Activation Enthalpy Of Diffusion Research Articles

Oxygen Diffusion in Li(Nb,Ta)O3 Single Crystals

Oxygen tracer self‐diffusion in LiNbO3, LiTaO3, and LiNb0.15Ta0.85O3 single crystals between 880 and 1050 °C is investigated. 18O2 isotope‐exchanged samples are analyzed by secondary ion mass spectrometry. The diffusivities of each of the three different materials can be described by the Arrhenius law with an activation enthalpy of diffusion of about 3.2–3.5 eV. The diffusivities are highest for LiNbO3 and are lower by about one order of magnitude for LiNb0.15Ta0.85O3 and LiTaO3. The change of the pre‐exponential factor is identified as the reason for the difference in diffusivities. The experimental results are compared to defect formation energy calculations as given in literature and to energy barrier calculations for the diffusion of a single O vacancy as determined by nudged elastic band calculations based on density‐functional theory. An oxygen vacancy mechanism is suggested to govern diffusion. The difference in diffusivities is tentatively attributed to a different number of freely migrating vacancies, probably due to defect complex formation.

Hydrogen diffusion in proton-exchanged congruent Lithium Niobate during post-annealing

We investigated the diffusion of hydrogen during post annealing of proton-exchanged congruent LiNbO3 single crystals in the temperature range between 200 and 400 °C. Proton exchange was done in benzoic acid with 3.6 mol% lithium benzoate added. This process results in a 180 nm thin surface layer with a sharp interface where Li is substituted by H for about 45%. Depth profile analysis was carried out by secondary ion mass spectrometry. From the experimental results, diffusivities were extracted which follow the Arrhenius law with an activation enthalpy of diffusion of (1.39 ± 0.17) eV. The diffusivities are about two orders of magnitude lower than hydrogen tracer diffusivities in pure and in proton-exchanged LiNbO3 but are in good agreement to effective interdiffusion coefficients, governing the proton exchange. Also the activation energy for the latter case of (1.24 ± 0.04) eV is identical within error limits. The results indicate that the diffusional redistribution of high amounts of hydrogen in LiNbO3 is an interdiffusion process between H and Li that is governed by the migration of Li.

Oxygen Diffusion in Platinum Electrodes: A Molecular Dynamics Study of the Role of Extended Defects

AbstractPlatinum serves as a model electrode in solid‐state electrochemistry and as the inert electrode in redox‐based resistive random‐access memory (ReRAM) technology. Experimental work has proposed that oxygen may diffuse faster along platinum's extended defects, but quantitative, unambiguous transport data do not exist. In this study, the diffusion of oxygen atoms in crystalline platinum and along its extended defects is studied as a function of temperature by means of molecular dynamics (MD) simulations with the ReaxFF interatomic potentials. The MD simulations indicate that platinum vacancies trap oxygen atoms, inhibiting their diffusion through the platinum lattice and leading to a high activation enthalpy of diffusion of around 3 eV. This picture of trapping is supported by static density‐functional‐theory calculations. MD simulations of selected dislocations and selected grain boundaries indicate that oxygen diffusion is much faster along these extended defects than through the Pt lattice at temperatures below 1400 K, exhibiting a much lower activation enthalpy of ≈0.7 eV for all extended defects examined. Producing specific electrode microstructures with controlled densities and types of extended defects thus offers a new avenue to improve the performance of ReRAM devices and to prevent device failure.

Behavior of cation vacancies in single-crystal and in thin-film SrTiO3 : The importance of strontium vacancies and their defect associates

Solid-state diffusion experiments were used to probe the behavior of cation vacancies in the perovskite oxide ${\mathrm{SrTiO}}_{3}$. Two types of nominally undoped (effectively acceptor-doped) ${\mathrm{SrTiO}}_{3}$ systems were studied: (1) single crystals and (2) epitaxial thin films with different Sr/Ti stoichiometries produced by pulsed laser deposition. As diffusion sources, thin films of the perovskite oxide ${\mathrm{BaZrO}}_{3}$ were employed, and diffusion anneals were carried out in air at $1323\ensuremath{\le}T/\mathrm{K}\ensuremath{\le}1523$ for single crystals and at $1073\ensuremath{\le}T/\mathrm{K}\ensuremath{\le}1223$ for thin films. Sample analysis by means of time-of flight secondary ion mass spectrometry (ToF-SIMS) yielded diffusion coefficients of Ba and Zr in ${\mathrm{SrTiO}}_{3}\phantom{\rule{4pt}{0ex}}({D}_{\mathrm{Ba}}$ and ${D}_{\mathrm{Zr}})$. Diffusion profiles in single-crystal samples showed the expected error-function form and yielded ${D}_{\mathrm{Ba}}\ensuremath{\approx}{D}_{\mathrm{Zr}}$ at each temperature, and hence, activation enthalpies of diffusion that are approximately the same, at $(3.0\ifmmode\pm\else\textpm\fi{}0.4)$ eV and $(2.8\ifmmode\pm\else\textpm\fi{}0.4)$ eV. Diffusion profiles in the thin-film samples were unexpectedly complex, showing multiple error-function features. They also yielded ${D}_{\mathrm{Ba}}\ensuremath{\approx}{D}_{\mathrm{Zr}}$ at each temperature, however, but no clear trend was found as a function of Sr/Ti ratio. Comparing results for the two systems, we conclude that the concentration of cation vacancies is orders of magnitude higher in our thin-film samples than in the single crystals. Our results also provide experimental evidence that oxygen vacancies, ${\mathrm{v}}_{\mathrm{O}}^{\ifmmode\bullet\else\textbullet\fi{}\ifmmode\bullet\else\textbullet\fi{}}$, can decrease the activation enthalpy of strontium-vacancy migration by forming ${({\mathrm{v}}_{\mathrm{O}}{\mathrm{v}}_{\mathrm{Sr}})}^{\ifmmode\times\else\texttimes\fi{}}$ defect associates, and we derive an analytical model for the cation diffusivity as a function of temperature and defect concentrations.

Grain Boundary Diffusion of 57Co in Nickel

Grain boundary diffusion of cobalt in Ni of purity level 99.98 wt% was measured over a wide temperature interval using the radiotracer technique and applying the 57Co radioisotope. The diffusion experiments were performed in Harrison’s type B and C kinetic regimes. Temperature dependences of triple product and grain boundary diffusivity of Co in Ni have been determined. The value of grain-boundary segregation factor of cobalt in nickel was determined to be about unity in the temperature interval under investigation. It is demonstrated that the purer the material, the higher is the grain-boundary diffusivity and the lower the corresponding activation enthalpy of diffusion.

Diffusion of boron in germanium at 800–900 °C revisited

Diffusion of boron (B) in germanium (Ge) at temperatures ranging between 800°C and 900°C is revisited following the most recent results reported by Uppal et al. [J. Appl. Phys. 96, 1376 (2004)] that have been obtained mainly with implantation doped samples. In this work, we determined the intrinsic B diffusivity by employing epitaxially grown alternating undoped and B-doped Ge layer structures with three different dopant concentrations of 4×1017 cm−3, 1×1018 cm−3, and 3×1018 cm−3. The diffusional broadening of B was analyzed by means of secondary ion mass spectrometry (SIMS) and numerically described to determine the diffusion coefficient. Additional SIMS analyses revealed a gradient in the oxygen (O) background concentration of the epitaxially doped Ge structure. A high O content observed in near-surface regions correlates with enhanced B diffusion. In contrast, B-doped regions with low O content showed a significantly lower B diffusivity representing the intrinsic diffusivity. The B diffusion coefficients are significantly lower compared to literature data and best described by a diffusion activation enthalpy and a pre-exponential factor of (4.09±0.21) eV and 265−237+2256 cm2 s−1, respectively.

Enhanced CO2/CH4 Separation Performance of a Mixed Matrix Membrane Based on Tailored MOF-Polymer Formulations.

Membrane‐based separations offer great potential for more sustainable and economical natural gas upgrading. Systematic studies of CO2/CH4 separation over a wide range of temperatures from 65 °C (338 K) to as low as −40 °C (233 K) reveals a favorable separation mechanism toward CO2 by incorporating Y‐fum‐fcu‐MOF as a filler in a 6FDA‐DAM polyimide membrane. Notably, the decrease of the temperature from 308 K down to 233 K affords an extremely high CO2/CH4 selectivity (≈130) for the hybrid Y‐fum‐fcu‐MOF/6FDA‐DAM membrane, about four‐fold enhancement, with an associated CO2 permeability above 1000 barrers. At subambient temperatures, the pronounced CO2/CH4 diffusion selectivity dominates the high permeation selectivity, and the enhanced CO2 solubility promotes high CO2 permeability. The differences in adsorption enthalpy and activation enthalpy for diffusion between CO2 and CH4 produce the observed favorable CO2 permeation versus CH4. Insights into opportunities for using mixed‐matrix membrane‐based natural gas separations at extreme conditions are provided.

Mg diffusion in Si on a thermodynamic basis

In the present work, magnesium diffusion in silicon studied recently in the temperature range 600–1200 °C (Astrov et al. in Phys Status Solidi A 214:1700192, 2017; Shuman et al. in Semiconductors 51:5, 2017) is investigated on the basis of the cBΩ thermodynamic model, which connects point defect parameters with the macroscopic elastic and expansion properties. The calculated activation Gibbs free energy, activation enthalpy, activation entropy, activation volume and activation specific heat of Mg diffusion exhibit non-linear temperature dependence, due to the anharmonic behavior of the isothermal bulk modulus of Si. The calculated activation enthalpy of diffusion (1.67–2.12 eV) is in agreement with the reported experimental value (1.83 ± 0.02 eV) of Mg diffusion in Si, whereas the calculated activation volume (60% of the mean atomic volume) is compatible with the reported interstitial diffusion of Mg impurities.

Effect of pressure on closure temperature of a trace element in cooling petrological systems

Closure temperature is important to many diffusion-related problems involving cooling. The classic model of Dodson and its modifications for cooling petrological systems are formulated at constant pressure. Many petrologic processes involve changes in both temperature and pressure. The effect of changing pressure on diffusional loss in cooling petrological systems has not been considered in Dodson’s model. During upwelling, the decompression rate is related to the cooling rate through the slope of the upwelling path. Simple analytical expressions for the average or mean closure temperature and closure pressure in cooling-upwelling mono-mineralic and bi-mineralic systems are obtained by noting that both temperature and pressure decrease as a function of time along the upwelling path. These pressure-adjusted equations are nearly identical to closure temperature equations for isobaric cases if one replaces the activation energy and pre-exponential factor for diffusion in the isobaric formulations by the path-dependent activation energy and pre-exponential factor. The latter also depend on the slope of the upwelling path. The competing effects between pressure and temperature on diffusion during upwelling result in reductions in the effective activation enthalpy for diffusion and exchange enthalpy for partitioning, which in turn leads to systematic deviations in closure temperatures from cases of constant pressure. For systems with large activation volume for diffusion, it may be possible to deduce upwelling path and upwelling rate from closure temperatures and closure pressures of selected elements. Examples of closure temperature and closure pressure for REE diffusion in garnet and clinopyroxene and in garnet–clinopyroxene aggregates are presented and discussed in the context of the minor’s rule and the REE-in-garnet–clinopyroxene thermobarometer. Closure temperatures for middle-to-heavy REE in garnet–clinopyroxene aggregates are controlled primarily by diffusion in clinopyroxene unless the modal abundance of garnet is very small or the effective grain size of clinopyroxene is considerably smaller than that of garnet.

Self-diffusion in crystalline silicon: A single diffusion activation enthalpy down to755∘C

Self-diffusion in silicon and the contribution of vacancies and self-interstitials have been controversially discussed for 50 yr. Most recent results show that the intrinsic silicon self-diffusion coefficient deviates from an Arrhenius-type, single exponential function for temperatures below $950{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$ [Y. Shimizu, M. Uematsu, and K. M. Itoh, Phys. Rev. Lett. 98, 095901 (2007); R. Kube, H. Bracht, E. H\uger, H. Schmidt, J. L. Hansen, A. N. Larsen, J. W. Ager, E. E. Haller, T. Geue, and J. Stahn, Phys. Rev. B 88, 085206 (2013)]. This led us to propose temperature-dependent thermodynamic properties of vacancies in order to achieve full consistency to vacancy-mediated dopant diffusion in silicon. Concepts of temperature-dependent properties of native defects or distinct forms of defects with different formation entropies suggested by Cowern et al. [N. E. B. Cowern, S. Simdyankin, C. Ahn, N. S. Bennett, J. P. Goss, J.-M. Hartmann, A. Pakfar, S. Hamm, J. Valentin, E. Napolitani, D. De Salvador, E. Bruno, and S. Mirabella, Phys. Rev. Lett. 110, 155501 (2013)] question the present understanding on atomic transport in semiconductors. To verify these concepts, additional self-diffusion experiments under particular gettering conditions were performed. As a result, silicon self-diffusion was found to be accurately described by one single diffusion activation enthalpy of $(4.73\ifmmode\pm\else\textpm\fi{}0.02)$ eV down to $755{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$. This provides full consistency to dopant diffusion without claiming native-defect concepts that were originally proposed by Seeger and Chik in 1968 [A. Seeger and K. P. Chik, Phys. Stat. Sol. 29, 455 (1968)] and confirms most recent density functional theory calculations on the activation energy of self-diffusion via vacancies and self-interstitials. Overall, this unravels the old debate of self-diffusion in silicon with the supposed intrinsic temperature dependence.

Adsorption Characteristics of Arsenite on Goethite by Flow Stirring Method

Adsorption characteristics of arsenite on goethite under the effects of the solution pH, concentration and temperature were investigated using a flow-stirring dynamic device. The results showed that the adsorption process of arsenic could be divided into rapid and slow reactions under different conditions.The maximum of arsenite adsorption fitted by the first order equation remarkably decreased with increase in the solution pH, for example, 246.9 mg·kg-1 at pH 3.0 and 99.8 mg·kg-1 at pH 7.0, respectively. The rate constant(k')of the apparent adsorption increased gradually along with the increase of solution pH, and so the half reaction time(t1/2)was smaller, and the equilibrium time of arsenic adsorption was shorter. At the same time, the b values of diffusion rate constant were reduced gradually. With the increase of arsenic concentration, the amounts of arsenic adsorption and the k' values increased gradually. The maximum amount of adsorption of arsenic was 96.5 mg·kg-1 and 249.1 mg·kg-1 when the arsenic concentration was 0.10 mg·L-1 and 1.00 mg·L-1, respectively. Adsorption constant(Kf)by the Freundlich equation decreased gradually with the extension of the reaction time and its ability of adsorption was gradually weakened. Distribution factor(RL)by Langmuir equation was between 0-1, and the adsorption of arsenic on goethite was accounted for the preferential adsorption. With the increase of temperature, the maximum amount of adsorption of arsenic was increased, for example, 241.1 mg·kg-1 at 298 K and 315.6 mg·kg-1 at 313 K, respectively. And the k' values of the apparent adsorption rate constant gradually rose in the meantime. The false thermodynamic constants were calculated using the b values of the diffusion rate by the parabolic diffusion equation. The reaction activation energy(Ea*)of Arsenic adsorption was 14.60 kJ·mol-1. The change of arsenic diffusion activation enthalpy(ΔHθ)decreased with the increase of temperature, and ΔHθ was positive in values and on behalf of the endothermic process. So the rising temperature was beneficial to the diffusion of arsenic. ΔGθ of activation free energy was increased as the temperatures rose, and helpful to accelerate the diffusion process. Entropy of activation(ΔSθ)was negative in all cases, suggesting that the system could improve its degree of order.

Creep of Fe3Al-based alloys with vanadium and carbon additions

Creep experiments were conducted on Fe3Al-based alloys with vanadium and carbon additions in the temperature range from 923 to 1023 K, corresponding to the occurrence of B2 lattice. The alloys contained (in atomic %) (i) 27.0 Al, 1.17 V, and 0.02 C and (ii) 27.0 Al, 1.13 V, and 0.73 C (Fe balance). The alloys were tested in the as-cast state and annealed at 1273 K for 50 h. Creep tests were performed in uniaxial compression at a constant load with stepwise loading. Stress exponents and activation energies for the creep rate were determined. The values of the stress exponent in low-carbon alloy correspond to a five-power-law creep. The activation energy is greater than the activation enthalpy of diffusion of both Fe and Al in Fe3Al and is substantially greater than the activation enthalpy of diffusion of V in Fe3Al. The creep rate is impeded in the high-carbon alloy by the presence of tiny carbide particles. Consequently, the creep resistance of the high-carbon alloy in the as-cast state is greater, especially for higher temperatures and lower stresses. The carbide particles coarsen during annealing at 1273 K and are unable to obstruct dislocation motion because the mean distance between them is too large. The high-carbon alloy is then creep-weaker due to the reduced amount of vanadium present in the matrix.

Shear band relaxation in a deformed bulk metallic glass

Relaxation of shear bands in a Pd40Ni40P20 bulk metallic glass was investigated by radiotracer diffusion allowing to determine for the first time the effective activation enthalpy of diffusion along shear bands in a deformed glass. The shear bands relax during annealing below the glass transition temperature and the diffusion enhancement reveals unexpectedly a non-monotonous, cross-over behavior. The development of shear bands and the subsequent relaxation of stresses after the shear had been switched off are characterized on microscopic to mesoscopic length scales by molecular dynamics simulation subjecting a model glass to a constant strain rate. Mean-squared displacements as well as strain maps indicate that the heterogeneity, as manifested by shear bands in the systems under shear, persist after the shear was switched off. We observe a continued relaxation of residual stresses that remain localized in regions where the shear band has been present before, although the system is – different from the macroscopic experiment – homogeneous with respect to the local density. These results indicate that even on a local scale one may expect strong dynamic heterogeneity in deformed glassy solids due to shear banding that correlates with the existence of short-circuit type diffusion on a macroscale. The results thus suggest that plastically deformed metallic glasses present poly-amorphous systems that necessitate descriptions that are analogous to multiphase materials including the presence of heterophase interfaces.

Investigation of Interfaces by Atom Probe Tomography

We investigated the thermodynamic and transport properties of buried interfaces with atom probe tomography. Owing to the 3D subnanometer resolution and single atom sensitivity of the method, it is possible to obtain composition profiles with high accuracy both along or normal to the interfaces. We have shown that the width of the chemical interface between the Fe and Cr system follows the Cahn–Hilliard relation with a gradient energy coefficient of 1.86 × 10−22 J nm2. Sharpening of the Ni/Cu interface as a result of kinetic control was directly observed. We investigated the grain boundary and triple junction transport in Fe/Cr and Ni/Cu. Cr segregation enthalpy into Fe triple junctions was found to be 0.076 eV, which falls in between the surface (0.159 eV) and grain boundary (0.03 eV) segregation enthalpies. In the investigated 563 K to 643 K (290 °C to 370 °C) range, Ni transport is 200 to 300 times faster in the triple junctions of Cu than in the grain boundaries. The diffusion activation enthalpy in the triple junctions is two-thirds that of the grain boundaries (0.86 and 1.24 eV, respectively). These investigations have shown that triple junctions are defects in their own right with characteristic segregation and diffusion properties: They are preferred segregation sites and can be considered as a diffusion shortcut in the grain boundary network.

Grain boundary self-diffusion in Fe films with a stable nanostructure

Grain boundary self-diffusion in Type-C regime was investigated in nano-crystalline bcc iron at low temperatures between 100 and 250 °C using neutron reflectometry in combination with [natFe(7 nm)/57Fe(3 nm)]10 isotope multilayers. The method allows to determine diffusivities in a stable nanostructure without concurrent grain growth. An activation enthalpy of diffusion of (0.9 ± 0.3) eV is found, comparable to the value of coarse-grained Fe.

Nitrogen self-diffusion in magnetron sputtered Si-C-N films

Self-diffusion was studied in magnetron sputtered nitrogen-rich amorphous compounds of the system Si-C-N by using nitrogen as a model tracer. As shown by infra-red spectroscopy a transient metastable region exists, where the structure of the material can be visualized as silicon nitride tetrahedra which are connected by carbo-diimide (-N=C=N-) bonds to a three dimensional amorphous network. In this region diffusion studies are carried out by neutron reflectometry and isotope multilayers as a function of annealing time, temperature and chemical composition. Low diffusivities between 10−20 and 10−24 m2/s were found. In the metastable region, diffusion is faster than diffusion in amorphous silicon nitride by 1 to 2 orders of magnitude, while the activation enthalpies of diffusion between 3.1 and 3.4 eV are the same within error limits. This can be explained by the fact that the diffusion mechanism along SiN4 tetrahedra is identical to that in amorphous silicon nitride, however, the carbo-diimide bonds seem to widen the structure, allowing faster diffusion. A correlation between diffusivities and the number of carbo-diimid bonds present in the material is found, where the highest diffusivities are observed for materials with the highest number of carbo-diimid bonds, close to the composition Si2CN4.

Effect of hydrostatic pressure on self-diffusion in metal nanoparticles

The thermodynamics approach has been developed to describe the self-diffusion in nano-sized solids. It has been established that identical homologous temperatures of metal nanoparticles with their fixed characteristic size give the identical coefficients of diffusion under different pressures. The dependence of the activation enthalpy of diffusion on pressure and on the characteristic size of nanoparticles is first obtained.

Self- and foreign alkaline-earth diffusion in mixed cation silicate glasses

Self-diffusion of alkaline-earth ions in various mixed cation silicate glasses of the composition A 2O·2MO·4SiO 2 was investigated by radiotracer diffusion measurements below the respective glass transition temperatures. Including previous measurements, we have analyzed the diffusivity of divalent ions in mixed cation systems with A = Li, Na, K, Cs and M = Ca, Sr, Ba. The activation enthalpy depends strongly on the type of cations, revealing an increasing diffusivity for glasses with cations of similar size. The behavior is consistent with mechanical loss spectroscopy measurements performed on the same glasses. In addition foreign atom diffusion of calcium and barium in strontium containing glasses were performed. In the case the ionic radius of the alkali ions exceeds that of the alkaline-earth ions the diffusion activation enthalpy of the foreign ion equals the activation enthalpy of self-diffusion. The results can be described on the basis of a theoretical model proposed by Kirchheim [R. Kirchheim, J. Non-Cryst. Solids 328 (2003) 157] that relates the activation enthalpy to electrostatic and elastic contributions.

Self-diffusion in germanium isotope multilayers at low temperatures

Self-diffusion in intrinsic single crystalline germanium was investigated between 429 and 596 °C using G70e/Gnate isotope multilayer structures. The diffusivities were determined by neutron reflectometry from the decay of the first and third order Bragg peak. At high temperatures the diffusivities are in excellent agreement with literature data obtained by ion beam sputtering techniques, while considerably smaller diffusion lengths between 0.6 and 4.1 nm were measured. At lower temperatures the accessible range of diffusivities could be expanded to D≈1×10−25 m2 s−1, which is three orders of magnitude lower than the values measured by sputtering techniques. Taking into account available data on Ge self-diffusion, the temperature dependence is accurately described over nine orders of magnitude by a single Arrhenius equation. A diffusion activation enthalpy of 3.13±0.03 eV and a pre-exponential factor of 2.54×10−3 m2 s−1 for temperatures between 429 and 904 °C are obtained. Single vacancies are considered to prevail self-diffusion in Ge over the whole temperature range.

Carbon impurity dissolution and migration in bcc Fe-Cr: First-principles calculations

First-principles density-functional theory calculations for C solution enthalpies, H-sol, and diffusion activation enthalpies, H-diff, in body-centered-cubic Fe and Cr are presented. The results for C in Fe compare well with experiments, provided that the effect of magnetic disordering is accounted for. Likewise, in Cr, the calculated Hsol and Hdiff agree well with available experiments. In both materials, the deviation between calculated enthalpies and critically assessed experimental enthalpies are less than 0.05 eV. Further, first-principles calculations for the interaction energies between a solute (e.g., a Cr atom in bcc Fe) and an interstitial C atom are presented. The results are in conflict with those inferred from internal friction (IF) experiments in disordered Fe-Cr-C alloys. A simple model of C relaxation in disordered Fe-Cr is used to compare theoretical and experimental IF curves directly. The results suggest that a more extensive study of the energetic, thermodynamic, and kinetic aspects of C migration in Fe-Cr is needed.