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Oxygen-18 tracer diffusion in nominally undoped and Sr-doped single crystals of mullite-type Bi2Ga4O9
Solid State Ionics 221 (2012) 40–42
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Oxygen-18 tracer diffusion in nominally undoped and Sr-doped single crystals of mullite-type Bi2Ga4O9☆ P. Fielitz a,⁎, G. Borchardt a, M. Burianek b, J. Ottinger b, M. Mühlberg b, Th.M. Gesing c, 1, R.X. Fischer c, H. Schneider b, c a b c
Institut für Metallurgie, Technische Universität Clausthal, Robert-Koch-Straße 42, D-38678 Clausthal-Zellerfeld, Germany Institut für Kristallographie, Universität Köln, Greinstraße 6, D-50939 Köln, Germany FB05 Kristallographie, Universität Bremen, Klagenfurter Straße, D-28359 Bremen, Germany
a r t i c l e
i n f o
Article history: Received 9 May 2012 Received in revised form 14 June 2012 Accepted 19 June 2012 Available online 15 July 2012 Keywords: Mullite-type Bi2Ga4O9 Oxygen-18 tracer diffusion Single crystals Sr-doped
a b s t r a c t Bi2M4O9 (M = Al, Ga, Fe) mullite-type compounds are currently being investigated with respect to their potential application as oxygen ion conductors or mixed ionic-electronic conductors. In the framework of these studies oxygen transport in (nominally) undoped and Sr-doped single crystals of Bi2Ga4O9 is of prime interest. 18O tracer diffusion in combination with secondary ion mass spectrometry (SIMS) depth profiling reveals that oxygen transport occurs via oxygen vacancies introduced by impurities of cations with lower valences in the undoped crystals grown by the top-seeded solution growth (TSSG) method. The fairly small enhancement of the oxygen diffusivity due to Sr doping leads to the conclusion that the solubility of Sr in Bi2Ga4O9 is extremely low with respect to the melt during the single crystal growing process. The measured enthalpies of activation ((163 ± 15) kJ/mol for undoped and (140 ± 15) kJ/mol for Sr-doped Bi2Ga4O9, respectively) must be considered as migration enthalpies. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Bi2M4O9 (M= Al3+, Ga 3+, Fe 3+ and possibly other M3+ cations) compounds with mullite-type structures [1–3] have obtained considerable technical interest in recent years. Especially their derivatives doped with M2+ ions (Sr2+, Ca 2+, Ba2+) were considered to be potential ceramic materials for oxygen sensors and for gas separation membranes [4]. A fairly high electrical conductivity of about 0.3 S cm−1 at 800 °C was reported in 2003 by Zha et al. [5] in Sr-doped Bi1.8Sr0.2Al4O9‐δ ceramics and a conductivity of about 2 × 10−3 S cm−1 at 800 °C in (nominally) undoped Bi2Al4O9 ceramics. It was assumed that Sr doping increased the conductivity via induced oxygen vacancies (in the bismuth aluminate) [5]. However, in recent work by Ohmann et al. [6] this promising report could not be verified. They found that the electrical conductivity of samples which had been deliberately prepared with an excess of either Bi2O3 or SrO can be shown to be entirely determined by a grain boundary film consisting of Bi2O3 or Bi2O3–SrO solid solutions or of SrO, respectively, if no free Bi2O3 is present [6]. This conclusion was supported by the finding that Sr-doped Bi2Al4O9 could be synthesized as powder material containing up to 6 mol% Sr instead of Bi [7] which
☆ Dedicated to Prof. Günther H. Frischat on the occasion of his 75th birthday. ⁎ Corresponding author. Tel.: +49 5323 72 2634; fax: +49 5323 72 3184. E-mail address: peter.fi[email protected] (P. Fielitz). 1 Present address: Chemische Kristallographie fester Stoffe, Universität Bremen, Leobener Straße, D-28359 Bremen, Germany. 0167-2738/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2012.06.018
decomposes in the presence of Bi2O3-rich melts to Sr-free Bi2Al4O9 and Sr-rich crystalline phases and/or melts [8]. These contradictory findings in Bi2Al4O9 ceramics demonstrate that the oxygen mobility in such compounds is yet an open question. The influence of the Sr doping on the oxygen mobility can be best observed by 18O tracer diffusion experiments in Sr-doped Bi2M4O9 single crystals. In this paper we present first 18O tracer diffusion experiments in Sr-doped and nominally undoped single crystals of Bi2Ga4O9. 2. Experimental In Bi2Ga4O9 the edge-connected chains of GaO6 octahedra are linked by corner-connected GaO4 tetrahedra forming Ga2O7 dimers and by highly asymmetric BiO6 groups. Between adjacent Ga2O7 dimers every second oxygen position remains unoccupied, probably due to the stereochemically active Bi 6s 2 electron lone pairs, which extend into these vacant sites. The crystal structure of mullite-type bismuth gallate, Bi2Ga4O9, was described by Tutov and Markin [9] in space group Pbam. Lattice parameters are a = 7.929 Å, b = 8.295 Å, and c = 5.893 Å [10,11]. Because Bi2Ga4O9 melts incongruently and hence single crystals must be grown from non-stoichiometric melts, top-seeded solution growth (TSSG) is the appropriate method for the synthesis of large single crystals of this compound [10,11]. Resistance heated 3-zone tubular Kanthal A1 furnaces equipped with crucible weighing control unit have been used for crystal growth. Adequate amounts of
P. Fielitz et al. / Solid State Ionics 221 (2012) 40–42
10
4 N Ga2O3 (ChemPur GmbH, Germany) and single crystal grade Bi2O3 (Hek-GmbH, Germany) were inserted into Pt crucibles (40– 100 ml) and thermally homogenized at about 1150 °C for several days. Based on small spontaneously formed Bi2Ga4O9 crystals (2– 4 mm), which subsequently were developed to [001]-oriented seed crystals, the final growth runs were carried out. Detailed growth parameters are given in Table 1. Sr-doped single crystals were grown from Bi 3+ rich melt compositions with a SrO concentration up to 5 mol%. The Sr concentration in Bi2Ga4O9 was determined by EDX. Sr can be incorporated in single crystals of Bi2Ga4O9 in very low concentration only (b100 ppm), in contrast to powder samples prepared by the glycerine or EDTA/citric acid synthesis method which are reported to incorporate up to about 6 mol% of Sr [7]. The Sr level in as grown crystals was shown to be independent of the Sr concentration of the starting composition of the melt, which varied from 2 to 5 mol% Sr. 2.1. Measurement of the oxygen tracer diffusivity From the single crystals (both nominally undoped and Sr-doped Bi2Ga4O9) small samples (≈4 × 4 × 1 mm 3) were cut in such a way that the large surfaces were of {110} type. One of the large surfaces was polished with diamond paste down to 1 μm and cleaned with ethanol in an ultrasonic bath. To remove stress induced by the polishing, all samples were pre‐annealed in pure 16O2 gas (200 mbar) at 800 °C for about 15 h. For the actual diffusion run the samples were placed on an alumina holder and were then introduced into the cold zone of the furnace, which was subsequently evacuated to a pressure of about 10 –3 mbar and then filled with 18O2-enriched oxygen gas (about 95% enrichment). A mechanical feed-through manipulator allowed to rapidly introduce the sample holder into the hot zone of the furnace, or to withdraw it, respectively. The resulting depth distribution of the 18O isotope was determined by SIMS using a Cameca IMS 3f instrument. Negative 14.5 keV oxygen ions were used as primary beam with 100 nA ion current and a spot size of about 50 μm. The raster-scanned area was 250 × 250 μm 2 and the diameter of the analysed zone was 60 μm. Positive secondary ions ( 16O +, 18O +, 69Ga ++) were used for the analysis of the samples. Typical SIMS depth profiles are shown in Fig. 1. Sample charging was prevented by coating the sample surface with a 50 nm thick carbon film. For depth calibration the SIMS crater depth was measured using a surface profiler (Tencor, Alpha Step 500). To evaluate the diffusion length, L, from the depth profiles the solution of the diffusion equation for a constant diffusion source was used [12] cðxÞ−c∞ ¼ ½c0 −c∞ erf c
x pffiffiffiffiffiffi with L ¼ 2 Dt L
ð1Þ
where D is the diffusion coefficient, t is the annealing time at the diffusion temperature, c0 is the constant concentration of the tracer isotope source located at x = 0 and c∞ is the concentration of the tracer isotope in the diffusion sample (for x → ∞). The black solid curve in Fig. 1 shows a least squares fit of Eq. (1) which results in a diffusion length L = 0.77 μm for the 18O tracer isotope. All parameters of the oxygen diffusion experiments and the resulting 18O tracer diffusion
41
6
166.8 h @ 675 °C 16
+
O
counts [1/s]
10
10
5
4
O+
18
L =0.77 µm 10
3
69
Ga++
10
2
0.0
0.5
1.0
1.5
Melt comp. xBi2O3 Tliqu. °C 0.75 Bi2Ga4O9 Bi2Ga4O9:Sr 0.855
Seed rotation Cooling rate Growth time K/d d min−1
1045 24 875 14–24
4–5 3–4
5–20 9–17
2.5
3.0
3.5
Fig. 1. Typical SIMS depth profiles of secondary ions (16O+, 18O+, 69Ga++) of a nominally undoped Bi2Ga4O9 single crystal. The single crystal was annealed for 166.8 h at 675 °C in 200 mbar 18O2. The black solid curve is the fit curve of Eq. (1) which results in an 18O tracer diffusion length L = 0.77 μm.
coefficients are compiled in Table 2. From these data one gets the following Arrhenius relations for the oxygen-18 tracer diffusivity in nominally undoped 2 ð163 15ÞkJ=mol þ10 −10 m Dundoped ¼ 2:1 −1:7 10 exp − RT s
ð2Þ
and in Sr-doped single crystals of Bi2Ga4O9 2 ð140 16ÞkJ=mol þ64 −11 m exp − DSr doped ¼ 9:8 −8:5 10 RT s
ð3Þ
Fig. 2 shows all measured 18O tracer diffusivities in nominally undoped and in Sr-doped single crystals of Bi2Ga4O9. 3. Results and discussion The key result is represented by the two activation enthalpies in Eqs. (2) and (3), which are fairly low if compared to oxygen diffusion in 2/1 and 3/2 alumina–silica mullite [13]. The activation enthalpy for the “classical” mullite structure is about 430 kJ/mol and comprises both the formation enthalpy and the migration enthalpy [13]. This suggests that in the studied Bi2Ga4O9 single crystals in both cases oxygen diffusion occurred via extrinsic defects, most probably oxygen vacancies, which were introduced by cations with lower valence than Bi 3+ or Ga 3+. Because of its small ionic radius (0.62 Å in octahedral oxygen coordination, CN = 6) the Ga 3+ site can be excluded as a possible substitution site for 2-valent cations. On the Bi 3+ site (1.03 Å, CN = 6), Na + (1.02 Å CN = 6) or Ca 2+ (1.00 Å, CN = 6) could principally be substituted [14]. These impurities are omnipresent even in the very pure substances used for the crystal growth. The
Table 2 Compilation of the diffusion experiment parameters, where T is the annealing temperature, t the annealing time at T, and L the diffusion length measured by SIMS depth profiling. Nominally undoped
Table 1 Growth parameter of Bi2Ga4O9 and Bi2Ga4O9:Sr.
2.0
depth [µm]
Sr doped
T °C
t h
L μm
D m2/s
T °C
t h
L μm
D m2/s
675 735 800 870
166.8 24.0 17.5 4.3
0.77 0.53 0.70 0.76
2.5 × 10−19 8.1 × 10−19 1.9 × 10−18 9.3 × 10−18
620 675 735 800
211.3 47.7 14.0 5.0
1.49 0.97 1.14 1.03
7.3 × 10−19 1.4 × 10−18 6.5 × 10−18 1.5 × 10−17
42
P. Fielitz et al. / Solid State Ionics 221 (2012) 40–42
T [°C] 950 900 850 800 750
-15
700
650
5 mol% Sr). The slight drop in the activation enthalpy as compared to the undoped Bi2Ga4O9 indicates that the activation barrier in the Sr-doped case is probably somewhat lower because of the less favourable stereochemical conditions (Sr 2+, 1.18 Å, CN = 6 [14]), which are, on the other hand, perhaps the main reasons for the low solubility of Sr.
600
10
single crystalline Bi2Ga4O9 -16
10
4. Conclusions -17
D [m2/s]
10
Sr doped -18
10
nominally undoped
10-19
-20
10
0.8
0.9
1.0
1.1
1.2
1000/T [1/K] Fig. 2. Arrhenius diagram of 18O tracer diffusivities in nominally undoped and in Sr-doped single crystals of Bi2Ga4O9.
same argument is used by Larose and Akbar [15] to explain the low conductivity of undoped polycrystalline Bi2Ga4O9. The defect formation caused by lower-valence cations, M 2 +, can be described by the following reaction using the Kröger–Vink notation
2MO þ 2BiBi þ OO ⇌2M
′
··
Bi
þ V O þ Bi2 O3
with M ¼ Sr; Ca…
ð4Þ
with M ¼ Sr; Ca…
ð5Þ
With Ca (or other lower-valence cations) concentrations, [M′Bi], in the ppm range a nominally undoped Bi2Ga4O9 crystal will exhibit according to Eq. (5) a corresponding oxygen vacancy concentration, [VO··], and hence according to ·· OO DO ¼ ½V O Dv
ð6Þ
a low, but measurable, oxygen mobility, where [OO×] and [VO· ·] are the concentration of oxygen and oxygen vacancies, respectively, and DO and Dv are the diffusivity of oxygen and oxygen vacancies, respectively. From Fig. 2 one can roughly estimate DOSr doped/DOundoped ≈ 7 in the investigated temperature interval so that one gets from Eqs. (5) and (6) (assuming DvSr doped ≈ Dvundoped) ·· Sr doped
½V O
·· undoped
=½V O
h i h i ′ ′ ¼ Sr Bi = M Bi ≈7
with M ¼ Ca…
Acknowledgements The authors are grateful to the Deutsche Forschungsgemeinschaft for substantial financial support (FI 881/4-1, MU 1006/8-1, FI 442/ 14-1, PAK 279) and to Mr. E. Ebeling for technical assistance. References
The electroneutrality condition is in this case h i ·· ′ 2½V O − M Bi ¼ 0
Oxygen-18 tracer diffusion in nominally undoped and nominally Sr-doped Bi2Ga4O9 is entirely determined by extrinsic defects, most probably cations of valence lower than 3 which are incorporated on Bi 3+ sites. The solubility of Sr in Bi2Ga4O9 is only about seven times as high as the low concentration level of impurities which are usually present. The (low) activation enthalpies obviously comprise the migration term only. The value is somewhat lower for the undoped material which can be rationalized considering the ionic radius of Sr2+ as compared to potential impurities. Furthermore, 18O/16O exchange experiments with powder samples in a series of compositions Bi2(M′xM1-x)4O9 (M′, M=Al, Ga, Fe; 0≤x≤1) demonstrate that the oxygen diffusivity is also very low in these material systems so that oxygen ions cannot contribute significantly to the conductivity [16–18]. Neither did nominal doping with Sr increase the oxygen diffusivity of these systems [19].
ð7Þ
That is, the solubility of Sr is only about a factor 7 higher than the concentration of low level impurities (Ca or other lower-valence cations) in the nominally undoped Bi2Ga4O9 single crystal. This conclusion is in accordance with the above mentioned observation that the Sr level (b 100 ppm) in the as grown crystals was independent of the Sr concentration of the starting composition of the melt (2–
[1] R.X. Fischer, H. Schneider, In: in: H. Schneider, S. Komarneni (Eds.), Mullite, Wiley-VCH, Weinheim, 2005, pp. 1–46, and 128–140. [2] R.X. Fischer, A. Gaede-Köhler, J. Birkenstock, H. Schneider, Int. J. Mater. Res. 103 (2012) 402. [3] H. Schneider, R.X. Fischer, Th.M. Gesing, J. Schreuer, Int. J. Mater. Res. 103 (2012) 422. [4] J.B. Goodenough, Annu. Rev. Mater. Res. 33 (2003) 91. [5] S. Zha, J. Cheng, Y. Liu, X. Liu, G. Meng, Solid State Ionics 156 (2003) 197. [6] S. Ohmann, P. Fielitz, L. Dörrer, G. Borchardt, Th.M. Gesing, R.X. Fischer, C.H. Rüscher, J.-C. Buhl, K.-D. Becker, H. Schneider, Solid State Ionics 211 (2012) 46. [7] Th.M. Gesing, M. Schowalter, C. Weidenthaler, M.M. Murshed, G. Nénert, C.B. Mendive, M. Curti, A. Rosenauer, J.-C. Buhl, H. Schneider, R.X. Fischer, J. Mater. Chem. (submitted for publication). [8] Th.M. Gesing, R.X. Fischer, M. Burianek, M. Mühlberg, T. Debnath, C.H. Rüscher, J. Ottinger, J.-C. Buhl, H. Schneider, J. Eur. Ceram. Soc. 31 (2011) 3055. [9] A.G. Tutov, V.N. Markin, Izv. Akad. Nauk SSSR Neorg. Mater. 6 (1970) 2014. [10] J. Schreuer, M. Burianek, M. Mühlberg, B. Winkler, D.J. Wilson, H. Schneider, J. Phys. Condens. Matter 18 (2006) 10977. [11] M. Burianek, M. Mühlberg, M. Woll, M. Schmücker, Th.M. Gesing, H. Schneider, Cryst. Res. Technol. 44 (2009) 1156. [12] J. Crank, The Mathematics of Diffusion, 2nd ed. Oxford University Press, Oxford, 1975. [13] P. Fielitz, G. Borchardt, M. Schmücker, H. Schneider, M. Wiedenbeck, D. Rhede, S. Weber, S. Scherrer, J. Am. Ceram. Soc. 84 (2001) 2845. [14] R.D. Shannon, Acta Crystallogr. A 32 (1976) 751. [15] S. Larose, S.A. Akbar, J. Solid State Electrochem. 10 (2006) 488. [16] T. Debnath, C.H. Rüscher, P. Fielitz, S. Ohmann, G. Borchardt, J. Solid State Chem. 183 (2010) 2582. [17] C.H. Rüscher, T. Debnath, P. Fielitz, S. Ohmann, G. Borchardt, Diffus. Fundam. 12 (2010) 50. [18] T. Debnath, C.H. Rüscher, P. Fielitz, S. Ohmann, G. Borchardt, Ceram. Trans. 217 (2010) 71. [19] T. Debnath, C.H. Rüscher, Th.M. Gesing, P. Fielitz, S. Ohmann, G. Borchardt, Ceram. Eng. Sci. Proc. 31 (2010) 81.
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Solid State Ionics journal homepage: www.elsevier.com/locate/ssi
Oxygen-18 tracer diffusion in nominally undoped and Sr-doped single crystals of mullite-type Bi2Ga4O9☆ P. Fielitz a,⁎, G. Borchardt a, M. Burianek b, J. Ottinger b, M. Mühlberg b, Th.M. Gesing c, 1, R.X. Fischer c, H. Schneider b, c a b c
Institut für Metallurgie, Technische Universität Clausthal, Robert-Koch-Straße 42, D-38678 Clausthal-Zellerfeld, Germany Institut für Kristallographie, Universität Köln, Greinstraße 6, D-50939 Köln, Germany FB05 Kristallographie, Universität Bremen, Klagenfurter Straße, D-28359 Bremen, Germany
a r t i c l e
i n f o
Article history: Received 9 May 2012 Received in revised form 14 June 2012 Accepted 19 June 2012 Available online 15 July 2012 Keywords: Mullite-type Bi2Ga4O9 Oxygen-18 tracer diffusion Single crystals Sr-doped
a b s t r a c t Bi2M4O9 (M = Al, Ga, Fe) mullite-type compounds are currently being investigated with respect to their potential application as oxygen ion conductors or mixed ionic-electronic conductors. In the framework of these studies oxygen transport in (nominally) undoped and Sr-doped single crystals of Bi2Ga4O9 is of prime interest. 18O tracer diffusion in combination with secondary ion mass spectrometry (SIMS) depth profiling reveals that oxygen transport occurs via oxygen vacancies introduced by impurities of cations with lower valences in the undoped crystals grown by the top-seeded solution growth (TSSG) method. The fairly small enhancement of the oxygen diffusivity due to Sr doping leads to the conclusion that the solubility of Sr in Bi2Ga4O9 is extremely low with respect to the melt during the single crystal growing process. The measured enthalpies of activation ((163 ± 15) kJ/mol for undoped and (140 ± 15) kJ/mol for Sr-doped Bi2Ga4O9, respectively) must be considered as migration enthalpies. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Bi2M4O9 (M= Al3+, Ga 3+, Fe 3+ and possibly other M3+ cations) compounds with mullite-type structures [1–3] have obtained considerable technical interest in recent years. Especially their derivatives doped with M2+ ions (Sr2+, Ca 2+, Ba2+) were considered to be potential ceramic materials for oxygen sensors and for gas separation membranes [4]. A fairly high electrical conductivity of about 0.3 S cm−1 at 800 °C was reported in 2003 by Zha et al. [5] in Sr-doped Bi1.8Sr0.2Al4O9‐δ ceramics and a conductivity of about 2 × 10−3 S cm−1 at 800 °C in (nominally) undoped Bi2Al4O9 ceramics. It was assumed that Sr doping increased the conductivity via induced oxygen vacancies (in the bismuth aluminate) [5]. However, in recent work by Ohmann et al. [6] this promising report could not be verified. They found that the electrical conductivity of samples which had been deliberately prepared with an excess of either Bi2O3 or SrO can be shown to be entirely determined by a grain boundary film consisting of Bi2O3 or Bi2O3–SrO solid solutions or of SrO, respectively, if no free Bi2O3 is present [6]. This conclusion was supported by the finding that Sr-doped Bi2Al4O9 could be synthesized as powder material containing up to 6 mol% Sr instead of Bi [7] which
☆ Dedicated to Prof. Günther H. Frischat on the occasion of his 75th birthday. ⁎ Corresponding author. Tel.: +49 5323 72 2634; fax: +49 5323 72 3184. E-mail address: peter.fi[email protected] (P. Fielitz). 1 Present address: Chemische Kristallographie fester Stoffe, Universität Bremen, Leobener Straße, D-28359 Bremen, Germany. 0167-2738/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2012.06.018
decomposes in the presence of Bi2O3-rich melts to Sr-free Bi2Al4O9 and Sr-rich crystalline phases and/or melts [8]. These contradictory findings in Bi2Al4O9 ceramics demonstrate that the oxygen mobility in such compounds is yet an open question. The influence of the Sr doping on the oxygen mobility can be best observed by 18O tracer diffusion experiments in Sr-doped Bi2M4O9 single crystals. In this paper we present first 18O tracer diffusion experiments in Sr-doped and nominally undoped single crystals of Bi2Ga4O9. 2. Experimental In Bi2Ga4O9 the edge-connected chains of GaO6 octahedra are linked by corner-connected GaO4 tetrahedra forming Ga2O7 dimers and by highly asymmetric BiO6 groups. Between adjacent Ga2O7 dimers every second oxygen position remains unoccupied, probably due to the stereochemically active Bi 6s 2 electron lone pairs, which extend into these vacant sites. The crystal structure of mullite-type bismuth gallate, Bi2Ga4O9, was described by Tutov and Markin [9] in space group Pbam. Lattice parameters are a = 7.929 Å, b = 8.295 Å, and c = 5.893 Å [10,11]. Because Bi2Ga4O9 melts incongruently and hence single crystals must be grown from non-stoichiometric melts, top-seeded solution growth (TSSG) is the appropriate method for the synthesis of large single crystals of this compound [10,11]. Resistance heated 3-zone tubular Kanthal A1 furnaces equipped with crucible weighing control unit have been used for crystal growth. Adequate amounts of
P. Fielitz et al. / Solid State Ionics 221 (2012) 40–42
10
4 N Ga2O3 (ChemPur GmbH, Germany) and single crystal grade Bi2O3 (Hek-GmbH, Germany) were inserted into Pt crucibles (40– 100 ml) and thermally homogenized at about 1150 °C for several days. Based on small spontaneously formed Bi2Ga4O9 crystals (2– 4 mm), which subsequently were developed to [001]-oriented seed crystals, the final growth runs were carried out. Detailed growth parameters are given in Table 1. Sr-doped single crystals were grown from Bi 3+ rich melt compositions with a SrO concentration up to 5 mol%. The Sr concentration in Bi2Ga4O9 was determined by EDX. Sr can be incorporated in single crystals of Bi2Ga4O9 in very low concentration only (b100 ppm), in contrast to powder samples prepared by the glycerine or EDTA/citric acid synthesis method which are reported to incorporate up to about 6 mol% of Sr [7]. The Sr level in as grown crystals was shown to be independent of the Sr concentration of the starting composition of the melt, which varied from 2 to 5 mol% Sr. 2.1. Measurement of the oxygen tracer diffusivity From the single crystals (both nominally undoped and Sr-doped Bi2Ga4O9) small samples (≈4 × 4 × 1 mm 3) were cut in such a way that the large surfaces were of {110} type. One of the large surfaces was polished with diamond paste down to 1 μm and cleaned with ethanol in an ultrasonic bath. To remove stress induced by the polishing, all samples were pre‐annealed in pure 16O2 gas (200 mbar) at 800 °C for about 15 h. For the actual diffusion run the samples were placed on an alumina holder and were then introduced into the cold zone of the furnace, which was subsequently evacuated to a pressure of about 10 –3 mbar and then filled with 18O2-enriched oxygen gas (about 95% enrichment). A mechanical feed-through manipulator allowed to rapidly introduce the sample holder into the hot zone of the furnace, or to withdraw it, respectively. The resulting depth distribution of the 18O isotope was determined by SIMS using a Cameca IMS 3f instrument. Negative 14.5 keV oxygen ions were used as primary beam with 100 nA ion current and a spot size of about 50 μm. The raster-scanned area was 250 × 250 μm 2 and the diameter of the analysed zone was 60 μm. Positive secondary ions ( 16O +, 18O +, 69Ga ++) were used for the analysis of the samples. Typical SIMS depth profiles are shown in Fig. 1. Sample charging was prevented by coating the sample surface with a 50 nm thick carbon film. For depth calibration the SIMS crater depth was measured using a surface profiler (Tencor, Alpha Step 500). To evaluate the diffusion length, L, from the depth profiles the solution of the diffusion equation for a constant diffusion source was used [12] cðxÞ−c∞ ¼ ½c0 −c∞ erf c
x pffiffiffiffiffiffi with L ¼ 2 Dt L
ð1Þ
where D is the diffusion coefficient, t is the annealing time at the diffusion temperature, c0 is the constant concentration of the tracer isotope source located at x = 0 and c∞ is the concentration of the tracer isotope in the diffusion sample (for x → ∞). The black solid curve in Fig. 1 shows a least squares fit of Eq. (1) which results in a diffusion length L = 0.77 μm for the 18O tracer isotope. All parameters of the oxygen diffusion experiments and the resulting 18O tracer diffusion
41
6
166.8 h @ 675 °C 16
+
O
counts [1/s]
10
10
5
4
O+
18
L =0.77 µm 10
3
69
Ga++
10
2
0.0
0.5
1.0
1.5
Melt comp. xBi2O3 Tliqu. °C 0.75 Bi2Ga4O9 Bi2Ga4O9:Sr 0.855
Seed rotation Cooling rate Growth time K/d d min−1
1045 24 875 14–24
4–5 3–4
5–20 9–17
2.5
3.0
3.5
Fig. 1. Typical SIMS depth profiles of secondary ions (16O+, 18O+, 69Ga++) of a nominally undoped Bi2Ga4O9 single crystal. The single crystal was annealed for 166.8 h at 675 °C in 200 mbar 18O2. The black solid curve is the fit curve of Eq. (1) which results in an 18O tracer diffusion length L = 0.77 μm.
coefficients are compiled in Table 2. From these data one gets the following Arrhenius relations for the oxygen-18 tracer diffusivity in nominally undoped 2 ð163 15ÞkJ=mol þ10 −10 m Dundoped ¼ 2:1 −1:7 10 exp − RT s
ð2Þ
and in Sr-doped single crystals of Bi2Ga4O9 2 ð140 16ÞkJ=mol þ64 −11 m exp − DSr doped ¼ 9:8 −8:5 10 RT s
ð3Þ
Fig. 2 shows all measured 18O tracer diffusivities in nominally undoped and in Sr-doped single crystals of Bi2Ga4O9. 3. Results and discussion The key result is represented by the two activation enthalpies in Eqs. (2) and (3), which are fairly low if compared to oxygen diffusion in 2/1 and 3/2 alumina–silica mullite [13]. The activation enthalpy for the “classical” mullite structure is about 430 kJ/mol and comprises both the formation enthalpy and the migration enthalpy [13]. This suggests that in the studied Bi2Ga4O9 single crystals in both cases oxygen diffusion occurred via extrinsic defects, most probably oxygen vacancies, which were introduced by cations with lower valence than Bi 3+ or Ga 3+. Because of its small ionic radius (0.62 Å in octahedral oxygen coordination, CN = 6) the Ga 3+ site can be excluded as a possible substitution site for 2-valent cations. On the Bi 3+ site (1.03 Å, CN = 6), Na + (1.02 Å CN = 6) or Ca 2+ (1.00 Å, CN = 6) could principally be substituted [14]. These impurities are omnipresent even in the very pure substances used for the crystal growth. The
Table 2 Compilation of the diffusion experiment parameters, where T is the annealing temperature, t the annealing time at T, and L the diffusion length measured by SIMS depth profiling. Nominally undoped
Table 1 Growth parameter of Bi2Ga4O9 and Bi2Ga4O9:Sr.
2.0
depth [µm]
Sr doped
T °C
t h
L μm
D m2/s
T °C
t h
L μm
D m2/s
675 735 800 870
166.8 24.0 17.5 4.3
0.77 0.53 0.70 0.76
2.5 × 10−19 8.1 × 10−19 1.9 × 10−18 9.3 × 10−18
620 675 735 800
211.3 47.7 14.0 5.0
1.49 0.97 1.14 1.03
7.3 × 10−19 1.4 × 10−18 6.5 × 10−18 1.5 × 10−17
42
P. Fielitz et al. / Solid State Ionics 221 (2012) 40–42
T [°C] 950 900 850 800 750
-15
700
650
5 mol% Sr). The slight drop in the activation enthalpy as compared to the undoped Bi2Ga4O9 indicates that the activation barrier in the Sr-doped case is probably somewhat lower because of the less favourable stereochemical conditions (Sr 2+, 1.18 Å, CN = 6 [14]), which are, on the other hand, perhaps the main reasons for the low solubility of Sr.
600
10
single crystalline Bi2Ga4O9 -16
10
4. Conclusions -17
D [m2/s]
10
Sr doped -18
10
nominally undoped
10-19
-20
10
0.8
0.9
1.0
1.1
1.2
1000/T [1/K] Fig. 2. Arrhenius diagram of 18O tracer diffusivities in nominally undoped and in Sr-doped single crystals of Bi2Ga4O9.
same argument is used by Larose and Akbar [15] to explain the low conductivity of undoped polycrystalline Bi2Ga4O9. The defect formation caused by lower-valence cations, M 2 +, can be described by the following reaction using the Kröger–Vink notation
2MO þ 2BiBi þ OO ⇌2M
′
··
Bi
þ V O þ Bi2 O3
with M ¼ Sr; Ca…
ð4Þ
with M ¼ Sr; Ca…
ð5Þ
With Ca (or other lower-valence cations) concentrations, [M′Bi], in the ppm range a nominally undoped Bi2Ga4O9 crystal will exhibit according to Eq. (5) a corresponding oxygen vacancy concentration, [VO··], and hence according to ·· OO DO ¼ ½V O Dv
ð6Þ
a low, but measurable, oxygen mobility, where [OO×] and [VO· ·] are the concentration of oxygen and oxygen vacancies, respectively, and DO and Dv are the diffusivity of oxygen and oxygen vacancies, respectively. From Fig. 2 one can roughly estimate DOSr doped/DOundoped ≈ 7 in the investigated temperature interval so that one gets from Eqs. (5) and (6) (assuming DvSr doped ≈ Dvundoped) ·· Sr doped
½V O
·· undoped
=½V O
h i h i ′ ′ ¼ Sr Bi = M Bi ≈7
with M ¼ Ca…
Acknowledgements The authors are grateful to the Deutsche Forschungsgemeinschaft for substantial financial support (FI 881/4-1, MU 1006/8-1, FI 442/ 14-1, PAK 279) and to Mr. E. Ebeling for technical assistance. References
The electroneutrality condition is in this case h i ·· ′ 2½V O − M Bi ¼ 0
Oxygen-18 tracer diffusion in nominally undoped and nominally Sr-doped Bi2Ga4O9 is entirely determined by extrinsic defects, most probably cations of valence lower than 3 which are incorporated on Bi 3+ sites. The solubility of Sr in Bi2Ga4O9 is only about seven times as high as the low concentration level of impurities which are usually present. The (low) activation enthalpies obviously comprise the migration term only. The value is somewhat lower for the undoped material which can be rationalized considering the ionic radius of Sr2+ as compared to potential impurities. Furthermore, 18O/16O exchange experiments with powder samples in a series of compositions Bi2(M′xM1-x)4O9 (M′, M=Al, Ga, Fe; 0≤x≤1) demonstrate that the oxygen diffusivity is also very low in these material systems so that oxygen ions cannot contribute significantly to the conductivity [16–18]. Neither did nominal doping with Sr increase the oxygen diffusivity of these systems [19].
ð7Þ
That is, the solubility of Sr is only about a factor 7 higher than the concentration of low level impurities (Ca or other lower-valence cations) in the nominally undoped Bi2Ga4O9 single crystal. This conclusion is in accordance with the above mentioned observation that the Sr level (b 100 ppm) in the as grown crystals was independent of the Sr concentration of the starting composition of the melt (2–
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