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Isotopic exchange between hydrogen from the gas phase and proton-conducting oxides: Theory and experiment
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 8 ) 1 e1 0
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Isotopic exchange between hydrogen from the gas phase and proton-conducting oxides: Theory and experiment* M.V. Ananyev a,b,*, A.S. Farlenkov a,b, E.Kh. Kurumchin a a
Institute of High Temperature Electrochemistry of Ural Branch of Russian Academy of Sciences, Ekaterinburg, Russia b Ural Federal University, Ekaterinburg, Russia
article info
abstract
Article history:
The interaction of hydrogen isotopes from the gas phase with proton-conducting oxides
Received 19 March 2018
with the perovskite structure La1x SrxScO3a (x ¼ 0; 0.04) was studied by means of
Accepted 25 May 2018
the hydrogen isotope exchange with gas phase equilibration in the temperature range
Available online xxx
T ¼ 300e800 C and in hydrogen pressure range pH2 ¼ 2e20 mbar.
Keywords:
taking into account the isotopic effects was developed. This model was implemented for the
Hydrogen isotope exchange
obtained experimental results. The heterogeneous exchange rates of hydrogen isotopes with
A novel kinetic model for the hydrogen isotope exchange experimental data treatment
Lanthanum-strontium scandate
investigated oxides La1xSrxScO3a (x ¼ 0; 0.04) were calculated. The mole fractions of hydrogen
Isotope effect
isotopes were determined for the investigated materials. It was found that deuterium satura-
Hydrogen
tion level is higher in comparison with protium, whereas the deuterium surface exchange co-
Deuterium
efficient for the proton-conducting oxide La0.96Sr0.04ScO3ea is smaller in comparison with the
Proton-conducting oxides
protium surface exchange coefficient. The thermodynamic isotope effect can be caused by the difference of energy of zero-point oscillations between OH- and OD-defects and molecular H2 and D2. The kinetic isotope effect can be explained by the different strength of OH and OD bonds. It is shown that the rate determining stage of hydrogen surface exchange is the process of the exchange between the forms of hydrogen in the gas phase and in the adsorption layer of the proton-conducting oxides (the stage of dissociative adsorption of hydrogen). A new statistical criterion is proposed for the first time allowing dividing the observed surface inhomogeneities caused by not only the natural surface roughness but also the presence of different isotopes of hydrogen (protium and deuterium) with different binding energies on a solid surface. The activity of the investigated proton-conducting oxides with respect to the hydrogen heterogeneous exchange is comparable to the hydrogen heterogeneous exchange activity for the oxides based on cerates and zirconates of alkaline earth metals. High catalytic activity with respect to the process of hydrogen exchange from the gas phase in reducing atmospheres allows us to consider proton-conducting oxides based on the lanthanum scandates as very promising electrolytes for numerous electrochemical applications. © 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
* This paper is the English version of the paper reviewed and published in Russian in International Scientific Journal for Alternative Energy and Ecology “ISJAEE”, 2017, issue 240e242, number 28e30, date 30.10.2017. * Corresponding author. Institute of High Temperature Electrochemistry of Ural Branch of Russian Academy of Sciences, Ekaterinburg, ul. Akademicheskaya 20, Ekaterinburg, Russia. E-mail address: [email protected] (M.V. Ananyev). https://doi.org/10.1016/j.ijhydene.2018.05.150 0360-3199/© 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: Ananyev MV, et al., Isotopic exchange between hydrogen from the gas phase and proton-conducting oxides: Theory and experiment, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.05.150
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Nomenclature Greek letters v deuterium mole fraction in the gas phase p protium mole fraction in the gas phase Definitions k oxygen surface exchange coefficient, cm/s p(D), p(H) probability of incorporation for deuterium and protium T temperature, ºC or K t time, s Y residual between the temporary HD-fraction in the gas phase (C3) and the equilibrium HD-fraction (C∞ 3 ) Subscripts time constants of the direct and backward aD, aH experiments C2, C3, C4 mole fractions of H2, HD, D2 vS deuterium mole fraction on the solid oxide surface deuterium form on the oxide surface (D)S parameters as ratios between the heterogeneous jD, jH exchange rates in case of direct and backward experiments equilibrium constants of incorporation reactions KD, KH of deuterium and protium ratios between the amount of hydrogen atoms in lD, lH the gas phase and in the oxide for deuterium and protium nOD, nOH deuterium and protium mole fractions in the oxide Ng, NO amount of hydrogen atoms in the gas phase and in the oxide, atom hydrogen pressure, mbar pH2 protium mole fraction on the solid oxide surface pS
Introduction Proton-conducting oxides attract considerable attention due to their numerous applications in electrochemical devices in hydrogen and renewable power generation (solid-oxide fuel cells, electrolysers, sensors, reformers and pumps) [1e5]. Such materials are particularly promising as electrolytes for proton-conducting SOFCs at intermediate temperature (400e700 C), which alleviate many of the cyclability and material lifetime challenges arising from the very high operation temperature (800e1000 C) of conventional zirconiabased SOFCs [2,6]. Oxides with perovskite structure are known to possess high proton conductivity [3]. The acceptor-doped perovskitelike oxides based on LaScO3 have been reported to have high proton conductivity in the presence of water vapor at intermediate temperatures [7e15]. Oxygen vacancies are wellknown to cause incorporation of water molecules from the gas phase and formation of protonic defects: one molecule of
rH(D), rH(H) heterogeneous hydrogen exchange rate of deuterium and protium, atom cm2 s1 r2(D), r2(H) rates of r2-type of hydrogen exchange for the direct and backward experiments, atom cm2 s1 (H)S protium form on the oxide surface r0, r1, r2 three types of exchange rates, atom cm2 s1 ra, ri dissociative adsorption and incorporation rates, atom cm2 s1 Superscripts deuterium mole fractions in the gas phase at the v0 initial time deuterium mole fractions in the oxide v0O electronic defect e0 , e E0OH , E0OD energy of zero-point oscillations between the products OH and OD, kJ/mol E0H2 , E0D2 energy of zero-point oscillations between the molecular H2 and D2, kJ/mol hydrogen ion Hþ oxygen ion OxO OHO OH-defect protium mole fractions in the gas phase at the p0 initial time protium mole fractions in the oxide p0O oxygen vacancy V O Units of Atom eV С kJ К mol s cm
measurement Atom Electronvolt Celcius degree Kilojoule Kelvin degree Mole Second Centimeter
water can interact with a vacancy and an oxygen ion to form two OH-defects [16e18]: x H2 OðgÞ þV O þOO ¼ 2OHO ;
(1)
€ gereVink notation is used to describe an oxygen where the Kro , oxygen ions O vacancy V O O at an oxygen lattice sites and OHdefects OHO on an oxygen sites. In the case of high reducing atmospheres (in a dry hydrogen atmosphere) the incorporation reaction can be written in general terms: 1 H2 ¼ Hþ þ e 2
(2.1)
€ gereVink notation: or using the Kro 1 H2ðgÞ þOxO ¼ OHO þe0 ; 2
(2.2)
where Hþ , e or e0 correspond to hydrogen ion and electronic defects, respectively. According to literature data [5e7] the process of water uptake in Sr-doped LaScO3 oxides is well described whereas
Please cite this article in press as: Ananyev MV, et al., Isotopic exchange between hydrogen from the gas phase and proton-conducting oxides: Theory and experiment, International Journal of Hydrogen Energy (2018), https://doi.org/10.1016/j.ijhydene.2018.05.150
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process of dry hydrogen uptake remains unclear. Moreover, the processes of hydrogen uptake, hydrogen surface exchange kinetics in lanthanum scandates have not been directly examined in the literature. This problem can be solved using hydrogen isotope exchange method with gas phase equilibration. Isotope exchange methods are powerful instruments to reveal information about surface reactions and ionic transport in oxide materials. The method of hydrogen isotope exchange with gas phase equilibration allows obtaining detailed information about the surface exchange kinetics. Hydrogen isotope exchange method was used earlier in many studies for surface exchange kinetic analysis on different metals [19e22] and simple oxides [23], whereas there are only a few works related to the isotope exchange of hydrogen from the gas phase and proton-conducting oxides [24e27]. The authors of these works neglect the isotopic effects implementing the mathematical apparatus developed for the oxygen isotope exchange methods. In this paper a novel theoretical approach for the detailed surface exchange mechanism investigation by means of the hydrogen isotope exchange method with gas phase equilibration has been developed. This approach is implemented to study the hydrogen surface exchange of La1xSrxScO3ea (x ¼ 0; 0.04) proton conducting oxides.
1 C3 þ C2 ; 2
(4)
v¼
1 C3 þ C4 : 2
(5)
Let us consider the surface exchange kinetics, which is not complicated by the hydrogen diffusion both in the gas phase and in the solid oxide. The heterogeneous hydrogen exchange rate of deuterium rH(D) and protium rH(H) will characterize the rates of the respective reactions (6) and (7) for the direct and backward experiments: rH ðDÞ
D2 þ ðHÞs ¼ HD þ ðDÞs ;
(6)
rH ðHÞ
H2 þ ðDÞs ¼ HD þ ðHÞs ;
(7)
where (H)s and (D)s correspond to the protium and deuterium forms on the oxide surface, respectively. Changes of the deuterium and protium mole fraction in the gas phase can be written via the mass action laws: v_ ¼ rH ðDÞvð1 vs Þ rH ðHÞð1 vÞvs ;
(8)
p_ ¼ rH ðHÞpð1 ps Þ rH ðDÞð1 pÞps ;
(9)
where ps and vs correspond to the protium and deuterium mole fractions on the solid oxide surface. It is very easy to show that if rH(D) ¼ rH(H) ¼ rH then Equations (8) and (9) turn to McKay's law:
Theory Basic equations In introduction we mentioned that in papers on the hydrogen isotope exchange with proton conducting oxides [24e27] the authors use McKay's law [28] for the calculation of the heterogeneous exchange rate or the surface exchange coefficient calculation. McKay's law can be correctly used only for relatively heavy molecules, like oxygen and nitrogen. In this case the possible isotopic effects can be negligible. In case of hydrogen the isotopic effects can be considerable, and they have to be taken into account. The first report on the kinetic equations with consideration of the isotopic effects was done by Baykov in 1980 [29]. In this preprint kinetic equations were derived for two cases of hydrogen exchange: predominant r1-and r2-types of exchange, respectively. Three types of exchange differ by the amount of oxygen atoms from the solid oxide surface involved into the one elementary act: 0, 1 and 2, respectively [30]. The kinetic equations derived by Baykov are very difficult to use in case of more complicated kinetics with the presence of all r0-, r1-and r2-types of exchange. Thus, a new model development for complicated mechanisms is necessary. Let us consider the reaction of hydrogen isotope exchange in the gas phase: H2 þ D2 ¼ 2HD:
p¼
(3)
We denote the protium and deuterium fractions in the gas phase as p and v, respectively. These values are associated with the mole fractions of molecular hydrogen H2, HD и D2 (C2, C3 and C4, respectively) in the gas phase, according to the following equations:
v_ ¼ rH ðv vs Þ or p_ ¼ rH ðp ps Þ:
(10)
If rH(D) s rH(H), let us introduce the parameters jH and jD as ratios between the heterogeneous exchange rates in case of direct and backward experiments: jH ¼
rH ðHÞ rH ðDÞ ; jD ¼ ; jH jD ¼ 1: rH ðDÞ rH ðHÞ
(11)
Ratios (11) will characterize the kinetic isotope effect. The solutions of (8) and (9) equations are trivial: ! jH v s exp rH ðDÞð1 þ vs ðjH 1ÞÞt ¼ v ¼ vs þ v 1 þ vs ðjH 1 ! jH v s 0 expðaD tÞ; ¼ vs þ v 1 þ v s jH 1 0
(12)
! jD ps exp rH ðHÞð1 þ ps jD 1 Þt ¼ p ¼ ps þ p 1 þ ps jD 1 ! jD ps expðaH tÞ: ¼ ps þ p0 1 þ ps jD 1 0
(13) Obviously, that in case of hydrogen isotope exchange the exponential kinetics will also be observed as in case of isotope exchange without isotopic effects. The difference is related to the time constants of the direct and backward experiments: aD and aH, respectively. Without the isotopic effects the time constants are directly equal to the heterogeneous exchange
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rate. In case of hydrogen isotope exchange with isotopic effect in order to find the precise values of rH(D) and rH(H) it is necessary to calculate the isotopic ratios (11). It is possible to do from the ratio (C) between the time constants of the direct and backward experiments: C¼
CH rH ðHÞ 1 þ ps jD 1 ¼ CD rH ðDÞ 1 þ vs jH 1
(14)
and we immediately obtain the isotopic ratio: jH ¼
C ðvs C þ ps Þ : 1 ðvs C þ ps Þ
(15)
The full description of the isotope redistribution kinetics in the gas phase with oxide catalysts can be done taking into consideration the kinetic Equations (16) and (17) written for Y value. Y value shows the residual between the temporary HDfraction in the gas phase (C3) and the equilibrium HD-fraction ∞ (C∞ 3 ): Y ¼ C3 e C3: Y_ ¼ rðDÞY þ 2r2 ðDÞðvs vÞ2 ;
(16)
Y_ ¼ rðHÞY þ 2r2 ðHÞðps pÞ2 ;
(17)
where r(D) and r(H) e the total exchange rates; r2(D) and r2(H) e the rates of r2-type of hydrogen exchange for the direct and backward experiments, respectively. The solution of Equations (16) and (17) is similar to the oxygen surface exchange kinetics [18]: Y ¼ expðrðDÞtÞ
2 2r2 ðDÞð1 þ lD Þ2 v0 v∞ ½exp½ðrðDÞ rðDÞ 2rH ðDÞð1 þ lD Þ
2rH ðDÞð1 þ lD Þt 1Þ;
(18) 2
2r2 ðHÞð1 þ lH Þ2 ðp0 p∞ Þ ½exp½ðrðHÞ Y ¼ expðrðHÞtÞ rðHÞ 2rH ðHÞð1 þ lH Þ 2rH ðHÞð1 þ lH Þt 1Þ;
(19)
where lD and lH correspond to the ratios between the amount of hydrogen atoms in the gas phase and in the oxide for deuterium and protium, respectively; p0 and v0 are protium and deuterium mole fractions in the gas phase at the initial time. The kinetic isotope effect can also be found for the r and r2 values. If r2 is not equal to zero, time dependence of Y-value will be extremal. Analyzing solutions (18) and (19) it is possible to show that if jH > 0, then the residual of HD-fraction from the equilibrium value is larger in case of backward experiment (when the deuterium inside the solid oxide exchanges with the gaseous protium from the gas phase). At the same time the position of maximum on Y ¼ f (t) dependence is almost independent on the type of the experiment (direct or backward).
Surface nonequality problem The three exchange types concept has been mentioned above and this concept can be used for the tracer redistribution kinetics description in any system including the molecular oxygen in the gas phase and a solid: r0 e the oxygen exchange type associated with the direct interaction of the oxygen
isotopes in the gas phase excluding the participation of the solid surface; r1 e the exchange type when 1 oxygen atom is replaced; r2 e the oxygen exchange type when 2 oxygen atoms are replaced. In our previous work [31] we suggested a model for the oxygen surface exchange kinetics taking into account the surface nonequality. According to this model the ratio between the rates of three pffiffiffiffiffiffi exchange types 2 rr10 r2 or the ratio rrr22 can be used as a criteria for H the usage of the two step model including two consecutive stages: dissociative adsorption and incorporation of hydrogen. If these ratios equal to 1, it is correct to use the two step model. And the distribution functions for the dissociative adsorption rate (ra) and incorporation rate (ri) are symmetric and close to Gaussian type. If these ratios are more than 1, that means that the adsorption centers on the solid oxide surface are not equivalent. The distribution functions for the dissociative adsorption and incorporation rates can be not Gaussian, can have 2 or more modes, different dispersion etc. As a result, we have to consider dissociative adsorption and incorporation stages separately for each adsorption center. From the very common point of view we can rewrite this statistical model for the hydrogen isotopic exchange, if three different types of hydrogen dissociative adsorption stages will be considered: H2 þ 2ð Þa ¼ 2ðHÞa ;
(20)
HD þ 2ð Þa ¼ ðHÞa þ ðDÞa ;
(21)
D2 þ 2ð Þa ¼ 2ðDÞa
(22)
and two types of hydrogen incorporation stages: ðHÞa þ ð Þs ¼ ð Þa þ ðHÞs ;
(23)
ðDÞa þ ð Þs ¼ ð Þa þ ðDÞs ;
(24)
where index “a” correspond to the hydrogen isotopic forms in the adsorption layer. Such set of reactions has to be written down for each adsorption center. The presence of at least three possible stages of dissociative adsorption even in case of homogeneous surface with equal adsorption cites leads to three-mode distribution function for the dissociative adsorption rates and two-mode distribution for the incorporation rates due to at least two possible incorporation stages of hydrogen for deuterium and protium forms in the adsorption layer. Mentioned above peculiarities for ra and ri distributions pffiffiffiffiffiffi immediately means that the ratios 2 rr10 r2 and rrr22 will be more H than 1 even in case of homogeneous surface due to the presence of the two isotopic forms of hydrogen in the adsorption pffiffiffiffiffiffi layer with different binding energy. Also the ratios 2 rr10 r2 or rrr22 H will be dependent on the ratio between mole fraction of protium and deuterium forms on the solid oxide surface: the ratio pffiffiffiffiffiffi 2 r0 r2 or rrr22 will be lower in case of almost pure protium or r1 H deuterium coverage of the solid oxide surface and it will have maximal value in case of presence of both protium and deuterium on the solid surface. This conclusion can be used for the distinguishing of the nonequality of the adsorption centers caused by the surface imhomogeneity and the presence of two isotopic forms of hydrogen with different binding pffiffiffiffiffiffi energy on the solid oxide surface. Thus ratio 2 rr10 r2 or rrr22 can be H
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 8 ) 1 e1 0
used as statistical criteria for the estimation of the surface nonequality in case of hydrogen isotope exchange as well.
Experimental Powdered samples of La1xSrxScO3ea (x ¼ 0; 0.04) proton conducting oxides were synthesized using citric-nitrate technology with reagents (La(NO3)$6Н2О, Sc(NО3)3$4Н2О, SrCO3) of a high purity grade (puriss. spec.). Standardized alcohol solutions of La(NO3)3 and Sc(NO3)3 were prepared for co-precipitation hydroxides. Necessary quantities of solutions were taken and mixed with each other. After that the alcohol solution of ammonia was added into the nitrate mixture until full precipitation. Precipitated hydroxides were filtered and dried at the temperature of 105 С in the baker Snol 67/350 LP (Umega, Lithuania). Strontium carbonate was added to the LaScO3 powder in order to obtain Sr-doped LaScO3. Precipitated hydroxides were filtered and dried at the temperature of 105 С in the baker Snol 67/350 LP (Umega, Lithuania). The dried mixture was annealed in ambient air at the temperature of 900 С during 1 h. After presynthesis at the temperature of 900 C during 1 h, obtained powders were ground and compacted in the form of tablets (diameter ~ 12 mm, thickness ~ 2 mm). The tablets were sintered in ambient air at the temperature of 1500 С during 5 h. After sintering the tablets were milled in a zirconia mortar. X-Ray powder diffraction analysis (XRD) was carried out by using the D/MAX-2200 RIGAKU (Japan) conventional diffracA) at room temperature tometer in CuK-radiation (l(Ka) ¼ 1.54 in ambient air. XRD shows that the La1xSrxScO3ea (x ¼ 0; 0.04) oxides do not have any impurities, Fig. 1. Structural Rietveld refinements of XRD patterns were carried out earlier in [8]. The results of Rietveld refinement showed that orthorhombic distortions decrease with the increasing of strontium concentration whereas the values of the unit cell parameters and the volume of unit cells slightly depend on the amount of acceptor impurity in the oxide lattice [8]. Chemical composition of the samples has been confirmed by the atomic emission spectroscopy with iCAP 6300 ICP
Fig. 1 e XRD pattern for La1¡xSrxScO3¡a (x ¼ 0; 0.04) proton conducting oxides.
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(Thermo Scientific, USA). Lanthanum scandate oxides are found to have impurities of calcium, potassium and silicium less than 0.001, 0.001 and 0.002 atomic %, respectively. The specific surface area of La1xSrxScO3ea (x ¼ 0; 0.04) powdered samples measured by BET method using Sorbi N.4.1 (Meta, Russia) are equal to 0.64 ± 0.20 m2/g and 0.37 ± 0.20 m2/g, respectively. Particle size distribution of the samples was analyzed by means of laser scattering analysis using the Malvern Mastersizer 2000 (Malvern Instruments, United Kingdom), Fig. 2. The hydrogen surface exchange kinetics was studied on powdered samples using the isotope exchange method with gas phase equilibration (IE GPE) on static experimental rig over the temperature range T ¼ 300e800 C and hydrogen pressure pH2 ¼ 2e20 mbar. The gaseous hydrogen of the natural isotope composition with the purity of 99.9996% and deuterium enriched hydrogen with the fraction of deuterium 99.9% were used for the isotope exchange experiment. The content of water vapor in hydrogen was no more than 104 %. The scheme of the experimental rig is shown in Fig. 3. The hydrogen isotope exchange experiment was done on powdered samples to reach the surface exchange controlled regime and avoid possible influence of hydrogen diffusion on the surface exchange process. The experiment consists of 4 base steps. Step 1. Thermal pretreatment of a sample. Before the experiment the sample of the proton conducting oxide was heated with the heating rate 1 K/min up to 950 С under the sustained pumping using the vacuum station including diaphragm and turbo molecular pumps. The sample was fired at 950 С during 2 h and then was cooled down with the same rate. Step 2. Hydrogen uptake. After the pretreatment the sample was equilibrated in the hydrogen atmosphere of the natural isotope composition at the particular hydrogen pressure and temperature in order to dissolve the hydrogen inside the crystal lattice of the sample. The equilibration state has been achieved after 60 min at the lowest temperature (300 С) and the hydrogen pressure in the gas circuit remains constant. Step 3. Direct experiment of the hydrogen exchange. That is the experiment when the protium inside the proton
Fig. 2 e Particle size distribution functions of La1¡xSrxScO3¡a (x ¼ 0, 0.04) powder samples.
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Fig. 3 e Scheme of the experimental rig for the hydrogen isotope exchange: 1) mass-spectrometer MicroVision 2 (MKS Instruments, USA); 2) quartz reactor with a sample; 3) spiral pump IDK-2 (Agilent, USA); 4) vacuum system MiniTask 24 (Agilent, USA); 5) ion pump Valcon Plus-40 (Agilent, USA); 6) Bayard-Alpert-Pirani pressure transducer FRG-720 (Agilent, USA); 7) high pressure transducer (Swagelok, USA); 8) leakage valve; 9) gas cylinder (Swagelok, USA); 10) T-type vacuum valve.
conducting oxide exchanges with gaseous deuterium from the gas phase. After the equilibrating of the sample at the particular hydrogen pressure and temperature the reactor with the sample was closed by means of the vacuum valve. The deuterium enriched hydrogen was inlet to the gas circuit. When the required hydrogen pressure is achieved, the reactor is opened and the hydrogen isotope exchange starts. The isotope composition of the gas phase is monitored by means of the mass-spectrometer. Step 4. Backward experiment. That is the experiment when the deuterium inside the proton conducting oxide exchanges with the gaseous protium from the gas phase. This step is necessary in order to observe the possible isotopic effects in hydrogen surface exchange process. This step is similar to the third one and differs by the isotope composition of hydrogen inlet to the gas circuit. In case of backward experiment natural hydrogen is used.
Results and discussion
Fig. 4 e Time dependencies of (a) protium and deuterium fraction in the gas phase and (b) residual of HD-fraction in the gas phase from the equilibrium value during the hydrogen isotope exchange experiment at hydrogen pressure 2 mbar and T ¼ 400 C for La0.96Sr0.04ScO3ea proton conducting oxide. The protium fractions p in the gas phase was obtained from backward D/H experiment and the deuterium fractions v in the gas phase d from direct H/D experiment. Red line in (b) correspond to fitting curve according to Equations (18) and (19); abbreviation of D and H in Y(D) and Y(H) correspond to the direct H/D and backward D/H experiments. (For interpretation of the references to color/colour in this figure legend, the reader is referred to the Web version of this article.)
Fig. 4a shows time dependencies of deuterium and protium fractions during the direct and backward experiments of hydrogen isotope exchange at T ¼ 400 C for La0.96Sr0.04ScO3ea proton conducting oxide. Since these experiments have been performed under the same hydrogen pressure (~2 mbar), it is absolutely clear to observe both thermodynamic and kinetic isotope effects. Thermodynamic isotope effect causes the different in the equilibrium values of the protium and deuterium in the gas phase: the lower equilibrium value of deuterium means, that the solubility of deuterium in the solid oxide is larger in comparison with protium. Kinetic isotopic effect causes different slopes of the initial part of time dependencies of
deuterium and protium fractions in the gas phase (Fig. 4a) and different residual of HD-fraction from the equilibrium value (Y-values) for direct and backward experiments (Fig. 4b). The rate of protium surface exchange is larger than the deuterium rate. Fig. 5a shows the temperature dependences of the deuterium and protium mole fraction in the La0.96Sr0.04ScO3ea oxide calculated as mean values from two parallel measurements in comparison with the undoped LaScO3 oxide. These mole fractions have been calculated using the mass conservation law:
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 8 ) 1 e1 0
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Observed thermodynamic isotope effect can be explained if we look at the reaction (2.2) of hydrogen uptake by the solid oxide. The difference between the equilibrium constants for the KD/KH reaction (2.2) in case of different isotopes can be written as follows: 0 1 0 KD EH2 E0D2 RT : (27) exp EOH E0OD 2 KH The thermodynamic isotope effect can be caused by the difference of energy of zero-point oscillations between the products OH and OD (E0OH and E0OD , respectively) of the reaction (2) and molecular H2 and D2 (E0H2 and E0D2 , respectively). The difference of the energy of zero-point oscillations of OH and OD is 5.85 kJ/mol and for H2 and D2 equals to 7.53 kJ/mol [32]. Substituting the values to (27) one can find that the difference is equal to 2.1 kJ/mol. As a result, deuterium solubility is thermodynamically more efficient process than protium solubility. The hydrogen pressure dependence of the protium and deuterium mole fraction for La0.96Sr0.04ScO3ea proton conducting oxide is shown in Fig. 4b. These dependencies have power-law form. Fig. 6a shows the hydrogen surface exchange coefficients calculated from the hydrogen heterogeneous exchange rates:
Fig. 5 e Protium and deuterium fraction as a function of (a) temperature at 2 mbar of hydrogen pressure and (b) hydrogen pressure dependencies in La0.96Sr0.04ScO3ea proton conducting oxide at different temperatures.
Ng v0 þ NO v0O ¼ v∞ Ng þ NO ;
(25)
Ng p0 þ NO p0O ¼ p∞ Ng þ NO ;
(26)
where Ng and NO the amount of hydrogen atoms in the gas phase and in the oxide; v0O and p0O correspond to the deuterium and protium fraction in the solid oxide. According to data presented in Fig. 5a, the temperature dependence of deuterium and protium mole fractions in the undoped LaScO3 corresponds to the absence of any considerable solubility of hydrogen in comparison with La0.96Sr0.04ScO3ea oxide. The saturation level of deuterium in La0.96Sr0.04ScO3ea is larger in contrast to protium over the whole temperature range. The solubility of hydrogen in La0.96Sr0.04ScO3ea oxide decreases with temperature such as at temperature >600 C the mole fraction of hydrogen isotopes is low and comparable with the hydrogen mole fractions in the undoped LaScO3 oxide. This residual amount of hydrogen at high temperatures is also comparable with the amount of hydrogen on the solid surface estimated from the value of the specific surface area and the assumption of monolayer coverage of the surface by hydrogen adatoms coupled with oxygen from the solid oxide lattice.
kðHÞ ¼
rH ðHÞ ; nOH
(28)
kðDÞ ¼
rH ðDÞ ; nOD
(29)
where nOH and nOD are protium and deuterium mole fraction in the solid oxide, respectively. According to Fig. 6a, there are two parts on the temperature dependencies of the hydrogen surface exchange coefficients: low temperature with apparent activation energy ~0.16 eV and high temperature with apparent activation energy ~0.12 eV. These two parts are in good agreement with two parts of temperature dependence of hydrogen mole fraction in solid oxide, Fig. 5a. The low temperature part of the hydrogen surface exchange coefficient dependence corresponds to hydrogen dissolved in the proton conducting oxide. The ratio between the pre-exponential factors for k(D) and k(H) is equal to 1.2 ± 0.2. That is in good agreement with the ratio between the zero-point oscillation frequencies for OD and OH vibration mode: 1.36 [33]. In the framework of the model for the hydrogen isotope exchange kinetics the mean values of the dissociative adsorption of hydrogen and hydrogen incorporation rates can be calculated using r, rH and r2 values from treatment of Yvalue time dependencies by means of (16) and (17) equations: ra ¼ r; ri ¼
(30)
rrH : r rH
(31)
The probability of incorporation for protium p(H) and deuterium p(D) is calculated as follows: pðHÞ ¼
ri ðHÞ ri ðDÞ and pðDÞ ¼ : ra ðHÞ þ ri ðHÞ ra ðDÞ þ ri ðDÞ
(32)
The temperature dependence of the probability incorporation for protium and deuterium shows that at low
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Fig. 7 e Time dependencies of H2, HD and D2 fractions as well as protium fraction in the gas phase during the series of hydrogen exchange experiments at hydrogen pressure 2 mbar and T ¼ 400 C for La0.96Sr0.04ScO3ea proton conducting oxide.
Fig. 6 e Temperature dependences of (a) protium and deuterium surface exchange coefficients and (b) protium and deuterium probability of incorporation at hydrogen pressure 2 mbar for La0.96Sr0.04ScO3ea proton conducting oxide.
temperature the kinetic isotope effect is caused by the different probability of protium and deuterium incorporation, Fig. 6b. At high temperatures without considerable solubility of hydrogen in the solid oxide the kinetic isotope effect on the probability of the incorporation is almost negligible. Since the probability of incorporation of hydrogen is larger than 0.5 the hydrogen dissociative adsorption stage is proved to be rate determining. This fact causes low apparent activation energies (~0.2 eV) of the hydrogen surface exchange coefficients. The last theoretical conclusion from our statistical model related to the different nature of the adsorption centers nonequality can be demonstrated in terms of the special experiment. The experiment consists of the same 3 base steps (Step 1, Step 2 and Step 3, mentioned above in the Experimental). The main difference is that we repeated the direct hydrogen exchange experiment one after another expecting different saturation level by the deuterium both the oxide volume and the oxide surface, Fig. 7.
In our case, the direct hydrogen exchange experiment was repeated 10 times. Fig. 7 shows changes of C2, C3 and C4 mole fractions in the gas phase for series of consecutive hydrogen exchange experiments. For each kinetic dependence r, rH and r2 in this series of the experiments have been calculated. Dependence of the ratio rrr22 on the number of the experiH ment is shown in Fig. 8. It demonstrates external behavior, and the reason can have the following explanation. Before the experiment we have initially only protium on the solid oxide surface with intrinsic nonequality of the surface adsorption centers and respective rrr22 -value is equal to 2.73. This value is larger than 1 H and caused mainly by the solid oxide surface inhomogeneity. During the experiment the fraction of deuterium increases changing the ratio between the protium and deuterium on the solid oxide surface. Nonequality of the adsorption centers increases with the number of the experiments until the
Fig. 8 e Dependence of the non-equivalence parameter on the number of the hydrogen exchange experiments at hydrogen pressure 2 mbar and T ¼ 400 C for La0.96Sr0.04ScO3ea proton conducting oxide.
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 8 ) 1 e1 0
Fig. 9 e Temperature dependences of the heterogeneous hydrogen exchange rates in dry hydrogen atmosphere for different proton conducting oxides. amounts of protium and deuterium become close to each other. At this point the maximal rrr22 -value equal to 3.11 and H maximal nonequality of the solid oxide surface are observed caused by not only by the surface inhomogeneity but also the presence of two hydrogen isotopes on the solid oxide surface with different binding energy. Further increasing of the deuterium concentration on the solid oxide surface lead to the protium concentration decreasing and as a result decrease of the rrr22 values. H Fig. 9 shows the comparison of the hydrogen surface exchange data known in the literature with our results on La0.96Sr0.04ScO3ea proton conducting oxide. In general, there is a very large spread in apparent activation energies even for identical oxides. Today, it is very difficult to reveal any common relations from observed data due to large scattering on hydrogen exchange rate values. The further serious work is required for the better understanding of the hydrogen incorporation into the proton conducting oxides. Now we can mention that acceptor dopant (Sr0 La ) play an important role in the process of hydrogen uptake, according to reaction (2.2), written formally without interaction with oxygen vacancies, formed by acceptor doping. One of the most fundamental problem is the nature of the electronic defects in the hydrogen uptake process (2.2). One of the possible mechanisms of the electronic compensation can be associated with localization of the electronic defects on oxygen vacancies with F-centers formation, according to: 0 V O þ e ¼ VO ;
(33)
VO þ e0 ¼ V O:
(34)
Unfortunately, the isotopic exchange method cannot prove or disprove the possibility of presence of reaction [33]. Additional physical methods giving information about the defect structure of band gap in the oxides is required.
Conclusions The theoretical models for the hydrogen surface exchange kinetics description have been derived. Previously developed
9
model taking into account the nonequality of the adsorption centers has been adopted for the hydrogen isotope exchange experiment. Developed theoretical approaches have been implemented for the detailed description of the hydrogen surface exchange kinetics on La1xSrxScO3ea (x ¼ 0, 0.04) proton conducting oxides. The heterogeneous exchange rates of hydrogen isotopes with oxides La1xSrxScO3a (x ¼ 0; 0.04) have been calculated. It has been found that the hydrogen dissociative adsorption process is rate determining (the stage of exchange between the forms of hydrogen in the gas phase and the adsorption layer). Mole fractions of hydrogen isotopes in the studied oxides have been calculated. It was found that the solubility of deuterium is higher than protium. The observed thermodynamic isotopic effect can be due to the difference in the energies of zero-point oscillations of OH- and OD-defects and molecular forms of hydrogen H2 and D2. It is shown that the deuterium surface exchange coefficient is smaller in comparison with the protium surface exchange coefficient for the proton-conducting oxide La0.96Sr0.04ScO3a. The observed kinetic isotopic effect can be explained by the different strengths of the OH and OD bonds. A new statistical criterion is proposed for the first time allowing dividing the observed surface inhomogeneities caused by not only the natural surface roughness but also the presence of different isotopes of hydrogen (protium and deuterium) and different binding energies, respectively. High catalytic activity with respect to the process of exchange with hydrogen of the gas phase in reducing atmospheres allows us to consider proton-conducting oxides La1xSrxScO3a as promising proton-conducting electrolytes for various solid-oxide electrochemical devices.
Acknowledgements This study is partly supported by the grant of the Russian Science Foundation (Project number N 16-13-00053) and Russian Foundation for Basic Research (N 16-08-01139). This work is done using the facilities of the Shared access center “Composition of Compounds” and Unique Scientific Setup “Isotope Exchange” of IHTE UB RAS. The education activity of Ph.D. and master students involved into this work is supported by Act 211 of Government of the Russian Federation, agreement No. 02.A03.21.0006 and the grant of the President of Russian Federation 2018e2019. Authors are grateful to Dr. A.V. Kuzmin for the samples supply, Dr. N.M. Porotnikova for BET and laser scattering analysis and Dr. B.D. Antonov for XRD analysis.
references
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[3] Kreuer KD. Proton-conducting oxides. Annu Rev Mater Res 2003;33:333e59. [4] Iwahara H, Asakura Y, Katahirac K, Tanakad M. Prospect of hydrogen technology using proton-conducting ceramics. Solid State Ionics 2004;168:299e310. [5] Norby T. Solid-state protonic conductors: principles, properties, progress and prospects. Solid State Ionics 1999;125:1e11. [6] Steele BCH, Heinzel A. Materials for fuel-cell technologies. Nature 2001;414:345e52. [7] Fujii H, Katayama Y, Shimura T, Iwahara H. Protonic conduction in perovskite-type oxide ceramics based on LnScO3 (Ln¼ La, Nd, Sm or Gd) at high temperature. J Electroceram 1998;2:119e25. [8] Lybye D, Bonanos N. Proton and oxide ion conductivity of doped LaScO3. Solid State Ionics 1999;125:339e44. [9] Lybye D, Poulsen FW, Mogensen M. Conductivity of a- and Bsite doped LaAlO3, LaGaO3, LaScO3 and LaInO3 perovskites. Solid State Ionics 2000;128:91e103. [10] Nomura K, Takeuchi T, Tanase S, Kageyama H, Tanimoto K, Miyazaki Y. Proton conduction in (La0.9Sr0.1)MIIIO3d (MIII ¼ Sc, In, and Lu) perovskites. Solid State Ionics 2002;154e155:647e52. [11] Nomura K, Takeuchi T, Kamo S, Kageyama H, Miyazaki Y. Proton conduction in doped LaScO3 perovskites. Solid State Ionics 2004;175:553e5. [12] Gorelov VP, Stroeva AYu. Solid proton conducting electrolytes based on LaScO3. Russ J Electrochem 2012;48:949e60. [13] Stroeva AYu, Gorelov VP, Kuzmin AV, Vykhodets VB, Kurennykh TE. Effect of scandium sublattice defectiveness on ion and hole transfer in LaScO3-based proton conducting oxides. Russ J Electrochem 2011;47:264e74. [14] Stroeva AYu, Gorelov VP, Kuzmin AV, Antonova EP, Plaksin SV. Phase composition and conductivity of La1xSrxScO3a (x ¼ 0.010.20) under oxidative conditions. Russ J Electrochem 2012;48:509e17. [15] Stroeva AYu, Gorelov VP. Nature of conductivity of perovskites La1xSrxScO3a (x ¼ 0.010.15) under oxidative and reducing conditions. Russ J Electrochem 2012;48:1079e85. [16] Farlenkov AS, Putilov LP, Ananyev MV, Antonova EP, Eremin VA, Stroeva AYu, et al. Water uptake, ionic and hole transport in La0.9Sr0.1ScO3ed. Solid State Ionics 2017;306:126e36. [17] Farlenkov AS, Smolnikov AG, Ananyev MV, Khodimchuk AV, Buzlukov AL, Kuzmin AV, et al. Local disorder and water uptake in La1exSrxScO3ed. Solid State Ionics 2017;306:82e8. [18] Okuyama Y, Kozaia T, Ikeda S, Matsuka M, Sakaid T, Matsumoto H. Incorporation and conduction of proton in Sr-
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Available online at www.sciencedirect.com
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Isotopic exchange between hydrogen from the gas phase and proton-conducting oxides: Theory and experiment* M.V. Ananyev a,b,*, A.S. Farlenkov a,b, E.Kh. Kurumchin a a
Institute of High Temperature Electrochemistry of Ural Branch of Russian Academy of Sciences, Ekaterinburg, Russia b Ural Federal University, Ekaterinburg, Russia
article info
abstract
Article history:
The interaction of hydrogen isotopes from the gas phase with proton-conducting oxides
Received 19 March 2018
with the perovskite structure La1x SrxScO3a (x ¼ 0; 0.04) was studied by means of
Accepted 25 May 2018
the hydrogen isotope exchange with gas phase equilibration in the temperature range
Available online xxx
T ¼ 300e800 C and in hydrogen pressure range pH2 ¼ 2e20 mbar.
Keywords:
taking into account the isotopic effects was developed. This model was implemented for the
Hydrogen isotope exchange
obtained experimental results. The heterogeneous exchange rates of hydrogen isotopes with
A novel kinetic model for the hydrogen isotope exchange experimental data treatment
Lanthanum-strontium scandate
investigated oxides La1xSrxScO3a (x ¼ 0; 0.04) were calculated. The mole fractions of hydrogen
Isotope effect
isotopes were determined for the investigated materials. It was found that deuterium satura-
Hydrogen
tion level is higher in comparison with protium, whereas the deuterium surface exchange co-
Deuterium
efficient for the proton-conducting oxide La0.96Sr0.04ScO3ea is smaller in comparison with the
Proton-conducting oxides
protium surface exchange coefficient. The thermodynamic isotope effect can be caused by the difference of energy of zero-point oscillations between OH- and OD-defects and molecular H2 and D2. The kinetic isotope effect can be explained by the different strength of OH and OD bonds. It is shown that the rate determining stage of hydrogen surface exchange is the process of the exchange between the forms of hydrogen in the gas phase and in the adsorption layer of the proton-conducting oxides (the stage of dissociative adsorption of hydrogen). A new statistical criterion is proposed for the first time allowing dividing the observed surface inhomogeneities caused by not only the natural surface roughness but also the presence of different isotopes of hydrogen (protium and deuterium) with different binding energies on a solid surface. The activity of the investigated proton-conducting oxides with respect to the hydrogen heterogeneous exchange is comparable to the hydrogen heterogeneous exchange activity for the oxides based on cerates and zirconates of alkaline earth metals. High catalytic activity with respect to the process of hydrogen exchange from the gas phase in reducing atmospheres allows us to consider proton-conducting oxides based on the lanthanum scandates as very promising electrolytes for numerous electrochemical applications. © 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
* This paper is the English version of the paper reviewed and published in Russian in International Scientific Journal for Alternative Energy and Ecology “ISJAEE”, 2017, issue 240e242, number 28e30, date 30.10.2017. * Corresponding author. Institute of High Temperature Electrochemistry of Ural Branch of Russian Academy of Sciences, Ekaterinburg, ul. Akademicheskaya 20, Ekaterinburg, Russia. E-mail address: [email protected] (M.V. Ananyev). https://doi.org/10.1016/j.ijhydene.2018.05.150 0360-3199/© 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
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Nomenclature Greek letters v deuterium mole fraction in the gas phase p protium mole fraction in the gas phase Definitions k oxygen surface exchange coefficient, cm/s p(D), p(H) probability of incorporation for deuterium and protium T temperature, ºC or K t time, s Y residual between the temporary HD-fraction in the gas phase (C3) and the equilibrium HD-fraction (C∞ 3 ) Subscripts time constants of the direct and backward aD, aH experiments C2, C3, C4 mole fractions of H2, HD, D2 vS deuterium mole fraction on the solid oxide surface deuterium form on the oxide surface (D)S parameters as ratios between the heterogeneous jD, jH exchange rates in case of direct and backward experiments equilibrium constants of incorporation reactions KD, KH of deuterium and protium ratios between the amount of hydrogen atoms in lD, lH the gas phase and in the oxide for deuterium and protium nOD, nOH deuterium and protium mole fractions in the oxide Ng, NO amount of hydrogen atoms in the gas phase and in the oxide, atom hydrogen pressure, mbar pH2 protium mole fraction on the solid oxide surface pS
Introduction Proton-conducting oxides attract considerable attention due to their numerous applications in electrochemical devices in hydrogen and renewable power generation (solid-oxide fuel cells, electrolysers, sensors, reformers and pumps) [1e5]. Such materials are particularly promising as electrolytes for proton-conducting SOFCs at intermediate temperature (400e700 C), which alleviate many of the cyclability and material lifetime challenges arising from the very high operation temperature (800e1000 C) of conventional zirconiabased SOFCs [2,6]. Oxides with perovskite structure are known to possess high proton conductivity [3]. The acceptor-doped perovskitelike oxides based on LaScO3 have been reported to have high proton conductivity in the presence of water vapor at intermediate temperatures [7e15]. Oxygen vacancies are wellknown to cause incorporation of water molecules from the gas phase and formation of protonic defects: one molecule of
rH(D), rH(H) heterogeneous hydrogen exchange rate of deuterium and protium, atom cm2 s1 r2(D), r2(H) rates of r2-type of hydrogen exchange for the direct and backward experiments, atom cm2 s1 (H)S protium form on the oxide surface r0, r1, r2 three types of exchange rates, atom cm2 s1 ra, ri dissociative adsorption and incorporation rates, atom cm2 s1 Superscripts deuterium mole fractions in the gas phase at the v0 initial time deuterium mole fractions in the oxide v0O electronic defect e0 , e E0OH , E0OD energy of zero-point oscillations between the products OH and OD, kJ/mol E0H2 , E0D2 energy of zero-point oscillations between the molecular H2 and D2, kJ/mol hydrogen ion Hþ oxygen ion OxO OHO OH-defect protium mole fractions in the gas phase at the p0 initial time protium mole fractions in the oxide p0O oxygen vacancy V O Units of Atom eV С kJ К mol s cm
measurement Atom Electronvolt Celcius degree Kilojoule Kelvin degree Mole Second Centimeter
water can interact with a vacancy and an oxygen ion to form two OH-defects [16e18]: x H2 OðgÞ þV O þOO ¼ 2OHO ;
(1)
€ gereVink notation is used to describe an oxygen where the Kro , oxygen ions O vacancy V O O at an oxygen lattice sites and OHdefects OHO on an oxygen sites. In the case of high reducing atmospheres (in a dry hydrogen atmosphere) the incorporation reaction can be written in general terms: 1 H2 ¼ Hþ þ e 2
(2.1)
€ gereVink notation: or using the Kro 1 H2ðgÞ þOxO ¼ OHO þe0 ; 2
(2.2)
where Hþ , e or e0 correspond to hydrogen ion and electronic defects, respectively. According to literature data [5e7] the process of water uptake in Sr-doped LaScO3 oxides is well described whereas
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process of dry hydrogen uptake remains unclear. Moreover, the processes of hydrogen uptake, hydrogen surface exchange kinetics in lanthanum scandates have not been directly examined in the literature. This problem can be solved using hydrogen isotope exchange method with gas phase equilibration. Isotope exchange methods are powerful instruments to reveal information about surface reactions and ionic transport in oxide materials. The method of hydrogen isotope exchange with gas phase equilibration allows obtaining detailed information about the surface exchange kinetics. Hydrogen isotope exchange method was used earlier in many studies for surface exchange kinetic analysis on different metals [19e22] and simple oxides [23], whereas there are only a few works related to the isotope exchange of hydrogen from the gas phase and proton-conducting oxides [24e27]. The authors of these works neglect the isotopic effects implementing the mathematical apparatus developed for the oxygen isotope exchange methods. In this paper a novel theoretical approach for the detailed surface exchange mechanism investigation by means of the hydrogen isotope exchange method with gas phase equilibration has been developed. This approach is implemented to study the hydrogen surface exchange of La1xSrxScO3ea (x ¼ 0; 0.04) proton conducting oxides.
1 C3 þ C2 ; 2
(4)
v¼
1 C3 þ C4 : 2
(5)
Let us consider the surface exchange kinetics, which is not complicated by the hydrogen diffusion both in the gas phase and in the solid oxide. The heterogeneous hydrogen exchange rate of deuterium rH(D) and protium rH(H) will characterize the rates of the respective reactions (6) and (7) for the direct and backward experiments: rH ðDÞ
D2 þ ðHÞs ¼ HD þ ðDÞs ;
(6)
rH ðHÞ
H2 þ ðDÞs ¼ HD þ ðHÞs ;
(7)
where (H)s and (D)s correspond to the protium and deuterium forms on the oxide surface, respectively. Changes of the deuterium and protium mole fraction in the gas phase can be written via the mass action laws: v_ ¼ rH ðDÞvð1 vs Þ rH ðHÞð1 vÞvs ;
(8)
p_ ¼ rH ðHÞpð1 ps Þ rH ðDÞð1 pÞps ;
(9)
where ps and vs correspond to the protium and deuterium mole fractions on the solid oxide surface. It is very easy to show that if rH(D) ¼ rH(H) ¼ rH then Equations (8) and (9) turn to McKay's law:
Theory Basic equations In introduction we mentioned that in papers on the hydrogen isotope exchange with proton conducting oxides [24e27] the authors use McKay's law [28] for the calculation of the heterogeneous exchange rate or the surface exchange coefficient calculation. McKay's law can be correctly used only for relatively heavy molecules, like oxygen and nitrogen. In this case the possible isotopic effects can be negligible. In case of hydrogen the isotopic effects can be considerable, and they have to be taken into account. The first report on the kinetic equations with consideration of the isotopic effects was done by Baykov in 1980 [29]. In this preprint kinetic equations were derived for two cases of hydrogen exchange: predominant r1-and r2-types of exchange, respectively. Three types of exchange differ by the amount of oxygen atoms from the solid oxide surface involved into the one elementary act: 0, 1 and 2, respectively [30]. The kinetic equations derived by Baykov are very difficult to use in case of more complicated kinetics with the presence of all r0-, r1-and r2-types of exchange. Thus, a new model development for complicated mechanisms is necessary. Let us consider the reaction of hydrogen isotope exchange in the gas phase: H2 þ D2 ¼ 2HD:
p¼
(3)
We denote the protium and deuterium fractions in the gas phase as p and v, respectively. These values are associated with the mole fractions of molecular hydrogen H2, HD и D2 (C2, C3 and C4, respectively) in the gas phase, according to the following equations:
v_ ¼ rH ðv vs Þ or p_ ¼ rH ðp ps Þ:
(10)
If rH(D) s rH(H), let us introduce the parameters jH and jD as ratios between the heterogeneous exchange rates in case of direct and backward experiments: jH ¼
rH ðHÞ rH ðDÞ ; jD ¼ ; jH jD ¼ 1: rH ðDÞ rH ðHÞ
(11)
Ratios (11) will characterize the kinetic isotope effect. The solutions of (8) and (9) equations are trivial: ! jH v s exp rH ðDÞð1 þ vs ðjH 1ÞÞt ¼ v ¼ vs þ v 1 þ vs ðjH 1 ! jH v s 0 expðaD tÞ; ¼ vs þ v 1 þ v s jH 1 0
(12)
! jD ps exp rH ðHÞð1 þ ps jD 1 Þt ¼ p ¼ ps þ p 1 þ ps jD 1 ! jD ps expðaH tÞ: ¼ ps þ p0 1 þ ps jD 1 0
(13) Obviously, that in case of hydrogen isotope exchange the exponential kinetics will also be observed as in case of isotope exchange without isotopic effects. The difference is related to the time constants of the direct and backward experiments: aD and aH, respectively. Without the isotopic effects the time constants are directly equal to the heterogeneous exchange
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rate. In case of hydrogen isotope exchange with isotopic effect in order to find the precise values of rH(D) and rH(H) it is necessary to calculate the isotopic ratios (11). It is possible to do from the ratio (C) between the time constants of the direct and backward experiments: C¼
CH rH ðHÞ 1 þ ps jD 1 ¼ CD rH ðDÞ 1 þ vs jH 1
(14)
and we immediately obtain the isotopic ratio: jH ¼
C ðvs C þ ps Þ : 1 ðvs C þ ps Þ
(15)
The full description of the isotope redistribution kinetics in the gas phase with oxide catalysts can be done taking into consideration the kinetic Equations (16) and (17) written for Y value. Y value shows the residual between the temporary HDfraction in the gas phase (C3) and the equilibrium HD-fraction ∞ (C∞ 3 ): Y ¼ C3 e C3: Y_ ¼ rðDÞY þ 2r2 ðDÞðvs vÞ2 ;
(16)
Y_ ¼ rðHÞY þ 2r2 ðHÞðps pÞ2 ;
(17)
where r(D) and r(H) e the total exchange rates; r2(D) and r2(H) e the rates of r2-type of hydrogen exchange for the direct and backward experiments, respectively. The solution of Equations (16) and (17) is similar to the oxygen surface exchange kinetics [18]: Y ¼ expðrðDÞtÞ
2 2r2 ðDÞð1 þ lD Þ2 v0 v∞ ½exp½ðrðDÞ rðDÞ 2rH ðDÞð1 þ lD Þ
2rH ðDÞð1 þ lD Þt 1Þ;
(18) 2
2r2 ðHÞð1 þ lH Þ2 ðp0 p∞ Þ ½exp½ðrðHÞ Y ¼ expðrðHÞtÞ rðHÞ 2rH ðHÞð1 þ lH Þ 2rH ðHÞð1 þ lH Þt 1Þ;
(19)
where lD and lH correspond to the ratios between the amount of hydrogen atoms in the gas phase and in the oxide for deuterium and protium, respectively; p0 and v0 are protium and deuterium mole fractions in the gas phase at the initial time. The kinetic isotope effect can also be found for the r and r2 values. If r2 is not equal to zero, time dependence of Y-value will be extremal. Analyzing solutions (18) and (19) it is possible to show that if jH > 0, then the residual of HD-fraction from the equilibrium value is larger in case of backward experiment (when the deuterium inside the solid oxide exchanges with the gaseous protium from the gas phase). At the same time the position of maximum on Y ¼ f (t) dependence is almost independent on the type of the experiment (direct or backward).
Surface nonequality problem The three exchange types concept has been mentioned above and this concept can be used for the tracer redistribution kinetics description in any system including the molecular oxygen in the gas phase and a solid: r0 e the oxygen exchange type associated with the direct interaction of the oxygen
isotopes in the gas phase excluding the participation of the solid surface; r1 e the exchange type when 1 oxygen atom is replaced; r2 e the oxygen exchange type when 2 oxygen atoms are replaced. In our previous work [31] we suggested a model for the oxygen surface exchange kinetics taking into account the surface nonequality. According to this model the ratio between the rates of three pffiffiffiffiffiffi exchange types 2 rr10 r2 or the ratio rrr22 can be used as a criteria for H the usage of the two step model including two consecutive stages: dissociative adsorption and incorporation of hydrogen. If these ratios equal to 1, it is correct to use the two step model. And the distribution functions for the dissociative adsorption rate (ra) and incorporation rate (ri) are symmetric and close to Gaussian type. If these ratios are more than 1, that means that the adsorption centers on the solid oxide surface are not equivalent. The distribution functions for the dissociative adsorption and incorporation rates can be not Gaussian, can have 2 or more modes, different dispersion etc. As a result, we have to consider dissociative adsorption and incorporation stages separately for each adsorption center. From the very common point of view we can rewrite this statistical model for the hydrogen isotopic exchange, if three different types of hydrogen dissociative adsorption stages will be considered: H2 þ 2ð Þa ¼ 2ðHÞa ;
(20)
HD þ 2ð Þa ¼ ðHÞa þ ðDÞa ;
(21)
D2 þ 2ð Þa ¼ 2ðDÞa
(22)
and two types of hydrogen incorporation stages: ðHÞa þ ð Þs ¼ ð Þa þ ðHÞs ;
(23)
ðDÞa þ ð Þs ¼ ð Þa þ ðDÞs ;
(24)
where index “a” correspond to the hydrogen isotopic forms in the adsorption layer. Such set of reactions has to be written down for each adsorption center. The presence of at least three possible stages of dissociative adsorption even in case of homogeneous surface with equal adsorption cites leads to three-mode distribution function for the dissociative adsorption rates and two-mode distribution for the incorporation rates due to at least two possible incorporation stages of hydrogen for deuterium and protium forms in the adsorption layer. Mentioned above peculiarities for ra and ri distributions pffiffiffiffiffiffi immediately means that the ratios 2 rr10 r2 and rrr22 will be more H than 1 even in case of homogeneous surface due to the presence of the two isotopic forms of hydrogen in the adsorption pffiffiffiffiffiffi layer with different binding energy. Also the ratios 2 rr10 r2 or rrr22 H will be dependent on the ratio between mole fraction of protium and deuterium forms on the solid oxide surface: the ratio pffiffiffiffiffiffi 2 r0 r2 or rrr22 will be lower in case of almost pure protium or r1 H deuterium coverage of the solid oxide surface and it will have maximal value in case of presence of both protium and deuterium on the solid surface. This conclusion can be used for the distinguishing of the nonequality of the adsorption centers caused by the surface imhomogeneity and the presence of two isotopic forms of hydrogen with different binding pffiffiffiffiffiffi energy on the solid oxide surface. Thus ratio 2 rr10 r2 or rrr22 can be H
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used as statistical criteria for the estimation of the surface nonequality in case of hydrogen isotope exchange as well.
Experimental Powdered samples of La1xSrxScO3ea (x ¼ 0; 0.04) proton conducting oxides were synthesized using citric-nitrate technology with reagents (La(NO3)$6Н2О, Sc(NО3)3$4Н2О, SrCO3) of a high purity grade (puriss. spec.). Standardized alcohol solutions of La(NO3)3 and Sc(NO3)3 were prepared for co-precipitation hydroxides. Necessary quantities of solutions were taken and mixed with each other. After that the alcohol solution of ammonia was added into the nitrate mixture until full precipitation. Precipitated hydroxides were filtered and dried at the temperature of 105 С in the baker Snol 67/350 LP (Umega, Lithuania). Strontium carbonate was added to the LaScO3 powder in order to obtain Sr-doped LaScO3. Precipitated hydroxides were filtered and dried at the temperature of 105 С in the baker Snol 67/350 LP (Umega, Lithuania). The dried mixture was annealed in ambient air at the temperature of 900 С during 1 h. After presynthesis at the temperature of 900 C during 1 h, obtained powders were ground and compacted in the form of tablets (diameter ~ 12 mm, thickness ~ 2 mm). The tablets were sintered in ambient air at the temperature of 1500 С during 5 h. After sintering the tablets were milled in a zirconia mortar. X-Ray powder diffraction analysis (XRD) was carried out by using the D/MAX-2200 RIGAKU (Japan) conventional diffracA) at room temperature tometer in CuK-radiation (l(Ka) ¼ 1.54 in ambient air. XRD shows that the La1xSrxScO3ea (x ¼ 0; 0.04) oxides do not have any impurities, Fig. 1. Structural Rietveld refinements of XRD patterns were carried out earlier in [8]. The results of Rietveld refinement showed that orthorhombic distortions decrease with the increasing of strontium concentration whereas the values of the unit cell parameters and the volume of unit cells slightly depend on the amount of acceptor impurity in the oxide lattice [8]. Chemical composition of the samples has been confirmed by the atomic emission spectroscopy with iCAP 6300 ICP
Fig. 1 e XRD pattern for La1¡xSrxScO3¡a (x ¼ 0; 0.04) proton conducting oxides.
5
(Thermo Scientific, USA). Lanthanum scandate oxides are found to have impurities of calcium, potassium and silicium less than 0.001, 0.001 and 0.002 atomic %, respectively. The specific surface area of La1xSrxScO3ea (x ¼ 0; 0.04) powdered samples measured by BET method using Sorbi N.4.1 (Meta, Russia) are equal to 0.64 ± 0.20 m2/g and 0.37 ± 0.20 m2/g, respectively. Particle size distribution of the samples was analyzed by means of laser scattering analysis using the Malvern Mastersizer 2000 (Malvern Instruments, United Kingdom), Fig. 2. The hydrogen surface exchange kinetics was studied on powdered samples using the isotope exchange method with gas phase equilibration (IE GPE) on static experimental rig over the temperature range T ¼ 300e800 C and hydrogen pressure pH2 ¼ 2e20 mbar. The gaseous hydrogen of the natural isotope composition with the purity of 99.9996% and deuterium enriched hydrogen with the fraction of deuterium 99.9% were used for the isotope exchange experiment. The content of water vapor in hydrogen was no more than 104 %. The scheme of the experimental rig is shown in Fig. 3. The hydrogen isotope exchange experiment was done on powdered samples to reach the surface exchange controlled regime and avoid possible influence of hydrogen diffusion on the surface exchange process. The experiment consists of 4 base steps. Step 1. Thermal pretreatment of a sample. Before the experiment the sample of the proton conducting oxide was heated with the heating rate 1 K/min up to 950 С under the sustained pumping using the vacuum station including diaphragm and turbo molecular pumps. The sample was fired at 950 С during 2 h and then was cooled down with the same rate. Step 2. Hydrogen uptake. After the pretreatment the sample was equilibrated in the hydrogen atmosphere of the natural isotope composition at the particular hydrogen pressure and temperature in order to dissolve the hydrogen inside the crystal lattice of the sample. The equilibration state has been achieved after 60 min at the lowest temperature (300 С) and the hydrogen pressure in the gas circuit remains constant. Step 3. Direct experiment of the hydrogen exchange. That is the experiment when the protium inside the proton
Fig. 2 e Particle size distribution functions of La1¡xSrxScO3¡a (x ¼ 0, 0.04) powder samples.
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Fig. 3 e Scheme of the experimental rig for the hydrogen isotope exchange: 1) mass-spectrometer MicroVision 2 (MKS Instruments, USA); 2) quartz reactor with a sample; 3) spiral pump IDK-2 (Agilent, USA); 4) vacuum system MiniTask 24 (Agilent, USA); 5) ion pump Valcon Plus-40 (Agilent, USA); 6) Bayard-Alpert-Pirani pressure transducer FRG-720 (Agilent, USA); 7) high pressure transducer (Swagelok, USA); 8) leakage valve; 9) gas cylinder (Swagelok, USA); 10) T-type vacuum valve.
conducting oxide exchanges with gaseous deuterium from the gas phase. After the equilibrating of the sample at the particular hydrogen pressure and temperature the reactor with the sample was closed by means of the vacuum valve. The deuterium enriched hydrogen was inlet to the gas circuit. When the required hydrogen pressure is achieved, the reactor is opened and the hydrogen isotope exchange starts. The isotope composition of the gas phase is monitored by means of the mass-spectrometer. Step 4. Backward experiment. That is the experiment when the deuterium inside the proton conducting oxide exchanges with the gaseous protium from the gas phase. This step is necessary in order to observe the possible isotopic effects in hydrogen surface exchange process. This step is similar to the third one and differs by the isotope composition of hydrogen inlet to the gas circuit. In case of backward experiment natural hydrogen is used.
Results and discussion
Fig. 4 e Time dependencies of (a) protium and deuterium fraction in the gas phase and (b) residual of HD-fraction in the gas phase from the equilibrium value during the hydrogen isotope exchange experiment at hydrogen pressure 2 mbar and T ¼ 400 C for La0.96Sr0.04ScO3ea proton conducting oxide. The protium fractions p in the gas phase was obtained from backward D/H experiment and the deuterium fractions v in the gas phase d from direct H/D experiment. Red line in (b) correspond to fitting curve according to Equations (18) and (19); abbreviation of D and H in Y(D) and Y(H) correspond to the direct H/D and backward D/H experiments. (For interpretation of the references to color/colour in this figure legend, the reader is referred to the Web version of this article.)
Fig. 4a shows time dependencies of deuterium and protium fractions during the direct and backward experiments of hydrogen isotope exchange at T ¼ 400 C for La0.96Sr0.04ScO3ea proton conducting oxide. Since these experiments have been performed under the same hydrogen pressure (~2 mbar), it is absolutely clear to observe both thermodynamic and kinetic isotope effects. Thermodynamic isotope effect causes the different in the equilibrium values of the protium and deuterium in the gas phase: the lower equilibrium value of deuterium means, that the solubility of deuterium in the solid oxide is larger in comparison with protium. Kinetic isotopic effect causes different slopes of the initial part of time dependencies of
deuterium and protium fractions in the gas phase (Fig. 4a) and different residual of HD-fraction from the equilibrium value (Y-values) for direct and backward experiments (Fig. 4b). The rate of protium surface exchange is larger than the deuterium rate. Fig. 5a shows the temperature dependences of the deuterium and protium mole fraction in the La0.96Sr0.04ScO3ea oxide calculated as mean values from two parallel measurements in comparison with the undoped LaScO3 oxide. These mole fractions have been calculated using the mass conservation law:
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7
Observed thermodynamic isotope effect can be explained if we look at the reaction (2.2) of hydrogen uptake by the solid oxide. The difference between the equilibrium constants for the KD/KH reaction (2.2) in case of different isotopes can be written as follows: 0 1 0 KD EH2 E0D2 RT : (27) exp EOH E0OD 2 KH The thermodynamic isotope effect can be caused by the difference of energy of zero-point oscillations between the products OH and OD (E0OH and E0OD , respectively) of the reaction (2) and molecular H2 and D2 (E0H2 and E0D2 , respectively). The difference of the energy of zero-point oscillations of OH and OD is 5.85 kJ/mol and for H2 and D2 equals to 7.53 kJ/mol [32]. Substituting the values to (27) one can find that the difference is equal to 2.1 kJ/mol. As a result, deuterium solubility is thermodynamically more efficient process than protium solubility. The hydrogen pressure dependence of the protium and deuterium mole fraction for La0.96Sr0.04ScO3ea proton conducting oxide is shown in Fig. 4b. These dependencies have power-law form. Fig. 6a shows the hydrogen surface exchange coefficients calculated from the hydrogen heterogeneous exchange rates:
Fig. 5 e Protium and deuterium fraction as a function of (a) temperature at 2 mbar of hydrogen pressure and (b) hydrogen pressure dependencies in La0.96Sr0.04ScO3ea proton conducting oxide at different temperatures.
Ng v0 þ NO v0O ¼ v∞ Ng þ NO ;
(25)
Ng p0 þ NO p0O ¼ p∞ Ng þ NO ;
(26)
where Ng and NO the amount of hydrogen atoms in the gas phase and in the oxide; v0O and p0O correspond to the deuterium and protium fraction in the solid oxide. According to data presented in Fig. 5a, the temperature dependence of deuterium and protium mole fractions in the undoped LaScO3 corresponds to the absence of any considerable solubility of hydrogen in comparison with La0.96Sr0.04ScO3ea oxide. The saturation level of deuterium in La0.96Sr0.04ScO3ea is larger in contrast to protium over the whole temperature range. The solubility of hydrogen in La0.96Sr0.04ScO3ea oxide decreases with temperature such as at temperature >600 C the mole fraction of hydrogen isotopes is low and comparable with the hydrogen mole fractions in the undoped LaScO3 oxide. This residual amount of hydrogen at high temperatures is also comparable with the amount of hydrogen on the solid surface estimated from the value of the specific surface area and the assumption of monolayer coverage of the surface by hydrogen adatoms coupled with oxygen from the solid oxide lattice.
kðHÞ ¼
rH ðHÞ ; nOH
(28)
kðDÞ ¼
rH ðDÞ ; nOD
(29)
where nOH and nOD are protium and deuterium mole fraction in the solid oxide, respectively. According to Fig. 6a, there are two parts on the temperature dependencies of the hydrogen surface exchange coefficients: low temperature with apparent activation energy ~0.16 eV and high temperature with apparent activation energy ~0.12 eV. These two parts are in good agreement with two parts of temperature dependence of hydrogen mole fraction in solid oxide, Fig. 5a. The low temperature part of the hydrogen surface exchange coefficient dependence corresponds to hydrogen dissolved in the proton conducting oxide. The ratio between the pre-exponential factors for k(D) and k(H) is equal to 1.2 ± 0.2. That is in good agreement with the ratio between the zero-point oscillation frequencies for OD and OH vibration mode: 1.36 [33]. In the framework of the model for the hydrogen isotope exchange kinetics the mean values of the dissociative adsorption of hydrogen and hydrogen incorporation rates can be calculated using r, rH and r2 values from treatment of Yvalue time dependencies by means of (16) and (17) equations: ra ¼ r; ri ¼
(30)
rrH : r rH
(31)
The probability of incorporation for protium p(H) and deuterium p(D) is calculated as follows: pðHÞ ¼
ri ðHÞ ri ðDÞ and pðDÞ ¼ : ra ðHÞ þ ri ðHÞ ra ðDÞ þ ri ðDÞ
(32)
The temperature dependence of the probability incorporation for protium and deuterium shows that at low
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Fig. 7 e Time dependencies of H2, HD and D2 fractions as well as protium fraction in the gas phase during the series of hydrogen exchange experiments at hydrogen pressure 2 mbar and T ¼ 400 C for La0.96Sr0.04ScO3ea proton conducting oxide.
Fig. 6 e Temperature dependences of (a) protium and deuterium surface exchange coefficients and (b) protium and deuterium probability of incorporation at hydrogen pressure 2 mbar for La0.96Sr0.04ScO3ea proton conducting oxide.
temperature the kinetic isotope effect is caused by the different probability of protium and deuterium incorporation, Fig. 6b. At high temperatures without considerable solubility of hydrogen in the solid oxide the kinetic isotope effect on the probability of the incorporation is almost negligible. Since the probability of incorporation of hydrogen is larger than 0.5 the hydrogen dissociative adsorption stage is proved to be rate determining. This fact causes low apparent activation energies (~0.2 eV) of the hydrogen surface exchange coefficients. The last theoretical conclusion from our statistical model related to the different nature of the adsorption centers nonequality can be demonstrated in terms of the special experiment. The experiment consists of the same 3 base steps (Step 1, Step 2 and Step 3, mentioned above in the Experimental). The main difference is that we repeated the direct hydrogen exchange experiment one after another expecting different saturation level by the deuterium both the oxide volume and the oxide surface, Fig. 7.
In our case, the direct hydrogen exchange experiment was repeated 10 times. Fig. 7 shows changes of C2, C3 and C4 mole fractions in the gas phase for series of consecutive hydrogen exchange experiments. For each kinetic dependence r, rH and r2 in this series of the experiments have been calculated. Dependence of the ratio rrr22 on the number of the experiH ment is shown in Fig. 8. It demonstrates external behavior, and the reason can have the following explanation. Before the experiment we have initially only protium on the solid oxide surface with intrinsic nonequality of the surface adsorption centers and respective rrr22 -value is equal to 2.73. This value is larger than 1 H and caused mainly by the solid oxide surface inhomogeneity. During the experiment the fraction of deuterium increases changing the ratio between the protium and deuterium on the solid oxide surface. Nonequality of the adsorption centers increases with the number of the experiments until the
Fig. 8 e Dependence of the non-equivalence parameter on the number of the hydrogen exchange experiments at hydrogen pressure 2 mbar and T ¼ 400 C for La0.96Sr0.04ScO3ea proton conducting oxide.
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Fig. 9 e Temperature dependences of the heterogeneous hydrogen exchange rates in dry hydrogen atmosphere for different proton conducting oxides. amounts of protium and deuterium become close to each other. At this point the maximal rrr22 -value equal to 3.11 and H maximal nonequality of the solid oxide surface are observed caused by not only by the surface inhomogeneity but also the presence of two hydrogen isotopes on the solid oxide surface with different binding energy. Further increasing of the deuterium concentration on the solid oxide surface lead to the protium concentration decreasing and as a result decrease of the rrr22 values. H Fig. 9 shows the comparison of the hydrogen surface exchange data known in the literature with our results on La0.96Sr0.04ScO3ea proton conducting oxide. In general, there is a very large spread in apparent activation energies even for identical oxides. Today, it is very difficult to reveal any common relations from observed data due to large scattering on hydrogen exchange rate values. The further serious work is required for the better understanding of the hydrogen incorporation into the proton conducting oxides. Now we can mention that acceptor dopant (Sr0 La ) play an important role in the process of hydrogen uptake, according to reaction (2.2), written formally without interaction with oxygen vacancies, formed by acceptor doping. One of the most fundamental problem is the nature of the electronic defects in the hydrogen uptake process (2.2). One of the possible mechanisms of the electronic compensation can be associated with localization of the electronic defects on oxygen vacancies with F-centers formation, according to: 0 V O þ e ¼ VO ;
(33)
VO þ e0 ¼ V O:
(34)
Unfortunately, the isotopic exchange method cannot prove or disprove the possibility of presence of reaction [33]. Additional physical methods giving information about the defect structure of band gap in the oxides is required.
Conclusions The theoretical models for the hydrogen surface exchange kinetics description have been derived. Previously developed
9
model taking into account the nonequality of the adsorption centers has been adopted for the hydrogen isotope exchange experiment. Developed theoretical approaches have been implemented for the detailed description of the hydrogen surface exchange kinetics on La1xSrxScO3ea (x ¼ 0, 0.04) proton conducting oxides. The heterogeneous exchange rates of hydrogen isotopes with oxides La1xSrxScO3a (x ¼ 0; 0.04) have been calculated. It has been found that the hydrogen dissociative adsorption process is rate determining (the stage of exchange between the forms of hydrogen in the gas phase and the adsorption layer). Mole fractions of hydrogen isotopes in the studied oxides have been calculated. It was found that the solubility of deuterium is higher than protium. The observed thermodynamic isotopic effect can be due to the difference in the energies of zero-point oscillations of OH- and OD-defects and molecular forms of hydrogen H2 and D2. It is shown that the deuterium surface exchange coefficient is smaller in comparison with the protium surface exchange coefficient for the proton-conducting oxide La0.96Sr0.04ScO3a. The observed kinetic isotopic effect can be explained by the different strengths of the OH and OD bonds. A new statistical criterion is proposed for the first time allowing dividing the observed surface inhomogeneities caused by not only the natural surface roughness but also the presence of different isotopes of hydrogen (protium and deuterium) and different binding energies, respectively. High catalytic activity with respect to the process of exchange with hydrogen of the gas phase in reducing atmospheres allows us to consider proton-conducting oxides La1xSrxScO3a as promising proton-conducting electrolytes for various solid-oxide electrochemical devices.
Acknowledgements This study is partly supported by the grant of the Russian Science Foundation (Project number N 16-13-00053) and Russian Foundation for Basic Research (N 16-08-01139). This work is done using the facilities of the Shared access center “Composition of Compounds” and Unique Scientific Setup “Isotope Exchange” of IHTE UB RAS. The education activity of Ph.D. and master students involved into this work is supported by Act 211 of Government of the Russian Federation, agreement No. 02.A03.21.0006 and the grant of the President of Russian Federation 2018e2019. Authors are grateful to Dr. A.V. Kuzmin for the samples supply, Dr. N.M. Porotnikova for BET and laser scattering analysis and Dr. B.D. Antonov for XRD analysis.
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