Ultra-fast grain boundary diffusion and its contribution to surface segregation on a martensitic steel. Experiments and modeling

Phosphorus surface segregation was measured by Auger Electron Spectroscopy on a 17-4 PH martensitic stainless steel at 450, 550 and 600 °C. Surface segregation was shown to be much faster than expected which was attributed to a high contribution of phosphorus diffusion along the former austenitic grain boundaries. A model of surface segregation was developed following the Darken–du Plessis approach and taking account of both bulk and grain boundary solute diffusion. The phosphorus grain boundary diffusion coefficient in 17-4 PH was estimated: D_GB^< = 6.2 10⁴ exp(? 157 kJ mol^? 1/RT)cm² s^? 1. It is found to be more than three orders of magnitude higher in 17-4 PH steel than in α-iron.     

Water and lipid diffusion MRI using chemical shift displacement-based separation of lipid tissue (SPLIT)

PurposeTo obtain water and lipid diffusion-weighted images (DWIs) simultaneously, we devised a novel method utilizing chemical shift displacement-based separation of lipid tissue (SPLIT) imaging.Materials and methodsSingle-shot diffusion echo-planar imaging without fat suppression was used and the imaging parameters were optimized to separate water and lipid DWIs by chemical shift displacement of the lipid signals along the phase-encoding direction. Using the optimized conditions, transverse DWIs at the maximum diameter of the right calf were scanned with multiple b-values in five healthy subjects. Then, apparent diffusion coefficients (ADCs) were calculated in the tibialis anterior muscle (TA), tibialis bone marrow (TB), and subcutaneous fat (SF), as well as restricted and perfusion-related diffusion coefficients (D and D*, respectively) and the fraction of the perfusion-related diffusion component (F) for TA.ResultsWater and lipid DWIs were separated adequately. The mean ADCs of the TA, TB, and SF were 1.56 ± 0.03 mm²/s, 0.01 ± 0.01 mm²/s, and 0.06 ± 0.02 mm²/s, respectively. The mean D*, D, and F of the TA were 13.7 ± 4.3 mm²/s, 1.48 ± 0.05 mm²/s, and 4.3 ± 1.6%, respectively.ConclusionSPLIT imaging makes it possible to simply and simultaneously obtain water and lipid DWIs without special pulse sequence and increases the amount of diffusion information of water and lipid tissue.     

Oxygen diffusion studies on (Y2O3)2(Sc2O3)9(ZrO2)89

The oxygen tracer diffusion coefficient (D?) has been measured for 9 mol% scandia 2 mol% yttria co-doped zirconia solid solution, (Y₂O₃)₂(Sc₂O₃)₉(ZrO₂)₈₉, using isotopic exchange and line scanning by Secondary Ion Mass Spectrometry, as a function of temperature. The values of the tracer diffusion coefficient are in the range of 10^? 8–10^? 7 cm² s^? 1 and the Arrhenius activation energy was calculated to be 0.9 eV; both valid in the temperature range of 600–900 °C. Electrical conductivity measurements were carried out using 2-probe and 4-probe AC impedance spectroscopy, and a 4-point DC method at various temperatures. There is a good agreement between the measured tracer diffusion coefficients (D?, Ea = 0.9 eV) and the diffusion coefficients calculated from the DC total conductivity data (D_σ, Ea = 1.0 eV), the latter calculated using the Nernst–Einstein relationship.     

Oxygen nonstoichiometry and transport properties of strontium substituted lanthanum cobaltite

Oxygen nonstoichiometry, structure and transport properties of the two compositions (La_0.6Sr_0.4)_0.99CoO_3−δ (LSC40) and La_0.85Sr_0.15CoO_3−δ (LSC15) were measured. It was found that the oxygen nonstoichiometry as a function of the temperature and oxygen partial pressure could be described using the itinerant electron model. The electrical conductivity, σ, of the materials is high (σ > 500 S cm^− 1) in the measured temperature range (650–1000 °C) and oxygen partial pressure range (0.209–10^− 4 atm). At 900 °C the electrical conductivity is 1365 and 1491 S cm^− 1 in air for LSC40 and LSC15, respectively. A linear correlation between the electrical conductivity and the oxygen vacancy concentration was found for both samples. The mobility of the electron-holes was inversely proportional with the absolute temperature indicating a metallic type conductivity for LSC40. Using electrical conductivity relaxation the chemical diffusion coefficient of oxygen was determined. It was found that accurate values of the chemical diffusion coefficient could only be obtained using a sample with a porous surface coating. The porous surface coating increased the surface exchange reaction thereby unmasking the chemical diffusion coefficient. The ionic conductivity deduced from electrical conductivity relaxation was determined to be 0.45 S cm^− 1 and 0.01 S cm^− 1 at 1000 and 650 °C, respectively. The activation energy for the ionic conductivity at a constant vacancy concentration (δ = 0.125) was found to be 0.90 eV.     

Extraction mechanism of ultrasound assisted extraction and its effect on higher yielding and purity of artemisinin crystals from Artemisia annua L. leaves

This study proposes an ultrasound-horn system for the extraction of a natural active compound “artemisinin” from Artemisia annua L. leaves as an alternative to hot maceration technique. Ultrasound leaching improves artemisinin recovery at all temperatures where only ten minutes is required to recover 70% (4.42 mg g⁻¹) compared to 60 min of conventional hot leaching for the same yield. For instance, ultrasound treatment at 30 °C produced a higher yield than the one obtained by conventional maceration at 40 °C. Kinetic study suggests that the extraction pattern can be assimilated, during the first ten minutes, to a first order steady state, from which activation energy calculations revealed that each gram of artemisinin required 7.38 kJ in ultrasound versus 10.3 kJ in the conventional system. Modeling results indicate the presence of two extraction stages, a faster stage with a diffusion coefficient of 19 × 10⁻⁵ cm² min⁻¹ for ultrasound technique at 40 °C, seven times higher than the conventional one; and a second deceleration stage similar for both techniques with diffusion coefficient ranging from 1.7 to 3.1 × 10⁻⁵ cm² min⁻¹. It is noted that the efficient ultrasound extraction potential implies extraction of higher amount of co-metabolites so low artemisinin crystal purity is engendered but a combination with a purification step using activated charcoal and celite adsorbents produced crystals with comparable purity for conventional and ultrasound samples.     

Differentiation of central gland prostate cancer from benign prostatic hyperplasia using monoexponential and biexponential diffusion-weighted imaging

PurposeTo investigate biexponential apparent diffusion parameters of prostate central gland (CG) cancer, stromal hyperplasia (SH), and glandular hyperplasia (GH) and compare with monoexponential apparent diffusion coefficient (ADC) value for discriminating prostate cancer from benign hyperplasia.Materials and MethodsTwenty-one CG cancer foci, 23 SH and 26 GH nodules in the CG were analyzed in 39 patients (19 with CG cancer, 20 with peripheral zone cancer but no CG cancer) who underwent preoperative conventional DWI (b-value 0, 1000 s/mm²) and a 10 b-value (range 0 to 3000 s/mm²) DWI. All of the cancer and hyperplastic foci on MR images were localized on the basis of histopathologic correlation. The ADC value of the monoexponential DWI, and the fast apparent diffusion coefficient (ADCf), slow apparent diffusion coefficient (ADCs) value and the fraction of ADCf (f) of the biexponential DWI were calculated for all of the lesions. Receiver operating characteristic (ROC) analysis was performed for the differentiation of CG cancer from SH and GH.ResultsThe ADC values (× 10^? 3 mm²/s) were 0.87 ± 0.11, 1.06 ± 0.15, and 1.61 ± 0.27 in CG cancer, SH and GH foci, respectively, and differed significantly, yielding areas under the ROC curve (AUCs) of 1.00 and 0.80 for the differentiation of carcinoma from GH and SH, respectively. The ADCf (× 10^? 3 mm²/s), ADCs (× 10^? 3 mm²/s) and f for cancer were 1.92 ± 0.38, 0.53 ± 0.17, and 47.7 ± 6.1%, respectively, which were lower than the same values for GH (3.43 ± 0.65, 1.12 ± 0.21, 61.1 ± 8.7%) (all p < 0.01). The ADCf and ADCs for cancer were also lower than those for SH (3.11 ± 0.30, 0.79 ± 0.21) (all p < 0.01). The ADCf yielded AUCs (1.00, p > 0.01) that were comparable to those from ADC for the differentiation of cancer from GH, while ADCf yielded higher AUCs (0.92) compared with ADC (p < 0.01) for the differentiation of cancer from SH. ADCs and f revealed AUCs of 0.97 and 0.90, respectively, for the differentiation of cancer from GH, and the ADCs offered relatively lower AUCs (0.68) for differentiating cancer from SH.ConclusionBiexponential DWI could potentially improve the differentiation of prostate cancer in CG, and the ADCf of the biexponential model offers better accuracy than ADC.     

Atomic surface diffusion on Pt nanoparticles quantified by high-resolution transmission electron microscopy

Aberration-corrected high-resolution transmission electron microscopy allows for the delocalization-free observation of atomic motions on metallic surfaces and thus enables measurements of the diffusion of single atoms on the surfaces of nanoscopic objects such as nanoparticles. Using this recently introduced method, the diffusion coefficient for surface self-diffusion of Pt nanoparticles is determined through the fluctuating occupation of the particle's atomic columns. This diffusion coefficient is determined to lie in the range D ∼ (10⁻¹⁷ … 10⁻¹⁶) cm²/s.     

Electronic conductivity and chemical diffusion in n-conducting barium titanate ceramics at high temperatures

The electronic conductivity as well as the chemical diffusion coefficient of barium titanate ceramics doped with Y and Mn (donor-doped and acceptor co-doped) have been determined by application of conductivity relaxation experiments. The equilibrium values of the electronic conductivity of n-conducting BaTiO₃ have been analyzed by application of a defect chemical model involving electrons and cation vacancies as the predominant defect species at oxidizing conditions (fairly high oxygen partial pressures). The relaxation curves of the electronic conductivity yield the chemical diffusion coefficient of the bulk by employing a spherical grain model where the appropriate diffusion length is the radius of grains (average grain size). The conductivity relaxation experiments have been performed as a function of temperature ranging from 1100 to 1250 °C at oxygen partial pressures between 0.01 and 1 bar. The kinetics of the oxygen exchange process can be interpreted in terms of extremely fast diffusion of oxygen via oxygen vacancies along the grain boundaries and slow diffusion of Ti (cation)-vacancies from the grain boundaries into the grains. The Ti-vacancy diffusion coefficients were extracted from the chemical diffusion coefficients as a function of temperature. Typical values for the Ti-vacancy diffusivity are around 10^− 15 cm² s^− 1 with an activation energy of 3.9 ± 0.7 eV.     

Application of ZnO nanorods loaded on activated carbon for ultrasonic assisted dyes removal: Experimental design and derivative spectrophotometry method

A method based on application of ZnO nanorods loaded on activated carbon (ZnO-NRs-AC) for adsorption of Bromocresol Green (BCG) and Eosin Y (EY) accelerated by ultrasound was described. The present material was synthesized under ultrasound assisted wet-chemical method and subsequently was characterized by FE-SEM, TEM, BET and XRD analysis. The extent of contribution of conventional variables like pH (2.0–10.0), BCG concentration (4–20 mg L⁻¹), EY concentration (3–23 mg L⁻¹), adsorbent dosage (0.01–0.03 g), sonication time (1–5 min) and centrifuge time (2–6 min) as main and interaction part were investigated by central composite design under response surface methodology. Analysis of variance (ANOVA) was adapted to experimental data and guide the best operational conditions mass by set at 6.0, 9 mg L⁻¹, 10 mg L⁻¹, 0.02 g, 4 and 4 min for pH, BCG concentration, EY concentration, adsorbent dosage, sonication and centrifuge time, respectively. At these specified conditions dye adsorption efficiency was higher than 99.5%. The suitability and well prediction of optimum point was tested by conducting five experiments and respective results revel that RSD% was lower than 3% and high quality of fitting was confirmed by t-test. The experimental data were best fitted in Langmuir isotherm equation and the removal followed pseudo second order kinetics. The experimentally obtained maximum adsorption capacities were estimated as 57.80 and 61.73 mg g⁻¹ of ZnO-NRs-AC for BCG and EY respectively from binary dye solutions. The mechanism of removal was explained by boundary layer diffusion via intraparticle diffusion.     

7Li and 51V NMR study on Li+ ionic diffusion in lithium intercalated LixV2O5

Li_xV₂O₅ (0.4 < x < 1.4) prepared by solid-state reaction were studied by ⁷Li and ⁵¹V NMR spectroscopy. ⁷Li NMR spectra showed a narrowing of the line width in relation to Li⁺ionic diffusion. Analysis of Li_xV₂O₅ using a Debye-type relaxation model showed a low activation energy ∼0.07 eV in the sample of x = 0.4 below room temperature, and revealed a Li⁺ionic diffusion with larger activation energy ∼0.5 eV above 450 K in lithium-rich samples. The latter is ascribed to the existence of a multi-phase system comprising stable ɛ- and γ-phases, resulting from complicated phase transitions at high temperature. These shapes and shifts enable the classification of the β-, ɛ-, δ-, and γ-phases. The ionic diffusion of Li⁺ ions is discussed in relation to the complicated phase transitions.     

Dependence on b-value of the direction-averaged diffusion-weighted imaging signal in brain

PurposeThe dependence of the direction-averaged diffusion-weighted imaging (DWI) signal in brain was studied as a function of b-value in order to help elucidate the relationship between diffusion weighting and brain microstructure.MethodsHigh angular resolution diffusion imaging (HARDI) data were acquired from two human volunteers with 128 diffusion-encoding directions and six b-value shells ranging from 1000 to 6000 s/mm² in increments of 1000 s/mm². The direction-averaged signal was calculated for each shell by averaging over all diffusion-encoding directions, and the signal was plotted as a function of b-value for selected regions of interest. As a supplementary analysis, similar methods were also applied to retrospective DWI data obtained from the human connectome project (HCP), which includes b-values up to 10,000 s/mm².ResultsFor all regions of interest, a simple power law relationship accurately described the observed dependence of the direction-averaged signal as a function of the diffusion weighting. In white matter, the characteristic exponent was 0.56 ± 0.05, while in gray matter it was 0.88 ± 0.11. Comparable results were found with the HCP data.ConclusionThe direction-averaged DWI signal varies, to a good approximation, as a power of the b-value, for b-values between 1000 and 6000 s/mm². The exponents characterizing this power law behavior were markedly different for white and gray matter, indicative of sharply contrasting microstructural environments. These results may inform the construction of microstructural models used to interpret the DWI signal.     

High mobility I− / I3− redox couple in a molecular plastic crystal: A potential new generation of electrolyte for solid-state photoelectrochemical cells

A series of new electrolyte materials based on a molecular plastic crystal doped by different iodide salts together with iodine have been prepared and characterized by thermal analysis, ionic conductivity, electrochemical and solid-state NMR diffusion measurements. In these materials, the plastic crystal phase of succinonitrile acts as a good matrix for the quaternary ammonium based iodides and iodine and appears to act in some cases as a solid-state “solvent” for the binary dopants. The materials were prepared by mixing the components in the molten state with subsequent cooling into the plastic crystalline state. This resulted in waxy-solid electrolytes in the temperature range from − 40 to 60 °C. The combination of structural variation of the cations, and fast redox couple diffusion (comparable with liquid-based electrolytes), as well as a high ionic conductivity of up to 3 × 10^− 3 S cm^− 1 at ambient temperature, make these materials very attractive for potential use in solid-state photoelectrochemical cells.     

Diffusion of a Ga adatom on the GaAs(001)‐c(4 × 4)‐heterodimer surface: A first principles study

The adsorption and diffusion behavior of a Ga adatom on the GaAs (001)‐c(4 × 4)-heterodimer surface were studied by employing ab initio density functional theory (DFT) computations in the local density approximation. Structural and bonding features of the c(4 × 4)-heterodimer reconstruction surface were examined. A comparison with the c(4 × 4)-ss reconstruction was performed. Minimum energy sites (MES) on the c(4 × 4)-heterodimer surface were located by mapping the potential energy surface for a Ga adatom. Barriers for diffusion of a Ga adatom between the neighboring MES were calculated by using top hopping- and exchange-diffusion mechanisms. We proposed two unique diffusion pathways for a Ga adatom diffusing between the global minimums of two neighboring unit cells. Signature differences between electronic structures of top hopping- and exchange‐diffusion mechanisms were studied for relevant atoms. We observed a higher diffusion barrier for exchange mechanism compared to top hopping.     

The interaction of O2 with the surface of polycrystalline gadolinium at the temperature range 300–670 K

Auger-Electron-Spectroscopy (AES) and Direct-Recoils-Spectrometry (DRS) were applied to study the interaction of O₂ with a polycrystalline gadolinium surface, in the temperature range 300–670 K and oxygen pressure up to 2 × 10^? 6 Torr. It has been found that initial uptake of oxygen, at coverage measurable by the techniques used here, results in rapid oxide island formation. The subsurface is believed to be a mixture of oxide particles and oxygen dissolved in the Gd metal, the latter being the mobile species, even at relatively low temperatures.Enhanced inward diffusion of oxygen starts as early as 420 K and dictates the surface oxygen concentration and effective thickness of the forming oxide. The oxygen accumulation rate at the near-surface region, as measured by the O(KLL) AES signal intensity, goes through a maximum as a function of temperature at 420 K. This is a result of the combination of still efficient oxygen chemisorption that increases surface occupation and slow inward diffusion. The thickest oxide, ~ 1.7 nm, is formed at 300 K and its effective thickness was found to decrease with increasing temperature (due to oxygen dissolution into the metal bulk).Diffusion coefficients of the oxygen dissolution into the bulk were evaluated for various temperatures utilizing models for infinitely thin oxide layer and thick oxide layer, respectively. The best fit under our experimental procedure was obtained by the thick layer model, and the coefficients that were calculated are D₀ = 2.2 × 10^? 16m²s^? 1 and E_a = 46kJ/mol.     

Mid-infrared InAsSb-based nBn photodetectors with AlGaAsSb barrier layers – Grown on GaAs,using an interfacial misfit array,and on native GaSb

InAsSb-based nBn photodetectors were fabricated on GaAs, using the interfacial misfit (IMF) array growth mode, and on native GaSb. At −0.1 V operating bias, 200 K dark current densities of 1.4 × 10⁻⁵ A cm⁻² (on GaAs) and 4.8 × 10⁻⁶ A cm⁻² (on GaSb) were measured. At the same temperature, specific detectivity (D^*) figures of 1.2 × 10¹⁰ Jones (on GaAs) and 7.2 × 10¹⁰ Jones (on GaSb) were calculated. Arrhenius plots of the dark current densities yielded activation energies of 0.37 eV (on GaAs) and 0.42 eV (on GaSb). These values are close to the 4 K bandgap of the absorption layers (0.32–0.35 eV) indicating diffusion limited dark currents and small valence band offsets. Significantly, these devices could be used for mid-infrared focal plane arrays operating within the temperature range of cost-effective thermoelectric coolers.     

Modeled quenching limits of spherical hydrogen diffusion flames

Hydrogen–air diffusion flames were modeled with an emphasis on kinetic extinction. The flames were one-dimensional spherical laminar diffusion flames supported by adiabatic porous burners of various diameters. Behavior of normal (H₂ flowing into quiescent air) and inverse (air flowing into quiescent H₂) configurations were considered using detailed H₂/O₂ chemistry and transport properties with updated light component diffusivities. For the same heat release rate, inverse flames were found to be smaller and 290 K hotter than normal flames. The weakest normal flame that could be achieved before quenching has an overall heat release rate of 0.25 W, compared to 1.4 W for the weakest inverse flame. There is extensive leakage of the ambient reactant for both normal and inverse flames near extinction, which results in a premixed flame regime for diffusion flames except for the smallest burners with radii on the order of 1 μm. At high flow rates H + OH(+M) → H₂O(+M) contributes nearly 50% of the net heat release. However at flow rates approaching quenching limits, H + O₂(+M) → HO₂(+M) is the elementary reaction with the largest heat release rate.     

Improved short-circuit photocurrent densities in dye-sensitized solar cells based on ordered arrays of titania nanotubule electrodes

We report on the synthesis of highly ordered arrays of titania nanotubules and their applications in enhanced photoelectrochemical cells. Ordered arrays of titania nanotubules of ∼120 nm external diameter, ∼100 nm internal diameter, and ∼5 μm length were fabricated on transparent conductive oxide (TCO) glass substrates by sol–gel processes using in-house prepared anodic alumina templates. After thermal bonding and template removal, the resultant nanotubule structures were applied in dye-sensitized solar cells (DSCs). Overall photoconversion efficiency of nearly 4.8% was achieved with Ru-bipyridine dye, N719, and iodolyte liquid electrolyte. This remarkable performance, for electrodes only ∼5 μm thick, is attributed to an unexpectedly high short-circuit photocurrent density of 16 mA/cm² for masked cells and up to 17 mA/cm² for unmasked cells. The enhanced short-circuit photocurrent (J_sc) is attributed to the high surface area (roughness factor ca. 1207) of the nanotubules and thus improved dye adsorption to the electrodes. The improved J_sc is also attributed to the parallel and vertical orientation of the nanostructures and thus to a well-defined electron diffusion path.     

Proton dynamics in Cs3(HSO4)2(HPO4) studied by 1H NMR

Proton dynamics in Cs₃(HSO₄)₂(H₂PO₄) has been studied by means of ¹H solid-state NMR as well as thermal analyses. The thermal analysis shows an endothermic peak at 408 K, which corresponds to a superprotonic transition. Above the transition temperature a mass loss is observed in a dry atmosphere, which is easily recovered in a conventional dry atmosphere below the transition temperature. The ¹H magic-angle-spinning NMR spectra at room temperature show two peaks at 13.5 and 15.8 ppm, and a shoulder at 11.3 ppm from tetramethylsilane, demonstrating a presence of several inequivalent proton sites. Translational diffusion of protons takes place in both a room-temperature phase (RT) and a high-temperature phase (HT). In both phases reorientation of the SO₄/PO₄ tetrahedron limits the rate of the proton transport. The ¹H mean residence times are estimated as E_a = 33 kJ mol^− 1 and τ₀ = 0.97 × 10^− 9 s for phase RT from the second moment analysis and as E_a = 20 kJ mol^− 1 and τ₀ = 5.0 × 10^− 12 s for phase HT from the analysis of the ¹H T₁ results.     

Intravoxel incoherent motion and diffusion tensor imaging of early renal fibrosis induced in a murine model of streptozotocin induced diabetes

IntroductionTo assess if parameters in intravoxel incoherent motion (IVIM) and diffusion tensor imaging (DTI) can be used to evaluate early renal fibrosis in a mouse model of diabetic nephropathy.Materials & methodsIn a population of 38 male CD1 mice (8 weeks old, 20–30 g), streptozotocin induced diabetes was created in 20 mice via a single intraperitoneal injection of streptozotocin at 150 mg/kg, while 18 mice served as control group. IVIM parameters were acquired at 0, 12 and 24 weeks after injection of streptozotocin using a range of b values from 0 to 1200 s/mm². DTI parameters were obtained using 12 diffusion directions and lower b values of 0, 100 and 400 s/mm². DTI and IVIM parameters were obtained using region of interests drawn over the renal parenchyma. Histopathological analysis of the right kidney was performed in all mice. Results were analyzed using an unpaired t-test with P < 0.05 considered statistically significant.ResultsRenal cortex fractional anisotropy (FA) was significantly lower in the diabetes group at week 12 as compared with the control group. Renal cortex apparent diffusion coefficient and tissue diffusivity were significantly higher in the diabetes group at week 12 compared with the control group at 12 weeks. Blood flow was significantly decreased at the renal medulla at 24 weeks. Histopathological analysis confirmed fibrosis in the diabetes group at 24 weeks.ConclusionFA is significantly reduced in diabetic nephropathy. FA might serve a potential role in the detection and therapy monitoring of early diabetic nephropathy.     

Proton diffusion in the superprotonic phase of [(NH4)1 − xRbx]3H(SO4)2 as studied by 1H spin-lattice relaxation

Proton diffusion in [(NH₄)_1 ? xRb_x]₃H(SO₄)₂ (0 < x < 1) has been studied by means of ¹H spin-lattice relaxation times, T₁. The relaxation times were measured at 200.13 MHz in the range of 296–490 K and at 19.65 MHz in the range of 300–470 K. In the high-temperature phase (phase I), translational diffusion of the acidic protons relaxes both the acidic protons and the ammonium protons. Spin diffusion averages the relaxation rate of the two kinds of protons, whereas proton exchange between them are slow. The spin-lattice relaxation times in phase I were analyzed theoretically, and parameters of proton diffusion were obtained. The mean residence time of the acidic protons increases with increase in x for [(NH₄)_1 ? xRb_x]₃H(SO₄)₂ (0 ≤ x ≤ 0.54). Rb₃H(SO₄)₂ does not obey this trend. The results of NMR well explain the macroscopic proton conductivity.