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Determination of the maximum solubility of hydrogen in α-alumina by DC polarization method
Solid State Ionics 213 (2012) 92–97
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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
Determination of the maximum solubility of hydrogen in α-alumina by DC polarization method Yuji Okuyama a,⁎, Noriaki Kurita b, Daisuke Sato b, Hisashi Douhara b, Norihiko Fukatsu b a b
Intellectual Property Division, Industry-Academia-Government Collaboration Center, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan Department of Materials Science and Engineering, Graduate School of Engineering, Omohi College, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan
a r t i c l e
i n f o
Article history: Received 15 September 2010 Received in revised form 27 February 2011 Accepted 23 May 2011 Available online 11 August 2011 Keywords: α-alumina Proton conductor Chemical potential profile Solubility of hydrogen Direct current polarization
a b s t r a c t In order to evaluate the solubility of hydrogen in polycrystalline α-alumina used as a proton conductor, the amount of absorbed or desorbed hydrogen based on the change in the polarization conditions of the specimen was measured by a coulometric method based on an electrochemical cell using CaZrO3 (+In2O3). The hydrogen chemical potential profile in the specimen was calculated for various states of imposed voltage. The solubility of hydrogen was evaluated from the measured amounts of the absorbed or desorbed hydrogen on the changes in the imposed voltage and the corresponding change in the potential profile. The obtained value of the maximum solubility in the hydrogen atmosphere was (2.0 ± 1.6) × 10−7 mol cm −3 and found to be independent of temperature in the experimental range of 1273–1573 K. © 2011 Elsevier B.V. All rights reserved.
1. Introduction It is known that the incorporation of hydrogen into an oxide forming a crystal defect has a significant effect upon its electrochemical properties. As a typical example, alkaline-earth cerates and zirconates doped with trivalent cations with perovskite structures contain the hydrogen defect as interstitial protons which become the dominant charge carrier at high temperatures [1]. These materials are called the defect-type oxide proton conductors and are attracting the attention of many researchers as the key material for the coming hydrogen energy system (fuel cell, hydrogen membrane, etc.). Among these oxides, Indoped CaZrO3 is chemically stable and mechanically strong in comparison to other proton conductors, and has been utilized as a hydrogen sensor probe for molten aluminum and copper [2–5]. The single crystal of acceptor-doped α-alumina is also reported to incorporate hydrogen [6,7] and shows proton conduction in a hydrogen atmosphere [8–12]. For commercially supplied α-alumina in the polycrystalline state, it is reported that the dominant charge carrier is a proton in the hydrogen atmosphere and a hole in an oxidizing atmosphere [13,14]. Therefore, commercially supplied αalumina is a promising candidate as the electrolyte for the galvanic cell-type hydrogen sensor for molten copper used in the industrial processes [15–17]. However, its proton conductivity is much lower than that of the perovskite-type proton conductor. This is due to the
⁎ Corresponding author. Tel.: +81 52 735 5315; fax: +81 52 735 5571. E-mail address: [email protected] (Y. Okuyama). 0167-2738/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2011.05.023
fact that the solubility of hydrogen in α-alumina is infinitesimally lower than other proton conductors. Roy and Coble determined the solubility of hydrogen in porous polycrystalline alumina by Sieverts' method [18]. In a previous study, we reported the amount of hydrogen in a single crystal of α-alumina doped with barium and calcium [11,12] from the measured mobility and the proton conductivity. In this study, the maximum solubility of hydrogen in polycrystalline α-alumina was determined by a DC polarization technique in the temperature range of 1273–1573 K. 2. Theory of experimental determination of the solubility of hydrogen 2.1. Determination of chemical potential profiles of hydrogen in the α-alumina when the chemical potentials on both ends are fixed The chemical potential profile in the ionic conductor in a polarized state is determined by the continuity of the ionic and electronic currents [19,20]. The internal chemical potential distribution is uniquely established when the chemical potentials at both ends and the applied voltage are given. We considered a hydrogen concentration cell made from the cylindrical electrolyte specimen with porous platinum electrodes on both sectional ends as shown on the left side of Fig. 1. The cell can be expressed by the following cell formula:
j
PtðLeftÞ;pH2 ðLeftÞ
x=0
α Al2 O3
x=L
jp
H2 ðRightÞ; PtðRightÞ
ð1Þ
Y. Okuyama et al. / Solid State Ionics 213 (2012) 92–97
93
where pH2⁎ is the activity of hydrogen. The acceptor doped α-alumina is known as a mixed-conductor of only a hole and a proton based on our recent studies. The currents of the proton and hole flowing at an arbitrary point in the mixed-conductor are generally represented as follows: IH• = − i
Ih• = −
AσH• dηH• i
F
ð2Þ
i
dx
Aσh• dηh• F dx
ð3Þ
where F is Faraday's constant, A is the sectional area of the electrolyte and x is the distance from the right to left end of the mixed-conductor. σi and ηi are the conductivity and the electrochemical potential of the charge carrier, i, respectively. The local equilibrium between the proton, the hole, and the ambient atmosphere as represented below are supposed to be maintained in the whole specimen [11], 1 • • H + h = Hi 2 2 • Hi K= 1= 2 ½h• pH2
ð4Þ ð5Þ
where K is the equilibrium constant of Eq. (4) and [i] is the concentration of species i represented by mole in one mole of Al2O3. Considering the balance of the electrochemical potential of the components in Eq. (4), we get, 1 μ + ηh• = ηH• : i 2 H2
ð6Þ
Fig. 1. Schematic illustration of the experimental apparatus.
the negatively-charged defects, M′Al (M = Mg, Ca) in the α-alumina. In this temperature, the negatively-charged defects are frozen in nonequilibrium state. As there is the relation of [Hi•] ≫ [h •] (or KpH2 1/2 ≫ 1) under this experimental condition (1 × 10 −6 ≤ pH2 b 1) [11], the conductivities of the proton and the hole are represented from Eqs. (5) and (11) as follows: • • Hi max Hi ≈ FmH• iV i VAl2 O3 Al2 O3
σH• = FmH• i
σh• = Fmh•
dηH• 1 dμ H2 dηh• i + = : 2 dx dx dx
ð7Þ
From Eqs. (2), (3) and (7), the current of the proton is expressed as follows: IH• ðxÞ = − i
• • Hi max h ≈ Fmh• 1=2 VAl2 O3 Kp VAl O H2
Differentiating by x,
A σH•i σh• dμ H2 2F rσH• −σh• dx
ð8Þ
ð12Þ
2
ð13Þ
3
where mi is the drift mobility of the charge carrier and VAl2O3 is the molar volume of α-Al2O3. By substituting Eqs. (12) and (13) into Eq. (10) and integrating both sides from x = 0 to x = x and from x = 0 to x = L, and then taking the ratio of the side-to-side, we obtain the relation representing the position in α-alumina x as an implicit function of the potential of hydrogen pH2(x = x) for the individual polarization condition to the parameter r as follows:
i
where we used the parameter r, the ratio of the current of the proton to that of the hole defined as, r=
Ih : IH• •
ð9Þ
=
0
1 mH• K −1 = 2 i Br− mh• pH2 ðx = xÞ C x=L = ln @ A mH• K −1 = 2 r− m i • pH ðx = 0Þ h
2
0
1 mH• K −1 = 2 i B r− mh• pH2 ðx = LÞ C ln @ A: mH• K −1 = 2 r− m i • pH ðx = 0Þ h
ð14Þ
2
i
In the steady state, each current has the same value through the specimen. Therefore, r is constant when the steady state was attained. As the current in the steady state is independent of position x, the current of the proton passing through the electrolyte is expressed from Eq. (8) as follows: σH• σh• A p i IH• x = − ∫ H2 ðx = xÞ dμ : i 2F pH2 ðx = 0Þ rσH• −σh• H2
ð10Þ
According to the result of our recent study on the emf of the mh• is hydrogen concentration cell using α-Al2O3 [16], the value mH•i K given as follows: 4
ln
mh• 1:96 × 10 =− + 10:5: mH• K T
ð15Þ
i
i
where [Hi•]max. is the maximum proton concentration possibly incorporated into the specimen, which equals the concentration of
The parameter r can be determined for the individual applied voltage. We suppose here that the polarization at the electrode can be ignored and equilibrium between the electrode and the electrolyte is perfectly attained. This might be a fairly good approximation because the current density practically observed in the experiment was very small. As the same metal, Pt, was used for both electrodes, the difference in the electrochemical potential of electrons between the sample electrodes is equivalent to the applied voltage, Eapply ,
⁎ The pH2 in this paper represents the activity of hydrogen with reference to one bar of hydrogen gas in the pure state.
Eapply = −
The electrical neutrality condition of the acceptor doped α-alumina is expressed as follows [10–12]: • • • ½M′Al = ½Hi + ½h ≈½Hi max
ð11Þ
sample
1 ηeðPt;RightÞ −ηeðPt;LeftÞ : F
ð16Þ
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Y. Okuyama et al. / Solid State Ionics 213 (2012) 92–97
As the heterogeneous equilibrium e′(Pt) + h •(Al2O3) = null is established at both electrodes, the above relation can be rewritten as follows: 1 1 x=L η • −ηh• ðx = 0Þ = ∫x = 0 dηh• : F h ðx = LÞ F
sample
Eapply =
ð17Þ
On the other hand, from Eqs. (2), (3) and (7), the gradient for the electrochemical potential of the hole is expressed as follows: dηh• 1 rσH•i dμ H2 =− : 2 rσH• −σh• dx dx
ð18Þ
i
From Eqs. (17) and (18), we obtain the following equation for the applied voltage: sample
Eapply = −
1 pH2 ðx = LÞ rσH•i ∫ dμ : 2F pH2 ðx = 0Þ rσH• −σh• H2
ð19Þ
i
Fig.2. Log pH2 vs. x/L profile inside a commercial α-alumina at 1273 K.
Substituting Eqs. (12) and (13) into Eq. (19), and by integration, we can obtain the following equation relating the applied voltage to the parameter r.
sample Eapply
0 1= 2 1 m p − h• RT B H2 ðx = LÞ rmH•i K C ln@ 1 = 2 =− m • A F pH ðx = 0Þ − rm h• K 2
H
ð20Þ
1=2
2.2. Evaluation of the amount of hydrogen released from the electrolyte on the change in the polarization condition We consider the situation in which the concentration of protons is much greater than that of the holes. Under this condition, the maximum amount of hydrogen dissolved in α-alumina can be determined from a small change in the amount of dissolved hydrogen in a sample upon the change in the chemical potential distribution. The small amount of hydrogen discharged from or absorbed by the specimen when the chemical potential distribution is modified by the change in the applied voltage is described below. When the applied voltage is E1, the amount of protons under the steady state is represented by Eqs. (5) and (11) as follows:
nH• ðE1 Þ = ∫x i
• 1=2 Hi max :KpH ðE 2
= 0
1+
1=2 KpH ðE Þ 2 1
1Þ
A dx VAl2 O3
ð21Þ
where nH•i(E1) is the amount of the protons under the imposed voltage, E1. The change in the concentration of the proton is, therefore, represented as follows: nH• ðE1 Þ −nH• ðE2 Þ = i
i
•
Hi
VAl
max
2 O3
0 :A @ x = L ∫x = 0
1=2 2 ðE1 Þ 1=2 KpH ðE Þ 2 1
KpH 1+
0
≈
4
ln K = ð1:98 0:04Þ × 10
i
where R is the gas constant. Finally, the potential distribution in αalumina can be estimated from Eqs. (14), (15) and (20) when the sample , temperature T, and the potentials of hydrogen applied voltage Eapply at positions x = 0 and x = L were fixed. Fig. 2 shows the result of the potential distribution calculation in α-alumina in the case pH2(x = 0) = 0.99, pH2(x = L) = 1 × 10 −6 at 1273 K for various polarization conditions. As shown in this figure, it was found that the chemical potential of hydrogen in the specimen changes with the applied voltage.
x = L
The equilibrium constant of Eq. (5), K, was determined in our previous study as follows [11]:
x = L
dx−∫x = 0
1=2 2 ðE2 Þ 1=2 KpH ðE Þ 2 2
KpH 1+
1 dxA
1
• 1=2 1=2 Hi max :A @ x = L pH2 ðE1 Þ −pH2 ðE2 Þ A ∫ dx : VAl O 1=2 1=2 x = 0 2 3 KpH ðE Þ pH ðE Þ 2
1
2
2
ð22Þ
1 −ð4:56 0:40Þ: T
1=2
−p p x = L H2 ðE1 Þ H2 ðE2 Þ 1=2 0 Kp1=2 p H2 ðE1 Þ H2 ðE2 Þ
The term, ∫x =
ð23Þ
dx, of Eq. (22) can be calculated from
the distribution of the hydrogen potential given by Eqs. (14) and (23). Therefore, the value of [Hi•]max. which indicates the level of the practical amount of hydrogen dissolved in the commercially supplied sintered alumina, can be obtained when the amount of absorbed or desorbed hydrogen, nH•i (E1) − nH•i(E2), due to the change in the applied voltage to E1 from E2 is experimentally determined. 3. Experiment The amount of hydrogen absorbed by or desorbed from α-alumina was measured by an apparatus developed based on the coulometric titration of an electrochemical cell using an oxide proton conductor, 10 mol% In-doped CaZrO3 (hydrogen pump) [21,22]. The schematic illustration of the experimental apparatus is shown in Fig. 1. As shown in this figure, the hydrogen pump and the α-alumina were arranged in series. Porous electrodes were applied to both surfaces of the electrolyte used as the hydrogen pump. We called the left and right electrodes in the figure the working and reference electrodes, respectively. The reference gas (1%H2–Ar) was made to flow through the right compartment of the hydrogen pump (reference electrode chamber) in order to hold the potential of hydrogen on the reference electrode at a constant value. The hydrogen potential on the working electrode for the hydrogen pump was represented as follows:
pH2 ðwork:Þ = pH2 ðref:Þ exp
pump −2FEapply
RT
! ð24Þ
pump is the applied voltage on the hydrogen pump, pH2 where Eapply (work.), pH2(ref.) is the hydrogen activity of the working electrode and on the reference electrode of the hydrogen pump, respectively. The hydrogen potential in the compartment between the hydrogen pump and the commercial α-alumina (working electrode chamber) pump was controlled at pH2 = 10 −6 or 10 −5 by applying a voltage (Eapply ). The amount of hydrogen to be removed from or added to the chamber in order to maintain the constant hydrogen potential can be
Y. Okuyama et al. / Solid State Ionics 213 (2012) 92–97
monitored by the current flowing through the circuit of the hydrogen pump. The hydrogen potential in the left chamber of the commercial α-Al2O3 (sample chamber) was controlled by pure H2 or a mixture of H2–Ar gas containing water vapor. Porous electrodes were attached to pump both surfaces of the specimen of α-alumina and a voltage (Eapply ) was applied. A schematic diagram of the change in current passing through the hydrogen pump and the α-alumina specimen when the voltage was applied to the α-alumina changed from E1 to E2 or from E2 to E1 (E2 N E1), is shown in Fig. 3. When the imposed voltage is changed to a higher value, the proton current passing through the specimen is suddenly suppressed at a lower value because the imposed voltage slows the protons. On the other hand, the current of the hole suddenly increases (to the more negative side). The observed total current, therefore, suddenly changes to a negative value. The next steady state is obtained when a new charge carrier distribution was attained after an amount of protons is removed from the specimen as hydrogen. The process of hydrogen liberation can be detected by the current passing through the hydrogen pump. As shown in this figure, the quantity of electricity, QH•i, corresponding to the hatched area of the decay curve of the hydrogen pump current is proportional to the amount of absorbed or desorbed hydrogen from the α-alumina. According to Faraday's law, the following relation is derived: QH• i
F
= nH• ðE1 Þ −nH• ðE2 Þ : i
i
ð25Þ
−1 , can be determined From Eqs. (22) and (25), the value, [Hi•]max.VAl 2O3 by measuring the change in the external current of the hydrogen pump when the voltage applied to the α-alumina is changed from E1 to E2.
a)
95
The commercially supplied α-alumina polycrystalline protecting tube was used as the specimen. The shape was a tube closed at one end, with a 15 mm outer diameter, 11 mm inner diameter, and 500 mm length. The main impurity contained in the specimen is shown in Table 1. As shown in the table, magnesium was the highest impurity and this sample shows proton conduction [14]. A schematic view of the experimental arrangement is shown in Fig. 4. The hydrogen pump was composed of a 10 mol% In-doped CaZrO3 polycrystalline ceramic supplied by the TYK Corporation. The shape was a tube closed at one end, with a 12 mm outer diameter, 8 mm inner diameter and 200 mm length. Porous platinum electrodes were applied to both the inner and outer surfaces over 50 mm from the closed end by coating with a platinum paste and subsequent sintering in air at 1123 K. Pt lead (0.4 mm diameter) wires were attached to each electrode by sintering. The electrolyte of the hydrogen pump was contained in a silica sheath and the reference gas (1% H2–Ar) was made to flow into the reference electrode chamber formed between the silica sheath and the electrolyte. The specimen, the hydrogen pump, a circulation pump and a 4-way valve were connected in series by stainless steel pipes. The diaphragm-type pump was used for circulating the gas into the working electrode chamber. The temperature of the hydrogen pump was 923 K. The hydrogen pump current was monitored using a digitalmultimeter (HP-3478A) by measuring the voltage drop across a reference resistor (996 Ω) connected in series to the external circuit. The hydrogen gas (1% H2O–H2 or 1% H2O–10% H2–Ar) was made to flow over the outside of the α-alumina tube. Porous platinum electrodes were applied to both the inner and outer surfaces of alumina specimen over 150 mm from the closed end by coating with platinum paste and subsequent sintering at 1123 K. A platinum wire (φ 0.4 mm diameter) was employed as the electrical lead. The measurements were performed in the temperature range from 1273 to 1573 K. The furnace, whose temperature was controlled by three separate heating elements, was used to keep a constant temperature over the 150 mm length. The voltage imposed on the α-alumina was changed from 0.1 V to 0.4, 0.8, and 1.2 V. The current flowing through the α-alumina was measured using a digital-multimeter (HP-3478A) by the voltage drop across a reference resistor connected in series to the external circuit. 4. Results and discussion 4.1. The steady state currents
b)
Fig. 5 shows a typical example of the measured currents passing through the specimen and the hydrogen pump. Stable currents observed when the polarization voltage was maintained at a constant value were found to change upon changing the imposed voltage. Fig. 6 shows the observed total currents in the steady state and the estimated currents of the protons passing through the specimen and hydrogen pump as a function of the voltage imposed on the α-alumina. In this experiment, the terminal potentials were kept at pH2(0) = 0.99 and pH2(L) = 1 × 10−6 and at a temperature of 1273 K. The proton current passing through α-alumina under the steady state was estimated according to the aforementioned theory as follows: IH• =
ItotalðαaluminaÞ
i
ð26Þ
ð1 + rÞ
where Itotal is the total current flowing through the α-alumina. The value, r, can be determined by the applied voltage using Eqs. (15) and
Fig. 3. Schematic view of the current changes when the applied voltage was changed from E1 to E2 (E2 N E1). The total current ( ), the current of proton ( ) and the current of hole ( ). (a) the current passing through the hydrogen pump. (b) The current passing through the specimen of α-alumina.
Table 1 The component elements in the commercial α-alumina used in this study. Element
Al2O3
MgO
SiO2
Na2O
CaO
wt.%
99.64
0.15
0.1
0.05
0.04
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Y. Okuyama et al. / Solid State Ionics 213 (2012) 92–97
Fig. 6. The currents passing through the hydrogen pump and the specimen of αalumina as a function of the applied voltage to α-alumina.
Fig. 4. Schematic layout of experimental setup.
(20). The calculated proton current based on Eq. (26) is plotted by the open circles in Fig. 6. On the other hand, the proton current passing through the hydrogen pump may be calculated from the total current by subtracting the electronic current under the Hebb–Wagner polarization condition [23,24]. In this study, the current under the Hebb–Wagner polarization condition was experimentally determined to be 0.053 mA by the measurement while lowering the temperature of the α-alumina specimen to room temperature. The evaluated proton current passing through the hydrogen pump was plotted by the closed circles in Fig. 6. As shown in the figure, the proton current passing through the hydrogen pump and that passing through the α-alumina are in good agreement with each other under a stable condition. This means that the aforementioned procedure to calculate the potential profile is valid for this experimental condition. 4.2. The maximum amount of hydrogen in α-alumina The change in the current of the hydrogen pump and α-alumina shown in Fig. 5 is obtained when the voltage applied to the α-alumina was changed from 0.1 to 0.8 V or from 0.8 to 0.1 V at 1273 K and the terminal condition, pH2(x = 0) = 0.99, pH2(x = L) = 1 × 10 −6. As shown
Fig. 5. The external currents for the hydrogen pump and the specimen of α-alumina (1273 K, pH2(x = 0) = 0.99, pH2(x = L) = 1 × 10−6).
in the figure, a gradual transient change in the external current of the hydrogen pump was observed with the change in the voltage applied to the α-alumina. This change occurs from pumping out the hydrogen released from the alumina specimen due to the change in the distribution of the hydrogen potential. The quantity of electricity, QH•i, corresponding to the amount of hydrogen desorbed from α-alumina was obtained from the hatched area under the decay curve for the −1 current of the hydrogen pump. The value, [Hi•]max.VAl , was 2 O3 determined by the quantity of electricity using Eqs. (22) and (25). The temperature dependence of [Hi•]max.V−1 Al2O3 is shown in Fig. 7. As shown in the figure, the solubility of hydrogen in the commercially supplied α-alumina determined in the present study was found to be one order of magnitude lower than that of the single crystal of the acceptor doped α-alumina reported in our previous study [11,12,25]. This phenomenon seems to be due to the fact that the concentration of the acceptor dopant in the commercially supplied α-alumina was lower than that in the single crystal grown in our laboratory. In the commercially supplied α-alumina, the impurities working as a donor dopant are also present. These donor impurities may compensate for the extra negative charge of the acceptor and significantly decrease the amount of the acceptor dopant.
Fig. 7. The solubility of proton in α-alumina.
Y. Okuyama et al. / Solid State Ionics 213 (2012) 92–97
Compared with the solubility of hydrogen in polycrystalline alumina reported by Roy and Coble [18], the value obtained in the present study was found to be three orders of magnitude lower than their value. Their experiment was performed in the temperature range from 1885 to 2089 K. The temperature dependence of the hydrogen solubility is also given in their report. Their larger value might arise from the enhancement of the solubility of the acceptor dopant from the second phase in equilibrium with the sample with the increasing temperature. On the other hand, the amount of dopant is considered to be frozen at the low level than the equilibrium value in our experimental conditions [25]. It is, therefore, reasonable that the maximum solubility of hydrogen determined in the present experiment is lower than that extrapolated from the data of Roy and Coble. Therefore, the hydrogen solubility might be independent of the temperature. 5. Conclusion Using a polarization method, the maximum solubility of hydrogen in a commercially supplied α-alumina was evaluated from the calculated potential profile change and the measurement of the corresponding amount of absorbed or desorbed hydrogen. The obtained value of the maximum solubility was (2.0 ±1.6)× 10−7 mol cm−3 and found to be independent of the temperature in the experimental range 1273–1573 K. Acknowledgment This work was partly supported by a Grant-in Aid for Science Research (19206081) from the Ministry of Education, Culture, Sports,
97
Science and Technology, Japan and research grants (191078) from the Iketani Science and Technology Foundation. References [1] H. Iwahara, T. Esaka, H. Uchida, N. Maeda, Solid State Ionics 3 (4) (1981) 359. [2] T. Yajima, K. Koide, H. Takai, N. Fukatsu, H. Iwahara, Solid State Ionics 79 (1995) 333. [3] N. Fukatsu, N. Kurita, T. Yajima, K. Koide, T. Ohashi, J. Alloy. Compd. 231 (1995) 706. [4] N. Kurita, N. Fukatsu, A. Naito, K. Koide, T. Ohashi, J. Min. Mater. Process. Inst. Jpn. 113 (1997) 45. [5] N. Kurita, N. Fukatsu, S. Miyamoto, F. Sato, H. Nakai, K. Irie, T. Ohashi, Metall. Mater. Trans. B 27B (1996) 927. [6] R. Müller, Hs.H. Günthard, J. Chem. Phys. 44 (1966) 365. [7] R. Ramírez, R. Gonzalez, I. Colera, R. Vila, J. Am. Ceram. Soc. 80 (1997) 847. [8] F.A. Kröger, Solid State Ionics 12 (1984) 189. [9] N. Fukatsu, N. Kurita, Y. Oka, S. Yamamoto, Solid State Ionics 162–163 (2003) 147. [10] Y. Okuyama, N. Kurita, N. Fukatsu, Adv. Mat. Res. 11–12 (2006) 145. [11] Y. Okuyama, N. Kurita, N. Fukatsu, Solid State Ionics 180 (2009) 175. [12] Y. Okuyama, N. Kurita, N. Fukatsu, Solid State Ionics 181 (2010) 142. [13] T. Norby, P. Kofstad, High Temp. High Press. 20 (1988) 345. [14] N. Kurita, N. Fukatsu, N. Miyamoto, M. Takada, J. Hara, M. Kato, T. Ohashi, Solid State Ionics 162–163 (2003) 135. [15] K. Katahira, T. Ohshima, N. Kurita, N. Fukatsu, J. JRICu 44 (2005) 268. [16] Y. Okuyama, N. Kurita, A. Yamada, H. Takami, T. Ohshima, K. Katahira, N. Fukatsu, Electrochim. Acta 55 (2009) 470. [17] N. Fukatsu, N. Kurita, Ionics 13 (13) (2007) 183. [18] S.K. Roy, R. Coble, J. Am. Ceram. Soc. 50 (1967) 435. [19] N.S. Choudhury, J.W. Patterson, J. Electrochem. Soc. 117 (1970) 1384. [20] N.S. Choudhury, J.W. Patterson, J. Electrochem. Soc. 118 (1971) 1398. [21] N. Kurita, N. Fukastu, T. Ohashi, J. Japan Inst. Metals 58 (1994) 782. [22] N. Kurita, N. Fukastu, H. Otsuka, T. Ohashi, Solid State Ionics 146 (2002) 101. [23] Z. Wgner, Physik Chem. B21 (1933) 25. [24] Z. Wagner, Electrochemistry 60 (1956) 4. [25] Y. Okuyam, N. Kurita, N. Fukatsu, J. Min. Mater. Process. Inst. Jpn. 125 (2009) 389.
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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
Determination of the maximum solubility of hydrogen in α-alumina by DC polarization method Yuji Okuyama a,⁎, Noriaki Kurita b, Daisuke Sato b, Hisashi Douhara b, Norihiko Fukatsu b a b
Intellectual Property Division, Industry-Academia-Government Collaboration Center, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan Department of Materials Science and Engineering, Graduate School of Engineering, Omohi College, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan
a r t i c l e
i n f o
Article history: Received 15 September 2010 Received in revised form 27 February 2011 Accepted 23 May 2011 Available online 11 August 2011 Keywords: α-alumina Proton conductor Chemical potential profile Solubility of hydrogen Direct current polarization
a b s t r a c t In order to evaluate the solubility of hydrogen in polycrystalline α-alumina used as a proton conductor, the amount of absorbed or desorbed hydrogen based on the change in the polarization conditions of the specimen was measured by a coulometric method based on an electrochemical cell using CaZrO3 (+In2O3). The hydrogen chemical potential profile in the specimen was calculated for various states of imposed voltage. The solubility of hydrogen was evaluated from the measured amounts of the absorbed or desorbed hydrogen on the changes in the imposed voltage and the corresponding change in the potential profile. The obtained value of the maximum solubility in the hydrogen atmosphere was (2.0 ± 1.6) × 10−7 mol cm −3 and found to be independent of temperature in the experimental range of 1273–1573 K. © 2011 Elsevier B.V. All rights reserved.
1. Introduction It is known that the incorporation of hydrogen into an oxide forming a crystal defect has a significant effect upon its electrochemical properties. As a typical example, alkaline-earth cerates and zirconates doped with trivalent cations with perovskite structures contain the hydrogen defect as interstitial protons which become the dominant charge carrier at high temperatures [1]. These materials are called the defect-type oxide proton conductors and are attracting the attention of many researchers as the key material for the coming hydrogen energy system (fuel cell, hydrogen membrane, etc.). Among these oxides, Indoped CaZrO3 is chemically stable and mechanically strong in comparison to other proton conductors, and has been utilized as a hydrogen sensor probe for molten aluminum and copper [2–5]. The single crystal of acceptor-doped α-alumina is also reported to incorporate hydrogen [6,7] and shows proton conduction in a hydrogen atmosphere [8–12]. For commercially supplied α-alumina in the polycrystalline state, it is reported that the dominant charge carrier is a proton in the hydrogen atmosphere and a hole in an oxidizing atmosphere [13,14]. Therefore, commercially supplied αalumina is a promising candidate as the electrolyte for the galvanic cell-type hydrogen sensor for molten copper used in the industrial processes [15–17]. However, its proton conductivity is much lower than that of the perovskite-type proton conductor. This is due to the
⁎ Corresponding author. Tel.: +81 52 735 5315; fax: +81 52 735 5571. E-mail address: [email protected] (Y. Okuyama). 0167-2738/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2011.05.023
fact that the solubility of hydrogen in α-alumina is infinitesimally lower than other proton conductors. Roy and Coble determined the solubility of hydrogen in porous polycrystalline alumina by Sieverts' method [18]. In a previous study, we reported the amount of hydrogen in a single crystal of α-alumina doped with barium and calcium [11,12] from the measured mobility and the proton conductivity. In this study, the maximum solubility of hydrogen in polycrystalline α-alumina was determined by a DC polarization technique in the temperature range of 1273–1573 K. 2. Theory of experimental determination of the solubility of hydrogen 2.1. Determination of chemical potential profiles of hydrogen in the α-alumina when the chemical potentials on both ends are fixed The chemical potential profile in the ionic conductor in a polarized state is determined by the continuity of the ionic and electronic currents [19,20]. The internal chemical potential distribution is uniquely established when the chemical potentials at both ends and the applied voltage are given. We considered a hydrogen concentration cell made from the cylindrical electrolyte specimen with porous platinum electrodes on both sectional ends as shown on the left side of Fig. 1. The cell can be expressed by the following cell formula:
j
PtðLeftÞ;pH2 ðLeftÞ
x=0
α Al2 O3
x=L
jp
H2 ðRightÞ; PtðRightÞ
ð1Þ
Y. Okuyama et al. / Solid State Ionics 213 (2012) 92–97
93
where pH2⁎ is the activity of hydrogen. The acceptor doped α-alumina is known as a mixed-conductor of only a hole and a proton based on our recent studies. The currents of the proton and hole flowing at an arbitrary point in the mixed-conductor are generally represented as follows: IH• = − i
Ih• = −
AσH• dηH• i
F
ð2Þ
i
dx
Aσh• dηh• F dx
ð3Þ
where F is Faraday's constant, A is the sectional area of the electrolyte and x is the distance from the right to left end of the mixed-conductor. σi and ηi are the conductivity and the electrochemical potential of the charge carrier, i, respectively. The local equilibrium between the proton, the hole, and the ambient atmosphere as represented below are supposed to be maintained in the whole specimen [11], 1 • • H + h = Hi 2 2 • Hi K= 1= 2 ½h• pH2
ð4Þ ð5Þ
where K is the equilibrium constant of Eq. (4) and [i] is the concentration of species i represented by mole in one mole of Al2O3. Considering the balance of the electrochemical potential of the components in Eq. (4), we get, 1 μ + ηh• = ηH• : i 2 H2
ð6Þ
Fig. 1. Schematic illustration of the experimental apparatus.
the negatively-charged defects, M′Al (M = Mg, Ca) in the α-alumina. In this temperature, the negatively-charged defects are frozen in nonequilibrium state. As there is the relation of [Hi•] ≫ [h •] (or KpH2 1/2 ≫ 1) under this experimental condition (1 × 10 −6 ≤ pH2 b 1) [11], the conductivities of the proton and the hole are represented from Eqs. (5) and (11) as follows: • • Hi max Hi ≈ FmH• iV i VAl2 O3 Al2 O3
σH• = FmH• i
σh• = Fmh•
dηH• 1 dμ H2 dηh• i + = : 2 dx dx dx
ð7Þ
From Eqs. (2), (3) and (7), the current of the proton is expressed as follows: IH• ðxÞ = − i
• • Hi max h ≈ Fmh• 1=2 VAl2 O3 Kp VAl O H2
Differentiating by x,
A σH•i σh• dμ H2 2F rσH• −σh• dx
ð8Þ
ð12Þ
2
ð13Þ
3
where mi is the drift mobility of the charge carrier and VAl2O3 is the molar volume of α-Al2O3. By substituting Eqs. (12) and (13) into Eq. (10) and integrating both sides from x = 0 to x = x and from x = 0 to x = L, and then taking the ratio of the side-to-side, we obtain the relation representing the position in α-alumina x as an implicit function of the potential of hydrogen pH2(x = x) for the individual polarization condition to the parameter r as follows:
i
where we used the parameter r, the ratio of the current of the proton to that of the hole defined as, r=
Ih : IH• •
ð9Þ
=
0
1 mH• K −1 = 2 i Br− mh• pH2 ðx = xÞ C x=L = ln @ A mH• K −1 = 2 r− m i • pH ðx = 0Þ h
2
0
1 mH• K −1 = 2 i B r− mh• pH2 ðx = LÞ C ln @ A: mH• K −1 = 2 r− m i • pH ðx = 0Þ h
ð14Þ
2
i
In the steady state, each current has the same value through the specimen. Therefore, r is constant when the steady state was attained. As the current in the steady state is independent of position x, the current of the proton passing through the electrolyte is expressed from Eq. (8) as follows: σH• σh• A p i IH• x = − ∫ H2 ðx = xÞ dμ : i 2F pH2 ðx = 0Þ rσH• −σh• H2
ð10Þ
According to the result of our recent study on the emf of the mh• is hydrogen concentration cell using α-Al2O3 [16], the value mH•i K given as follows: 4
ln
mh• 1:96 × 10 =− + 10:5: mH• K T
ð15Þ
i
i
where [Hi•]max. is the maximum proton concentration possibly incorporated into the specimen, which equals the concentration of
The parameter r can be determined for the individual applied voltage. We suppose here that the polarization at the electrode can be ignored and equilibrium between the electrode and the electrolyte is perfectly attained. This might be a fairly good approximation because the current density practically observed in the experiment was very small. As the same metal, Pt, was used for both electrodes, the difference in the electrochemical potential of electrons between the sample electrodes is equivalent to the applied voltage, Eapply ,
⁎ The pH2 in this paper represents the activity of hydrogen with reference to one bar of hydrogen gas in the pure state.
Eapply = −
The electrical neutrality condition of the acceptor doped α-alumina is expressed as follows [10–12]: • • • ½M′Al = ½Hi + ½h ≈½Hi max
ð11Þ
sample
1 ηeðPt;RightÞ −ηeðPt;LeftÞ : F
ð16Þ
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Y. Okuyama et al. / Solid State Ionics 213 (2012) 92–97
As the heterogeneous equilibrium e′(Pt) + h •(Al2O3) = null is established at both electrodes, the above relation can be rewritten as follows: 1 1 x=L η • −ηh• ðx = 0Þ = ∫x = 0 dηh• : F h ðx = LÞ F
sample
Eapply =
ð17Þ
On the other hand, from Eqs. (2), (3) and (7), the gradient for the electrochemical potential of the hole is expressed as follows: dηh• 1 rσH•i dμ H2 =− : 2 rσH• −σh• dx dx
ð18Þ
i
From Eqs. (17) and (18), we obtain the following equation for the applied voltage: sample
Eapply = −
1 pH2 ðx = LÞ rσH•i ∫ dμ : 2F pH2 ðx = 0Þ rσH• −σh• H2
ð19Þ
i
Fig.2. Log pH2 vs. x/L profile inside a commercial α-alumina at 1273 K.
Substituting Eqs. (12) and (13) into Eq. (19), and by integration, we can obtain the following equation relating the applied voltage to the parameter r.
sample Eapply
0 1= 2 1 m p − h• RT B H2 ðx = LÞ rmH•i K C ln@ 1 = 2 =− m • A F pH ðx = 0Þ − rm h• K 2
H
ð20Þ
1=2
2.2. Evaluation of the amount of hydrogen released from the electrolyte on the change in the polarization condition We consider the situation in which the concentration of protons is much greater than that of the holes. Under this condition, the maximum amount of hydrogen dissolved in α-alumina can be determined from a small change in the amount of dissolved hydrogen in a sample upon the change in the chemical potential distribution. The small amount of hydrogen discharged from or absorbed by the specimen when the chemical potential distribution is modified by the change in the applied voltage is described below. When the applied voltage is E1, the amount of protons under the steady state is represented by Eqs. (5) and (11) as follows:
nH• ðE1 Þ = ∫x i
• 1=2 Hi max :KpH ðE 2
= 0
1+
1=2 KpH ðE Þ 2 1
1Þ
A dx VAl2 O3
ð21Þ
where nH•i(E1) is the amount of the protons under the imposed voltage, E1. The change in the concentration of the proton is, therefore, represented as follows: nH• ðE1 Þ −nH• ðE2 Þ = i
i
•
Hi
VAl
max
2 O3
0 :A @ x = L ∫x = 0
1=2 2 ðE1 Þ 1=2 KpH ðE Þ 2 1
KpH 1+
0
≈
4
ln K = ð1:98 0:04Þ × 10
i
where R is the gas constant. Finally, the potential distribution in αalumina can be estimated from Eqs. (14), (15) and (20) when the sample , temperature T, and the potentials of hydrogen applied voltage Eapply at positions x = 0 and x = L were fixed. Fig. 2 shows the result of the potential distribution calculation in α-alumina in the case pH2(x = 0) = 0.99, pH2(x = L) = 1 × 10 −6 at 1273 K for various polarization conditions. As shown in this figure, it was found that the chemical potential of hydrogen in the specimen changes with the applied voltage.
x = L
The equilibrium constant of Eq. (5), K, was determined in our previous study as follows [11]:
x = L
dx−∫x = 0
1=2 2 ðE2 Þ 1=2 KpH ðE Þ 2 2
KpH 1+
1 dxA
1
• 1=2 1=2 Hi max :A @ x = L pH2 ðE1 Þ −pH2 ðE2 Þ A ∫ dx : VAl O 1=2 1=2 x = 0 2 3 KpH ðE Þ pH ðE Þ 2
1
2
2
ð22Þ
1 −ð4:56 0:40Þ: T
1=2
−p p x = L H2 ðE1 Þ H2 ðE2 Þ 1=2 0 Kp1=2 p H2 ðE1 Þ H2 ðE2 Þ
The term, ∫x =
ð23Þ
dx, of Eq. (22) can be calculated from
the distribution of the hydrogen potential given by Eqs. (14) and (23). Therefore, the value of [Hi•]max. which indicates the level of the practical amount of hydrogen dissolved in the commercially supplied sintered alumina, can be obtained when the amount of absorbed or desorbed hydrogen, nH•i (E1) − nH•i(E2), due to the change in the applied voltage to E1 from E2 is experimentally determined. 3. Experiment The amount of hydrogen absorbed by or desorbed from α-alumina was measured by an apparatus developed based on the coulometric titration of an electrochemical cell using an oxide proton conductor, 10 mol% In-doped CaZrO3 (hydrogen pump) [21,22]. The schematic illustration of the experimental apparatus is shown in Fig. 1. As shown in this figure, the hydrogen pump and the α-alumina were arranged in series. Porous electrodes were applied to both surfaces of the electrolyte used as the hydrogen pump. We called the left and right electrodes in the figure the working and reference electrodes, respectively. The reference gas (1%H2–Ar) was made to flow through the right compartment of the hydrogen pump (reference electrode chamber) in order to hold the potential of hydrogen on the reference electrode at a constant value. The hydrogen potential on the working electrode for the hydrogen pump was represented as follows:
pH2 ðwork:Þ = pH2 ðref:Þ exp
pump −2FEapply
RT
! ð24Þ
pump is the applied voltage on the hydrogen pump, pH2 where Eapply (work.), pH2(ref.) is the hydrogen activity of the working electrode and on the reference electrode of the hydrogen pump, respectively. The hydrogen potential in the compartment between the hydrogen pump and the commercial α-alumina (working electrode chamber) pump was controlled at pH2 = 10 −6 or 10 −5 by applying a voltage (Eapply ). The amount of hydrogen to be removed from or added to the chamber in order to maintain the constant hydrogen potential can be
Y. Okuyama et al. / Solid State Ionics 213 (2012) 92–97
monitored by the current flowing through the circuit of the hydrogen pump. The hydrogen potential in the left chamber of the commercial α-Al2O3 (sample chamber) was controlled by pure H2 or a mixture of H2–Ar gas containing water vapor. Porous electrodes were attached to pump both surfaces of the specimen of α-alumina and a voltage (Eapply ) was applied. A schematic diagram of the change in current passing through the hydrogen pump and the α-alumina specimen when the voltage was applied to the α-alumina changed from E1 to E2 or from E2 to E1 (E2 N E1), is shown in Fig. 3. When the imposed voltage is changed to a higher value, the proton current passing through the specimen is suddenly suppressed at a lower value because the imposed voltage slows the protons. On the other hand, the current of the hole suddenly increases (to the more negative side). The observed total current, therefore, suddenly changes to a negative value. The next steady state is obtained when a new charge carrier distribution was attained after an amount of protons is removed from the specimen as hydrogen. The process of hydrogen liberation can be detected by the current passing through the hydrogen pump. As shown in this figure, the quantity of electricity, QH•i, corresponding to the hatched area of the decay curve of the hydrogen pump current is proportional to the amount of absorbed or desorbed hydrogen from the α-alumina. According to Faraday's law, the following relation is derived: QH• i
F
= nH• ðE1 Þ −nH• ðE2 Þ : i
i
ð25Þ
−1 , can be determined From Eqs. (22) and (25), the value, [Hi•]max.VAl 2O3 by measuring the change in the external current of the hydrogen pump when the voltage applied to the α-alumina is changed from E1 to E2.
a)
95
The commercially supplied α-alumina polycrystalline protecting tube was used as the specimen. The shape was a tube closed at one end, with a 15 mm outer diameter, 11 mm inner diameter, and 500 mm length. The main impurity contained in the specimen is shown in Table 1. As shown in the table, magnesium was the highest impurity and this sample shows proton conduction [14]. A schematic view of the experimental arrangement is shown in Fig. 4. The hydrogen pump was composed of a 10 mol% In-doped CaZrO3 polycrystalline ceramic supplied by the TYK Corporation. The shape was a tube closed at one end, with a 12 mm outer diameter, 8 mm inner diameter and 200 mm length. Porous platinum electrodes were applied to both the inner and outer surfaces over 50 mm from the closed end by coating with a platinum paste and subsequent sintering in air at 1123 K. Pt lead (0.4 mm diameter) wires were attached to each electrode by sintering. The electrolyte of the hydrogen pump was contained in a silica sheath and the reference gas (1% H2–Ar) was made to flow into the reference electrode chamber formed between the silica sheath and the electrolyte. The specimen, the hydrogen pump, a circulation pump and a 4-way valve were connected in series by stainless steel pipes. The diaphragm-type pump was used for circulating the gas into the working electrode chamber. The temperature of the hydrogen pump was 923 K. The hydrogen pump current was monitored using a digitalmultimeter (HP-3478A) by measuring the voltage drop across a reference resistor (996 Ω) connected in series to the external circuit. The hydrogen gas (1% H2O–H2 or 1% H2O–10% H2–Ar) was made to flow over the outside of the α-alumina tube. Porous platinum electrodes were applied to both the inner and outer surfaces of alumina specimen over 150 mm from the closed end by coating with platinum paste and subsequent sintering at 1123 K. A platinum wire (φ 0.4 mm diameter) was employed as the electrical lead. The measurements were performed in the temperature range from 1273 to 1573 K. The furnace, whose temperature was controlled by three separate heating elements, was used to keep a constant temperature over the 150 mm length. The voltage imposed on the α-alumina was changed from 0.1 V to 0.4, 0.8, and 1.2 V. The current flowing through the α-alumina was measured using a digital-multimeter (HP-3478A) by the voltage drop across a reference resistor connected in series to the external circuit. 4. Results and discussion 4.1. The steady state currents
b)
Fig. 5 shows a typical example of the measured currents passing through the specimen and the hydrogen pump. Stable currents observed when the polarization voltage was maintained at a constant value were found to change upon changing the imposed voltage. Fig. 6 shows the observed total currents in the steady state and the estimated currents of the protons passing through the specimen and hydrogen pump as a function of the voltage imposed on the α-alumina. In this experiment, the terminal potentials were kept at pH2(0) = 0.99 and pH2(L) = 1 × 10−6 and at a temperature of 1273 K. The proton current passing through α-alumina under the steady state was estimated according to the aforementioned theory as follows: IH• =
ItotalðαaluminaÞ
i
ð26Þ
ð1 + rÞ
where Itotal is the total current flowing through the α-alumina. The value, r, can be determined by the applied voltage using Eqs. (15) and
Fig. 3. Schematic view of the current changes when the applied voltage was changed from E1 to E2 (E2 N E1). The total current ( ), the current of proton ( ) and the current of hole ( ). (a) the current passing through the hydrogen pump. (b) The current passing through the specimen of α-alumina.
Table 1 The component elements in the commercial α-alumina used in this study. Element
Al2O3
MgO
SiO2
Na2O
CaO
wt.%
99.64
0.15
0.1
0.05
0.04
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Y. Okuyama et al. / Solid State Ionics 213 (2012) 92–97
Fig. 6. The currents passing through the hydrogen pump and the specimen of αalumina as a function of the applied voltage to α-alumina.
Fig. 4. Schematic layout of experimental setup.
(20). The calculated proton current based on Eq. (26) is plotted by the open circles in Fig. 6. On the other hand, the proton current passing through the hydrogen pump may be calculated from the total current by subtracting the electronic current under the Hebb–Wagner polarization condition [23,24]. In this study, the current under the Hebb–Wagner polarization condition was experimentally determined to be 0.053 mA by the measurement while lowering the temperature of the α-alumina specimen to room temperature. The evaluated proton current passing through the hydrogen pump was plotted by the closed circles in Fig. 6. As shown in the figure, the proton current passing through the hydrogen pump and that passing through the α-alumina are in good agreement with each other under a stable condition. This means that the aforementioned procedure to calculate the potential profile is valid for this experimental condition. 4.2. The maximum amount of hydrogen in α-alumina The change in the current of the hydrogen pump and α-alumina shown in Fig. 5 is obtained when the voltage applied to the α-alumina was changed from 0.1 to 0.8 V or from 0.8 to 0.1 V at 1273 K and the terminal condition, pH2(x = 0) = 0.99, pH2(x = L) = 1 × 10 −6. As shown
Fig. 5. The external currents for the hydrogen pump and the specimen of α-alumina (1273 K, pH2(x = 0) = 0.99, pH2(x = L) = 1 × 10−6).
in the figure, a gradual transient change in the external current of the hydrogen pump was observed with the change in the voltage applied to the α-alumina. This change occurs from pumping out the hydrogen released from the alumina specimen due to the change in the distribution of the hydrogen potential. The quantity of electricity, QH•i, corresponding to the amount of hydrogen desorbed from α-alumina was obtained from the hatched area under the decay curve for the −1 current of the hydrogen pump. The value, [Hi•]max.VAl , was 2 O3 determined by the quantity of electricity using Eqs. (22) and (25). The temperature dependence of [Hi•]max.V−1 Al2O3 is shown in Fig. 7. As shown in the figure, the solubility of hydrogen in the commercially supplied α-alumina determined in the present study was found to be one order of magnitude lower than that of the single crystal of the acceptor doped α-alumina reported in our previous study [11,12,25]. This phenomenon seems to be due to the fact that the concentration of the acceptor dopant in the commercially supplied α-alumina was lower than that in the single crystal grown in our laboratory. In the commercially supplied α-alumina, the impurities working as a donor dopant are also present. These donor impurities may compensate for the extra negative charge of the acceptor and significantly decrease the amount of the acceptor dopant.
Fig. 7. The solubility of proton in α-alumina.
Y. Okuyama et al. / Solid State Ionics 213 (2012) 92–97
Compared with the solubility of hydrogen in polycrystalline alumina reported by Roy and Coble [18], the value obtained in the present study was found to be three orders of magnitude lower than their value. Their experiment was performed in the temperature range from 1885 to 2089 K. The temperature dependence of the hydrogen solubility is also given in their report. Their larger value might arise from the enhancement of the solubility of the acceptor dopant from the second phase in equilibrium with the sample with the increasing temperature. On the other hand, the amount of dopant is considered to be frozen at the low level than the equilibrium value in our experimental conditions [25]. It is, therefore, reasonable that the maximum solubility of hydrogen determined in the present experiment is lower than that extrapolated from the data of Roy and Coble. Therefore, the hydrogen solubility might be independent of the temperature. 5. Conclusion Using a polarization method, the maximum solubility of hydrogen in a commercially supplied α-alumina was evaluated from the calculated potential profile change and the measurement of the corresponding amount of absorbed or desorbed hydrogen. The obtained value of the maximum solubility was (2.0 ±1.6)× 10−7 mol cm−3 and found to be independent of the temperature in the experimental range 1273–1573 K. Acknowledgment This work was partly supported by a Grant-in Aid for Science Research (19206081) from the Ministry of Education, Culture, Sports,
97
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