phenomena did not change even if either the temperature were very slowly increased or decreased, or the temperature was hold for long time in those temperature ranges. Since the temperature gradient of the sample holder is less than 18C in these experimental conditions, these phenomena are not attributed to the temperature gradient in the samples. If a slight compositional heterogeneity exists in the sample, it will make an apparent width for the transition temperature T c . In fact, even compositional heterogeneity of Dx50.01 in (Nd x , Sm 12x )AlO 3 will make a temperature width of about 108C for T c from the relation of T c to x in Table 2. This might be quite reasonable because such a compositional heterogeneity in the powder sample will be probable in preparation by a solid state reaction even though the syntheses are carefully performed.

Table 2 Transition temperature T c from orthorhombic to trigonal phase against x in (Nd x , Sm 12x )AlO 3 R

N

31

Eu Sm 31 (Sm x ,Nd 12x ) Nd 31

63 62.0 61.2 60.8 60.54 60

x

0.00 0.40 0.60 0.73 1.0

˚ r/A

1.09 1.102 1.108 1.112 1.12

R; Rare earth ion for RAlO 3 . N; Averaged atomic number given by 60x162(12x). r; Averaged atomic radius given by r5x?r(Nd 31 )1(12x)?r(Sm 31 ). Relation of T c to x; T c 521043.4x1785.8. Estimated T c for EuAlO 3 and NdAlO 3 were calculated by above relation. a Transition temperature from O’Bryan et al. [6].

T c (8C)

Difference

Observed

Estimated

785.0 a 370.0 160.0 23.0

1307.8 785.8 368.4 159.7 24.1 2257.3

20.8 1.6 0.3 21.1

A. Yoshikawa et al. / Journal of Alloys and Compounds 266 (1998) 104 – 110

Fig. 6. Change of molar volume against the ionic radius r R of R in RAlO 3 . The ionic radii r R in (Nd x , Sm 12x )AlO 3 are given by r R ? r(Nd 31 )1(12x)?r(Sm 31 ).

3.2. Effects of temperature and ionic radius on the unit cell volume Molar volumes of a series of RAlO 3 are plotted against ionic radii of R31 in Fig. 6. As a first approximation, they are linearly related to each other, in particular, in the narrow range around the phases of (Nd x ,Sm 12x )AlO 3 . This linearity will be probable because the difference of ionic radii r R in these phases is very small as shown in Table 2, although the volume should be related to r 3R in fact. As a result, the value of dV / dr R , can be estimated to be 21.6 ˚ 3 / mol?A ˚ from Fig. 6. Our recent results of the structure A analyses of (Nd x ,Sm 12x )AlO 3 and other RAlO 3 showed that Al–O distances of AlO 6 octahedra are not affected so much by a selection of R [10]. Therefore, it is considered that the value of dV / dr R is approximately depending only on the kinds of R, therefore, the value of dV / dr R becomes | dVR / nearly equal to dVR / dr R , then it results in dV / dr R 5 dr R where VR is the volume of RO 12 polyhedra in the structure. On the other hand, the change of the molar volumes against temperature increase for (Nd 0.4 , Sm 0.6 )AlO 3 and (Nd 0.6 , Sm 0.4 )AlO 3 were plotted in Fig. 7. These unit cell volumes were calculated from the lattice constants listed in Table 2. As a result, the value of dV / dT is estimated to be ˚ 3 / mol?8C for both (Nd 0.4 , around 1.17310 23 A

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Sm 0.6 )AlO 3 and (Nd 0.6 , Sm 0.4 )AlO 3 . Where, V is the unit cell volume which is given by the sum of V5VR 1VAl , where, VR and VAl are the volume of RO 12 and AlO 6 polyhedra in RAlO 3 , respectively. In discussion of thermal expansion, it is considered to be the sum of both expansion of VR and VAl . In an ideal cubic perovskite-type structure of ABO 3 , since the volume ratio of AO 12 to BO 6 polyhedra is 5:1, then V approximately satisfies V51.2 VR in RAlO 3 structures. Therefore, if the thermal expansion is assumed to be uniform in the structure, the equation of dVR / dT5(1 / 1.2) dV / dT will be satisfied. As a result, the value of ˚ 3 / mol?8C. If we compare dVR / dT becomes 0.98310 23 A ˚ 3 / mol?A ˚ using this value of dVR / dT with dVR / dr R 521.6 A a constant k as dVR / dT5k?dVR / dr R , k results in k54.53 ˚ / 8C. This means that the temperature change of 18C 10 25 A ˚ of ionic is roughly equivalent to the change of 4.5310 25 A radius r R against the volume change of RO 12 polyhedron. In fact, the thermal expansion may not be uniform in the structure, however, the above estimation will be adequate as an approximation.

3.3. Characteristics of the crystal structures Possible space groups of the structures of orthorhombic phases of (Nd x ,Sm 12x )AlO 3 can be concluded to be Pbnm from our recent structural studies on a series of RAlO 3 and (Nd x ,Sm 12x )AlO 3 [10]. Thus, these structures are isomorphic with orthorhombic perovskite-type phases such as CaTiO 3 [11], GdFeO 3 [12], MgSiO 3 [13] and SmAlO 3 [14] and so on. Detailed results of structure analyses of a series of RAlO 3 will be published elsewhere. Structural change from orthorhombic to trigonal of these phases is considered to be a first-order phase transition. This consideration will be reasonable because the orthorhombic space group, Pbnm, does not belong to the ¯ which is the space group of their highsubgroup of R3c temperature phases, and also because the phase transition of SmAlO 3 , which is one of end-members of (Nd x ,Sm 12x )AlO 3 , shows a first-order phase transition [6].

3.4. Conclusion

Fig. 7. The change of molar volume against temperatures for (Nd 0.4 , Sm 0.6 )AlO 3 and (Nd 0.6 , Sm 0.4 )AlO 3 . Open circles; orthorhombic phase, Closed circles; trigonal phases.

1) Phase transitions from orthorhombic to trigonal structures were observed in perovskite-type (Nd x ,Sm 12x )AlO 3 and the transition temperatures T c are linearly related to x, showing T c (8C)521043.4x1785.8, as a first approximation. 2) Phase transition in these phase is reversible against the increase and decrease of the temperature. 3) Phase boundary between trigonal and orthorhombic structures of RAlO 3 against average atomic number of R was decided as a result, and this diagram will imply a phase diagram of a fixed composition under various temperature and pressure conditions. 4) The change of ionic size of R31 will be intimately related to the

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effects of changes of temperature and / or pressure in RAlO 3 structures. As an example, change of ionic radii of ˚ by an appropriate selection of R will imply an 4.5310 25 A effect of the change of 18C on the structural change of RAlO 3 . Thus, selection of an appropriate average ionic size which can be given by r R 5x?r(Nd 31 )1(12x)? r(Sm 31 ) or other appropriate combination of neighbouring rare-earth ions is one of important keys in order to predict a stable structure for RAlO 3 , and an adjustment of ionic radius of R31 in the structure of RAlO 3 will imply a role so as to control temperature and / or pressure for the structural change.

Acknowledgements The authors are grateful to Mr. R. Note of the Institute for Materials Research, Tohoku University for his help on the syntheses of the samples, and Mr. K. Ando and Dr. I. Minato of X-ray Laboratory of JEOL, Ltd. for their kind help on the high-temperature powder X-ray diffraction experiments. This work was financially supported by Grant-in-Aid for General Scientific Research (B)-07459008(HH) and Scientific Research on Priority Area 09242208(HH) and 07230102(TS) of the Ministry of Education, Science and Culture of Japanese Government. This investigation was

carried out under the Inter-University Cooperative Research Program of the Institute for Materials Research, Tohoku University, Japan.

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