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Proton transfer in HnRhI3 + n: Conductivity and 1H NMR studies
Solid State Ionics 177 (2007) 3385 – 3388 www.elsevier.com/locate/ssi
Proton transfer in HnRhI3 + n: Conductivity and 1 H NMR studies N.K. Moroz a,⁎, S.G. Kozlova a,b , N.F. Uvarov c , K.V. Yusenko a , S.V. Korenev a a
Nikolaev Institute of Inorganic Chemistry, Russian Academy of Sciences, Siberian Branch, Ave. Lavrentiev 3, 630090 Novosibirsk, Russian Federation b Boreskov Institute of Catalysis, Russian Academy of Sciences, Siberian Branch, Ave. Lavrentiev 5, 630090 Novosibirsk, Russian Federation c Institute of Solid State Chemistry and Mechanochemistry, Russian Academy of Sciences, Siberian Branch, Kutateladze 18, 630128 Novosibirsk, Russian Federation Received 10 May 2006; received in revised form 29 September 2006; accepted 24 October 2006
Abstract Proton transfer in the solid HI-enriched rhodium iodide (H0.81RhI3.81) at 150–400 K was studied using conductivity measurements and H NMR. The compound displays rather high proton conductivity (10− 4 S/cm at 360 K) associated with the activation energy for proton migration of ≈ 0.32 eV which is very close to the activation energy reported earlier for solid iodine doped with HI. From quantum-chemical calculations it was supposed that the interaction between HI molecules and I− ions results in symmetrical or quasi-symmetrical H-bonded complexes [HI2]−, and the conductivity mechanism is apparently a two-stage proton transfer: proton displacement along the hydrogen bond followed by HI reorientation. © 2006 Elsevier B.V. All rights reserved. 1
Keywords: Layered iodides; Rhodium iodide; Hydrogen–rhodium iodide; Proton transfer; Proton conductivity; 1H NMR
1. Introduction It was shown earlier that HI molecules dissolved in solid iodine dissociate to yield excess protons which are able to migrate through the iodine lattice and produce noticeable proton conductivity [1]. It is conceivable that HI-induced conductivity is not unique for HI–I2 system and HI molecules can exhibit similar behavior in various solids with branched networks formed by iodine atoms or ions, for example, in layered iodides much studied these recent years (e.g. [2,3] and references therein). The subject of our study is the proton transfer in layered RhI3 doped with HI. In rhodium iodide, the iodine ions form quasi two-dimensional networks with I–I distances of 3.8–4.1 Å and 4.2–5.6 Å inside a layer and between the layers, respectively [4]. The water-insoluble RhI3 can be precipitated from water solutions of complex rhodium chlorides under the action of alkali-metal iodides or hydrogen iodide [5]. We found out that in the latter case the product may contain a substantial amount of HI and hypothesized that this material might be a potential
⁎ Corresponding author. Fax: +7 383 3309489. E-mail address: [email protected] (N.K. Moroz). 0167-2738/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2006.10.021
proton-conducting medium. With this assumption we examined the proton mobility in the HI-doped RhI3 using conductivity measurements and the proton magnetic resonance technique. 2. Experimental Samples. An excess of aqueous HI distilled with sodium hypophosphite prior to use was added to a 0.2 M rhodium solution prepared by dissolving commercial RhCl3·4H2O in aqueous HCl. The reaction mixture was held for 15–20 min at room temperature, and then it was brought to the boiling-point and boiled for 5–10 min. The obtained black precipitate was collected on a glass filter, washed with a small volume of water and dried for 2 h at 340–350 K. Elemental analysis showed that the obtained compounds are HI-containing rhodium iodides with HI content depending on the starting Rh/HI ratio in the reaction mixture. The HI-enriched rhodium iodides are X-ray amorphous. However, when heated up to 750–800 K in helium they form a phase with the rhodium content of 21.3%, and XRD powder pattern typical [4] of stoichiometric RhI3. Being heated in air, the samples demonstrate two marked steps of weight loss (Fig. 1): the first at 420–650 K is due to HI removal, and the second at 670–900 K corresponds to the transformation of rhodium iodide into rhodium (III) oxide. The IR spectra of HI-
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N.K. Moroz et al. / Solid State Ionics 177 (2007) 3385–3388
Fig. 1. Heating curve of H0.81RhI3.81 in air (Q-1000 derivatograph, heating rate = 10 K/min).
enriched samples (Scimitar FTS 2000 Fourier Spectrometer, KBr pellet) are monotonic functions with no individual absorption lines in the range 1700–2500 cm− 1; the absence of the band expected for H–I vibrations (∼2230 cm− 1 [6]) tells against the presence of adsorbed HI molecules in the solid phase and might be indicative of HI protons distributed over the iodine layers according to the formula HnRhI3 + n rather than RhI3·nHI. The results below relate to the most hydrogen enriched iodide samples with n reaching 0.81(2). Conductivity, σ, was measured in the temperature range 296–436 K on two H0.81RhI3.81 pellets (Samples I and II, respectively) compacted at 500 MPa together with two Ag powder electrodes. The conductivity measurements were carried out in air using 4284A Precision LCR Meter at frequencies from 20 Hz to 1 MHz. The σ values were estimated to the accuracy ≈ 5% using a complex impedance method by fitting experimental active–reactive resistance curves to semicircles calculated for standard equivalent electrochemical circuits. 1 H NMR measurements were carried out for powder H0.81RhI3.81 at 140–290 K. The broad-line spectra resulting from the magnetic dipole–dipole proton interactions were recorded in the form of the first derivative of the NMR absorption line by sweeping the frequency in the neighborhood of 25 MHz using a homemade NMR spectrometer with signal accumulation.
Fig. 2. Temperature dependences of conductivity for Samples I (▴) and II (▿): 1 — freshly prepared pellets, 2 — after heating up to 440 K. Solid curves show σ(T) calculated according to the chosen parameters (see the text).
significant HI removal has not been recorded below 400 K in the course of the relatively fast heating H0.81RhI3.81 in the process of thermogravimetric analysis (Fig. 1), it might take place in more prolonged conductivity measurements. The derived Ea values are very close to the activation energy for the HI-doped solid iodine (≈ 0.34 eV [1]), and we suppose that the H+ ions are charge carriers in the HI-doped rhodium iodide as it was hypothesized for the protonated iodine.
3. Results and discussion Reproducible temperature dependences of conductivity were observed for both Samples I and II (Fig. 2). The conductivity of freshly prepared pellets at T = 296–360 K varies from 2 × 10− 5 to 10− 4 S/cm (trace 1) corresponding to a dependence σT = A exp(− Ea / kBT) with the pre-exponential factor A = (7.5 ± 2.5)× 102 S K/cm and activation energy Ea = 0.31 ± 0.02 eV. The conductivity behavior changes with further heating: after slight decrease at 360–400 K the σ values obey a new σ(T) dependence (trace 2) with the following parameters: A = (6.5 ± 2.5) × 102 S K/cm and Ea = 0.34 ± 0.02 eV. These changes can be attributed to a decreased number of charge carriers due to partial removal of the HI molecules from the samples. Although
Fig. 3. a— 1H NMR absorption spectra obtained from experimental derivatives for powder H0.81RhI3.81 at different temperatures (Δf is the frequency deflection from the Larmor frequency). b — Temperature dependences of the spectrum half-width: (○) — experimental, (—) — calculated from Eq. (1).
N.K. Moroz et al. / Solid State Ionics 177 (2007) 3385–3388
To confirm the hypothesis on proton nature of conductivity, the 1H NMR wide-line spectra (Fig. 3a) were obtained and analyzed. At 250–290 K the spectra look like narrow Lorentzian-shaped lines with the half-width δωHW ≤ 0.4 kHz and are indicative of fast (in the NMR time scale) mobility of protons which results in effective suppression of the spin–spin interactions. The transformation of the spectra resulting from the retardation of the proton motion takes place at 200–160 K; the corresponding δωHW(T) dependence is shown on Fig. 3b. From this dependence we attempted to estimate the protonmigration activation energy assuming that: (i) the H+-jump correlation frequency, νc, changes with temperature in accord with the Arrhenius equation νc = νo exp(Ea / kBT); (ii) in perfect analogy to the relation between the correlation frequency and the second moment of the spectrum, the relation between νc and δωHW can be expressed as [7] δω2HW
¼
δω2∞
þ
δω2o −δω2∞
αδωHW argtg ; π νc
2
ð1Þ
where δωo and δω∞ are the low-temperature and hightemperature limits of δωHW corresponding to νc → 0 and νc → ∞, respectively, and α is a coefficient in the order of 1 considered as temperature independent in the first approximation. With these assumptions, the δωHW(T) dependence is specified by the following four parameters: δωo, δω∞, Ea, and νo (or, more precisely, νo / α). The best fit to the experimental data was obtained for δωo = 10 kHz, δω∞ = 0.3 kHz, νo / α = 7 × 1012 s− 1 and Ea = 0.32 ± 0.02 eV. In our case δω∞ is determined mainly by instrumental limitations (modulation and inhomogeneity of the external magnetic field) and therefore corresponds to almost total averaging of the magnetic dipole–dipole proton interactions at high correlation frequencies. This kind of averaging should be expected for a motion associated with proton self-diffusion. This fact together with the coincidence between the activation energy and Ea estimated from the above conductivity measurements is a definite indication that the charge transfer in HnRhI3 + n is due to the proton migration through the iodide lattice. As a rough approximation, the mean length of the ffiproton jumps can be estimated as pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi λ≈ 6AkB =cp e2 νo ; where cp = 2.6 × 1021 cm− 3 is the proton bulk concentration found from the density of H0.81RhI3.81 (3.15 g/cm3). Then, supposing that α ≈ 1 in Eq. (1), we obtain a rather realistic value λ ≈ 1.2 Å. The energy minima of protons in the studied compound can be presumably attributed to their location between two I− ions to make structural defects in the form of symmetrical or asymmetrical [IHI]- complexes. If this is the case, the conductivity mechanism is a two-stage proton transfer: first the proton moves along I–I direction to form an H-bonded molecular-ion complex IH·I−, and then the HI molecule reorients to create a new [IHI]- complex at the adjacent site. A similar conduction mechanism is generally attributed to superionic materials of the M3H(AO4)2 type [8]. The suggested mechanism was tested against quantumchemical calculations of [IHI]− complex through ADF2005 code [9]. We found out that the optimum geometry for the
3387
Fig. 4. [IHI]− energy increase as a function of the proton displacement from the bond center at RII: 3.90 (1); 4.10 (2); 4.25 (3) Å. The curves are drawn till the points corresponding to RIH = 1.63 Å.
complex corresponds to the bond energy of − 4.5 eV (compared with the total energy of isolated fragments HI and I−) with I–I distance RII ≈ 3.9 Å and the proton in the central position. As is seen in Fig. 4, the proton is localized in a rather flat potential well which transforms into a double-well when RII exceeds 4.1 Å. Note that in solids the complex symmetry may be distorted by the influence of the surrounding atoms. At RII corresponding to the single-well region the displacement of the proton from the center toward an iodine ion is associated with a 0.25–0.30 eV energy increase when I–H distance approaches 1.63 Å, a distance typical of HI molecules. These estimations and experimental Ea suggest that the activation energy for proton migration through the iodide crystal is limited by the energy needed to make a molecular-ion complex rather than the energy barrier for the reorientation of HI molecule. In other words, HI molecule can act as a transition state when a proton jumps between the equilibrium positions. Of course, it does not rule out the fact that HI molecules may be present in the form of steady-state defects which increase in number with temperature. 4. Conclusions The capture of hydrogen iodide molecules in layered rhodium iodide leads to the formation of a defective protonated structure where excess protons are distributed dynamically over the iodine layers. This compound, which may be assigned to proton glasses, remains stable up to ≈ 400 K and displays rather high proton conductivity (10− 4 S/cm at 360 K). Conductivity and 1H NMR measurements allowed tracing the development of proton mobility in a wide temperature range (150–415 K) associated with the change of the proton-jump frequency from 2 × 102 s− 1 to 109 s− 1. No sign of proton ordering was observed in the considered temperature range, and the proton subsystem is likely to remain disordered up to 0 K. Since the activation energy for the proton migration in the HnRhI3 + n system was found out identical to the one reported for solid iodine doped with HI [1], we suggest that the mechanisms of proton transport are identical in these materials in spite of fundamental differences in their structures. A two-stage proton transfer is suggested as a possible mechanism of conductivity: a proton displacement along an I–H–I bridge (intrabond transfer)
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N.K. Moroz et al. / Solid State Ionics 177 (2007) 3385–3388
followed by inter-bond proton transfer due to HI reorientation. Note that local rearrangement of iodine ions can be essential for both processes. The discussed mechanism is expected to be rather common for various iodine-based proton conductors whatever their structure might be. References [1] [2] [3] [4] [5] [6]
K. Tennakone, Solid State Ionics 13 (1984) 241. L.M. Castro-Castro, A.M. Guloy, Inorg. Chem. 43 (2004) 4537. J.-I. Fujisawa, T. Ishihara, Phys. Rev. B 70 (2004) 205330. K. Brodersen, G. Thiele, I. Reche, J. Less-Common Met. 15 (1968) 151. A.V. Belyaev, A.B. Venedictov, Russ. J. Coord. Chem. 12 (1986) 116. K. Nakamoto, Infrared and Raman Spectra of Inorganic and Coordination Compounds, Wiley, NY, 1997.
[7] A. Abragam, The Principles of Nuclear Magnetism, Clarendon Press, Oxford, 1961. [8] A.V. Belushkin, C.J. Carlile, L.A. Shuvalov, Ferroelectrics 167 (1995) 21. [9] Amsterdam Density Functional (ADF) program, Release 2005.02; Vrije Universteit: Amsterdam, The Netherlands, 2005. The standard ADF TZP basic sets without core-potentials were used; the VWN parameterisation (S.H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58 (1980) 1200) was applied for the local density approximation; the gradient corrections were added to account for the exchange (A.D. Becke, Phys. Rev. A 38 (1988) 3098) and correlation (J.P. Perdew, Phys. Rev. B 33 (1986) 8822) interactions; the relativistic corrections were accounted by the scalar zeroth-order approximation method (E. Van Lenthe, A.E. Ehlers, E.J. Baerends, J. Chem. Phys. 110 (1999) 8943).
Proton transfer in HnRhI3 + n: Conductivity and 1 H NMR studies N.K. Moroz a,⁎, S.G. Kozlova a,b , N.F. Uvarov c , K.V. Yusenko a , S.V. Korenev a a
Nikolaev Institute of Inorganic Chemistry, Russian Academy of Sciences, Siberian Branch, Ave. Lavrentiev 3, 630090 Novosibirsk, Russian Federation b Boreskov Institute of Catalysis, Russian Academy of Sciences, Siberian Branch, Ave. Lavrentiev 5, 630090 Novosibirsk, Russian Federation c Institute of Solid State Chemistry and Mechanochemistry, Russian Academy of Sciences, Siberian Branch, Kutateladze 18, 630128 Novosibirsk, Russian Federation Received 10 May 2006; received in revised form 29 September 2006; accepted 24 October 2006
Abstract Proton transfer in the solid HI-enriched rhodium iodide (H0.81RhI3.81) at 150–400 K was studied using conductivity measurements and H NMR. The compound displays rather high proton conductivity (10− 4 S/cm at 360 K) associated with the activation energy for proton migration of ≈ 0.32 eV which is very close to the activation energy reported earlier for solid iodine doped with HI. From quantum-chemical calculations it was supposed that the interaction between HI molecules and I− ions results in symmetrical or quasi-symmetrical H-bonded complexes [HI2]−, and the conductivity mechanism is apparently a two-stage proton transfer: proton displacement along the hydrogen bond followed by HI reorientation. © 2006 Elsevier B.V. All rights reserved. 1
Keywords: Layered iodides; Rhodium iodide; Hydrogen–rhodium iodide; Proton transfer; Proton conductivity; 1H NMR
1. Introduction It was shown earlier that HI molecules dissolved in solid iodine dissociate to yield excess protons which are able to migrate through the iodine lattice and produce noticeable proton conductivity [1]. It is conceivable that HI-induced conductivity is not unique for HI–I2 system and HI molecules can exhibit similar behavior in various solids with branched networks formed by iodine atoms or ions, for example, in layered iodides much studied these recent years (e.g. [2,3] and references therein). The subject of our study is the proton transfer in layered RhI3 doped with HI. In rhodium iodide, the iodine ions form quasi two-dimensional networks with I–I distances of 3.8–4.1 Å and 4.2–5.6 Å inside a layer and between the layers, respectively [4]. The water-insoluble RhI3 can be precipitated from water solutions of complex rhodium chlorides under the action of alkali-metal iodides or hydrogen iodide [5]. We found out that in the latter case the product may contain a substantial amount of HI and hypothesized that this material might be a potential
⁎ Corresponding author. Fax: +7 383 3309489. E-mail address: [email protected] (N.K. Moroz). 0167-2738/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2006.10.021
proton-conducting medium. With this assumption we examined the proton mobility in the HI-doped RhI3 using conductivity measurements and the proton magnetic resonance technique. 2. Experimental Samples. An excess of aqueous HI distilled with sodium hypophosphite prior to use was added to a 0.2 M rhodium solution prepared by dissolving commercial RhCl3·4H2O in aqueous HCl. The reaction mixture was held for 15–20 min at room temperature, and then it was brought to the boiling-point and boiled for 5–10 min. The obtained black precipitate was collected on a glass filter, washed with a small volume of water and dried for 2 h at 340–350 K. Elemental analysis showed that the obtained compounds are HI-containing rhodium iodides with HI content depending on the starting Rh/HI ratio in the reaction mixture. The HI-enriched rhodium iodides are X-ray amorphous. However, when heated up to 750–800 K in helium they form a phase with the rhodium content of 21.3%, and XRD powder pattern typical [4] of stoichiometric RhI3. Being heated in air, the samples demonstrate two marked steps of weight loss (Fig. 1): the first at 420–650 K is due to HI removal, and the second at 670–900 K corresponds to the transformation of rhodium iodide into rhodium (III) oxide. The IR spectra of HI-
3386
N.K. Moroz et al. / Solid State Ionics 177 (2007) 3385–3388
Fig. 1. Heating curve of H0.81RhI3.81 in air (Q-1000 derivatograph, heating rate = 10 K/min).
enriched samples (Scimitar FTS 2000 Fourier Spectrometer, KBr pellet) are monotonic functions with no individual absorption lines in the range 1700–2500 cm− 1; the absence of the band expected for H–I vibrations (∼2230 cm− 1 [6]) tells against the presence of adsorbed HI molecules in the solid phase and might be indicative of HI protons distributed over the iodine layers according to the formula HnRhI3 + n rather than RhI3·nHI. The results below relate to the most hydrogen enriched iodide samples with n reaching 0.81(2). Conductivity, σ, was measured in the temperature range 296–436 K on two H0.81RhI3.81 pellets (Samples I and II, respectively) compacted at 500 MPa together with two Ag powder electrodes. The conductivity measurements were carried out in air using 4284A Precision LCR Meter at frequencies from 20 Hz to 1 MHz. The σ values were estimated to the accuracy ≈ 5% using a complex impedance method by fitting experimental active–reactive resistance curves to semicircles calculated for standard equivalent electrochemical circuits. 1 H NMR measurements were carried out for powder H0.81RhI3.81 at 140–290 K. The broad-line spectra resulting from the magnetic dipole–dipole proton interactions were recorded in the form of the first derivative of the NMR absorption line by sweeping the frequency in the neighborhood of 25 MHz using a homemade NMR spectrometer with signal accumulation.
Fig. 2. Temperature dependences of conductivity for Samples I (▴) and II (▿): 1 — freshly prepared pellets, 2 — after heating up to 440 K. Solid curves show σ(T) calculated according to the chosen parameters (see the text).
significant HI removal has not been recorded below 400 K in the course of the relatively fast heating H0.81RhI3.81 in the process of thermogravimetric analysis (Fig. 1), it might take place in more prolonged conductivity measurements. The derived Ea values are very close to the activation energy for the HI-doped solid iodine (≈ 0.34 eV [1]), and we suppose that the H+ ions are charge carriers in the HI-doped rhodium iodide as it was hypothesized for the protonated iodine.
3. Results and discussion Reproducible temperature dependences of conductivity were observed for both Samples I and II (Fig. 2). The conductivity of freshly prepared pellets at T = 296–360 K varies from 2 × 10− 5 to 10− 4 S/cm (trace 1) corresponding to a dependence σT = A exp(− Ea / kBT) with the pre-exponential factor A = (7.5 ± 2.5)× 102 S K/cm and activation energy Ea = 0.31 ± 0.02 eV. The conductivity behavior changes with further heating: after slight decrease at 360–400 K the σ values obey a new σ(T) dependence (trace 2) with the following parameters: A = (6.5 ± 2.5) × 102 S K/cm and Ea = 0.34 ± 0.02 eV. These changes can be attributed to a decreased number of charge carriers due to partial removal of the HI molecules from the samples. Although
Fig. 3. a— 1H NMR absorption spectra obtained from experimental derivatives for powder H0.81RhI3.81 at different temperatures (Δf is the frequency deflection from the Larmor frequency). b — Temperature dependences of the spectrum half-width: (○) — experimental, (—) — calculated from Eq. (1).
N.K. Moroz et al. / Solid State Ionics 177 (2007) 3385–3388
To confirm the hypothesis on proton nature of conductivity, the 1H NMR wide-line spectra (Fig. 3a) were obtained and analyzed. At 250–290 K the spectra look like narrow Lorentzian-shaped lines with the half-width δωHW ≤ 0.4 kHz and are indicative of fast (in the NMR time scale) mobility of protons which results in effective suppression of the spin–spin interactions. The transformation of the spectra resulting from the retardation of the proton motion takes place at 200–160 K; the corresponding δωHW(T) dependence is shown on Fig. 3b. From this dependence we attempted to estimate the protonmigration activation energy assuming that: (i) the H+-jump correlation frequency, νc, changes with temperature in accord with the Arrhenius equation νc = νo exp(Ea / kBT); (ii) in perfect analogy to the relation between the correlation frequency and the second moment of the spectrum, the relation between νc and δωHW can be expressed as [7] δω2HW
¼
δω2∞
þ
δω2o −δω2∞
αδωHW argtg ; π νc
2
ð1Þ
where δωo and δω∞ are the low-temperature and hightemperature limits of δωHW corresponding to νc → 0 and νc → ∞, respectively, and α is a coefficient in the order of 1 considered as temperature independent in the first approximation. With these assumptions, the δωHW(T) dependence is specified by the following four parameters: δωo, δω∞, Ea, and νo (or, more precisely, νo / α). The best fit to the experimental data was obtained for δωo = 10 kHz, δω∞ = 0.3 kHz, νo / α = 7 × 1012 s− 1 and Ea = 0.32 ± 0.02 eV. In our case δω∞ is determined mainly by instrumental limitations (modulation and inhomogeneity of the external magnetic field) and therefore corresponds to almost total averaging of the magnetic dipole–dipole proton interactions at high correlation frequencies. This kind of averaging should be expected for a motion associated with proton self-diffusion. This fact together with the coincidence between the activation energy and Ea estimated from the above conductivity measurements is a definite indication that the charge transfer in HnRhI3 + n is due to the proton migration through the iodide lattice. As a rough approximation, the mean length of the ffiproton jumps can be estimated as pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi λ≈ 6AkB =cp e2 νo ; where cp = 2.6 × 1021 cm− 3 is the proton bulk concentration found from the density of H0.81RhI3.81 (3.15 g/cm3). Then, supposing that α ≈ 1 in Eq. (1), we obtain a rather realistic value λ ≈ 1.2 Å. The energy minima of protons in the studied compound can be presumably attributed to their location between two I− ions to make structural defects in the form of symmetrical or asymmetrical [IHI]- complexes. If this is the case, the conductivity mechanism is a two-stage proton transfer: first the proton moves along I–I direction to form an H-bonded molecular-ion complex IH·I−, and then the HI molecule reorients to create a new [IHI]- complex at the adjacent site. A similar conduction mechanism is generally attributed to superionic materials of the M3H(AO4)2 type [8]. The suggested mechanism was tested against quantumchemical calculations of [IHI]− complex through ADF2005 code [9]. We found out that the optimum geometry for the
3387
Fig. 4. [IHI]− energy increase as a function of the proton displacement from the bond center at RII: 3.90 (1); 4.10 (2); 4.25 (3) Å. The curves are drawn till the points corresponding to RIH = 1.63 Å.
complex corresponds to the bond energy of − 4.5 eV (compared with the total energy of isolated fragments HI and I−) with I–I distance RII ≈ 3.9 Å and the proton in the central position. As is seen in Fig. 4, the proton is localized in a rather flat potential well which transforms into a double-well when RII exceeds 4.1 Å. Note that in solids the complex symmetry may be distorted by the influence of the surrounding atoms. At RII corresponding to the single-well region the displacement of the proton from the center toward an iodine ion is associated with a 0.25–0.30 eV energy increase when I–H distance approaches 1.63 Å, a distance typical of HI molecules. These estimations and experimental Ea suggest that the activation energy for proton migration through the iodide crystal is limited by the energy needed to make a molecular-ion complex rather than the energy barrier for the reorientation of HI molecule. In other words, HI molecule can act as a transition state when a proton jumps between the equilibrium positions. Of course, it does not rule out the fact that HI molecules may be present in the form of steady-state defects which increase in number with temperature. 4. Conclusions The capture of hydrogen iodide molecules in layered rhodium iodide leads to the formation of a defective protonated structure where excess protons are distributed dynamically over the iodine layers. This compound, which may be assigned to proton glasses, remains stable up to ≈ 400 K and displays rather high proton conductivity (10− 4 S/cm at 360 K). Conductivity and 1H NMR measurements allowed tracing the development of proton mobility in a wide temperature range (150–415 K) associated with the change of the proton-jump frequency from 2 × 102 s− 1 to 109 s− 1. No sign of proton ordering was observed in the considered temperature range, and the proton subsystem is likely to remain disordered up to 0 K. Since the activation energy for the proton migration in the HnRhI3 + n system was found out identical to the one reported for solid iodine doped with HI [1], we suggest that the mechanisms of proton transport are identical in these materials in spite of fundamental differences in their structures. A two-stage proton transfer is suggested as a possible mechanism of conductivity: a proton displacement along an I–H–I bridge (intrabond transfer)
3388
N.K. Moroz et al. / Solid State Ionics 177 (2007) 3385–3388
followed by inter-bond proton transfer due to HI reorientation. Note that local rearrangement of iodine ions can be essential for both processes. The discussed mechanism is expected to be rather common for various iodine-based proton conductors whatever their structure might be. References [1] [2] [3] [4] [5] [6]
K. Tennakone, Solid State Ionics 13 (1984) 241. L.M. Castro-Castro, A.M. Guloy, Inorg. Chem. 43 (2004) 4537. J.-I. Fujisawa, T. Ishihara, Phys. Rev. B 70 (2004) 205330. K. Brodersen, G. Thiele, I. Reche, J. Less-Common Met. 15 (1968) 151. A.V. Belyaev, A.B. Venedictov, Russ. J. Coord. Chem. 12 (1986) 116. K. Nakamoto, Infrared and Raman Spectra of Inorganic and Coordination Compounds, Wiley, NY, 1997.
[7] A. Abragam, The Principles of Nuclear Magnetism, Clarendon Press, Oxford, 1961. [8] A.V. Belushkin, C.J. Carlile, L.A. Shuvalov, Ferroelectrics 167 (1995) 21. [9] Amsterdam Density Functional (ADF) program, Release 2005.02; Vrije Universteit: Amsterdam, The Netherlands, 2005. The standard ADF TZP basic sets without core-potentials were used; the VWN parameterisation (S.H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58 (1980) 1200) was applied for the local density approximation; the gradient corrections were added to account for the exchange (A.D. Becke, Phys. Rev. A 38 (1988) 3098) and correlation (J.P. Perdew, Phys. Rev. B 33 (1986) 8822) interactions; the relativistic corrections were accounted by the scalar zeroth-order approximation method (E. Van Lenthe, A.E. Ehlers, E.J. Baerends, J. Chem. Phys. 110 (1999) 8943).