Diffusion Enthalpy Research Articles

Quantum Isotope Effects in Gas Transport Through Polymers

A diffusing gas molecule of sufficiently light mass (e.g. H2 and D2) dispersed in sufficiently small cavities of a polymer will posses ground — state quaentization of energy, both in the cavity and in the transition state. Hence one can observe isotope effects in the activation energies for diffusion and permeation and enthalpies of sorption for two isotopic species, providing the mass ratio of the lighter to the heavier is sufficiently small. These isotope effects were determined for four sorts of polymers and were used to estimate parameters involved in the “Free Volume Theory” of gas diffusion through polymers.

Confirmation of the one-interstitial model for α-iron from positron annihilation experiments in thermal equilibrium on pure and carbon doped samples

The value of the vacancy migration enthalpy in α-iron has been the subject of a long standing controversy. In the one-interstitial model, the value of 0.55 eV has been put forward, whereas in the two-interstitial model a value of about 1.3 eV is given. In a review paper l, it was concluded that the majority of experimental data is in favour of the one-interstitial model. It was also pointed out that, if one accepts this model, an important problem remained to be solved: the vacancy migration enthalpy that can be obtained by subtracting the vacancy formation enthalpy from the self diffusion enthalpy (provided that self-diffusion is driven by a vacancy mechanism), was more than twice the vacancy migration enthalpy of the one-interstitial model. We report here on research we performed concerning this problem. The values of the enthalpies of vacancy formation and self diffusion were carefully re-investigated, taking into account: 1) the influence of ferromagnetic ordering, and 2) the influence of the strong interaction between residual carbon atoms and vacancies. To determine the ferromagnetic self diffusion enthalpy QS D,f, we used reliable literature data on self diffusion in iron. The main conclusion of our analysis is that only an upperlimit to QS D,f, can be given 2: QS D,f ⩽2.75 eV. We also performed positron annihilation measurements in thermal equilibrium on pure and carbon doped (50 and 750 appm) samples to determine the ferromagnetic vacancy formation enthalpy H V f,f. In very pure iron no trapping of positrons is observed below the Curie point, so that H V f,f cannot be determined. However in carbon-doped samples the carbon-vacancy pair can be used as a probe to determine H V f,f. We obtained: H V f,f = (2.0 ± 0.2) eV. This value is the first fully experimental determination of this parameter. By combining the data given above, we conclude that an upperlimit to the ferromagnetic vacancy migration enthalpy H V m,f is: H V m,f ⩽ 0.95 eV. On the other hand, it can be shown 3 that H V m,f ⩾ 0.16 eV. We therefore conclude that there is no longer an inconsistency between the one-interstitial model and the vacancy migration enthalpy derived from thermal equilibrium measurements.

Activation enthalpy of diffusion for well fractionated dextrans in aqueous solutions

Interdiffusion coefficients have been determined for seven well defined dextran fractions in aqueous solutions at 20. 25. 30 and 35°C. For dextrans with number average molecular weights ( M̄ n) greater than about 20 000. a plot of the apparent activation energy of diffusion ( E D) against M̄ n is given by: E D = 2.763 × 1O −5 M̄ n +3.38. Similarly, for weigh molecular weight ( M̄ w): E D = 1.889 × 1O −5 M̄ w + 3.61. The extrapolated E D values (3.38 and 3.61) are in reaso agreement with published data for the activation energy of self-diffusion for water.

Quenched-in defects in UC and UCN

The quenched-in resistivity of uranium monocarbide (UC) and uranium carbonitride (UCN) was studied and the activation energies of formation and migration for defects that are mobile in two recovery stages at about 200 and 700° C were obtained. These values were compared with the published diffusion enthalpies and with the migration energies obtained from recovery experiments on neutron irradiated UC. It is commonly suggested that the two recovery stages are due to isolated carbon and uranium vacancies. This is not compatible with recent diffusion data. It is argued here that dissociation of impurity-vacancy complexes is a more probable alternative for the stage at 700° C. Higher defect energies and recovery temperatures are obtained for UCN (and UN) as compared to UC, in agreement with other kinetic data in the series UC-UCN-UN. The migration energy of uranium vacancies was determined to be 2.4 ± 0.4 eV for UC and to increase for UCN.

A limit of validity of a “basic” thermodynamical relation between activation enthalpy and entropy of diffusion and defect formation

A limit of validity of a “basic” thermodynamical relation between activation enthalpy and entropy of diffusion and defect formation

The activation energy for clustering of Pb2+vacancy pairs in NaCl and a comparison with the diffusion activation energy

An accurate measurement has been made of the activation energy (0.85 eV) of the aggregation of Pb2+ vacancy pairs in NaCl:Pb2+, using measurements of the intensity of the dielectric absorption. This is compared with the enthalpy of diffusion (0.98 eV) for a Pb2+ vacancy pair in NaCl. The significance of the difference is discussed in relation to the concentration of dimers which may occur in doped alkali halides.

Some basic creep characteristics of ZrSn&.z.sbnd;Mo and ZrSnMoNb alloys part I. Steady state creep

The steady state creep rate, dot ϵ s , of five ZrSnMo alloys and a ZrSnMoNb alloy was measured within a temperature interval of 623–823 K, and a broad, applied stress interval. The stress sensitivity parameter, m′ = (∂ ln dot ϵ s /∂ ln σ) T , where σ and T are applied stress and temperature, respectively, was found to increase with applied stress from about 3 at dot ϵ s ⋍ 10 −9 s −1 to eventually more than 20 at dot ϵ s ∼- 10 −5 s −1 . The apparent activation energy of creep, Q, increases with temperature from values lower to values considerably higher than the expected value of activation enthalpy of lattice diffusion, ΔH . Correction of Q for the temperature dependence of the elastic modulus does not lead to the value of the activation energy of creep which is temperature independent and close to ΔH . Nevertheless, it is suggested that creep in the alloys investigated is controlled by recovery at medium applied stresses, while at low applied stresses the modified Nabarro-Herring or Coble mechanism is probably the rate controlling one. At high applied stresses (and lower temperatures) the measured steady state creep rates are significantly contributed to by an athermal deformation mechanism, at least at the lowest tin concentration studied, i.e., 3 wt.%. Creep in the alloys investigated cannot be interpreted in terms of measured effective stress. The influence of alloy composition on steady state creep rate and steady state flow stress, respectively, was evaluated and the creep strengthening effect of tin, molybdenum and niobium is discussed.

Diffusion enthalpies and entropies in thermally forming NiO and (Ni, Fe)O from 800–1200°C

The oxidation of pure Ni and a Ni-1.98 wt.% Fe alloy in air between 800–1200°C has been investigated gravimetrically using a thermobalance. Parabolic reaction kinetics were observed and analysed by the Arrhenius–Zener and Eyring theories. The enthalpies and entropies of activation for the Ni were 174.4 ± 13.6 kJ mol–1 and –28.4 ± 10.9 J mol–1 K–1, and 164.1 ± 13.6 kJ mol–1 and –46.0 ± 10.9 J mol–1 K–1 for the Zener and Eyring theories respectively. For the alloy the enthalpies and entropies of activation were 206.8 ± 8.1 kJ mol–1 and 36.8 ± 6.4 J mol–1 K–1, and 196.3 ± 8.0 kJ mol–1 and 19.1 ± 6.3 J mol–1 K–1 for the Zener and Eyring theories respectively. Enthalpies calculated by the two theories are similar but the difference in entropies is large. The enthalpies account quantitatively for the diffusion processes occurring during oxidation of Ni. Zener's theory provides a physical basis for understanding entropy changes during diffusion and the entropies are consistent with the theory.

Activation enthalpy of diffusion for iodine in mixed solvents

The diffusion coefficients of iodine diluted in two different binary mixed solvents have been measured as a function of temperature. The enthalpy of activation of diffusion was evaluated from the Arrhenius plot of the data in cyclohexane + ethanol and +iso-octane solutions. The enthalpy value for iodine in an equimolar mixture of cyclohexane + ethanol was found to be ∼1 kcal mol–1 larger than that for iodine in the two pure solvents.

Low-frequency dielectric relaxation of Cs +-ions in single-crystals of mica-type layer-silicates

Measurements of the permittivity ϵ′ and of the dielectric loss ϵ″ have been made on oriented single-crystals of mica-type layer silicates (vermiculites) in the frequency range 30 Hz–10 MHz. A low-frequency region of dielectric absorption has been observed which has been assigned to the migration of Cs +-interlayer cations on free cation sites. In a close relation to this migration we have to assume the reorientation of large electric dipoles—originated in interstitial cation and negative layer charges. Applying the BAUER equation there results an activation enthalpy of diffusion across the lattice of 11.21 kcal mol . Estimates of an effective dipole moment and of the number of cations contributing to the process agree well with the structural and our experimental data.

Self-diffusion of iron in α-phase of iron and Fe-Cr alloys

In the present paper the self-diffusion coefficients of iron in α-iron and in Fe-Cr alloys in the temperature range 660–890°C and in the concentration interval 0–11.8 wt.% Cr were determined. The residual activity method has been applied using the isotope 59Fe. Special attention was payed to the close neighbourhood of the Curie temperature. The obtained data confirmed the effect of ferromagnetic ordering on the iron self-diffus ion in pure Fe and in all the investigated Fe-Cr alloys. An empiric relation was found between the excess free activation enthalpy of diffusion and the spontaneous magnetization that yields a picture about the magnetic ordering of the used materials.

Ionische dielektrische Relaxationsprozesse in Festkörpern, I / Ionic Dielectric Relaxation Processes in Solids, I

Dielectric measurements have been made on single-crystals of mica-type layer silicates (vermiculites) in the frequency range between 30 Hz and 10 MHz. The migration of K+-and NH4 +-interlayer cations by free cation sites causes a low-frequency relaxation. It is interpreted by the orientation of large dipoles they form with parent negative layer charges. For both ions the activation enthalpy of diffusion across the lattice is 11.94 kcal/mole. Additional N-H · · · O hydrogen bonds are formed by the NH4 + ions at low temperatures. There results a bond enthalpy of 1.3 kcal/mole and a life-time of 1.2 · 10-5 sec (at 40°C). A discussion of the different rate process equations yields the applicability of the Bauer equation.

Vacancy formation parameters in organic crystals

Measurements of the temperature dependence of the X-ray and bulk densities of succinonitrile and of cyclooctane single crystals are reported. Actual and upper limiting values of the vacancy concentrations are calculated from these results. In addition, heat capacity data from the literature are analyzed to obtain the vacancy formation enthalpy and entropy of benzene, hexamethylethane, pentaerythrityl fluoride, perfluoropiperdine, 2,2,3-trimethylbutane, 1,1-dimethylcyclohexane, cyclooctane, and cis-1,2-dimethylcyclohexane. The vacancy triple point concentrations obtained range from less than 0·1 per cent in succinonitrile and benzene to as high as 0·76 per cent in 2,2,3-trimthylbutane. The corresponding vacancy formation enthalpies range from 0·52 to 1·2 of the triple point sublimation enthalpy, low fractions being found for compounds with low entropy of fusion, S m ≈ R. The effect of defect relaxation, zero point energy, and many body forces upon vacancy formation enthalpy is considered. For benzene and hexamethylethane, the ratios of experimental vacancy formation enthalpy to diffusion enthalpy are respectively 0·50 and 0·56, or about the same as is observed in f.c.c. metals. However, the experimental vacancy formation entropiesare significantly higher than is observed in metals. The entropic contribution from torsional lattice modes, which contributes to this difference, is calculated. For both vacancy formation and diffusion parameters in these organic crystals, a linear correlation exists between enthalpy, normalized to the melting point, and entropy. Despite the difference in bonding, one empirical equation correlates the available diffusion parameters in both metals and organic crystals.

The Proton Diffusion Coefficient for the Nickel Hydroxide Electrode

The diffusion coefficient for protons moving in the hydrated nickel hydroxide lattice has been determined using a potential step technique. It was found to have the value about during charging and during discharging for the nickel hydroxide structure usually found in the nickel electrode of the nickel‐cadmium battery. The temperature dependence of the coefficient has been determined, and it has been concluded that the proton moves in the lattice by thermal diffusion. The enthalpy of diffusion was found to be 2.2 kcal deg−1 mole−1 during charging and 2.3 kcal deg−1 mole−1 during discharging of the electrode.

On uranium self-diffusion in UO2 and UO2+x

Self-diffusion coefficients of uranium in sinters and single crystals of uranium oxide with varying oxygen content were measured between 1200 and 1600 °C using the method of α-energy degradation. Carefully determined D-rmvalues for UO2 heated in hydrogen were found to be very low compared to most previously published results, provided the annealing time was long ( > 100 h). The most probable reasons for this discrepancy are either the effect of impurities with valences < 4 (extrinsic diffusion) or else reduction of the UO2 to substoichiometry. For UO2+x, higher uranium diffusion coefficients were observed, in accordance with theory and previous results. At 1500 °C, the dependence of D on x in UO2+x could be described by log D = −10.85 + 1.5 log x. A value of 4.8 ± 0.3 eV (110 ± 7 kcal/mole) is suggested as the most probable value for the activation enthalpy of uranium diffusion in UO2.