Bi-2212 and Y123 highly curved single-crystal-like objects: whiskers, bows and ring-like structures

This is the author's final version of the contribution published as:

Petre Badica, Angelo Agostino, Mohammad Mizanur Rahman Khan, Stefano

Cagliero, Carmen Plapcianu, Linda Pastero, Marco Truccato, Yuichiro Hayasaka,

Gerhard Jakob,

Bi-2212 and Y123 highly curved single-crystal-like objects: whiskers, bows and

ring-like structures

Superconductor Science Technology. 25 (10), 105003, (2012)

DOI:

10.1088/0953-2048/25/10/105003

The publisher's version is available at:

stacks.iop.org/SUST/25/10500

When citing, please refer to the published version.

Link to this full text:

http://hdl.handle.net/2318/119664

Bi-2212 and Y123 highly curved

single-crystal-like objects: whiskers, bows and

ring-like structures

Petre Badica

1

,

2

, Angelo Agostino

3

,

Mohammad Mizanur Rahman Khan

, Stefano Cagliero

,

Carmen Plapcianu

, Linda Pastero

, Marco Truccato

,

Yuichiro Hayasaka

7

and Gerhard Jakob

2

1 _{National Institute of Materials Physics, Atomistilor 105bis, 077125 Magurele, Romania} 2

Institute of Physics, Mainz University, Staudingerweg 7, D-55127 Mainz, Germany

3 _{NIS Center of Excellence, Department of Chemistry, University of Torino, Via P. Giuria 7,}

I-10125, Torino, Italy

4 _{Department of Chemistry, Shahjalal University of Science and Technology, Sylhet-3114,}

Bangladesh 5 CNISM and NIS Center of Excellence, Department of Physics, University of Torino, Via P. Giuria 1, I-10125 Torino, Italy

6 _{Department of Earth Sciences, University of Torino, Via Valperga Caluso 35, I-10125 Torino, Italy} 7 _{High Voltage Electron Microscopy Laboratory, IMR, Tohoku University, Katahira 2-1-1,}

Aoba, Sendai, 980-8577, Japan E-mail: badica2003@yahoo.com

Received 18 April 2012, in final form 26 June 2012

Published 31 July 2012

Online at

stacks.iop.org/SUST/25/105003

Abstract

High-temperature superconducting objects of Bi2Sr2CaCu2O8 and YBa2Cu3O7 highly curved in the ab-plane, such as curved/kinked whiskers, bows and ring-like structures, were obtained within a solid–liquid–solid (SLS) grass-like growth mechanism. As-grown objects are crystals with three-dimensional epitaxy similar to conventional single crystals: they can be viewed as crystal parts ‘cut’ from a conventional rectangular crystal. Between our curved objects and conventional crystals, whiskers or thin films there are some differences in the superconducting properties induced only by the shape factors and no new physics is observed. Some details of the growth mechanism are discussed, emphasizing curved-line formation.

1. Introduction

Shape control is one essential ingredient for the generation of materials with new functionalities. Shape formation usually takes place from simple to complex through a process of organized ‘assembly’ (or ‘self-assembly’) [1, 2] or by controlled ‘processing’ (or ‘self-processing’), e.g. by bending, twisting, rolling [3, 4]. ‘Assembly’ and ‘processing’ can sometimes overlap, but typically they are governed by different forces between the building elements and the environment. Knowledge of the corresponding forces and mechanisms represents an essential preliminary requirement

for controlling shape formation in both cases.

Concerning the ‘assembly’, there are two important

observations, and their implications.

Firstly the smallest building elements are usually in the nanosize range, but the resulting objects can be at nano, micro- or larger scale. The relevant forces for assembly and shape formation can be different at different scales (e.g. due to surface to volume ratio changes). However, there are cases when it can be considered that assembly proceeds with the same driving force, from the nano-scale all the way up to the micro-scale or higher range. One such example is growth in a mainly layer-by-layer physical condensation

regime driven by supersaturation (involving, or not, chemical reactions) of inorganic single-crystal-like micro-objects such as conventional single crystals or one-dimensional (1D) whiskers. This observation suggests that knowledge of micro-crystal growth can also be exploited in the downscaling direction and transferred, at least in principle, to the growth and shape formation of single-crystal-like nano-objects. Another consequence is that crystal growth mechanisms of 1D objects such as vapour–liquid–solid (VLS) [5], solution–liquid–solid (SoLS) [6] and the related supercritical fluid–liquid–solid (SFLS) [7] or conventional vapour–solid (VS) are very general. Based on the fact that the first three mechanisms involve a LS growth interface, they have often been considered analogous and included in the same category as the so-called ‘flux’ growth mechanisms [8]. Following the same idea we add to this group the solid–liquid–solid mechanism (S1LS2, with S2 standing for the crystal object to be grown). This mechanism also allows the growth of 1D objects, but usually in the micrometre range [9, 10]. However, it is necessary to observe that not all of the mentioned growth mechanisms of 1D crystal objects are based on a LS interface. Hence, the classification of the growth mechanisms based on the phases present during the growth is to some extent arbitrary and the key point is what is going on at the growth interface. From this perspective, learning about the growth by means of one of these mechanisms can be useful for the others, within certain limitations.

The second observation is that other shapes more complex than the basic ones are possible. The simplest complex ones are planar two-dimensional (2D) structures made of 1D elements (we shall use the notation 1D (2D)). Among them, polygonal networks ([1] and references therein), rings, bows, curved ([1,

11, 12] and therein refs.) and zig-zag [13] whiskers were obtained. Most of these structures, even if they show single-crystal-like features, are stressed, defected, twinned or compositionally graded [14]. They also rarely form by template-free assembly [1]. It should also be considered that, according to [20, 21], kinked whiskers are desirable because they could help to fabricate novel devices with fewer welding joints and improved or convenient electric connections. For some applications curved objects should be perfect single crystals, while in others defects are necessary. Unfortunately, in the literature there are only limited examples of continuously highly curved 1D (2D) crystal objects such as bows and rings [1], while some more information is available on the growth of kinked whiskers obtained by VLS [13, 15–18]or VS [19]mechanisms.

In this work we report the template-free growth and characterization of highly curved 1D (2D) single crystal bows, curved whiskers and ring-like structures of YBa2Cu3O7 (Y123) and Bi2Sr2CaCu2O8 (Bi-2212) high-temperature superconductors (HTS). The superconducting features of these materials, being very sensitive to stoichiometric and structural defects, have the interesting advantage of providing insight into such objects at the electronic level. Notably, we have also obtained similar highly curved crystal objects of the Bi–(Sr, Ca)–Co–O thermoelectric materials and the corresponding results will be reported elsewhere. It is

envisaged that our results can be applied to other materials and to other crystal growth mechanisms as well. Analysis of the growth details suggests that curved objects from this work are growing in a similar manner to the straight HTS whiskers by a solid–liquid–solid grass-like mechanism [10] or as for conventional single crystals obtained by melt-flux growth methods. It also allows us to speculate that curved shape formation is due to a shape and size changing, moving and multiple growth interface (SCMMGI) that involves shadow effects (SE).

2. Experimental details

Whiskers of Y123 were grown by a method similar to the one proposed by Nagao et al [22]. Namely, powders with cationic ratios Y:Ba:Cu:Ca:Te D 1:2:3:1:0.5 were synthesized by solid-state reaction. The simultaneous presence of Te and Ca is required for Y123 whisker growth. Starting materials (Sigma-Aldrich, Germany) were Y2O3 (99.99%), BaCO3 (99.999%), CuO (99.999 99%), TeO2 (99.995%) and CaCO3 (99.9999%). They were thoroughly mixed and calcined at 900 C in alumina crucibles for 10 h in air with three intermediate grindings. The calcined powders were then pressed into pellets of about 13 mm in diameter and 2 mm in thickness. Each pellet was used as a substrate for the whisker growth. Pellets were located in a pure alumina boat that was placed in a tube furnace with a controlled oxygen flow of 0:2 l min 1. The pellets were heated at a rate of 5 C min 1 up to 1005 C, where they dwelled for 5 h. Subsequently, the substrates were cooled with 1 C min 1 down to 915–993 C, followed by furnace cooling. Due to the pellet–crucible reaction, some Al was found in the pellets after the whisker growth. To understand some growth details, in some experiments we intentionally added some Al2O3 (Sigma-Aldrich, 99.99%) to the pellets. More information on the role of the addition of Al2O3 can be found in [23].

Bi-2212 whiskers were grown from glassy substrates as proposed by Matsubara et al [9]. In this case the catalytic impurity is Al2O3 and it is introduced from the Al2O3 crucible during melting for the Bi–Sr–Ca–Cu–O (BSCCO) glass-substrate preparation. Next, glass glass-substrates are heat treated for the whisker growth. Details are presented in [24].

For the characterization of the samples, scanning and transmission electron microscopes SEM JEOL JSM6300/ Oxford Leica Stereoscan 420 and HTEM JEOL JEM 3010 were used, respectively. For HTEM investigations, one curved whisker of Y123 was fixed with epoxy resin between two Mo meshes. Thinning of the whisker was realized by ion milling etching. Initially we applied an acceleration voltage and a current of 5 kV and 5 mA, respectively. After this step of rough milling, finishing was done at 2 kV and 2 mA. Etching at the lowest voltage and current was carried out for 1 h. Crystal structure was investigated by two- (X’Pert Panalytical–X’Celeretor ultrafast line detector, Cu K radiation) and four-circle (home made system with rotating Cu-anode from Schneider, goniometer circles from Huber and STOE control unit) x-ray diffraction (XRD). For x-ray measurements, whiskers were either fixed with

Supercond. Sci. Technol. 25 (2012) 105003 P Badica et al

Figure 1. (a) Optical microscopy image of a substrate and Y123 whiskers (objects 1–7 indicated with arrows; see text). Inset is a SEM image showing a curved whisker and the region on the substrate around the bottom-end of the whisker. (b)–(f), W1, W2 and (g) are SEM images showing in detail apparently highly curved objects of Y123 and Bi-2212, respectively. Insets to (g) are images of ring-like objects. Red lines in (g) and W1 indicate the position of the EDS measurements points.

vacuum grease on Si wafer substrates (four circles) or simply mounted on amorphous quartz holders (two circles). The magnetic properties of the whiskers were tested with a superconducting quantum interference device magnetometer (Quantum Design, MPMS-7T). Conventional plastic straws recommended by Quantum Design and vacuum grease (Apiezon M) were used to fix the whiskers. Measurements of only the straw-holder and the grease indicated that the magnetic signal versus temperature for the applied magnetic fields (parallel to the c-axis of the HTS object) is of the same order of magnitude as the field-cooling (FC) magnetic signal measured on the whisker fixed with the grease in the straw. Hence, in order to compensate for possible contributions from the fluctuating diamagnetism, the zero-field-cooling (ZFC) curves were corrected by subtracting FC curves.

3. Results

3.1. Morphology of the curved objects

Straight and curved objects grow from the same substrate (figure

1). In figure 1(a) one can distinguish bows (1, 2) and in-plane curved/kinked whiskers (3–7) of Y123. Curved whiskers (3–5) show curvature in one direction, while other crystals (6, 7) are curved in several directions. But the curved line lies only in the (ab)-plane of the presented objects. Some of the Y123 curved objects can be observed in more detail in figures 1(b)–(f), W1, W2. The radius of the curved line can significantly change from one object to another. For some crystals the shape is of a continuously curved object (e.g. bows in figures 1(b)–(d)), while others appear to be composed of straight segments making different angles (usually higher

or equal to 90 ) between them (figure 1(f)). Between the angles we could not find a specific relationship and they can be considered random. However, between the straight-line segments of the object there are small regions with a curved line (e.g. see figure 1(f), left inset). Remarkably there is no preferential orientation of the straight or curved line versus the substrate or the gas flow direction.

In figure 1(g) some curved objects of Bi-2212 are presented. Similarly to Y123, curved/kinked whiskers (not shown) and bows (figure 1(g)) were obtained. Bows of both Y123 (figures 1(b) and (d)) and Bi-2212 (figure 1(g)) may show fully or partially missing stripes running parallel to the curved line. Ring-like closed objects of Bi-2212 are also presented in the inset of figure 1(g).

In the next paragraphs we describe the results of compositional, structural and magnetic measurements of such curved objects. For presentation we selected larger objects to easily detect compositional and structural variation, if any, and also to have enough volume for superconductivity detection in magnetic measurements. 3.2. Compositional characterization of the curved objects Curved objects such as bows of Bi-2212 (from figure 1(g)) and of Y123 (from figure 1 W1, W2) were measured on the (ab)-plane-face by energy dispersive spectroscopy (EDS). Measurements were done along the radius of curvature (i.e. along the ‘width’ of the bows as indicated on the objects; see figure 1(g), W1 and W2) and along the longitudinal (i.e. along the ‘length’) direction.

For the Bi-2212 bow from figure

1

(g), the average

compositions along the radius of curvature (‘width’) and

along the longitudinal direction (‘length’) are

Bi

Sr

Ca

Cu

O

and Bi

Sr

Ca

Cu

O

(normalized to Ca

),

respectively. Scattering on the two indicated directions

2:99 3:07Sr1:48 1:67Ca2Cu2:35 3:15Ox and Bi2:55 3:12

Sr1:21 1:63Ca2Cu2:46 2:875Ox. We could not detect a sys-tematic compositional change on the length or width of

the bow. This result somehow rules out formation of

the curvature as for the compositionally graded crystals

or whiskers [14]. Moreover, the average composition and scattering of the whisker are similar to the non-stoichiometric straight Bi-2212 whiskers that are usually reported in the literature (Bi2:9 3:5Sr2Ca1:7 2:05Cu2:4 3:2Ox, normalized to Sr2 [10]). Internal substitutions noted for our whisker are well documented for BSCCO phases and were also noted for the straight Bi-2212 whiskers ([10] and references therein). Finally, we have to note that sometimes EDS has shown the presence of very small amounts of Al on the surface of the whiskers. This situation is similar to straight whiskers as well. As presented in [10] and references therein, Al is part of the liquid flux phase and if this phase is wetting the whisker, some Al can be detected on the surface, although in the bulk of the whisker the Al content is below the EDS detection limit. Therefore, both the average stoichiometric composition and the occasional presence of Al on the surface represent an indication that the same mechanism could be active during the growth of both curved and straight crystals.

The two curved Y123 objects from figure 1 W1, W2 show longitudinal average and scattering composi-tions (normalized to Y) of YBa2:038Cu2:99Ca0:147Al0:154Ox,

YBa

2:014 2:075Cu2:91 3:09Ca0:123 0:166Al0:122 0:191Ox and

YBa

1:903Cu2:764Ca0:139Al0:16Ox, YBa1:86 1:974Cu2:68 2:887

Ca0:126 0:15Al0:131 0:191Ox, respectively. The first whisker, along

its radius of curvature, has compositions YBa2:075

Cu

3:042 Ca0:159 Al0:143 Ox, Y Ba2:04 2:101 Cu2:965 3:112 Ca0:153 0:165Al0:132 0:151Ox. Observations on the composi-tion of the BSCCO whiskers are entirely valid also for the Y123 whiskers. Extra aspects and differences are: the Te content in the Y123 whiskers is below the detection limit of the EDS, a well-known situation reported in the literature (e.g. [22]), while Ca and Al enter into the structure of the Y123 whiskers. Our experiments [23] show that the content of Al depends on its availability in the substrate. Curved Y123 objects are obtained from substrates with or without added Al. This leads to the conclusion that the presence of Al is not the reason for the curved-line growth.

EDS measurements on the curved whiskers with

fully (figure

1

(b)) or partially (figure

1

(d)) missing

stripes did not show any new features versus the other

straight or curved objects.

3.3. Structural characterization of the curved objects

To look into the crystal nature of the curved objects we have performed careful structural XRD analysis (figure 2) of the Y123 bows from figure 1 W1 and W2. Only (00l) lines are detected in the 2 – measurement, which is indicative of c-axis orientation along the thickness of the object (figure 2(a)). The rocking curve (omega scan) of the (005)

Figure 2. XRD results: (a) 2 scan on W1, (b) rocking curve of (005) peak for W2 and (c) -scan of (013) peak for W1.

plane shows splitting of the diffraction peak (figure 2(b)). This is less evident for the crystal W1. These data show that the Y123 bows are composed of crystal blocks. They have misaligned c-axes with a higher angle (1.1457 ) for W2 than for W1. Similar rocking curves showing double peaks were also reported for Bi-2212 straight single crystal whiskers [25]. We centred on the maximum of the peak of the rocking curve for W1 and on the most intensive peak for W2 and performed -scans of the (013) plane. For W1 it was possible to detect the average in-plane alignment (figure 2(c); see also figure

3). In-plane misalignment angles are 0 , 7 , 37 , 44 , 53 and 90 , in agreement with the theoretical values of 36.87 , 43.6 , 53:13 D 90 36:87 and 90 [26]. Rotation angles of 6 –9 were observed by TEM in thin films at triple junctions [26] and a theoretical value considering

the detected rotations in our whiskers can be, for

example, 6:73 D 43:6 36:87 .

The most interesting observation is that in-plane orientations other than the ones at 90 show a rather low cumulative intensity contribution (figure 2(c)). The ratio between the intensity of the 90 -orientation lines and the intensity of the lines for the other orientations does not reflect accurately the quantitative orientation distribution in the whisker, due to misalignment issues with the crystal blocks. Despite this problem, it seems that the orientations at 90 are the major ones in the crystal W1. For W2, or more precisely for the better resolved c-axis crystal block when centred on its maximum in the rocking curve, we have obtained only the reflections at 90 in the phi-scan of the (013) plane. Since 0 and 90 ab-plane orientations are the main ones, and considering also the XRD information related to the c-axis orientation presented above, it transpires that

Figure 3. Reciprocal space HK-scans on whisker W1 around the peaks: (a) (113), and (b) (103). Insets are three-dimensional plots for easy visualization of the peaks splitting and the structural model of twinning induced by martensitic transformation.

the curved objects of this work are three-dimensional

(3D) epitaxial objects. In other words, they are of single

crystal nature as in the case of straight whiskers or

conventional single crystals. As a consequence, an

explanation of the highly curved-line formation through

a sort of twin-like mechanism can be dismissed.

Y123 crystal objects are grown at high temperatures and at these temperatures they have a tetragonal structure. Martensitic transformation, i.e. splitting of the tetragonal structure .a D b/ into the final superconducting orthorhombic structure (a < b) because of the intake of oxygen during cooling, produces twinning in Y123. In-plane twinning rotation of the assembly units to release the stress is very possible, but it cannot account for the curved-line formation.

Indeed, martensitic transformation occurs in Y123,

while it is not observed in BSCCO, but both materials

are grown as curved crystal-like objects. However,

twinning due to martensitic transformation is one

element composing the fine structure of Y123.

For the observation of the fine structure of the curved Y123 whiskers, reciprocal space XRD HK-scans were measured for W1 (figure 3). A scan around the (003) peak shows two maxima (not shown) and this is in agreement with the presence in the whiskers of two main crystal blocks with misaligned c-axes. Scans around (103) and (013) are complementary and in fact are rotated with 90 on the circular band. This suggests that, in a first rough approximation, each of the c-axis crystal blocks are approximately epitaxial in the ab-plane. A more detailed look at the (103) scan shows two ellipsoidal peaks. These peaks are also split into two (figure

3(b)). The situation is very similar to that usually observed in the Y123 superconducting c-axis epitaxial thin films [27], i.e. we observe an (a < b) orthorhombic cell with ab-plane twins due to martensitic transformation. One convenient situation is when the twin plane is (110). In the (100) or (010) initial directions of the tetragonal structure (a D b), arrangements with units with alternate a or b (of the newly orthorhombic structure, a 6D b) will develop. To accommodate stress in the newly formed orthorhombic situation, a mosaic structure is very probable. For the (110) twins, experimental misalignment (determined from the HK four peaks positions) between initial and resulting structures is about D 0:75 , which can be considered reasonably similar and in agreement with the value obtained assuming an ideal orthorhombic Y123 crystal structure (a D 0:382 nm, b D 0:388 nm, D 2atan.b=a/ 90 D 0:89 ). We shall also note that ellipsoids are inclined versus H and K axes due to centring issues. The presented structural fine arrangement generates three ellipsoidal peaks (figure 3(a)) in the HK-scan around (113), one central and two others that are symmetrically located. The axes of symmetry are not at 45 versus H and K directions, as would be expected. Perhaps this is due to the above-mentioned centring problems. Centring and the limited number of points probably result in an apparent five-fold split of the main ellipsoid. Although this needs further confirmation, the probability of the occurrence of a five-fold split is rather low. To our knowledge, it was not observed for 3D epitaxial single crystal thin films. However, we should recall that such details only concern the fine structure of the Y123 curved crystals and, as already mentioned, they cannot explain the highly curved-line formation.

XRD measurements are supported by HTEM results. The image in figure 4 was taken normally to the (ab)-plane of a curved Y123 whisker and close to its edge. The high resolution image and the selected area (electron) diffraction (SAED) pattern (figure 4 insets) indicate the single crystal nature of the curved whisker. Similar images were taken at different locations, showing that the in-plane orientation is preserved from one image to another. Recent careful synchrotron-radiation local measurements on small (ab)-plane areas located in different regions of a curved whisker confirm the in-plane epitaxial orientation between

Supercond. Sci. Technol. 25 (2012) 105003 P Badica et al

Figure 4. HTEM image taken close to the edge of the whisker. Details show the HTEM image at a higher magnification and the SAED pattern.

Figure 5. ZFC reduced magnetization curves taken at different fields parallel to the c-axis on W1, W2 and five straight whiskers (s) (see text). Curves between arrows are measured at the same field of 100, 200, 500, 1000, 5000 Oe, respectively.

different regions of the curved object. Results of synchrotron measurements will be published elsewhere [28].

In summary, the crystal structure details of the curved HTS objects show no essential differences between these objects and HTS conventional single-crystal-like crystals, whiskers or thin films: curved objects from this work are 1D (2D) objects with a 3D epitaxial single crystal arrangement. Implications of these results for the formation mechanism of the apparently curved line in the (ab)-plane of our objects are presented in section 4.

3.4. Magnetization versus temperature:

superconducting transitions of the curved objects

Zero-field-cooling reduced curves for the whiskers W1 and W2 are presented in figure 5for different values of applied field. In this figure analogous data are also plotted for a set of five straight whiskers with an average composition of YBa2:079Cu3:049Ca0:165Al0:09Ox that were extracted from a substrate with cationic composition Y:Ba:Cu:Ca:Te:Al D 1:2:3:1:0.5:0.025. A general observation is that all the curves show the onset of the superconducting transition at 78–80 K. In more detail, the curves at a field H D 100 Oe show temperature-independent magnetization values for temperatures lower than 20–35 K, depending on the sample, while for the curves at H D 200 Oe the same occurs for temperatures lower than 10–20 K. This holds both for straight and curved whiskers. Following the interpretation of [29] about Y123 single crystals, we associate such temperature-independent behaviour with the presence of full diamagnetism (Meissner state) in the samples and the decrease in its temperature range with increasing the applied field with the usual temperature behaviour of the lower critical field Hc1. The presence of temperature-independent magnetization values at H D 500 Oe is questionable, and is

certainly not detected in the curves at 1000 and 5000 Oe, which therefore do not show any trace of full diamagnetism.

It is also possible to notice the presence of two different slopes in each of the magnetization curves for H 200 Oe, with a steeper decrease at low temperatures that is followed by a more moderate one at higher temperatures. Continuing in the same framework as [29], the steepest slope can be associated with the penetration of the magnetic field from the edges of the samples, starting from a partial or full field exclusion state (depending on the applied field) in the low-temperature region and ending at the low-temperature where the magnetic flux fronts meet at the crystal centres. Then, in the moderate slope region observed at higher temperatures, the internal field distribution becomes less and less inhomogeneous because of lower critical current density, Jc, values that limit the internal magnetic field gradient and therefore the sample magnetization.

Such interpretation is also supported by the observation that a trend exists for the double slope to disappear at the lowest magnetic field values of our experiment (H 100 Oe; data for H < 100 Oe are not shown). Indeed, in this case the Meissner state can be maintained up to temperatures quite near Tc that correspond to almost vanishing Jc values and, therefore, to nearly zero magnetic field gradients in the samples. Under these circumstances, the crystals are virtually fully penetrated by the field, irrespectively of their sizes, and could switch directly from the Meissner state to the full penetration state, so that no change in the slope can be clearly recognized.

However, a more quantitative comparison to [29] from the point of view of Hc1 is prone to very large uncertainties and does

not make much sense because shape irregularities and size determinations induce uncertainties about the real value of the demagnetization factor for our samples that are too large. In this sense, the picture of [29] has to be considered

from a qualitative point of view and not from a

quantitative one.

We also observe that for H 500 Oe the collection of five spatially separated straight whiskers of small width generally shows higher magnetization values compared to the wider ones of comparable volume. This would indicate a lower demagnetization factor for this sample, which would take advantage of the large distance between the different crystals and basically of its lower average width-to-thickness ratio. The quality of the crystals might also contribute to the fine details of this process, but the general trend is the same for all samples.

We conclude that there is no special superconducting behaviour for the curved versus ‘straight’ objects. Observed differences are simply due to the well-known influence of shape factors on magnetic measurements.

4. Discussion

4.1. Growth and shape formation of the straight 1D

and 2D conventional whiskers and crystals

HTS Bi-2212 and Y123 are multicomponent materials composed of both insulating and superconducting layers that are weakly bonded and stacked in the c-axis direction. Their crystal structure is anisotropic. Namely, at room and at low temperatures the unit cell of these materials is tetragonal and orthorhombic, respectively. As already mentioned, at the high temperatures of growth, Y123 crystallizes as tetragonal and during cooling the orthorhombic split occurs due to oxygen intake. For orthorhombic Y123 the difference between the size of a- and b-lattice parameters is minimal. Although geometrically a and b are identical for tetragonal Y123 or Bi-2212, from the crystal chemistry viewpoint they show well-known differences so that the easy growth direction is along the a-axis and the difficult growth direction is along the c-axis [10]. However, it is noteworthy that the crystal chemistry difference (chemical bonding strength) found between the a and b directions is not large (strong bonding along both a-and b-axes), while between the a- or b- a-and the c-axis directions it is significant (weak bonding along the c-axis). This is supported by literature reports demonstrating the growth of single crystal ribbon-like straight whiskers and of the in-plane equiaxial single crystals for both Y123 and Bi-2212. Their plate-like morphology with the c-axis along the thickness (T) of the crystal object and with the largest face coinciding with the ab-plane reflects the crystal chemistry anisotropic features addressed above. Special attention should be given to the difference in the aspect ratio of the ‘straight’ crystal objects, i.e. the ratio between the length (L) and width (W) taken in the aplane and along the a- and b-directions, respectively. If the ratio R D L=W 1, the shape of the crystal is defined as a 1D whisker, and if R 1 the shape is considered to be of an in-plane equiaxial conventional crystal. Considering that the crystal chemistry for a straight whisker and for a conventional single crystal is the same, this means that the only difference is in the growth rates in the a and b directions. As a consequence, in

principle there is no difference between the growth of a single crystal, of a straight whisker or of other single crystal objects (e.g. single crystal thin films). Growth proceeds through the assembly of solid-state building elements crystallized at the growth interface. It is commonly accepted from structural and morphological observations (e.g. reflection high-energy electron diffraction, HTEM/STEM, atomic force microscopy) versus growth (e.g. growth of thin films with different orientations, growth of monolayer thin films or heterostructures containing one layer of HTS) that the building elements are half a c-axis tetragonal unit cell for Bi-2212 and one unit cell for Y123 (e.g. [30–32]). From the crystal chemistry considerations, the most convenient situation is when tetragonal building elements stack in a square-cuboid on square-cuboid sequence.

It is possible to observe that up to this level of discussion there has been no need to introduce any specific growth mechanism or any particular type of growth interface such as VS or LS to explain the single crystal growth and the habit formation of plate-like 1D or 2D ‘straight’-line crystal objects. From a practical viewpoint, tuning of the growth rate, leading to a particular habit, will depend on the environmental conditions influencing the growth in different directions.

For example, in the case of single crystal thin films that are growing by a VS method, Bi-2212 or Y123 thin films with different orientations, e.g. a-axis or c-axis, can be obtained depending on the growth conditions. The strong influence of the substrate on film growth (e.g. through the substrate–film lattice matching relationship) should also be considered. Growth conditions and the substrate can be considered to form the environmental conditions.

On the other hand, growth of Bi-2212 or Y123 straight whiskers and conventional crystals proceeds from a LS interface. For straight Bi-2212 whiskers, analysis of the literature [10] and reported in situ growth observations ([10] and references therein) point to a grass-like bottom-end S1LS2 growth mechanism as the main and most probable growth mechanism. Similar conclusions can be reached for Y123 [22] and other straight whiskers [33]. The growth interface LS2 is located on the substrate, and Matsubara et al [9] proposed that the mixture between S1 and L forms a ‘microcrucible’ from which the straight whiskers grow. There is a strong resemblance between the growth of straight single crystal whiskers by S1LS2 and the growth of conventional crystals from the melt inside ‘cavities’ by the melt-flux methods. Wanklyn [34] proposed the general flux (or self-flux) growth criteria, observing the relationship between the starting composition (type of components and their ratio in the substrate), the growth temperature and the habit of many complex as-grown crystals. For anisotropic materials such as tetragonal ones he obtained both straight single crystal whiskers and plate-like or more equiaxial single crystals. Growth rates were modified by different starting compositions and growth conditions. Within the S1LS2 mechanism, growth rates in different directions can also be modified via spatial conditions imposed on the LS2 interface, e.g. by the presence of S1 and its geometry. Namely, if we assume that the LS growth interface is the same for straight

whiskers and conventional crystals, geometrically confined spaces will limit the size of such interfaces and, thus, will suppress the straight whisker growth rate in the width and/or thickness directions, imposing a more 1D-like habit. We shall emphasize that, despite the more 1D- or 2D-like final habit, straight whiskers and conventional (‘straight’) crystals show a similar single crystal nature [10], meaning that for both of these objects the growth proceeds through the same oriented aggregation by stacking the tetragonal building elements in the already mentioned square-cuboid on square-cuboid sequence. As for the growth of single crystal thin films with different orientations, addressed above, for the whiskers and crystals the growth conditions and spatial limitations imposed on the ‘microcrucible’ or ‘cavity’ can be considered to form the environmental conditions. Therefore, it is possible to state that environmental conditions influence the habit of ‘straight’ crystal objects.

4.2. Growth and highly curved-line formation of the 1D

(2D) curved objects

As presented in section 3.1, all of the straight and curved objects from this work grow from the same substrate and do not show any preferential orientation versus substrate. In addition, SEM/EDS investigations (not presented) on the substrate regions around the roots of the curved objects (figure 1(a) inset) do not reveal different phases, compositions or morphological aspects when compared to those for straight whiskers growing from the same substrate or for the other reported straight Bi-2212 [35] and Y123 [23] whiskers. These results strongly suggest that straight and curved objects from this work grow by the same S1LS2 growth mechanism. At the same time, section 3.2 indicates the single crystal nature (3D epitaxial) of our curved objects. They have crystal features similar to those of straight whiskers and conventional single crystals. In addition, section

3.3

indicates that for curved objects there is no new superconducting behaviour. Superconducting properties show some differences between the curved objects and conventional ‘straight’ ones, but this is only due to the influence of the shape factors on magnetic measurements. It turns out that the scenario of oriented aggregation as for straight whiskers and conventional single crystals is probably the most appropriate to explain the growth of curved objects.

If we assume this idea, the formation of a highly curved line in the ab-plane of the whiskers, bows and rings of Bi-2212 and Y123 should be adapted to such a mechanism. From this perspective, our curved single crystal objects can be defined as straight ribbon-like whiskers or rectangular plate-like crystals from which some parts are missing (e.g. partially of fully missing stripes; figure 6). The curved line located in the (ab)-plane is actually an ‘apparent’ one in the sense that the so-called curved or straight crystals are structurally the same and it is no surprise that they show properties defined by well-know physics. In other words, exactly as for the case of straight 1D whisker and 2D plate crystal habit formation, changes in the growth rate in the a and b directions are responsible for the formation of the apparently highly curved growth line.

For the control of the growth rates in the a and b directions for our Y123 or Bi-2212 curved objects, one can return to Wanklyn’s criteria or, more generally, to the influence of environmental conditions on the growth and habit formation. In our case, the starting composition of the substrate and the growth conditions are approximately constant for all the objects growing with a very different shape and within the same growth run. Obviously, local growth conditions can show some variations, e.g. in terms of local thermal gradients. However, looking at Wanklyn’s experiments and at the differences obtained in the crystal habit versus growth conditions, it may be inferred that, to explain the habit of our single-crystal-like and apparently highly curved objects, local gradients should be large, which is incompatible with our experimental conditions. In such circumstances, it is appropriate to take into consideration also a mechanism based on spatial limitations acting on the LS2 growth interface. This does not mean that growth instabilities are not active and important. For a straight whisker or conventional single crystal one can consider that the LS interface is similar and planar [18]. As already explained, a straight whisker grows with the a-axis direction normal to it. We propose that the apparently curved line of our curved objects is the result of a SCMMGI accompanied by SE. During the growth evolution, changes that occur in the ‘microcrucible’ will influence the growth interface. Namely, we assume that the LS2 growth interface can be non-planar and that it can take some kind of multi-branch fractal shape being formed of planar regions of different size (figure 6, schematic drawings). The size and shape of the growth interface can change in time, and this will produce an apparent movement of the interface on the one hand, and on the other hand it will generate variable stacking rates of the tetragonal building blocks in the a and b directions. The growing crystal will be similar to a conventional one, i.e. it will have a 3D epitaxial arrangement, but its shape in the (ab)-plane may show the highly apparent curved-line growth as for our curved or kinked whiskers and bows.

Due to shadow effects induced by the presence of a solid phase at a certain moment, a mono-growth interface may split into multiple growth interfaces. The appearance of the object growing from a mono- to double-growth interface sequence will be a 3D epitaxial crystal, straight or curved, with fully or partially missing stripes running parallel to the edge. Schematically, the growth of a curved single crystal whisker with missing stripes is presented in figure 6 left. A mono–double sequence interface can also generate a 3D epitaxial continuously curved bow (figure 6 right). Furthermore, a sequence mono–double–mono in the development of the interface can result in closed ring-like structures ring-like those in the insets of figure 1(g).

Precise control of the interface splitting, size, shape and movement is highly desirable. This would allow habit control of the crystal objects. Although this is beyond the scope of this work, the present results are expected to give some hints at stimulating ideas and solutions for curved-line control, so that such an achievement could be envisaged. An immediate idea suggested by our data is to propose a route for

Supercond. Sci. Technol. 25 (2012) 105003 P Badica et al

Figure 6. Schematic drawing showing the formation of the apparent curved line of a curved whisker with a fully missing stripe (left) and of a bow (right). Note that the oriented stacking of the tetragonal building elements is similar and is also the same as for the conventional 3D epitaxial ‘straight’-line objects (such as for a rectangular single crystal, right). The SCMMGI and SE are active and influence stacking rates in the a and b directions inducing a mono–double splitting of the growth interface: red (thick) lines indicate a possible active growth interface region at arbitrary moments 1–6 (left) and 1–2 (right), blue is for missing stripe and green indicates expansion, splitting or a missing part compared to the last (6 or 2) interface. controlled growth of curved objects by driving the movement

of the growth interface by the means of a strongly localized heat source. We also observe that shadow effects can be of purely mechanical type, but can also be induced chemically, e.g. through precipitation of a solid phase that may disrupt the liquid from the LS2 growth interface at a certain moment.

We shall underline that the proposed mechanism

of the curved-line formation, although it is possible,

probably needs further experimental confirmation.

We also want to stress that the principles of SCMMGI and SE growth appear to be more general than what has been reported in this paper. For example, purely mechanical SEs have been proved to influence the VS growth interface geometry for a vapour deposition technique producing helical 3D (1D) whiskers [36].

As a final remark, we shall mention that a possible advantage of the 3D epitaxial as-grown objects with different shapes and small sizes versus conventional crystals or thin films relies on the possibility of avoiding post-growth processing for device shaping or integration. It is recognized that HTS are very sensitive to external factors, and focused ion beam processing, for example, is well known to easily produce local damage so that superconductivity is lost. This results in severe limitations with reproducibility and

miniaturization of the HTS-based devices. At the same time, at smaller size scales closer to penetration depth or coherence length, new phenomena useful for applications are possible ([10] and references therein). Although further research is required to address these ideas, we believe that as-grown 3D epitaxial HTS crystals with a certain shape and size can be useful, and this work tries to make the very first steps in this direction.

5. Conclusions

HTS curved objects such as curved/kinked whiskers, bows and ring-like structures were grown and characterized. They are 3D epitaxial single crystals with the same compositional, structural and superconducting properties and behaviour as for conventional straight whiskers, crystals or thin films. They can be considered as crystal parts ‘cut’ from conventional plate-like 1D straight whiskers or 2D rectangular single crystals. They grow by the same flux-type S1LS2 growth mechanism.

Based on growth details and comparative analysis with literature we discussed the general concepts of shape and size changing, moving and multiple growth interface (SCMMGI) and of shadow effects (SE). It is proposed that SCMMGI

and SE are responsible and explain the growth within the S1LS2 mechanism of HTS highly curved crystal objects. Namely, SE and SCMMGI, considering the crystal chemistry aspects of Y123 and Bi-2212 HTS, will produce different and variable in time growth rates in the a- and b-axis directions. The consequence is that the growth proceeds through the same oriented stacking aggregation of the tetragonal building elements as for the HTS straight crystal objects, but in this case a curved line may form in the (ab)-plane. Further experiments are necessary.

Re-evaluation of the S1LS2 growth mechanism for

anisotropic materials as a more general and important

mechanism as part of the so-called flux group growth

mechanisms could prove rewarding.

Acknowledgments

PB acknowledges support from PCCE-9/2010

(Romania) and Alexander von Humboldt Foundation.

CP and MMRK acknowledge post-doc and PhD

scholarships, respectively, at the University of Torino.

References

[1] Tang Z and Kotov A N 2005 Adv. Mater. 95117

[2] Mann M 2009 Nature Mater. 8 781

[3] Schmidt O G and Eberl K 2001 Nature 410 168

[4] Terrones H, Terrones M and Moran-Lopez J L 2001 Curr. Sci. 81 1011

[5] Wagner R S and Ellis W C 1964 Appl. Phys. Lett. 4 89

[6] Trentler J T, Hickman M K, Goel C S, Viano M A, Gibbons C P and Buhro E W 1995 Science 270 1791

[7] Hanrath T and Korgel B A 2003 Adv. Mater. 15 437

[8] Wang F, Dong A, Sun J, Tang R, Yu H and Buhro E W 2006

Inorg. Chem. 45 7511

[9] Matsubara I, Kageyama H, Tanigawa H, Ogura T, Yamashita H and Kawai T 1989 Japan. J. Appl. Phys. 2 28 L1121

[10] Badica P, Togano K, Awaji S, Watanabe K and Kumakura H 2006 Supercond. Sci. Technol. 19 R81

[11] Barsoum M W, Hoffman E N, Doherty R D, Gupta S and Zavaliangos A 2004 Phys. Rev. Lett. 93 206104

[12] Schmidt-Mende L and MacManus-Driscoll J L 2007 Mater. Today 4010

[13] Tian B, Xie P, Kempa J T, Bell C D and Lieber M C 2009

Nature Nanotechnol. 4 824

[14] Avakian R O, Avetyan K T, Ispirian K A and

Melikian E G 2003 Nucl. Instrum. Methods Phys. Res. A

508 496

Radnoczi G Z, Seppanen¨ T, Pecz B, Hultman L and Birch J 2005 Phys. Status Solidi a 202 R76

[15] Westwater J, Gosain D P, Tomiya S and Usui S 1997 J. Vac. Sci. Technol. 15 554

[16] Bootsma G and Gassen H J 1971 J. Cryst. Growth 10 223

[17] Hyun Y J, Lugstein A, Steinmair M, Bertagnolli E and Pongratz P 2009 Nanotechnology 20 125606

[18] Madras P, Dailey E and Drucker J 2009 Nano Lett. 9 3826

[19] Li S, Zhang X, Zhang L and Gao M 2010 Nanotechnology 21 436602

[20] Chen H, Wang H, Zhang X H, Lee CS and Lee S T 2010 Nano Lett. 10 864

[21] Tian B, Kohen-Karni T, Quing Q, Duan X, Xie P and Lieber C M 2010 Science 830329

[22] Nagao M, Sato M, Maeda H, Yun K S, Takano Y, Hatano T and Kim S 2003 Appl. Phys. Lett. 82 1899

[23] Calore L, Rahman Khan M M, Cagliero S, Agostino A, Truccato M and Operti L 2012 submitted

[24] Truccato M, Rinaudo G, Manfredotti G, Agostino A, Benzi P, Volpe P, Paolini C and Olivero P 2002 Supercond. Sci. Technol. 15 1304

[25] Golubkov M V, Gorina Yu I, Kaluzhnaya G A, Rodin V V, Sentyurina N N, Stepanov V A and Chernook S G 2009

Inorg. Mater. 67145

[26] Tietz A L and Carter C B 1991 Physica C 182 241

[27] Kamigaki K, Terauchi H, Terashima T, Iijima K, Yamamoto K, Hirata K and Bando Y 1988 Japan. J. Appl. Phys. 27 L1899

[28] Cagliero S, Borfecchia E, Mino L, Calore L, Martinez-Criado G, Agostino A, Truccato M, Badica P and Lamberti C 2012 submitted

[29] Krusin-Elbaum L, Malozemoff A P, Yeshurun Y, Cronemeyer D C and Holtzberg F 1989 Phys. Rev. B 39 2936

[30] Endo K, Badica P, Sato H and Akoh H 2006 Supercond. Sci. Technol. 19 S221

[31] Zhao Y, Gu G D, Russell G J, Nakamura N, Tajima S,

Wen J G, Uehara K and Koshijuka N 1995 Phys. Rev., B

513134

[32] Terashima T, Shimura K, Satoh T, Bando Y, Matsuda Y, Fujiyama A, Komiyama S, Kamigaki K and

Terauchi H 1991 J. Cryst. Growth 115 745

[33] Funahashi R, Matsubara I and Shikano M 2001 Chem. Mater.

134473

[34] Wanklyn B M 1977 J. Cryst. Growth 37 334

[35] Badica P and Togano K 2005 J. Mater. Res. 20 3358