Migration Enthalpy Research Articles

Calcium self-diffusion in diopside at high temperature: implications for transport properties

We have investigated 44Ca self-diffusion in natural diopside single crystals (containing ∼2 atomic % Fe) at temperatures up to 1320 °C (i.e. 30 °C below the nominal melting point). Oxygen fugacity was controlled by gaseous mixtures. Diffusion profiles ranging from ∼50 to 500 nm were analysed by Rutherford Back-Scattering Spectrometry (RBS). The present results are complementary to previous studies, and show that in both synthetic (Fe-poor) and natural (Fe-rich) diopside, there are two different diffusion regimes for Ca with a transition at ∼1230±15 °C. Below this temperature diffusion is characterised by an activation enthalpy of ∼284±10 kJ/mol, while at higher temperatures it increases up to ∼1006±75 kJ/mol. These regimes are proposed to be respectively extrinsic and intrinsic. For the intrinsic regime Ca self-diffusion may involve Ca-Frenkel point defects. These are pairs of a vacancy on a M2 site and a calcium cation on an interstitial (normally unoccupied) site. The concentration of such point defects depends only on temperature, and it is especially important at very high temperatures. The activation enthalpy for intrinsic diffusion may represent the half defect formation enthalpy plus the migration enthalpy for movement through interstitial sites. For the extrinsic regime we propose Ca self-diffusion to involve extrinsic interstitial point defects with concentration proportional to (\(\))–0.19±0.03. We suggest that for both regimes, Ca diffusion involves the well known M3 sites in the octahedral layers, as well as sites in the tetrahedral layers, that we call M4. These sites are especially convenient to explain the observed isotropic diffusion. Increasing concentration of Ca-Frenkel point defects may be related to the onset of premelting, which affects the thermodynamic properties of Fe-“free” diopside above 1250 °C. In the light of the present results, premelting is also expected to occur in natural Fe-bearing diopside and it could strongly influence its thermodynamic and transport properties. Subsequently, in deep upper mantle conditions (T≈1250 °C–1300 °C) where premelting could occur, diffusional cation exchanges with surrounding phases and diffusion controlled creep might be facilitated. Finally, our diffusion data support a previous suggestion that electrical conductivity may be electronic rather than ionic.

Determination of thermodynamics and kinetics of point defects in NiO using the Rosenburg method

The Rosenburg method has been used to investigate the deviation from stoichiometry and the defect diffusion coefficient in NiO between 1200 and 1300°C and in the oxygen pressure range 0.05–0.25 atmospheres. Simple point defect chemistry has been applied to interpret the oxygen pressure and temperature dependence of the data. The formation enthalpy and entropy of nickel vacancies at constant oxygen pressure have been estimated to be 75 kJ/mol and −15 J/mol K, respectively. The defect diffusion coefficient is essentially independent of the oxygen pressure and the migration enthalpy is determined to be approximately 150 kJ/mol. Combination of the enthalpies for formation and migration of the defects yields an activation enthalpy of 225 kJ/mol for Ni self diffusion. From the oxygen pressure dependence of the nonstoichiometry, singly charged nickel vacancies have been concluded to be the predominating point defect.

Radiation enhanced diffusion in MgO

Radiation enhanced diffusion and ion beam mixing of O18, Ca, and Zn buried tracer layers in MgO, grown by molecular beam epitaxy, have been measured following irradiation with 2.0 MeV Kr+ and 1.0 MeV Ne+, He+, and H+ from 30 to 1500 °C. The ion beam mixing parameter varied between 1.0 and 5.0 Å5 eV−1 for the different tracers at 30 °C and increased slowly with increasing temperature. These results are consistent with ballistic mixing. In the highest temperature range investigated, 1350–1500 °C, the radiation enhanced diffusion coefficient for O18 was proportional to the square root of the irradiation flux and displayed an apparent activation enthalpy of 1.2 eV. These dependencies on flux and temperature are indicative of recombination-limited kinetics, with the measured activation enthalpy representing one-half the migration enthalpy of anion vacancies. From 1150 to 1350 °C an activation enthalpy of 4.1 eV was obtained. The unexpectedly high value is attributed to the dissociation energy of small vacancy clusters. Measurements on the cation sublattice were limited to temperatures below 900 °C owing to the excessive thermal diffusion associated with extrinsic vacancies, which are present for trivalent impurity charge compensation.

Vacancy self-diffusion parameters in tungsten: Finite electron-temperature LDA calculations

An ab initiopseudopotential study of the monovacancy properties in bcc tungsten is presented. The formation and migration enthalpies are calculated for relaxed configurations using supercells containing up to 54 atomic sites, both in the electronic ground state and at finite electron temperature. The electronic contribution to the formation entropy --- usually neglected in point defect calculations --- is shown to be positive and equal to ${1.74k}_{B}$ at melting temperature. This large value is related to peaks in the electronic density of states just below the Fermi level due to states localized around the vacancy. The calculated values of the migration and formation enthalpies are found to be in excellent agreement with experiments at low temperatures, and their significant quadratic temperature dependence --- due to electronic excitations --- is shown to explain part of the experimentally observed temperature dependence of the migration enthalpy and self-diffusion activation energy. The tracer self-diffusion coefficient is calculated within the rate theory: the Arrhenius slope is in excellent agreement with experiments, and so are the absolute values provided that the electronic entropies are taken into account.

Electronic conductivity of gadolinia doped ceria

AbstractThe electronic conductivity of gadolinia doped ceria (Ce0.8Gd0.2O1.8) was measured as a function of oxygen activity (aOz=1 corresponding to a gas with oxygen partial pressure pO2= 1.013 bar) in the range from aOz≈︁101 to aO2≈︁10−13 for temperatures between 600 and 750°C. The Hebb‐Wagner polarization technique was used with an encapsulated Pt‐microcontact in N2 atmosphere and a Cu2O/CuO reference electrode. For instance, a minimum value of 3.10−7 S/cm was found for the electronic conductivity at 600°C and an oxygen activity of 9.10−7. The minimum is shifted to higher activity with increasing temperature. The activity dependence of the electronic conductivity in the n‐type and p‐type range agrees well with the theoretically expected values (p‐type range σp≈︁a , n‐type range σn≈︁a ). Extrapolation of the measured electronic conductivities, the electrolytic domain boundaries of Gd‐doped CeO2 were obtained as log aO2= 13 to log aO2=‐24.7 at 600°C and log aO2=11 to log aO2=‐20.1 at 700°C (the oxygen ion conductivity being 4.05.10−3 S/cm at 600°C and 1.29.10−2 S/cm at 700°C).The activation energy was determined from the temperature dependence of the electronic conductivity giving EA,e=(2.59±0.07) eV for electrons in the n‐type range and EA,h=(1.16±0.04) eV for the holes in the p‐type range. The migration enthalpy of electrons was Hmig,e = 0.49 eV.

Ionic transport mechanisms in oxide based glasses in the supercooled and glassy states

A model for ionic transport in glasses is proposed assuming that, like for ionic crystals, the displacement of cations would result from the migration of interstitial pairs. The formation of these pairs is supposed to be an activated function of the temperature and their migration to be dominated by an activated jump mechanism at low temperature and by a free volume co-operative mechanism above the vitreous temperature. Using numerical fits for conductivity data in the whole temperature range, that change of mechanism enables the determination of the defect formation enthalpy and its migration enthalpy in the low temperature domain.

Grain Boundary Migration in Fe-3wt.%Si Alloys

The studies of three different laboratories on grain boundary migration in Fe-3wt.%Si alloys are presented. In all cases bicrystal techniques employing capillarity as driving force were used. [100] tilt boundaries were studied in the temperature range from 1223 K to 1373 K, and [110] tilt boundaries in the range from 1220 K to 1625 K. Proportionality between grain boundary velocity and driving force was confirmed. All data fulfil a linear relation between activation enthalpies and logarithms of the pre-exponential factors, corresponding to a compensation temperature of 1386 K where all boundaries theoretically should possess the same mobility. A considerably lower activation enthalpy was found in one case for an asymmetrical grain boundary compared to the symmetrical boundary of the same misorientation. High values of activation enthalpy of migration were found for special [100] boundaries compared to general ones although an opposite tendency was also observed for [100] boundaries.

Atomic Defects in Intermetallic Compounds and Diffusion Processes

ABSTRACTFor the understanding of the properties of the technically important intermetallic compounds as transition metal aluminides and silicides the understanding of atomic defect properties is pivotal. From recent positron lifetime studies high or low values for the effective vacancy formation enthalpy were found for close-packed or for more open-structured bcc type compounds, respectively, which can be well understood theoretically. In B2-FeAl the vacancy migration enthalpy could be additionally derived at high temperatures from vacancy equilibration processes. It is shown here by a study on B2-FeAl in comparison to the positron annihilation experiments that the thermal formation and migration of defects can be specifically investigated by time-dependent length-change experiments at high temperatures by the defect equilibration behavior after temperature changes. With the present data on vacancy formation and migration the wide variation of the transition-metal self-diffusivities in intermetallic compounds can be understood.

Microchemistry of Proton-Irradiated Austenitic Alloys Under Conditions Relevant to Lwr Core Components

AbstractOver 1200 measurements of grain boundary composition and microstructure have been made on 14 different austenitic Fe-Cr-Ni alloys following proton irradiation in the temperature range 200-600°C and in the dose range 0.1-3.0 dpa. Grain boundary composition measurements revealed that Cr depletes at grain boundaries, Ni enriches and Fe can either enrich or deplete depending on alloy composition. Analysis of temperature and composition dependence of RIS revealed that the magnitude and direction of grain boundary segregation depends on alloy composition because the value of migration enthalpy differs among the alloy constituents, and diffusivities of the alloy constituents are composition-dependent. The dose dependence of segregation revealed ordering in Ni-base alloys and temperature dependence was used to show that RIS occurs by vacancy exchange rather than an interstitial binding mechanism. The dependence of segregation on composition is consistent with all known, relevant neutron data.

Annealing kinetics of quenched point defects in ordered feal intermetallic compounds

Summary The vacancy migration kinetic was examined in ordered FeAl intermetallic compounds containing 49, 50, 52 and 60 at.%Fe. The used technique was magnetic susceptibility measurements, during isothermal annealing. The influence of alloy composition induces different activation energies which vary from 1,22 to 1,47 eV. The identification of these energies with the vacancy migration enthalpy is only a first approximation. It is consequently necessary to take into account some terms linked to the formation of vacancy sinks. These terms must depend on atomic disorder therefore on the iron content; this could explain the observed variations of the activation energies.

Defect types and defect properties in FeAl alloys

Abstract The thermomechanical behavior of high temperature intermetallic alloys is related to point defects and their concentration. Positron annihilation is a sensitive tool to obtain various information about defect properties. In the FeAl system the formation enthalpy of defects decreases from 1.6 to 2.0 eV in pure α -Fe to 1.37 eV (Fe–7at.%Al) and 0.91eV in the D0 3 structure. Additionally, the formation volume of the defects increases from 0.88 Ω in Fe–7at.%Al to 1.42 Ω in Fe–40at.%Al (Ω=mean atomic volume). The change of the formation volume indicates different types of defects. In quenching experiments the migration enthalpy is measured using the fast Doppler broadening technique and changes from 0.5 to 1.2 eV. Furthermore, the knowledge of the positron lifetimes gives an additional hint about the main defects and their positions in the lattice. The results suggest that thermal defects in the B2 phase are mainly triple defects at low temperature and double vacancies at higher temperatures. In the A2 as well as in the D0 3 structure single vacancies are supposed to be the predominant defect types.

Lattice dynamics and related diffusion properties of intermetallics: II.

The phonon dispersion of the intermetallic has been studied by inelastic neutron scattering in its high-temperature phase of structure, stable above . The dispersion has been examined at a temperature of ; some selected branches were also studied at (i.e. very close to the phase transition) and at . In general, the phonons are very strongly damped and some branches have not been found at all. For transverse phonons with propagation, the frequency does not change as a function of the temperature, but the widths become larger towards higher temperatures. The migration enthalpy and several other thermodynamic quantities have been calculated from the densities of states. The anomalous behaviour of the alloy is related to high vacancy densities.

Mass transfer surface diffusion of noble gases

Molecular dynamics simulations employing the Lennard-Jones potential have been performed for Ne, Ar, and Kr on Ar(111) to investigate the nature of surface diffusion at elevated temperatures. Despite the inapplicability of such a simple potential to materials other than noble gases, these simulations qualitatively reproduce the characteristic experimental features of high-temperature surface diffusion on metals and semiconductors. All species exhibit Arrhenius curves with discontinuities at temperatures ranging from 0.65–0.73 T m. Below this temperature, Ne does not island and diffuses by a standard site-hopping mechanism, whereas mobile adatoms of Kr and Ar are formed from the edges of immobile islands, yielding an activation energy which includes both an enthalpy of formation and an enthalpy of migration. Above the discontinuity in the Arrhenius curve at which the surface disorders, surface diffusion is dominated by mass transfer effects, with all surface species diffusing predominantly by a novel mechanism of adatom-vacancy pair formation, which sharply increases the number of mobile species. Perhaps surprisingly, this mechanism is operative for Ne surface diffusion at elevated temperatures despite surface segregation. In addition, high-temperature heterodiffusion is seen to decrease with increasing surface coverage as the adspecies quench surface disordering in the top substrate layer. These and other results demonstrate the importance of surface preparation during high-temperature surface diffusion measurements.

Implantation-induced disordering of CuPtB-ordered GaInP

In this article, a comprehensive treatment of the implantation-induced disordering (IID) of CuPtB-ordered GaInP with regard to microstructuring is presented. Ion implantation reduces the thermal stability of the crystal, so that disordering occurs at temperatures smaller than 800 °C for which the ordered phase normally is stable. It is shown that IID is mediated by implantation defects and can be described quantitatively by a model based on defect annealing. From the temperature dependence of the disordering process an activation energy of 2.15 eV has been evaluated, which is supposed to be the migration enthalpy of group III vacancies. Lateral order/disorder structures were achieved by masked implantation using high resolution electron beam lithography for the definition of wire and dot implantation masks down to 35 nm width. These structures were examined using photoluminescence and transmission electron microscopy. Both methods show that the spatial resolution is determined by implantation straggling, whereas defect diffusion can be neglected. This is also confirmed by extracting the defect diffusion length from the disordering model.

Thermal Vacancies and High-Temperature Mechanical Properties of FeAl

The formation and the kinetics of migration of thermal vacancies in Fe61Al39 have been studied by positron lifetime spectroscopy. From the temperature variation of the equilibrium vacancy concentration an effective vacancy formation enthalpy of HFV = 0.98 eV has been determined. From the equilibrium of the thermal vacancy concentration after temperature changes the vacancy migration enthalpy (HMV = 1.7 eV) could be derived. As observed recently, vacancy-type defects give rise to an internal friction maximum at 680 K (2 s—1) after quenching of FeAl. This reorientation effect as well as its recovery by long-range migration of defects is characterized by the above vacancy migration enthalpy. For the defects of the 680 K internal-friction maximum, a complex of a vacancy on the Fe sublattice and an antisite atom is suggested. A direct relationship between the high-temperature mechanical properties and atomic defects arises from the time dependence of the yield stress anomaly in Fe60Al40 measured after fast heating, which fits perfectly with the equilibration kinetics of the thermal vacancy concentration. From this we conclude that the yield stress anomaly is sensitively affected by thermal defects.

Defect analysis with positron annihilation ? Applications to Fe aluminides

Measurements of positron annihilation at various temperatures at constant pressure give information about the formation of thermal defects and their enthalpy in metals and alloys. In the FeAl system the formation enthalpy decreases from 1.6-2.0eV in pure α-Fe to 1.37eV (Fe7at%nAl) and 0.91eV in the D0 3 structure. Additionally, the formation volume of the defects can be determined from measurements varying the pressure at constant temperature. The formation volume increases from 0.88Ω in Fe7at%Al to 1.42Ω in Fe40at%Al(Ω = mean atomic volume). The change of the formation volume indicates different types of defects. With the further knowledge of the positron lifetimes in these materials we suggest triple defects as the main defects in this system. In quenching experiments the migration enthalpy is measured using the fast Doppler broadening technique. In Fe 3 Al we observe a migration enthalpy of 0.5 eV. which is influenced by an apparing change of order in a temperature range above the DO 3 B 2 transition as determined from the phase diagram by Massalski. Thickness reduction of Fe6.3at%Si single crystals changes positron lifetimes with increasing deformation, particularly by rolling less than 5%.

Experimental Determination of Migration Enthalpies in Iron-Rich Fe-Al Alloys and DO<sub>3</sub> and B2 Compounds

Experimental Determination of Migration Enthalpies in Iron-Rich Fe-Al Alloys and DO<sub>3</sub> and B2 Compounds

Dislocation Relaxation Processes due to Kink Migration

The interpretation of the Bordoni relaxation and of related relaxation phenomena in terms of the thermally activated, stress-assisted formation of kink pairs on dislocation lines is well established on assuming that the migration of kinks along dislocation lines is described by a high kink mobility μk. This assumption, however, is not valid if the activation enthalpy for kink migration, H m , is comparable with or even larger than the formation enthalpy of kink pairs or if even when small compared with the formation energy of kinks, H m is larger than the lowest thermal energies accessible in internal friction experiments. In those cases not only migration but also annihilation and trapping of thermal kink pairs may produce internal friction peaks. The difference-differential equations governing the thermal kink pairs evolution along dislocation lines under the action of a homogeneous applied shear stress are set up and their time-dependent solutions characterized by a set of relaxation times. It is shown how to obtain, from these solutions, the internal friction spectrum under conditions that are experimentally realized. Quantitative descriptions of geometrical kink migration and kink pair evolution are compared with selected experimental results.

Lattice dynamics and migration enthalpies in iron-rich Fe - Al alloys and ordered and B2 compounds

The phonon dispersion curves of iron-rich Fe - Al alloys have been studied using inelastic neutron scattering. Measurements were performed on three single crystals at three temperatures, 300 K, 800 K and 1250 K, corresponding to the bcc solid solution for x = 0.2 and to three different states of order , B2 and A2 for x = 0.25 and 0.30. The migration enthalpies are deduced from the phonon density of states through a model proposed by Schober. They decrease with increasing temperature and have a minimum value at the composition. A comparison of the present determination of in Fe - Al with similar -measurements on Fe - Si confirms the contribution of the effective pair interaction energies to the migration enthalpy, as described in models of Monte Carlo simulations of ordering kinetics in B2 and compounds. In the phase, the three separate determinations of (present work), of the formation enthalpy of the vacancies , and of the activation enthalpy of the ordering kinetics , which are all average quantities, satisfy the addition law: .

Enhanced diffusion in nonstoichiometric quantum wells and the decay of supersaturated vacancy concentrations

Enhanced superlattice disordering in nonstoichiometric AlAs/GaAs quantum wells exhibits weak temperature dependence because of the decay of the supersaturated concentration of group-III vacancies. We present a formalism for transient enhanced diffusion in nonstoichiometric materials with which we can extract migration enthalpies Hm by assuming that the vacancy decay is thermally activated with an enthalpy Ha. By analyzing the electroabsorption from the quantum-confined Stark effect for a set of isochronal and isothermal anneals, we extract a migration enthalpy Hm=(1.8±0.2) eV for group-III vacancies, as well as an activation enthalpy Ha=(0.7±0.2) eV for vacancy annihilation.