- Email: [email protected]
X-ray perfection study of Verneuil-grown SrTiO3 crystals
Journal of Crystal Growth 191 (1998) 483—491
X-ray perfection study of Verneuil-grown SrTiO crystals 3 J. Yoshimura*, T. Sakamoto, S. Usui, S. Kimura Institute of Inorganic Synthesis, Faculty of Engineering, Yamanashi University, 4-3-11 Takeda, Kofu 400-8511, Japan Received 9 January 1998
Abstract Dislocations, subgrain textures and other long-range strains in Verneuil-grown SrTiO crystals, used widely as 3 a substrate for growing high-¹ superconducting thin films, have been studied by reflection and transmission X-ray # topography to characterize the crystal in regard to structural perfection. It was found that dislocations are nearly aligned along the S1 0 0T directions and most of them are of pure edge type, presumably as a property of annealed crystals with simple cubic lattice. This entire dislocation alignment causes a strong long-range distortion about the [0 0 1] axis in anisotropic (1 1 0)-oriented crystal plates. Burgers vectors both of S1 0 0T and S1 1 0T types were observed. It was also found that the surfaces of some samples were finished highly strain-free as well as optically flat by the mechanochemical polishing. ( 1998 Elsevier Science B.V. All rights reserved. PACS: 61.66.Fn; 61.72.Dd; 61.72.Ff; 61.72.Lk; 61.72.Mn Keywords: X-ray topography; Strontium titanate; Verneuil growth; Dislocations; Subgrain texture; Crystal-surface perfection
1. Introduction After the discovery of high-¹ superconducting # oxides in 1986, SrTiO crystals have been found to 3 be a good substrate material for growing thin films of superconducting oxides [1—3]. Commercially available Verneuil-grown crystals [4—6] have
* Corresponding author. Tel.: #81 552 20 8612; fax: #81 552 54 3035; e-mail: [email protected].
been used widely although solution growth [7,8] produces more perfect crystals. We have studied the perfection of such Verneuil-grown SrTiO crys3 tals by X-ray topography, to contribute to the progress in the thin film growth and from the basic interest on structural defects of the crystal. So far, there is little literature on the defects of SrTiO 3 crystals [9—11], while many works have been performed on other properties [12]. In rather recent years some detailed studies on dislocations have started appearing [13,14]. In this paper we report a general observation of dislocations, subgrain textures, and other defects of SrTiO crystals, 3 along with some specific characters of existing
0022-0248/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 2 2 - 0 2 4 8 ( 9 8 ) 0 0 1 6 5 - 1
484
J. Yoshimura et al. / Journal of Crystal Growth 191 (1998) 483–491
dislocations and striking perfection of mechanochemically polished surfaces.
3. Results and discussion 3.1. S(1 0 0) samples
2. Experimental procedure Samples were (1 0 0)- and (1 1 0)-oriented SrTiO 3 plates (N -undoped) supplied by Shinkosha Co. " Ltd. and Nakazumi Crystal Laboratory. The two sources are identified by letters S and N in what follows. Original crystals were grown by the Verneuil method and annealed under some appropriate conditions [5] to remove oxygen vacancies and reduce strain. The sample crystals were cut out perpendicularly to the growth axis from a boule in the respective cases of (1 0 0) and (1 1 0) plates of S samples, and cut parallel to the growth axis in the case of N samples. The plate surface was already polished to mirror finish by a mechanochemical method by the suppliers. A few to several samples were studied for each group of (1 0 0) and (1 1 0) plates of S samples, and (1 0 0) plates of N samples. They were first observed by reflection topography in their as-received state or after being etched slightly, and then lapped and etched to 0.2—0.3 mm thickness for observation by transmission topography. The etching was made with HF (50%): HNO : H O"1 : 2 : 2 solution [15]. 3 2 X-ray topographs were taken by the Lang method using a conventional sealed-off X-ray tube with Ag or Cu anode. The sample thickness for kt"3 with Ag Ka radiation is t"0.22 mm, where k is the linear absorption coefficient and t the sample thickness. If samples are in this thickness, they can be handled without difficulty and topographs of them can be taken in a tolerable exposure time. As well as transmission topography with Ag Ka radiation, reflection topography using Cu Ka radiation could be employed usefully with much shorter exposure time than transmission topography. Topographs then were taken at an off-peak position on the rocking curve to enhance misorientation contrast. The samples were further studied by X-ray double crystal diffractometry using a nearly parallel setting of Si (monochromator) and SrTiO 3 (sample) crystals to measure misorientation exactly. The results are only mentioned when needed in this paper and details are described elsewhere.
Fig. 1 illustrates reflection and transmission X-ray topographs of a representative sample of S(1 0 0) plates. Many vertical striations seen in Fig. 1a show dislocations lying near the plate surface. When the incidence wave vector K is in the 0 vertical plane (K o[0 1 0]), these vertical disloca0 tions all disappear even with the same 400 reflection and another group of dislocations lying in the horizontal [0 1 0] direction instead get in contrast. When the X-ray beam is incident from an oblique direction as in Fig. 1b, these two groups of dislocations along [0 0 1] and [0 1 0] alike get in contrast. Like this, dislocations in the crystal are nearly aligned along the two S1 0 0T directions parallel to the surface. The image extinction of dislocations as above depending on K could be explained partly by re0 membering that the effective misorientation due to diffraction contrast [16] is given by 1 Du@"! 2K sin h
A
B
B
#tanh (u ) u). B x z
(1)
Here, u is the diffraction vector, u the displacement, x and z the coordinates normal and parallel to the diffracting plane, respectively, within the plane [K ]K ]; K denotes the wave number, h the 0 ' B Bragg angle, and K "K #2pu. If we now con' 0 sider only the first term (u ) u)/z, i.e. the inclination of lattice plane, aside from the second term, dislocations should get out of contrast even with (u ) u)O0 when (u ) u)/z"0. This condition is met if, for example, the dislocations are of pure edge type and zE(K #K ) is along the dislocation line. 0 ' This would presumably be the case with the present observation. The second term tan h (u ) u)/x B would vanish by surface relaxation. Satisfactory explanation will be given elsewhere. The density of dislocations is estimated in Fig. 1a to be more than ten per mm, i.e. in the order of 104 cm~2 in the two-dimensional density. It should be added that not a small part of the sample (e.g. upper left and right corners in Fig. 1a) is dislocation-free while so many doslocations are present in the main part.
J. Yoshimura et al. / Journal of Crystal Growth 191 (1998) 483–491
485
Fig. 1. X-ray topographs of a S(1 0 0) plate. Sample S1. (a) Reflection topograph, Cu Ka, 400 reflection. Taken from the surface after etching for 4 min. (b) Same as (a), but with X-rays incident from the 45°-rotated direction. (c) Transmission topograph, Ag Ka, 0 21 0 refl. The inset is an enlargement of a part of the field. (d) Transmission topograph, Ag Ka, 0 0 2 refl. The u vector in (a) and (b) is normal to the plane of the topograph. The in-plane orientation in topographs (c) and (d) is the same as (a). Scale marks give 1 mm, which is in common with all other following topographs.
486
J. Yoshimura et al. / Journal of Crystal Growth 191 (1998) 483–491
In transmission topographs in Fig. 1c and Fig. 1d black clustered striae show dislocations. Images of individual dislocations within the clusters are not well resolved (see inset in Fig. 1c). Isolated dislocations other than the clustered ones are not imaged with enough contrast in the topographs although such dislocations seem to exist in some proportion. This insufficient visibility (i.e. resolu-
tion and contrast) of dislocations would probably be due to some imperfections in the crystal, invisible beyond the topographic resolution, rather than the experimental imaging technique. The transmission topographs thus show that a large part of dislocations are present in clusters. Although this appearance rather differs from that in Fig. 1a and Fig. 1b, the observed dislocations likewise lie nearly
Fig. 2. X-ray topographs of another S(100) plate. Sample S3. (a) Reflection topograph, Cu Ka, 400 refl. taken from the surface of the as-received sample. (b) Same as (a), but with X-rays incident from the 90°-rotated direction. (c) Transmission topograph, Ag Ka, 1 0 1 refl. (d) Same as (c), but with 1 0 11 refl.
J. Yoshimura et al. / Journal of Crystal Growth 191 (1998) 483–491
along the S1 0 0T directions parallel to the surface. They are confirmed to be mostly of pure edge type with the Burgers vector b in the (0 0 1) or (0 1 0) plane, as mentioned earlier. This can be concluded from the image extinction rule for (u ) b)"0 and the fact that dislocations lying parallel to vector u disappear in Fig. 1c and Fig. 1d. In this S1 sample any subgrain-like texture is not found. White-contrasted areas seen in each topograph show a misoriented region, and their indistinct borders show that misorientation increases gradually there. Reflection topographs (Fig. 1a and Fig. 1b) of long-range misorientation also vary with the incidence wave vector K since only the 0 component of the misorientation about the axis [K ]u] is effective in making a diffraction con0 trast, according to Eq. (1). The magnitude of the misorientations (i.e. variation in the orientation of lattice plane) was found to be 70—80 arcsec over the whole 10]10 mm sample surface by the double crystal diffractometry. The cause of the misorientation is yet unknown. Fig. 2 shows topographs of another representative S(1 0 0) sample. Dislocations are decreased considerably in this sample compared with the first one. In the reflection topographs ((a) and (b)) vertical (a , b , c) and horizontal (d, e), comparatively i i thick line contrasts show arrayed or bundled dislocations. Band images a , b and c in the transmis2 1,2 sion topographs ((c) and (d)) show that they really correspond to dislocation arrays lying in the thickness direction of the plate. Large misorientation occurs around these dislocation clusters, and a weak subgrain-like texture appears to be produced by them. We attempted to determine the Burgers vector of some dislocations relatively easy to identify among different topographs. Table 1 gives the result. Burgers vectors assigned on the extinction rule for (u ) b)"0 are given in the last row. Only three dislocation and dislocation groups could be assigned a plausible Burgers vector. Other dislocations could not be assigned, probably because of their non-singleness and/or the insufficient number of reflections studied. The occurrence of Burgers vectors both of S1 0 0T and S1 1 0T types agrees with the previous electron-microscopic study [14].
487
Table 1 (u ) b) analysis of dislocation images in Fig. 2 u
a 2
b 3
b 4
c
f 1
f 2
g
4 0 0* 3 0 1* 3 0 11 * 101 1 0 11 0 21 0 002 103 1 0 31
L L L L L ] L L L
L L L L L ] L L L
] L L L L ] L L L
L L L L L L L L L
L L L L L ] L L L
— — — ] L ] L ] L
— — — L ] ] L L ]
b
—
—
001
—
—
1 0 11
101
Note: L indicates “in contrast”, ] “out of contrast”, and — “not determined”. * Reflection topograph.
3.2. S(1 1 0) samples Fig. 3 shows reflection topographs of S(1 1 0) samples. Unlike S(1 0 0) samples, S(1 1 0) samples generally exhibit a definite subgrain texture as shown in Fig. 3b, with their 10]10 mm area split into one to a few or more subgrains. It is worth commenting that besides such main subgrains there occur many finer subgrains in the corners and near the edges of the plate. Misorientation at the grain boundary a in Fig. 3b for example was less than a minute of arc about the [0 0 1] axis according to the double-crystal diffractometry, which is much smaller than the misorientation within each main subgrain. Fig. 3a and Fig. 3b show that the sample plates satisfy the Bragg condition only on the blackcontrasted strip areas and thus they are strongly curved about the [0 0 1] axis. When the K vector is 0 in the vertical plane, that strong distortion seen in Fig. 3a disappear completely as in Fig. 3c for the same sample, although a much weaker curvature (marked b) is instead observed about the horizontal [1 11 0] axis. The misorientations about the [0 0 1] and [1 11 0] axes were found to be ca. 10 min of arc and one minute of arc, respectively, over the 10]10 mm area of the samples by the doublecrystal diffractometry. S(1 1 0) samples thus have a strong and anisotropic lattice distortion. Intensely black contrast in the strip areas in Fig. 3a and Fig. 3b show densely arranged dislocations.
488
J. Yoshimura et al. / Journal of Crystal Growth 191 (1998) 483–491
Fig. 3. Reflection X-ray topographs of S(1 1 0) plates. (a) Sample S6. Cu Ka, 3 3 0 refl. taken from the surface of the as-received sample. (b) Sample S7. Cu Ka, 3 3 0 refl. (c) Same as (a), but with X-rays incident from the 90°-rotated direction. The in-plane orientation in (b) and (c) is the same as (a).
The dislocation density is so high that dislocation images are not almost resolved in the strips. The density is roughly estimated to be in the order of 105 cm~2 or more by assuming the image width of a dislocation to be a few tens lm. In the topograph in Fig. 3c, taken with K o[1 11 0], a vast number of 0 dislocations appearing in Fig. 3a completely get out of contrast, and about ten dislocations instead appear in places of the sample. This makes a strik-
ing contrast to the observation in Fig. 3a. Similarly to the case of Fig. 1, the image extinction here could be explained by assuming that the highdensity dislocations all are of pure edge type, and a small number of dislocations appearing in Fig. 3c are of type having a screw component. Fig. 4 shows transmission topographs of S (1 1 0) sample corresponding to the reflection topographs in Fig. 3a and Fig. 3c. Fig. 4a was taken with the
J. Yoshimura et al. / Journal of Crystal Growth 191 (1998) 483–491
489
Fig. 4. Transmission X-ray topographs of a S(1 1 0) plate (sample S6). (a) Ag Ka, 1 11 0 refl. (b) Ag Ka, 0 0 2 refl.
sample oscillated within an angular range of ca. 20@ to image its whole area, because only a narrow strip area could be imaged when it was angularly fixed. Fig. 4b was taken normally without such a rotation. Black vertical striations, observed in a large number in Fig. 4a and only sparsely in Fig. 4b, respectively show dislocations. The visibility behavior of the densely distributed dislocations which appear in Fig. 4a and disappear in Fig. 4b confirmed that almost all of them are pure edge dislocations, on the basis of the (u ) b) rule. The determination of their exact Burgers vectors was not very easy though attempted to some extent, and needs further work. Only a central high-density cluster (marked a in Fig. 4a) could be assigned the Burgers vector bE[1 0 0] from the experimental result that they appear in (1 11 0), (2 0 0) and (3 11 0), and disappear in (0 0 2), (0 2 0) and (11 3 0). By the similar (u ) b) reasoning, a small number of vertical dislocations in contrast in Fig. 4b, which mostly corresponds to dislocation images in Fig. 3c, are confirmed to be screw or mixed dislocations. In the transmission as well as reflection topographs, dislocations lying along the horizontal [1 11 0] direction
are not at all observed in the main area of the (1 1 0) plates (except an unidentified lines near the left edge in Fig. 3c). However, black linear contrasts with different thicknesses observed along subgrain boundaries (marked with arrow) seem to be also dislocations or related defects. If so, they are near screw dislocation rather than the edge one, from the visibility behavior with various reflections. In the S(1 1 0) samples, like this, dislocations of pure edge type are arranged in high density nearly along the [0 0 1] direction. Screw dislocations are very few, and so are the dislocations lying in the horizontal (0 0 1) plane. The strong and anisotropic lattice distortion about the [0 0 1] axis mentioned would be induced by such highly anisotropic dislocation arrangement. 3.3. N(1 0 0) samples Fig. 5 shows reflection and transmission topographs of an N(1 0 0) plate. N samples with ca. 12]7 mm area generally split into a few or more subgrains, and a sample with the least subgrains is presented here. Around the subgrain boundary
490
J. Yoshimura et al. / Journal of Crystal Growth 191 (1998) 483–491
Fig. 5. X-ray topographs of an N(1 0 0) plate. Sample N3. (a) Reflection topograph, Cu Ka, 4 0 0 refl. Taken from the lapped and etched surface. (b) Transmission topograph, Ag Ka, 0 21 0, refl.
(marked a) misorientation by 7@—8@ occurs about the [0 1 0] axis (the black strip in Fig. 5a show an overlapping of the diffracted images of two misoriented regions). In the region A on the left of the boundary, very thin and feeble line contrasts (marked with an arrow) along the horizontal [0 0 1] direction show dislocations, which were known to be of pure edge type from the complete disappearance in (2 0 0) transmission topographs (not presented). Vertical dislocations along the [0 1 0] direction also are found in the crystal, though not clearly visible in the presented topographs except a few thick lines near the left edge. Thus the dislocation alignment along the S1 0 0T directions is also observed in the N samples. Furthermore, more marked and straight line contrasts along the oblique [0 1 1] and [0 1 11 ] directions would also show dislocations. These lines seem to correspond to macroscopic slip lines though not
yet verified. Easily visible macrosteps are correspondingly found on the lapped and etched surface of the sample. In the region B on the right side of the boundary defects like a dislocation are not found at all, except for spot-like short lines on the upper and the right-side edges, and a thick diffuse line (marked b in Fig. 5b) in the center (oblique lines around the line b are surface damages due to lapping). The thick diffuse line and one more similar irregular line in the region A (also marked b) would probably be due to aggregated dislocations. Dislocations in general places are few although the overall crystal perfection does not seem to be very high from the appearance in the topographs. Like other N samples, dislocations do not exist in large numbers within each of the subgrains although the samples are split into subgrains and large misorientations occurs on the subgrain boundaries.
J. Yoshimura et al. / Journal of Crystal Growth 191 (1998) 483–491
4. Concluding remarks The present study is concluded with the following remarks: (1) Dislocations, subgrain textures and longrange strains on the surface and in the bulk of Verneuil-grown SrTiO crystals were revealed by 3 X-ray topography to characterize the crystals in perfection. The crystals were found to have some peculiarities in the configuration and the preferred type of dislocations, and in having an anisotropic lattice distortion in S(1 1 0) samples. The appearance in X-ray topographs suggests that defects with weak strain and/or minute in size other than clearly visualized in the topographs would exist in a considerable density in the crystals. (2) The preferred dislocation arrangement along the S1 0 0T directions could be understood to show a property of annealed crystals with simple cubic lattice. The well-aligned dislocations along the selected directions makes a difference from the observation in fcc crystals [17]. (3) It should be mentioned that the reflection topographs in Figs. 1—3 were all taken from mechanochemically polished surfaces of the as-received samples. Although some of them were taken after a light etching, it gives no substantial change in the topographs. It should be noted that the defects observed are all intrinsic crystal defects and almost no polishing damage is found in spite of omitted strain-removing etching, although one or two flaws of that kind happen to be found in the 10]10 mm area. The sample surface is optically flat and highly free of polishing damage with the sensitivity of X-ray topography. (4) Reflection topography could be used conveniently in this work, imaging dislocations with pretty good visibilty. As well as directly examining the surface perfection, it provides also information on the dislocation density, subgrain texture, etc. of
491
the bulk crystal with much shorter exposure time than transmission topography. Acknowledgements The authors would like to thank Dr. Y. Nakazumi for supplying samples and encouraging this work. They also thank Mr. N. Tamura of Shinkosha Co. Ltd. for supplying samples and giving information of them. References [1] H. Adachi, K. Setsune, K. Wasa, Phys. Rev. B 35 (1987) 8824. [2] H. Hasegawa, T. Fukazawa, T. Aida, Jpn. J. Appl. Phys. 28 (1989) L2210. [3] M. Kawasaki, K. Takahashi, T. Maeda, R. Tsuchiya, M. Shinohara, O. Ishiyama, T. Yonezawa, M. Yoshimoto, H. Koinuma, Science 266 (1994) 1540. [4] L. Merker, Trans. AIME Min. Eng. 202 (1955) 645. [5] Y. Nakazumi, Ceramics (Tokyo) 3 (1968) 731. [6] J.G. Bednorz, H.J. Scheel, J. Crystal Growth 41 (1977) 5. [7] K. Oka, H. Unoki, Bull. Electrotech. Lab. (Ministry of Int. Trade and Industry, Japan) 39 (1975) 853. [8] D. Rytz, B.A. Wechsler, C.C. Nelson, K.W. Kirby, J. Crystal Growth 99 (1990) 864. [9] H.J. Scheel, Z. Kristallogr. 143 (1976) 417. [10] H.J. Scheel, J.G. Bednorz, P. Dill, Ferroelectrics 13 (1976) 507. [11] M.Y. Aleksandrova, E.P. Dubrovin, V.A. Mokievskii, V.V. Smirnyi, Inorg. Mater. 12 (1976) 1052. [12] K. Nassau, A.E. Miller, J. Crystal Growth 91 (1988) 373. [13] S. Takeuchi, K. Suzuki, M. Ichihara, T. Suzuki, in: T. Suzuki, S. Takeuchi (Eds.), JJAP Ser. 2 Lattice Defects in Ceramics, Publication Office Jpn. J. Appl. Phys., Tokyo, 1989, pp. 17—24. [14] J. Nishigaki, K. Kuroda, H. Saka, Phys. Stat. Sol. A 128 (1991) 319. [15] J.S. Waugh, A.E. Paladino, B. diBenedetto, R. Wantman, J. Am. Ceram. Soc. 46 (1963) 60. [16] A. Authier, Adv. X-Ray Anal. 10 (1967) 9. [17] Y. Deguchi, N. Kamigaki, K. Kashiwaya, T. Kino, Jpn. J. Appl. Phys. 17 (1978) 611.
X-ray perfection study of Verneuil-grown SrTiO crystals 3 J. Yoshimura*, T. Sakamoto, S. Usui, S. Kimura Institute of Inorganic Synthesis, Faculty of Engineering, Yamanashi University, 4-3-11 Takeda, Kofu 400-8511, Japan Received 9 January 1998
Abstract Dislocations, subgrain textures and other long-range strains in Verneuil-grown SrTiO crystals, used widely as 3 a substrate for growing high-¹ superconducting thin films, have been studied by reflection and transmission X-ray # topography to characterize the crystal in regard to structural perfection. It was found that dislocations are nearly aligned along the S1 0 0T directions and most of them are of pure edge type, presumably as a property of annealed crystals with simple cubic lattice. This entire dislocation alignment causes a strong long-range distortion about the [0 0 1] axis in anisotropic (1 1 0)-oriented crystal plates. Burgers vectors both of S1 0 0T and S1 1 0T types were observed. It was also found that the surfaces of some samples were finished highly strain-free as well as optically flat by the mechanochemical polishing. ( 1998 Elsevier Science B.V. All rights reserved. PACS: 61.66.Fn; 61.72.Dd; 61.72.Ff; 61.72.Lk; 61.72.Mn Keywords: X-ray topography; Strontium titanate; Verneuil growth; Dislocations; Subgrain texture; Crystal-surface perfection
1. Introduction After the discovery of high-¹ superconducting # oxides in 1986, SrTiO crystals have been found to 3 be a good substrate material for growing thin films of superconducting oxides [1—3]. Commercially available Verneuil-grown crystals [4—6] have
* Corresponding author. Tel.: #81 552 20 8612; fax: #81 552 54 3035; e-mail: [email protected].
been used widely although solution growth [7,8] produces more perfect crystals. We have studied the perfection of such Verneuil-grown SrTiO crys3 tals by X-ray topography, to contribute to the progress in the thin film growth and from the basic interest on structural defects of the crystal. So far, there is little literature on the defects of SrTiO 3 crystals [9—11], while many works have been performed on other properties [12]. In rather recent years some detailed studies on dislocations have started appearing [13,14]. In this paper we report a general observation of dislocations, subgrain textures, and other defects of SrTiO crystals, 3 along with some specific characters of existing
0022-0248/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 2 2 - 0 2 4 8 ( 9 8 ) 0 0 1 6 5 - 1
484
J. Yoshimura et al. / Journal of Crystal Growth 191 (1998) 483–491
dislocations and striking perfection of mechanochemically polished surfaces.
3. Results and discussion 3.1. S(1 0 0) samples
2. Experimental procedure Samples were (1 0 0)- and (1 1 0)-oriented SrTiO 3 plates (N -undoped) supplied by Shinkosha Co. " Ltd. and Nakazumi Crystal Laboratory. The two sources are identified by letters S and N in what follows. Original crystals were grown by the Verneuil method and annealed under some appropriate conditions [5] to remove oxygen vacancies and reduce strain. The sample crystals were cut out perpendicularly to the growth axis from a boule in the respective cases of (1 0 0) and (1 1 0) plates of S samples, and cut parallel to the growth axis in the case of N samples. The plate surface was already polished to mirror finish by a mechanochemical method by the suppliers. A few to several samples were studied for each group of (1 0 0) and (1 1 0) plates of S samples, and (1 0 0) plates of N samples. They were first observed by reflection topography in their as-received state or after being etched slightly, and then lapped and etched to 0.2—0.3 mm thickness for observation by transmission topography. The etching was made with HF (50%): HNO : H O"1 : 2 : 2 solution [15]. 3 2 X-ray topographs were taken by the Lang method using a conventional sealed-off X-ray tube with Ag or Cu anode. The sample thickness for kt"3 with Ag Ka radiation is t"0.22 mm, where k is the linear absorption coefficient and t the sample thickness. If samples are in this thickness, they can be handled without difficulty and topographs of them can be taken in a tolerable exposure time. As well as transmission topography with Ag Ka radiation, reflection topography using Cu Ka radiation could be employed usefully with much shorter exposure time than transmission topography. Topographs then were taken at an off-peak position on the rocking curve to enhance misorientation contrast. The samples were further studied by X-ray double crystal diffractometry using a nearly parallel setting of Si (monochromator) and SrTiO 3 (sample) crystals to measure misorientation exactly. The results are only mentioned when needed in this paper and details are described elsewhere.
Fig. 1 illustrates reflection and transmission X-ray topographs of a representative sample of S(1 0 0) plates. Many vertical striations seen in Fig. 1a show dislocations lying near the plate surface. When the incidence wave vector K is in the 0 vertical plane (K o[0 1 0]), these vertical disloca0 tions all disappear even with the same 400 reflection and another group of dislocations lying in the horizontal [0 1 0] direction instead get in contrast. When the X-ray beam is incident from an oblique direction as in Fig. 1b, these two groups of dislocations along [0 0 1] and [0 1 0] alike get in contrast. Like this, dislocations in the crystal are nearly aligned along the two S1 0 0T directions parallel to the surface. The image extinction of dislocations as above depending on K could be explained partly by re0 membering that the effective misorientation due to diffraction contrast [16] is given by 1 Du@"! 2K sin h
A
B
B
#tanh (u ) u). B x z
(1)
Here, u is the diffraction vector, u the displacement, x and z the coordinates normal and parallel to the diffracting plane, respectively, within the plane [K ]K ]; K denotes the wave number, h the 0 ' B Bragg angle, and K "K #2pu. If we now con' 0 sider only the first term (u ) u)/z, i.e. the inclination of lattice plane, aside from the second term, dislocations should get out of contrast even with (u ) u)O0 when (u ) u)/z"0. This condition is met if, for example, the dislocations are of pure edge type and zE(K #K ) is along the dislocation line. 0 ' This would presumably be the case with the present observation. The second term tan h (u ) u)/x B would vanish by surface relaxation. Satisfactory explanation will be given elsewhere. The density of dislocations is estimated in Fig. 1a to be more than ten per mm, i.e. in the order of 104 cm~2 in the two-dimensional density. It should be added that not a small part of the sample (e.g. upper left and right corners in Fig. 1a) is dislocation-free while so many doslocations are present in the main part.
J. Yoshimura et al. / Journal of Crystal Growth 191 (1998) 483–491
485
Fig. 1. X-ray topographs of a S(1 0 0) plate. Sample S1. (a) Reflection topograph, Cu Ka, 400 reflection. Taken from the surface after etching for 4 min. (b) Same as (a), but with X-rays incident from the 45°-rotated direction. (c) Transmission topograph, Ag Ka, 0 21 0 refl. The inset is an enlargement of a part of the field. (d) Transmission topograph, Ag Ka, 0 0 2 refl. The u vector in (a) and (b) is normal to the plane of the topograph. The in-plane orientation in topographs (c) and (d) is the same as (a). Scale marks give 1 mm, which is in common with all other following topographs.
486
J. Yoshimura et al. / Journal of Crystal Growth 191 (1998) 483–491
In transmission topographs in Fig. 1c and Fig. 1d black clustered striae show dislocations. Images of individual dislocations within the clusters are not well resolved (see inset in Fig. 1c). Isolated dislocations other than the clustered ones are not imaged with enough contrast in the topographs although such dislocations seem to exist in some proportion. This insufficient visibility (i.e. resolu-
tion and contrast) of dislocations would probably be due to some imperfections in the crystal, invisible beyond the topographic resolution, rather than the experimental imaging technique. The transmission topographs thus show that a large part of dislocations are present in clusters. Although this appearance rather differs from that in Fig. 1a and Fig. 1b, the observed dislocations likewise lie nearly
Fig. 2. X-ray topographs of another S(100) plate. Sample S3. (a) Reflection topograph, Cu Ka, 400 refl. taken from the surface of the as-received sample. (b) Same as (a), but with X-rays incident from the 90°-rotated direction. (c) Transmission topograph, Ag Ka, 1 0 1 refl. (d) Same as (c), but with 1 0 11 refl.
J. Yoshimura et al. / Journal of Crystal Growth 191 (1998) 483–491
along the S1 0 0T directions parallel to the surface. They are confirmed to be mostly of pure edge type with the Burgers vector b in the (0 0 1) or (0 1 0) plane, as mentioned earlier. This can be concluded from the image extinction rule for (u ) b)"0 and the fact that dislocations lying parallel to vector u disappear in Fig. 1c and Fig. 1d. In this S1 sample any subgrain-like texture is not found. White-contrasted areas seen in each topograph show a misoriented region, and their indistinct borders show that misorientation increases gradually there. Reflection topographs (Fig. 1a and Fig. 1b) of long-range misorientation also vary with the incidence wave vector K since only the 0 component of the misorientation about the axis [K ]u] is effective in making a diffraction con0 trast, according to Eq. (1). The magnitude of the misorientations (i.e. variation in the orientation of lattice plane) was found to be 70—80 arcsec over the whole 10]10 mm sample surface by the double crystal diffractometry. The cause of the misorientation is yet unknown. Fig. 2 shows topographs of another representative S(1 0 0) sample. Dislocations are decreased considerably in this sample compared with the first one. In the reflection topographs ((a) and (b)) vertical (a , b , c) and horizontal (d, e), comparatively i i thick line contrasts show arrayed or bundled dislocations. Band images a , b and c in the transmis2 1,2 sion topographs ((c) and (d)) show that they really correspond to dislocation arrays lying in the thickness direction of the plate. Large misorientation occurs around these dislocation clusters, and a weak subgrain-like texture appears to be produced by them. We attempted to determine the Burgers vector of some dislocations relatively easy to identify among different topographs. Table 1 gives the result. Burgers vectors assigned on the extinction rule for (u ) b)"0 are given in the last row. Only three dislocation and dislocation groups could be assigned a plausible Burgers vector. Other dislocations could not be assigned, probably because of their non-singleness and/or the insufficient number of reflections studied. The occurrence of Burgers vectors both of S1 0 0T and S1 1 0T types agrees with the previous electron-microscopic study [14].
487
Table 1 (u ) b) analysis of dislocation images in Fig. 2 u
a 2
b 3
b 4
c
f 1
f 2
g
4 0 0* 3 0 1* 3 0 11 * 101 1 0 11 0 21 0 002 103 1 0 31
L L L L L ] L L L
L L L L L ] L L L
] L L L L ] L L L
L L L L L L L L L
L L L L L ] L L L
— — — ] L ] L ] L
— — — L ] ] L L ]
b
—
—
001
—
—
1 0 11
101
Note: L indicates “in contrast”, ] “out of contrast”, and — “not determined”. * Reflection topograph.
3.2. S(1 1 0) samples Fig. 3 shows reflection topographs of S(1 1 0) samples. Unlike S(1 0 0) samples, S(1 1 0) samples generally exhibit a definite subgrain texture as shown in Fig. 3b, with their 10]10 mm area split into one to a few or more subgrains. It is worth commenting that besides such main subgrains there occur many finer subgrains in the corners and near the edges of the plate. Misorientation at the grain boundary a in Fig. 3b for example was less than a minute of arc about the [0 0 1] axis according to the double-crystal diffractometry, which is much smaller than the misorientation within each main subgrain. Fig. 3a and Fig. 3b show that the sample plates satisfy the Bragg condition only on the blackcontrasted strip areas and thus they are strongly curved about the [0 0 1] axis. When the K vector is 0 in the vertical plane, that strong distortion seen in Fig. 3a disappear completely as in Fig. 3c for the same sample, although a much weaker curvature (marked b) is instead observed about the horizontal [1 11 0] axis. The misorientations about the [0 0 1] and [1 11 0] axes were found to be ca. 10 min of arc and one minute of arc, respectively, over the 10]10 mm area of the samples by the doublecrystal diffractometry. S(1 1 0) samples thus have a strong and anisotropic lattice distortion. Intensely black contrast in the strip areas in Fig. 3a and Fig. 3b show densely arranged dislocations.
488
J. Yoshimura et al. / Journal of Crystal Growth 191 (1998) 483–491
Fig. 3. Reflection X-ray topographs of S(1 1 0) plates. (a) Sample S6. Cu Ka, 3 3 0 refl. taken from the surface of the as-received sample. (b) Sample S7. Cu Ka, 3 3 0 refl. (c) Same as (a), but with X-rays incident from the 90°-rotated direction. The in-plane orientation in (b) and (c) is the same as (a).
The dislocation density is so high that dislocation images are not almost resolved in the strips. The density is roughly estimated to be in the order of 105 cm~2 or more by assuming the image width of a dislocation to be a few tens lm. In the topograph in Fig. 3c, taken with K o[1 11 0], a vast number of 0 dislocations appearing in Fig. 3a completely get out of contrast, and about ten dislocations instead appear in places of the sample. This makes a strik-
ing contrast to the observation in Fig. 3a. Similarly to the case of Fig. 1, the image extinction here could be explained by assuming that the highdensity dislocations all are of pure edge type, and a small number of dislocations appearing in Fig. 3c are of type having a screw component. Fig. 4 shows transmission topographs of S (1 1 0) sample corresponding to the reflection topographs in Fig. 3a and Fig. 3c. Fig. 4a was taken with the
J. Yoshimura et al. / Journal of Crystal Growth 191 (1998) 483–491
489
Fig. 4. Transmission X-ray topographs of a S(1 1 0) plate (sample S6). (a) Ag Ka, 1 11 0 refl. (b) Ag Ka, 0 0 2 refl.
sample oscillated within an angular range of ca. 20@ to image its whole area, because only a narrow strip area could be imaged when it was angularly fixed. Fig. 4b was taken normally without such a rotation. Black vertical striations, observed in a large number in Fig. 4a and only sparsely in Fig. 4b, respectively show dislocations. The visibility behavior of the densely distributed dislocations which appear in Fig. 4a and disappear in Fig. 4b confirmed that almost all of them are pure edge dislocations, on the basis of the (u ) b) rule. The determination of their exact Burgers vectors was not very easy though attempted to some extent, and needs further work. Only a central high-density cluster (marked a in Fig. 4a) could be assigned the Burgers vector bE[1 0 0] from the experimental result that they appear in (1 11 0), (2 0 0) and (3 11 0), and disappear in (0 0 2), (0 2 0) and (11 3 0). By the similar (u ) b) reasoning, a small number of vertical dislocations in contrast in Fig. 4b, which mostly corresponds to dislocation images in Fig. 3c, are confirmed to be screw or mixed dislocations. In the transmission as well as reflection topographs, dislocations lying along the horizontal [1 11 0] direction
are not at all observed in the main area of the (1 1 0) plates (except an unidentified lines near the left edge in Fig. 3c). However, black linear contrasts with different thicknesses observed along subgrain boundaries (marked with arrow) seem to be also dislocations or related defects. If so, they are near screw dislocation rather than the edge one, from the visibility behavior with various reflections. In the S(1 1 0) samples, like this, dislocations of pure edge type are arranged in high density nearly along the [0 0 1] direction. Screw dislocations are very few, and so are the dislocations lying in the horizontal (0 0 1) plane. The strong and anisotropic lattice distortion about the [0 0 1] axis mentioned would be induced by such highly anisotropic dislocation arrangement. 3.3. N(1 0 0) samples Fig. 5 shows reflection and transmission topographs of an N(1 0 0) plate. N samples with ca. 12]7 mm area generally split into a few or more subgrains, and a sample with the least subgrains is presented here. Around the subgrain boundary
490
J. Yoshimura et al. / Journal of Crystal Growth 191 (1998) 483–491
Fig. 5. X-ray topographs of an N(1 0 0) plate. Sample N3. (a) Reflection topograph, Cu Ka, 4 0 0 refl. Taken from the lapped and etched surface. (b) Transmission topograph, Ag Ka, 0 21 0, refl.
(marked a) misorientation by 7@—8@ occurs about the [0 1 0] axis (the black strip in Fig. 5a show an overlapping of the diffracted images of two misoriented regions). In the region A on the left of the boundary, very thin and feeble line contrasts (marked with an arrow) along the horizontal [0 0 1] direction show dislocations, which were known to be of pure edge type from the complete disappearance in (2 0 0) transmission topographs (not presented). Vertical dislocations along the [0 1 0] direction also are found in the crystal, though not clearly visible in the presented topographs except a few thick lines near the left edge. Thus the dislocation alignment along the S1 0 0T directions is also observed in the N samples. Furthermore, more marked and straight line contrasts along the oblique [0 1 1] and [0 1 11 ] directions would also show dislocations. These lines seem to correspond to macroscopic slip lines though not
yet verified. Easily visible macrosteps are correspondingly found on the lapped and etched surface of the sample. In the region B on the right side of the boundary defects like a dislocation are not found at all, except for spot-like short lines on the upper and the right-side edges, and a thick diffuse line (marked b in Fig. 5b) in the center (oblique lines around the line b are surface damages due to lapping). The thick diffuse line and one more similar irregular line in the region A (also marked b) would probably be due to aggregated dislocations. Dislocations in general places are few although the overall crystal perfection does not seem to be very high from the appearance in the topographs. Like other N samples, dislocations do not exist in large numbers within each of the subgrains although the samples are split into subgrains and large misorientations occurs on the subgrain boundaries.
J. Yoshimura et al. / Journal of Crystal Growth 191 (1998) 483–491
4. Concluding remarks The present study is concluded with the following remarks: (1) Dislocations, subgrain textures and longrange strains on the surface and in the bulk of Verneuil-grown SrTiO crystals were revealed by 3 X-ray topography to characterize the crystals in perfection. The crystals were found to have some peculiarities in the configuration and the preferred type of dislocations, and in having an anisotropic lattice distortion in S(1 1 0) samples. The appearance in X-ray topographs suggests that defects with weak strain and/or minute in size other than clearly visualized in the topographs would exist in a considerable density in the crystals. (2) The preferred dislocation arrangement along the S1 0 0T directions could be understood to show a property of annealed crystals with simple cubic lattice. The well-aligned dislocations along the selected directions makes a difference from the observation in fcc crystals [17]. (3) It should be mentioned that the reflection topographs in Figs. 1—3 were all taken from mechanochemically polished surfaces of the as-received samples. Although some of them were taken after a light etching, it gives no substantial change in the topographs. It should be noted that the defects observed are all intrinsic crystal defects and almost no polishing damage is found in spite of omitted strain-removing etching, although one or two flaws of that kind happen to be found in the 10]10 mm area. The sample surface is optically flat and highly free of polishing damage with the sensitivity of X-ray topography. (4) Reflection topography could be used conveniently in this work, imaging dislocations with pretty good visibilty. As well as directly examining the surface perfection, it provides also information on the dislocation density, subgrain texture, etc. of
491
the bulk crystal with much shorter exposure time than transmission topography. Acknowledgements The authors would like to thank Dr. Y. Nakazumi for supplying samples and encouraging this work. They also thank Mr. N. Tamura of Shinkosha Co. Ltd. for supplying samples and giving information of them. References [1] H. Adachi, K. Setsune, K. Wasa, Phys. Rev. B 35 (1987) 8824. [2] H. Hasegawa, T. Fukazawa, T. Aida, Jpn. J. Appl. Phys. 28 (1989) L2210. [3] M. Kawasaki, K. Takahashi, T. Maeda, R. Tsuchiya, M. Shinohara, O. Ishiyama, T. Yonezawa, M. Yoshimoto, H. Koinuma, Science 266 (1994) 1540. [4] L. Merker, Trans. AIME Min. Eng. 202 (1955) 645. [5] Y. Nakazumi, Ceramics (Tokyo) 3 (1968) 731. [6] J.G. Bednorz, H.J. Scheel, J. Crystal Growth 41 (1977) 5. [7] K. Oka, H. Unoki, Bull. Electrotech. Lab. (Ministry of Int. Trade and Industry, Japan) 39 (1975) 853. [8] D. Rytz, B.A. Wechsler, C.C. Nelson, K.W. Kirby, J. Crystal Growth 99 (1990) 864. [9] H.J. Scheel, Z. Kristallogr. 143 (1976) 417. [10] H.J. Scheel, J.G. Bednorz, P. Dill, Ferroelectrics 13 (1976) 507. [11] M.Y. Aleksandrova, E.P. Dubrovin, V.A. Mokievskii, V.V. Smirnyi, Inorg. Mater. 12 (1976) 1052. [12] K. Nassau, A.E. Miller, J. Crystal Growth 91 (1988) 373. [13] S. Takeuchi, K. Suzuki, M. Ichihara, T. Suzuki, in: T. Suzuki, S. Takeuchi (Eds.), JJAP Ser. 2 Lattice Defects in Ceramics, Publication Office Jpn. J. Appl. Phys., Tokyo, 1989, pp. 17—24. [14] J. Nishigaki, K. Kuroda, H. Saka, Phys. Stat. Sol. A 128 (1991) 319. [15] J.S. Waugh, A.E. Paladino, B. diBenedetto, R. Wantman, J. Am. Ceram. Soc. 46 (1963) 60. [16] A. Authier, Adv. X-Ray Anal. 10 (1967) 9. [17] Y. Deguchi, N. Kamigaki, K. Kashiwaya, T. Kino, Jpn. J. Appl. Phys. 17 (1978) 611.