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Applied Surface Science 258 (2012) 9175– 9180

Contents lists available at SciVerse ScienceDirect

Applied Surface Science

j our nal ho me p age: www.elsev ier .com/ loc ate /apsusc

nhancement of superconductivity in LFZ-grown BSCCO fibres by steeper axialemperature gradients

.M. Vieiraa, R.A. Silvab, R.F. Silvaa, F.M. Costac,∗

Ceramic and Glass Engineering Department, CICECO, University of Aveiro, 3810-193 Aveiro, PortugalPhysics Institute, Federal de Goiás University, C.P. 131, 74001-970, Goiânia, GO, BrazilPhysics Department, I3N, University of Aveiro, 3810-193 Aveiro, Portugal

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rticle history:vailable online 21 November 2011

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Laser floating zone (LFZ) method was employed to grow superconducting polycrystalline Bi–Sr–Ca–Cu–Ofibres of 2:2:1:2 nominal composition with two different diameters (1.75 and 2.50 mm). The temperatureprofile at the solid/liquid interface was calculated along the fibre radii from estimations of the heat trans-

5 −1

eywords:uperconducting fibresSCCOaser floating zone techniquehermal gradient

fer coefficient and thermal conductivity of the fibres. Values of temperature gradient G = 3.17 × 10 K mand G = 2.65 × 105 K m−1 at the fibre centre were obtained for the thinner and the thicker fibres, respec-tively. Growth under a steep temperature gradient has significant consequences on the microstructureof the thinner fibres: an improved texture and the absence of the copper-free Bix(Sr,Ca)yOz secondaryphase. These features lead to the superior transport properties of the thinner fibres that present a highervalue of critical current density (JC = 2200 A cm−2) than the wider ones (JC = 1400 A cm−2).

. Introduction

Grain alignment is a well-known strategy to reduce the detri-ental contribution of grain boundaries to the transport properties

n high-TC 2212-BSCCO (Bi2Sr2CaCu2O8) polycrystalline ceramicuperconductors. Laser floating zone (LFZ) is a recognized tech-ique to grow textured BSCCO fibres [1]. Fibres developed by LFZechnology can be used as power cables as well as current limiters.he low thermal conductivity associated with the absence of elec-rical resistance allows the transfer of large amounts of power with

inimal losses and heating. LFZ grown fibres were already used aslements in hybrid current leads in a prototype for the LHC (Largeadron Collider), at CERN.

The intrinsic very localized heating in the LFZ process generatesteep thermal gradients at the growth interface that allow higherulling rates than in other crystal growth methods, keeping under-ooling conditions for dendritic growth [2]. On the other hand,he grain orientation outcomes from the competition between theirection of the thermal gradient and the preferential crystal latticerowth direction. The effect of a preferred crystalline orientation isredominant at high solidification rates [3]. In the case of BSCCO

FZ growth, the superconducting grains always grow with the pref-rential [0 1 0] orientation along the fibre axis [4]. In directionalrowth (texturing), besides the favourable contribution of ori-

∗ Corresponding author. Tel.: +351234378111.E-mail address: flor@ua.pt (F.M. Costa).

169-4332/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.apsusc.2011.11.054

© 2011 Elsevier B.V. All rights reserved.

ented grains to current transport along the fibre axis, an additionaleffect takes place: the number of grain boundaries also dimin-ishes because misaligned grains are blocked at the grain boundariesof the well-aligned crystals, converging into a dendrite trunk[5].

The thermal gradient, whose role in texturing is of main impor-tance as above described, is highly dependent on the fibre radius,Rf, which can be deduced from Brice’s equation that establishes thetemperature distribution in the growing fibre [6]:

T(r, z) = To + (Tm − T0)(1 − �r2/2Rf )

(1 − �Rf /2)exp[−(2�/Rf )

1/2z] (1)

where To is the ambient temperature, Tm the temperature at therotation axis in the liquid/solid interface, � = h/K a cooling con-stant given by ratio between surface heat transfer coefficient h andthe thermal conductivity K, z the axial direction of growing and rthe radial direction. Eq. (1) is a useful single-term approximationto the series solutions provided by Brice for the heat conductionproblem in the growing crystal [7] of cylindrical shape with flatcrystal–melt interface, having assumed that radiative heat transferat the crystal surface follows the Newton’s law of cooling with con-stant dimensionless ratio (hRf/K). Brice analytical series solutionsof the temperature distribution in the crystal are consistent with

experimental measurements [6–8]. For long crystals of aspect ratioabove a critical value lc/R ∝ R−1/2 where l is the distance from thecrystal–melt interface to the cool end of the crystal at temperatureT0, the heat flow at the interface becomes independent of length

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and the single term approximation Eq. (1) can be used withoutppreciable loss of accuracy compared to the series solutions [7].

Differentiation of Eq. (1) in order to the fibre axial direction giveshe axial temperature gradient at an arbitrary radius point:

(r, z) = ∂T(r, z)∂z

= −(Tm − T0)

(2�Rf

)1/2 (1 − (�r2/2Rf ))

(1 − (�Rf /2))exp[−(2�/Rf )

1/2z] (2)

The impact of the fibre radius, Rf, on the superconducting prop-rties of LFZ 2212-BSCCO grown fibres due to the control of thebre texture and phase composition, via the thermal gradient, istill an open issue to be explored in the present study.

. Experimental procedure

Two different diameters rods (2 mm and 3 mm) were preparedrom a melt of Bi:Sr:Ca:Cu = 2:2:1:2 nominal composition and useds feed and seed rods for LFZ. Details of precursors’ preparationnd growth technique are described elsewhere [9]. Fibres of about0 cm in length, with 1.75 mm (d) and 2.50 mm (D) diameters,ere pulled by LFZ at 15 mm/h with a pedestal speed of about

1 mm/h. Feed and seed rods rotate at 15 and 12 rpm, respectively,n opposition directions. The ambient temperature at the periph-ry of the fibres was measured with a thermocouple giving a valuef T0 ≈ 200 ◦C. All fibres were afterwards annealed at 845 ◦C during6 h plus 24 h at 800 ◦C in air.

Scanning electron microscopy coupled with energy dispersivepectroscopy (SEM/EDS) and X-ray diffraction (XRD) analysis wereerformed in order to characterize the as-grown and annealed fibreicrostructures and phase compositions. An X-ray diffractometer

quipped with a texture goniometer, was used to quantify the grainlignment of the Bi-2212 superconducting crystalline phase [9].

The transport properties were evaluated by the electric resis-ance (�) as a function of temperature, using a four-point probe inamples with a length of approx. 30 mm, and by the critical currentensity at 77 K (JC), taking the 1 �V/cm criterion. The superconduct-

ng volume fraction (fSC) was estimated by magnetic susceptibilityeasurements in a superconducting quantum interference device

SQUID) magnetometer.

. Results and discussion

.1. Temperature gradient effect on phase distribution

Phase distribution along the 2212-BSCCO fibre axis and the fibreadius strongly depend on the axial temperature gradient along thebre that is given by Eq. (2). Here, for the evaluation of G(r,z), theooling constant � needs to be estimated taking the heat trans-er coefficient h and the thermal conductivity K. As the meltingemperature is approached, h increases due to radiative heat trans-er as black-body radiation, being also dependent on turbulencend velocity of the cooling melt [10]. A value of h ≈ 200 W m−2 K−1

as reported for liquid nitrogen quenched alumina ceramics [10],here the rapid formation of a gaseous film yields relatively con-

tant values of h, which are lower than the heat transfer coefficientsor water or oil quenching media.

The thermal conductivity, K, of polycrystalline samples ofelt textured ceramic thin rods and of single crystals of 2212-

SCCO superconductors was determined from the superconductingritical temperature up to 200 K [11–13]. The in-plane thermal con-uctivity of the 2212 single crystal, K = 5.5 W m−1 K−1 (at 200 K), isigher than the conductivity of melt textured rods, that lies in the.7–3.7 W m−1 K−1 range, or of other similar polycrystalline bulk

amples of 2212 composition [12]. The room temperature ther-al conductivity of a magnetically textured 2212 sample of about

W m−1 K−1 overlaps with the values of K for the single crystal [13].he values of K are weakly dependent on the 2212 composition

ience 258 (2012) 9175– 9180

but increase with the amount of Bi-free cuprates as secondaryphases in the melt textured rods. A value of K = 1.6 W m−1 K−1

(at 150 K) is reported for the core region of 2212 thin rods aftergrinding the outer layer with high proportion of the Sr1−xCaxCuO2phase [12]. The measured values of K for the 2212 materials inthe normal state are continuous and slowly changing functions oftemperature. Bi-based superconductors have comparatively lowDebye temperatures (�D) in the set of superconducting copperoxides [14]. The Debye temperature of a superconducting sin-gle crystal of Bi2Sr2CaCu2O8 was determined as �D = 250 K fromthe temperature dependence of the in-plane thermal conductiv-ity [11]. Measurements of specific heat of annealed polycrystallineBi1.8Pb0.2Sr2CaCu2O8−ı yield values of 295.6 K <�D < 303.5 K [15].By accounting for the low value of �D and for the phonon (lattice)contribution to the thermal conductivity of 2212 above room tem-perature, the temperature dependence of K of 2212 materials athigh temperature would be almost constant or may even show atrend for a small decreasing with increasing temperature [16].

Estimated values of the cooling constant �, Eq. (1), for the LFZgrowth of 2212 fibres give � = 125 m−1, based on K and h val-ues reported above (h ≈ 200 W m−2 K−1; K = 1.6 W m−1 K−1). Brice’s[6] Eq. (1) was fit to original data of Andreeta et al. [2] forthe surface temperature profile of laser heated pedestal growth(LHPG) 0.80 mm diameter fibres of the 2212 phase, by usingthe Minerr function [17] for nonlinear Least Squares Fitting withthe Levenberg–Marquardt method to minimize the summing andsquaring of the residuals. A value of �LSF = 118 m−1 was obtained.This value of � is close to � = 110 m−1 reported for improved LHPGof Y2O3–ZrO2 single crystal fibres of 6 mm diameter [18].

In the referred work of Andreeta et al. [2], the temperatureon the fibre surface ranges from 908 ◦C at the S/L interface downto 622 ◦C at one fibre diameter length away from the solidifica-tion interface, for a parallel laser beam profile that produces steepthermal gradients at the S/L interface [2]. Plots of temperature pro-files for the as-grown thin fibres (d-LFZ) and thick fibres (D-LFZ),as given by single-term approximation in Eq. (1), calculated with�LSF = 118 m−1 and TS/L = 908 ◦C, are shown in Fig. 1a and b, respec-tively. The isothermal contour lines reveal an inward concavity, thespan of temperature being wider in the large diameter fibre withlower thermal gradients. All isothermal contours calculated withEq. (1) have the same inward curvature due to the parabolic termof the radial position, r. The position of the isothermal contour forTS/L = 908 ◦C is also plotted in each of Fig. 1a and b.

The concave shape of the S/L interface towards the liquid inFig. 2a confirms that the hottest spot is located at the centre. Thisis in accordance to the models of Jeong et al. [19] and Yeckel et al.[20], where the interface meniscus in the case of silicon is convexdue to the location of the hot spot at the fibre periphery. The moltenzone is homogenized by strong flow from the hottest regions dueto the Marangoni effect [20]. These strong convective currents arehighly visible by eye during fibre growth.

The thermal gradient plotting, Fig. 1c and d, shows zones ofdiverging heat flux at the outer edge of the S/L interface. The plottingof gradient vectors in Fig. 1c and d was restricted to grid of pointswith T ≤ TS/L. The thermal gradient in the radial direction, as wellas along the axial direction, sets the conditions for interface stabil-ity and the balance with constitutional supercooling near the outeredge of the S/L interface. At the outer edge of the S/L interface, theradial component of the thermal gradient rises up to 24% and 29% ofthe axial component of the thermal gradient for the d-LFZ and D-LFZfibres, respectively. The extent of diverging heat flux zones at theperiphery, Fig. 1c and d, is in close correspondence to the periph-

eral zones of increased amounts of dark dendrites of (Sr,Ca)CuO2(1/1) cuprate that appear in the micrographs of the d-LFZ and D-LFZfibres in Fig. 3a(I and II), respectively. These pictures refer to imagesof steady state growth regions of the fibres. In the Bi–Sr–Ca–Cu–O

J.M. Vieira et al. / Applied Surface Science 258 (2012) 9175– 9180 9177

d d) a

sgiodttca

Fig. 1. Axial temperature profiles (a and b) and gradient plotting (c an

ystem, the 1/1 cuprate is the primary phase to crystallize by LFZrowth technique due to the liquid immiscibility gap that resultsn the formation of two liquids before crystallization: a Bi-richne and another with low Bi content, as it was described withetailed in a previous paper from the authors [21]. According to

he pioneer work of Gazit and Feigelson [22], the crystallization ofhis metastable phase is favoured by the increasing of the radialomponent of the thermal gradient leading to a higher cooling ratet the fibre periphery.

Fig. 2. (a) Solid/liquid (S/L) interface shape (dotted lines) in LFZ grown fibres; (b

long the fibre radius for: (a and c) d-LFZ fibres; (b and d) D-LFZ fibre.

The modulus of the temperature gradient vector was calculatedfrom the partial derivatives of T(r,z), Eq. (1), for the z ≈ 0 plane, theaxial component of the thermal gradient G(r,z) at the rotation axis(r ≈ 0) being G = 3.34 × 105 K m−1 and G = 2.86 × 105 K m−1 for d-LFZand D-LFZ fibres, respectively. From Eqs. (1) and (2), the value of

the axial component of the thermal gradient is constant on isother-mal contours calculated with Eq. (1), while the radial componentis linearly proportional to r, being null at the origin, r = 0. As thesteady state shapes of concave melt–crystal interfaces are close to

) temperature gradients at the S/L interface for the d-LFZ and D-LFZ fibres.

9178 J.M. Vieira et al. / Applied Surface Science 258 (2012) 9175– 9180

Fig. 3. (a) SEM micrographs of d-LFZ (Ø = 1.75 mm) fibres and (b) of D-LFZ (Ø = 2.50 mm) fibres: (I) transversal section of as-grown fibre; (II) longitudinal section of annealedfibre; (III) transversal section of as-grown fibre; (IV) longitudinal section of annealed fibre. The dotted lines delimit the cuprate-rich peripherical region.

Fig. 4. Pole plots of (0 0 8) planes of 2212 phase on the d-LFZ (Ø = 1.75 mm) fibre (a) and D-LFZ (Ø = 2.50 mm) fibre (b). Plot of reflection intensity taken from the verticalsection cut on pole plots, along = −90◦ , 90◦ for the d-LFZ fibre (c) and D-LFZ fibre (d).

face Science 258 (2012) 9175– 9180 9179

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J.M. Vieira et al. / Applied Sur

he isothermal contours with T = TS/L given by single-term approx-mation, Eq. (1), the approximated values of the modulus of thehermal gradient on the concave S/L interface (T = TS/L) were cal-ulated from the partial derivatives of T in Eq. (1) and are plottedn Fig. 2b. The thermal gradient increases from the centre to theorder of the solidification interface. The axial component of thehermal gradient G(r,z) at the rotation axis (r ≈ 0) on the isothermalontour are G = 3.17 × 105 K m−1 and G = 2.65 × 105 K m−1 for d-LFZnd D-LFZ fibres, respectively, the ratio between values of G beingroportional Rf

−1/2. Solidification at the S/L interface of the widerD-LFZ) fibres proceeds at a lower value of the G/R ratio than for thehinner (d-LFZ) fibres.

As the fibre diameter increases, the maximum allowable growthate to avoid constitutional supercooling decreases due to decreas-ng of the thermal gradient, as established from the constitutionalupercooling criterion from Chalmers [23]. The selected experi-ental conditions of the present work all lead to breakdown of

he solid/liquid interface, cellular growth being always observed.et, the change of fibre diameter had an effective effect on thenal microstructure of the pulled fibres and on their superconduct-

ng properties after the annealing step. The temperature gradientharacteristic of the LFZ growth processes is responsible for theigher concentration of Bi-free cuprates (dark dendrites) on thebre periphery, the effect being more pronounced in fibres ofmaller diameter, where almost 40% is a cuprate-rich area, Fig. 3a(I),ontrasting to 35% in the wider fibres, Fig. 3b(I), according to theelative extensions of the outer regions from the dotted lines.

.2. Temperature gradient effect on crystal alignment anduperconducting properties

Fig. 4a and b presents the (0 0 8) pole plots of 2212 phase in thes-grown fibres d-LFZ and D-LFZ, respectively. The texture degree isuantified considering that this diffracted intensity is proportionalo the volume of crystallites in a specific direction. The pole plotshow the highest reflection concentration at low angles, almostentred at 0◦, thus denoting a very high density of (0 0 8) planesarallel to the fibre axis. In order to compare both fibres, a Gaussianunction was fitted to the reflection intensity curve taken from theertical section cut on pole plots, along = −90◦, +90◦, Fig. 4c and

for d-LFZ and D-LFZ fibres, respectively. These figures show thathe (0 0 8) reflection in the perpendicular direction to the fibre axiss more intense in the thinner fibre, since the width at half-heightf Gaussian is smaller in d-LFZ fibre (FHMW ∼ 7◦) than in the D-LFZbre (FHMW ∼ 18◦), reflecting a higher degree of alignment of the-axis of 2212 crystals parallel to the fibre axis.

SEM micrographs of the d-LFZ fibre after annealing are shownn Fig. 3a(III) (cross-section) and a(IV) (longitudinal section). Theame is given in Fig. 3b(III and IV) for the annealed D-LFZ thickbres. The first phase to disappear in the thin fibres during thennealing step is the residual melt (RM). During this heat treatment,he 1/1 cuprate reacts with this constituent and with Bi2Sr2CuO62201) in order to form the Bi2Sr2CaCu2O8 (2212) superconduct-ng phase [21]. Another reaction product is the (Sr,Ca)14Cu24O4114/24) cuprate [24] that appears as dark crystals in the annealed

icrostructures. The 14/24 cuprate is one of the equilibrium phaseshat crystallize in fibres grown by the conventional LFZ at pullingates lower than 8 mm/h [25]. In the thicker D-LFZ fibres, the crys-als of Bix(Sr,Ca)yOz phase remain after the heat-treatment step26], contrarily to what happens in a O2-rich atmosphere, wherehese crystals reacted with 2201 leading to the 2212 phase [27].

The electric resistivity as function of temperature, �(T), is plot-

ed in Fig. 5a for the d-LFZ and D-LFZ fibres. The transition to theuperconducting state takes place at approximately the same tem-erature (TC = 91 K and 92 K) in both fibres, due to the presence ofhe 2212 phase after annealing. For temperatures above 115 K, �(T)

Fig. 5. Superconducting properties of the heat-treated d-LFZ and D-LFZ fibres: (a)electric resistivity as function of temperature; (b) electric field (E) as a function ofcurrent density (J), measured at 77 K.

becomes a linear function of temperature, �(T) = mT + �0, wherem = d�/dT and �0 = � (T = 0 K). Values of �0 = 47 �� cm and of theslope m = 2.9 �� cm K−1 are found for the d-LFZ fibre, whereas forthe D-LFZ fibre �0 = 83 �� cm and m = 3.9 �� cm K−1. The lowervalue of the former parameter in the d-LFZ fibres attests its supe-rior superconducting quality. Data of electric field (E) versus currentdensity (J) given in Fig. 5b, were fitted to the following exponen-tial equation: E(J) = E0 exp(J/J0), where E0 and J0 are constants. Thevalues of the critical current at 77 K, JC (77 K), as determined fromthe E(J) curves according to 1 �m V/cm criterion, are 2200 A/cm2

and 1400 A/cm2, respectively for d-LFZ and D-LFZ fibres. The val-ues of JC at 77 K are much higher in the fibres of small diameterthan in the wider ones. Moreover, the slope of the curve corre-sponding to the d-LFZ fibre is less steep than in the D-LFZ curve,denoting a gradual transition from the superconducting to the nor-mal state. Although the superior transport properties of the d-LFZfibres, the volume fraction of superconducting phase (fSC) in theannealed fibres, determined by magnetic susceptibility measure-ments, is smaller (73%, comparing to 82% for the D-LFZ fibres). Thesuperior superconducting current carrying capacity of the thinnerd-LFZ fibres is explained by taking into account the highest degreeof axial alignment above discussed. The pole-plots and the Gaussianfittings of Fig. 4 show that the reflection concentration becomeshigher when the fibre diameter decreases, corroborating such high

thermal gradients in the axial direction, Fig. 2b. The dependenceof the JC value on the fibre diameter probably explains the highervalue of JC = 5500 A/cm2 reported for fibres grown by LFZ with thesame composition but with a smaller diameter (Ø ∼ 1 mm) [1].

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The lower thermal gradient in the D-LFZ fibres led toavourable conditions for nucleation and growth of the copper-freeix(Sr,Ca)yOz type crystals, differently to what happens in the d-LFZbres where the steeper thermal gradient avoids such crystalliza-ion, keeping a RM. The presence of such precipitates in the D-LFZbres is kept during annealing, contrarily to the residual melt phase

n the d-LFZ ones, leading to a partial disruption of the electricalurrent paths decreasing the critical current density values. A sur-lus contribution to the higher JC values in the small diameter d-LFZbres is the superior alignment of the superconducting grains alonghe fibre axis that outcomes from the higher axial temperature gra-ient (and hence a high G/R ratio), Fig. 2b. Texture improvements byhe application of an external electrical current during the growthrocess [9] or by optimizing the pulling rate [28] are also strategies,mong others, to improve JC. Besides the improvement on the trans-ort properties induced by the grain alignment degree, it must beoted that modifications of phase composition may also improvehe JC values, namely the increase of the intergrowth Bi2223 con-ent [29].

. Conclusions

Calculations of the axial temperature gradient at the S/L inter-ace show a dependence on the LFZ fibre radius: values of

= 3.17 × 105 K m−1 and G = 2.65 × 105 K m−1 on T = TS/L isother-al contour, were estimated for thinner (d = 1.75 mm) and thicker

D = 2.50 mm) fibres, respectively, at the rotation axis. This differ-nce is kept along the radii until the fibres periphery.

The main consequences of the higher temperature gradient inhe microstructures of the thinner fibres, comparing to the thickernes, are the following: (i) a relatively wider region of 1/1 primaryuprates occurrence at the fibre periphery; (ii) the presence of aesidual melt constituent that vanishes during annealing, contrar-ly to the copper-free Bix(Sr,Ca)yOz phase that persists in the thickerbres; (iii) a higher alignment degree of 2212 superconductinghase.

The most notable feature that outcomes from the improveduality of the thinner fibres is the higher value of criti-al current density (JC = 2200 A cm−2) than for the wider onesJC = 1400 A cm−2), under the same experimental LFZ growth con-itions.

cknowledgment

The financial funding from the FCT Project PTDC/CTM/6195/2006 is acknowledged.

eferences

[1] L.A. Angurel, J.C. Diez, G.F. Fuente, Laser induced cylindrical zone melting ofBi2Sr2CaCu2O8 superconductors, Z. Anorg. Allg. Chem. 635 (2009) 1767–1772.

[2] M.R.B. Andreeta, E.R.M. Andreeta, A.C. Hernandes, R.S. Feigelson, Thermal gra-dient control at the solid–liquid interface in the laser-heated pedestal growthtechnique, J. Cryst. Growth 234 (2002) 759–761.

[3] J. Deschamps, M. Gergelin, A. Pocheau, Growth directions of microstructures indirectional solidification of crystalline materials, Phys. Rev. E 78 (2008) 011605.

[

[

ience 258 (2012) 9175– 9180

[4] F.M. Costa, R.F. Silva, J.M. Vieira, Influence of epitaxial growth on supercon-ducting properties of LFZ Bi–Sr–Ca–Cu–O fibres. Part I. Crystal nucleation andgrowth, Phys. C 289 (1997) 161–170.

[5] F. Gonzales, M. Rappaz, Grain selection and texture evolution in directionallysolidified Al–Zn alloys, Metall. Mater. Trans. A 39A (2008) 2148–2160.

[6] J.C. Brice, The cracking of Czochralski-grown crystals, J. Cryst. Growth 42 (1977)427–430.

[7] J.C. Brice, Analysis of the temperature distribution in pulled crystals, J. Cryst.Growth 2 (1968) 395–401.

[8] J.H. Jeong, I.S. Kang, Optimization of the crystal surface temperature distribu-tion in the single-crystal growth process by the Czochralski method, J. Comput.Phys. 177 (2002) 284–312.

[9] M.F. Carrasco, M.R. Soares, V.S. Amaral, J.M. Vieira, R.F. Silva, F.M. Costa,Bi–Sr–Ca–Cu–O superconducting fibres processed by laser floating zone underdifferent electrical current intensities, Supercond. Sci. Technol. 19 (2006)373–380.

10] W.J. Lee, E.D. Case, The effect of quenching media on the heat transfer coefficientof polycrystalline alumina, J. Mater. Sci. 28 (1993) 2079–2083.

11] M. Houssa, M. Ausloos, S. Sergeenkov, The electronic contribution to the ther-mal conductivity of layered high-material, J. Phys.: Condens. Matter 8 (1996)2043.

12] E. Natividad, M. Castro, R. Burriel, L.A. Angurel, J.C. Diez, R. Navarro, Correla-tion of normal and superconducting transport properties on textured Bi-2212ceramic thin rods, Supercond. Sci. Technol. 15 (2002) 1022.

13] J. Mucha, S. Dorbolo, H. Bougrine, K. Durczewski, M. Ausloos, Analysis ofexperimental conditions for simultaneous measurements of transport andmagnetotransport coefficients of high temperature superconductors, Cryogen-ics 44 (2004) 145–149.

14] A. Mourachkine, The oxygen isotope effect on critical temperature in super-conducting copper oxides, Supercond. Sci. Technol. 17 (2004) 721.

15] K.Q. Wang, Z.Q. Mao, Y. Feng, L.Z. Cao, The relations of specific heat anomalywith variation of oxygen content in BiSrCaCuO (2212), Phys. C 282–287 (1997)1415–1416.

16] M. Yasukawa, N. Murayama, High-temperature thermoelectric propertiesof the sintered Bi2Sr2Ca1 − xYxCu2Oy (x = 0–1), J. Mater. Sci. 35 (2000)3409–3413.

17] Mathcad 13, MathsoftTM, Mathcad resources, Mathsoft Engineering & Educa-tion, Inc. U.S.A. (2006).

18] L. Tong, Growth of high-quality Y2O3–ZrO2 single-crystal optical fibersfor ultra-high-temperature fiber-optic sensors, J. Cryst. Growth 217 (2000)281–286.

19] J.H. Jeong, J. Oh, I.S. Kang, Analytical studies on the crystal–melt interface shapein the Czochralski process, J. Cryst. Growth 177 (1997) 303–314.

20] A. Yeckel, A.G. Salinger, J.J. Derby, Theoretical analysis and design consider-ations for float-zone refinement of electronic grade silicon sheets, J. Cryst.Growth 152 (1995) 51–64.

21] F.M. Costa, R.F. Silva, J.M. Vieira, Diffusion phenomena and crystallization pathduring the growth of LFZ Bi–Sr–Ca–Cu–O superconducting fibres, Supercond.Sci. Technol. 14 (2001) 910–920.

22] D. Gazit, R.S. Feigelson, Laser-heated pedestal growth of high Tc Bi–Sr–Ca–Cu–Osuperconducting fibers, J. Cryst. Growth 91 (1988) 318–330.

23] B. Chalmers, Principles of Solidification, John Wiley & Sons, Inc., New York,1964.

24] F.M. Costa, R.F. Silva, J.M. Vieira, Phase transformation kinetics during ther-mal annealing of LFZ Bi–Sr–Ca–Cu–O superconducting fibers in the range800–870 ◦C, Phys. C 323 (1999) 23–41.

25] M.J. Cima, X.P. Jiang, H.M. Chow, J.S. Haggerty, M.C. Flemings, H.D. Brody, R.A.Laudise, D.W. Johnson, Influence of growth parameters on the microstruc-ture of directionally solidified bismuth strontium calcium copper oxide(Bi2Sr2CaCu2Oy), J. Mater. Res. 5 (1990) 1834–1849.

26] M.F. Carrasco, R.A. Silva, N.J.O. Silva, R.F. Silva, J.M. Vieira, F.M. Costa, Radialinhomogeneities induced by fiber diameter in electrically assisted LFZ growthof Bi-2212, Appl. Surf. Sci. 255 (2009) 5503–5506.

27] H.M. Chow, X.P. Jiang, M.J. Cima, J.S. Haggerty, H.D. Brody, M.C. Flemings, Effectson annealing on the microstructure and phase chemistry of directionally solid-ified Bi2Sr2CaCu2O8, J. Am. Ceram. Soc. 74 (1991) 1391–1396.

28] L.A. Angurel, J.C. Diez, E. Martínez, J.L. Pena, G.F. de la Fuente, R. Navarro, Growthrate effects on thin Bi2Sr2CaCu2O8+ı texture rods, Phys. C 302 (1998) 39–50.

29] K. Takahasahi, S. Awaji, P. Badica, K. Watanabe, K. Togano, Influence of inter-growth Bi-2223 phase on the E–J properties of Bi2Sr2CaCu2Oı whiskers, Phys.C 460–462 (2007) 823–824.