J. Phys. Chem. C 2007, 111, 2809-2818
2809
Absorption Kinetics of Hydrogen In Nanocrystals of BaCe0.95Yb0.05O3-δ Proton-Conducting Perovskite Santander Nieto, Ramo´ n Polanco, and Rolando Roque-Malherbe* School of Science, Turabo UniVersity, P.O. Box 3030, Gurabo, Puerto Rico, 00778-3030 ReceiVed: NoVember 8, 2006; In Final Form: December 18, 2006
Powders of BaCe0.95Yb0.05O3-δ were synthesized using the standard solid-state reaction method. The produced materials were characterized by XRD, SEM, and Raman spectrometry. The absorption kinetics of hydrogen was studied using the TA-TQ500 TGA. The XRD study established the following: the phase composition, cell parameters, and crystallite size. The SEM investigation allowed us to confirm the crystallite size. The Raman study permitted us to confirm the sample phase composition. The absorption study revealed higher absorption magnitudes than those possible if we consider that the proton can only be located in the oxide anions of the perovskite. To explain these results, we proposed that at high temperature the proton could be interstitially located in tetrahedral and octahedral sites because of the increment with temperature of electrons in the conduction band during hydrogen absorption. The enthalpy of absorption, ∆H0ab, was measured, and it was found that ∆H0ab ) 3.6 eV, a positive value in agreement with the increase with temperature of electrons in the conduction band. Besides, the chemical and self-diffusion coefficients were computed. Subsequently, were calculated the activation energy, Ea, and the pre-exponential factor, D/0, using the self-diffusion data. The values obtained were Ea ) 1.6 eV and D/0) 0.5 × 10-9 m2/s.
1. Introduction Hydrogen seems to be a potential source for satisfying the world’s energy needs. Consequently, the scientific community is, at present, all over the world, attempting to discover ways to employ this source of energy so that it can be applied in practice.1 Hydrogen is an excellent energy carrier, which during combustion does not produce greenhouse gases. Besides, hydrogen holds more chemical energy per weight than any other fuel. Finally, it can be produced from different available resources, such as natural gas, coal, biomass, and even water.1 However, hydrogen, in general, is not produced pure; so to produce pure hydrogen flows, it will be necessary to carry out its separation from mixed gas streams containing different gases, by, for example, membrane processes. Nevertheless, currently there are no viable high-temperature separation membranes capable of producing pure hydrogen flows. In this sense, protonconducting perovskites are one of the choices to develop such membranes. Consequently, the aim of the present paper is the study of hydrogen transport in BaCe0.95Yb0.05O3-δ perovskite. Besides, we will explore the hydrogen storage capacity of this perovskite at high temperature. 1.1. Perovskite Composition and Structure. The perovskite group of materials are oxides possessing similar structures, with the general formula ABO3 where A is a cation of larger size than B. Although the most numerous and, as a rule, interesting compounds with the perovskite structure are oxides, some carbides, nitrides, halides, and hydrides also crystallize in this structure.2 The extensive variety of properties that these compounds show is derived from the fact that around 90% of the metallic natural elements of the periodic table are known to be stable in a perovskite-type oxide structure2 and also from the possibility of synthesizing multicomponent perovskites by partial substitution of cations in positions A and B. * Corresponding author. E-mail:
[email protected].
In the ABO3 perovskite structure the A site can be A+, A2+, or, A3+ and the B site can be, correspondingly, occupied by B 5+, B 4+, or, B3+ metals. In the case of doped perovskites, the general formula is: A1-yA′yB1-xB′xO3-δ, where y and x are the molar fractions of dopants A′ and B′ incorporated in the A and B sites, respectively, and δ is the number of oxygen vacancies.3 The resulting materials can be insulators, semiconductors, superconductors, and ionic conductors.2 The ideal close-packed perovskite cubic structure,2 with space group Pm3m-Oh is shown in Figure 1a and b. In Figure 1a is shown the structure in which the center of the cube is occupied by the A cation.2 Alternatively, this structure can be viewed with the B cation placed in the center the cube (see Figure 1b). The perovskite structure is a superstructure with a ReO3-type framework developed by the incorporation of A cations into the BO6 octahedra.2 In the ideal structure, where the atoms are contacting one another, the B-O distance is equal to a/2, where a is the cubic unit cell parameter; likewise, the A-O distance is a/x2. Besides, the following correlation between the ionic radii holds:2 (rA + rO) ) x2(rB + rO). To measure the departure from the ideal structure, Goldschmidt4 introduced a tolerance factor, t, defined by the equation: t ) ((rA + rO))/(x2(rB+rO)), which is applicable at room temperature to the empirical ionic radii. A large number of perovskite structures has been found,2,5 which are distorted to orthorhombic, rhombohedral, or tetragonal, which can be approximated as cubic with t deviated from 1. In most cases 0.75 < t < 1. We are particularly interested in the BaCeO3 structure, which has been widely studied.5 The structure and phase transitions of BaCeO3 have been investigated by conventional X-ray diffraction, neutron diffraction, infrared spectroscopy, and Raman spectroscopy. In Table 1 are listed the phase transitions of BaCeO3 from room temperature to high temperature.5
10.1021/jp067389i CCC: $37.00 © 2007 American Chemical Society Published on Web 01/25/2007
2810 J. Phys. Chem. C, Vol. 111, No. 6, 2007
Nieto et al. fill lattice positions with oxide ions, OxO, and produce interstitial protons, H•i , according to6,24
H2O(g) + V••O + OxO f 2OH•O If only hydrogen is included in the gas stream, then it is incorporated directly into the material as protons and electrons, e-, through interaction with oxide ions in the absence of moisture according to28
(21)H + O 2
Figure 1. ABO3 cubic ideal perovskite structure; (a) the center of the cube is occupied by cation A; (b) cation B is placed in the center of the cube.
TABLE 1: Phase Transitions of BaCeO35 temperature [K]
phase
a [Å]
b [Å]
c [Å]
473 573 773 1223
orthorombic orthorombic rhombohedral cubic
8.79056 8.79532 8.84150 4.44467
6.25167 6.26224 R ) 90.1560
6.22714 6.23342
2CexCe + OxO + Me2O3 f 2Me′Ce + V••O + 2CeO2 where CexCe is a neutral (with respect to the lattice), Ce4+ cation in a lattice site, OxO is a neutral (as well with respect to the lattice), O2- anion in a lattice site, Me′Ce is the doping metal, Me3+ included in the lattice, which has a unitary negative charge with respect to the lattice, and V•• O is a twice positively charged oxygen vacancy.24,25 The introduction of protons into the perovskite is typically carried out with the help of gas streams, containing: H2O(g) or H2. Applying again the Kroger-Vink notation, it is possible to describe that the oxygen vacancies, V•• O, react with water to
f OH•O + e′
In relation with other ions, the proton is exceptional owing to its tiny dimensions and the fact that it is a bare ion without an electron cloud.23 Then the proton will effectively interact with the neighboring electron density, which will, consequently, takes in certain way, the H1s nature.23 In nonmetallic compounds, the proton strongly interacts with the valence electron density of no more than one or two nearest neighbors.23 Subsequently, the proton should be located inside the electron shell of some anion with which it is associated. Then, in oxides, the proton attains its equilibrium site profoundly implanted in the valence electron density of the oxygen.23 In metals where the conduction electrons are delocalized in the whole crystal, the H+ neighborhood is the electron density of the conduction band.23 Then, in metals the proton could have a high coordination number and could be interstitially located in tetrahedral and/or octahedral sites.29 In this sense in metals, or small band gap semiconductors, the reaction of hydrogen with the material will be29
(21)H (g) f H + e′ 2
1.2. Protons and Defects in Perovskites. Particularly in ACeO3-Based Perovskites. The introduction of defects in some perovskite structures and their distribution in the structure are key factors that determine the protonic conductivity of these materials.6,7 In relation with proton transport in perovskites, Iwahara and collaborators8,9 were the first to investigate protonic conductivity in SrCeO3 and BaCeO3 doped with trivalent cations such as Y, Yb, Gd, and Eu. These researchers identified these materials as good high-temperature proton conductors. Thereafter, the corresponding application in solid oxide fuel cells (SOFCs) and other applications were proposed, and extensive research has been carried out in this field.10-26 The inclusion of trivalent dopants, in an ACeO3 perovskite, ideally take place as described in the Kroger-Vink notation27 by25
x O
• i
where H•i ′ is an interstitial proton and e′ is a conduction electron. 1.3. Hydrogen Absorption and Proton Transport in Perovskites. In a perovskite, during hydrogen absorption, the molecule is first dissociated in the surface of the oxide. Then, the adsorbed hydrogen atoms are ionized and incorporated directly into the material as protons and electrons, e-, through interaction with the oxide ions and also, as will be explained later, by another mechanism that is interstitially located in tetrahedral and octahedral sites. Two fundamental types of proton transport mechanism in oxides are recognized: explicitly, the free migration and the vehicle mechanisms.23 Concretely, during the first mechanism, that is, the free migration mechanism, the charge carrier, specifically, the proton, moves by cation hopping or jumping between immobile host oxygen ions. Alternatively, the second mechanism, the vehicle mechanism,23,29 entails the movement of the proton as a passenger on a larger ion like OHor H3O+. The main proton conduction mechanism in oxides entails proton transfer between adjacent OH- and O2- and OH reorientation, that is, the Grotthuss mechanism, rather than OH diffusion as sometimes have been stressed.23 In particular, proton conduction in perovskites occurs by proton migration through free proton migration (Grotthuss mechanism).23,28,29 That is, the proton diffuses by way of molecular orientation and proton displacement or cation (proton) hopping.
Absorption Kinetics of Hydrogen Quantum molecular dynamic simulation studies30-33 of proton conduction in BaCeO3, BaZrO3, LaAlO3, LaMnO3, and CaZrO3 indicated that the proton locally relaxes the lattice to allow the transitory arrangement of hydrogen bonds and after that the proton transfer between adjacent oxygen ions.30,33 The calculated energy difference between the ground state and the barrier state is less than 0.2 eV for most of the perovskites that are studied, which is much less than the experimentally observed activation energy (Ea) in ABO3 perovskites.33 Nevertheless, additional investigation discloses the fact that the energy necessary for the neighboring oxygen ions to obtain an equivalent lattice surroundings to go into the barrier state is of the same amount of the activation energy.33 Explicitly, there is a transitional state between the ground and barrier states; consequently, the relaxation step is a main contribution to the proton conductivity activation energy.33 In the case of BaCeO3, the quantum molecular dynamics calculations34,35 suggested that the degree of covalence between B site cations and oxygen anions and the degree of hydrogen bonding within the lattice are responsible for proton transport. Proton conductivity in BaCeO3 involves O-Ce-O bending and rapid rotation of the OH- around the Ce-OH bond.34 The simulation discloses a rapid rotation of the proton around the oxygen positions, whereas proton transfer between neighboring oxygen, which is assisted by extended oxygen vibrations, is a relatively rare event.23 1.4. Band Structure of Perovskites. The electronic structures of proton-conducting perovskites have been investigated using photoemission spectroscopy (PES) and X-ray absorption spectroscopy (XAS).35-37 For various proton conductors, such as CaZrO3, SrTiO3, and SrCeO3, the Fermi levels (EF) of dryannealed proton conductors are located in the band gap, at the valence band side.37 Moreover, in H2-annealed conductors, the position of EF is higher than that in dry-annealed proton conductors.37 In dry-annealed proton conductors, it has been found that the hole state and acceptor-induced level are located at the top of the valence band and just above EF , respectively.37 The intensities of hole state and acceptor-induced level decrease and the hydrogen-induced level is created at just below EF in H2-annealed conductors.37 These findings are the effect of the hydrogen doping of the electronic structure expected from the rigid band model.37 Similar phenomena might be expected in BaCeO3doped perovskites. Thus, in BaCe0.9Y0.1O3-δ dry annealed and H2-annealed the Fermi level (EF) is in the band gap region as expected from rigid band model, as was reported previously in the cases of CaZrO3, SrTiO3, and SrCeO3.37 The valence band (VB) of BaCe0.9Y0.1O3-δ is composed of the O 2p states hybridized with Ce 4f states. The band gap between the valence and conduction bands is approximately 5 eV.37 The EF of BaCe0.9Y0.1O3-δ dry annealed is located at approximately 0.6 eV above the top of the VB, and in the case of BaCe0.9Y0.1O3-δ H2-annealed the EF shifts to the conduction band by 0.4 eV; that is, it is located higher on the energy scale.37 This fact indicates the introduction of electrons during the H2 incorporation into the perovskite. In air-annealed37 BaCe0.9Y0.1 O3-δ, the holes and acceptor level are observed at the top of the valence band and just above EF , respectively. In H2annealed37 BaCe0.9Y0.1O3-δ, the hole states are absent and the intensities of acceptor and Ce 4f defect-induced level decrease, indicating that the doped hydrogen exchanges with the hole at the top of the valence band; besides, a new hydrogen-induced level is introduced just below EF.
J. Phys. Chem. C, Vol. 111, No. 6, 2007 2811 1.5. Proton Diffusion in Oxides. The self-diffusion coefficient for protons can be described as an Arrhenius expression38
(
D ) D0 exp -
)
∆Hm RT
where
D0 )
( ) (
)
∆Sm zNl2ν exp 6 R
in which z is the number of possible jump directions, N is the fraction of vacant jump destinations, l is the jump distance, ν is the vibration frequency, and ∆Sm is the jump entropy. Besides, Ea ) ∆Hm is the activation energy for proton migration. It can be supposed39,40 that proton jumps merely in one direction, z ) 1, and over a distance identical to the oxygenoxygen separation in the oxide, usually 3 Å. Besides, N ) 1, for low proton concentrations, the vibration frequency νo ) 1014 s-1 from IR measurements, while exp(-(∆Sm)/(R)) ≈ 10. These figures gives the following value for the pre-exponential factor, Do ) 1.5 × 10-5 m2/s. However, real values may differ because of complex migration routes.40 For instance, the pre-exponential values for proton diffusion in rutile-, TiO2-, and Yb-doped SrCeO3 were found to be lower to the calculated value of 10-5 m2/s, by 2 orders of magnitude.40 It was then suggested that only a fraction of protons take part in the conduction process.41 Previously, we have given the expression for the calculation of the self-diffusion coefficient. However, the diffusion in concentration gradients is described with the chemical diffusion coefficient.42 The driving force for chemical diffusion, in oxides, is the gradient of the electrochemical potential, ηi
ηi ) µi + zi FΦ where µi is the chemical potential, zi is the charge number of the charge carrier, Φ is the electric potential, and F is the Faraday constant. The diffusion flux is subsequently given by
Ji ) -Lii ∇(µi + zi FΦ) where Lii is the Onsager transport coefficient.42 In the case of hydrogen diffusion in an oxide to preserve local electrical neutrality during diffusion, we will have
J H + Je ) 0 where JH is the proton flux and Je is the electron flux. Then, the proton flux could be written through the ambipolar diffusion equation43
JH ) -LHHtel
( )
∂µH ∇CH ) -D ˜ H∇CH ∂CH
which defines the chemical diffusion coefficient, D ˜ H, in which LHH is the Onsager transport coefficient, tel is the electronic transference number, µH is the chemical potential, and CH is the proton concentration.42 Now, using the Einstein relation LHH ) D/H(CH)/(RT) and making use of µH ) µ0H + RT ln aH, it could be obtained that the chemical diffusion coefficient is given by42
D ˜ H ) D/Htel
∂ ln aH ∂ ln CH
2812 J. Phys. Chem. C, Vol. 111, No. 6, 2007 where D/H is the proton self-diffusion coefficient and aH is the proton activity. 2. Experimental Section 2.1. Materials. The source materials for the perovskite synthesis by the solid-state reaction method were the following: BaCO3 (Fisher, 99.9%), CeO2 (Acros Organics, 99.9%), and Yb2O3 (Acros Organics, 99%) powders. The gases used in the absorption study were pure N2 (99.99% purity) provided by Praxair and a mixture of 4 wt % H2 + 96 wt % N2 prepared by Praxair using pure gases (99.99% purity). 2.2. Perovskite Synthesis. Polycrystalline powders samples of composition BaCe0.95Yb0.05O3-δ were synthesized using the conventional solid-state reaction method. This methodology is a relatively simple procedure, which has been widely applied for the production of perovskite powders,3,7,24,44 normally giving positive results. The raw materials for the synthesis of BaCe0.95Yb0.05O3-δ with the solid-state reaction methodology were BaCO3, CeO2, and Yb2O3 powders. The appropriate molar amount for the selected composition was calculated using basic molar concentrations. Then, the raw materials were weighed, and after that, ball milled with isopropanol for 48 h. This process was followed by a drying treatment at 373 K for 10 h, calcination at 773 K for 5 h, and sintering at 1573 K for 15 h. In all cases, the rates of heating and cooling were 2 K/min. The perovskite production reaction is
BaCO3 + (0.95)CeO2 + (0.025)Yb2O3 f BaCe0.95Yb0.05O3-δ + CO2v 2.3. Characterization Methods. The X-ray diffractograms were obtained in a Siemens D5000 X-ray Diffractometer in vertical setup: θ-2θ geometry in the range 150 < 2θ < 750 with a Cu KR radiation source, Ni filter, and graphite monochromator. The phase composition, crystal system, and cell parameters of the synthesized perovskite were determined using the obtained XRD diffraction pattern. The XRD method was also used for the measurement of the crystallite size of the synthesized powder applying the Scherrer-Williamson-Hall methodology.45,46 The selected diffraction peaks were scanned at a slow scanning speed of 0.6 °min-1. From the recorded XRD pattern, the accurate peak position, integrated intensities, as well as the full-width at half-maximum (FWHM) (β) of each slow scanned diffraction peaks were estimated by fitting them with Pearson VII amplitude function. The fitting process was carried out with the peak separation and analysis software PeakFit (Seasolve Software Inc., Framingham, MA) based on a least-square procedure.47 These values were used to calculate the crystallite size and lattice strain of the synthesized powder using the Williamson-Hall equation.45 The SEM study was carried out with a JEOL CF 35 microscope in secondary electron mode at an accelerating voltage of 25 kV to image the surface of the perovskite powders. The sample grains were adhered to the sample holder with an adhesive tape and then coated at vacuum by cathode sputtering with a 30-40 nm gold film prior to observation. The surface morphology was revealed from SEM images, and the average grain size was estimated, albeit qualitative. Raman measurements were performed using a Jobin-Yvon T64000 spectrophotometer consisting of a double premonochromator coupled to a third monochromator/spectrograph with 1800 grooves/mm grating.48 The 514.5 nm radiation of an Ar+
Nieto et al. laser was focused in a less than 2-µm-diameter circle area by using a Raman microprobe with an 80X objective. The same microscope was used to collect the signal in backscattering geometry and to focus it at the entrance of the premonochromator.48 The scattered light dispersed by the spectrophotometer was detected by a charge coupled device detection system. 2.4. Absorption Kinetics Measurement. The amount of hydrogen uptake in proton-conducting perovskites has frequently been measured with thermogravimetric analyzers.7 However, in certain instances thermogravimetric methods are inappropriate, given that the possibility of hydrogen reduction exists and consequently weight change owing to oxygen loss.7 In our case, the metals included in the perovskite, that is, Ba, Ce, and Yb, have particularly negative reduction potentials and consequently are hardly reduced by hydrogen.49 In fact, we did not note any weight decrease owing to oxygen loss during our experiments. Therefore, the absorption kinetics of hydrogen in nanocrystals of the BaCe0.95 Yb0.05O3-δ proton-conducting perovskite was studied with the help of a TQ500 thermogravimetric analyzer (TGA) produced by TA Instruments. Prior to the measurement of the diffusion coefficient and the equilibrium absorption magnitude, the tested samples were carefully degassed at 1273 K during 6 h in a flow of the pure purge gas, that is N2. After degassing, the sample is set at the desired experimental temperature in a flow of the pure purge gas and after that kept at this temperature. Subsequently, the flowing gas is changed to a mixture of 4 wt % H2 + 96 wt % N2. The data collection, the temperature control, the programmed heating rate, which was always 5 K/min, and the gas switching, was automatically controlled by the software of the TA, TQ500 TGA. The TGA data was collected as a Mt (mg) versus t (s) plot where Mt is the mass of hydrogen absorbed at time t. With the help of the Mt versus t plot, the chemical diffusion coefficient will be evaluated using a solution of Fick’s second law for a geometry appropriate for the experimental setup.50 For the spherical geometry, which is the crystal geometry that we are considering here,51 and the appropriate, for the experimental setup, boundary and initial conditions, the solution of the Fick’s second law is50
{ ( ) ( )} ( ) ( )∑
βa2 D ˜ )1-3 exp(-βt) 1 M∞ D ˜ βa2 Mt
6βa2
∞
D ˜ π2
1
1/2
βa2
1/2
( ) cot
exp
[
+
D ˜
-D ˜ n2π2t a2
n2 (n2π2) -
( )] βa2
(1)
D ˜
where Mt is the mass absorbed at time t, M∞ is the mass absorbed at equilibrium, and D ˜ is the chemical diffusion coefficient in the case of the single component diffusion of hydrogen. In addition, r ) a is the radius of the perovskite crystallite and β is a time constant that describes the evolution of the absortive partial pressure in the dead space of the TGA furnace; that is,50,51 P ) P0[1 - exp(-βt)], where, P0 is the steady-state partial pressure and P is the partial pressure at time t. Consequently, the initial nonstationary partial pressure of the sorbate in the gas stream is accounted for with the help of the parameter β. Cutting the series in eq 1, and using only the first four terms, an approximation to the solution of Fick’s diffusion equation is obtained, which is numerically fitted to experimental data.51,52 Then, for each experiment the numerical values of the chemical
Absorption Kinetics of Hydrogen
J. Phys. Chem. C, Vol. 111, No. 6, 2007 2813
Figure 2. XRD powder diffraction pattern of the BaCe0.95Yb0.05O3-δ perovskite.
diffusion coefficient, D ˜ , are calculated with the help of a nonlinear regression method.51 The fitting process was carried out with the peak separation and analysis software PeakFit program based on a least-square procedure,47 which allows one to calculate the best fitting parameters, that is, the numerical values of the relation between the chemical diffusion coefficient and the square of the particle radius, D ˜ /a2, the equilibrium absorption mass, M∞, the parameter β, the regression coefficient, and the standard errors.51,52 3. Results and Discussion 3.1. X-ray Diffraction (XRD), Scanning Electron Microscopy (SEM), and Raman Spectrometry Study of the BaCe0.95Yb0.05O3-δ Perovskite Powder. In Figure 2 is shown the XRD diffraction pattern of the synthesized perovskite. It is evident, by comparing the obtained pattern with the powder diffraction data contained in the International Center for Diffraction Data, Powder Diffraction File database, and as well with literature data,3,24 that a highly crystalline perovskite was obtained. Additionally, no other crystalline phases were detected. In addition, with the help of the measured interplanar distances corresponding to Miller indexes (110), (200), and (213), and applying the equation relating the interplanar distance between adjacent planes (dhkl) in the set of planes (hkl) with the a, b, and c parameters of the orthorombic cell46
h2 k2 l2 1 ) + + d2hkl a2 b2 c2 is created a system of three linear equations with three unknowns, that is, the cell parameters. Then, solving this system were calculated the cell parameters of the room-temperature orthorombic phase. The calculated cell parameters were a ) (8.796 ( 0.001) Å, b ) (6.231 ( 0.001) Å, and c ) (6.215 ( 0.001) Å, in good agreement with literature data.3,5 The crystallite size of the BaCe0.95Yb0.05O3-δ perovskite powder was calculated following the method explained previ-
ously, that is, the Scherrer-Williamson-Hall methodology.45,46 The calculated radius of the perovskite crystallite, considered as spherical particles was
d a ) ) 71 ( 1 nm 2 The average grain size was estimated, albeit qualitative, with the help of the reported SEM micrographs (Figure 3). The estimated value of the crystallite size, as can be observed in Figure 3a and b, corroborates the results obtained with the help of the Scherrer-Williamson-Hall methodology.45,46 The calculated crystal radius was used for the computation of the chemical diffusion coefficient with the help of eq 1 because the parameter determined during the fitting process is A1 ) D ˜ /a2; consequently, D ˜ ) A1a2. Raman spectroscopy is a sensitive tool to analyze the composition of a tested material through the symmetry-allowed phonon modes.53 The room-temperature micro-Raman spectrum of the BaCe0.95Yb0.05O3-x powder is shown in Figure 4. The spectra show the most intense bands in the frequency range of 300-400 cm-1. The low-frequency region (35-140 cm-1) of the spectrum is dominated by a relatively intense envelop of peak at 35-140 cm-1. These peaks could be assigned in accordance with the orthorhombic factor group analysis, assigning these bands to stretching vibrational and bending vibrational modes of the CeO6 octahedra, corresponding to the BaCe0.95Yb0.05O3-x perovskite Raman spectrum.54,55 Thus, our micro-Raman results are in good agreement with the X-ray data, confirming the perovskite structure phase at room temperature. Besides, impurity phases were not detected. 3.2. Absorption of H2 in BaCe0.95Yb0.05O3-δ. As was formerly affirmed, in a perovskite, during hydrogen absorption, the molecule is first dissociated in the surface of the oxide. Subsequently, the adsorbed hydrogen atoms are ionized and incorporated directly into the material as protons and electrons, e-, through interaction with the oxide ions, and, as will be explained later, by another mechanism, that is, interstitially
2814 J. Phys. Chem. C, Vol. 111, No. 6, 2007
Nieto et al.
Figure 4. Raman spectrum at 300 K of the BaCe0.95Yb0.05O3-δ perovskite.
maximum value, C0H. Consequently, the relation between the hydrogen concentration and the pressure of hydrogen in the gas phase will be given by a Langmuir-type absorption isotherm equation57
CH )
Figure 3. SEM micrographs of a powder of the BaCe0.95Yb0.05O3-δ perovskite (a) 2000× and (b) 10 000×.
located in tetrahedral and octahedral sites. Besides, because the proton will interact with the neighboring electron density, it will consequently take, in certain way, the form an hydrogen atom.23 Therefore, it is possible to consider that a neutral dissociation of hydrogen occurs as follows
(21)H (g) f H + e′ = H • i
2
that is56
(21)H (gas) f H(solid solution) 2
The equilibrium constant for this reaction is56
KH )
CH
xPH
(2) 2
which is equivalent to Sievert’s law, where CH is the hydrogen concentration in the perovskite, which is equivalent to the proton concentration CH+, and PH2 is the pressure of hydrogen in the gas phase. However, in our case the number of sites for hydrogen absorption in the perovskite is limited. Therefore, the hydrogen concentration in the perovskite is restricted to a
C0HKxPH2 1 + KxPH2
(3)
because we are assuming that in our system the absorption process occurs in a finite number of immobile sites.57-59 In this case it is possible to show that it is a Langmuir-type absorption isotherm59 because one of the conditions for Langmuir-type absorption, or adsorption, is the existence of a fixed number, N, of absorption immobile sites, or adsorption, immobile sites, in the case of a surface.57-59 In our case, we have a volume filling and not a surface recovery; however, the final result is a Langmuir-type absorption isotherm,59 that is, eq 3, where it is, also, considered the dissociation of the hydrogen molecule.57 In Table 2 and Figure 5 we reported the absorption magnitude (Am, in wt %) at different temperatures, where Am ) M∞/Sw, M∞ is the hydrogen mass absorbed at equilibrium, and Sw is the initial perovskite sample weight included in the TGA ceramic sample holder. The numerical value of M∞ was calculated with the help of eq 1 using the Mt (mg) versus t (s) data collected with the TGA, where Mt is the mass of hydrogen absorbed at time t (see Figure 6). The relative error for Am, calculated with the values of the standard error of M∞, computed with the nonlinear regression methodology,47,51 was around 25%. In the case of the test at 1073 K, the absorption was so small that the reported values are only estimations. Currently, as was stated previously, it is accepted that hydrogen absorption into a perovskite is carried out through the proton interaction with oxide ions according to28 (1/2)H2 + OxO f OH•O + e′. Then, the proton-conducting perovskite BaCe0.95Yb0.05O3-δ, following the previously explained mechanism, can accommodate, on average, about 2.95 protons per cell in the ideal perovskite crystal lattice because 2.95 oxide ions are included in the perovskite cell (see Figure 1b). Consequently, because the perovskite cell has 1 Ba, 0.95 Ce,
Absorption Kinetics of Hydrogen
J. Phys. Chem. C, Vol. 111, No. 6, 2007 2815
TABLE 2: Experimental Values of the Mass Absorbed at Equilibrium (M∞), the Absorption Magnitude (Am ) M∞/Sw × 100) of H2 in BaCe0.95Yb0.05O3-δ at Different Temperatures, and the Sample Weight of the Tested Samples (Sw) T [K]
1273
1223
1173
1123
1073
M∞ [mg] Am [wt %]
0.52 ( 0.09 4.3 ( 0.7
0.14 ( 0.03 1.3 ( 0.3
0.16 ( 0.04 1.2 ( 0.3
0.005 ( 0.001 0.06 ( 0.01
0.001 ( 0.001 0.01 ( 0.01
12.131
10.674
13.304
8.208
10.960
Sw [mg]
0.05 Yb and 2.95 O, the maximum amount of hydrogen that can be absorbed in this perovskite is, in atomic wt % of H
Nm A )
2.97 × 100 ) 0.00903 × 100 ) 0.9 wt %H 329.27
Because the atomic weights of Ba, Ce, O, and H, in atomic mass units (amu) per atom, are Ba ) 137.34, Ce ) 140.12, Yb ) 173.04, O ) 15.999, and H ) 1.008, the molecular weight of the perovskite in this case is 329.27 amu per cell. However, in Table 2 are reported experimental results that indicate higher absorption magnitudes. As was stated previously, in metals the conduction electrons are delocalized in the whole crystal, and consequently the H+ neighborhood is the electron density of the conduction band.23,29 Then, hydrogen in metals and small band gap semiconductors exists as a screened proton.56 As a result, it is possible that the proton could have a high coordination number and could be interstitially located in tetrahedral and/or octahedral sites.29 Consequently, in order to explain our results, that is, the high absorption magnitudes measured, we will advance the following hypothesis: at high enough temperature, as is our case here, the proton could have a high coordination number and could be interstitially located in tetrahedral and octahedral sites. Therefore, the reaction of hydrogen with the perovskite will be given by (1/2)H2(g) f H•i + e′ = Hi for the absorption in interstitial sites and (1/2)H2 + OxO f OH•O + e′ = HO, in the case of interaction with the oxide anions. For that reason, notwithstanding the fact that currently the accepted paradigm is that the proton needs an oxygen to exist inside a perovskite,23,28,29 in order to explain our results we need to accept the previously stated hypothesis. To validate our hypothesis, we can use the existing knowledge in relation with the band structure of BaCe0.9Y0.1O3-δ perovskite H2-annealed.37 For these materials, as was stated previously, the Fermi level (EF) is in the band gap region.37 The band gap is approximately 5 eV.37 Besides, the EF is located approximately 1 eV above the top of the valence band, that is, shifted to the conduction band.37 All of these facts indicate the introduction of electrons during the H2 incorporation into the perovskite. In addition, in H2-annealed37 BaCe0.9Y0.1O3-δ, the hole states are absent and the intensities of acceptor and Ce 4f defect-induced level decrease, indicating that the doped hydrogen exchanges with the hole at the top of the valence band. Besides, a new hydrogen-induced level is introduced just below EF. In our case, we have introduced more hydrogen than those incorporated in the previously referred paper (ref 37). Therefore, more electrons were introduced during the H2 incorporation into the perovskite. Consequently, we can conclude that the studied material at 1023-1273 K behaves as a small band gap semiconductor because of the increment with temperature of electrons in the conduction band,60 due to the shifting to the conduction band of the Fermi level and the hydrogen-induced level. Then, there will be enough electrons in the conduction band to screen the proton and allow it to have a high coordination number and be interstitially located in the tetrahedral and octahedral sites.
Subsequently, the results reported in Table 2 could be explained if we include, besides the three oxygens, all of the sites in the ideal perovskite structure as possible absorption sites for hydrogen (Figure 1b). That is, if we incorporate, besides the three oxygens, the eight tetrahedal sites and three of the four octahedral sites because one octahedral site is occupied by Ce, that is, atom B. We will then have a maximum of 13.95 hydrogen sites in the perovskite. Because the molecular weight of the synthesized perovskite is 326.296 and the maximum weight of the hydrogen absorbed is 14.112, the weight of the perovskite plus absorbed hydrogen is 340.408, which in weight percent is
Nm A )
14.112 × 100 ) 0.0415 × 100 ) 4.15 wt % 340.408
The above-stated hypothesis is also supported by the existence of a high positive enthalpy of absorption, ∆H0ab, in the studied material (see Table 2 and Figure 5), which is consistent with the increment with temperature of electrons in the conduction band.60 The value measured for the enthalpy of absorption, ∆ H0ab, for this material using the following expression (see Figure 5)
Am ) A0me
-∆H0ab
(4)
kT
in linear form, that is
ln Am ) ln A0m -
∆H0ab 1 k T
()
(4a)
was ∆H0ab ) (3.6 ( 0.5) eV, and the linear regression coefficient was r 2 ) 0.93. It is necessary at this point to affirm that positive values for the enthalpy of absorption are possible in metals61 and oxides.28 The justification of eq 4 is simple. It is based on the equilibrium reaction (1/2)H2(gas) f H(solid solution), whose equilibrium constant is56,57
K0H
)e
-∆G0ab kT
where ∆G0ab is the standard Gibbs energy change during the absorption process. Therefore, because ∆G0ab ) ∆H0ab - T∆S0ab, eq 4 results from eqs 2 and 4b, where the pre-exponential factor, A0m, includes the square root of the hydrogen pressure, which is constant, together with the entropic factor and a constant for dimensional consistency. It is necessary now to acknowledge that eq 4a allows us to get an approximate value of the enthalpy of absorption, ∆H0ab, because the equilibrium is really described by the Langmuir-type absorption isotherm. In Figure 6 are reported the absorption kinetic data of hydrogen in BaCe0.95Yb0.05O3-δ at 1123 K (Figure 6a), 1173 K (Figure 6b), 1223 K (Figure 6c), and 1273 K (Figure 6d). In Table 3 are reported the chemical diffusion coefficients (D ˜ ) for hydrogen diffusion in BaCe0.95Yb0.05O3-δ at different temperatures and the sample coverage or fractional saturation of the
2816 J. Phys. Chem. C, Vol. 111, No. 6, 2007
Nieto et al.
Figure 5. Plot of ln Am vs (1/T × 104) for the calculation of the enthalpy of absorption.
Figure 7. Plot of ln(D/H × 1018) vs (1/T × 104) for the calculation of the activation energy and the pre-exponential factor.
TABLE 4: Self-Diffusion Coefficient (D/H) for the Hydrogen Diffusion in BaCe0.95Yb0.05O3-δ at Different Temperatures T [K]
D/H × 1018 [m2/s]
1273 1223 1173 1123 1072
7(4 6(3 3(2 1 ( 0.9
With eq 1, which is a solution of the Fick’s second law, as was stated previously, it was measured the chemical diffusion coefficient. However, to calculate the activation energy of the proton transport process we need to calculate the self-diffusion coefficient. Then, the obtained chemical diffusion coefficient, D ˜ H, must be corrected in order to obtain the self-diffusion coefficients, D/H, with the help of the following equation:42
D ˜ H ) D/Htel
∂ ln aH ∂ ln CH
If we apply for the calculation of the self-diffusion coefficient the Barrer and Jost model,62 which is valid for a Langmuir system where the probability of a successful jump is proportional to the number of vacant sites,63 then Figure 6. Absorption kinetic of hydrogen in BaCe0.95Yb0.05O3-δ at (a) 1123, (b) 1173, (c) 1223, and (d) 1273 K.
TABLE 3: Chemical Diffusion Coefficient (D ˜ ) and Sample Coverage (θ ) Am/Nm A ) for Hydrogen Diffusion in the BaCe0.95Yb0.05O3-δ Perovskite at Different Temperatures T [K]
˜D × 1018 [m2/s]
θ ) Am/Nm A
1273 1223 1173 1123 1072
26 ( 10 8(3 7(3 2(1 1(1
1.000 0.316 0.289 0.015 0.002
perovskite, θ ) Am/Nm A , where Am is the amount absorbed and Nm is the maximum amount absorbed. A The chemical diffusion and absorption parameters were calculated with the help of the fitting of eq 1 with the obtained experimental data51,52 (see Table 3). The regression coefficient, r 2, for the nonlinear regression fitting process47 calculated by the Peakfit software was r 2 ) 0.97 ( 0.01. The relative error for D ˜ , calculated with the values of the standard error of A1 ) D ˜ /a2 computed with the help of the nonlinear regression methodology,47,51 was around 35% including the error in the determination of the particle size. In the case of the test at 1073 K, the absorption was so small that the reported values are only estimations.
D/H ≈
D ˜ H(1 - θ) 2tel
(5)
in which θ ) Am/Nm A is the fractional saturation of the perovskite. In Table 4 are reported the self-diffusion coefficients, D/H, for hydrogen diffusion in BaCe0.95Yb0.05O3-δ at different temperatures. To calculate D/H, it was necessary to make use of the values of the electronic transference number, reported in literature for mixed proton-electronic conductors, in general,64 and in particular for the open circuit permeation of hydrogen in a SrCe0.95Yb0.05O3-δ perovskite,26 that is, a material very similar to the perovskite studied here. The values for tel reported26 allows us to affirm that tel ) 0.4 ( 0.2. Subsequently, the equation59,63
( )
D/H ) D/0 exp -
Ea RT
in linear form, that is, ln D/H ) ln D/0 - Ea/k(1/T), was used for the calculation of the activation energy, Ea, and the preexponential factor, D/0. To calculate these parameters, in Figure 7 is plotted ln(D/H × 1018) versus 1/T × 104. The diffusional activation energy and the pre-exponential factor were
Absorption Kinetics of Hydrogen calculated, where Ea ) (1.6 ( 0.4) eV, D/0) (0.5 ( 0.2) × 10-9 m2/s, and the linear regression coefficient was r 2 ) 0.93. Proton migration, in perovskites, has activation energies ranging from below 0.5 to 2 eV.28 Besides, as was stated previously,38 D/0 ) (zNνl2/6) exp(-∆Sm/R), which gives the estimated value of D/0 ) 1.5 × 10-5 m2/s; however, experimentally measured values are lower,40 as is our case here. Finally, it is necessary to clarify now that in the previous calculation the experimental result for the self-diffusion coefficient at 1273 K was excluded. At this temperature, the hydrogen concentration in the perovskite is very high and the approximate expression for the calculation of the self-diffusion coefficient, that is, eq 5, is not applicable. 4. Conclusions Powders of composition BaCe0.95Yb0.05O3-δ were synthesized using the standard solid-state reaction method. The produced materials were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), and Raman spectrometry. The absorption kinetics of hydrogen in the nanocrystals of the BaCe0.95 Yb0.05O3-δ was studied using the TQ500 thermogravimetric analyzer (TGA) produced by TA Instruments. The phase composition, cell parameters, and crystallite size were established with the help of the XRD study. The SEM investigation allowed us to confirm the crystallite size. The Raman analysis of the sample at room temperature confirmed the XRD data about the phase composition of the sample. In addition, the absorption study reveals higher absorption magnitudes than those possible if we consider that the proton can only be located in the oxide anions of the perovskite. Consequently, to explain these results we proposed the hypothesis that at high enough temperature the proton could have a high coordination number and could be interstitially located in tetrahedral and/or octahedral sites. Because, at high temperatures and during hydrogen absorption, there will be sufficient electrons in the conduction band to screen the proton and permit it to have a high coordination number and be interstitially located in the tetrahedral and octahedral sites. To support this hypothesis, we used the existing knowledge in relation with the band structure of BaCe0.9Y0.1O3-δ perovskite H2-annealed and concluded that the introduction of electrons during the H2 incorporation into the perovskite at 1023-1273 K provokes that this perovskite behaves as a small band gap semiconductor because of the increment with temperature of electrons in the conduction band, due to the shifting to the conduction band of the Fermi level and the hydrogen-induced level. Then, there will be enough electrons in the conduction band to screen the proton. The enthalpy of absorption for this material was measured. The magnitude found was ∆Hab ) 3.6 eV, a positive value in concordance with the increment of the temperature of electrons in the conduction band. The chemical diffusion coefficient was calculated by fitting a solution of Fick’s second equation to our experimental kinetic data. Nevertheless, to calculate the activation energy of the proton transport process we need to calculate the self-diffusion coefficient. Then, the obtained chemical diffusion coefficient, D ˜ H, was corrected in order to obtain the self-diffusion coefficients, D/H, with the help of the equation obtained using the Barrer-Jost model. Furthermore, to calculate D/H it was necessary to make use of the values of the electronic transference number reported in literature for mixed proton-electronic conductors. Afterward, the activation energy, Ea, and the preexponential factor, D/0, were calculated and the values obtained
J. Phys. Chem. C, Vol. 111, No. 6, 2007 2817 were Ea ) 1.6 eV and D/0) 0.5 × 10-9 m2/s, which are in agreement with literature data. Acknowledgment. We gratefully recognize the financial support provided by the Department of Energy through the Massey Chair project at Turabo University. We also acknowledge the support given by Dr. Roberto Loran, Mr. Will Gomez, and the undergraduate students Miss Karla Algorri and Miss Tayri Mele´ndez. In addition, we gratefully appreciate the help provided by Dr. Edgard Resto, from the Materials Characterization Center of the UPR-Rio Piedras Campus, for the kind consent to use the XRD equipment. We also recognize the assistance given by Mr. Edgar Mosquera Vargas in the SEM study, Dr. Ram S. Katiyar for the authorization to use the Raman facility, and Mr. William Perez for the technical assistance provided in the operation of the Raman equipment. Finally, we acknowledge the help offered by Dr. Abel Gaspar-Rosas, from TA Instruments, for all of the very helpful information supplied. References and Notes (1) Crabtree, G. W.; Dresselhaus, M. S.; Buchanan, M. V. Phys. Today 2004, 57, 39. (2) Pen˜a, M. A.; Fierro, J. L. G. Chem. ReV. 2001, 101, 1981. (3) Wu, J. Ph.D. Dissertation, California Institute of Technology, Pasadena, CA, 2005. (4) Goldschmidt, V. M. Skr. Nor. Viedenk.-Akad., Kl. I: Mater.Naturvidensk. Kl., 1926; No. 8. (5) Knight, K. S. Solid State Ionics 1994, 74, 109. (6) Haile, S. M. Acta Mater. 2003, 51, 5981. (7) Jones, C. Y.; Wu, J.; Li, L.-P; Haile, S. M. J. Appl. Phys. 2005, 97, 114908. (8) Iwahara, H.; Uchida, H.; Morimoto, K. J. Electrochem. Soc. 1990, 137, 462. (9) Iwahara, H.; Uchida, K.; Ogaki, K. J. Electrochem. Soc. 1988, 135, 529. (10) Kreuer, K. D. Solid State Ionics 1997, 97, 1. (11) Bonanos, N.; Ellis, B.; Knight, K. S.; Mahmood, M. N. Solid State Ionics 1989, 35, 179. (12) Bonanos, N. Solid State Ionics 1992, 967, 53-56. (13) Bonanos, N. J. Phys. Chem. Solids 1993, 54, 867. (14) Iwahara, H.; Uchida, H.; Morimoto, K. J. Electrochem. Soc. 1990, 137, 462. (15) Shima, D.; Haile, S. Solid State Ionics 1997, 97, 443. (16) Yajima, T.; Iwahara, H. Solid State Ionics 1992, 50, 281. (17) Liang, K.; Nowick, A. Solid State Ionics 1993, 61, 77. (18) Norby, T. Solid State Ionics 1990, 40-41, 857. (19) Bonanos, N.; Knight, K.; Ellis, B. Solid State Ionics 1995, 79, 161. (20) Rao, C. N. R.; Gopalakrishnan, J.; Vidyasagar, K. Indian J. Chem., Sect. A: Inorg., Bioinorg., Phys., Theor. Anal. Chem. 1984, 23, 265. (21) Smyth, D. M. Annu. ReV. Mater. Sci. 1985, 15, 329. (22) Smyth, D. M. In Properties and Applications of PeroVskite-Type Oxides; Tejuca, L., Fierro, J. L. G., Eds.; Marcel Dekker: New York, 1993; p 47. (23) Kreuer, K.-D. Chem. Mater. 1996, 8, 610. (24) Wu, J.; Li, L. P.; Espinosa, W. T. P.; Haile, S. M. J. Mater. Res. 2004, 19, 2366. (25) Wu, J.; Davies, R. A.; Islam, M. S.; Haile, S. M. Chem. Mater. 2005, 17, 846. (26) Li, L.; Li, A.; Iglesia, E. Stud. Surf. Sci. Catal. 2001, 136, 357. (27) Kroger, F.; Vink, V. Solid State Phys. 1956, 3, 307. (28) Norby, T.; Wideroe, M.; Glo¨ckner, R.; Larring, Y. Dalton Trans. 2004, 3012. (29) Oesten, R.; Higgins, R. A. Ionics 1995, 1, 427. (30) Islam, M. S. J. Mater. Chem. 2000, 10, 1027. (31) Davies, R. A.; Islam, M. S.; Gale, J. D. Solid State Ionics 1999, 126, 323. (32) Davies, R. A.; Islam, M. S.; Chadwick, A. V.; Rush, G. E. Solid State Ionics 2000, 130, 115. (33) Cherry, M.; Islam, M. S.; Gale, J. D.; Catlow, C. R. A. J. Phys. Chem. 1995, 99, 14614. (34) (a) Munch, W.; Seifert, G.; Kreuer, K. D.; Maier, J. J. Solid State Ionics 1996, 86-88, 647. (b) Munch, W.; Seifert, G.; Kreuer, K. D.; Maier, J. J. Solid State Ionics 1997, 97, 39. (35) Higuchi, T.; Tsukamoto, T.; Sata, N.; Ishigame, M.; Tezuka, Y.; Shin, S. Phys. ReV. B 1998, 57, 6978. (36) Yamaguchi, S.; Kobayashi, K.; Higuchi, T.; Shin, S.; Iguchi, Y. Solid State Ionics 2000, 136-137, 305.
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