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Surface morphology and incommensurate modulation of self-flux grown Bi2Sr2CaCu2O8+x single crystals
Physica C 406 (2004) 72–78 www.elsevier.com/locate/physc
Surface morphology and incommensurate modulation of self-flux grown Bi2Sr2CaCu2O8þx single crystals P. Kumar a, B. Kumar
a,*
, I. Bdikin
b,c
, A.L. Kholkin c, G.C. Trigunayat
a
a
c
Department of Physics and Astrophysics, University of Delhi, 110007 Delhi, India b Institute of Solid State Physics, RAS, 142432 Chernogolovka, Russia Department of Ceramics and Glass Engineering, CICECO, University of Aveiro, 3810-193 Aveiro, Portugal Accepted 9 February 2004 Available online 13 April 2004
Abstract Structural studies have been carried out in large size superconducting single crystals of Bi2 Sr2 CaCu2 O8þx grown by self-flux method. Surface morphology of the crystals in respect of growth steps, slip lines/bands and etch pits has been examined by scanning electron microscopy (SEM). A quantitative study of grain misorientation in the crystals has been conducted by X-ray diffraction, which has also revealed the existence of incommensurate modulation of the crystal structure. A detailed analysis of first and second order satellite reflections associated with the Bragg reflections 0 2 0 and 0 0 3 6, in terms of incommensurate b -components and modulation wave vector q ¼ 0:21b þ c , has been made. It is proposed that while the second order satellite reflections observed around 0 0 3 6 are linked with the existent neighboring Bragg reflections, the first order satellite reflections are correlated with a forbidden reflection. 2004 Elsevier B.V. All rights reserved. Keywords: Bi2 Sr2 CaCu2 O8þx HTSC; Single crystal growth; Defect structure; Modulated structure; SEM; X-ray characterization
1. Introduction The discovery of superconductivity with a high critical temperature Tc in the Bi–Sr–Ca–Cu–O system has led to its extensive investigation. Three phases, generally represented by Bi2 Sr2 Can1 Cun O2nþ4 , n ¼ 1; 2; 3 and respectively termed as 2 2 0 1, 2 2 1 2, 2 2 2 3 phases, are the first three members of a family [1–3]. The first member, Bi2 Sr2 CuO6 , attracts less interest because of its low
*
Corresponding author. Fax: +91-011-27667061. E-mail addresses: [email protected], b3kumar69@ yahoo.co.in (B. Kumar).
Tc and the third member, Bi2 Sr2 Ca2 Cu3 O8þx , cannot be prepared easily as a single-phase sample. We have chosen the second phase, Bi2 Sr2 CaCu2 O8þx (2 2 1 2 phase), for the study of superconducting properties, surface morphology and structural characteristics. The 2 2 1 2 phase has a modulated structure which is characterised in the X-ray and electron diffraction patterns through the emergence of a number of satellites reflections in the b –c plane [4–8]. The modulation is incommensurate in nature [2,9–11]. A consensus has emerged that the extra oxygen atoms inserted in the Bi–O layers are linked to a displacive modulation with its origin in the mismatch between the crystallographic blocks
0921-4534/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2004.02.180
P. Kumar et al. / Physica C 406 (2004) 72–78
of the perovskite Cu–O planes and the rocksalt type Bi–O layers. The nature of the satellites needs to be elucidated. But there is controversy about the position of the super reflections arranged about the base reflections. For instance, besides the wellknown super reflections in the Bbmb space group, Kenichi and Kawaguchi [6] have observed additional super reflections around the Bragg reflections 0 0 2 0 and 0 0 3 6. These additional super reflections are characteristic of the well-known modulations, with the assumption that the formation of such superstructural reflections is also possible around the sites of the Bragg reflections forbidden in the main lattice symmetry. However, according to the theory of X-ray scattering by modulated structures [12–14], intensities of the superstructural reflections are proportional to those of the structural reflections and, consequently, unambiguously determine the absence of the superstructural reflections. We have carefully determined the modulation phases and grain misorientation in the crystals, as these factors play an important role in the interpretation of structural quality of the single crystals. So far, not many studies have been reported on the structural quality of the Bi-2212 single crystals. The earlier scanning electron microscopy (SEM) studies on Bi-2212 crystals had been mostly employed to provide information regarding crystal size and surface smoothness. The growth steps and fractured planes, seen near the edges of crystals, were mostly attributed to the mechanical strain suffered by crystals during extraction from the flux [15,16]. Chaudhury et al. [17] had reported that the thicker crystals actually consisted of a large number of platy crystals having well-aligned c-axis. They also reported the growth of crystals along (1 1 0) faces. We have observed features like growth steps, slip lines/bands, etch pits, etc., from which supplementary information have been gained regarding defect surface structure of the crystals.
2. Experimental High purity Bi2 O3 , SrCO3 , CuO, CaCO3 (purity > 99.999%, ALDRICH) powders were used
73
as starting material for the growth of single crystals. The components were taken in the stoichiometric proportion, thoroughly mixed and transferred into a high purity alumina cylindrical crucible (purity > 99.0%; CERAC). The single crystals were prepared by slowly cooling the melted charge from 1000 to 800 C at the rate 2 C/h, using a box type programmable furnace (HERAEUS K-1252). X-ray diffraction studies were performed on DRON-2 and SIEMENS (D 500) diffractometers, using CuKa radiation. While the sample was rotated at an angular rate x, a photographic film, placed directly in front of the X-ray detector and perpendicular to the diffracted beam, was either rotated at an angular rate 2x (for h–2h scanning topography) or was motionless (for h-scanning topography). The samples were aligned with their b and c directions in the horizontal scattering plane. The samples were examined by scanning electron microscopy (SEM), employing a JEOL JSM840 electron microscope. The samples were mounted on copper stubs with carbon electroconducting paint and a thin uniform gold film was sputtered on them, using an ion sputterer (JFC1100). The gold coating faithfully contours the surface features, improves electrical conductivity of the surface and minimizes the thermal degradation. An attached camera recorded the observed features on a photographic film.
3. Results and discussion The as-grown crystals had shiny flat surfaces and measured upto 5 mm across (mostly 4 · 3 mm2 ) and upto 0.3 mm in thickness (Fig. 1(a)). Their single crystalline nature was confirmed by Xray diffraction methods. The critical temperature Tc was determined to be 85 K for most of the crystals by resistivity measurements in the abplane. The transition width DTc measured nearly 2 K. The crystal structure of Bi2 Sr2 CaCu2 O8þx is tetragonal with the lattice parameters as a ¼ b ¼ c ¼ 30:842 A. 5:412 A, The surface features of the crystals were examined by scanning electron microscopy. The
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Fig. 1. (a) Scanning electron micrograph of an as-grown crystal, measuring upto 5 mm along one diagonal. (b) Zig-zag growth steps, indicating two-dimensional layer growth.
Fig. 1(a) shows the entire surface of a crystal. The crystal surfaces were largely found to be smooth even upto a high magnification of ·500. However, crack-like lines were seen in many crystals, which possibly formed during the extraction of the crystals from the bulk. In some cases zigzag layered steps were observed near the corners of the crystals, indicating that the crystals had grown by two-dimensional layer growth process (Fig. 1(b)). Although no deliberate etching of the crystal surface had been carried out, etch pits were seen on some portions of the crystals. They looked shallow, with no definite shape. They apparently originated from atmospheric attacks on the crystals. In many cases they lay along parallel rows, as seen in Fig. 2(a). The etch pits are known to be
Fig. 2. (a) Parallel rows of etch pits on the basal surface of a crystal. (b) Intersection rows of etch pits. Their mutual inclination is preferentially observed to be 30.
preferentially created at the sites of dislocations, which could be either edge dislocations or screw dislocations. They are either directed along crystallographic axes or have components along them. If the dislocations are preferentially produced along only one set of planes, a single row or a set of parallel rows of dislocations is produced, resulting in the etch pits arranged along a set of parallel rows, as seen in Fig. 2(a). In some cases intersecting rows of etch pit were observed, as in Fig. 2(b). Although the angle of their mutual inclination was not well defined in most of the cases, a preferential inclination of 30 was observed in some cases. At lower magnifications, patterns of parallel slip lines have been observed on the basal surfaces (Fig. 3(a)). During the growth process, directional thermal stresses are
P. Kumar et al. / Physica C 406 (2004) 72–78
Fig. 3. (a) Patterns of parallel slip lines on the basal surface of a crystal. (b) Patterns of slip bands on the basal surface of a crystal.
produced at the time of solidification of melt, resulting in the generation and propagation of defects. The differential contraction caused by the cooling produces tangential stresses, which are relieved by the movement of dislocations, followed by the creation of the observed slip lines. The movement can take place both by glide and climb of the dislocations lying in the basal planes. At higher magnifications, the slip lines are actually seen to be consisting of slip bands, which have slip lines lying between two adjacent bands (Fig. 3(b)). They are similar to the ones observed in a-brass single crystals [18,19]. The X-ray diffractogram of a crystal along [0 0 1] direction (Fig. 4(a)) shows the presence of even reflections (l ¼ 2n) for the 2h-range 0–120, with dominating peaks at (0 0 8), (0 0 1 0), (0 0 1 2),
75
Fig. 4. (a) X-ray diffractogram along [0 0 1] direction for a single crystal, in the 2h-range (h–2h scanning) 0–120. The inset shows resolved CuKa1 and CuKa2 peaks of 0 0 3 6 reflection. (b) Rocking curve around 2h ¼ 60, corresponding to (a), elaborating the angular spread of 0 0 2 0 reflection (h-scanning).
(0 0 1 6) and (0 0 2 0). The observed absence of odd reflections l ¼ 2n þ 1 is consistent with the space group Bbmb of the 2 2 1 2 phase. It further implies that other structural phases are practically nonexistent in the crystal. The formation of various structural modifications is known to result from the existence of non-equilibrium conditions during the growth process [20–24]. The observed absence of such modifications implies that a high order of equilibrium conditions had existed during the crystal growth, which additionally helped in the growth of larger size crystals. Many crystals measuring up to 5 · 5 mm2 were also seen in the flux but, unfortunately, they could not be
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extracted unbroken. Some weak reflections, marked as X1 , X2 and X3; in Fig. 4(a), might represent the odd reflections with l ¼ 2n þ 1 and correspond to the indices 0 0 1 5, 0 0 3 3 and 0 0 3 5, respectively, if one assumes that the 2 2 1 2 phase lattice is not B-centered but primitive [25]. Fig. 4(b) shows the rocking curve for the Bragg angle 2h ¼ 60:1 (h-scanning X-ray diffraction), in which a reflection by the planes (0 0 2 0) in different grains constituting the crystal has been recorded. Since these grains have slight mutual misorientation, the same reflection 0 0 2 0 is recorded at slightly different angles around h ¼ 30. The existence of several sub-peaks, marked as 1; 2; 3; . . . ; 7, is seen, but it is to be noted that the diffracted intensity never drops to zero within the spread of the main peak, viz. between 28 and 30, thus implying that the misorientation of the grains is continuous. The various sub-peaks correspond to the preferred directions of orientation of the grains, in which the number of grains is relatively high. The most preferred angle of orientation, corresponding to the highest peak, is h ¼ 29:10. The number of grains oriented on either side of h ¼ 30:05 are nearly equal, as indicated by the near equality of the areas under the curve on either side of this angle, which means that the misorientation is nearly symmetric around the mean position h ¼ 30:05. The total angular spread is nearly 5, suggesting that the misorientation of the grains is limited to nearly ±2.5. A close looks at other peaks in Fig. 4(a) reveals that the angular spreads of other reflections and hence the corresponding misorientation of grains are also the same order. To detect the presence of any modulation structures in the crystal and for their necessary follow-up analysis, h–2h scanning was carried out around the reflections 0 0 3 6 and 0 2 0 (Figs. 5(a) and 6(a)). Around the 0 0 3 6 reflection, four satellite peaks Q1 , Q2 and Q3 , Q4 are observed at incommensurate positions, symmetrically on either side of the main peak. These satellites are seen to be symmetric not only in respect of their position around 0 0 3 6, but also in respect of their respective intensities. Q2 and Q3 are weaker first order satellites resulting from a relatively large grain misorientation, as suggested by their compara-
Fig. 5. (a) X-ray diffraction h–2h scanning of a crystal around 0 0 3 6 reflection. (b) Schematic of the reciprocal space near 0 0 3 6 reflection.
tively large half-widths. Since they have small intensity, it follows that the number of grains with relatively large misorientation is small. They are situated very close to the 0 0 3 6 reflection at spacing of 0:21b . The satellites Q1 and Q4; with double the value of the b -component, viz. 0:42b , have higher intensities. Their smaller half-widths imply that they result from grains with relatively smaller misorientation. Thus the number of grains with smaller misorientations is larger than the number of grains with larger misorientations. The values of respective b components are determined with the help of a vector diagram (Fig. 5(b)). The point Q4 can be reached from the central point O, corresponding to the 0 0 3 6 reflection by traversing through the vectors OA and AB.
P. Kumar et al. / Physica C 406 (2004) 72–78
77
Q1 : 34c þ 2q ¼ 34c þ 2ð0:21b þ c Þ ¼ 36c 0:42b : However, for the satellite reflections Q2 and Q3; one can show that they cannot be linked with reflections 0 0 3 6 or 0 0 3 4 in terms of modulation wave vector q. They are actually originating from forbidden reflection 0 0 3 5, with a displacement vector q added to it as follows: Q2 : 35c þ q ¼ 35c þ ð0:21b þ c Þ ¼ 36c 0:21b ; Q3 : 35c þ q ¼ 35c þ ð0:21b þ c Þ ¼ 36c þ 0:21b :
Fig. 6. (a) X-ray diffraction h–2h scanning a crystal around 0 2 0 reflection. (b) Schematic of the reciprocal space near 0 2 0 reflection.
Q4 : 36c þ OA þ OB ¼ 36c þ ð0:21b þ c Þ þ ð0:21b c Þ ¼ 36c þ 0:42b
ðstarting with 36c Þ:
Now the same position Q4 may also be obtained starting with 0 0 3 4 as follows. Q4 : 34c þ 2q ¼ 34c þ 2ð0:21b þ c Þ
¼ 34c þ 2c þ 0:42b
¼ 36c þ 0:42b
Thus, the satellites Q1 , Q4 and Q2 , Q3 may be associated with the Bragg reflections 0 0 3 4 and 0 0 3 5, respectively. Since the reflection 0 0 3 5 is forbidden, the relatively weaker intensity of Q2 , Q3 is qualitatively accounted for. Similarly, the h–2h scanning diagram, taken around the Bragg reflection 0 0 2 0 and the corresponding vector diagram, explaining the occurrence of the satellite reflections Q1 , Q2 , are shown in Fig. 6(a) and (b), respectively. The two satellite reflections Q1 and Q2 are symmetrically placed around the principal reflection 0 2 0. They are weaker second-order satellites, situated at incommensurate positions, with an apparently incommensurate value for the b component as 1:58b and 2:42b , respectively, which imparts a displacement of 0:42b for them on either side of the 0 2 0 reflection. The positions of the pikes Q1 and Q2 with respect to the parent peak are indicated as follows: Q1 : 2b ð0:21b þ c Þ ð0:21b c Þ
¼ 2b 0:42b ¼ 1:58b :
ðstarting with 34c Þ:
Thus, it may be concluded that Q4 is satellite reflection of 0 0 3 4, with a displacement vector 2q added to it. Similarly Q1 may be seen as arising from 0 0 3 4 by adding the same displacement vector 2q on the other side i.e., by replacing 0:21b by 0:21b , as follows (not shown in the Fig. 5(b)):
Q2 : 2b ð0:21b þ c Þ þ ð0:21b c Þ ¼ 2b þ 0:42b ¼ 2:42b : Initially several models were proposed to account for creation of the incommensurate structure, but gradually the experimental facts have led to the consensus that the presence of additional oxygen atoms in the Bi–O layer leads to a
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P. Kumar et al. / Physica C 406 (2004) 72–78
displacive modulation [26]. A mismatch exists between the crystallographic units of the rocksalttype Bi–O layer and the more rigid perovskite Cu–O layers, to accommodate which the Bi atoms adjust their coordination, leading to an excess of oxygen atoms within the plane.
4. Conclusion Surface morphology and modulation structure in superconducting single crystals of Bi2 Sr2 CaCu2 O8þx grown by self-flux method have been presented. The observed surface features suggest that the crystals grow by two-dimensional nucleation, etch pits are created by atmospheric attack and the thermal stress caused during crystal growth produce dislocations and make them to move about. The misorientation of the grains in the crystals is limited to nearly ±2.5. The grains with relatively smaller misorientations outnumber those with larger misorientations. The occurrence of satellite reflections around Braggs reflections 0 0 3 6 and 0 2 0, their position and intensity are explained in terms of modulation wave vector q ¼ 0:21b þ c .
Acknowledgements The financial assistance from the University Grants Commission (UGC) under the research project ‘‘Superconductivity R&D Programme’’ and necessary support by Prof. G.K. Chadha is thankfully acknowledged.
References [1] H. Maeda, Y. Tanaka, M. Fukutomi, T. Asano, Jpn. J. Appl. Phys. 327 (1988) L209. [2] M.A. Subramaniam, C.C. Torardi, J.C. Calabrese, et al., Science 239 (1988) 1015. [3] J.L. Tallon, R.G. Buckely, P.W. Gilberd, et al., Nature 333 (1988) 153. [4] Y. Gao, P. Lee, P. Coppens, et al., Science 241 (1988) 954. [5] Y. Matsui, H. Maeda, Y. Tanaka, Sh. Hariuchi, Jpn. J. Appl. Phys. 27 (1988) L372. [6] K. Kawaguchi, S. Sasaki, H. Mukaida, M. Nakao, Jpn. J. Appl. Phys. 27 (1988) L1015. [7] O. Eibl, Solid State Commun. 69 (1989) 509. [8] Z.C. Kang, O. Monnereau, F. Remy, et al., J. Phys. (Paris) 50 (1989) 1227. [9] S.A. Sunshine, T. Siegrist, et al., Phys. Rev. B 38 (1988) 893. [10] J.M. Tarascon, Y.Le. Page, et al., Phys. Rev. B 37 (1988) 9382. [11] P. Bordet, J.J. Capponl, et al., Physica C 156 (1988) 189. [12] A.P. Mayer, R.A. Cowley, J. Phys. C: Solid State Phys. 31 (1986) 6131. [13] W. Adlhart, H. Blank, H. Jagodzinski, Acta Cryst. A 38 (1982) 505. [14] J.M. Perez-Mato, G. Madariaga, F.J. Zuniga, A. Garcia, Acta Cryst. A 43 (1987) 216. [15] J.-C. Grivel et al., Physica C 274 (1997) 66. [16] J.J. Gorina et al., Solid State Commun. 85 (8) (1993) 695. [17] A.J.S. Chaudhury et al., Physica C 225 (1994) 388. [18] Z.R. Wang, T.B. Massalski, H. Margolin, Acta Metall. 32 (1984) 977. [19] V.N. Timfeev, I.G. Gorlova, Physica C 309 (1998) 113. [20] K.K. Fung, R.L. Withers, Y.F. Yan, et al., J. Phys. Condens. Matter 1 (1989) 317. [21] J.X. Zhang, G.M. Lin, et al., Supercond. Sci. Technol. 3 (1990) 113. [22] N.D. Zhigadlo, V.V. Zaretskii, JETP Lett. 49 (1989) 572. [23] E. Salje, Phil. Mag. Lett. 59 (1989) 219. [24] E. Salje, K. Parlinski, Supercond. Sci. Technol. 4 (1991) 93. [25] O. Eibl, Physica C 168 (1990) 215. [26] Y.Le. Page, W.R. McKinnon, J.M. Tarascon, P. Barboux, Phys. Rev. B 40 (1989) 6810.
Surface morphology and incommensurate modulation of self-flux grown Bi2Sr2CaCu2O8þx single crystals P. Kumar a, B. Kumar
a,*
, I. Bdikin
b,c
, A.L. Kholkin c, G.C. Trigunayat
a
a
c
Department of Physics and Astrophysics, University of Delhi, 110007 Delhi, India b Institute of Solid State Physics, RAS, 142432 Chernogolovka, Russia Department of Ceramics and Glass Engineering, CICECO, University of Aveiro, 3810-193 Aveiro, Portugal Accepted 9 February 2004 Available online 13 April 2004
Abstract Structural studies have been carried out in large size superconducting single crystals of Bi2 Sr2 CaCu2 O8þx grown by self-flux method. Surface morphology of the crystals in respect of growth steps, slip lines/bands and etch pits has been examined by scanning electron microscopy (SEM). A quantitative study of grain misorientation in the crystals has been conducted by X-ray diffraction, which has also revealed the existence of incommensurate modulation of the crystal structure. A detailed analysis of first and second order satellite reflections associated with the Bragg reflections 0 2 0 and 0 0 3 6, in terms of incommensurate b -components and modulation wave vector q ¼ 0:21b þ c , has been made. It is proposed that while the second order satellite reflections observed around 0 0 3 6 are linked with the existent neighboring Bragg reflections, the first order satellite reflections are correlated with a forbidden reflection. 2004 Elsevier B.V. All rights reserved. Keywords: Bi2 Sr2 CaCu2 O8þx HTSC; Single crystal growth; Defect structure; Modulated structure; SEM; X-ray characterization
1. Introduction The discovery of superconductivity with a high critical temperature Tc in the Bi–Sr–Ca–Cu–O system has led to its extensive investigation. Three phases, generally represented by Bi2 Sr2 Can1 Cun O2nþ4 , n ¼ 1; 2; 3 and respectively termed as 2 2 0 1, 2 2 1 2, 2 2 2 3 phases, are the first three members of a family [1–3]. The first member, Bi2 Sr2 CuO6 , attracts less interest because of its low
*
Corresponding author. Fax: +91-011-27667061. E-mail addresses: [email protected], b3kumar69@ yahoo.co.in (B. Kumar).
Tc and the third member, Bi2 Sr2 Ca2 Cu3 O8þx , cannot be prepared easily as a single-phase sample. We have chosen the second phase, Bi2 Sr2 CaCu2 O8þx (2 2 1 2 phase), for the study of superconducting properties, surface morphology and structural characteristics. The 2 2 1 2 phase has a modulated structure which is characterised in the X-ray and electron diffraction patterns through the emergence of a number of satellites reflections in the b –c plane [4–8]. The modulation is incommensurate in nature [2,9–11]. A consensus has emerged that the extra oxygen atoms inserted in the Bi–O layers are linked to a displacive modulation with its origin in the mismatch between the crystallographic blocks
0921-4534/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2004.02.180
P. Kumar et al. / Physica C 406 (2004) 72–78
of the perovskite Cu–O planes and the rocksalt type Bi–O layers. The nature of the satellites needs to be elucidated. But there is controversy about the position of the super reflections arranged about the base reflections. For instance, besides the wellknown super reflections in the Bbmb space group, Kenichi and Kawaguchi [6] have observed additional super reflections around the Bragg reflections 0 0 2 0 and 0 0 3 6. These additional super reflections are characteristic of the well-known modulations, with the assumption that the formation of such superstructural reflections is also possible around the sites of the Bragg reflections forbidden in the main lattice symmetry. However, according to the theory of X-ray scattering by modulated structures [12–14], intensities of the superstructural reflections are proportional to those of the structural reflections and, consequently, unambiguously determine the absence of the superstructural reflections. We have carefully determined the modulation phases and grain misorientation in the crystals, as these factors play an important role in the interpretation of structural quality of the single crystals. So far, not many studies have been reported on the structural quality of the Bi-2212 single crystals. The earlier scanning electron microscopy (SEM) studies on Bi-2212 crystals had been mostly employed to provide information regarding crystal size and surface smoothness. The growth steps and fractured planes, seen near the edges of crystals, were mostly attributed to the mechanical strain suffered by crystals during extraction from the flux [15,16]. Chaudhury et al. [17] had reported that the thicker crystals actually consisted of a large number of platy crystals having well-aligned c-axis. They also reported the growth of crystals along (1 1 0) faces. We have observed features like growth steps, slip lines/bands, etch pits, etc., from which supplementary information have been gained regarding defect surface structure of the crystals.
2. Experimental High purity Bi2 O3 , SrCO3 , CuO, CaCO3 (purity > 99.999%, ALDRICH) powders were used
73
as starting material for the growth of single crystals. The components were taken in the stoichiometric proportion, thoroughly mixed and transferred into a high purity alumina cylindrical crucible (purity > 99.0%; CERAC). The single crystals were prepared by slowly cooling the melted charge from 1000 to 800 C at the rate 2 C/h, using a box type programmable furnace (HERAEUS K-1252). X-ray diffraction studies were performed on DRON-2 and SIEMENS (D 500) diffractometers, using CuKa radiation. While the sample was rotated at an angular rate x, a photographic film, placed directly in front of the X-ray detector and perpendicular to the diffracted beam, was either rotated at an angular rate 2x (for h–2h scanning topography) or was motionless (for h-scanning topography). The samples were aligned with their b and c directions in the horizontal scattering plane. The samples were examined by scanning electron microscopy (SEM), employing a JEOL JSM840 electron microscope. The samples were mounted on copper stubs with carbon electroconducting paint and a thin uniform gold film was sputtered on them, using an ion sputterer (JFC1100). The gold coating faithfully contours the surface features, improves electrical conductivity of the surface and minimizes the thermal degradation. An attached camera recorded the observed features on a photographic film.
3. Results and discussion The as-grown crystals had shiny flat surfaces and measured upto 5 mm across (mostly 4 · 3 mm2 ) and upto 0.3 mm in thickness (Fig. 1(a)). Their single crystalline nature was confirmed by Xray diffraction methods. The critical temperature Tc was determined to be 85 K for most of the crystals by resistivity measurements in the abplane. The transition width DTc measured nearly 2 K. The crystal structure of Bi2 Sr2 CaCu2 O8þx is tetragonal with the lattice parameters as a ¼ b ¼ c ¼ 30:842 A. 5:412 A, The surface features of the crystals were examined by scanning electron microscopy. The
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Fig. 1. (a) Scanning electron micrograph of an as-grown crystal, measuring upto 5 mm along one diagonal. (b) Zig-zag growth steps, indicating two-dimensional layer growth.
Fig. 1(a) shows the entire surface of a crystal. The crystal surfaces were largely found to be smooth even upto a high magnification of ·500. However, crack-like lines were seen in many crystals, which possibly formed during the extraction of the crystals from the bulk. In some cases zigzag layered steps were observed near the corners of the crystals, indicating that the crystals had grown by two-dimensional layer growth process (Fig. 1(b)). Although no deliberate etching of the crystal surface had been carried out, etch pits were seen on some portions of the crystals. They looked shallow, with no definite shape. They apparently originated from atmospheric attacks on the crystals. In many cases they lay along parallel rows, as seen in Fig. 2(a). The etch pits are known to be
Fig. 2. (a) Parallel rows of etch pits on the basal surface of a crystal. (b) Intersection rows of etch pits. Their mutual inclination is preferentially observed to be 30.
preferentially created at the sites of dislocations, which could be either edge dislocations or screw dislocations. They are either directed along crystallographic axes or have components along them. If the dislocations are preferentially produced along only one set of planes, a single row or a set of parallel rows of dislocations is produced, resulting in the etch pits arranged along a set of parallel rows, as seen in Fig. 2(a). In some cases intersecting rows of etch pit were observed, as in Fig. 2(b). Although the angle of their mutual inclination was not well defined in most of the cases, a preferential inclination of 30 was observed in some cases. At lower magnifications, patterns of parallel slip lines have been observed on the basal surfaces (Fig. 3(a)). During the growth process, directional thermal stresses are
P. Kumar et al. / Physica C 406 (2004) 72–78
Fig. 3. (a) Patterns of parallel slip lines on the basal surface of a crystal. (b) Patterns of slip bands on the basal surface of a crystal.
produced at the time of solidification of melt, resulting in the generation and propagation of defects. The differential contraction caused by the cooling produces tangential stresses, which are relieved by the movement of dislocations, followed by the creation of the observed slip lines. The movement can take place both by glide and climb of the dislocations lying in the basal planes. At higher magnifications, the slip lines are actually seen to be consisting of slip bands, which have slip lines lying between two adjacent bands (Fig. 3(b)). They are similar to the ones observed in a-brass single crystals [18,19]. The X-ray diffractogram of a crystal along [0 0 1] direction (Fig. 4(a)) shows the presence of even reflections (l ¼ 2n) for the 2h-range 0–120, with dominating peaks at (0 0 8), (0 0 1 0), (0 0 1 2),
75
Fig. 4. (a) X-ray diffractogram along [0 0 1] direction for a single crystal, in the 2h-range (h–2h scanning) 0–120. The inset shows resolved CuKa1 and CuKa2 peaks of 0 0 3 6 reflection. (b) Rocking curve around 2h ¼ 60, corresponding to (a), elaborating the angular spread of 0 0 2 0 reflection (h-scanning).
(0 0 1 6) and (0 0 2 0). The observed absence of odd reflections l ¼ 2n þ 1 is consistent with the space group Bbmb of the 2 2 1 2 phase. It further implies that other structural phases are practically nonexistent in the crystal. The formation of various structural modifications is known to result from the existence of non-equilibrium conditions during the growth process [20–24]. The observed absence of such modifications implies that a high order of equilibrium conditions had existed during the crystal growth, which additionally helped in the growth of larger size crystals. Many crystals measuring up to 5 · 5 mm2 were also seen in the flux but, unfortunately, they could not be
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extracted unbroken. Some weak reflections, marked as X1 , X2 and X3; in Fig. 4(a), might represent the odd reflections with l ¼ 2n þ 1 and correspond to the indices 0 0 1 5, 0 0 3 3 and 0 0 3 5, respectively, if one assumes that the 2 2 1 2 phase lattice is not B-centered but primitive [25]. Fig. 4(b) shows the rocking curve for the Bragg angle 2h ¼ 60:1 (h-scanning X-ray diffraction), in which a reflection by the planes (0 0 2 0) in different grains constituting the crystal has been recorded. Since these grains have slight mutual misorientation, the same reflection 0 0 2 0 is recorded at slightly different angles around h ¼ 30. The existence of several sub-peaks, marked as 1; 2; 3; . . . ; 7, is seen, but it is to be noted that the diffracted intensity never drops to zero within the spread of the main peak, viz. between 28 and 30, thus implying that the misorientation of the grains is continuous. The various sub-peaks correspond to the preferred directions of orientation of the grains, in which the number of grains is relatively high. The most preferred angle of orientation, corresponding to the highest peak, is h ¼ 29:10. The number of grains oriented on either side of h ¼ 30:05 are nearly equal, as indicated by the near equality of the areas under the curve on either side of this angle, which means that the misorientation is nearly symmetric around the mean position h ¼ 30:05. The total angular spread is nearly 5, suggesting that the misorientation of the grains is limited to nearly ±2.5. A close looks at other peaks in Fig. 4(a) reveals that the angular spreads of other reflections and hence the corresponding misorientation of grains are also the same order. To detect the presence of any modulation structures in the crystal and for their necessary follow-up analysis, h–2h scanning was carried out around the reflections 0 0 3 6 and 0 2 0 (Figs. 5(a) and 6(a)). Around the 0 0 3 6 reflection, four satellite peaks Q1 , Q2 and Q3 , Q4 are observed at incommensurate positions, symmetrically on either side of the main peak. These satellites are seen to be symmetric not only in respect of their position around 0 0 3 6, but also in respect of their respective intensities. Q2 and Q3 are weaker first order satellites resulting from a relatively large grain misorientation, as suggested by their compara-
Fig. 5. (a) X-ray diffraction h–2h scanning of a crystal around 0 0 3 6 reflection. (b) Schematic of the reciprocal space near 0 0 3 6 reflection.
tively large half-widths. Since they have small intensity, it follows that the number of grains with relatively large misorientation is small. They are situated very close to the 0 0 3 6 reflection at spacing of 0:21b . The satellites Q1 and Q4; with double the value of the b -component, viz. 0:42b , have higher intensities. Their smaller half-widths imply that they result from grains with relatively smaller misorientation. Thus the number of grains with smaller misorientations is larger than the number of grains with larger misorientations. The values of respective b components are determined with the help of a vector diagram (Fig. 5(b)). The point Q4 can be reached from the central point O, corresponding to the 0 0 3 6 reflection by traversing through the vectors OA and AB.
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Q1 : 34c þ 2q ¼ 34c þ 2ð0:21b þ c Þ ¼ 36c 0:42b : However, for the satellite reflections Q2 and Q3; one can show that they cannot be linked with reflections 0 0 3 6 or 0 0 3 4 in terms of modulation wave vector q. They are actually originating from forbidden reflection 0 0 3 5, with a displacement vector q added to it as follows: Q2 : 35c þ q ¼ 35c þ ð0:21b þ c Þ ¼ 36c 0:21b ; Q3 : 35c þ q ¼ 35c þ ð0:21b þ c Þ ¼ 36c þ 0:21b :
Fig. 6. (a) X-ray diffraction h–2h scanning a crystal around 0 2 0 reflection. (b) Schematic of the reciprocal space near 0 2 0 reflection.
Q4 : 36c þ OA þ OB ¼ 36c þ ð0:21b þ c Þ þ ð0:21b c Þ ¼ 36c þ 0:42b
ðstarting with 36c Þ:
Now the same position Q4 may also be obtained starting with 0 0 3 4 as follows. Q4 : 34c þ 2q ¼ 34c þ 2ð0:21b þ c Þ
¼ 34c þ 2c þ 0:42b
¼ 36c þ 0:42b
Thus, the satellites Q1 , Q4 and Q2 , Q3 may be associated with the Bragg reflections 0 0 3 4 and 0 0 3 5, respectively. Since the reflection 0 0 3 5 is forbidden, the relatively weaker intensity of Q2 , Q3 is qualitatively accounted for. Similarly, the h–2h scanning diagram, taken around the Bragg reflection 0 0 2 0 and the corresponding vector diagram, explaining the occurrence of the satellite reflections Q1 , Q2 , are shown in Fig. 6(a) and (b), respectively. The two satellite reflections Q1 and Q2 are symmetrically placed around the principal reflection 0 2 0. They are weaker second-order satellites, situated at incommensurate positions, with an apparently incommensurate value for the b component as 1:58b and 2:42b , respectively, which imparts a displacement of 0:42b for them on either side of the 0 2 0 reflection. The positions of the pikes Q1 and Q2 with respect to the parent peak are indicated as follows: Q1 : 2b ð0:21b þ c Þ ð0:21b c Þ
¼ 2b 0:42b ¼ 1:58b :
ðstarting with 34c Þ:
Thus, it may be concluded that Q4 is satellite reflection of 0 0 3 4, with a displacement vector 2q added to it. Similarly Q1 may be seen as arising from 0 0 3 4 by adding the same displacement vector 2q on the other side i.e., by replacing 0:21b by 0:21b , as follows (not shown in the Fig. 5(b)):
Q2 : 2b ð0:21b þ c Þ þ ð0:21b c Þ ¼ 2b þ 0:42b ¼ 2:42b : Initially several models were proposed to account for creation of the incommensurate structure, but gradually the experimental facts have led to the consensus that the presence of additional oxygen atoms in the Bi–O layer leads to a
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displacive modulation [26]. A mismatch exists between the crystallographic units of the rocksalttype Bi–O layer and the more rigid perovskite Cu–O layers, to accommodate which the Bi atoms adjust their coordination, leading to an excess of oxygen atoms within the plane.
4. Conclusion Surface morphology and modulation structure in superconducting single crystals of Bi2 Sr2 CaCu2 O8þx grown by self-flux method have been presented. The observed surface features suggest that the crystals grow by two-dimensional nucleation, etch pits are created by atmospheric attack and the thermal stress caused during crystal growth produce dislocations and make them to move about. The misorientation of the grains in the crystals is limited to nearly ±2.5. The grains with relatively smaller misorientations outnumber those with larger misorientations. The occurrence of satellite reflections around Braggs reflections 0 0 3 6 and 0 2 0, their position and intensity are explained in terms of modulation wave vector q ¼ 0:21b þ c .
Acknowledgements The financial assistance from the University Grants Commission (UGC) under the research project ‘‘Superconductivity R&D Programme’’ and necessary support by Prof. G.K. Chadha is thankfully acknowledged.
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