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Examination of X-ray diffraction pattern of BaTiO3
0038-1098/88 $3.00 + .00 Pergamon Press plc
Solid State Communications, Vol. 68, No. 6, pp. 571-574, 1988. Printed in Great Britain.
E X A M I N A T I O N OF X - R A Y D I F F R A C T I O N P A T T E R N OF BaTiO3 N. Ohnishi*, N. Koshiji, K. Iriet and A. Okazaki Department of Physics, Kyushu University, Fukuoka 812, Japan
(Received 28 June 1988 by W. Sasaki) Anomalous diffraction patterns with several 4 0 0 and 0 0 4 peaks were observed for butterfly crystals of BaTiO3 at and just below the cubic-totetragonal phase transition [1]. The appearance of similar phenomena has been confirmed for a flux-grown crystal of different origin and for a crystal which is grown by the top-seeded solution growth. Using the same experimental technique with some improvements, it is proved, in the temperature region mentioned above, that the low-temperature phase consists of several grains. The crystal structure in these grains has a tetragonal symmetry and the same lattice constants; the crystal axes of grains are scattered around a set of the orthogonal directions.
IN T H E H I G H - R E S O L U T I O N experiment by means of the high-angle double-crystal X-ray diffractometry ( H A D O X ) , the present authors and the colleagues found a change in the diffraction pattern of a butterfly BaTiO3 crystal [I]: the 4 0 0 and 0 0 4 peaks in the (o scanning split into several fragments, as shown in Fig. I(a), when the crystal temperature approaches the ferroelectric-to-paraelectric transition, at T, = 393 K, from lower temperatures. Although it was obvious that the specimen was, in an exact sense, no longer a single crystal but a polycrystal consisting of several grains, we did not know the detailed situation. In the present paper we examine whether or not each grain has a tetragonal structure with the same lattice constants; the spatial and orientational distributions of the grains are also discussed. The principle of the measurement and the fundamental arrangement of the diffractometer are the same as those described in [I]. As schematically shown in Fig. 2, the incident FeKat beams were monochromatized with 0 0 4 of SrTiO3 at 0 ~ 82.5°; the second crystal, that was the BaTiO 3 specimen, was mounted on a pulsemotor-driven single-axis goniometer with the angular precision 0.1 s o f a r c [2]. The 0 0 4 and 4 0 0 diffractions at 0 ~ 74 ° were detected with a scintillation counter with an active area 20 m m in diameter. In the previous experiments on BaTiO3 [I] and other crystals [3], no slits were placed in front of the detector: the window of the detector was fully open. In such
cases, the observed diffraction pattern in 09 scanning can be interpreted in terms of the lattice constants only when the direction of the scattering vector is kept unchanged. In the present case we need to limit the width of the active area of the detector in order to get a reasonable resolution in 20. The detector with a slit of variable widths is therefore mounted on a stage which can be linearly moved, in the diffraction plane, in the direction normal to the finally diffracted beams. In Fig. 3, the Ewald construction in the reciprocal space is given, which corresponds to the situation in the real space shown in Fig. 2. The line drawn at the tip of the wavevector k of the scattered X-rays is normal to k, and represents the range covered by the detector with an open window. In the present doublecrystal arrangement, Ak/k is as small as 10-4; the thickness of the line is therefore negligible. The inset
O04tetr
~
4 0 0 c u b 4 0 0 tet r
~
(a)
(b) -
-
-
(c)
/10 3, Fig. I. The H A D O X (o-scan patterns of BaTiO3 at T,. (a) For the case with an open slit and (b)-(d) for those of 240 s resolution in 0. The assignment of the peaks are given.
* Present address: Mitsubishi Kasei Corporation, Sakaide Plant, Sakaide 762, Japan. t Present address: Kurume College of Technology, Kurume 830, Japan. 571
572
X-RAY D I F F R A C T I O N P A T T E R N OF BaTiO~
monochromator crystal ~ ' FeKo~1 .~........,.~ ~ specimen . ~ / crystal 2e,w '~ ~_
detector
"~ slide stage Fig. 2. The experimental arrangement in HADOX. In the new version, 20 scanning of the detector with a slit is available in addition to to scanning of the specimen crystal.
shows, in a very expanded scale, a plausible example of the distribution of the split reciprocal-lattice points of 400. In the case of a simple domain-structure of a tetragonal phase, 4 0 0 and 0 0 4 appear on a radial direction from the origin; a set of points marked 400,¢, and 004,., corresponds to the grains with slightly different orientations. The line mentioned above is also shown. In the ~o scanning, the points move nearly vertically in the figure; when the points cross the line, we observe the diffraction. For the clockwise rotation of the crystal (~o), i.e. the upwards movement of the reciprocal lattice points, we successively observe a set of 004,o. first, and then 400,~,~; if the cubic phase coexists, 40 0~, will be observed in the middle. The pattern in Fig. I(a) can be explained by assuming this situation. For quantitatively discussing the distance from the origin for each point, i.e. the dvalue for each grain, we must improve the resolution in 20, limiting the beam-receiving area with a slit. This introduces a shortening of the line in the inset of Fig. 3. To avoid the intensity loss owing to cutting the diffracted beam. the slit 2 mm in width is used at the distance 860 mm from the specimen crystal. (Unless the beam path is evacuated, the path-length over 2 m will result in serious X-ray absorption by air.) In this geometry we get a
I \400cu b /~OOtet~. ! O04tetr 0
Fig. 3. The Ewald construction for H A D O X . The inset shows an example of the splitting of the reciprocal lattice point 4 0 0 at T, in an expanded scale.
Vol. 68, No. 6
resolution 240s for 0, and a precision 10-s or better for Ad/d. After getting the ,) scanning pattern shown in Fig. I(a), the tJ~ position of the specimen was tixed in turn at the peak positions; from the position of the maximum intensity in the step-scan measurements of the detector with a slit (Fig. 2). we determine the 0 value for each peak in the o~ scanning. It turned out that the 0 values lbr the three peaks of 0 0 4 .... coincide within the experimental precision. A similar situation is found for 400,~tr: For the four peaks a single 0 value is found which is different from that for 0 04~,,,,. For 400~oh, another 0 value is observed between the other two. The patterns given in Fig. l(b)-(d) are then observed, in the o, scanning, with the detector and slit fixed at the relevant 0 positions. In (b), tbr example, only three peaks corresponding to the same dvalue are observed: the other peaks seen in (a) therefore have different d values. We can conclude from Fig. I that the pattern of the low temperature phase can be assigned with the two d values, namely those based on the lattice constants a and c; this is compatible with the tetragonal symmetry. A slight difference in the relative intensities of the peaks observed without and with the slit, namely those in (a) and (b) respectively for instance, can be attributed to the thct as follows: The slit 2 mm in width may cut, partly and unequally, the beams diffracted from the grains which are inhomogeneously distributed in the diffraction area of the specimen 2 mm in diameter. It might happen that the grain distribution is variable with time. In fact, as mentioned in [I], the distribution was unstable around r~ at the earlier stage of a series of experiments; after about 20 thermal cycles of experiments crossing T, over a two-year period, it was realized that the grain distribution at 7], became stable, for a week at least. This change made the present authors possible to make the measurements mentioned above, and others described in the following. Another point to be noted in Fig. 1 is that the separation of peaks for 4 0 0,~,, or 0 0 4,~,r is reproducible to some degree, though the number of peaks of them is not constant. ()wing to this. and the fact that such splitting is not observed for 40 0~.,h, a model of twinning in the tetragonal structure could elucidate the pattern. Actually the twin structure in tetragonal BaTiO~, mainly at room temperature, has been extensively studied [4]; the twins with the ~tI 0 1 } boundaries bring about the slightly tilted (I 0 0) planes. However, instead of the observed separation 300-600 s in o), the ~I 0 I I model predicts the value of 830s on the basis of the experimental value of a/c near 71, 0.996 given by Shebanov [5]; the peak separation observed in the present experiment about 2 K below 71 confirms this
Vol. 68, No. 6
573
X - R A Y D I F F R A C T I O N P A T T E R N O F BaTiO3
Table 1. Energy, wavelength and penetration depth of X-rays relevant to each h 0 0 reflection h00
Fig. 4. A sketch of a pseudo-twin structure with a {I I I} boundary in a tetragonal lattice. The arrows indicate the direction of spontaneous polarization.
200 400 600 800 1000 1200
X-rays scattered at 0 = 74 ° Energy (keV)
Wavelength (,~)
Penetration depth (#m)
3.2 6.4 9.6 12.8 16.0 19.2
3.87 [ .94 1.29 0.97 0.77 0.65
< 1 2.0 5.3 1 I. I 20.4 33.8
value. A second model is the twins, or pseudo-twins, with the ft I I 1} boundaries, which are formed, across vectors, and hence those of the crystal axes of the the interface, by a relative rotation of 120 ° about grains, are scattered around a set of the cubic axes but ( 1 1 1 ) ; they correspond to the ferroelectric 90 ° only in a limited range. domains as schematically shown in Fig. 4. In contrast The information on the grain distribution along to the ~101} boundary, {1 l l } are not ideal twin the depth from the specimen surface can be obtained boundaries: The twin cannot be formed without a by means of the energy-dispersive version of H A D O X , misfit of the components. This fact may introduce which was developed by Soejima, Okazaki and Mfiller some uncertainty in the tilt angles of the components: [7] and applied to the case of SrTiO3 [8]. In this method, this may also bc connected with the observation that with white incident X-rays and a Ge detector, we the peak splitting occurs in the temperature range observe a series of h 0 0 reflections simultaneously. about 0.3 K below T, only. In other words, the grain Sincc each reflection occurs at a different X-ray energy structure we are concerned is not so stable that it is and therefore at a different effective depth from the only observed in a narrow temperature range below specimen surface, we get the information needed. In /]. This might be just a speculation; a more detailed Table I, the energy and wavelength of X-rays and the examination is necessary. It is worth mentioning, in penetration dcpth for each h 0 0 reflection of BaTiO 3 at addition, that Hatta and Ikushima [6] found a short 0 = 74 ° are shown; for 4 0 0 with FeK~q (6.4keV), we plateau in the heat capacity of BaTiO3 in a range of can survey thc specimen down to the depth of only 0.3-0.1 K below 71. 2 F~m. The measurements were made at several o~ posiCrystals of other origins were also examined in tions of maximum and minimum intensities of the connection with the characteristic features mentioned pattern like that in Fig. l(a). It was found that the above: They are those grown by the Materials relative intensities of the peaks are different for difPreparation G r o u p of the Clarendon Laboratory, UK ferent h 0 0. This suggcsts that the grain distribution is with K F flux, and those by Sanders Association Incor- inhomogeneous along thc dcpth, even in a range of porated, USA with the top-seeded solution method. It 5 ~m. was tbund that they all showed the peak splitting A final remark is related to an anomalous annealsimilar to that described above. It is probable that the ing or relaxation of the structure in the cubic phase phenomenon is inherent in the cubic-to-tetragonal "after passing T,; the phenomenon was found first in transition in BaTiO3. irreproducible to versus tcmperature curves. A correIn the experiments so far mentioned, the measure- sponding anomaly observed in the 20 (or d) versus ments were made on one plane in the reciprocal lattice tempcrature relation is shown in Fig. 5. The d value as shown in Fig. 3; owing to the principle of the for 4 0 0, consequently the lattice constant, is longer double-crystal arrangement, the high-resolution can than the normal value when the annealing in thc cubic be altained in this plane only. In order to examine the phase is not enough. The average heating and cooling diffraction pattern on another plane, perpendicular to rates for (a) and (b) arc 2 and 0.5 K h ~ respectively, the first one, the specimen crystal was remounted after whilc the measurements were made when the temperaturning by 90 ° about the scattering vector: a very turc was fixed at the relevant temperatures. It appears similar peak-splitting was observed again. We infer, that, for faster heating, the excess interatomic distance from the reproducibility of the peak splitting in the is larger, and the temperature above which the heating original mounting, that the directions of the scattering and cooling curves coincide is higher. Hatta and
574
X-RAY D I F F R A C T I O N P A T T E R N OF BaTiO3
Vol. 68, No. 6
Acknowledgements - The authors are grateful to Drs. N. Ohama, Y. Soejima, H. Sakashita and N. Achiwa for discussions and comments. They are also indebted to Drs. B.M. Wanklyn, A. Linz and T. Pollak for growing crystals.
°1 1Itl L
i
!
REFERENCES I. 2.
(b)
3. I
I
/-..0 0
410
TIK
Fig. 5. The lattice constant a determined from the 20 value of 4 0 0 as a function of temperature. The scale for a is arbitrary but common for (a) and (b).
4. 5.
lkushima [6] found, in the specific heat versus temperature curve, a broad hump at T, + 20 K. Although it is hoped to examine further, the anomalies in the lattice constant and in the specific heat might be connected to each other.
6. 7. 8.
K. lrie, M. Shiono, H. Nakamura, N. Ohnishi & A. Ok aza k i, Solid State Commun. 62, 691 ( 1987). N. Ohama, H. Sakashita & A. Okazaki, J. Appl. Cryst. 12, 455 (1979). For example, M. Sato, Y. Soejima, N. Ohama, A. Okazaki, H.J. Scheel & K.A. M/Jller, Phase Transitions 5, 207 (1985). W, Kfinzig, Solid State Phi'sits, Vol. 4, pp. 97124 (edited by F. Seitz and D. Turnbull), Academic Press, New York, London (1957). L.A. Shebanov, Phys. Status Solidi (a) 65, 321 (1981). I. Hatta & A. lkushima, J. Phys. Soc. Japan 41, 558 (1976). Y. Soejima, A. Okazaki & K.A. M(iller, unpublished. A. Okazaki, N. Ohama & K.A. Mfiller, J. Ph)'s. C." Solid State Phys. 19, 5019 (1986).
Solid State Communications, Vol. 68, No. 6, pp. 571-574, 1988. Printed in Great Britain.
E X A M I N A T I O N OF X - R A Y D I F F R A C T I O N P A T T E R N OF BaTiO3 N. Ohnishi*, N. Koshiji, K. Iriet and A. Okazaki Department of Physics, Kyushu University, Fukuoka 812, Japan
(Received 28 June 1988 by W. Sasaki) Anomalous diffraction patterns with several 4 0 0 and 0 0 4 peaks were observed for butterfly crystals of BaTiO3 at and just below the cubic-totetragonal phase transition [1]. The appearance of similar phenomena has been confirmed for a flux-grown crystal of different origin and for a crystal which is grown by the top-seeded solution growth. Using the same experimental technique with some improvements, it is proved, in the temperature region mentioned above, that the low-temperature phase consists of several grains. The crystal structure in these grains has a tetragonal symmetry and the same lattice constants; the crystal axes of grains are scattered around a set of the orthogonal directions.
IN T H E H I G H - R E S O L U T I O N experiment by means of the high-angle double-crystal X-ray diffractometry ( H A D O X ) , the present authors and the colleagues found a change in the diffraction pattern of a butterfly BaTiO3 crystal [I]: the 4 0 0 and 0 0 4 peaks in the (o scanning split into several fragments, as shown in Fig. I(a), when the crystal temperature approaches the ferroelectric-to-paraelectric transition, at T, = 393 K, from lower temperatures. Although it was obvious that the specimen was, in an exact sense, no longer a single crystal but a polycrystal consisting of several grains, we did not know the detailed situation. In the present paper we examine whether or not each grain has a tetragonal structure with the same lattice constants; the spatial and orientational distributions of the grains are also discussed. The principle of the measurement and the fundamental arrangement of the diffractometer are the same as those described in [I]. As schematically shown in Fig. 2, the incident FeKat beams were monochromatized with 0 0 4 of SrTiO3 at 0 ~ 82.5°; the second crystal, that was the BaTiO 3 specimen, was mounted on a pulsemotor-driven single-axis goniometer with the angular precision 0.1 s o f a r c [2]. The 0 0 4 and 4 0 0 diffractions at 0 ~ 74 ° were detected with a scintillation counter with an active area 20 m m in diameter. In the previous experiments on BaTiO3 [I] and other crystals [3], no slits were placed in front of the detector: the window of the detector was fully open. In such
cases, the observed diffraction pattern in 09 scanning can be interpreted in terms of the lattice constants only when the direction of the scattering vector is kept unchanged. In the present case we need to limit the width of the active area of the detector in order to get a reasonable resolution in 20. The detector with a slit of variable widths is therefore mounted on a stage which can be linearly moved, in the diffraction plane, in the direction normal to the finally diffracted beams. In Fig. 3, the Ewald construction in the reciprocal space is given, which corresponds to the situation in the real space shown in Fig. 2. The line drawn at the tip of the wavevector k of the scattered X-rays is normal to k, and represents the range covered by the detector with an open window. In the present doublecrystal arrangement, Ak/k is as small as 10-4; the thickness of the line is therefore negligible. The inset
O04tetr
~
4 0 0 c u b 4 0 0 tet r
~
(a)
(b) -
-
-
(c)
/10 3, Fig. I. The H A D O X (o-scan patterns of BaTiO3 at T,. (a) For the case with an open slit and (b)-(d) for those of 240 s resolution in 0. The assignment of the peaks are given.
* Present address: Mitsubishi Kasei Corporation, Sakaide Plant, Sakaide 762, Japan. t Present address: Kurume College of Technology, Kurume 830, Japan. 571
572
X-RAY D I F F R A C T I O N P A T T E R N OF BaTiO~
monochromator crystal ~ ' FeKo~1 .~........,.~ ~ specimen . ~ / crystal 2e,w '~ ~_
detector
"~ slide stage Fig. 2. The experimental arrangement in HADOX. In the new version, 20 scanning of the detector with a slit is available in addition to to scanning of the specimen crystal.
shows, in a very expanded scale, a plausible example of the distribution of the split reciprocal-lattice points of 400. In the case of a simple domain-structure of a tetragonal phase, 4 0 0 and 0 0 4 appear on a radial direction from the origin; a set of points marked 400,¢, and 004,., corresponds to the grains with slightly different orientations. The line mentioned above is also shown. In the ~o scanning, the points move nearly vertically in the figure; when the points cross the line, we observe the diffraction. For the clockwise rotation of the crystal (~o), i.e. the upwards movement of the reciprocal lattice points, we successively observe a set of 004,o. first, and then 400,~,~; if the cubic phase coexists, 40 0~, will be observed in the middle. The pattern in Fig. I(a) can be explained by assuming this situation. For quantitatively discussing the distance from the origin for each point, i.e. the dvalue for each grain, we must improve the resolution in 20, limiting the beam-receiving area with a slit. This introduces a shortening of the line in the inset of Fig. 3. To avoid the intensity loss owing to cutting the diffracted beam. the slit 2 mm in width is used at the distance 860 mm from the specimen crystal. (Unless the beam path is evacuated, the path-length over 2 m will result in serious X-ray absorption by air.) In this geometry we get a
I \400cu b /~OOtet~. ! O04tetr 0
Fig. 3. The Ewald construction for H A D O X . The inset shows an example of the splitting of the reciprocal lattice point 4 0 0 at T, in an expanded scale.
Vol. 68, No. 6
resolution 240s for 0, and a precision 10-s or better for Ad/d. After getting the ,) scanning pattern shown in Fig. I(a), the tJ~ position of the specimen was tixed in turn at the peak positions; from the position of the maximum intensity in the step-scan measurements of the detector with a slit (Fig. 2). we determine the 0 value for each peak in the o~ scanning. It turned out that the 0 values lbr the three peaks of 0 0 4 .... coincide within the experimental precision. A similar situation is found for 400,~tr: For the four peaks a single 0 value is found which is different from that for 0 04~,,,,. For 400~oh, another 0 value is observed between the other two. The patterns given in Fig. l(b)-(d) are then observed, in the o, scanning, with the detector and slit fixed at the relevant 0 positions. In (b), tbr example, only three peaks corresponding to the same dvalue are observed: the other peaks seen in (a) therefore have different d values. We can conclude from Fig. I that the pattern of the low temperature phase can be assigned with the two d values, namely those based on the lattice constants a and c; this is compatible with the tetragonal symmetry. A slight difference in the relative intensities of the peaks observed without and with the slit, namely those in (a) and (b) respectively for instance, can be attributed to the thct as follows: The slit 2 mm in width may cut, partly and unequally, the beams diffracted from the grains which are inhomogeneously distributed in the diffraction area of the specimen 2 mm in diameter. It might happen that the grain distribution is variable with time. In fact, as mentioned in [I], the distribution was unstable around r~ at the earlier stage of a series of experiments; after about 20 thermal cycles of experiments crossing T, over a two-year period, it was realized that the grain distribution at 7], became stable, for a week at least. This change made the present authors possible to make the measurements mentioned above, and others described in the following. Another point to be noted in Fig. 1 is that the separation of peaks for 4 0 0,~,, or 0 0 4,~,r is reproducible to some degree, though the number of peaks of them is not constant. ()wing to this. and the fact that such splitting is not observed for 40 0~.,h, a model of twinning in the tetragonal structure could elucidate the pattern. Actually the twin structure in tetragonal BaTiO~, mainly at room temperature, has been extensively studied [4]; the twins with the ~tI 0 1 } boundaries bring about the slightly tilted (I 0 0) planes. However, instead of the observed separation 300-600 s in o), the ~I 0 I I model predicts the value of 830s on the basis of the experimental value of a/c near 71, 0.996 given by Shebanov [5]; the peak separation observed in the present experiment about 2 K below 71 confirms this
Vol. 68, No. 6
573
X - R A Y D I F F R A C T I O N P A T T E R N O F BaTiO3
Table 1. Energy, wavelength and penetration depth of X-rays relevant to each h 0 0 reflection h00
Fig. 4. A sketch of a pseudo-twin structure with a {I I I} boundary in a tetragonal lattice. The arrows indicate the direction of spontaneous polarization.
200 400 600 800 1000 1200
X-rays scattered at 0 = 74 ° Energy (keV)
Wavelength (,~)
Penetration depth (#m)
3.2 6.4 9.6 12.8 16.0 19.2
3.87 [ .94 1.29 0.97 0.77 0.65
< 1 2.0 5.3 1 I. I 20.4 33.8
value. A second model is the twins, or pseudo-twins, with the ft I I 1} boundaries, which are formed, across vectors, and hence those of the crystal axes of the the interface, by a relative rotation of 120 ° about grains, are scattered around a set of the cubic axes but ( 1 1 1 ) ; they correspond to the ferroelectric 90 ° only in a limited range. domains as schematically shown in Fig. 4. In contrast The information on the grain distribution along to the ~101} boundary, {1 l l } are not ideal twin the depth from the specimen surface can be obtained boundaries: The twin cannot be formed without a by means of the energy-dispersive version of H A D O X , misfit of the components. This fact may introduce which was developed by Soejima, Okazaki and Mfiller some uncertainty in the tilt angles of the components: [7] and applied to the case of SrTiO3 [8]. In this method, this may also bc connected with the observation that with white incident X-rays and a Ge detector, we the peak splitting occurs in the temperature range observe a series of h 0 0 reflections simultaneously. about 0.3 K below T, only. In other words, the grain Sincc each reflection occurs at a different X-ray energy structure we are concerned is not so stable that it is and therefore at a different effective depth from the only observed in a narrow temperature range below specimen surface, we get the information needed. In /]. This might be just a speculation; a more detailed Table I, the energy and wavelength of X-rays and the examination is necessary. It is worth mentioning, in penetration dcpth for each h 0 0 reflection of BaTiO 3 at addition, that Hatta and Ikushima [6] found a short 0 = 74 ° are shown; for 4 0 0 with FeK~q (6.4keV), we plateau in the heat capacity of BaTiO3 in a range of can survey thc specimen down to the depth of only 0.3-0.1 K below 71. 2 F~m. The measurements were made at several o~ posiCrystals of other origins were also examined in tions of maximum and minimum intensities of the connection with the characteristic features mentioned pattern like that in Fig. l(a). It was found that the above: They are those grown by the Materials relative intensities of the peaks are different for difPreparation G r o u p of the Clarendon Laboratory, UK ferent h 0 0. This suggcsts that the grain distribution is with K F flux, and those by Sanders Association Incor- inhomogeneous along thc dcpth, even in a range of porated, USA with the top-seeded solution method. It 5 ~m. was tbund that they all showed the peak splitting A final remark is related to an anomalous annealsimilar to that described above. It is probable that the ing or relaxation of the structure in the cubic phase phenomenon is inherent in the cubic-to-tetragonal "after passing T,; the phenomenon was found first in transition in BaTiO3. irreproducible to versus tcmperature curves. A correIn the experiments so far mentioned, the measure- sponding anomaly observed in the 20 (or d) versus ments were made on one plane in the reciprocal lattice tempcrature relation is shown in Fig. 5. The d value as shown in Fig. 3; owing to the principle of the for 4 0 0, consequently the lattice constant, is longer double-crystal arrangement, the high-resolution can than the normal value when the annealing in thc cubic be altained in this plane only. In order to examine the phase is not enough. The average heating and cooling diffraction pattern on another plane, perpendicular to rates for (a) and (b) arc 2 and 0.5 K h ~ respectively, the first one, the specimen crystal was remounted after whilc the measurements were made when the temperaturning by 90 ° about the scattering vector: a very turc was fixed at the relevant temperatures. It appears similar peak-splitting was observed again. We infer, that, for faster heating, the excess interatomic distance from the reproducibility of the peak splitting in the is larger, and the temperature above which the heating original mounting, that the directions of the scattering and cooling curves coincide is higher. Hatta and
574
X-RAY D I F F R A C T I O N P A T T E R N OF BaTiO3
Vol. 68, No. 6
Acknowledgements - The authors are grateful to Drs. N. Ohama, Y. Soejima, H. Sakashita and N. Achiwa for discussions and comments. They are also indebted to Drs. B.M. Wanklyn, A. Linz and T. Pollak for growing crystals.
°1 1Itl L
i
!
REFERENCES I. 2.
(b)
3. I
I
/-..0 0
410
TIK
Fig. 5. The lattice constant a determined from the 20 value of 4 0 0 as a function of temperature. The scale for a is arbitrary but common for (a) and (b).
4. 5.
lkushima [6] found, in the specific heat versus temperature curve, a broad hump at T, + 20 K. Although it is hoped to examine further, the anomalies in the lattice constant and in the specific heat might be connected to each other.
6. 7. 8.
K. lrie, M. Shiono, H. Nakamura, N. Ohnishi & A. Ok aza k i, Solid State Commun. 62, 691 ( 1987). N. Ohama, H. Sakashita & A. Okazaki, J. Appl. Cryst. 12, 455 (1979). For example, M. Sato, Y. Soejima, N. Ohama, A. Okazaki, H.J. Scheel & K.A. M/Jller, Phase Transitions 5, 207 (1985). W, Kfinzig, Solid State Phi'sits, Vol. 4, pp. 97124 (edited by F. Seitz and D. Turnbull), Academic Press, New York, London (1957). L.A. Shebanov, Phys. Status Solidi (a) 65, 321 (1981). I. Hatta & A. lkushima, J. Phys. Soc. Japan 41, 558 (1976). Y. Soejima, A. Okazaki & K.A. M(iller, unpublished. A. Okazaki, N. Ohama & K.A. Mfiller, J. Ph)'s. C." Solid State Phys. 19, 5019 (1986).