Migration Enthalpy Research Articles

Beryllium Diffusion in the Supercooled Liquid and Glassy State of the Zr<sub>41.2</sub>Ti<sub>13.8</sub>Cu<sub>12.5</sub>Ni<sub>10</sub>Be<sub>22.5</sub> Alloy

The self diffusivity of Be in the bulk metallic amorphous Zr_(41.2)Ti_(13.8)Cu_(12.5)Ni_(10)Be_(22.5) alloy is investigated by high energy elastic backscattering of ^4He^(2+) ions in the temperature range between 433K and 663K. Below the glass transition temperature, the data suggest a single atomic jump diffusion behavior of Be with a migration enthalpy of 1.05eV/atom and a pre-exponential factor of 1.8·10^(-11)m^2/s. Above the glass transition, the diffusivity of Be increases by two orders of magnitude over a temperature interval of 40K. By taking into account the change in configurational entropy due to the glass transition, we can explain the mechanism for diffusion of Be in the supercooled liquid state of Zr_(41.2)Ti_(13.0)Ni _(10)Cu_(12.5)Be_(22.5) by single atomic jumps in a slowly changing configuration of neighboring atoms. The corresponding migration enthalpy is the same as in the solid glass, and the number of neighboring atoms which influence the diffusion of Be is about 22.

Ion beam mixing, diffusion, and phase stability in Cu/Al2O3 interfaces

Ion beam mixing, diffusion properties, and phase stability have been investigated in Cu/Al2O3 bilayer samples. Specimens were prepared by vapor deposition and irradiated with 150 keV Ar+ ions up to a fluence of 1.5 · 1017 Ar+/cm2. Sample temperature under irradiation was varied between 77 K and 673 K. The mixing behavior was studied by analyzing the concentration depth profiles, determined by Rutherford Backscattering Spectroscopy. It was found that mixing efficiencies of Cu, Al, and O scale with Ar+ fluence. Radiation enhanced diffusion (RED), observed above room temperature, is separated from ballistic mixing and high temperature diffusion. The migration enthalpy for interdiffusion in the RED region (between RT and 300 °C) was estimated to be approximately 0.3 eV. Sputtering yields depending on temperature gradient near to sample and phase stability versus ion dose and temperature are also discussed.

The mechanism of surface heterodiffusion at elevated temperatures

Molecular dynamics simulations employing the Lennard-Jones potential have been performed on Kr/Ar(111) to investigate the nature of high-temperature surface heterodiffusion. These suggest that high activation energies and preexponential factors observed experimentally at temperatures above approximately 0.70 T m arise from adatom-vacancy pair formation, which sharply increases the number of mobile species. Evidence is also obtained that at intermediate temperatures (0.45 T m < T < 0.66 T m), Arrhenius curves mass transfer diffusivity can depend on both coverage and adsorbate interactions. For adsorbates which exhibit islanding, low coverage diffusion is characterized by an activation energy equal to the enthalpy of migration, whereas at moderate coverage the activation energy contains an additional term due to the enthalpy of formation of mobile adatoms from immobile islands.

Vacancy activation enthalpies of AuFe alloys determined from SRO-induced resistivity changes

The kinetics of atomic short-range ordering (SRO) in Au-14-at.% Fe were investigated by measuring residual resistivity after up-quenching and down-quenching over a suitable temperature interval, thus inducing different initial vacancy concentrations and vacancy mobilities. In addition, resistivity variations of Au-5-, 10-, 14- and 20-at.% Fe were measured during isochronal annealing of mechanically deformed and recrystallised samples. By assuming a certain model for SRO relaxation kinetics, migration and formation enthalpies of vacancies as well as vacancy sink densities (dislocation densities) were determined from experimental results. The parameters determined in this way correspond well with each other and with literature data.

CuBr by impedance spectroscopy

The electrical properties of polycrystalline copper(I) bromide were investigated between 20 and 430 °C by impedance spectroscopy with copper electrodes. Extrinsic and intrinsic regions in γ-CuBr and a domain of fast ionic conduction in β-CuBr are separated. Enthalpies of migration of copper interstitials (25 kJ/mol) and copper vacancies (50 kJ/mol) and the enthalpy of formation of Frenkel defects (160 kJ/mol) are deduced. The phase boundary copper/copper(I) bromide can be represented by a parallel circuit of an interfacial resistance and a constant phase-angle (CPA) element. The interfacial resistance depends exponentially on temperature and is practically negligible above 350 °C. Contributions of charge transfer resistance and space charge resistance are discussed. Prefactors of CPA elements depend also exponentially on temperature; they are compared with interfacial capacitances.

Interstitial Defect Reactions In Silicon

AbstractThe interaction between self-interstitials (Sii), impurities, and dopants in Si leads the formation of undesirable point defects which affect device operation. Electron beam irradiation has been used to generate Sii and initiate defect reactions, and the hierarchy and competition of interstitial defect reactions involving O, C, B, and P in Si have been explored by DLTS measurements. We describe the interstitial defect reactions as a three-step process: (i) displacement reaction for the generation of Sii, (ii) Watkins replacement reaction for the generation of C and B interstitials (Ci and Bi), and (iii) diffusion limited reaction for the formation of pairs. Within the framework of reaction kinetics, for the first time, we have successfully set up a nonlinear system model to simulate the reaction processes. The interstitial migration enthalpy and the pair formation capture radius are two parameters used in the model to describe long range migration and near neighbor interaction. The good agreement between the model and experiments not only supports the defect assignments by DLTS, but also provides an initial glimpse into the interaction of point defects in Si.

Properties of intrinsic point defects in silicon determined by zinc diffusion experiments under nonequilibrium conditions.

The present paper deals with self- and foreign-atom diffusion processes in Si. We focus on the foreign-atom Zn whose diffusion behavior is shown to be influenced by intrinsic point defects like Si self-interstitials (I) and vacancies (V). Diffusion experiments with Zn in dislocation-free Si were carried out between 1208 and 870 \ifmmode^\circ\else\textdegree\fi{}C applying a special method to perform isothermal diffusion anneals as short as a few seconds. Concentration-depth profiles measured with the help of spreading-resistance analysis are completely described by simultaneous diffusion via the kickout and dissociative mechanism. The evolution of Zn diffusion with time is characterized by short-, intermediate-, and long-time diffusion regimes. Profiles belonging to the long-time regime are suitable to extract transport capacities of intrinsic defects given by the product of thermal equilibrium concentration and diffusion coefficient. Zn profiles after intermediate diffusion times are shown to be sensitive to the prevailing thermal equilibrium concentration of Si self-interstitials. Results are presented for the thermal equilibrium concentrations of self-interstitials and vacancies as well as their transport properties. From the temperature dependence of these quantities the formation and migration enthalpy of I and V are obtained. These data are compared to previous experimental results as well as theoretical calculations.

Activation entropy and Gibbs free energy for conduction in yttria-stabilized-zirconia single crystals.

The temperature dependence of the activation Gibbs free energy [\ensuremath{\Delta}G(T)] and entropy [\ensuremath{\Delta}S(T)] associated with electric conduction in 12 mol % yttria--stabilized-zirconia single crystals was analyzed. In order to determine the \ensuremath{\Delta}G(T) and \ensuremath{\Delta}S(T) functions exactly, it was necessary to impose temperature-behavior conditions on the activation Gibbs free energy to give \ensuremath{\Delta}S(T\ensuremath{\rightarrow}\ensuremath{\infty})=0. The temperature dependence of the entropy was similar to that of the activation enthalpy. Both reach stable values at low temperatures (extrinsic associated range). In this temperature range, \ensuremath{\Delta}G(T) shows a linear behavior. At higher temperatures, \ensuremath{\Delta}G(T) decreases asymptotically to a value approximately equal to the migration enthalpy of the oxygen vacancies. A value of 5.6\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}7}$ eV/K was calculated for the variation of entropy associated with the migration of the vacancies. Assuming the cation-vacancy-cation association to be a first-neighbor structure, a value of 4.85\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$ eV/K was found for the association entropy of the vacancies. These results are in very good agreement with those obtained by applying the method used in alkaline halide studies.

Fractional polarization, a new technique of the thermally stimulated current method to study the physical and morphological structure of materials

Segregation phenomena in copolymers are studied using thermally stimulated current method. The origin of the peaks observed with the thermally stimulated current technique can also be investigated; but molecular parameters such as the relaxation times, the free activation energy, the migration enthalpy and entropy, and the degree of disorder number in polymers are calculated analysing the relaxation map obtained by the fractional polarization method. This method represents an important technological advance with regard to the study of inner responses and characterization of the amorphous states of polymers.

Self-diffusion and lattice dynamics in a b.c.c. TlIn solid solution

A combined study of tracer diffusion of 204Tl and inelastic neutron scattering in a b.c.c. TlIn (17 at%) solid solution is presented. In contrast to self-diffusion behaviour in b.c.c. alkali and transition metals, which is characterized by a certain systematics and non-linear Arrhenius relations, the classification of self-diffusion for the only main group b.c.c. metal β-Tl in terms of normal or “anomalous” is still unclear because the small temperature range of existence of its b.c.c. phase does not allow decisive experiments. Alloying the homologous element In to Tl extends this range drastically and improves the possibility to study both the temperature dependence of self-diffusion and of the phonon dispersion. On the basis of the phonon measurements vacancy migration enthalpies are calculated, being independent of temperature. This result is conform with the measured perfectly straight Arrhenius plot of self-diffusion in b.c.c. TlIn (17 at%). Our combined investigations provide arguments for classifying self-diffusion of β-Tl — opposite to the diffusion behaviour of b.c.c. transition metals — as normal.

Thermal formation of vacancies in Fe3Si.

The formation of thermal vacancies in the intermetallic compound ${\mathrm{Fe}}_{3}$Si was studied below and at the ferromagnetic-paramagnetic phase transition by means of positron-lifetime spectroscopy. Low values of the vacancy formation enthalpies ${\mathit{H}}_{\mathit{V},\mathit{f}}^{\mathit{F}}$=0.77 eV in the ferromagnetic state and ${\mathit{H}}_{\mathit{V},\mathit{p}}^{\mathit{F}}$=0.74 eV in the paramagnetic state are derived in the case of stoichiometric ${\mathrm{Fe}}_{75}$${\mathrm{Si}}_{25}$. These values substantially increase to ${\mathit{H}}_{\mathit{V},\mathit{f}}^{\mathit{F}}$=1.11 eV and ${\mathit{H}}_{\mathit{V},\mathit{p}}^{\mathit{F}}$=1.07 eV in the case of Fe-rich ${\mathrm{Fe}}_{79}$${\mathrm{Si}}_{21}$. In addition, an upper limit of the vacancy migration enthalpy was derived from measurements after fast temperature changes. The results are discussed with respect to recent tracer diffusion measurements in ${\mathrm{Fe}}_{3}$Si.

Rapid thermal annealing of low-temperature GaAs layers

Electron microscopy studies of annealed GaAs layers grown by molecular beam epitaxy at low temperature (200 °C) were used to monitor growth of As precipitates. Ostwald ripening kinetics was used to deduce a migration enthalpy of 1.4±0.3 eV for the diffusion mediating defect. A conclusive picture of the dominant diffusion mechanism can be given, attributing this value to the migration enthalpy of gallium vacancies (VGa), which is well established by other experiments. The present studies indicate that growth of As precipitates is driven by supersaturation of VGa.

Magnetothermal investigation of the kinetics of defect reaction in the CoGa intermetallic compound

The kinetics of the formation and of the annealing out of Co antistructure atoms in the CoGa intermetallic compound have been investigated by magnetothermal analysis. The annealing out was found to be influenced by a single defect type. A quantitative analysis of the susceptibility vs. temperature curve of quenched Co 50Ga 50 sample yielded the fraction of antistructure atoms. The triple defect model was used to calculate the amount of vacancies. The migration enthalpy H m was determined for the quenching temperatures 1000 °C, 900 °C, and 850 °C and found to be 1.78 ± 0.12 eV, 2.16 ± 0.12 eV, and 1.8 ± 0.2 eV respectively. The triple defect type, the amount of vacancies and the migration enthalpy for 1000 °C are in agreement with data reported in the literature.

Electrical properties of CuI and the phase boundary Cu ¦ CuI

The electrical conductivity of copper (I) iodide was investigated between 50 and 450 °C by ac measurements at different frequencies and four-point dc experiments. The resistance and capacitance of the phase boundary copper/copper iodide depend exponentially on temperature. The interfacial resistance is practically negligible in the α- and β-phases, whereas the interfacial capacitance is very high. The electrical conductivity is in good agreement with previous electrochemical experiments. The enthalpy of formation of Frenkel defects and enthalpies of migration of copper vacancies and interstitials in copper iodide are reported.

Iron diffusivity in silicon: Impact of charge state

The effect of iron charge state on its diffusion in p-type Si near room temperature has been investigated by C–V and depth dependent deep-level transient spectroscopy measurements. The migration enthalpies of both positively charged and neutral iron were found to be 0.92 and 0.56 eV, respectively. Disagreement between the theoretical predictions and experimentally observed trend in iron diffusion is briefly discussed in terms of diffusion path, elastic strain, and Coulombic interaction versus impurity charge state.

Properties of monovacancies and self-interstitials in bcc Na: An ab initio pseudopotential study.

By means of ab initio pseudopotential theory and the local-density approximation various properties of monovacancies and self-interstitials in bcc Na, viz. the formation energies and formation volumes and the electric field gradients in the neighborhood of the defects, are calculated. As in the case of Li treated earlier, comparison with experimental results leads to the following conclusions. (i) An interstitialcy mechanism of self-diffusion may be excluded. (ii) The vacancy formation enthalpy is so close to the activation enthalpy of self-diffusion that either the vacancy migration enthalpy must be extraordinarily small (this raises the question of the validity of the transition state theory) or the low-temperature self-diffusion in Na is due to a direct exchange of neighboring atoms or to a ring mechanism involving three atoms. A nonvacancy mechanism is supported by the fact that the calculated monovacancy formation volume at 0.51 atomic volumes is substantially larger than the experimentally determined activation volume of the low-temperature mechanism of self-diffusion.

Investigation of intrinsic point defects in rapidly quenched copper by nuclear quadrupole double resonance

Abstract This letter reports nuclear quadrupole double-resonance (NQDOR) measurements on Cu specimens that were rapidly quenched from the melt either by Duwez's gun technique or by melt spinning. Comparison with measurements of the recovery of the residual electrical resistivity and with previous NQDOR studies of electron-irradiated Cu leads to the conclusion that the defects annealing out in the so-called recovery stage III after low-temperature electron irradiation are self-interstitials. Among the vacancy-type imperfections introduced by the rapid-quenching techniques employed in the present work there is at least one defect (presumably the divacancy) that becomes mobile in the same temperature range as self-interstitials. This is in agreement with the evidence from other work that in Cu the enthalpies of migration of divacancies and of self-interstitials are almost the same.

Self-diffusion in indium antimonide

In the present paper indium and antimony self-diffusion was studied in the temperature range 400–500 °C in single crystals of indium antimonide. The crystals were grown by the Bridgman technique. The radioactive tracer diffusion method was employed using In114m and Sb125 isotopes. Anodic oxidation technique was developed and used for serial sectioning. The penetration profiles were fitted to the error function solution of diffusion equations. For indium self-diffusion, the activation energy and pre-exponential factor were found to be 1.45 eV and 6.0×10−7 cm2/s, respectively, while for antimony diffusion the activation energy was obtained as 1.91 eV with a pre-exponential factor of 5.35×10−4 cm2/s. The results were compared with the earlier experimental studies and theoretical calculations. The migration enthalpies of indium and antimony atoms are estimated to be 0.66 and 0.70 eV, respectively. The corresponding formation enthalpies are 0.79 eV for In vacancy and 1.21 eV for Sb vacancy formation.

A single microscopic approach for ionic transport in glassy and polymer electrolytes

A micro-structural model is developed for non crystalline materials presenting a glass transition phenomenon. A singled expression of the conductivity temperature relationship, both below and above the glass transition temperature, is obtained while the electrical behaviour of such materials is usually described by different relationships depending on the temperature domain. In this model, below and above T g, the charge carrier formation results from the partial dissociation of ionic pairs as it is the case for the formation of the Frenkel defects. In the solid state, the defect migration proceeds from an indirect interstitial mechanism, while in the super-cooled state, a cooperative mechanism involving the neighbouring atoms is superposed to the first one, justifying a deviation from an Arrhnius law to the so called “free volume” behaviour. This approach allows numerical fits of experimental data in the whole temperature range which leads to accurate determinations of the main thermodynamic parameters of the ionic transport: the ideal glass transition temperature and both the formation and migration enthalpies.

Atomic short-range ordering in AuFe alloys: a resistometric study

Kinetics and equilibrium of atomic short-range order (SRO) in Au 1− x − Fe x ( x=0.05, 0.10, 0.14, 0.20) have been investigated by measurement of residual electrical resistivity for a cold-rolled and a well-annealed state. Activation enthalpies of SRO relaxation correspond well to the sum of formation and migration enthalpies of vacancies, both determined separately In contrast to Mössbauer measurements a strong temperature dependence of SRO-induced electrical resistivity was observed. It was found that, because of the high density of vacancy sinks, SRO kinetics in the cold-rolled state in considerably slower than in the well-annealed state. Surprisingly, the as-rolled state for the alloys with 5, 10 and 14 at.% Fe has a high degree of SRO, whereas for Au-0.2.%Fe the initial state is disordered.No indications for precipitation of α-Fe were found for the samples with 5,10 and 14 at.% Fe, for both the cold-rolled and the recrystallized state. For 20 at.% Fe, however, a resistivity drift in the cold-rolled state was observed, which may be caused by precipitation of α-Fe.