Grain growth, microstructure and surface modification of textured CeO2 thin films on Ni substrate

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Acta Materialia 59 (2011) 4875–4885 www.elsevier.com/locate/actamat

Grain growth, microstructure and surface modification of textured CeO2 thin films on Ni substrate V. Mihalache ⇑, I. Pasuk National Institute of Materials Physics, PO Box MG-7, RO-77125 Bucharest-Magurele, Romania Received 23 January 2011; received in revised form 3 April 2011; accepted 13 April 2011 Available online 7 May 2011

Abstract CeO2 films were prepared from solutions of different concentrations (0.05–1.0 M) on textured Ni substrates. Homogeneous nucleation and growth of CeO2 nanocrystals <8 nm occurs upon calcination at 350–500 °C. At the heating and sintering stage, the homogeneous growth is inhibited in favor of the development of grains with (0 0 l) texture. The grain growth normal to the film surface is well described by a stretched exponential function with a relaxation time of up to 60 min and with Kohlrausch exponent values of less than unity. The increase in grain size is accompanied by the relaxation of the microstrain. During the relaxation time, the grain coarsening is controlled by surface diffusion characterized by an activation energy as low as 0.6 eV. At the relaxation time, the surface morphology is strongly concentration dependent. The surface morphology changes from separated (agglomerated) grains to a continuous grain configuration as the concentration increases from 0.05 M to 0.8 M. After the relaxation time, both the grain size normal to the film surface and the lateral grain size continue to grow, and the grain configuration continues to change. These processes are concentration dependent. In the films with a nominal thickness >170 nm (>0.8 M), the transition to classical curvature-driven grain-growth kinetics is evident (at 1000 °C, below the literature value of 1100 °C). The decrease in the Kohlrausch exponent for these thick films suggests that the grain coarsening through grain boundary migration is responsible for the stretched regime of grain-size relaxation. Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Cerium oxide (CeO2); Texture; Microstructure; Relaxation; Kohlrausch exponent

1. Introduction Promising applications of ceria and ceria-based thin films are the electrolytes for micro-solid oxide fuel cells (SOFC) [1,2] and the biaxially aligned templates for the transmission of the texture through the subsequently deposited layers (i.e., YBCO-coated conductors [3,4]). The (thermal) stability of the working parameters (i.e., electrical properties) in these applications is affected by the modification of the thin film microstructure and morphology. It is therefore imperative to control the dependence on processing time, temperature and film thickness of a number of factors, such as the degree of crystallinity, degree of texture, grain coarsening, grain configuration, ⇑ Corresponding author. Tel.: +40 21 3690170/109; fax: +40 21 3690177.

E-mail address: vmihal@infim.ro (V. Mihalache).

surface roughness and microstrain. However, understanding the mechanisms that determine the kinetics of grain (film) growth and microstructure evolution is still a challenge. In undoped and gadolinia-doped spray-pyrolysis ceria thin films on sapphire single-crystal substrates, the fine microstructures attain a limited grain size after a short exposure to relatively low temperatures, after which metastable microstructures develop. In this self-limited graingrowth regime, the experimental data are described by an exponential relaxation function [5,6]. In nanocrystalline ceria, the grain growth process was consistent with surface and grain-boundary (GB) diffusion kinetics, and this process was accompanied by a gradual relaxation of the microstrain [5,6]. For average grain sizes >140 nm and annealing temperatures >1100 °C, a transition to classical curvaturedriven grain-growth kinetics occurs [5–7].

1359-6454/$36.00 Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2011.04.029

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V. Mihalache, I. Pasuk / Acta Materialia 59 (2011) 4875–4885

The present work contains an extensive study of the influence of annealing time and solution concentration upon the microstructural and morphological evolution of chemically deposited textured CeO2 films on Ni substrates. The schedule proposed in this paper can be successfully applied by any study on the modification of the film microstructure and surface morphology vs given processing parameters towards controlling and/or obtaining the desired working parameters of devices based on CeO2 thin films. In this context, some original aspects of this study are as follows. The grain growth normal to the film surface is well described by a stretched exponential function with a Kohlrausch exponent of less than unity. Unlike those described in the literature, the films derived from the solution of the highest concentrations show common graingrowth kinetics: coarsening through GB migration. Thus, the transition to classical curvature-driven grain-growth kinetics occurs at 1000 °C (a temperature below that reported in the literature) for films with nominal thickness >170 nm. Moreover, this transition appears to be responsible for the broadening of the regime of grain-size relaxation with increasing concentration. 2. Experimental procedures Cerium-oxide thin films were fabricated by a sol–gel/ dip-coating process on Ni substrates. The precursor solutions (0.05–1.0 M) were prepared by dissolving cerium (III) acetate hydrate ((CH3CO2)3CexH2O, Alfa Aesar, 99.9%) in propionic acid (CH3CH2COOH, Merck, >99%). Methanol was then added in a methanol:propionic acid ratio of 1:2 under stirring at 60 °C. Continuous stirring was maintained for 4 h, and homogeneous sols were obtained. Textured (0 0 1) nickel substrates with dimensions 5  10  0.09 mm were used. Uniform coatings of CeO2 were obtained by dipping the Ni substrates in the colloidal solution (suspension) for 40 s and then withdrawing them at a speed of 0.1–0.15 cm s1. The films were dried at 60 °C. After drying, the thin films were calcined in air at different temperatures (350– 500 °C) depending on the solution concentration. The calcined films were quickly inserted (60 s) into a preheated quartz tube furnace at 1000 °C, annealed for 5– 600 min and quenched to room temperature at the same rate. Annealing was performed in an atmosphere of 95% Ar and 5% H2 to prevent the oxidation of the nickel substrate. CeO2 powders were also produced from the same sols, as references for the microstructural characterizations. The sols were maintained under continuous stirring at 80 °C until a gel was obtained. After the gel had been dried at 200 °C for 2 h in air, the resultant powders were treated at 500 °C for 4 h in air. The final CeO2 powders were obtained by annealing at 960 °C for 60– 600 min in an atmosphere of 95% Ar and 5% H2. The top-view microstructures and surface roughness of the thin films were characterized by scanning electron microscopy (SEM) using a FEI Quanta Inspect F

microscope and by atomic force microscopy (AFM). An AFM microscope with a MultiView 4000 Nanonics System working in non-contact mode with a probe resonance frequency of 38–40 kHz was used. The X-ray diffraction (XRD) measurements, which were used for qualitative phase analysis and the estimation of the grain (crystallite) size normal to the film surface (normal coherence length) and microstrain, were performed on a Bruker D8 Advance diffractometer in Bragg–Brentano geometry using a copper target X-ray tub. The instrumental line width needed for size and strain determination from the line broadening was determined using a heat-treated ceria powder, proved to produce no observable size and strain broadening. In order to increase the detected signal of the film, the dried and calcined films were measured also in grazing incidence geometry, at a 2° incidence angle, using a parallelbeam X-ray diffractometer. 3. Results and discussion 3.1. Texture development with varying annealing times Fig. 1a shows the XRD patterns of the CeO2/Ni films after different annealing times. Weak and broadened 111, 002, 220 and 311 CeO2 reflections for t = 0 (Fig. 1b) demonstrate the nucleation of CeO2 and its presence as randomly oriented nanocrystals, even in the calcination stage. The size of these nanocrystals, as estimated from the XRD patterns (described in Section 3.2.1) is 7–8 nm and is concentration independent. The reflections corresponding to CeO2 are detected in the dried films (Fig. 1b) as well. Because of the small amount of material in the thin films used, the amorphous phase in the dried and calcined films is hardly detectable in the X-ray pattern, despite the long acquisition time. However, some C reflections are present in the patterns of the dried films, unlike in patterns of the calcined and annealed films (Fig. 1b). After 4 min of annealing, the films show c-axis orientation, but the 002 peak is still weakly developed. The intensities of the 00l peaks increase, and the reflections sharpen with increasing dwell time up to 60 min (s  60 min), indicating an improvement in the crystalline quantity and quality of the films. At t = s, the films show strong c-axis orientation, and the further modification of the 00l peak intensities and widths (and thus the evolution of the texture) slows above this value. This finding means that the increase in the number and size of CeO2 grains slows above t = s. Besides the 00l reflections, an insignificant 111 peak appears for all annealed films and has an intensity that is generally weakly time dependent. A careful examination of the XRD patterns shows the presence of very weak 220 and 311 reflections in all films (Fig. 2a), the intensities of which are clearly time independent. At the same time, the intensities of the 220 and 311 reflections increase with increasing concentration, as illustrated in Fig. 2b. These features of the 111 and especially the 220 and 311 reflections indicate the homogeneous nucleation and growth of

540 min

5

420 min 240 min

2x10

60 min

5

30 min

0 30

*

60 min 30 min

4

1.0x10

15 min

60

45

70

50

2.0x10

1.5x10 4

calcined t = 0 min

NiO

NiO

0.0 10

20

30

40

dried

50

4

* 1.0x10

4

5.0x10

3

*

0.35 M 0.10 M

0.0

60

2θ (degree) Fig. 1. (a) XRD patterns of CeO2 films prepared from 0.5 to 0.8 M solutions and annealed for different times at 1000 °C. (b) XRD pattern details for the 0.5 M film dried at 60 °C, 0.7 M film calcined at 450 °C (annealed for 0 min), 0.8 M film annealed for 240 min at 1000 °C, and CeO2 powder derived from the 0.4 M precursor solution. The diffraction pattern of the powder is normalized to the 111 peak intensity of 0.8 M film. The asterisks () indicate weak-intensity parasite lines of the X-ray tube reflected by the highly textured Ni substrate.

CeO2 throughout the whole film volume in the early stage of film growth. In this context, the increase in the intensity of the 220 and 311 peaks with increasing solution concentration can be explained by the increasing density of the nucleation sites. This conclusion is sustained by the following. While the dimension of the nanoparticles (nucleus) is concentration independent, the intensity of all broadened CeO2 reflections (1 1 1, 0 0 2, 2 2 0 and 3 1 1) of the calcined films (as illustrated in Fig. 1b for the 0.7 M film at t = 0) are concentration dependent, increasing with increasing solution concentration (not shown here). For the films obtained in very similar technological conditions, from the immersion stage up to the thermal annealing stage, the intensity of the 111 peak is weakly time (Fig. 1a) and concentration dependent. However, the ratio of the intensities I(111)/I(220) and I(111)/I(311) in the annealed films is higher than in the CeO2 powder (Fig. 1b). At the

1.00 M 0.60 M

002 Ni

002 Ni

1.5x10

311 222

002

powder C (ICDD 74-2328)

*

Intensity (counts)

5.0x10 3

** 220

1.0x10

* 111

Intensity (counts)

t = 240 min

65

(b)

311

220

*

60

4

annealed *

4

55

2θ (degree)

2θ (degree)

(b)

5 min 0 min

002 Ni

0.0

50

420 min 240 min

4

2.0x10

after calcination

40

(a)

311

220

15 min 4 min 0 min

4877

*

Intensity (counts)

I (counts)

4x10

4

3.0x10 004

002

111

(a)

002 Ni

V. Mihalache, I. Pasuk / Acta Materialia 59 (2011) 4875–4885

45

50

0.05 M

55

60

65

2θ (degree) Fig. 2. (a) Details of the XRD patterns of CeO2 films annealed for different times at 1000 °C. (b) Details of the XRD patterns of CeO2 films prepared from 0.05 to 0.8 M solutions and treated for 60 min at 1000 °C.

same time, these ratios for the calcined films are close to those of CeO2 powder (Fig. 1b). This result indicates that the 111 reflections in the annealed films are given not only by the homogeneous nucleation and growth of grains, but also by the heterogeneous nucleation and growth. The decrease in the degree of (0 0 1) texture in favor of (1 1 1) texture and/or misoriented grains was attributed to a number of factors. A common hypothesis in the literature is that the misoriented CeO2 grains adopt the orientation of the misaligned Ni grains [8] or nucleate on Ni grain boundaries. However, it is generally recognized that, in fluoritetype structures such as that of CeO2, the (1 1 1) plane is more stable than the other low-index planes [9], (1 1 0) and especially (0 0 1) [10], because of the difference in the surface energy of these faces. Another reason for the affected texture is that CeO2 films annealed in a reducing atmosphere, required to protect metallic substrates from oxidation, are not sufficiently effective for the elimination of the organic fraction of the precursor solution [11]. Moreover, residues of the organic precursors (i.e., carbon) in the films from organic solutions could be present even after thermal treatment at 1000 °C in air [12]. The carbon

V. Mihalache, I. Pasuk / Acta Materialia 59 (2011) 4875–4885

impurities on the CeO2–Ni interface can affect the heterogeneous nucleation, whereas the carbon impurities in the film volume can serve as nucleation sites for the undesired oriented CeO2 phase. The present study reveals three aspects of the mechanism of development of the desired (0 0 1) texture in sol– gel-derived CeO2 films, to the detriment of (1 1 1) texture and/or misoriented grains. (i) The thermodynamic driving force for crystallization from the amorphous phase increases as the temperature decreases below the melting point ([13] and references therein). The detection of broadened 111, 200, 220 and 311 reflections, even at the calcination stage (Fig. 1b), indicates that the process of homogeneous nucleation throughout the whole volume of CeO2 film is stable, and can thus begin, at quite low temperatures of 350–500 °C (see Fig. 1b) (see also Refs. [14,15]). (ii) However, the high heating rate to reach the annealing temperature delays the process of homogeneous nucleation to higher temperatures, the temperature region with lower driving force ([16] and references therein). Thus, at the heating and sintering stage, the homogeneous growth is inhibited in favor of the heterogeneous nucleation of epitaxial grains, (0 0 1) and/or (1 1 1), the texture of which is transmitted throughout the volume of the film upon sintering. (iii) Unlike the (0 0 1) epitaxial growth of some RE2O3 (where RE is “rare earth”) oxides (consistent with formation of a c(2  2)–sulfur superstructure, owing to the surface segregation of sulfur contained in the metal [17]), the mechanism of the heterogeneous nucleation of the (0 0 1) CeO2 epitaxial layer on biaxially textured Ni surfaces is still unclear. X-ray photoelectron spectroscopy investigation failed to detect any metallic Ni on the substrate surface, even in the post-etching state (not shown here). NiO is dominant on the Ni surface. The presence of NiO is also evident in the XRD patterns obtained by long-term measurement of the dried and calcined films (Fig. 1b). The presence of a few atomic layers of NiO, either textured or randomly oriented, on the Ni surface may seriously promote or inhibit the nucleation of (0 0 1) texture. In particular, a more oxidized substrate should promote the (0 0 1) epitaxy, because these atomic subplanes do not contain oxygen in the CeO2 fluorite structure. Thus, the nucleation of cerium oxide probably starts with the bond of the Ce atoms of the (0 0 1) face to the oxygen atoms on the oxide-covered metallic substrate. 3.2. Grain-growth kinetics 3.2.1. Time evolution of grain growth An estimation of the nominal film thickness d was done by direct weighting [18]. The data were represented as a function of concentration (Fig. 3) and found to have a linear dependence. The average crystallite size (coherence length) normal to the film surface S was estimated from the diffraction peaks’ integral widths using the Scherrer formula

film thickness, d S (60 min) S (540 min) Smax L (60 min) L (540 min)

250

grain size, film thickness (nm)

4878

200 150

powder

100 50 0 0.0

0.5

1.0

concentration (M) Fig. 3. The variation in lateral grain size L and grain size normal to the film substrate S with time and concentration. All data are for the films annealed at 1000 °C. The error bars of the lateral grain sizes (L) correspond to the standard deviation of the average size, estimated by measuring 50 grains in each SEM image (five different images for each film). The error bars of d were derived from the standard error of the mean weight of the film, estimated from five consecutive weightings. The error bars of the normal (to the film surface) grain sizes (S) were estimated by applying the error propagation rules to Eq. (1) and are based on the errors of the XRD peak breadths and positions given by the fitting routine.

S ¼ k=b cos h

ð1Þ

where b is the broadening obtained from the peak’s width corrected for the instrumental breadth, h is the diffraction angle, and k is the X-ray wavelength. This relation between the crystallite size and peak breadth is only valid if there is no strain broadening, i.e., no local disorder associated with the microstrains. The microstrain estimations presented later prove that this condition is an acceptable approximation for the objectives proposed in the present paper. Only the 00l diffraction peaks were considered, because the (0 0 1) textured fraction prevails in the films. The normal-coherence-length dependence on annealing time at different solution concentrations is given in Fig. 4. Using Eq. (1), the crystallite size for the thickest films (0.5–1 M) immediately after calcinations was also estimated, which was 7–8 nm. The normal-coherence-length dependence on the solution concentration of the films treated for 60– 70 min, S (60 min), is also given in Fig. 3 and shows that this parameter increases with increasing concentration. The isothermal-grain-growth data in Fig. 4 show that the grain size S increases rapidly in the first 30–60 min of dwell, but then slows to almost constant values after t  60 min. The time evolution of the grain growth was first proposed by Burke and Turnbull [19], on the assumption that the driving force for boundary migration arises from pressure differences associated with the curvatures at the grain faces: S 2  S 20 ¼ k 2 t

ð2Þ

V. Mihalache, I. Pasuk / Acta Materialia 59 (2011) 4875–4885

grain size, S (nm)

during the so-called relaxation time, after which the grain growth ceased, and a metastable microstructure developed [5,6]. The fit with Eq. (4) of the isothermal curves in Fig. 4 gives exponents n between 2.5 and 3.5 for the first 30– 60 min of the treatment, but >7 in the late stages. Thus, the classical model of grain growth does not describe the time evolution of grain size of CeO2 film deposited on Ni substrate over the whole range of annealing times. A similar evolution was reported by Rupp et al. on the grain growth of doped and undoped ceria thin films [5,6] deposited on a sapphire single-crystalline substrate. Their experimental data were described by implying a common exponential relaxation function. The present experimental data are well described by implying a Kohlrausch exponential relaxation function, which fits the experimental data over the whole range of the measurement:

0.7-0.8 M 0.4-0.5 M 0.2-0.25 M 0.05-0.1 M

160

120

80

40

0

200

400

600

t (min) Fig. 4. Time evolution of the coherence length (grain size normal to the film surface) of CeO2 films for different concentrations treated at 1000 °C. The data are fitted according to Eq. (5) (continuous line) and a common exponential function [5,6] (dotted line). Concerning the error bar estimation, see the caption for Fig. 3.

b

SðtÞ  S 0 ¼ ðS max  S 0 Þð1  expðt=sÞ Þ

ð3Þ

where S is the average grain size, k is a characteristic material constant, and E is the activation energy. Many sets of experimental data reported in the literature cannot be described by the square-root dependence (3) of the grain size on time, but instead follow the generalized model (see, e.g., Ref. [20]): S n  S n0 ¼ k n t

ð5Þ

where Smax is the maximum grain size reached after the characteristic relaxation time s, S0 is the grain size at the beginning of the isothermal dwell, and b is the Kohlrausch exponent. The isothermal curves in Fig. 4 for all concentrations were fitted by Eq. (5), considering S0 = 8 nm (the maximal grain size after calcination). The fit parameters s and b are given in Table 1, and the values of Smax for different concentrations are shown in Fig. 3. The values of relaxation times lie between 17 and 50 min, whereas the values obtained for the exponent b lie between 0.2 and 0.75. The self-limited grain-growth regime of the present films is consistent with the above-mentioned grain growth of spray-pyrolysis ceria films on sapphire substrates reported by Rupp et al. [6]. At the same time, the successful fit of the experimental data by a relaxation function of the form of Eq. (5) denotes a broadening of the regime of grain-size relaxation. The experimental data for b and s for the thinnest films proved to be very close to those reported on amorphous alloys (e.g., those reported by Loffler and Johnson for Zr–Ti–Cu–Ni–Be alloys [21], see also [22]), the nucleation and crystal growth of which occur simultaneously until a new metastable chemical equilibrium is established (for a two-phase microstructure

with k 2 ¼ k 0 expðE=k B T Þ

4879

ð4Þ

The experimental results show very different values for the grain-growth exponent n, up to n = 7. The values obtained for n are attributed to different mechanisms of the grain growth process, such as volume diffusion, GB diffusion and surface diffusion. Whereas grain-growth data for some microcrystalline ceramics and metals follow this generalized model, deviation from the classical grain-growth model of time evolution is usually observable for nanocrystalline materials [5,6]. In some nanosized materials, the grain grew

Table 1 Relaxation time s, Kohlrausch exponent b and the grain size at the relaxation time Ss, obtained from fitting the time evolution of the grain size normal to the film surface using Eq. (5); also given are the values of diffusion coefficients D and of the critical grain size for agglomeration Lag; the characteristic relaxation time s0 was obtained from fitting the time evolution of the grain size normal to the film surface, using the common exponential relaxation function (removing the b exponent) [5,6]. Concentration

s (min)

s0 (min)

b

Ss (nm)

Lag

D (m2 s1)

0.05–0.1 0.2a–0.25 0.4–0.5 0.7–0.8 0.85 0.9 1.0

17 12 25 50

18 12 9 7

0.75 0.59 0.27 0.20

31 47 75 111

108 270 460 648 1140 1200 1380

1.2  1019 5.3  1019 7.5  1019 8.8  1019

a

The average dimension of plate-like regions is 200 nm.

V. Mihalache, I. Pasuk / Acta Materialia 59 (2011) 4875–4885

containing nanocrystals in an amorphous matrix). However, the self-limited grain-growth regime of the present films is consistent with the model proposed for crystallization and grain growth for biphasic amorphous–crystalline metal oxides [6]: the driving force for grain growth is the reduction in free volume and crystallization enthalpy (the transformation of the amorphous into a crystalline phase) during an isothermal hold. Once the crystallization enthalpy is zero, stable microstructures are established and grain growth ceases. It is also notable that, with increasing solution concentration, the maximum grain size Smax of the CeO2 films on Ni substrate increases considerably (Table 1). At the same time, the decrease in the Kohlrausch exponent as the solution concentration increases indicates the broadening of the regime of grain-size relaxation for the thicker films. To verify the consistency of the data with the models proposed in the literature for crystallization and grain growth [6], the isothermal curves in Fig. 4 were fitted with a common exponential relaxation function as well (removing the b exponent). The fitting curves obtained in this way are drawn with dotted lines in Fig. 4. The resulting values for the characteristic relaxation time, in this case labelled s0 , are given in Table 1. First, it is notable that the deviation of these fitting curves from the experimental data increases as the concentration increases. This finding is not surprising; the lasting regime of grain-size relaxation for higher concentrations (thicker films) turns to the self-limited graingrowth regime [5,6] after the Kohlrausch exponent has been removed. The smaller values for the time constants resulting from fitting with the common exponential equation in the case of the higher concentrations (compare s with s0 in Table 1) are determined by the same removal of the Kohlrausch exponent. Furthermore, the s0 values obtained in this study (<60 min) for the isothermal dwell at 1000 °C are comparable with the values of the characteristic relaxation constant for the same temperature found by Rupp et al. (see Fig. 10 in Ref. [5] and Table 2 (extrapolating the data to higher temperatures) in Ref. [6]). However, the decrease in this characteristic constant with increasing concentration (film thickness) is consistent with the decrease in this constant with increasing dwell temperature reported by Rupp et al. [5,6]. Thus, the diagram in Fig. 15a of Ref. [6] showing the model of crystallization and grain growth is valid for the films presented in the present paper if one considers the solution concentration (film thickness) as the variable instead of the dwell temperature [5,6]. 3.2.2. Grain-growth mechanism and surface diffusion The diffusion coefficient of grain growth D during the relaxation time was calculated using

coefficients were calculated for all four concentration intervals, and the results are listed in Table 1. D increases by approximately one order of magnitude, from 1.2  1019 to 8.8  1019 m2 s1, with increasing concentration from 0.05 M to 0.8 M. These values are close to those reported for Ce0.8 Gd0.2 O1.9x [5] and CeO2 [6] sprayed films. The estimation of the activation energy of diffusion E (for the films of the intermediate concentration) was done using the Arrhenius equation: DðT Þ ¼ D0 expðE=k B T Þ

ð7Þ

where kB is the Boltzmann constant. For this estimation, additional films treated at 900 and 1100 °C were used. An activation energy of 0.6 (±0.1) eV and a pre-exponential factor D0 = 1.2  1016(±1) m2 s1 were obtained from the Arrhenius plot shown in Fig. 5. This quite low value of the activation energy is comparable with those reported for other chemical solution deposition (CSD)-derived ceria or ceria-doped films [5,6,11] and for other types of materials [23–25]. The values reported in the literature in this range were attributed mainly to a surface mass-diffusion mechanism [5,6,23,26]. E values of 0.7 eV and 1.32 eV reported for CeO2 and gadolinia-doped ceria sprayed nanosized films on sapphire substrate [5,6] were attributed to grain coarsening through surface- and interface-diffusion processes. The average activation energy for mass transport on gold surfaces is 0.9 eV [23]. In situ investigation of grain growth and GB migration performed on a polycrystalline gold film demonstrated that GB motion (migration) and surface morphology changes (surface diffusion) occurred simultaneously [26]. However, Rupp et al. [5] demonstrated on Ce0.8Gd0.2O1.9x ceramic polycrystalline films that the GB-migration kinetics (curvature-driven Burke–Turnbull) are only valid at temperatures >1100 °C and grain size >140 nm.

-41.0 E = 0.6 ± 0.1 eV -41.5

ln D (m2/s)

4880

-42.0

-42.5 0.70

0.75

0.80

1000 / T

D ¼ ðS s  S 0 Þ2 =4s

ð6Þ

where Ss is the grain size at the relaxation time. With s taken from Table 1 and Ss from Fig. 4 at t = s, the diffusion

0.85

(K-1)

Fig. 5. Temperature dependence (Arrhenius plot) of the diffusion coefficient D for CeO2 thin films and fit to the data. The error bars of the D values were estimated applying the error propagation rules to Eq. (6) and are determined by the crystallite size uncertainties obtained by XRD.

V. Mihalache, I. Pasuk / Acta Materialia 59 (2011) 4875–4885

Based on the results in Sections 3.1 and 3.2, one can conclude that crystallization and grain growth in CeO2 films on Ni substrate occur simultaneously during a certain relaxation time, t = s 6 60 min, until a metastable equilibrium is reached, at which point the grain growth slows. The low activation energy (0.6 eV) and the values obtained for the diffusion coefficients indicate that the grain coarsening in the relaxation regime is controlled mainly by surface diffusion for the films derived from solutions with concentrations <0.8 M. However, as will be shown later, the coarsening through GB-migration kinetics becomes important in films at higher concentrations and at long annealing times for films derived from solutions of intermediate concentrations. 3.3. Microstructural and morphological evolution 3.3.1. Microstrain relaxation The residual strain due to the local distortions of the lattice (microstrain), expressed by the root mean square of the 0.4

film (0.5 - 0.9 M)

0.2

<ε >

2 1/2

(%)

powder

0.0 0

200

400

4881

relative variation of the interplanar spacing he2i1/2, where e = Dl/l (l is the interplanar spacing), was determined using the Williamson–Hall method, which allows the separation of the crystallite-size and strain contributions to line broadening [27]. Three reflections, 200, 400 and 600, were used for the Williamson–Hall plot. The data were fitted by straight lines, and the microstrain extracted from the slopes is plotted against dwell time in Fig. 6. The residual strain corresponding to CeO2 powder derived from the same precursor solutions is also included for comparison. Fig. 6 shows that all the films have a larger microstrain than the powder and that, unlike the powder, the films’ microstrain decreases with dwelling time. The microstrain decreases rapidly within the first 60 min of isothermal hold and then relaxes, reaching a constant value for t > 60 min, which is higher than the microstrain of the powder. This finding suggests that, even at higher annealing times, the films are only partially relaxed. It is notable that the relaxation time of the microstrain is comparable with the relaxation time of the grain growth (Table 1, Fig. 4). The fact that the grain growth and microstrain show the same relaxation times indicates that one of the mechanisms of strain relaxation in the CSD-derived CeO2 film on the Ni substrate is the grain-growth process. At the same time, the microstrain decreases with increasing concentration, particularly owing to the increase in the coherence length (crystallite size) [18]. Thus, at the beginning of isothermal annealing, the strain is large because of the amorphous nature of the films, poorly developed grains and smaller crystallites. During the relaxation time, the microstrain relaxes owing to the ordering of the atoms in the crystal lattice and advances in crystallization and grain growth. As the films are treated above the relaxation time, microstrain decreases very slowly because the grain growth normal to the film surface slows (Fig. 4).

600

t (min) Fig. 6. The dependence of microstrain on the annealing time of 0.5–0.9 M CeO2 films (estimated from the XRD patterns). The microstrain of CeO2 powders derived from the precursor solutions is also shown. The error bar of each point was estimated as the uncertainty of the slope of the Williamson–Hall plot, which was obtained by weighted least square fit.

3.3.2. Surface morphology of CeO2 films prepared from 0.05 to 0.8 M precursor solutions The SEM investigations of CeO2 films of different annealing times and different concentrations are presented in Figs. 7 and 8. The evolution of the surface morphology of the films annealed for 60–70 min (Fig. 8a1–d1) is

Fig. 7. SEM images of the surface morphology of: (a) 0.5 M film annealed for 1 min; the image in the inset has dimensions 1.0  1.0 lm; (b) 0.7 M film calcined at 450 °C; (c) 0.05 M film annealed for 20 min.

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Fig. 8. Low-magnification (main panel) and high-magnification (lower insets) SEM images of the surface morphology of the CeO2 films derived from solutions with different concentrations ((a1 and a2) 0.05 M, (b1 and b2) 0.2 M, (c1 and c2) 0.8 M, (d1 and d2) 0.85 M, (e1) 0.9 M and (f1) 1.0 M) and annealed for different times ((a1–f1) 60 min, (a2–d2) 540–600 min). The magnification bars on the right side of the images refer to the main panel. The images in the insets have vertical (a–e) and horizontal (f) sides of 1.5 lm.

consistent with the model for agglomeration [18]. As the concentration increases, the films pass through three regions of grain configuration: unconnected grain configuration (see Fig. 8a1 for the 0.05 M film), partially connected grain configuration (see Fig. 8b1 for the 0.2 M film) and connected grain configuration (see Fig. 8c1 for the 0.8 M film, and Fig. 8d1 for the 0.85 M film). The competition between the growth/grooving rate at the GB (or agglomeration rate) and the rate of mass transport along the grain surface (flattening) are responsible for the morphology of the CeO2 surface [18]. The surface microstructure of the 0.5 M film heated for 1 min (Fig. 7a), exhibiting poorly developed grains, indicates the presence of thermally induced microgrooves. Nevertheless, there are also regions with widespread, more developed grains (inset in Fig. 7a). The high spread in the dimensions of poorly developed grains and the presence of the aggregates of small crystallites and microgrooves (observed in AFM investigations as well) make the films treated for short times unexpectedly rough (as evidenced by AFM measurements, the root mean square (RMS) roughness of the 0.5 M film is of 2.5 nm for a 2  2 lm scanned area). Another feature of these films is that their surface is covered with a network of cracks (Fig. 7a), suggesting that the cracking of CeO2 films occurs at the densification and/or heating stages, prior to crystallization.

Detailed SEM investigation reveals that the surfaces of all the dried films are continuous without cracks. Instead, the SEM investigation of the calcined films reveals the presence of primarily superficial cracks (that do not form a percolation network) on the surface of the films of intermediate, 0.4–0.8 M, concentrations (Fig. 7b). The surface of the thinnest calcined films lacks any defects. No grains are visible in both the dried and calcined films. During heating to 1000 °C, the surface of the calcined films of intermediate concentrations undergoes a strong transformation (compare Fig. 7a and b). As t increases to 60 min (the relaxation time s), the grain size increases rapidly, and the microstructure exhibits grains with well-defined shapes (Fig. 8c1). It is noteworthy that no network of cracks appeared at this annealing time in the 0.05–0.8 M films; the surface recovers owing to mass transport and relaxation through the agglomeration process. As in the case of grain size normal to the film surface S, some increase in the average lateral grain size L still exists after the relaxation time (Figs. 3 and 8). As will be shown later, the evolution of L and of the surface morphology above the relaxation time depends on concentration and thus on the grain configuration at the relaxation time. The 0.05 M film is completely agglomerated at 60 min of isothermal hold (Fig. 8a1). Further thermal treatment up to 600 min did not significantly change the grain configura-

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tion (Fig. 8a2). The only modification is that the lateral grain size increases slightly. The increase in the grain size is accompanied by a decrease in the density of the separated grains (inset in Fig. 8a2). Because the thinnest films are completely agglomerated, the following question arises: How do the separated grains (dots) continue to increase above the relaxation time? This contradiction can be solved if one supposes that the surface diffusion is the mechanism of mass redistribution between the separated grains [28]. The surface configuration of the partial agglomerated films after 60 min of heating (0.2 M in Fig. 8b1) does not correspond to the equilibrium configuration characterized by a constant curvature of the grain surface [26,29,30]. A high rate of GB grooving (and agglomeration) is observable in this early stage of isothermal annealing. Increasing the dwell time up to 540 min, the lateral grain size increases and a drastic change in the surface morphology occurs (compare Fig. 8b1 and b2). First, a process of sever agglomeration is obvious. Moreover, a careful analysis of the SEM micrographs in Fig. 8b reveals the grain reconfiguration: in particular, the development of extended plate-like regions with flat surfaces, connected to the normal–rounded grains (Fig. 8b2). It is likely that the plate-like regions were generated by surface diffusion and simultaneously served as channels in the process of surface mass transport and/ or mass redistributions between the rounded grains. The final stage of this process would be the complete agglomeration of the grain configuration (separated grains), similar to that displayed in Fig. 8a1 for the 0.05 M film. This similarity is sustained by the grain configuration of 0.05 M films in the earlier stage of annealing (20 min) displayed in Fig. 7c. The grain configuration of the films of higher concentrations treated for 60 min (0.8 M in Fig. 8c1) is closer to the equilibrium state with constant curvature surface, i.e., the resultant equilibrium morphology of a grain is a convex surface (dome-shaped top) [26,29,30]. The surface of these films is smooth. Despite the grain coarsening during the relaxation time, the RMS roughness does not increase (2.5 nm for the 0.5 M film annealed for 4 min, and 1.9 nm for the 0.8 M film annealed for 60 min), most likely due to the domination of diffusion on the grain surface (flattening) over grooving at GB (agglomeration) for this intermediate concentration range. Nevertheless, the grain configuration does not reach an equilibrium grain size during the relaxation time since, after heating for a longer time, further normal (Figs. 4 and 3) and lateral (Figs. 8c2 and 3) grain coarsening occurs. At the same time, a moderate advance in the agglomeration process may occur (compare SEM images of the insets of Fig. 8c1 and c2), which makes the films rougher (the RMS roughness of the 0.8 M film annealed for 540 min is 3.5 nm). Altogether, the in-plane microstructures with coordination numbers of 5–7 and the grain shape do not change for up to 600 min of thermal treatment. All these results reveal the (relatively) stable microstructure of these films.

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A ratio Lag/d = 6 (Lag is the critical grain size for agglomeration) is predicted in the model for agglomeration proposed by Rha and Park [29]. In the CeO2 films on Ni substrates with nominal thickness d, the predicted critical size for agglomeration will be Lag = 6d. The values of Lag obtained for the films derived from the solutions of different concentrations are given in Table 1. The predicted critical size for agglomeration in the finest (0.05 M) films is close to the largest grains viewed in SEM (Fig. 8a1 and a2). In the partially agglomerated films (0.2 M), Lag exceeds the size of the largest rounded grains viewed in SEM (Fig. 8b1 and b2), but is very close to the average dimension of the plate-like regions (Fig. 8b2). Lag in the 0.8 M CeO2 films is well above the largest lateral grain size observed in SEM (Fig. 8c1 and c2). This evolution of lateral grain size toward Lag indicates the increased stability of the microstructure against agglomeration with increasing concentration and thus film thickness. Fig. 3 summarizes the modification of the normal S and lateral L grain size with varying time and concentration. In the range 0.05–0.8 M, S  L for 60 min dwell. The values of S, L, S (540 min), L (540 min) and Smax exceed the nominal film thickness d for concentrations <0.3 M. For concentrations >0.3 M, S and L are below d. The value of S tends to Smax and both are limited to the nominal film thickness with increasing time and concentration. At 540 min isothermal hold, L exceeds the film thickness for any concentration. In fact, Fig. 3 can be viewed as a diagram which explains how to select the conditions to achieve a desired grain configuration. The important conclusion is that the rate of normal and lateral grain coarsening after the relaxation time increases with increasing concentration. 3.3.3. Surface morphology of CeO2 films prepared from precursor solutions of concentrations >0.8 M: GB-migration kinetics The surfaces of the films derived from the solutions of highest concentrations (0.85–1.0 M) show severe defects (Fig. 8d–f). The 0.85 M film (Fig. 8d) is characterized by a deformed, undulated surface covered with a percolation network of cracks. With increasing concentration (0.9 M in Fig. 8e), these defects evolve into disruptions that expose large portions of the substrate surface. It is notable that the films undergo agglomeration again >0.8 M. However, unlike the thinnest films, which agglomerate into separated grains, the thickest films agglomerate into islands of grains (Fig. 8f). It is known that film densification and shrinkage occur in the heating stage of the as-prepared (deposited) films. The tensile stress evolves in the film and causes macroscopic cracking. The stress magnitude increases as the concentration (film thickness) increases. As already described, the cracking starts at the calcination stage for the films studied here (Fig. 7a). However, unlike the calcined films of intermediate concentrations, the cracks form a percolation network in the calcined films of highest concentration; they do not recover during heating up to 1000 °C. Thus,

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the island structure is preserved and transmitted to the annealed stage. At the relaxation time, the average lateral grain size of the thickest films already exceeds the normal grain size (coherence length) such that it equals the nominal film thickness d for a concentration of 1 M (Fig. 3 and Table 1). Furthermore, the surface morphology of the portion of the 1 M film displayed in the inset in Fig. 8f reveals the presence of a large number of curved grain boundaries. The high rate of grain growth, the higher area fraction covered by the largest grains and the large number of curved grain boundaries in the thickest films gives evidence that the largest grains are grown at the expense of the smaller ones, the process corresponding to grain growth through GB-migration kinetics. The curved grain boundaries are also viewed in the SEM images of 0.8–0.9 M films (Fig. 8c–e). For 0.8 M and 0.85 M films, they are present preponderantly in the films treated for longer times (Fig. 8c2 and d2). It is remarkable that the same (thick) films undergo a broadening of the regime of grain-size relaxation (or a decrease in the Kohlrausch exponent) (Table 1 and Fig. 4). This trend suggests that the grain coarsening through GB boundary migration is responsible for the stretched regime of grain-size relaxation. Rupp et al. demonstrated that the GB-migration kinetics are only valid at temperatures >1100 °C and grain sizes >140 nm on ceria and ceria-based ceramic polycrystalline films [5,6]. The discrepancy between their results and the results herein may be explained as follows. Rupp et al. showed that the establishment of classical grain-growth kinetics is determined by the non-isothermal average grain size (the degree of crystallization) at the beginning of the isothermal dwell. By heating the as-prepared amorphous metal oxides (equivalent to the calcined films in the present study) above the temperature where non-isothermal crystallization ceases, typical parabolic grain-growth kinetics driven by the curvature of neighboring grains prevail. As previously mentioned, this temperature is 1100 °C, and the corresponding grain size is 140 nm. The establishment of the classical grain-growth regime in the present films (where the concentration was varied and the annealing temperature was kept at T = 1000 °C) was determined by crystallization rate and grain-growth rate which are higher for higher concentrations because of the higher density of the metal-oxide nucleus in the calcination stage. The high packing density of the large grains in the thickest films at the relaxation time energetically favors grain coarsening through the GB boundary migration kinetics at temperatures <1100 °C. Regarding the RMS roughness, the grain coarsening (increase in grain diameter) may increase the grain height; even without any increase in GB energy, this effect would make the film rough ([26] and references therein). Thus, a drastic increase in RMS roughness is observed for concentrations >0.8 M (12.8 nm), even during the relaxation time.

4. Summary and conclusions In solution-derived textured CeO2 films on Ni substrates, the grain growth normal to the film surface follows a stretched exponential function with a relaxation time of <60 min. During the relaxation time, the CeO2 grains grow rapidly, and full crystallization is achieved. In this regime, the grain coarsening is controlled by surface diffusion, and the microstructure evolution is accompanied by microstrain relaxation. In this context, it is important to use CeO2 films annealed for times not less than the relaxation time in a number of applications, when a metastable microstructure is reached and grain growth slows. However, the decrease in the Kohlrausch exponent indicates a lasting regime of grain-size relaxation as the concentration increases. After the relaxation time, the grains continue to grow in both normal (to the film surface) and lateral directions, and the rate of grain coarsening increases with increasing concentration. Regarding the modification of the surface configuration, three regions are distinguished, depending on the configuration at the relaxation time. The surface configuration of the completely agglomerated thin films is stable, and the grain growth seems to occur through surface mass transport to and/or mass redistributions between the separated grains. In the partially agglomerated films, drastic changes in morphology occur, the surface becomes severely agglomerated, and grain reconfiguration occurs. In the non-agglomerated films, the grain configuration is stable, but a moderate advance in the process of agglomeration may occur. The surfaces of the films derived from the solutions of the highest concentrations show severe defects. These films undergo agglomeration again; however, unlike the thinnest films, they agglomerate into islands of grains. The high rate of grain growth, the high ratio of large grains and the presence of a large number of curved grain boundaries in the thickest films are evidence that the largest grains are grown at the expense of the smaller ones and thus of coarsening through GB-migration kinetics. The decrease in the Kohlrausch exponent for the same thick films suggests that the grain coarsening through GB migration is responsible for the stretched regime of grain-size relaxation. The transition to classical curvature-driven graingrowth kinetics occurs at a transition temperature (1000 °C) below that reported in the literature (1100 °C). Significantly, this transition makes the films rougher. Acknowledgements The authors would like to express their gratitude to C. Negrila, D. Predoi, M. Socol, M. Cernea and N. Vasilescu for their help in the experimental and technical work. This work was supported by Romanian Ministry of Education and Research under the NUCLEU Program – Contract PN09 - 450101.

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