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High-temperature proton conductivity and defect structure of TiP2O7
Solid State Ionics 181 (2010) 510–516
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Solid State Ionics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s s i
High-temperature proton conductivity and defect structure of TiP2O7 Vajeeston Nalini, Reidar Haugsrud, Truls Norby ⁎ Department of Chemistry, University of Oslo, Centre for Materials Science and Nanotechnology, FERMiO, Gaustadalleen 21, NO-0349 Oslo, Norway
a r t i c l e
i n f o
Article history: Received 27 December 2009 Received in revised form 27 January 2010 Accepted 15 February 2010 Keywords: Titanium pyrophosphate TiP2O7 Al-substituted TiP2O7 Proton conduction Defect structure
a b s t r a c t Nominally undoped TiP2O7 and TiP2O7 with 2 mol-% substitution of Ti by Al were synthesized from TiO2 (Al2O3) and H3PO4(aq), sintered at 1050 °C, and characterized by XRD, TEM and SEM. The electrical conductivity was investigated at 300–1000 °C as a function of p(O2), p(H2O), and p(D2O). The material's phase transition around 700 °C is clearly visible in the conductivity curves. Al substitution hardly increased the conductivity. The conductivity was higher in H2O- than in D2O-containing and dry atmospheres, indicating the dominance of proton conduction. The conductivity was accordingly mainly independent of p(O2). A slight increase in the conductivity with decreasing p(O2) at the highest temperatures was indicative of a minor contribution of n-type electronic conduction. The p(H2O) and temperature dependencies of the conductivity have been modelled as a sum of proton and electron partial conductivities under a situation with protons charge compensated by oxygen interstitials as dominating defects. © 2010 Elsevier B.V. All rights reserved.
1. Introduction High-temperature solid state proton conducting materials find potential application and advantages as electrolytes in fuel cells, electrolysers, hydrogen pumps, and sensors [1–4]. A leading candidate class comprises acceptor-substituted perovskite oxides that become hydrated and proton conducting in the presence of water vapour at high temperatures [3,5–8]. Moreover, many acidic alkali sulphate, selenate, phosphate, and arsenate salts (“solid acids”) are good proton conductors at more moderate temperatures [9,10]. However, it remains a challenge to identify materials that combine sufficient proton conductivity and thermodynamic stability. A number of rare-earth phosphates, LnPO4, acceptor-doped with alkaline earth cations, exhibit considerable and often dominating proton conductivities below typically 1000 °C [11–13]. In dry atmospheres the acceptors are compensated presumably by oxygen deficiency in the form of pyrophosphate groups [12]. In humid atmospheres the materials take up water, filling the oxygen deficiency and letting protons in the form of hydrogen phosphate take over the charge compensation. The protons are reasonably mobile, and give rise to protonic conductivity [11]. Similar behaviour is observed also for lanthanum borate, LaBO3 [14]. Proton conductivity was recently reported at intermediate temperatures in pyrophosphate-containing composites NH4PO3/ TiP2O7 and NH4PO3/SiP2O7 [15,16]. Soon after, members of the family of tetravalent metal pyrophosphates (AP2O7, A = Si, Ge, Sn, Ti, Ce) were reported to exhibit remarkably high proton conductivities and
⁎ Corresponding author. Tel.: + 47 22840654; fax: + 47 22840651. E-mail address: [email protected] (T. Norby). 0167-2738/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2010.02.017
to work as fuel cell electrolytes at intermediate temperatures [17–20]. However, the mechanism of the high conductivity was not clear. This has motivated us to study the proton conductivity in tetravalent pyrophosphates in more detail, focusing on equilibrium conditions at high temperatures. In this article we describe the synthesis and characterization of TiP2O7 and 2 mol-% Al-substituted TiP2O7. The intention with Al doping is to make Al3+ substituting Ti4+ act as acceptors and possibly enhance the concentration of charge compensating protons. The conductivity is studied as a function of T and p(H2O) in order to clarify defect structure and energetics of conduction, and H2O/D2O isotope exchange is done to clarify the predominant proton conduction mechanism. The results are discussed in terms of the thermodynamics and mobility of proton and electron defects. 2. Experimental 2.1. Synthesis and fabrication TiO2 (nano-powder, 99.9%, Aldrich) and 85 wt.% H3PO4 (aq) (99.999%, Aldrich) were mixed in the appropriate stoichiometric ratio into a homogeneous slurry and heated at 200 °C for 3 h. The obtained sample was ground and dried at 100 °C for 24 h. Then the sample was calcined at 700 °C for 3 h, and the formation of TiP2O7 with some crystallinity was confirmed by XRD using a Siemens D5000 diffractometer with CuKα radiation. 2 mol-% Al-substituted TiP2O7 was similarly prepared from TiO2, H3PO4 (aq) and Al2O3 (99.99%, Fluka) as starting materials. The atomic ratio of the sum of Al and Ti to P was kept at 1:2. The calcined powders were uniaxially coldpressed into pellets of 10 mm diameter and approximately 2 mm thickness.
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Bamberger et al. [21] reported that TiP2O7 decomposes at ∼1150 °C into titanyl phosphate, (TiO)2P2O7, and P2O5, and further at 1200 °C into TiO2 and P2O5:
3. Results and discussion
2TiP2 O7 →ðTiOÞ2 P2 O7 þ P2 O5
ð1Þ
ðTiOÞ2 P2 O7 →2TiO2 þ P2 O5
ð2Þ
The observed XRD patterns for TiP2O7 and 2 mol-% Al-substituted TiP2O7 after sintering at 1050 °C are shown in Fig. 1. They match those from the study by Norberg et al. [24], and suggest that single-phase materials were obtained after sintering. The lattice parameter for undoped TiP2O7 was calculated by the least-squares method to be a = 23.533(1) Å, as compared with the literature value a = 23.5340 Å [24], for a cubic superstructure (space group:Pa3 ̅ ; no. 205). The lattice parameter decreased to 23.524(2) Å for 2 mol-% Al-substituted TiP2O7. We also prepared and characterized 5 mol-% Al-substituted TiP2O7, but a shoulder at the (5,5,2) peak at 2θ = 27.4 o was indicative of a secondary AlPO4 phase, and this composition was thus not included in the conductivity measurements. It should be noted that Malshikov and Bondar [25] found two polymorphic forms for TiP2O7; a high temperature form (above 458 °C) with cubic symmetry and a low temperature form with pseudo-hexagonal symmetry. On the other hand, Chernorukov et al. [26] reported that below 730 °C TiP2O7 exists in the cubic α modification (a = 23.52 Å) and above 730 °C transforms into a cubic β modification (a = 7.80 Å). This phase transition was seemingly observed also in the present study at similar temperatures by conductivity measurements as will be shown below. TEM bright field images of the undoped sample indicated a single phase of homogeneous structure (no domains) at room temperature [27]. Selected area diffraction (SAD) TEM patterns seen along the [010] and [1̄40] zone axes are reproduced from Ref. [27] in Fig. 2(a) and (b). They are indexed according to the crystal structure with space group Pa3 ̅ (no. 205). Although the crystal structure is primitive cubic, all reflections are not present in the SAD pattern. The reflection conditions for this space group are given by: general: 0kl: k = 2n and h00: h = 2n, special: h + k, h + l, k + l = 2n for atom positions 2(a) and 2(b). Closely spaced reflections and the presence of the First Order Laue Zone (FOLZ) seen in the Fig. 2(b) confirm the large unit cell dimension of the cubic superstructure. Bright field TEM images of a region at room temperature and after heating to 753 °C in vacuo are shown in Fig. 3(a) and (b), respectively. Instead of revealing information about the phase transformation, the specimen disintegrated into nanosized particles at high temperature in the TEM, Fig. 3 (b), possibly accompanying loss of gaseous phosphorous oxides as a result of the vacuum at elevated temperature and accelerated by the electron beam.
We observed that annealing at 1100 °C for 24 h led to yellowish discolouration and presence of small amounts of (TiO)2P2O7 by XRD. The samples for further studies were thus sintered at only 1050 °C, for 3 h. The relative densities obtained by this route were approximately 74%, calculated from the unit-cell dimensions and mass and dimensions of the final pellets, and supported qualitatively by microscopy.
2.2. Characterization The sintered samples were crushed and investigated by powder XRD, from which unit cell parameters were obtained by least-squares fitting of all peak positions. The structure was, furthermore, studied by selected area diffraction (SAD) in a transmission electron microscope (TEM, JEOL 2000FX). The microstructure at high temperature was also studied using a high temperature stage in the TEM. Microstructural and elemental analyses were performed with a scanning electron microscope (SEM; FEI Quanta 200 FEG) equipped with an EDAX Pegasus 2200 X-ray energy dispersive spectroscopy (EDS) analysis system. For two-electrode conductivity measurements, circular platinum electrodes were attached to each side of the specimen by painting one layer of platinum ink (Metalor, Pt A3788A), then adding a Pt net fastened by painting two more layers of Pt ink. The specimens with electrodes were annealed at 900 °C for 2 h to burn off residual organics from the ink. The electrical characterization was performed in a ProboStatTM measurement cell (NorECs AS, Norway) with twoelectrode setup, using a Hewlett Packard 4192A impedance analyzer at 10 kHz and an oscillation voltage of 1.1 V (rms). Impedance spectroscopy (5–106 Hz) was performed at selected temperatures to determine the impedance contributions from grain interior (bulk), grain boundaries, and electrodes. This showed the general absence of significant grain boundary impedance and that the AC conductivity at 10 kHz is mainly reflecting bulk transport. Specific bulk conductivities were calculated based on the area of the electrodes and thickness of the sample, and are corrected for sample porosity using a simple first approximation empirical relationship based on data from [22]; σ = σdm2 where σm is the measured conductivity and d the relative density. The conductivity was measured in the temperature range 300– 1000 °C. p(O2) was 1 or approximately 10− 5 atm by using pure O2 or Ar, respectively. p(H2O) was varied from dry to wet (0.025 atm H2O) by mixing gas dried over P2O5 and gas wetted by bubbling through pure water and then a saturated solution of KBr(aq) at room temperature. The actual water vapour content in the dry gas in the high temperature cell is in our experience typically 30 ppm (p(H2O) ≈ 3 · 10− 5 atm) [23]. Since the material in this investigation is extraordinarily sensitive to p(H2O) also under such dry conditions over the entire temperature range a refinement of the actual value of p(H2O) of the dry gas was possible and necessary as part of the modelling of the conductivity curves, and amounted in this investigation on average to 4.5 · 10− 5 atm (45 ppm). The conductivity in D2O-wetted atmospheres obtained in a corresponding manner was also measured. The difference in final p(D2O) vs. p(H2O) due to the slightly different vapour pressure and solubility of KBr of D2O vs. H2O are neglected here, in view of the limited possibility to analyse the isotope effect more than qualitatively, as will be discussed later.
3.1. Crystal structure and microstructure
Fig. 1. (a) XRD pattern of TiP2O7 from Ref. [24]. Observed XRD patterns of (b) TiP2O7 and (c) 2 mol-% Al-substituted TiP2O7 after sintering at 1050 °C for 3 h.
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Fig. 3. Bright field TEM images of TiP2O7 (a) at room temperature and (b) at 753 °C.
Fig. 2. TEM selected area diffraction (SAD) patterns of TiP2O7 after sintering seen along the [010] (a) and [1̅40] (b) zone axes. After Ref. [27].
Fig. 4(a) and (b) show SEM images of the materials after sintering. As stated above, the porosity was estimated from the images to be roughly 26%. No secondary phase was observed. According to EDS analyses, the Ti:P and (Ti + Al):P ratios are both close to the nominal 1:2. The grain diameters were typically in the range 1–4 μm for the undoped sample, while the Al-substituted sample had larger grains, typically 2–10 μm. 3.2. Conductivity measurements Fig. 5(a) and (b) present the temperature dependence of the conductivity of the materials in wet H2O-containing, D2O-containing, and dry O2 atmospheres. Each curve is obtained after equilibration at 1000 °C, and was recorded during cooling ramps of 18 °C/h. For TiP2O7 the plots show bends at approximately 695 °C, indicative of a phase transition, probably the one Chernorukov et al. reported at 730 °C [26]. For the Al-substituted sample a corresponding transition was observed at around 650 °C. The conductivity of the materials in wet atmosphere was significantly higher than in dry and in D2O-containing atmospheres. The temperature dependency of the isotope effect ratio σ(H2O)/ σ(D2O) is shown in Fig. 6. The ratios, being in the range 1.3–1.8, can be considered a clear isotope effect and suggest that the conductivity is mainly protonic and, moreover, that the transfer of protons in the material takes place by a free proton (Grotthuss-type) hopping
Fig. 4. SEM images of (a) TiP2O7 (back-scatter electron image) and (b) 2 mol-% Alsubstituted TiP2O7 (secondary electron image) after sintering.
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2 mol-% Al-substituted TiP2O7 was only slightly and insignificantly higher than for undoped TiP2O7, in contrast to the often dramatic effects of aliovalent doping in semiconductors and ionic conductors. This suggests that the Al3+ substituents have little solubility or that the applied substituent level is modest compared to the level of native or waterinduced defects. The conductivities in dry O2 (Fig. 5 (a) and (b)) are as said above lower than those in wet O2, but the temperature dependencies are for the most part similar, suggesting that the conductivity is mainly protonic also in dry atmospheres. However, at the highest temperatures in dry atmospheres, a contribution with higher activation energy is evident. We shall see below that this can be attributed to ntype electronic conduction. The conductivity vs 1/T is shown at two different p(O2) (O2 and Ar) at constant p(H2O) for undoped and doped materials in Fig. 7a) and b). Conductivities were almost independent of p(O2) at 500–900 °C, indicating that the contribution of electronic conduction to the total conductivity in the materials is negligible and protonic conduction is predominant in this temperature range. On the other hand, towards 1000 °C conductivities in wet Ar atmosphere became higher than in wet O2, suggesting that an n-type electronic contribution is becoming significant. This may be attributed to the reducibility of Ti4+ into Ti3+ states. From the similarity in activation energy and level, it appears that the high temperature part of the conductivity in dry O2 (Fig. 5) is also ntype electronic. This would imply that the p(H2O) dependency of electrons is smaller than for protons, since the n-type electronic conduction remains more prominent under dry conditions. The dependency of the conductivity of 2 mol-% Al-substituted TiP2O7 on p(H2O) at constant p(O2) (∼ 1 atm) in the temperature range 300–900 °C is shown in Fig. 8. The primarily protonic conductivity increases with increasing p(H2O), as concluded also from the temperature ramps in wet and dry atmosphere earlier, and are approximately proportional to p(H2O)1/3. A tendency of levelling out is seen for the driest conditions. This may partly be due to the n-type electronic contribution having a smaller p(H2O)-dependency, but may also typically reflect variations in the finite p(H2O) in the “dry” gas. We will model the overall p(H2O) and temperature dependencies below. First we note, however, that Nagao et al. [17] reported conductivities of TiP2O7 based materials much higher than ours at low temperatures. They found that the high proton conductivity was diminished about 2 orders magnitude in samples with pyrophosphate deficiency
Fig. 5. Temperature dependence of the conductivity for (a) TiP2O7 and (b) 2 mol-% Alsubstituted TiP2O7 in wet, D2O-containing, and dry O2.
mechanism. The isotope effect may for our data qualitatively be attributed to a slightly higher activation energy for deuteron than for proton mobility arising from the difference in zero-level energy (the so-called semi-classical effect). Also other effects may play a role, such as slightly different p(H2O) vs. p(D2O) over saturated solutions of KBr in H2O vs. D2O, different thermodynamics of dissolution of protons vs. deuterons, and different pre-exponentials of mobility due to the classical reduced mass effect and other effects. However, our inability to separate concentration and mobility in this work makes an attempt of more detailed consideration of all these factors meaningless. The activation energy for the total conductivity in TiP2O7 in H2Ocontaining atmosphere was evaluated from ln(σT) vs. 1/T plots as 0.70 eV (68 kJ/mol) below the phase transition (using data in the range 500– 674 °C) and 0.47 eV (45 kJ/mol) above (692–1000 °C). The conductivity of
Fig. 6. Temperature dependence of the H/D isotope effect on conductivity of the TiP2O7 and 2 mol-% Al-substituted TiP2O7 in wet O2.
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we mention that in many oxides, protons charge compensate acceptor substituents in competition with a native, positive defect, like oxygen vacancies [29]: x • H2 OðgÞ þ v•• O þOO ¼ 2OHO
ð3Þ
The electroneutrality condition of an acceptor-doped oxide with oxygen vacancies and protons then reads = • 2½v•• O þ ½OHO ¼ ½A ¼ constant
ð4Þ
where the square brackets denote molar fractions or volume concentrations and where A/ is the acceptor. From combination of the equilibrium constant and electroneutrality the concentration of protons and hence proton conductivity obtain a p(H2O)1/2-dependency when vacancies dominate at low p(H2O), and independency of p(H2O) when the proton concentration dominates and saturates at high p(H2O). In orthophosphates such as LaPO4, acceptor substitution and hydration are believed to involve oxygen deficiency in the form of a pyrophosphate ion defect located over two adjacent orthophosphate •• , and hydrogen phosphate groups at orthophosion sites, (P2O7)2PO 4 • [12,30,31]. The hydration reaction can then phate ion sites, (HPO4)PO 4 be written •• • ðP2 O7 Þ2PO4 þ H2 OðgÞ ¼ 2ðHPO4 ÞPO 4
ð5Þ
Otherwise this gives the same behaviour as for oxides, and predicts a p(H2O)1/2-dependency of minor proton concentrations and a p(H2O)independent saturation for acceptor-doped samples, which is not in accordance with our observed p(H2O)1/3-dependency of the proton conductivity. In pyrophosphates such as TiP2O7 the pyrophosphate group is not a defect, it is the host anion. It may expectedly be hydrated to form hydrogen pyrophosphate defects at pyrophosphate sites, denoted as (HP2O7)•P2O7 . These may charge compensate acceptor dopants. However, our results indicate that the protons dissolve in quantities exceeding the dopant level. This means that water dissolves as protons and some negative defect, for instance interstitial oxide ions.
Fig. 7. Temperature dependence of the conductivity of (a) TiP2O7 and (b) 2 mol-% Alsubstituted TiP2O7 in wet argon and in wet O2.
(from FTIR measurements). Shirai et al. [28] reported that a sample prepared by the solid state reaction method and sintered at 1200 °C gave a lower conductivity (b10− 7 S/cm at 400 °C), i.e. in better agreement with our results. They state that the high conductivities of less sintered samples stem from core-shell microstructures, with a highly conductive amorphous outer phase. Our results serve to support this, in that our samples do not exhibit the anomalous conductivity, are sintered at relatively high temperatures, and seem therefore not to have contained grain shells of such an amorphous phase. 3.3. Defect–chemical model The p(H2O) dependencies of the conductivities of our samples will now be discussed in detail in terms of a defect–chemical model. First,
Fig. 8. p(H2O) dependence of the conductivity of 2 mol-% Al-substituted TiP2O7 in O2. The solid lines are the modelled sum of partial protonic and electronic conductivities.
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This has been suggested as a prevailing situation in undoped Y2O3, an oxide with native empty interstitial oxygen sites [32]: x
==
2OO þ H2 OðgÞ ¼ Oi þ 2OHO•
ð6Þ
In a pyrophosphate the interstitial oxygen may be denoted as phosphate ions at a pyrophosphate site, (2PO4)P//2O7 . The hydration reaction can in this case be written x == 3ðP2 O7 ÞP2 O7 þ H2 OðgÞ ¼ ð2PO4 ÞP2 O7 þ 2ðHP2 O7 ÞP•2 O7
ð7Þ
515
The partial conductivity of a charge carrier i can be expressed as σi ¼ zi eci μi
ð14Þ
where σi, zie, ci and μi are the partial conductivity (S/cm), charge (C), volume concentration (cm− 3) and charge mobility (cm2/Vs), respectively. The charge mobility of a diffusing charge carrier i is further given by −ΔHm;i 1 μi = μ0;i exp T RT
ð15Þ
, with the equilibrium constant expressed as h K1 =
ih i2 ! ! ðHP2 O7 Þ•P2 O7 ΔS01 −ΔH10 = exp exp h i3 R RT ðP2 O7 ÞxP2 O7 pðH2 OÞ
== ð2PO4 ÞP O 2 7
ð8Þ
in which concentrations are volume concentrations or mole fractions, and partial pressure given in bar (≈atm). The electroneutrality condition limited to oxygen interstitials and protons can accordingly be written == 2½ð2PO4 ÞP2 O7 ¼ ½ðHP2 O7 Þ•P2 O7
ð9Þ
By inserting this into the expression for the hydration equilibrium constant, and assuming small defect concentrations ([(P2O7)Px2O7] ≈ 1) we obtain the concentration of protonic defects expressed as h
• ðHP2 O7 ÞP2 O7
i
=2
1=3
1=3
1=3
K1 pðH2 OÞ
0 1 01 − ΔH1 ApðH2 OÞ1=3 = c0;Hþ exp@ 3 RT
where μ0,i is the pre-exponential (cm2K/Vs) of charge mobility and ΔHm,i is the migration enthalpy. We assume that electrons migrate by a small polaron hopping mechanism in this material, so that Eq. (15) is applicable to electrons and protons alike. The conductivities of dominating protons and minority electrons are from all the above expressed as
σHþ
1 0 1 0 þ − ΔH + ΔH 1 m;H 1 1=3 3 A exp@ = zec0;Hþ μ0;Hþ pðH2 OÞ T RT −ΔHHþ 1 = 31 exp = σ0;Hþ pðH2 OÞ T RT
ð16Þ
1 0 1 0 1 0 − ΔH2 −3 ΔH1 + ΔHm;n 2 A exp@ σn = zen0 μ0;n pðH2 OÞ pðO2 Þ T RT 1 −ΔHn = σ0;n pðH2 OÞ1 = 6 pðO2 Þ−1 = 4 exp T RT 1=6
−1 = 4 1
ð10Þ
ð17Þ
in qualitative agreement with the p(H2O)-dependency of the proton conductivity, and where c0,H+ is the pre-exponential of proton concentration and ΔH01 is the standard enthalpy change of the hydration reaction (Eqs. (7) and (8)). At higher temperatures a contribution of n-type conductivity is significant. An equilibrium relating defect electrons and protons can be written
The p(H2O) dependency of the measured total conductivity of the Alsubstituted sample has been fitted at each temperature as a sum of the contributions from dominating protons and minority electrons with, respectively, p(H2O)1/3 and p(H2O)1/6 dependencies from the above derivations. The model fits our data reasonably well, see Fig. 8. The somewhat worse fit at 300 °C is probably due to the problem to reach full equilibrium. The fitted partial conductivities at various temperatures have been further fitted to Arrhenius-type expressions to obtain the activation enthalpies and pre-exponentials of the partial conductivities according to Eqs. (16) and (17). The activation enthalpy of the partial proton conductivity (ΔHH+) is 68 ± 5 kJ/mol at 300–600 °C and 36 ± 8 kJ/mol at 700–900 °C, the former in full agreement with that obtained for the total conductivity ramps, and the latter somewhat lower as the electronic contribution is now excluded. The preexponential (σ0H+) is (2 ± 1.5) · 103 SK/cm at low and 60 ± 35 SK/cm at high temperatures. The hydration reaction Eq. (7) is bound to have a negative standard entropy change (ΔS01) and the standard enthalpy change (ΔH01) must then be also negative (exothermic) for the reaction to have a non-negligible equilibrium constant. This means that the activation energies for proton mobilities are larger than the values reported for ΔHH+ above, but a further quantification cannot be made as the parameters for hydration thermodynamics are not known. The difference in the activation enthalpy of the partial proton conductivity between low and high temperature is assigned to the phase transformation. In perovskite-related oxides it is found that lower symmetry, e.g. distortions from cubicity, decreases the proton mobility [33]. In TiP2O7 both phases are cubic, but the low temperature modification has a 3 × 3 × 3 supercell and the higher activation enthalpy of protons at low temperatures may thus be related to this decrease in local symmetry, affecting primarily the activation enthalpy of migration, but also the enthalpy of hydration. The increase in pre-exponential indicates that this is accompanied by
•
x
=
1 2
2ðP2 O7 ÞP2 O7 + H2 OðgÞ = 2ðHP2 O7 ÞP2 O7 + 2e + O2
ð11Þ
and the equilibrium constant of this can be expressed h
i2 ! ðHP2 O7 Þ•P2 O7 n2 pðO2 Þ1=2 −ΔH20 K2 = = K0;2 exp h i2 RT ðP2 O7 ÞxP2 O7 pðH2 OÞ
ð12Þ
where n is the concentration of electrons, and the use of a preexponential constant is used instead of a standard entropy change, as the standard state of the concentration of electrons is not straightforward to define. Assuming that electrons are minority defects, and that we can again assume small overall defect concentrations, we can insert the dominating concentration of protons from Eq. (10) into Eq. (12) and get for the concentration of electrons K2 pðH2 OÞ1=6 pðO2 Þ1=4 1=2
n=
1=3
21=3 K1 1 0 1 0 1 0 − ΔH2 − ΔH1 2 3 ApðH2 OÞ1=6 pðO2 Þ−1 = 4 = n0 exp@ RT
ð13Þ
where n0 is the pre-exponential of electron concentration, and we recognize the positive but smaller dependency on p(H2O) for the minority electrons than for the dominating protons, as the conductivity curves suggested.
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an increased vibrational attempt frequency and/or a difference in the thermodynamics. The activation enthalpy of the partial electron conductivity (ΔHn) is 110 ± 20 kJ/mol and the pre-exponential (σ0,n) is 104 ± 1 SK/cm at 700–900 °C. (The electronic conductivity and corresponding parameters cannot be extracted with any confidence for the low temperature phase). The undoped sample exhibited a conductivity only slightly lower than the doped one, and similar p(H2O) and p(O2) dependencies, suggesting as mentioned early on that the level of dissolved dopant is small compared to the level of defects introduced by hydration. We have seen that TiP2O7 exhibits a strong, mathematically welldescribed, and relatively uniform water vapour dependency all the way down to very low p(H2O) at all temperatures investigated. This rather unique property makes the material an interesting candidate for conductivity based water vapour sensors. 4. Summary The AC bulk conductivity of sintered, porous samples of TiP2O7 and 2 mol-% Al-substituted TiP2O7 increases with humidity and has a clear H/D isotope effect, which demonstrates that the conductivity is mainly protonic and that protons migrate through a hopping mechanism. The isotope effect is attributed to a higher activation energy of the mobility of deuterons than of protons. The p(O2) dependence indicated that the materials are mainly ionic (proton) conductors and that a minor n-type conductivity contributes significantly above 900 °C at reduced oxygen activities. Arrhenius plots exhibit clear signs of the reported phase transition at around 700 °C. The observed p(H2O)1/3 dependency of the conductivity of 2 mol-% Al-substituted TiP2O7 has been modelled assuming that protons are charge compensated by oxygen interstitials. On this basis the partial conductivities and their temperature dependencies have been derived as follows: the low temperature phase has below 600 °C a proton conductivity given as −68 5kJ=mol 3 1 = 31 σHþ ;LT ðS = cmÞ = ð2 1:5Þ⋅10 ⋅ðpðH2 OÞ =barÞ exp T RT
ð18Þ while the high temperature phase has above 700 °C a partial proton conductivity given as −36 8kJ=mol exp T RT
1 = 31
σHþ ;HT ðS = cmÞ = 60 35⋅ð pðH2 OÞ =barÞ
41
1=6
⋅ðpðH2 OÞ =barÞ
ðpðO2 Þ= barÞ
Acknowledgements This work was carried out with financial support from a grant under the FUNMAT@UiO program of the University of Oslo (UiO). The authors thank Dr. Anuradha Ashok, Centre for Materials Science and Nanotechnology (SMN), UiO, for the TEM work. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]
ð19Þ
[30]
−110 20kJ=mol exp T RT
[31] [32] [33]
and a partial electronic n-type conductivity given as σn;HT ðS = cmÞ = 10
encourage further studies of proton conductivity in tetravalent metal pyrophosphates and analogous materials at elevated temperatures. Signs of abnormally high proton conductivities at low temperatures as reported in literature have not been observed.
−1 = 4 1
ð20Þ These relationships seem to hold over large temperature ranges and down to very low p(H2O) making the materials of interest as sensors, and this and the presence of proton conduction itself
K.D. Kreuer, Chem. Mat. 8 (1996) 610. K.D. Kreuer, Solid State Ionics 97 (1997) 1. H. Iwahara, T. Esaka, H. Uchida, N. Maeda, Solid State Ionics 3/4 (1981) 359. T. Norby, Nature 410 (2001) 877. W.K. Lee, A.S. Nowick, L.A. Boatner, Solid State Ionics 18/19 (1986) 989. Y. Du, A.S. Nowick, Solid State Ionics 77 (1995) 137. T. Norby, P. Kofstad, J. Am. Ceram. Soc. 67 (1984) 786. K.D. Kreuer, Solid State Ionics 125 (1999) 285. S.M. Haile, D.A. Boysen, C.R.I. Chisholm, R.B. Merle, Nature 410 (2001) 910. A. Pawlowski, M. Polomska, Solid State Ionics 176 (2005) 25. T. Norby, N. Christiansen, Solid State Ionics 77 (1995) 240. K. Amezawa, H. Maekawa, Y. Tomii, N. Yamamoto, Solid State Ionics 145 (1–4) (2001) 233. K. Amezawa, Y. Tomii, N. Yamamoto, Solid State Ionics 176 (2005) 135. K. Amezawa, N. Takahashi, N. Kitamura, Y. Tomii, N. Yamamoto, Solid State Ionics 175 (1–4) (2004) 575. T. Matsui, S. Takeshita, Y. Iriyama, T. Abe, Z. Ogumi, J. Electrochem. Soc. 152 (2005) A167. T. Matsui, T. Kukino, R. Kikuchi, K. Eguchi, Electrochem. Solid-State Lett. 8 (2005) A256. M. Nagao, T. Kamiya, P. Heo, A. Tomita, T. Hibino, M. Sano, J. Electrochem. Soc. 153 (2006) A1604. M. Nagao, A. Takeuchi, P. Heo, T. Hibino, M. Sano, A. Tomita, J. Electrochem. SolidState Lett. 9 (2006) A105. A. Tomita, N. Kajiyama, T. Kamiya, M. Nagao, T. Hibino, J. Electrochem. Soc. 154 (2007) B1265. X. Sun, S. Wang, Z. Wang, X. Ye, T. Wen, F. Huang, Solid State Ionics 179 (2008) 1138. C.E. Bamberger, G.M. Begun, J. Less-Common Metals 134 (1987) 201. J. Mizusaki, S. Tsuchiya, K. Waragai, H. Tagawa, Y. Arai, Y. Kuwayama, J. Am. Ceram. Soc. 79 (1) (1996) 109. T. Norby, P. Kofstad, J. Am. Ceram. Soc. 67 (1984) 786. S.T. Norberg, G. Svensson, J. Albertsson, Acta Cryst. C57 (2001) 225. A.E. Mal'shikov, I.A. Bondar, Neorg. Mater. 25 (6) (1989) 984. N.G. Chernorukov, M.I. Zhuk, E.P. Moskvichev, Tr. Khim. Tekh. 3 (1974) 9. V. Nalini, T. Norby, A.M. Anuradha, Proc. 10th Asian Conf. Solid State Ionics, Sri Lanka, World Scientific, ISBN: 981-256-877-8, 2006, p. 321. T. Shirai, S. Satou, Y. Saito, M. Saito, J. Kuwano, H. Shiroishi, Phosphorous. Res. Bull. 21 (2007) 31. Y. Larring, T. Norby, in: R. Waser (Ed.), Proc. Electroceramics IV, Verlag der Augustinus Buchhandlung, Aachen, 1994, p. 703. N. Kitamura, K. Amezawa, Y. Tomii, N. Yamamoto, Solid State Ionics 162–163 (2003) 161. K. Amezawa, S. Kjelstrup, T. Norby, Y. Ito, J. Electrochem. Soc. 145 (1999) 3313. T. Norby, P. Kofstad, J. Am. Ceram. Soc. 69 (1986) 780. Y. Larring, T. Norby, Solid State Ionics 70–71 (1994) 305.
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Solid State Ionics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s s i
High-temperature proton conductivity and defect structure of TiP2O7 Vajeeston Nalini, Reidar Haugsrud, Truls Norby ⁎ Department of Chemistry, University of Oslo, Centre for Materials Science and Nanotechnology, FERMiO, Gaustadalleen 21, NO-0349 Oslo, Norway
a r t i c l e
i n f o
Article history: Received 27 December 2009 Received in revised form 27 January 2010 Accepted 15 February 2010 Keywords: Titanium pyrophosphate TiP2O7 Al-substituted TiP2O7 Proton conduction Defect structure
a b s t r a c t Nominally undoped TiP2O7 and TiP2O7 with 2 mol-% substitution of Ti by Al were synthesized from TiO2 (Al2O3) and H3PO4(aq), sintered at 1050 °C, and characterized by XRD, TEM and SEM. The electrical conductivity was investigated at 300–1000 °C as a function of p(O2), p(H2O), and p(D2O). The material's phase transition around 700 °C is clearly visible in the conductivity curves. Al substitution hardly increased the conductivity. The conductivity was higher in H2O- than in D2O-containing and dry atmospheres, indicating the dominance of proton conduction. The conductivity was accordingly mainly independent of p(O2). A slight increase in the conductivity with decreasing p(O2) at the highest temperatures was indicative of a minor contribution of n-type electronic conduction. The p(H2O) and temperature dependencies of the conductivity have been modelled as a sum of proton and electron partial conductivities under a situation with protons charge compensated by oxygen interstitials as dominating defects. © 2010 Elsevier B.V. All rights reserved.
1. Introduction High-temperature solid state proton conducting materials find potential application and advantages as electrolytes in fuel cells, electrolysers, hydrogen pumps, and sensors [1–4]. A leading candidate class comprises acceptor-substituted perovskite oxides that become hydrated and proton conducting in the presence of water vapour at high temperatures [3,5–8]. Moreover, many acidic alkali sulphate, selenate, phosphate, and arsenate salts (“solid acids”) are good proton conductors at more moderate temperatures [9,10]. However, it remains a challenge to identify materials that combine sufficient proton conductivity and thermodynamic stability. A number of rare-earth phosphates, LnPO4, acceptor-doped with alkaline earth cations, exhibit considerable and often dominating proton conductivities below typically 1000 °C [11–13]. In dry atmospheres the acceptors are compensated presumably by oxygen deficiency in the form of pyrophosphate groups [12]. In humid atmospheres the materials take up water, filling the oxygen deficiency and letting protons in the form of hydrogen phosphate take over the charge compensation. The protons are reasonably mobile, and give rise to protonic conductivity [11]. Similar behaviour is observed also for lanthanum borate, LaBO3 [14]. Proton conductivity was recently reported at intermediate temperatures in pyrophosphate-containing composites NH4PO3/ TiP2O7 and NH4PO3/SiP2O7 [15,16]. Soon after, members of the family of tetravalent metal pyrophosphates (AP2O7, A = Si, Ge, Sn, Ti, Ce) were reported to exhibit remarkably high proton conductivities and
⁎ Corresponding author. Tel.: + 47 22840654; fax: + 47 22840651. E-mail address: [email protected] (T. Norby). 0167-2738/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2010.02.017
to work as fuel cell electrolytes at intermediate temperatures [17–20]. However, the mechanism of the high conductivity was not clear. This has motivated us to study the proton conductivity in tetravalent pyrophosphates in more detail, focusing on equilibrium conditions at high temperatures. In this article we describe the synthesis and characterization of TiP2O7 and 2 mol-% Al-substituted TiP2O7. The intention with Al doping is to make Al3+ substituting Ti4+ act as acceptors and possibly enhance the concentration of charge compensating protons. The conductivity is studied as a function of T and p(H2O) in order to clarify defect structure and energetics of conduction, and H2O/D2O isotope exchange is done to clarify the predominant proton conduction mechanism. The results are discussed in terms of the thermodynamics and mobility of proton and electron defects. 2. Experimental 2.1. Synthesis and fabrication TiO2 (nano-powder, 99.9%, Aldrich) and 85 wt.% H3PO4 (aq) (99.999%, Aldrich) were mixed in the appropriate stoichiometric ratio into a homogeneous slurry and heated at 200 °C for 3 h. The obtained sample was ground and dried at 100 °C for 24 h. Then the sample was calcined at 700 °C for 3 h, and the formation of TiP2O7 with some crystallinity was confirmed by XRD using a Siemens D5000 diffractometer with CuKα radiation. 2 mol-% Al-substituted TiP2O7 was similarly prepared from TiO2, H3PO4 (aq) and Al2O3 (99.99%, Fluka) as starting materials. The atomic ratio of the sum of Al and Ti to P was kept at 1:2. The calcined powders were uniaxially coldpressed into pellets of 10 mm diameter and approximately 2 mm thickness.
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Bamberger et al. [21] reported that TiP2O7 decomposes at ∼1150 °C into titanyl phosphate, (TiO)2P2O7, and P2O5, and further at 1200 °C into TiO2 and P2O5:
3. Results and discussion
2TiP2 O7 →ðTiOÞ2 P2 O7 þ P2 O5
ð1Þ
ðTiOÞ2 P2 O7 →2TiO2 þ P2 O5
ð2Þ
The observed XRD patterns for TiP2O7 and 2 mol-% Al-substituted TiP2O7 after sintering at 1050 °C are shown in Fig. 1. They match those from the study by Norberg et al. [24], and suggest that single-phase materials were obtained after sintering. The lattice parameter for undoped TiP2O7 was calculated by the least-squares method to be a = 23.533(1) Å, as compared with the literature value a = 23.5340 Å [24], for a cubic superstructure (space group:Pa3 ̅ ; no. 205). The lattice parameter decreased to 23.524(2) Å for 2 mol-% Al-substituted TiP2O7. We also prepared and characterized 5 mol-% Al-substituted TiP2O7, but a shoulder at the (5,5,2) peak at 2θ = 27.4 o was indicative of a secondary AlPO4 phase, and this composition was thus not included in the conductivity measurements. It should be noted that Malshikov and Bondar [25] found two polymorphic forms for TiP2O7; a high temperature form (above 458 °C) with cubic symmetry and a low temperature form with pseudo-hexagonal symmetry. On the other hand, Chernorukov et al. [26] reported that below 730 °C TiP2O7 exists in the cubic α modification (a = 23.52 Å) and above 730 °C transforms into a cubic β modification (a = 7.80 Å). This phase transition was seemingly observed also in the present study at similar temperatures by conductivity measurements as will be shown below. TEM bright field images of the undoped sample indicated a single phase of homogeneous structure (no domains) at room temperature [27]. Selected area diffraction (SAD) TEM patterns seen along the [010] and [1̄40] zone axes are reproduced from Ref. [27] in Fig. 2(a) and (b). They are indexed according to the crystal structure with space group Pa3 ̅ (no. 205). Although the crystal structure is primitive cubic, all reflections are not present in the SAD pattern. The reflection conditions for this space group are given by: general: 0kl: k = 2n and h00: h = 2n, special: h + k, h + l, k + l = 2n for atom positions 2(a) and 2(b). Closely spaced reflections and the presence of the First Order Laue Zone (FOLZ) seen in the Fig. 2(b) confirm the large unit cell dimension of the cubic superstructure. Bright field TEM images of a region at room temperature and after heating to 753 °C in vacuo are shown in Fig. 3(a) and (b), respectively. Instead of revealing information about the phase transformation, the specimen disintegrated into nanosized particles at high temperature in the TEM, Fig. 3 (b), possibly accompanying loss of gaseous phosphorous oxides as a result of the vacuum at elevated temperature and accelerated by the electron beam.
We observed that annealing at 1100 °C for 24 h led to yellowish discolouration and presence of small amounts of (TiO)2P2O7 by XRD. The samples for further studies were thus sintered at only 1050 °C, for 3 h. The relative densities obtained by this route were approximately 74%, calculated from the unit-cell dimensions and mass and dimensions of the final pellets, and supported qualitatively by microscopy.
2.2. Characterization The sintered samples were crushed and investigated by powder XRD, from which unit cell parameters were obtained by least-squares fitting of all peak positions. The structure was, furthermore, studied by selected area diffraction (SAD) in a transmission electron microscope (TEM, JEOL 2000FX). The microstructure at high temperature was also studied using a high temperature stage in the TEM. Microstructural and elemental analyses were performed with a scanning electron microscope (SEM; FEI Quanta 200 FEG) equipped with an EDAX Pegasus 2200 X-ray energy dispersive spectroscopy (EDS) analysis system. For two-electrode conductivity measurements, circular platinum electrodes were attached to each side of the specimen by painting one layer of platinum ink (Metalor, Pt A3788A), then adding a Pt net fastened by painting two more layers of Pt ink. The specimens with electrodes were annealed at 900 °C for 2 h to burn off residual organics from the ink. The electrical characterization was performed in a ProboStatTM measurement cell (NorECs AS, Norway) with twoelectrode setup, using a Hewlett Packard 4192A impedance analyzer at 10 kHz and an oscillation voltage of 1.1 V (rms). Impedance spectroscopy (5–106 Hz) was performed at selected temperatures to determine the impedance contributions from grain interior (bulk), grain boundaries, and electrodes. This showed the general absence of significant grain boundary impedance and that the AC conductivity at 10 kHz is mainly reflecting bulk transport. Specific bulk conductivities were calculated based on the area of the electrodes and thickness of the sample, and are corrected for sample porosity using a simple first approximation empirical relationship based on data from [22]; σ = σdm2 where σm is the measured conductivity and d the relative density. The conductivity was measured in the temperature range 300– 1000 °C. p(O2) was 1 or approximately 10− 5 atm by using pure O2 or Ar, respectively. p(H2O) was varied from dry to wet (0.025 atm H2O) by mixing gas dried over P2O5 and gas wetted by bubbling through pure water and then a saturated solution of KBr(aq) at room temperature. The actual water vapour content in the dry gas in the high temperature cell is in our experience typically 30 ppm (p(H2O) ≈ 3 · 10− 5 atm) [23]. Since the material in this investigation is extraordinarily sensitive to p(H2O) also under such dry conditions over the entire temperature range a refinement of the actual value of p(H2O) of the dry gas was possible and necessary as part of the modelling of the conductivity curves, and amounted in this investigation on average to 4.5 · 10− 5 atm (45 ppm). The conductivity in D2O-wetted atmospheres obtained in a corresponding manner was also measured. The difference in final p(D2O) vs. p(H2O) due to the slightly different vapour pressure and solubility of KBr of D2O vs. H2O are neglected here, in view of the limited possibility to analyse the isotope effect more than qualitatively, as will be discussed later.
3.1. Crystal structure and microstructure
Fig. 1. (a) XRD pattern of TiP2O7 from Ref. [24]. Observed XRD patterns of (b) TiP2O7 and (c) 2 mol-% Al-substituted TiP2O7 after sintering at 1050 °C for 3 h.
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Fig. 3. Bright field TEM images of TiP2O7 (a) at room temperature and (b) at 753 °C.
Fig. 2. TEM selected area diffraction (SAD) patterns of TiP2O7 after sintering seen along the [010] (a) and [1̅40] (b) zone axes. After Ref. [27].
Fig. 4(a) and (b) show SEM images of the materials after sintering. As stated above, the porosity was estimated from the images to be roughly 26%. No secondary phase was observed. According to EDS analyses, the Ti:P and (Ti + Al):P ratios are both close to the nominal 1:2. The grain diameters were typically in the range 1–4 μm for the undoped sample, while the Al-substituted sample had larger grains, typically 2–10 μm. 3.2. Conductivity measurements Fig. 5(a) and (b) present the temperature dependence of the conductivity of the materials in wet H2O-containing, D2O-containing, and dry O2 atmospheres. Each curve is obtained after equilibration at 1000 °C, and was recorded during cooling ramps of 18 °C/h. For TiP2O7 the plots show bends at approximately 695 °C, indicative of a phase transition, probably the one Chernorukov et al. reported at 730 °C [26]. For the Al-substituted sample a corresponding transition was observed at around 650 °C. The conductivity of the materials in wet atmosphere was significantly higher than in dry and in D2O-containing atmospheres. The temperature dependency of the isotope effect ratio σ(H2O)/ σ(D2O) is shown in Fig. 6. The ratios, being in the range 1.3–1.8, can be considered a clear isotope effect and suggest that the conductivity is mainly protonic and, moreover, that the transfer of protons in the material takes place by a free proton (Grotthuss-type) hopping
Fig. 4. SEM images of (a) TiP2O7 (back-scatter electron image) and (b) 2 mol-% Alsubstituted TiP2O7 (secondary electron image) after sintering.
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2 mol-% Al-substituted TiP2O7 was only slightly and insignificantly higher than for undoped TiP2O7, in contrast to the often dramatic effects of aliovalent doping in semiconductors and ionic conductors. This suggests that the Al3+ substituents have little solubility or that the applied substituent level is modest compared to the level of native or waterinduced defects. The conductivities in dry O2 (Fig. 5 (a) and (b)) are as said above lower than those in wet O2, but the temperature dependencies are for the most part similar, suggesting that the conductivity is mainly protonic also in dry atmospheres. However, at the highest temperatures in dry atmospheres, a contribution with higher activation energy is evident. We shall see below that this can be attributed to ntype electronic conduction. The conductivity vs 1/T is shown at two different p(O2) (O2 and Ar) at constant p(H2O) for undoped and doped materials in Fig. 7a) and b). Conductivities were almost independent of p(O2) at 500–900 °C, indicating that the contribution of electronic conduction to the total conductivity in the materials is negligible and protonic conduction is predominant in this temperature range. On the other hand, towards 1000 °C conductivities in wet Ar atmosphere became higher than in wet O2, suggesting that an n-type electronic contribution is becoming significant. This may be attributed to the reducibility of Ti4+ into Ti3+ states. From the similarity in activation energy and level, it appears that the high temperature part of the conductivity in dry O2 (Fig. 5) is also ntype electronic. This would imply that the p(H2O) dependency of electrons is smaller than for protons, since the n-type electronic conduction remains more prominent under dry conditions. The dependency of the conductivity of 2 mol-% Al-substituted TiP2O7 on p(H2O) at constant p(O2) (∼ 1 atm) in the temperature range 300–900 °C is shown in Fig. 8. The primarily protonic conductivity increases with increasing p(H2O), as concluded also from the temperature ramps in wet and dry atmosphere earlier, and are approximately proportional to p(H2O)1/3. A tendency of levelling out is seen for the driest conditions. This may partly be due to the n-type electronic contribution having a smaller p(H2O)-dependency, but may also typically reflect variations in the finite p(H2O) in the “dry” gas. We will model the overall p(H2O) and temperature dependencies below. First we note, however, that Nagao et al. [17] reported conductivities of TiP2O7 based materials much higher than ours at low temperatures. They found that the high proton conductivity was diminished about 2 orders magnitude in samples with pyrophosphate deficiency
Fig. 5. Temperature dependence of the conductivity for (a) TiP2O7 and (b) 2 mol-% Alsubstituted TiP2O7 in wet, D2O-containing, and dry O2.
mechanism. The isotope effect may for our data qualitatively be attributed to a slightly higher activation energy for deuteron than for proton mobility arising from the difference in zero-level energy (the so-called semi-classical effect). Also other effects may play a role, such as slightly different p(H2O) vs. p(D2O) over saturated solutions of KBr in H2O vs. D2O, different thermodynamics of dissolution of protons vs. deuterons, and different pre-exponentials of mobility due to the classical reduced mass effect and other effects. However, our inability to separate concentration and mobility in this work makes an attempt of more detailed consideration of all these factors meaningless. The activation energy for the total conductivity in TiP2O7 in H2Ocontaining atmosphere was evaluated from ln(σT) vs. 1/T plots as 0.70 eV (68 kJ/mol) below the phase transition (using data in the range 500– 674 °C) and 0.47 eV (45 kJ/mol) above (692–1000 °C). The conductivity of
Fig. 6. Temperature dependence of the H/D isotope effect on conductivity of the TiP2O7 and 2 mol-% Al-substituted TiP2O7 in wet O2.
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we mention that in many oxides, protons charge compensate acceptor substituents in competition with a native, positive defect, like oxygen vacancies [29]: x • H2 OðgÞ þ v•• O þOO ¼ 2OHO
ð3Þ
The electroneutrality condition of an acceptor-doped oxide with oxygen vacancies and protons then reads = • 2½v•• O þ ½OHO ¼ ½A ¼ constant
ð4Þ
where the square brackets denote molar fractions or volume concentrations and where A/ is the acceptor. From combination of the equilibrium constant and electroneutrality the concentration of protons and hence proton conductivity obtain a p(H2O)1/2-dependency when vacancies dominate at low p(H2O), and independency of p(H2O) when the proton concentration dominates and saturates at high p(H2O). In orthophosphates such as LaPO4, acceptor substitution and hydration are believed to involve oxygen deficiency in the form of a pyrophosphate ion defect located over two adjacent orthophosphate •• , and hydrogen phosphate groups at orthophosion sites, (P2O7)2PO 4 • [12,30,31]. The hydration reaction can then phate ion sites, (HPO4)PO 4 be written •• • ðP2 O7 Þ2PO4 þ H2 OðgÞ ¼ 2ðHPO4 ÞPO 4
ð5Þ
Otherwise this gives the same behaviour as for oxides, and predicts a p(H2O)1/2-dependency of minor proton concentrations and a p(H2O)independent saturation for acceptor-doped samples, which is not in accordance with our observed p(H2O)1/3-dependency of the proton conductivity. In pyrophosphates such as TiP2O7 the pyrophosphate group is not a defect, it is the host anion. It may expectedly be hydrated to form hydrogen pyrophosphate defects at pyrophosphate sites, denoted as (HP2O7)•P2O7 . These may charge compensate acceptor dopants. However, our results indicate that the protons dissolve in quantities exceeding the dopant level. This means that water dissolves as protons and some negative defect, for instance interstitial oxide ions.
Fig. 7. Temperature dependence of the conductivity of (a) TiP2O7 and (b) 2 mol-% Alsubstituted TiP2O7 in wet argon and in wet O2.
(from FTIR measurements). Shirai et al. [28] reported that a sample prepared by the solid state reaction method and sintered at 1200 °C gave a lower conductivity (b10− 7 S/cm at 400 °C), i.e. in better agreement with our results. They state that the high conductivities of less sintered samples stem from core-shell microstructures, with a highly conductive amorphous outer phase. Our results serve to support this, in that our samples do not exhibit the anomalous conductivity, are sintered at relatively high temperatures, and seem therefore not to have contained grain shells of such an amorphous phase. 3.3. Defect–chemical model The p(H2O) dependencies of the conductivities of our samples will now be discussed in detail in terms of a defect–chemical model. First,
Fig. 8. p(H2O) dependence of the conductivity of 2 mol-% Al-substituted TiP2O7 in O2. The solid lines are the modelled sum of partial protonic and electronic conductivities.
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This has been suggested as a prevailing situation in undoped Y2O3, an oxide with native empty interstitial oxygen sites [32]: x
==
2OO þ H2 OðgÞ ¼ Oi þ 2OHO•
ð6Þ
In a pyrophosphate the interstitial oxygen may be denoted as phosphate ions at a pyrophosphate site, (2PO4)P//2O7 . The hydration reaction can in this case be written x == 3ðP2 O7 ÞP2 O7 þ H2 OðgÞ ¼ ð2PO4 ÞP2 O7 þ 2ðHP2 O7 ÞP•2 O7
ð7Þ
515
The partial conductivity of a charge carrier i can be expressed as σi ¼ zi eci μi
ð14Þ
where σi, zie, ci and μi are the partial conductivity (S/cm), charge (C), volume concentration (cm− 3) and charge mobility (cm2/Vs), respectively. The charge mobility of a diffusing charge carrier i is further given by −ΔHm;i 1 μi = μ0;i exp T RT
ð15Þ
, with the equilibrium constant expressed as h K1 =
ih i2 ! ! ðHP2 O7 Þ•P2 O7 ΔS01 −ΔH10 = exp exp h i3 R RT ðP2 O7 ÞxP2 O7 pðH2 OÞ
== ð2PO4 ÞP O 2 7
ð8Þ
in which concentrations are volume concentrations or mole fractions, and partial pressure given in bar (≈atm). The electroneutrality condition limited to oxygen interstitials and protons can accordingly be written == 2½ð2PO4 ÞP2 O7 ¼ ½ðHP2 O7 Þ•P2 O7
ð9Þ
By inserting this into the expression for the hydration equilibrium constant, and assuming small defect concentrations ([(P2O7)Px2O7] ≈ 1) we obtain the concentration of protonic defects expressed as h
• ðHP2 O7 ÞP2 O7
i
=2
1=3
1=3
1=3
K1 pðH2 OÞ
0 1 01 − ΔH1 ApðH2 OÞ1=3 = c0;Hþ exp@ 3 RT
where μ0,i is the pre-exponential (cm2K/Vs) of charge mobility and ΔHm,i is the migration enthalpy. We assume that electrons migrate by a small polaron hopping mechanism in this material, so that Eq. (15) is applicable to electrons and protons alike. The conductivities of dominating protons and minority electrons are from all the above expressed as
σHþ
1 0 1 0 þ − ΔH + ΔH 1 m;H 1 1=3 3 A exp@ = zec0;Hþ μ0;Hþ pðH2 OÞ T RT −ΔHHþ 1 = 31 exp = σ0;Hþ pðH2 OÞ T RT
ð16Þ
1 0 1 0 1 0 − ΔH2 −3 ΔH1 + ΔHm;n 2 A exp@ σn = zen0 μ0;n pðH2 OÞ pðO2 Þ T RT 1 −ΔHn = σ0;n pðH2 OÞ1 = 6 pðO2 Þ−1 = 4 exp T RT 1=6
−1 = 4 1
ð10Þ
ð17Þ
in qualitative agreement with the p(H2O)-dependency of the proton conductivity, and where c0,H+ is the pre-exponential of proton concentration and ΔH01 is the standard enthalpy change of the hydration reaction (Eqs. (7) and (8)). At higher temperatures a contribution of n-type conductivity is significant. An equilibrium relating defect electrons and protons can be written
The p(H2O) dependency of the measured total conductivity of the Alsubstituted sample has been fitted at each temperature as a sum of the contributions from dominating protons and minority electrons with, respectively, p(H2O)1/3 and p(H2O)1/6 dependencies from the above derivations. The model fits our data reasonably well, see Fig. 8. The somewhat worse fit at 300 °C is probably due to the problem to reach full equilibrium. The fitted partial conductivities at various temperatures have been further fitted to Arrhenius-type expressions to obtain the activation enthalpies and pre-exponentials of the partial conductivities according to Eqs. (16) and (17). The activation enthalpy of the partial proton conductivity (ΔHH+) is 68 ± 5 kJ/mol at 300–600 °C and 36 ± 8 kJ/mol at 700–900 °C, the former in full agreement with that obtained for the total conductivity ramps, and the latter somewhat lower as the electronic contribution is now excluded. The preexponential (σ0H+) is (2 ± 1.5) · 103 SK/cm at low and 60 ± 35 SK/cm at high temperatures. The hydration reaction Eq. (7) is bound to have a negative standard entropy change (ΔS01) and the standard enthalpy change (ΔH01) must then be also negative (exothermic) for the reaction to have a non-negligible equilibrium constant. This means that the activation energies for proton mobilities are larger than the values reported for ΔHH+ above, but a further quantification cannot be made as the parameters for hydration thermodynamics are not known. The difference in the activation enthalpy of the partial proton conductivity between low and high temperature is assigned to the phase transformation. In perovskite-related oxides it is found that lower symmetry, e.g. distortions from cubicity, decreases the proton mobility [33]. In TiP2O7 both phases are cubic, but the low temperature modification has a 3 × 3 × 3 supercell and the higher activation enthalpy of protons at low temperatures may thus be related to this decrease in local symmetry, affecting primarily the activation enthalpy of migration, but also the enthalpy of hydration. The increase in pre-exponential indicates that this is accompanied by
•
x
=
1 2
2ðP2 O7 ÞP2 O7 + H2 OðgÞ = 2ðHP2 O7 ÞP2 O7 + 2e + O2
ð11Þ
and the equilibrium constant of this can be expressed h
i2 ! ðHP2 O7 Þ•P2 O7 n2 pðO2 Þ1=2 −ΔH20 K2 = = K0;2 exp h i2 RT ðP2 O7 ÞxP2 O7 pðH2 OÞ
ð12Þ
where n is the concentration of electrons, and the use of a preexponential constant is used instead of a standard entropy change, as the standard state of the concentration of electrons is not straightforward to define. Assuming that electrons are minority defects, and that we can again assume small overall defect concentrations, we can insert the dominating concentration of protons from Eq. (10) into Eq. (12) and get for the concentration of electrons K2 pðH2 OÞ1=6 pðO2 Þ1=4 1=2
n=
1=3
21=3 K1 1 0 1 0 1 0 − ΔH2 − ΔH1 2 3 ApðH2 OÞ1=6 pðO2 Þ−1 = 4 = n0 exp@ RT
ð13Þ
where n0 is the pre-exponential of electron concentration, and we recognize the positive but smaller dependency on p(H2O) for the minority electrons than for the dominating protons, as the conductivity curves suggested.
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an increased vibrational attempt frequency and/or a difference in the thermodynamics. The activation enthalpy of the partial electron conductivity (ΔHn) is 110 ± 20 kJ/mol and the pre-exponential (σ0,n) is 104 ± 1 SK/cm at 700–900 °C. (The electronic conductivity and corresponding parameters cannot be extracted with any confidence for the low temperature phase). The undoped sample exhibited a conductivity only slightly lower than the doped one, and similar p(H2O) and p(O2) dependencies, suggesting as mentioned early on that the level of dissolved dopant is small compared to the level of defects introduced by hydration. We have seen that TiP2O7 exhibits a strong, mathematically welldescribed, and relatively uniform water vapour dependency all the way down to very low p(H2O) at all temperatures investigated. This rather unique property makes the material an interesting candidate for conductivity based water vapour sensors. 4. Summary The AC bulk conductivity of sintered, porous samples of TiP2O7 and 2 mol-% Al-substituted TiP2O7 increases with humidity and has a clear H/D isotope effect, which demonstrates that the conductivity is mainly protonic and that protons migrate through a hopping mechanism. The isotope effect is attributed to a higher activation energy of the mobility of deuterons than of protons. The p(O2) dependence indicated that the materials are mainly ionic (proton) conductors and that a minor n-type conductivity contributes significantly above 900 °C at reduced oxygen activities. Arrhenius plots exhibit clear signs of the reported phase transition at around 700 °C. The observed p(H2O)1/3 dependency of the conductivity of 2 mol-% Al-substituted TiP2O7 has been modelled assuming that protons are charge compensated by oxygen interstitials. On this basis the partial conductivities and their temperature dependencies have been derived as follows: the low temperature phase has below 600 °C a proton conductivity given as −68 5kJ=mol 3 1 = 31 σHþ ;LT ðS = cmÞ = ð2 1:5Þ⋅10 ⋅ðpðH2 OÞ =barÞ exp T RT
ð18Þ while the high temperature phase has above 700 °C a partial proton conductivity given as −36 8kJ=mol exp T RT
1 = 31
σHþ ;HT ðS = cmÞ = 60 35⋅ð pðH2 OÞ =barÞ
41
1=6
⋅ðpðH2 OÞ =barÞ
ðpðO2 Þ= barÞ
Acknowledgements This work was carried out with financial support from a grant under the FUNMAT@UiO program of the University of Oslo (UiO). The authors thank Dr. Anuradha Ashok, Centre for Materials Science and Nanotechnology (SMN), UiO, for the TEM work. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]
ð19Þ
[30]
−110 20kJ=mol exp T RT
[31] [32] [33]
and a partial electronic n-type conductivity given as σn;HT ðS = cmÞ = 10
encourage further studies of proton conductivity in tetravalent metal pyrophosphates and analogous materials at elevated temperatures. Signs of abnormally high proton conductivities at low temperatures as reported in literature have not been observed.
−1 = 4 1
ð20Þ These relationships seem to hold over large temperature ranges and down to very low p(H2O) making the materials of interest as sensors, and this and the presence of proton conduction itself
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