A reversible wetting transition in strontium titanate and its influence on grain growth and the grain boundary mobility

Acta Materialia 101 (2015) 80–89

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A reversible wetting transition in strontium titanate and its influence on grain growth and the grain boundary mobility Wolfgang Rheinheimer a,⇑, Michael Bäurer b, Michael J. Hoffmann a a b

Institute of Applied Materials, KIT, Haid-und-Neu-Str. 7, 76131 Karlsruhe, Germany Sirona Dental Systems GmbH, Fabrikstr. 31, 64625 Bensheim, Germany

a r t i c l e

i n f o

Article history: Received 22 May 2015 Revised 27 August 2015 Accepted 29 August 2015 Available online 21 September 2015 Keywords: Wetting transition Grain boundary mobility Anisotropy Abnormal grain growth Kinetic grain boundary shape

a b s t r a c t The impact of the oxygen partial pressure on grain growth in high purity strontium titanate is evaluated by observing microstructures, the grain growth constant k and the relative mobility of strontium titanate. The microstructures indicate a reversible wetting transition between 1460 °C and 1500 °C. The wetting second phase is titania-rich and free from any detectable solutes. Exaggerated grain growth was found close to the wetting transition and is explained by a temperature dependent anisotropy of the grain boundary mobility in conjunction with a high mobility of wetted grain boundaries. The grain growth constant in reducing atmosphere shows two transitions at 1350 °C and at 1460 °C. At the first transition the grain growth constant decreases with temperature. A strong increase of k with temperature at the second transition is attributed to the wetting transition. The relative grain boundary mobility of different orientations ({1 0 0}, {1 1 0}, {1 1 1}, and {3 1 0}) was measured in oxidizing and reducing atmosphere by observing the growth of oriented single crystals into polycrystals. At 1550 °C in reducing atmosphere the wetting liquid phase enhances the mobility by a factor of
10 compared to oxidizing atmosphere. Additionally, the atmosphere changes grain growth kinetics: in oxidizing, but not in reducing atmosphere growth stagnation occurs for long dwell times. Ó 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

1. Introduction Wetting of grain boundaries in polycrystals is a phenomenon of great importance in sintering [1–3] and is known to change grain boundary characteristics and grain growth considerably [4]. For example, diffusion, faceting and grain boundary motion are fundamentally changed by a wetting second phase. In dense high purity solids grain growth is expected to show parabolic time dependence due to the linear coupling of driving force and boundary migration [5,6]. This is the case different high purity ceramics, e.g. alumina [7,8], BaTiO3 [9] and SrTiO3 [10,11]). However, if the relationship between driving force and boundary migration is more complex, the kinetics is changed toward cubic or even higher exponents [5,6]. In the presence of a wetting liquid film, grain growth kinetics depends on the type of the rate controlling mechanism: interface reaction controlled grain boundary motion results in parabolic kinetics; if diffusion limits coarsening the kinetics change to cubic [3,12–14]. Additionally, a wetting liquid phase influences the local orientation of grain boundary planes: since the geometric constraints for both adjacent interfaces are lowered, the grain ⇑ Corresponding author. E-mail address: [email protected] (W. Rheinheimer). http://dx.doi.org/10.1016/j.actamat.2015.08.069 1359-6454/Ó 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

boundary planes can rotate freely to low energy or low mobility orientations [15–18]. A special case of second phase segregation at interfaces is known as ‘‘complexions”: adsorption transitions of segregants at the grain boundary change the grain boundary characteristics, grain boundary mobility and hence grain growth drastically [7,19–23]. These complexion transitions are thermodynamically stable [24] and exist at temperatures below the wetting transition of the grain boundaries [21]. In sintering these transitions can be used to optimize the shrinkage behavior [19,25,26]. In general, wetting is based on a minimization of the interfacial energy. Perovskite ceramics include good model materials (e.g. barium titanate and strontium titanate) to study energetically driven interface effects in detail, since the grain boundary energy can be influenced by the defect chemistry (i.e. dopants and oxygen partial pressure [27–30]). Additionally a variety of useful data is available e.g. for strontium titanate. For instance, the grain growth constant is documented [10,11]: grain growth does not follow classical Arrhenius behavior, instead a decrease of the grain growth constant with temperature was found between 1350 °C and 1425 °C. The temperature dependent anisotropy of the grain boundary mobility was also measured recently [31]. Several studies observed the grain boundary energy via the inverse correlation

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of the frequency of a specific grain boundary plane and its energy (Grain Boundary Plane Distribution, GBPD [27,32–36]). The GBPD shows an increase of the grain boundary energy anisotropy with temperature. In contrast, the Wulff shape shows a decrease of the surface energy anisotropy with temperature, which points toward a change of the relationship between the binding energy and the absolute surface energy [27]. However, almost all studies are confined to oxidizing atmosphere; little information is available on the impact of the atmosphere on grain growth. The Wulff shape is available for reducing atmosphere [27]. Some information on the atmosphere and dopant dependent mobility was also published [28], however, this study does not use high purity raw materials and no quantification of growth is given. The purity of raw materials is crucial for grain boundary wetting: small amounts of SiO2 or other dopants can result in a wetting second phase in strontium titanate [37,38] and barium titanate [39]. Even a wetting transition at the eutectic point of 1440 °C [40] was reported [41,42]. In high purity strontium titanate a titania-rich phase is known to exist, but no wetting was observed in oxidizing atmosphere [43–45]. The current study completes the data on grain growth by observing the grain growth constant and relative grain boundary mobility in reducing atmosphere. It is shown that a control of atmosphere and temperature can result in the formation of a wetting titania-rich second phase. The wetting is shown to be a reversible process and seems to be anisotropic. In different applications a controlled change of the oxygen partial pressure is important, e.g. for PTC materials [46,47] or cofiring of layered structures with base metal electrodes [48–50]. In all these application the role of a wetting transition would be of great interest. 2. Experimental procedure 2.1. Grain growth experiments on polycrystals Stoichiometric polycrystalline ceramic material was prepared by a mixed oxide/carbonate route based on SrCO3 (99.9+%, Sigma Aldrich Chemie GmbH, Taufkirchen, Germany) and TiO2 (99.9+%, Sigma Aldrich). The resulting powder has a very high purity; especially no silicon is detectable by ICP-OES [44]. The green bodies were presintered at 1425 °C for 1 h in oxygen to obtain a dense fine-grained microstructure (relative density of 99.5 ± 0.2%, average grain radius <1 lm, cf. Fig. 1a). Further details of the synthesis are published elsewhere [44]. All grain growth experiments were performed in tubular furnaces (Gero GmbH, Neuhausen, Germany) at temperatures between 1300 °C and 1550 °C. The atmosphere was either pure oxygen or forming gas (95% N2 and 5% H2, p(O2)  8  108 Pa) at ambient pressure. The heating rate was 20 K/min and the cooling rate 10 K/min for the experiments below 1350 °C. Above 1350 °C samples were quenched with
200 K/min to avoid any influence during cooling. During quenching the atmosphere was not changed. The grain size of the polycrystals was measured using the line intersection method (at least 284 grains, typically 1200). The mean grain size R at time t was used to obtain the grain growth constant k by applying a standard grain growth law [9,10,51]:

R2 ðtÞ  R2 ðt ¼ 0Þ ¼

1 kt 4

ð1Þ

2.2. Grain growth experiments on embedded single crystals The seeded polycrystal method requires joining a single crystal and a polycrystal. Stoichiometric polycrystalline ceramic material

Fig. 1. (a) Microstructure of the samples presintered at 1425 °C for 1 h in oxygen and (b) a single crystal growing into a polycrystalline matrix at 1550 °C after 6 min (1), after 1.5 h (2) and after 4.4 h (3). The white dotted line highlights the rows of small pores, which indicate the original position of the interface of the single crystal at time 0.

was presintered at 1425 °C for 1 h in oxygen (Fig. 1a). Samples were cut into discs and polished (diamond slurry, 0.25 lm) and then scratched with a polishing disc (30 lm diamonds) to create pore channels [31]. The strontium titanate single crystals (impurity content: <10 ppm Si, <2 ppm Ba, <1 ppm Ca, SurfaceNet GmbH, Rheine, Germany) were chemical–mechanical polished and placed between two polished and scratched polycrystalline discs. Stacks were joined at 1430 °C for 20 min in air with a load of 1 MPa. During diffusion bonding the pore channels created by scratches break up into rows of small pores. As the interface of the single crystal migrates into the polycrystalline matrix, pores become isolated within the single crystal and appear as a row in the micrographs marking the original interface of the single crystal (white dotted lines in Fig. 1b). These pores were used as a reference for measuring the growth distance. A set of samples was prepared for the four different surface orientations {1 0 0}, {1 1 0}, {1 1 1} and {3 1 0} of the single crystals. Further details of this procedure can be found elsewhere [27,31].

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Growth experiments were carried out in the same tubular furnaces at 1350 °C and 1550 °C either in oxygen or in forming gas. The dwell time was interrupted repeatedly to determine the position of the interface and mean grain size for a given time. The growth distance was measured by SEM on slices which were cut off the sandwich samples. The heating rate was 20 K/min and the cooling rate 10 K/min for the experiments at 1350 °C. At 1550 °C samples were quenched with
200 K/min to prevent any influence during cooling. A typical microstructure evolution is shown in Fig. 1b. The distance between the row of pores and the actual interface of the single crystal indicates the growth length L of the single crystal. Due to the curvature of the interface, the growth length of the single crystal was measured statistically. The distribution of the growth length was measured continuously over a width of approximately 100 times the growth. These statistics give the mean growth length L and its standard deviation r; both parameters are used for further analysis. More details on this technique can be found elsewhere [31]. The sample geometry of a single crystal growing into a polycrystalline matrix offers the possibility to measure the relative mobility of the single crystal independent of its grain boundary energy. A mean field approach was used to analyze the growth kinetics and the relative mobility [8,31]. Following this approach, the growth length L of the single crystal is

LðtÞ ¼ a

mSC mm

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  3 km t þ 4R20  6R0 þ Lðt ¼ 0Þ

ð2Þ

with a geometric constant a  1, the mobility of the single crystal mSC, the average mobility of the polycrystalline matrix mm, the grain growth constant of the matrix km and the mean grain size of the matrix R0 at time t = 0 The term in square brackets represents the growth of the polycrystal and was extracted from the grain growth of the polycrystalline matrix. Accordingly a measurement of L(t) allows for evaluating the relative mobility of the single crystal mSC/mm. Since during joining of the stacks at 1430 °C some growth of the single crystals occurred (2.6–4.5 lm depending on the single crystal orientation), R0 and L(t = 0) were observed prior to growth experiments. Since L(t = 0) gives an offset of the growth length, it was subtracted from the growth data and, thus, eliminated in Eq. (2). 3. Results and discussion 3.1. Microstructures: a reversible wetting transition At 1350 °C the microstructures in oxidizing and reducing atmosphere are very similar, although the grain size is larger by a factor of
5 in reducing atmosphere (Fig. 2a and b). The grain size distribution is uniform and no wetting liquid phase was observed. Occasionally nonwetting second phase particles were found (white arrow in Fig. 2a). However, nominally stoichiometric strontium titanate synthesized similarly to the present material is known to form small amounts of a titania-rich second phase, which originates in abrasion of the zirconia balls during milling [44]. However, SrTiO3 and SrZrO3 form a solid solution [52], hence the only effect of the zirconia is the formation of a slight excess of
0.2 mol% with respect to the Ti-site of the perovskite structure [44], which is visible as small particles in the microstructure. The microstructure at 1550 °C in oxidizing atmosphere (Fig. 3a) is very similar to 1350 °C in oxidizing or reducing atmosphere (Fig. 2a and b), but it becomes different at 1550 °C in reducing atmospheres: after 6 min a wetting liquid phase film was found at the grain boundaries and in triple pockets (Fig. 3b). An EDS

Fig. 2. Microstructure of the samples presintered at 1425 °C in oxygen and subsequently annealed at 1350 °C for 45 h in oxygen (a) and in N2–H2 (b). Note the different scale.

measurement (M series, Bruker AXS, Germany) at a triple pocket gave the composition of 2.2 mol% Sr, 17.0 mol% Ti, 50.6 mol% O and 30.2 mol% C, no other elements were found. The carbon is due to the coating of the sample. The microstructures in Fig. 3 show a large grain size in reducing atmosphere compared to oxidizing conditions; apparently the wetting film results in a much faster grain growth. This will be quantified later in this study. A part of the sample shown in Fig. 3b indicating a wetting liquid film was reannealed at 1350 °C for 10 h in oxidizing (Fig. 3c) or reducing atmosphere (Fig. 3d). In both cases the wetting film decomposed to single particles at the grain boundaries and at the triple pockets. If the material showing dewetted interfaces (i.e. with single particles at the grain boundaries, Fig. 3c) is reannealed at 1550 °C in reducing atmosphere, again a wetting liquid phase film appears (Fig. 3e). Hence the micrographs shown in Fig. 3 indicate a reversible wetting transition at a temperature below 1550 °C in reducing atmosphere. Note that the wetting liquid films are only visible, if the material is quenched. Slow cooling results in a dewetting similar to Fig. 4. As mentioned above, the existence of a titania-rich second phase was documented recently even for nominally stoichiometric strontium titanate [44]; in high purity strontium titanate in oxidizing atmosphere this second phase does not wet the grain boundaries [43,45]. Only in presence of solutes (e.g. silicon) a wetting transition in strontium titanate was reported earlier [28,42,53–55]. Therefore, it is the first report of a wetting transition for highly pure strontium titanate (i.e. no silicon is detectable [44]).

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Fig. 3. Microstructure of the samples presintered at 1425 °C for 1 h in oxygen and subsequently annealed at 1550 °C for 1.5 h in oxygen (a) and at 1550 °C for 6 min in N2–H2 (b). The arrows in b highlight a wetting phase at the grain boundaries. The same material is shown in (c) and (d) after reannealing at 1350 °C in oxygen (c) or in N2–H2 (d). The wetting films at the boundaries dewetted and formed single particles (white arrows). (e) Shows again the same material, which additionally was reannealed at 1550 °C for 2 h in N2–H2. The white arrow highlights a wetting liquid phase film. All microstructures were not etched.

3.2. Wetting and exaggerated grain growth At temperatures between 1460 °C and 1500 °C exaggerated grain growth was found (Fig. 4a–d). Particularly the number of exaggerated grains per area increases with temperature. This trend continues until the exaggerated grains impinge (Fig. 4d). At 1550 °C the microstructure is composed only of exaggerated grown grains; wetting liquid films are visible (Fig. 3b and c). Even at 1490 °C a wetting film was visible by SEM between two exaggerated grains (white arrow in Fig. 4c). At lower temperatures no wetting film could be found around exaggerated grains. However, the films may be too thin to be visible in the SEM. TEM imaging is needed to confirm the presence and nature of wetting films at exaggerated grains below 1490 °C. According to the microstructural findings, exaggerated grain growth is proposed to be caused by a partial wetting of grain boundaries in conjunction with a high mobility of wetted grain boundaries. Accordingly the wetting transition seems to be anisotropic; some grain boundaries seem to be wetted at lower temperatures than others. Anisotropy of wetting transitions at given temperatures is a known phenomenon [15,17,56,57] and it is also

known that the anisotropy of wetting may change with temperature [58,59]. Wetting of a grain boundary is driven by interfacial energy, which is anisotropic for strontium titanate [27]. Consequently the anisotropy of wetting caused by the interface energy anisotropy is reasonable for strontium titanate. A thermodynamically stable liquid phase will wet a grain boundary, if the overall interfacial energy is lowered. In general, high energy grain boundaries should be wetted first [58]. Since the Wulff shape of strontium titanate is known [27], it can be compared with the shape of exaggerated grains. Although the 3D shape of a grain is hard to guess from 2D sections, the symmetry of exaggerated grains in Fig. 4a–d seems to show a preference for a termination by {1 0 0}-planes, which is a low energy orientation. Probably this is caused by a kinetic influence on the shape: once a grain boundary is wetted, it could start growing fast and its grain boundary planes start to rotate to low mobility orientations [60,61]. As will be shown later, the slowest orientation at 1550 °C is {1 0 0}, which is in good agreement with the shapes shown in Fig. 4. Due to this kinetic influence the grain shape of exaggerated grains does not allow estimating the anisotropy of wetting itself.

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Fig. 4. Microstructure of the samples presintered at 1425 °C in oxygen and subsequently annealed in N2–H2 at 1460 °C for 20 h (a), at 1480 °C for 1 h (b), at 1490 °C for 0.5 h (c) and at 1490 °C for 2.5 h (d). The arrow in c highlights a wetting film at a grain boundary of two exaggerated grains. In (d) all boundaries are wetted by a second phase. Note the different scale.

3.3. Grain growth constant in reducing atmosphere By fitting Eq. (1) to the evolution of the mean grain size in reducing atmosphere, the grain growth constant k was obtained. The data is plotted in Fig. 5 (solid squares) as Arrhenius type diagram. If grain growth would proceed by the same mechanism for all temperatures, a single line is expected. However, two discontinuities exist in Fig. 5 according to non-Arrhenius behavior. Between 1350 °C and 1390 °C the growth constant decreases with increasing temperature. This behavior is similar in oxidizing atmosphere (Fig. 5, open squares); its origin is not understood so far [10,11,31]. However, Fig 5 shows that the transition behavior

Fig. 5. Grain growth constant of strontium titanate in reducing atmosphere. Two discontinuities are visible, between 1350 °C and 1390 °C and between 1460 °C and 1500 °C. For comparison, grain growth constants in oxidizing atmosphere were added [11].

found in oxidizing atmosphere between 1350 °C and 1425 °C is different in reducing atmosphere. Between 1460 °C and 1500 °C a transition of the growth constant to faster growth is found in reducing atmosphere. This increase can be explained by the enhancement of the grain boundary mobility by the wetting transition of the grain boundaries shown above. In this temperature range exaggerated growth was visible as shown in Fig. 4. 3.4. Single crystalline seeds: morphology The grain growth constant k reflects the grain boundary energy and grain boundary mobility, but no direct information is available for the grain boundary mobility. According to Section 2.3 the growth kinetics of single crystal seeds growing into a polycrystal allows evaluating the relative mobility for different orientations and estimating their absolute mobility. But before quantifying the mobility the morphology of the growing single crystals should be addressed. A more detailed discussion of the morphology in oxidizing atmosphere was published recently [31]. The morphology of single crystals at 1350 °C is shown in Fig. 6. In oxidizing atmosphere (Fig. 6a and c) the interface of the single crystal is macroscopically curved. This curvature is slightly more pronounced for {1 1 0}. Occasionally steps can be found at the interface (arrows in Fig. 6a). In reducing atmosphere the interface shows less curved boundaries. Nevertheless a macroscopic waviness is present, which is more pronounced for {1 1 0} (Fig. 6b and d). As in oxidizing atmosphere, occasionally steps are present at the interface (arrows in Fig. 6b and d). The orientations {1 1 1} and {3 1 0} show the same morphology as {1 1 0}. The morphology at 1550 °C is shown in Fig. 7 and is different to 1350 °C. The interface oriented in {1 0 0} shows relatively flat boundaries (Fig. 7a and b), however locally some curvature is present especially in reducing atmosphere. For other orientations (b– h) the local curvature is larger; in conjunction the interfaces

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Fig. 6. Morphology of the interface of the single crystals at 1350 °C after 45 h in oxygen (a, c) and in N2–H2 (b, d). In the upper row the orientation of the single crystal at the interface is {1 0 0}; in the lower row it is {1 1 0}. Note the different scale in b and d. The white arrow in a, b and d highlights kinks at the interface.

Fig. 7. Morphology of the interface of the single crystals at 1550 °C after 0.4 h in oxygen (a, c, e, g) and in N2–H2 (b, d, f, h). The orientation of the single crystal at the interface is {1 0 0} in the first row (a, b), {1 1 0} in the second row (c, d), {1 1 1} in the third row (e, f) and {3 1 0} in the last row (g, h). Note the different scale. The white lines in c–f and h highlight the local reorientation of the interface to {1 0 0}.

macroscopically rotates to {1 0 0} as indicated by white lines in Fig. 7c–f and h. This effect corresponds well with the shape of abnormal grains (Fig. 4); it was discussed recently for oxidizing atmosphere [31]. In this study the macroscopic realignment was proposed to resemble a kinetic influence on the shape of the boundary: a growing crystal is bound by its slowest orientations [61]. As will be shown later, at 1550 °C in both oxidizing and reducing atmosphere {1 0 0} is the slowest orientation, which fits well with the microstructures in Fig. 7. The macroscopic rotation

to {1 0 0} seems to be much more pronounced in reducing atmospheres and, thus, with a wetting liquid phase present. This is a well-known effect of a wetting phase on a grain boundary [15,16,18]. It should be noted that contrary to the polycrystals shown in Fig. 3b no wetting liquid film is visible at the boundaries in Fig. 7b, d, f and h. This is caused by the thermal etching for SEM imaging, which results in a dewetting of the films to particles on the polished surface (Fig. 8).

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The growth length of the single crystals at 1350 °C is shown in Fig. 9 for oxidizing (a) and reducing atmospheres (b). In oxidizing atmospheres {1 1 1} shows the fastest growth, followed by {3 1 0}, {1 0 0} and {1 1 0}. After 13 h the growth of the single crystals as well as the polycrystals is strongly retarded. The phenomenon of growth retardation was discussed in detail elsewhere [31] and will be addressed briefly below. At 1350 °C in reducing atmospheres the growth of the single crystals is larger by a factor of
5. No

growth retardation for long dwell times was observed. All orientations show almost the same behavior; hence the grain boundary mobility is almost isotropic. The growth of the single crystals at 1550 °C in oxidizing atmospheres is shown in Fig. 10a. Compared to Fig. 9a {1 1 0} shows faster growth compared to other orientations, otherwise the data are very similar to the growth at 1350 °C in oxidizing atmosphere. Similar to Fig. 9a after 1.5 h growth stagnates. At 1550 °C in reducing atmosphere the growth increases by a factor of
10 (Fig. 10b) compared to Fig. 10a. {1 0 0} is still the slowest orientation, but {1 1 1} is no longer the fastest. No growth stagnation seems to exist. The data in Figs. 9 and 10 can be used to evaluate the relative mobility of the four orientations {1 0 0}, {1 1 0}, {1 1 1} and {3 1 0}. However, in oxidizing atmosphere the retarding effects need to be considered, since the growth kinetics split in two parts: growth is inhibited after long dwell times. For short times no influence is visible, consequently the growth law (Eq. (2)) was fitted to these data (i.e. the first 15 h in Fig. 9a and the first 1.4 h in Fig. 10a). It was shown recently in a similar study, that parabolic growth kinetics fits these data best [31]. In contrast, in reducing atmosphere no significance for growth retardation was found (Figs. 9b and 10b). To evaluate the growth kinetics, parabolic and cubic growth laws were fitted to the entire dataset; the corresponding R2 values are shown in Table 1. According to Table 1 the growth kinetics in reducing atmosphere are assumed to be parabolic as well. Another possible influence on growth at 1550 °C for very short dwell times could arise from the heating and cooling cycle. The cooling cycles can be neglected due to the very high cooling rate of
200 K/min. However, the heating rate was 20 K/min. According to Fig. 5, growth constants are more than two orders of magnitude lower below 1460 °C compared to 1550 °C. Hence growth during

Fig. 9. Growth length of the single crystals and evolution of the mean grain size at 1350 °C in oxidizing (a) and reducing atmosphere (b). Note the different scale of the growth length.

Fig. 10. Growth length of the single crystals and evolution of the mean grain size at 1550 °C in oxidizing (a) and reducing atmosphere (b). Note the different scale of the growth length.

Fig. 8. Second phase film at the grain boundary at 1550 °C after 0.4 h, which dewetted and decomposed to particles during thermal etching at 1115 °C for 3 h.

3.5. Single crystal seeds: growth and mobility

W. Rheinheimer et al. / Acta Materialia 101 (2015) 80–89 Table 1 R2 values for the fits of parabolic and cubic growth equations to the growth kinetics of single crystals in reducing atmosphere. Temperature (°C)

Orientation

R2 (parabolic)

R2 (cubic)

1350

{1 0 0} {1 1 0} {1 1 1} {3 1 0}

0.97324 0.8693 0.87859 0.96003

0.90372 0.70164 0.83822 0.8829

1550

{1 0 0} {1 1 0} {1 1 1} {3 1 0}

0.97189 0.8547 0.97471 0.8771

0.83908 0.65062 0.91286 0.68099

mSC mm

relative mobility of {1 0 0} is about 3 times higher than the relative mobility of {1 1 0}, which is different to the present study (m{100}/ m{110} 0.45–1.2 depending on temperature and atmosphere). In Ref. [28] no significant difference arises from the change of the atmosphere, which differs considerably from the present results. The authors used a polycrystalline matrix with very low density and the purity of the ceramic powder is low (99.8%), hence the differences are most probably based on pore drag effects and solutes. 3.6. Influence of the atmosphere on grain growth kinetics

heating can be neglected below 1460 °C. The interval from 1460 °C to 1550 °C results in a maximum error of 5 min. Given the data in Fig. 10a and b, a shift of 5 min to longer dwell times of the very first data point (or any later data point) seems not to change the characteristics of the dataset significantly. Assuming parabolic kinetics, Table 2 shows the relative mobility of the single crystals. In general, the relative mobility is close to 1, i.e. the mobility of the single crystals is very similar to the average mobility of the polycrystals. However; at 1550 °C in reducing atmosphere the mobility of the single crystals is above the average mobility of the polycrystal by a factor of
3–6. This could be related to abnormal grain growth [31]. An estimation of the absolute mobility can be obtained using the data in Table 2 and the equation [31]:

kSC ¼ 2acm mSC ¼ km

87

ð3Þ

The macroscopic rotation of the interface to {1 0 0}-planes (Figs. 4 and 7) influences the local orientation of the single crystals. For example at 1550 °C in reducing atmosphere in Fig. 7h the overall orientation of the single crystal is {3 1 0}, while the interface locally realigns to {1 0 0}. Consequently the orientation of the single crystals cannot be controlled exactly in experiment. It should be noted that at 1550 °C in reducing atmosphere the relative mobility of {3 1 0} is higher by a factor of 2 compared to {1 0 0} (Table 2), although {3 1 0} realigned to {1 0 0} and the angle between {1 0 0} and {3 1 0} is only 18.4°. Thus the impact of the local realignment on the measured mobility is not clear; more investigation is needed. A previous study compared the growth of a single crystal seed in air and in N2–H2 (95%/5%) at 1470 °C [28], which is in the order of the wetting transition reported in this study. However, the authors give no information on a possible wetting of the boundaries and no quantification of growth. From Fig. 7 in Ref. [28] the mean grain diameter is
5 lm in air and in N2–H2. The growth length in air can be estimated from Fig. 3a in Ref. [28] and is
100 lm for {1 0 0} and
30 lm for {1 1 0}, no other orientations are available. For N2–H2 two different micrographs are given, showing that the growth lengths of {1 0 0} and {1 1 0} are
100 lm and
30 lm (Fig. 4a in Ref. [28]) and
70 lm and
20 lm (Fig. 6a in Ref. [28]), respectively. From these data the Table 2 Grain growth constants and relative mobility for different orientations in oxidizing and reducing atmosphere. T (°C)

Atmosphere

km (m2/s)

(1 0 0)

(1 1 0)

(1 1 1)

(3 1 0)

1350 1350

O2 95% N2/5% H2

4.88  1016 1.17  1015

0.73 1.26

0.60 1.04

1.15 1.12

0.91 1.19

1550 1550

O2 95% N2/5% H2

4.80  1014 2.01  1013

0.99 2.83

1.52 6.22

1.88 4.47

1.31 5.68

mSC/mm

In the presence of a wetting liquid phase film at the interfaces, growth kinetics are influenced by the rate controlling migration mechanism. Interface reaction controlled growth results in parabolic kinetics [5,6]; cubic kinetics result for diffusion controlled growth [3,6,12–14]. In the present experiments the growth kinetics for polycrystals and single crystals are parabolic in the presence of a wetting liquid phase film, which accords to the interface reaction being the rate controlling mechanism. Within this study grain growth stagnated for sufficient long heating times in oxygen, but not in reducing atmosphere (N2– H2). The stagnation results in growth deviating from parabolic kinetics. This phenomenon was reported and discussed recently [31]; most likely it is attributed to a nonlinearity of the grain boundary mobility. Many studies were published on the existence of such nonlinearities for barium titanate and strontium titanate, if the boundaries are facetted (‘‘nucleation barriers”, [28–30,39,62–67]). In perovskite ceramics faceting seems to be closely related to the oxygen partial pressure p(O2) with rough boundaries at low p(O2) and an increasing fraction of facetted boundaries with increasing p(O2) [28–30,68–70]. However, in the present study, even in pure oxygen the grain boundaries in strontium titanate seem not to be completely facetted on a macroscopic scale. Below 1350 °C some macroscopic faceting is visible for both oxidizing (Fig. 6a) and reducing atmosphere (Fig. 6b and d), but interfaces are predominantly macroscopically curved. On atomic scale no pronounced difference in faceting could be found by TEM with respect to oxygen partial pressure; all boundaries showed atomic steps at the interfaces [71]. Overall the faceting behavior of strontium titanate is not clear and consequently the influence of nucleation barriers is unclear for the present experiments. An intrinsic drag effect similar to solute drag, but based on intrinsic defects, was proposed to cause the nonlinearity of the grain boundary mobility [31]. In this case the nonlinearity should depend on the defect concentration and, hence, on the oxygen partial pressure, which is the case in the present experiments. In general, a low oxygen partial pressure gives a high oxygen vacancy concentration and a low strontium vacancy concentration [72]. While the bulk defect chemistry is well known for strontium titanate, so far no clear relationship between the oxygen partial pressure and the space charge properties at grain boundaries was found [73,74]. Accordingly the influence of oxygen partial pressure on the nonlinearity of the mobility needs to be investigated more in detail. 4. Summary and conclusion A wetting transition was documented in high purity strontium titanate in reducing atmosphere between 1460 °C and 1500 °C. This wetting transition was shown to be reversible; the wetting phase is titania-rich and free from any detectable solutes. The grain boundary mobility is increased considerably by the wetting. Exaggerated grain growth was found in the temperature range of the wetting transition. The fraction of exaggerated grains increased

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with temperature. This exaggerated grain growth was interpreted as a temperature dependent anisotropy of the grain boundary wetting. Some grain boundaries wet prior to others; the increased mobility of these boundaries results in exaggerated growth. The grain growth constant was measured in reducing atmosphere between 1300 °C and 1550 °C. Two discontinuities were found: at 1350 °C the grain growth constant decreases by more than one order of magnitude with temperature; at 1460 °C an increase by more than two orders of magnitude was found. The first is similar to the recently published grain growth anomaly; the second was attributed to the wetting transition. The relative grain boundary mobility was measured by the seeded polycrystal method at 1350 °C (below the wetting transition) and at 1550 °C (above the wetting transition). Four different orientations were analyzed: {1 0 0}, {1 1 0}, {1 1 1} and {3 1 0}. In oxidizing atmosphere (but not in reducing atmosphere) retarding effects on the growth were observed. The grain boundary mobility in reducing atmosphere was higher by a factor of
5 at 1350 °C and by a factor of
10 at 1550 °C compared to oxidizing atmosphere. At 1550 °C the interfaces tend to macroscopically realign to {1 0 0}planes. The realignment seems to be caused by kinetics. Even under the presence of a wetting liquid film grain growth was found to be interface reaction controlled. The wetting transition is well controllable with temperature and atmosphere. Consequently it may be used to tailor boundary characteristics (wetted or not wetted) and overall microstructure for a specific application. A careful control of atmosphere and temperature even allows converting polycrystalline strontium titanate to single crystals similar to Fig. 4d. A change in the atmosphere or temperature causes a decomposition of wetting films into particles, which then possibly drag the interface motion and prevent further grain growth. However, the present study focuses on high purity strontium titanate. Electronic applications require doping; consequently further experiments are needed to reveal the influence of the chemical composition on the wetting transition. Acknowledgment A part of this work was supported by the Deutsche Forschungsgemeinschaft (DFG) under contract BA4143/2. References [1] S.-J.L. Kang, Sintering: Densification, Grain Growth, and Microstructure, Elsevier Butterworth-Heinemann, Amsterdam, 2005. [2] Y.-M. Chiang, D. Birnie, W. Kingery, Physical Ceramics: Principles for Ceramic Science and Engineering, MIT Series in materials science & engineering, Wiley, New York, 1997. [3] M. Rahaman, Ceramic Processing and Sintering, Marcel Decker, New York, Basel, 2003. [4] W.A. Kaysser, M. Sprissler, C.A. Handwerker, J.E. Blendell, Effect of a liquidphase on the morphology of grain-growth in alumina, J. Am. Ceram. Soc. 70 (1987) 339–343. [5] J.D. Powers, A.M. Glaeser, Grain boundary migration in ceramics, Interface Sci. 6 (1998) 23–39. [6] G.S. Rohrer, Influence of interface anisotropy on grain growth and coarsening, Annu. Rev. 35 (2005) 99–126. [7] S. Dillon, M. Harmer, Direct observation of multilayer adsorption on alumina grain boundaries, J. Am. Ceram. Soc. 90 (2007) 996–998. [8] R. Akiva, A. Katsman, W.D. Kaplan, Anisotropic grain boundary mobility in undoped and doped alumina, J. Am. Ceram. Soc. 97 (2014) 1610–1618. [9] M. Bäurer, M. Syha, D. Weygand, Combined experimental and numerical study on the effective grain growth dynamics in highly anisotropic systems: application to barium titanate, Acta Mater. 61 (2013) 5664–5673. [10] M. Bäurer, D. Weygand, P. Gumbsch, M.J. Hoffmann, Grain growth anomaly in strontium titanate, Scr. Mater. 61 (2009) 584. [11] W. Rheinheimer, M.J. Hoffmann, Non-arrhenius behavior of grain growth in strontium titanate: New evidence for a structural transition of grain boundaries, Scr. Mater. 101 (2015) 68–71. [12] W. Ostwald, Studien über die bildung und umwandlung fester körper, Z. Phys. Chem. 22 (1897) 289–330. [13] C. Wagner, Theorie der alterung von niederschlaegen durch umloesen, Zeitschrift für Elektrochemie 65 (1961) 581–591.

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