INSTITUTE OF PHYSICS PUBLISHING

SUPERCONDUCTOR SCIENCE AND TECHNOLOGY

Supercond. Sci. Technol. 18 (2005) 239–248

doi:10.1088/0953-2048/18/3/006

Nucleation of YBa2Cu3O7−x on buffered metallic substrates in thick precursor films made by the BaF2 process Vyacheslav F Solovyov, Harold J Wiesmann and Masaki Suenaga Materials Science Department, Brookhaven National Laboratory, 76 Cornell Avenue, Upton, NY 11973, USA

Received 23 August 2004, in final form 21 October 2004 Published 14 December 2004 Online at stacks.iop.org/SUST/18/239 Abstract We present experimental data on direct measurements of area densities of YBa2 Cu3 O7−x , YBCO, nuclei in fluorinated precursor films which are on CeO2 buffered metallic and single-crystalline SrTiO3 substrates. The area density of the YBCO nuclei was measured by polarized-light microscopy after the nuclei had grown to the surface of the film. The density was found to depend strongly not only on processing conditions, but also on the type of the substrate. We also established a correlation between the area density of the nuclei and the nucleation of the randomly and c-axis oriented YBCO grains in the films. A model which was based on classical nucleation theory predicted that the nucleation was a result of collective interactions among the existing nuclei. Also, it predicted qualitatively some aspects of the functional dependence of the nucleus density on processing parameters. It was found that Jc values of very-large-grained c-axis-oriented YBCO films were low due to weak connectivity at grain boundaries.

1. Introduction Significant progress has been made toward fabrication of YBa2 Cu3 O7 , YBCO, coated conductors over the last few years. However, reproducible synthesis of multi-µm thick films of YBCO with high critical current density Jc (>1 MA cm−2 in self-field) has been a long-standing problem in YBCO coated-conductor development. Although recently thick YBCO films (
1 µm) with high critical current densities, Jc (>1 MA cm−2 ), were successfully made by a pulsed-laser deposition, PLD, technique using improved buffer layers on metallic substrates [1], this is not the case for the so-called barium fluoride, BaF2 , process, an ex situ process. The latter process is considered to be a more commercially viable process for coated conductors than a PLD process [2, 3]. Thus, substantial efforts are being expended on the investigation for the improvement of Jc for thicker films using this process. There are two primary variations in the BaF2 process. In one case a precursor film consisting of Y, BaF2 , and Cu is deposited on a substrate and is heated in an atmosphere of flowing O2 , H2 O, and N2 to convert the film to YBCO [3–8]. In the other case, a sol–gel process utilizing a solution, e.g., trifluoroacetates, containing Y, Ba, and Cu ions, can also be 0953-2048/05/030239+10$30.00 © 2005 IOP Publishing Ltd

used to fabricate YBCO films by treating the precursor in the same atmosphere as above and is being developed as a technology for coated-conductor fabrication [2, 9–11]. In both of these processes, attempts to grow YBCO films which are thicker than 1–2 µm on buffered metallic substrates generally result in films with very high content of randomly and/or aaxis-oriented grains. Since the crystallographic orientations of YBCO grains in the fully processed films are mostly determined by the orientation of the YBCO nuclei at the beginning of the process, it is important to understand the nucleation process of YBCO in this process for successful coated-conductor development. In this work, we investigate the difficulties with growing high-current thick YBCO films from a new perspective. We use the BaF2 process, which employs the precursor films deposited by vacuum evaporation. Here we report on the relationship between the crystallographic orientations of the grains in YBCO films and the area densities of YBCO nuclei on buffered metallic tapes. We show that the YBCO nucleus density is a function of the processing conditions, and determines microstructure and thus the properties of the fully processed films. To our knowledge this is the first systematic attempt to understand the factors influencing the crystallographic

Printed in the UK

239

V F Solovyov et al

(B)

(A)

40 µm

40 µm

Figure 1. Optical micrographs of 0.2 µm thick partially processed YBCO films on (A) SrTiO3 and (B) a buffered metallic tape showing a very large difference in the densities of the nuclei depending on the types of the substrates. The inset in (A) is zoomed in by 2× to show small nuclei on SrTiO3 . YBCO nuclei are dark circles and the light background area is the unreacted precursor. The specimens were heated for 5 min at T = 740 ◦ C in a flowing gas mixture of p(H2 O) = 70 Torr, p(O2 ) = 100 mTorr, and the balance N2 .

(B)

(A)

30 µm

30 µm

Figure 2. Optical images of YBCO nuclei from a 0.2 µm thick film on a buffered tape showing two different stages of nucleus ripening after it was consecutively processed for (A) 5 min and (B) 10 min. An arrow connects identical areas of the two images. p(H2 O) = 70 Torr, p(O2 ) = 100 mTorr, and T = 740 ◦ C.

orientations of YBCO nuclei in the BaF2 process. A brief account is given of the relationship between the nucleus density and Jc of the fully processed films.

2. Experimental details The primary emphasis of this work was on those specimens with 2 µm thick precursor films on buffered metallic tapes with a CeO2 cap layer1 . A small number of specimens with 0.2 µm thick precursors on SrTiO3 and buffered metallic substrates were also examined for the purpose of showing the difference in the nucleation rates of YBCO on different substrates and with different thicknesses. The precursor films, which were approximately stoichiometric composition for YBCO, were deposited on SrTiO 3 and the buffered metallic tapes by vacuum evaporation of Y, BaF2 , and Cu. These specimens were heat treated in a tubular furnace at atmospheric pressure. The flowing processing gas consisted of O2 , H2 O, and the balance N2 . The partial pressures of O2 and H2 O were varied to study their effects on density and crystallographic orientations of the nuclei. The partial pressure of H2 O, which was measured by a capacitance humidity meter, was varied between 5 and 70 Torr by having the process gas run through a heated water bubbler which was held at temperatures from 0 to 50 ◦ C. The partial pressure of O2 was varied by controlling the oxygen 1

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content of the incoming gas mixture, and was monitored by an AMETEK TM-1B oxygen analyser. Details of the deposition and heat treatment methods were described elsewhere [6]. YBCO nuclei were observed by optical polarization contrast of the surface of partially processed films. A metallographic microscope, Reichert-Jung MEF-3, was used for the purpose. By adjusting the polarization angle, we were able to obtain good contrast between YBCO nuclei and polycrystalline unreacted precursor material. YBCO islands appeared as dark circular discs on a light background as illustrated in figures 1 and 2. In this method we could only see those nuclei which had grown high enough to reach the film surface. Therefore, the nuclei had to be sufficiently far apart to be individually distinguishable. Since a typical aspect ratio, γ , of YBCO grains in this process was ∼1:10, the nuclei in a film of thickness d will be distinguishable only if the distances between the neighbouring nuclei are greater than ∼10 × d. Thus, if d = 1 µm, the internucleus spacing has to be greater than 10 µm. Fortunately and surprisingly, it turned out that the density of the c-axis-oriented YBCO nuclei was unusually low on the present set of buffered metallic substrates as shown in figures 1(B) and 2(A) and (B). The internucleus spacing was a few µm to several tens of µm depending on the types of substrates and heat treating conditions, and thus it was possible for us to study the YBCO nucleation phenomena using thicker precursor films on the substrates.

Nucleation of YBa2 Cu3 O7−x on buffered metallic substrates in thick precursor films made by the BaF2 process

80

p(H2O) = 70 Torr

p(H2O) = 25 Torr p(O2) = 100 mTorr

Inter-nuclei spacing, a (µm)

Inter-nuclei spacing, a (µm)

100

o

T = 740 C

60

40

20

0

2

4

6

8

10

Sample width, W (mm)

Figure 3. Internucleus spacing a as a function of sample width W for 2 µm thick YBCO precursor films on buffered metallic tapes. The reaction conditions were p(H2 O) = 25 Torr, p(O2 ) = 100 mTorr and T = 740 ◦ C, and the specimens were heated for 30 min.

On the other hand, YBCO on a SrTiO3 single-crystalline substrate, for instance, has typical internucleus spacing of ∼3 µm and therefore we could observe the nuclei only in the films which are thinner than ∼0.2 µm as shown in figure 1(A). These figures also illustrate that the types of substrates have a strong influence on the nucleus density of YBCO. Furthermore, we have found that among the same type of substrates the nucleus densities can be very different depending on their surface conditions. Figures 2(A) and (B) show typical polarization contrast images from the surface of a partially processed 0.2 µm thick film on buffered metallic substrates after the specimen was consecutively heated for 5 and 10 min, respectively, at T = 740 ◦ C, p(O2 ) = 120 mTorr, and p(H2 O) = 70 Torr. Since these figures were taken from exactly the same location on the tape, one can clearly see how nuclei enlarge in the course of the heat treatment, and these eventually coalesce into a uniform film. Also, figures 2(A) and (B) illustrate that most of the nucleation of YBCO takes place within a short initial time span. This is because the size of the majority of the nuclei in figure 2(B) is approximately the same, while the nucleus density in figure 2(B) is not much greater than that in figure 2(A). To facilitate optical observation of the nucleus densities and of their relationships to the crystallographic orientations of YBCO nuclei in the films, we have chosen a length of a buffered metallic tape. On a set of the substrates from this length, we were able to produce repeatedly a relatively low and uniform nucleus density of YBCO under a given processing condition. In addition, a systematic study of the relationship between the heat-treating conditions and the nucleus densities and their crystallographic orientations was performed for 2 µm thick films on the substrates. This is because 0.2 µm thick precursor films on SrTiO3 and the buffered tapes always grew totally c-axis-oriented YBCO films under the reaction conditions employed in this experiment. The nucleus density n was determined by counting manually the nuclei over a specific area. The size of the area

o

T = 740 C

100

p(H2O) = 25 Torr p(H2O) = 5 Torr

10

0

50

100

150

200

Oxygen partial pressure, p (O2)(mTorr)

Figure 4. Influence of oxygen and water vapour partial pressures on the internucleus spacing for 6 × 6 mm2 specimens which were deposited with 2 µm thick YBCO precursor films on buffered metallic tapes.

which was used for counting was generally ∼100 × 100 µm2 , but sometimes it varied depending on the nucleus density. We adjusted processing timing to give the nuclei enough time to mature, but stopped their growth before nuclei started to coalesce. The period of heat treatment was ∼0.5 h for 2 µm thick films. In this way we tried to minimize the counting error originating from overlapping nuclei. Nevertheless, the counting error could be as much as 20% or greater when the nucleus spacing became closer than 10 µm. Also, other sources of variations in the nucleus density data were due to the nonuniformity of the nucleus distributions over a large area, and to the slight differences in the surface conditions of the substrates which were presumably identical. In the following analysis we used a more convenient measure for the nucleus density, which was the average internucleus spacing, a = 1/n 1/2 . The standard θ –2θ x-ray diffraction technique was used to characterize crystallographic orientations of YBCO nuclei in partially and fully processed YBCO films on the buffered metallic substrates. Also, some of the specimens were measured for their critical currents at 77 K in self-field by a standard four-probe measurement after the films were fully processed.

3. Experimental results In order to establish the relationship between the YBCO growth rate and the nucleus density, we used a set of square specimens of different sizes. This was based on our earlier observation that the growth rate of YBCO depended inversely on the size of the specimens [12]. The processing condition was kept constant at p(H2 O) = 25 Torr, p(O2 ) = 100 mTorr, and T = 740 ◦ C, and the heat treatment period was 0.5 h while the size of the specimens was varied. As shown in figure 3, the size of the specimens had a strong influence on the internucleus distances, which increased approximately linearly with the size. Changes in the partial pressures of H2 O and O2 also had strong effects on the internucleus distances as shown in figure 4 which plots the relationship between nucleus spacing 241

Normalized random peak intensity, arb. units.

V F Solovyov et al

o

T = 740 C 2 µm thick YBCO

300

200

100

0 0

50

100

150

Inter-nuclei spacing a,(µm)

Figure 5. Normalized x-ray diffraction intensities of (013, 103) lines of YBCO, which are from randomly oriented nuclei, versus YBCO internucleus spacing a. The data were obtained from θ–2θ x-ray scans of the specimens that are presented in figures 3 and 4.

and the compositions of the processing gas atmosphere. For this experiment, a set of square samples of 6 × 6 mm 2 with 2 µm thick precursors was used, and they were processed at 740 ◦ C. The oxygen partial pressures were varied between 75 and 160 mTorr while those of water were kept at 5, 25, and 70 Torr. We found that oxygen concentration had a strong effect on the nucleus density. A limited range of p(O2 ) which was available for this experiment, due to a large counting error for the nucleus density at low p(O2 ), e.g.,
50 mTorr, prevented us from finding a meaningful functional dependence for the a versus p(O2 ) relationships for different p(H2 O). However, qualitatively, we observed that the nucleation density was extensively reduced when p(O2 ) approached some critical value, which was ≈70 mTorr for all p(H2 O). This figure also demonstrates that p(H2 O) has a moderate influence on the nucleus density of YBCO. Although there are not sufficient data points to deduce a functional dependence of the internucleus distance on p(H2 O), the data are qualitatively consistent with the relationship a ∝ p(H2 O)1/2 . Each sample corresponding to the data points in figures 3 and 4 was analysed by the θ –2θ x-ray diffraction technique to determine the content of randomly oriented YBCO nuclei. The intensity of the (103, 013) line for each sample was normalized by its area and the results were plotted as a function of optically determined internucleus distance, a, in figure 5. The (103, 013) line intensity of YBCO was used for this purpose since the non-c-axis-oriented nuclei were primarily randomly oriented nuclei and only a very few of them were a-axis oriented in this experiment. (From this point on, only randomly oriented nuclei are mentioned for simplicity.) The sudden rise in the (103, 013) line intensity with decreasing a in this figure clearly illustrates that some drastic changes are taking place in the conditions for the nucleation of c-axis-oriented YBCO as a becomes smaller than ∼15 µm. We consider this as evidence that the internucleus spacing a is a universal parameter which may be used to predict the onset of the condition favouring the nucleation of the non-c-axis-oriented nuclei. As mentioned above, we noted that 0.2 µm thick samples, which were 242

processed along with 2 µm thick ones, did not show any signs of randomly oriented nuclei. In figure 6, the morphology of YBCO grain structures is shown from the fully processed 2 µm thick films on the metallic substrates. The film in figure 6(A) had large YBCO grains, i.e., large a, and they were all c-axis oriented, while that in figure 6(B) had substantially smaller grains, i.e., smaller a, than those in figure 6(A), but a significant number of randomly oriented nuclei was observed as indicated by the arrows. These films were processed at the same temperature and at a partial pressure of 735 ◦ C, and 70 Torr, respectively. However, the oxygen partial pressures for these were different. The films in figures 6(A) and (B) were reacted with p(O2 ) of 200 and 350 mTorr, respectively. Samples shown in figure 6 were larger, 6 × 15 mm, than samples used to collect data presented in figure 4. Therefore, for these larger samples we needed somewhat higher p(O2 ) to achieve the same grain size. As shown in figure 4, a higher p(O2 ) at the same p(H2 O) led to smaller internucleus spacing a which resulted in the growth of non-c-axis-oriented grains as shown in figure 5.

4. Thermodynamics of the ex situ YBCO nucleation 4.1. The Gibbs free energy for nucleation In order to gain a qualitative understanding of the aboveobserved variations in the nucleation of YBCO nuclei, we present a thermodynamic analysis of the YBCO nucleation on a substrate. Classical theory [13] describes nucleation as a process of formation of a new phase from an undercooled metastable ‘mother’ phase. Nucleation is an activation process with a free energy barrier separating the two phases. Only nuclei larger than some critical size can overcome this barrier and form a stable phase. In our analysis we follow general guidelines of this theory, and try to find possible causes for the transition in the nucleation of the c-axis to randomly oriented YBCO nuclei when the thickness of the films or the reaction condition changes. From a thermodynamic point of view, the phase which has the lowest Gibbs energy of the critical nucleus will have the highest probability for nucleation, and eventually will dominate over other phases. Our objective would be to determine the Gibbs energy of a c-axis-oriented nucleus. We assume that a YBCO nucleus is a thin square platelet with side equal to r and height γ r . Factor γ is the aspect ratio which is taken as fixed and equal to approximately 0.1. Here, for simplicity, we treat only the case for a c-axis nucleus. However, the following analysis will also apply to an a-axis nucleus by taking its length and height to be r and the thickness to be γ r . The Gibbs free energy G for the nucleation is a sum of the surface energy G s of a nucleus and the change in the volume energy G v in forming a nucleus from a precursor, and is given by G = (G s + G v ) = σr 2 + δµ

γ r3 V

(1)

where V is the unit-cell volume of YBCO and σ is the surface energy of the nuclei. Also, here δµ (=µy − µp ) is a difference in the thermodynamic potential per unit cell between YBCO, µy , and the precursor, µp . Omitting nonessential numerical

Nucleation of YBa2 Cu3 O7−x on buffered metallic substrates in thick precursor films made by the BaF2 process

Figure 6. Optical micrographs of fully processed 2 µm thick YBCO films showing (A) a film with c-axis oriented large grains and (B) a film with smaller grains but with some randomly oriented YBCO grains among c-axis oriented grains. The randomly oriented grains are needle-shaped grains in this picture. Both films were processed under the same processing conditions of p(H2 O) = 70 Torr, T = 735 ◦ C, and processing period 4 h, except for p(O2 ) which were 200 and 350 mTorr, for (A) and (B), respectively.

factors we obtain the Gibbs free energy G ∗ and size r ∗ for the critical nucleus as 
σV V 2 ∗ 3 and r∗ ≈ − G ≈ σ . (2) γ δµ γ δµ The nucleus formation is driven by the local deviation of the chemical potential δµ, hence G ∗c , from its equilibrium in the YBCO–precursor system. Here, we assume that this deviation, δµ, which controls the nucleation of YBCO, is caused by the local variations of p(HF) only. This is because pe (HF) (≈1 mTorr) [12] is very small relative to p(H2 O) (5 Torr) and p(O2 ) (75 mTorr), and thus a small variation in the absolute values of p(HF) will cause a larger fractional change from pe (HF) than those for the other two gases. To support this argument, we give an example for the change in p(H2 O), δp(H2 O), for a given variation δp(HF) in p(HF) using the equilibrium relationship between these variables, i.e., p(HF)/[ p(H2 O)]1/2 = K e where K e is the equilibrium constant for this reaction, approximately 10−3 (Torr)1/2 for the present reaction conditions [12]. Then, δp(H2 O) = [2 p(HF)δp(HF)]/K 2 . For δp(HF) = 0.1 mTorr, δp(H2 O) = 0.2 Torr, which is much smaller than the p(H2 O) which are used for this study. Furthermore, it has been shown that the growth of YBCO in this process is controlled by the removal rate of HF from the surface of the precursor, and the variations in p(O2 ) have very little effect on the growth rate of YBCO in this process [14]. Thus, in the following, we calculate δµ and G ∗c for the deviation of p(HF) from pe (HF) for two limiting cases, i.e., thin and thick film limits. In order to proceed with the investigation of the nucleation, we need to find the thermodynamic potential of the chemical reaction for the formation of YBCO from the precursor. This reaction is schematically given by YO3/2 + 2BaF2 + 3CuO + 2H2 O = YBa2 Cu3 O6 + 4HF + (1/4)O2 .

(3)

The left side of equation (3) represents a formal precursor phase composition prior to YBCO formation. The actual precursor films at elevated temperatures may contain a number of transient phases such as Y2 Cu2 O5 , BaCuO2 and Y–Ba oxyfluoride depending on how the precursor films were made

and processed [15, 16]. Then, the thermodynamic potential µ of this reaction is µ = µ0 + kT [4 ln p(HF) − 2 ln p(H2 O) + 0.25 ln p(O2 )] (4) where µ0 is the thermodynamic potential under standard conditions. Since, as stated above, the main factor in the nucleation is the deviation of p(HF ) from its equilibrium value, the chemical potential, δµ, for the nucleation can be simply written as 
p(HF) . (5) δµ = 4kT ln pe (HF) Deriving equation (5) we have taken the ratio F/Ba = 2. Recent results of the MIT group [17] indicate that this ratio may be somewhat lower for precursors manufactured by the TFA route. If this is the case, a corrected numerical factor should be used in equation (5) to account for lower fluorine content in the precursor. As shown below, the use of this expression allows us to derive an expression for G ∗ in terms of the deviation of p(HF) from pe (HF). An important factor in determining G ∗c and r ∗ in equation (2) is the surface energy σ . This is a sum of two interfacial energies, i.e., σ = σ y−p + σ y−s where σ y−p and σ y−s are the energies associated with the YBCO/precursor and YBCO/substrate interfaces, respectively. The crystallographic orientations and the densities of the nuclei are likely to be strongly influenced by the relative size of these energies which depend on the type of substrates. Understanding the nature of σy−s is particularly important since the gain in this interfacial energy makes the BaF2 process possible since the nuclei only form on the substrate, i.e., YBCO does not nucleate in the middle of the precursor film. Unfortunately, very little is known about these energies at the present time. Thus, in the following we will only investigate the kinetics of the nucleation due to the variations in the potential, δµ, through the variations in the processing conditions since the surface conditions of the present set of the substrates are likely to be relatively unchanged from one to another. Another crucial factor in determining the orientations and the densities of the YBCO nuclei is the surface defects which favour one orientation or another for the nuclei. This factor is not included in the above thermodynamical analysis of the 243

V F Solovyov et al p(HF)=0

F2HF F1

HF

W

Potential YBCO nucleus

p(HF)=p(HF)e A

Precursor

d

Substrate

a Existing YBCO nucleus

Figure 7. Geometry used for the derivation of the chemical potential of a YBCO nucleus for the thin and the thick cases. In both cases a
d, but for the thick case d is much greater than for the thin case. Point A is the location of a potential YBCO nucleus between two existing nuclei.

nucleation phenomena in spite of its importance. However, since very little is known about the nature of surface defects in these substrates, we will not be able to include this factor in our experiment or analysis. Thus, the possible roles of the defects, which might have influenced our experiment, will be inferred in the discussion section. Below we will derive approximate expressions for the chemical potentials for thin and thick film limits. In the case of the thin film limit, we will derive an expression for the nucleation rate since the expression for δµ is simple. 4.2. Thin film limit In order to determine the chemical potential δµ for a nucleus in equation (2), first we consider a case of an infinitely thin film, which means that we neglect impedance for HF outdiffusion through the precursor film. This case is interesting because c-axis-oriented nucleation is very robust in thin films as mentioned above. We will start with the determination of the Gibbs free energy for YBCO nuclei which are at the critical size for the growth. First, we consider the probability of the YBCO nucleus formation at a position A which is at the middle of two existing and growing nuclei separated by 2a on a square substrate of size W (
a). Figure 7 schematically shows the local geometry of our model for the analysis. Since the chemical potential δµ for a YBCO nucleus is related by the deviation of p(HF) from pe (HF), we determine pA (HF) at position A for HF originating from the nuclei. HF partial pressure is equal to pe (HF) at the surface of the film above the existing nuclei since the precursor above the nuclei does not provide an additional diffusive resistance in this thin film limit. Then, pA (HF) is determined by the gaseous diffusion of HF from the existing nuclei along the surface. In this model, HF partial pressure has a minimum at point A, and therefore this point is a potential nucleation site. To find δµ of a potential nucleus at point A, we need to determine the difference in the partial pressure of HF, p(HF), between the equilibrium HF partial pressure and that at point A, pA (HF), i.e., p(HF) = pe (HF)− pA (HF). Since the profile of p(HF) is determined by HF diffusion in the gas phase, pA (HF) can be found from flux conservation between the lateral flux F1HF and the normal flux F2HF . The problem is greatly simplified by the fact that the major HF pressure drop is associated with flux F2HF ≈ pA (HF)/ W since a  W . Here, W is the 244

distance from the surface for which the concentration of HF becomes zero, and this is shown to be the same as the size of the specimen, W , for a small specimen [12]. Thus, we find the HF partial pressure at point A from the flux conservation is given by pe (HF) − pA (HF) pA (HF) = F2HF = . (6) a W From equations (5) and (6), the thermodynamic potential of a potential nucleus at point A is derived as a δµ ≈ −4kT . (7) W Now, the Gibbs free energy, equation (2), of the critical nucleus is 2 

WV WV 2 ∗ 3 3 =σ n. (8) G ≈ σ 4γ kT a 4γ kT In this expression, it is important to note that this nucleation process in the BaF2 ex situ process is a collective phenomenon since the critical nucleation energy is dependent on the internucleus distance a. As the nucleus density grows the new nuclei have to overcome, in effect, a higher energy barrier since the the driving force for the next nucleus decreases. At some point the nucleation rate will be so slow that the nucleus density will practically reach the saturation point. To determine the saturation density of the YBCO nuclei, we need to solve the following equation, which ties the rate of the nucleus production to the critical nucleus free energy given by equation (8): 
∂n n0 −G ∗ (n) , (9) = exp ∂t τ kT F1HF =

where n 0 and n are the number of available nucleation sites and of the nuclei, respectively, and τ is the attempt time. Solving equation (9) using the relationship G ∗ (n) in equation (8), we obtain the time dependence of the nucleus density as a function of time as
 t n(t) = n s ln +1 , (10) τ0 where as =

1 1/2

ns

and

≈

WV γ




σ 4kT

3/2 ,

(10a)

2
γ n 0 (4kT )3 . (10b) τσ3 WV As expected the c-axis nuclei multiply fast at the beginning of the heat treatment and practically cease to nucleate after t > τ0 and reach saturation density n s = 1/as2 . (Although this function does not saturate, a more detailed calculation for the nucleation shows the nucleus density to saturate at a faster rate than a logarithmic function [18].) It follows from equation (10a) that the nucleus density will increase with the film growth rate since the growth rate is inversely proportional to W , the diffusion distance [12], and that a substrate with the lower interfacial surface energy will produce more nuclei. We also note in equation (10b) that the time for the nuclei to saturate τ0 is a function of the surface energy, primarily the interfacial energy at the substrate. Both a and τ0 are independent of the film thickness d. This is due to our assumption that the film does not provide any diffusive resistance to the out-diffusion of HF. τ0 ≈

Nucleation of YBa2 Cu3 O7−x on buffered metallic substrates in thick precursor films made by the BaF2 process

F2HF

d

HF

A

Precursor

Substrate

s = δµ /kT, supersaturation

F1

W Thick film a>>d case, Eq. 11 Thick film a<
d=a

Thin film case, Eq. 7

a Figure 8. Geometry used for calculation of the chemical potential for a YBCO nucleus for the thick film case with a  d. The difference from the sketch in figure 7 is that the lateral flux F1HF is confined in the precursor solid.

4.3. Thick film limit To extend our analysis for the practically important thick film case, we have to take into account the impedance to HF diffusion which is created by the solid precursor. First we consider the limiting case for a
d. Our basic geometry for this case is the same as shown in figure 7 except that the precursor thickness is greater than for the previous case. The influence of the film thickness becomes relevant when impedance for HF diffusion created by the film becomes comparable to the gas-phase impedance, or d/Ds ≈ a/Dg , where Dg and Ds are the diffusivity of HF in the process gas and the precursor film, respectively. To account for the HF pressure drop across the precursor thickness d, we have to add a corresponding term to the HF flux-conservation expression. Then, the thermodynamic potential of a nucleus in this case becomes approximately
 Dg 4kT a+ d a
d. (11) δµ ≈ − W Ds The second, ‘thickness’, term uniformly elevates the thermodynamic potential. In the other limit a  d, the HF diffusion geometry changes dramatically due to the proximity of the nuclei. This geometry is illustrated in figure 8. The major difference from the other limiting case is that the lateral HF flux F1HF is confined in the precursor solid, while the normal flux F2HF is still in the gas phase. Using the same flux-conservation principle we obtain the thermodynamic potential for this case: δµ ≈ −

4kT Dg a W Ds

a  d.

(12)

In figure 9 we combine the results of equations (7), (11) and (12) and schematically plot the dependence of the supersaturation s = −δµ/kT , i.e., in a measure of deviation of a potential nucleus from the equilibrium, on the internucleus distance a for thick and thin films. What this figure illustrates are the followings. (1) The main difference in the chemical potential δµ between the thin and thick films is the level of the supersaturation, s.

a, inter-nuclei distance Figure 9. Qualitative dependence of supersaturation s(a) = −δµ/kT on internucleus spacing a for thin and thick film cases. Solid lines are theoretical approximations (see text) and the dotted line is a composite s(a) dependence for a film of arbitrary thickness.

(2) A thick film thermodynamically behaves like a thin one if nuclei are sufficiently far apart that a
d Dg /Ds . The collective component, a, in equation (11) becomes less important as the nuclei become further apart since the second, ‘thickness’, term in the equation prevails. (3) When the nuclei become closer than d, collective effects dominate again, as reflected by equation (12). However, we cannot explore the latter regime experimentally by our present optical method since the nuclei will agglomerate in this thick film limit before the nuclei emerge to the surface. The possible significance of this figure for the present study is discussed in section 5.4.

5. Discussion 5.1. Effects of the substrate materials As illustrated in figure 1, the nucleus densities of YBCO in the BaF2 process are strongly dependent on the substrate materials. Generally, it has been found that the growth of c-axis YBCO is significantly more difficult on CeO2 than SrTiO3 . Furthermore, it is well known that CeO2 tends to react with the precursor to form BaCeO3 at the YBCO/CeO2 interface, and this tendency may affect the nucleation of YBCO on CeO2 relative to that on SrTiO3 . It was also found that the precursor and a CeO2 buffer layer on LaAlO3 reacted to form a liquid Ba–Ce–O layer even prior to the formation of a YBCO layer [19]. These results clearly indicate that CeO2 has a very different chemical compatibility with the precursor and YBCO, and most likely the interfacial energy σy−s of YBCO on CeO2 is significantly greater than that on SrTiO3 . If this is the case, equation (10a) predicts that the saturation nucleus density of YBCO on SrTiO3 should be greater than that on CeO2 , and this is suggested in figures 1(A) and (B), although the paticular condition of each surface tends to control n s as will be mentioned below. We observed that the nucleation density depended strongly on the variations of the surface conditions of the substrates 245

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even among the same materials. For example, the nucleus density of YBCO was much higher on CeO2 /LaAlO3 than on the CeO2 -capped metallic substrates. Also, there were batchto-batch variations in the nucleus density for SrTiO3 substrates depending on their sources. All of these results suggest that it is important to keep the surface conditions of the buffer layer constant to obtain consistent properties of YBCO which is grown on it.

in p(O2 ). This possibility is due to the fact that some evidence exists from transmission electron microscopy and scanning tunnelling microscopy studies that the first nucleating layer is a fractional YBCO plane [20, 21]. Then, there are possibilities that variations of p(O2 ) have a strong influence on the nucleation of the first layer of YBCO having the oxygen content and cation composition different from the equilibrium YBCO phase at the reaction condition. If this is the case, it is reasonable to expect that a is a strong function of p(O2 ).

5.2. Role of oxygen and water-vapour partial pressure The above treatment of the nucleation process was based on a thermodynamic approach, and it was assumed that the nucleus is chemically identical to the bulk phase at a given atmospheric condition and temperature. Also, the small local variations in other parameters, such as p(O2 ) and p(H2 O), are expected to have little influence on the nucleation. As stated above, this is because the partial pressures of oxygen and water present in the processing atmosphere are so large that one would expect any small local variations of the partial pressures of these gases to have a negligible effect on the nucleation process of YBCO from the precursor. However, when the global partial pressures of H2 O and O2 were changed by large amounts, variations in the internucleus spacing were expected and experimentally observed as shown in figure 4. The growth rate of YBCO layers is shown to be proportional to the square root of the water-vapour pressure, p(H2 O)1/2 , and the effect of p(H2 O) on the nucleus spacing is approximately consistent with a ∝ p(H2 O)1/2 . Thus, perhaps, these phenomena are related and the observed dependence of p(H2 O) on a may not be too surprising. However, the decreasing partial pressure of O2 results in an approximately exponential increase in the internucleus distance a, and this is very surprising, especially considering the fact that the oxygen partial pressure has little or no effect on the growth rate of YBCO in this synthesis process [14]. This observed dependence of a on p(O2 ) is possibly an indication that the condition for the nucleating YBCO crystallites is very close to the stability line of YBCO in the p(O2 ) versus 1/ T diagram [5]. More specifically, as briefly mentioned above, in our opinion the observed strong influence of p(O2 ) on the internucleus distance a is possibly due to the fact that the oxygen content for YBa2 Cu3 Ox , which is formed at the reaction conditions used in this experiment, is around or below x = 6.1. This is very close to the line of stability in the p(O2 ) versus 1/ T diagram for YBCO structure. For example, at T = 740 ◦ C, p(H2 O) = 25 Torr, and p(O2 ) = 150 mTorr the oxygen content x is somewhat below 6.1, while at the same conditions except for p(O2 ) = 75 mTorr x is much closer to 6.0 or the stability limit of YBCO structure. Thus, as the p(O2 ) is reduced, G ∗ becomes very small. Since the nucleation rate for YBCO nuclei depends exponentially on G ∗ , one may expect the internucleus spacing to have an approximately exponential dependence on the decreasing p(O2 ) near the stability line. At the same time, it is interesting to note that the c-axis-oriented films can be grown at very low p(O2 ) (∼10 mTorr) at ∼750 ◦ C, below the stability line [8]. Another possibility for the strong dependence of a on p(O2 ) is related to the variation of the interfacial energy between the nucleus and the substrate due to the changes 246

5.3. The nucleus densities versus the thermodynamic analysis of the nucleation kinetics As discussed above, the surface conditions of the cap layers, which affect the interfacial energy between the YBCO and the substrate, are the important factors in controlling the nucleation of YBCO on a given substrate and are variable. Also, the applicability of this expression to 2 µm thick specimens may not be totally justified as it is observed in the figure that the linear extrapolation of the data does not intersect at the vertical axis a at zero when W = 0. Nevertheless, equation (10a) correctly predicts the general dependence of the observed nucleation density on the specimen size W as shown in figure 3. Furthermore, the analysis, equation (8), correctly predicts the qualitative temporal dependence of the nucleation density, i.e., the nucleation rate is very fast at the beginning, and slows down with time. This was supported by the observation that the nucleus densities did not change significantly from those in figures 2(A) to (B), while the nuclei grew substantially from those in (A) to (B). The above qualitative agreement between the thermodynamic analysis and the experimental results also supports the assumption that the variations in the surface conditions from one CeO2 buffered metallic substrate to another were relatively small. 5.4. Randomly oriented nuclei As discussed above, the thermodynamic analysis of the nucleation kinetics, which was derived in section 4, qualitatively described some aspects of the YBCO nucleation phenomena which were experimentally observed. At the same time, this analysis did not directly address the factors which determined the orientation of the nuclei. However, it predicted the difference in the dependence of the supersaturation for thick and thin films as shown schematically in figure 9. In terms of this figure, we will discuss possible sources for the crystallographic orientation transition from the c-axis to the randomly oriented nuclei as the internucleus spacing a is reduced as shown in figure 5. When the films are very thin, the supersaturation −δµ/kT is very low as shown in figure 9 since a/ W is generally very small in the present experiment. This means that the driving force for the YBCO nucleation is low, and the rate of the nucleation is expected to be slow. This condition generally favours the nucleation of c-axis-oriented nuclei, which are thought to be the lowest-energy orientation. This appears to be the case for thin films (0.2 µm) where the nucleation of the c-axis-oriented YBCO thick films was extremely robust. The positive slope in −δµ/kT versus a should be interpreted as the fact that the formation of a nucleus between a pair of existing

Nucleation of YBa2 Cu3 O7−x on buffered metallic substrates in thick precursor films made by the BaF2 process

nuclei becomes increasingly difficult as the spacing a between these continues to be smaller. When the thickness of the films increases, the main difference is the increased level of the supersaturation for a
d from that for the thin film limit since Dg /Ds
1 as illustrated in figure 9. (As mentioned above, we only discuss the case for a
d since the other case a  d is not applicable for the present study.) The greater values of the supersaturation reduce the critical nucleus sizes and increase the rate of the nucleation. This condition qualitatively assists the nucleation of the nuclei with different orientations since the nuclei do not have sufficient time to orient themselves to the lowest-energy geometry. Naturally, in our experiment we do not measure the supersaturation or the critical nucleus energy directly. The only information accessible to us is the nucleus density. Qualitatively, the number of nuclei is related to the height of the energy barrier for nucleation: the lower the barrier, the more nuclei we have. Given a substrate, we can reduce the barrier and increase the number of YBCO nuclei by increasing p(O2 ), reducing p(H2 O), or removing HF faster, as illustrated by figures 3 and 4. However, at some point the barrier becomes so low that random grains start to appear. If we interpret internucleus distance a as a parameter related to the height of the nucleation energy barrier, figure 5 simply tells us that for this substrate/precursor combination at a ≈ 10 µm this energy barrier is low enough to allow random nucleation.

6. Critical current density As shown above, it is possible to grow c-axis-oriented 2 µm thick YBCO on CeO2 -capped metallic tapes in a wide range of processing conditions. Hence, one would expect that critical current densities Jc of these films would be very high, >1 MA cm−2 at 77 K in self-field. However, it turns out that Jc of the films which were processed to make caxis-oriented films by having large internucleus spacing a were very low in spite of their excellent c-axis orientation and in-plane alignment. The reason for this was due to the poor intergranular connectivity among these large grains as observed by a magneto-optical imaging technique [22]. In fact, those films which gave higher Jc values had small grains, and these were made in the conditions which were very close to those in which sharp increases in randomly oriented grains were observed. These grains were better connected across the grains. A possible reason for this is that the growth front of YBCO nuclei accumulates off-stoichiometric or impurity elements as it moves from the nucleation site outward. The amount of the elements at the growth front is proportional to the travel distance of the growth front which is equal to the grain radius. That is why grains larger than ∼20 µm are not connected well to each other. One of the reasons for the impurity accumulation in the large-grained YBCO films is the fact that the composition of the precursor films is not truly stoichiometric due to the limited composition control (∼5%) in our e-beam evaporation system. If the composition were made closer to the stoichiometric value, this problem might be minimized. Here we did not discuss possibilities of low Jc due to misoriented grains because of poor substrate texture. We

believe the degrees of the texture of the substrates are excellent since the Jc values of some of the films exceeded 1 MA cm−2 . Also, since this present set of data was taken from a single batch of substrate, this should not influence the variations in Jc with the processing conditions.

7. Summary One of the most important and outstanding questions in processing highly textured YBCO films on single-crystalline or buffered and textured metallic substrates is what are the primary controlling factors which determine whether a YBCO nucleus is c-axis or a-axis/randomly oriented. Some of the difficulties in attempts to understand this problem are, for example, that (1) the difference in the energies associated in the nucleation of c- or a-axis oriented grains is expected to be very small and (2) it is very difficult to observe the nuclei experimentally even with extensive transmission electron microscopy studies [16]. Thus, developing methods to study the nucleation phenomena of YBCO is an important step in finding an answer to the above question. In this article, we have shown that the internucleus spacing of YBCO, particularly on CeO2 , is surprisingly large, tens of µm, and can be studied by a simple optical microscopy technique. Using this method, the dependence of the area nucleus density/the internucleus spacing on the variations in the YBCO growth rates, the substrate materials, and the partial pressures of O2 and H2 O was determined. It was shown that the thermodynamic analysis of the nucleation of YBCO, which is based on classical nucleation theory, could qualitatively describe some of the experimental observations. For example, these were the dependence of the internucleus spacing a on the sample size, W , and on the interfacial energy differences of the nuclei on CeO2 and SrTiO3 . However, most importantly, the analysis suggests that the nucleation of YBCO grains is a thermodynamic phenomenon which has its roots in collective interactions between YBCO nuclei. As shown above, large grained YBCO films are not suitable for synthesis of high Ic specimens owing to the problems associated with weak superconducting coupling at the grain boundaries. Thus, one needs to find processing parameters to produce small grained YBCO films in thick films without having a large number of the non-c-axis-oriented grains. As shown in figure 4, the pressures of H2 O and O2 can strongly influence the internucleus spacing, but with associated increases in the randomly oriented grains. Thus, the variations in p(O2 ) and p(H2 O) can only make limited reductions in the YBCO grain size as shown in figure 5 for this particular set of the buffered substrates. What this implies here is that substrate surface is required to have high densities of defects, which are favourable to c-axis nucleation, so that the densely populated grains are mostly c-axis oriented in spite of larger supersaturation. Besides being a template which determines the texture of the YBCO layer, a substrate is also a catalyst of the precursor → YBCO conversion reaction. The efficiency of such a catalyst can be measured by density of YBCO nucleation centres. Our technique allows for direct measurement of nucleus density, thus complementing x-ray diffraction and TEM as tools for the substrate characterization. 247

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Acknowledgments The authors greatly appreciate American Superconductor Corp. for providing their substrates for this study. Without it, we could not carry out this study. The authors also appreciated Z Ye and Q Li for performing magneto-optical imaging of some of our films which were studied here and D O Welch for helpful discussions. This work was performed under the auspices of the US Department of Energy, under contract No AC02-98CH10886.

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