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Grain growth anomaly in strontium titanate
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Scripta Materialia 61 (2009) 584–587 www.elsevier.com/locate/scriptamat
Grain growth anomaly in strontium titanate M. Ba¨urer,a,* D. Weygand,b P. Gumbschb and M.J. Hoffmanna a
Institut fu¨r Keramik im Maschinenbau, Universita¨t Karlsruhe, Haid-und-Neu-Straße 7, Germany Institut fu¨r Zuverla¨ssigkeit von Bauteilen und Systemen, Universita¨t Karlsruhe, Kaiserstraße 12, Germany
b
Received 9 March 2009; revised 20 May 2009; accepted 21 May 2009 Available online 27 May 2009
The grain growth studies presented here show anomalies in the growth dynamics in SrTiO3. For the temperature range investigated, the overall grain growth does not follow the classical Arrhenius-type temperature dependence. At a critical temperature the grain growth rate decreases substantially with increasing temperature. Such a decrease is reported for the first time in bulk ceramic material. Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Grain growth; Grain boundaries; Interfaces; Ceramics
Perovskite materials are widely used in electronic devices, e.g. as grain boundary (GB) barrier layer capacitors [1,2], PTC (positive temperature coefficient) elements [3] and piezoelectric actuators [4]. Despite the small volume fraction of material which is close to grain boundaries, many macroscopic material properties that are relevant for applications are governed by the grain boundaries and therefore depend strongly on grain size. In nearly all technical applications ceramics are produced by powder technology methods. Therefore the behaviour of grain boundaries at high temperature, e.g. during sintering and grain coarsening, is crucial for designing the macroscopic behaviour of the final product. In the present study strontium titanate (SrTiO3) is used as a model material for the investigation of perovskites. SrTiO3 is well suited since the pure material shows no phase transitions in the relevant temperature range. At 1440 °C a eutectic point exists with an excess of Ti; the coexisting phase below this temperature is TiO2 in rutile form [5]. Despite the vast number of publications on SrTiO3, understanding of the grain growth behaviour in bulk material is limited. Only one publication exists for Nb-doped material [6] where the average grain size was used to normalize the growth velocity to the driving force. Even there, only two temperatures were tested, 1200 and 1490 °C. In other publications data for the grain structures and therefore the driving
* Corresponding ruhe.de
author. E-mail:
[email protected]
force for growth is unknown [7,8], which makes detailed analysis impossible. Recently it has been demonstrated in alumina that grain growth studies are a powerful approach to identify structural changes at grain boundaries [9]. Additionally, grain growth experiments avoid the problem that the state of the grain boundaries might be different at low temperatures compared to the sintering temperature. This has been described by Waser et al. for the receding of a TiO2 liquid phase to triple pockets during cooling [10]. This study focuses on the characterization of grain growth behaviour in the temperature range from 1100 to 1600 °C which is of interest for processing of bulk SrTiO3 ceramics. It is the first study to cover such a wide temperature range with an extremely well-defined ceramic material. The powders used were prepared by the mixed-oxide route from SrCO3 and TiO2 (both 99.9+%, Sigma Aldrich Chemie, Taufkirchen, Germany). In order to exclude influences from small random variations in Sr/Ti ratio, this ratio has been varied deliberately: Sr/Ti = 1.005, 1.002 and 0.996. The powders were attrition milled, calcined at 975 °C for 6 h and subsequently milled again to break up agglomerations formed during the preceding heat treatment. Further details of the powder preparation are described elsewhere [11]. Samples were prepared by uniaxial and subsequent cold isostatic pressing of the powder to discs of approximately 12 mm diameter and 3 mm thickness. The samples were then heated to sintering temperature in a tube furnace (HTRV70, Gero GmbH, Neuhausen, Germany) at a rate of 20 °C min1 and held there for variable times in an O2 atmosphere. At the end of the
1359-6462/$ - see front matter Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2009.05.028
M. Ba¨urer et al. / Scripta Materialia 61 (2009) 584–587
annealing time the samples were quenched by removing them from the hot zone of the furnace. All samples sintered by this thermal cycle reached a density higher than 99% of the theoretical value for SrTiO3. Due to the slow sintering kinetics, the samples for growth experiments below 1300 °C were sintered to more than 99% of the theoretical density at a higher temperature (1350 °C) and then annealed at the test temperature. During annealing at 1100 °C no significant increase in the average grain size was measured even after 100 h. Grain size was measured by the linear intercept method. Mean grain sizes are given in Figure 1 for sintering temperatures between 1300 and 1600 °C. The evolution of the grain size d was normalized with respect to the driving force to compare different annealing times, Sr/Ti stoichiometries and temperatures. Grain growth is usually described by the equation [12]: d n d n0 ¼ kDt
ð1Þ
where d is the grain size, d0 the initial grain size, k the growth factor and Dt the annealing time. If one assumes that the driving force for grain growth is given by the local curvature and GB energy as c/d, and introduces mobility M as the proportionality constant between the driving force and velocity dd/dt of the GB, one obtains n = 2 and k = 2acM, where c is the average GB energy and a is a geometrical factor. The GB mobility is expected to be thermally activated and to follow a clas-
Figure 1. Mean grain sizes measured by the linear intercept method for samples with Sr/Ti = 0.996, Sr/Ti = 1.002 and Sr/Ti = 1.005.
585
sical Arrhenius law if there is no change in the basic mechanism for boundary movement. Deviations from the Arrhenius-type behaviour are therefore a way of identifying changes at grain boundaries occurring at higher temperatures. The growth factor k can be extracted from the experimentally measured grain sizes (Fig. 1) by fitting to Eq. (1) and is used in the following to characterize grain growth. The results on the extracted growth factor k, which represents the effective GB mobility, are given in Figure 2. At temperatures of 1390 °C and below, normal grain growth occurs for all Sr/Ti ratios. The Sr/Ti ratios do not yield substantial differences in the effective mobility. In this regime of normal growth, two different temperature ranges can be identified in which the temperature dependency of the effective mobility deviates from the expected Arrhenius law temperature dependency: one between 1300 and 1350 °C and the other between 1390 and 1425 °C. The activation energy for grain growth was estimated by fitting an Arrhenius law to the points in Figure 2. An activation energy of 15 eV is obtained for the behaviour between 1350 and 1390 °C. In the lower temperature range the activation energy is 9 eV but with a higher uncertainty due to the large error bar at 1200 °C. Above 1390 °C abnormal grain growth is observed, which leads to two populations of grains: normally growing matrix grains and abnormally growing grains. Surprisingly, normal grain growth in matrix grains as well as in the abnormally growing grains proceeds much slower than expected. Even the effective mobility of the abnormally growing grains is smaller than the one extrapolated from the low-temperature behaviour of the normally growing grains based on an Arrhenius fit. However, the activation energy remains of the order of 15 eV for both types of grains with a slightly higher activation energy for abnormally growing grains. Error bars given in Figure 2 are for a 5% error in grain size measurement. For the points of abnormal growth at 1425 and 1460 °C the effective mobility is estimated by the method proposed by Dillon et al. [9]. To
Figure 2. Arrhenius-type diagram of effective mobility k = (d2d 20 )/Dt as a function of the thermal activation energy for strontium titanate with various Sr/Ti ratios. Closed symbols represent normal growth, open symbols abnormal growth.
586
M. Ba¨urer et al. / Scripta Materialia 61 (2009) 584–587
account for the high uncertainty of this estimate, the errors are estimated differently there. The lower limit of the effective mobility (error bar) is given by the mobility ratio between abnormal and normal grains estimated by the size ratio as calculated by Humphreys [13]. This assumes that abnormal grains were present from the beginning. The upper limit is estimated assuming that the nucleation of the abnormal grain occurred after 90% of the annealing time according to the method used for the centre point of the error range [9]. Further experiments have been performed to exclude a possible influence of the following factors on growth behaviour: (i) impurities introduced by the furnace; (ii) a non-linear dependency between mobility and grain size as driving force, leading to results that are sensitive to the initial grain size; and (iii) the possibility that impurities present in the material segregate towards the boundary and slow down or enhance the growth kinetics. To exclude impurities due to the furnace, sintering and growth experiments were performed in a different furnace (HT70, Nabertherm, Lilienthal, Germany) in air for the ceramic with Sr/Ti = 0.996. To also exclude the influence of initial grain size and impurity content at the GBs, samples were either sintered at 1425 °C for 1 h and then annealed at 1350 °C to examine grain growth or sintered for 1 h at 1350 °C and then annealed at 1425 °C. The results for the effective GB mobility k of these experiments, referred to as the ‘‘reversibility test”, are given in Figure 3 in comparison with the results already described above. The magnitude of the increase in growth speed with a reduction in temperature is clearly visible in Figure 4 which gives the evolution of the grain size distribution. At 1425 °C the microstructure is nearly stagnant, whereas annealing of the same initial microstructure at 1350 °C leads to an increase in grain size of almost 500% of the initial size after the same annealing time. The distributions are unimodal and do not show any unexpected feature. These experiments, however, show the same discontinuous drop in effective mobility as before. Therefore, it is concluded that an influence of additional impurities, due to the fur-
Figure 3. Effective mobility of samples with Sr/Ti = 0.996 sintered at two different temperatures (reversibility test) in comparison to data from Figure 2.
Figure 4. Evolution of grain size distribution during annealing at 1425 °C (left) and at 1350 °C after sintering to full density at 1425 °C (right). Area under the distribution is normalized to unity.
nace, can be ruled out. The Sr/Ti ratio should have a strong influence on behaviour controlled by impurities as all impurities have a higher affinity for either the A or the B side of the perovskite lattice. This effect has been described for Si impurities occupying the Ti site of the perovskite lattice [6,14], where excess Ti expels the impurities from the crystal structure. The mobilities published in Ref. [6] for a doped material at 1490 °C are in the range measured here. The point in Ref. [6] at 1200 °C is three orders of magnitude higher than for the present experiments. No literature data is available for the activation energy for grain growth in SrTiO3, which makes a direct comparison impossible. However, the activation energy for grain growth of approximately 15 eV is high compared to values for bulk diffusion in the cation sublattice measured by tracer experiments of 3.9 eV for Sr and 3.3 eV for Ti [15,16]. The value for grain growth in alumina is much lower, with a value of 4.6 eV in ultrapure alumina [17]. The values of activation energies for sintering are generally attributed to GB diffusion and agree well with those from growth data, ranging from 4.6 eV in pure material [18] to 7.6 eV in alumina with a second phase [19]. The high value for the activation energy in SrTiO3 could be due to faceting of the grain boundaries as already suggested by Hwang et al. [20] for sintering of tungsten, but is more likely connected to the formation of Ti vacancies in SrTiO3 which have a formation energy of approximately the same value (15 eV) as calculated by Tanaka et al. [21]. Therefore it is concluded that Ti vacancies are probably the rate-limiting species for boundary motion. The discontinuous drops in the kinetic factor k are not dependent on the precise values of the exponent n in Eq. (1). For convenience, a value of n = 2 has been chosen, which describes rather well the overall growth dynamics for the investigated range of grain growth, where changes in the grain size by 20–500% are observed. The observed drops in k are quite drastic, between one to more than three orders of magnitude. For a possible interpretation of this observation, it should be noted that two physical quantities are collapsed in k, the GB mobility and the GB energy and a geometrical factor, which for normal grain growth is
M. Ba¨urer et al. / Scripta Materialia 61 (2009) 584–587
known from grain growth simulations in two and three dimensions to be of the order of unity [22,23]. As the transition temperatures where the drops occur are independent of the precise Sr/Ti ratio for the temperatures tested, it is assumed that segregation of one species to the GB is not controlling these drops. It is therefore suggested that structural transitions at the GB are a possible origin for this observation. One possible structural change could be a faceting/defaceting transition upon decreasing/increasing temperature. This can markedly change GB mobility [24] and thereby lead to the observed changes. Transitions in the faceting behaviour have been observed in strontium titanium oxide bicrystals in the temperature range examined in this study [25] but are highly non-trivial to detect in a ceramic. The adsorption of a species at the GB will generally lead to a retardation of GB motion due to solute drag [26]. Thermal activation would reduce this effect with increasing temperature in contradiction to the findings in Figures 2 and 3. Under the assumption of an activation energy that is approximately constant for the two high-temperature regions in the Arrhenius-type diagram, a change to lower GB mobility must be connected with a drop in entropy. This has been shown for various grain boundaries in alumina [9], where a temperature increase leads to more disorder in the GB. The drops in growth speed with increasing temperature cannot be explained by this. However, the drops indicate a change in the basic mechanism of GB motion and the drop in entropy is most likely associated with a decrease in the volume activated through the process of motion. In summary, the present paper shows a growth anomaly with two distinct drops in GB mobility with increasing temperature. This grain growth anomaly is probably linked to structural changes of the grain boundaries at high temperatures, e.g. changes in faceting behaviour. Further work is certainly required to clarify this situation and more detailed investigations of grain growth are needed for a better understanding of the basic mechanisms of growth during sintering. The changes identified through the growth experiments are very likely to be of a general nature and therefore relevant to other perovskite materials. This work has been financially supported by the European Commission under Contract No. NMP3CT-2005-013862 (INCEMS). [1] N. Stenton, M.P. Harmer, Advances in Ceramics: Additives and Interfaces in Electronic Ceramics VII (1984) 156.
587
[2] M. Fujimoto, W.D. Kingery, Journal of the American Ceramic Society 68 (4) (1985) 169–173. [3] R. Waser, Solid State Ionics 75 (1995) 89. [4] M.J. Hoffmann, H. Kungl, Current Opinion in Solid State & Materials Science 8 (2004) 51. [5] M. Drys, W. Trzebiatowski, Phase Diagrams for Ceramists, American Ceramics Society, Columbus, OH, 1957, p. 119. [6] C.-J. Peng, Y.-M. Chiang, Journal of Materials Research 5 (6) (1990) 1237–1245. [7] S.-Y. Chung, S.-J.L. Kang, Journal of the American Ceramic Society 85 (2002) 2805. [8] S.-Y. Chung, D.Y.g. Yoon, S.-J.L. Kang, Acta Materialia 50 (2002) 3361. [9] S.J. Dillon, M. Tang, W.C. Carter, M.P. Harmer, Acta Materialia 55 (2007) 6208. [10] R. Waser, T. Baiatu, K.-H. Ha¨rdtl, Journal of the American Ceramic Society 73 (1990) 1645. [11] M. Ba¨urer, H. Kungl, M.J. Hoffmann, Journal of the American Ceramic Society 92 (2009) 601. [12] J.E. Burke, D. Turnbull, Progress in Metal Physics 3 (1952) 220. [13] F.J. Humphreys, Acta Materialia 45 (1997) 4231. [14] C.-J. Peng, Y.-M. Chiang, in: J.A. Pask, A.G. Evans (Eds.), Ceramic Microstructures ’86: Role of Interfaces, Proceedings of the 22nd University Conference on Ceramics, and the International Materials Symposium, Plenum Press, New York, 1987, pp. 555–568. [15] K. Go¨mann, G. Borchardt, A. Gunhold, W. MausFriedrichs, H. Baumann, Physical Chemistry Chemical Physics 6 (2004) 3639. [16] K. Go¨mann, G. Borchardt, M. Schulz, A. Go¨mann, W. Maus-Friedrichs, B. Lesage, O. Kaitasov, S. HoffmannEifert, T. Schneller, Physical Chemistry Chemical Physics 7 (2005) 2053. [17] S.J. Dillon, M.P. Harmer, Journal of the American Ceramic Society 89 (2006) 3885. [18] H. Su, D.L. Johnson, Journal of the American Ceramic Society 79 (1996) 3211. [19] J. Wang, R. Raj, Journal of the American Ceramic Society 73 (1990) 1172. [20] N.M. Hwang, Y.J. Park, D-Y Kim, D.Y. Yoon, Scripta Materialia 42 (2000) 421. [21] T. Tanaka, K. Matsunaga, Y. Ikuhara, T. Yamamoto, Physical Review B 68 (2003) 205213. [22] D. Weygand, Y. Bre´chet, J. Le´pinoux, Philosophical Magazine B 78 (1998) 329. [23] D. Weygand, Y. Bre´chet, J. Le´pinoux, W. Gust, Philosophical Magazine B 79 (1999) 703. [24] V.G. Sursaeva, B.B. Straumal, A.S. Gornakova, L.S. Shvindlerman, G. Gottstein, Acta Materialia 56 (2008) 2728. [25] S.B. Lee, W. Sigle, W. Kurtz, M. Ru¨hle, Acta Materialia 51 (2003) 975. [26] J.W. Cahn, Acta Metallurgica 10 (1962) 789.
Scripta Materialia 61 (2009) 584–587 www.elsevier.com/locate/scriptamat
Grain growth anomaly in strontium titanate M. Ba¨urer,a,* D. Weygand,b P. Gumbschb and M.J. Hoffmanna a
Institut fu¨r Keramik im Maschinenbau, Universita¨t Karlsruhe, Haid-und-Neu-Straße 7, Germany Institut fu¨r Zuverla¨ssigkeit von Bauteilen und Systemen, Universita¨t Karlsruhe, Kaiserstraße 12, Germany
b
Received 9 March 2009; revised 20 May 2009; accepted 21 May 2009 Available online 27 May 2009
The grain growth studies presented here show anomalies in the growth dynamics in SrTiO3. For the temperature range investigated, the overall grain growth does not follow the classical Arrhenius-type temperature dependence. At a critical temperature the grain growth rate decreases substantially with increasing temperature. Such a decrease is reported for the first time in bulk ceramic material. Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Grain growth; Grain boundaries; Interfaces; Ceramics
Perovskite materials are widely used in electronic devices, e.g. as grain boundary (GB) barrier layer capacitors [1,2], PTC (positive temperature coefficient) elements [3] and piezoelectric actuators [4]. Despite the small volume fraction of material which is close to grain boundaries, many macroscopic material properties that are relevant for applications are governed by the grain boundaries and therefore depend strongly on grain size. In nearly all technical applications ceramics are produced by powder technology methods. Therefore the behaviour of grain boundaries at high temperature, e.g. during sintering and grain coarsening, is crucial for designing the macroscopic behaviour of the final product. In the present study strontium titanate (SrTiO3) is used as a model material for the investigation of perovskites. SrTiO3 is well suited since the pure material shows no phase transitions in the relevant temperature range. At 1440 °C a eutectic point exists with an excess of Ti; the coexisting phase below this temperature is TiO2 in rutile form [5]. Despite the vast number of publications on SrTiO3, understanding of the grain growth behaviour in bulk material is limited. Only one publication exists for Nb-doped material [6] where the average grain size was used to normalize the growth velocity to the driving force. Even there, only two temperatures were tested, 1200 and 1490 °C. In other publications data for the grain structures and therefore the driving
* Corresponding ruhe.de
author. E-mail:
[email protected]
force for growth is unknown [7,8], which makes detailed analysis impossible. Recently it has been demonstrated in alumina that grain growth studies are a powerful approach to identify structural changes at grain boundaries [9]. Additionally, grain growth experiments avoid the problem that the state of the grain boundaries might be different at low temperatures compared to the sintering temperature. This has been described by Waser et al. for the receding of a TiO2 liquid phase to triple pockets during cooling [10]. This study focuses on the characterization of grain growth behaviour in the temperature range from 1100 to 1600 °C which is of interest for processing of bulk SrTiO3 ceramics. It is the first study to cover such a wide temperature range with an extremely well-defined ceramic material. The powders used were prepared by the mixed-oxide route from SrCO3 and TiO2 (both 99.9+%, Sigma Aldrich Chemie, Taufkirchen, Germany). In order to exclude influences from small random variations in Sr/Ti ratio, this ratio has been varied deliberately: Sr/Ti = 1.005, 1.002 and 0.996. The powders were attrition milled, calcined at 975 °C for 6 h and subsequently milled again to break up agglomerations formed during the preceding heat treatment. Further details of the powder preparation are described elsewhere [11]. Samples were prepared by uniaxial and subsequent cold isostatic pressing of the powder to discs of approximately 12 mm diameter and 3 mm thickness. The samples were then heated to sintering temperature in a tube furnace (HTRV70, Gero GmbH, Neuhausen, Germany) at a rate of 20 °C min1 and held there for variable times in an O2 atmosphere. At the end of the
1359-6462/$ - see front matter Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2009.05.028
M. Ba¨urer et al. / Scripta Materialia 61 (2009) 584–587
annealing time the samples were quenched by removing them from the hot zone of the furnace. All samples sintered by this thermal cycle reached a density higher than 99% of the theoretical value for SrTiO3. Due to the slow sintering kinetics, the samples for growth experiments below 1300 °C were sintered to more than 99% of the theoretical density at a higher temperature (1350 °C) and then annealed at the test temperature. During annealing at 1100 °C no significant increase in the average grain size was measured even after 100 h. Grain size was measured by the linear intercept method. Mean grain sizes are given in Figure 1 for sintering temperatures between 1300 and 1600 °C. The evolution of the grain size d was normalized with respect to the driving force to compare different annealing times, Sr/Ti stoichiometries and temperatures. Grain growth is usually described by the equation [12]: d n d n0 ¼ kDt
ð1Þ
where d is the grain size, d0 the initial grain size, k the growth factor and Dt the annealing time. If one assumes that the driving force for grain growth is given by the local curvature and GB energy as c/d, and introduces mobility M as the proportionality constant between the driving force and velocity dd/dt of the GB, one obtains n = 2 and k = 2acM, where c is the average GB energy and a is a geometrical factor. The GB mobility is expected to be thermally activated and to follow a clas-
Figure 1. Mean grain sizes measured by the linear intercept method for samples with Sr/Ti = 0.996, Sr/Ti = 1.002 and Sr/Ti = 1.005.
585
sical Arrhenius law if there is no change in the basic mechanism for boundary movement. Deviations from the Arrhenius-type behaviour are therefore a way of identifying changes at grain boundaries occurring at higher temperatures. The growth factor k can be extracted from the experimentally measured grain sizes (Fig. 1) by fitting to Eq. (1) and is used in the following to characterize grain growth. The results on the extracted growth factor k, which represents the effective GB mobility, are given in Figure 2. At temperatures of 1390 °C and below, normal grain growth occurs for all Sr/Ti ratios. The Sr/Ti ratios do not yield substantial differences in the effective mobility. In this regime of normal growth, two different temperature ranges can be identified in which the temperature dependency of the effective mobility deviates from the expected Arrhenius law temperature dependency: one between 1300 and 1350 °C and the other between 1390 and 1425 °C. The activation energy for grain growth was estimated by fitting an Arrhenius law to the points in Figure 2. An activation energy of 15 eV is obtained for the behaviour between 1350 and 1390 °C. In the lower temperature range the activation energy is 9 eV but with a higher uncertainty due to the large error bar at 1200 °C. Above 1390 °C abnormal grain growth is observed, which leads to two populations of grains: normally growing matrix grains and abnormally growing grains. Surprisingly, normal grain growth in matrix grains as well as in the abnormally growing grains proceeds much slower than expected. Even the effective mobility of the abnormally growing grains is smaller than the one extrapolated from the low-temperature behaviour of the normally growing grains based on an Arrhenius fit. However, the activation energy remains of the order of 15 eV for both types of grains with a slightly higher activation energy for abnormally growing grains. Error bars given in Figure 2 are for a 5% error in grain size measurement. For the points of abnormal growth at 1425 and 1460 °C the effective mobility is estimated by the method proposed by Dillon et al. [9]. To
Figure 2. Arrhenius-type diagram of effective mobility k = (d2d 20 )/Dt as a function of the thermal activation energy for strontium titanate with various Sr/Ti ratios. Closed symbols represent normal growth, open symbols abnormal growth.
586
M. Ba¨urer et al. / Scripta Materialia 61 (2009) 584–587
account for the high uncertainty of this estimate, the errors are estimated differently there. The lower limit of the effective mobility (error bar) is given by the mobility ratio between abnormal and normal grains estimated by the size ratio as calculated by Humphreys [13]. This assumes that abnormal grains were present from the beginning. The upper limit is estimated assuming that the nucleation of the abnormal grain occurred after 90% of the annealing time according to the method used for the centre point of the error range [9]. Further experiments have been performed to exclude a possible influence of the following factors on growth behaviour: (i) impurities introduced by the furnace; (ii) a non-linear dependency between mobility and grain size as driving force, leading to results that are sensitive to the initial grain size; and (iii) the possibility that impurities present in the material segregate towards the boundary and slow down or enhance the growth kinetics. To exclude impurities due to the furnace, sintering and growth experiments were performed in a different furnace (HT70, Nabertherm, Lilienthal, Germany) in air for the ceramic with Sr/Ti = 0.996. To also exclude the influence of initial grain size and impurity content at the GBs, samples were either sintered at 1425 °C for 1 h and then annealed at 1350 °C to examine grain growth or sintered for 1 h at 1350 °C and then annealed at 1425 °C. The results for the effective GB mobility k of these experiments, referred to as the ‘‘reversibility test”, are given in Figure 3 in comparison with the results already described above. The magnitude of the increase in growth speed with a reduction in temperature is clearly visible in Figure 4 which gives the evolution of the grain size distribution. At 1425 °C the microstructure is nearly stagnant, whereas annealing of the same initial microstructure at 1350 °C leads to an increase in grain size of almost 500% of the initial size after the same annealing time. The distributions are unimodal and do not show any unexpected feature. These experiments, however, show the same discontinuous drop in effective mobility as before. Therefore, it is concluded that an influence of additional impurities, due to the fur-
Figure 3. Effective mobility of samples with Sr/Ti = 0.996 sintered at two different temperatures (reversibility test) in comparison to data from Figure 2.
Figure 4. Evolution of grain size distribution during annealing at 1425 °C (left) and at 1350 °C after sintering to full density at 1425 °C (right). Area under the distribution is normalized to unity.
nace, can be ruled out. The Sr/Ti ratio should have a strong influence on behaviour controlled by impurities as all impurities have a higher affinity for either the A or the B side of the perovskite lattice. This effect has been described for Si impurities occupying the Ti site of the perovskite lattice [6,14], where excess Ti expels the impurities from the crystal structure. The mobilities published in Ref. [6] for a doped material at 1490 °C are in the range measured here. The point in Ref. [6] at 1200 °C is three orders of magnitude higher than for the present experiments. No literature data is available for the activation energy for grain growth in SrTiO3, which makes a direct comparison impossible. However, the activation energy for grain growth of approximately 15 eV is high compared to values for bulk diffusion in the cation sublattice measured by tracer experiments of 3.9 eV for Sr and 3.3 eV for Ti [15,16]. The value for grain growth in alumina is much lower, with a value of 4.6 eV in ultrapure alumina [17]. The values of activation energies for sintering are generally attributed to GB diffusion and agree well with those from growth data, ranging from 4.6 eV in pure material [18] to 7.6 eV in alumina with a second phase [19]. The high value for the activation energy in SrTiO3 could be due to faceting of the grain boundaries as already suggested by Hwang et al. [20] for sintering of tungsten, but is more likely connected to the formation of Ti vacancies in SrTiO3 which have a formation energy of approximately the same value (15 eV) as calculated by Tanaka et al. [21]. Therefore it is concluded that Ti vacancies are probably the rate-limiting species for boundary motion. The discontinuous drops in the kinetic factor k are not dependent on the precise values of the exponent n in Eq. (1). For convenience, a value of n = 2 has been chosen, which describes rather well the overall growth dynamics for the investigated range of grain growth, where changes in the grain size by 20–500% are observed. The observed drops in k are quite drastic, between one to more than three orders of magnitude. For a possible interpretation of this observation, it should be noted that two physical quantities are collapsed in k, the GB mobility and the GB energy and a geometrical factor, which for normal grain growth is
M. Ba¨urer et al. / Scripta Materialia 61 (2009) 584–587
known from grain growth simulations in two and three dimensions to be of the order of unity [22,23]. As the transition temperatures where the drops occur are independent of the precise Sr/Ti ratio for the temperatures tested, it is assumed that segregation of one species to the GB is not controlling these drops. It is therefore suggested that structural transitions at the GB are a possible origin for this observation. One possible structural change could be a faceting/defaceting transition upon decreasing/increasing temperature. This can markedly change GB mobility [24] and thereby lead to the observed changes. Transitions in the faceting behaviour have been observed in strontium titanium oxide bicrystals in the temperature range examined in this study [25] but are highly non-trivial to detect in a ceramic. The adsorption of a species at the GB will generally lead to a retardation of GB motion due to solute drag [26]. Thermal activation would reduce this effect with increasing temperature in contradiction to the findings in Figures 2 and 3. Under the assumption of an activation energy that is approximately constant for the two high-temperature regions in the Arrhenius-type diagram, a change to lower GB mobility must be connected with a drop in entropy. This has been shown for various grain boundaries in alumina [9], where a temperature increase leads to more disorder in the GB. The drops in growth speed with increasing temperature cannot be explained by this. However, the drops indicate a change in the basic mechanism of GB motion and the drop in entropy is most likely associated with a decrease in the volume activated through the process of motion. In summary, the present paper shows a growth anomaly with two distinct drops in GB mobility with increasing temperature. This grain growth anomaly is probably linked to structural changes of the grain boundaries at high temperatures, e.g. changes in faceting behaviour. Further work is certainly required to clarify this situation and more detailed investigations of grain growth are needed for a better understanding of the basic mechanisms of growth during sintering. The changes identified through the growth experiments are very likely to be of a general nature and therefore relevant to other perovskite materials. This work has been financially supported by the European Commission under Contract No. NMP3CT-2005-013862 (INCEMS). [1] N. Stenton, M.P. Harmer, Advances in Ceramics: Additives and Interfaces in Electronic Ceramics VII (1984) 156.
587
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