Migration Enthalpy Research Articles

Mechanisms of surface dissociation the Si(111)-(2 × 1) surface

Atomic modelling of dissociation of the Si(111)-(2 × 1) surface is studied. The introduction of known relations between microscopic parameters (force constants) and thermodynamic ones (entropy and enthalpy of migration, dissociation) permits to classify the probability of occurrence of various atomic paths. It is shown that: (1) more than one path have the same activation energy; (2) in general, migration does not favour dissociation; (3) reconstruction renders dissociation more difficult; (4) steps facilitate dissociation in most cases; (5) direction of dissociation is important for both surfaces with and without steps.

Temperature dependence of lattice & defect properties of MgO and Li2O

Methods are described for calculating the temperature dependence of lattice and defect properties of crystals based on a combination of lattice statics and dynamics. For defect thermodynamic parameters, constant pressure quantities are obtained directly, in contrast to previously-suggested approaches. Detailed results are presented for MgO and Li2O: these include the temperature dependence of the lattice energy, the total free energy, the vibrational free energy and elastic and dielectric constants. For MgO, defect formation and migration enthalpies and entropies are also discussed. Finally, results are included for the lowest index surfaces of MgO which illustrate present shortcomings of the theory.

On the correlation between self-diffusion and the low-frequency LA ⅔⟨111⟩ phonon mode in b.c.c. metals

Abstract A new approach is proposed for understanding the strongly diverging self-diffusion behaviour in b.c.c. metals by relating the atomic mobility to the characteristic low-frequency LA 2/3⟨111⟩ phonon mode. The frequency v 2/3 of this mode is controlled by restoring forces, which oppose in particular the atomic displacements for a diffusion jump in the ⟨111⟩ direction, influencing in this way the migration enthalpy H M. A simple semi-empirical expression is derived which relates H M to the square of v 2/3. On the basis of experimental results an excellent correlation between the activation energy for self-diffusion and the LA 2/3⟨111⟩ phonon frequency is found. It is concluded that the extremely different mobilities in b.c.c. metals result from corresponding alterations in H M. Changes in H M originate from systematic variation in the d electron charge density distribution, which is responsible for the strength of the ⟨111⟩ directional bond-bending forces in b.c.c. transition metals. This model of ph...

The ionic conductivity profile of thin evaporated AgCl films on a planar sapphire substrate

The ionic conductivity profile of AgCl-films stepwise evaporated onto a sapphire-substrate has been measured. After each step the films have been annealed. A bombardment of the uncompleted films by argon-ions (just before the successive evaporation processes) enhances the ionic conductivity. The first sheet (about 350 nm thick) of these films adjacent to the interface shows extremely high conductivity values up to about 10−4 S/cm at 25°C. But also the remaining part of each film between about 350 and 800 nm away from the interface still shows an unexpectedly good conductivity of the same magnitude as the highest conductivity value (of 6×10−6 S/cm at 25°C) found so far for disperse systems AgCl/Al-oxide. The measureds activation energies (between 0.34 and 0.47 eV) of these films are markedly higher than the migration enthalpy of Ag-vacancies (0.28 eV). The discussion suggests that the high conductivity and its profile are essentially determined by the microscopical structure of the films.

Influence of nickel concentration on point defect migration in high-nickel Fe-Cr-Ni alloys

Point defect migration enthalpies were determined in high-nickel Fe-Cr-Ni alloys by studying electrical resistivity recovery in low-temperature irradiated fcc ternary alloys (16 wt.% Cr, 45 and 75 wt.% Ni). The results, together with previously obtained data, show that the mobility of self-interstitial defects increases progressively for higher nickel alloys. By contrast, vacancy migration is insensitive to composition in the range 20–45 wt.% Ni; a higher migration enthalpy value is observed for 75 wt.% Ni. The comparison with self-diffusion measurements shows that vacancy-formation enthalpy tends to decrease for increasing nickel contents.

Diffusion characteristics of hydrogen in amorphous Pd 80Si 20. Part II

Measurement of the kinetics of hydrogen uptake and outgassing in response to the application or release of gas pressure enabled us to make a detailed analysis of the hydrogen mobility in melt-spun Pd 80Si 20. The diffusion coefficient of hydrogen was found to be dependent on hydrogen concentration. It increased by a factor of about two when the concentration of dissolved gas increased from 0 to 0.2 at.% The progressive enhancement of hydrogen mobility reflects the existence of a broad continuous energy spectrum of the available sites. At very low concentrations, a typical value for the migration enthalpy of hydrogen is 0.43 eV (41 kJ mol −1).

Kinetics of silver precipitation in dilute Pb(Ag) alloys

Using a heat flux differential calorimeter, silver precipitation in lead was studied over the temperature range 90–15°C. It was observed that the kinetics of precipitation depends on the silver concentration: present results only concern dilute alloys (96–290 · 10 −6 at/at). For these concentrations thermal effects lead to a precipitation enthalpy value in fair agreement with silver dissolution enthalpy in lead and to first order reactions. The precipitation occurs in a single stage with an activation enthalpy equal to (0.51 ± 0.03) eV. It is suggested that this activation enthalpy represents the migration enthalpy of the mixed dumbbell Ag-Pb, rather than that of either the Ag-vacancy pair or the dumb-bell Ag-Ag.

Vacancy migration enthalpy in tungsten at high temperatures

Abstract The curvature found in the Arrhenius plot for tungsten self-diffusion has been commonly interpreted in terms of simultaneous diffusion by two different defect processes. An alternative interpretation has been in terms of the temperature dependence of the migration enthalpy H m 1V and/or the formation enthalpy H f 1V for single vacancies. In order to study the magnitude of the temperature dependence of the migration enthalpy H m, the present experiments were done to study the annealing of a supersaturation of vacancies at high temperatures in tungsten. The annealing of vacancies was monitored by interrupting quenches from 2900 K at well-defined anneal temperatures T a for a series of different time periods, followed by a quench to 300 K. The quenched-in resistivity Δρq was subsequently measured at 4 K. The decay of Δρq was observed for approximately ten delay times at each anneal temperature in order to define a characteristic decay time τ1/2. Analysis of the decay curves showed that at all the an...

Cation diffusion in alkaline-earth oxides

Absolute jump rates for cation-vacancy interchanges in MgO, CaO, SrO and BaO are calculated from a set of model inter-ionic potentials. Internal energies and vibrational entropies over a wide range of temperatures (i.e. at expansions which within the models correspond to these temperatures in the quasi-harmonic approximation) are evaluated and, from these, migration enthalpies and pre-exponential frequency factors are deduced. Correlations between these two diffusion parameters for the family of oxides are investigated.

On the Anomalous Self‐Diffusion in B.C.C. Titanium

AbstractSelf‐diffusion of 44Ti is measured in β‐Ti under UHV conditions in the whole range of existence of the b.c.c. phase. The Arrhenius plot shows a strong upward curvature in agreement with previous investigations of Murdock et al. The anomalous diffusion behaviour is related to the experimentally observed softening of the LA ⅔〈111〉 phonon mode and is explained by a monovacancy mechanism with a temperature‐dependent migration enthalpy. When separating the phonon related diffusion contribution the analysis yields a frequency factor and an activation enthalpy consistent with normal vacancy diffusion parameters.

Ionic transport in rubidium aluminogermanate glasses

Measurements of the electrical conductivity have been made in a series of x Na 2O: y Al 2O 3: (1 − x − y) GeO 2 glasses where x ≅ 0.01, 0.05, 0.10, 0.15, 0.22 and 0.29 and y x ≅ 0.033 and 1.0. The dc conductivities of the rubidium germanate glasses show a minimum in rubidium ion mobility at x ≅ 0.1 that is a result of a maximum in the activation enthalpy for ion migration. Above x ⩾ 0.1 the activation enthalpies appear to be related to the packing density of the network forming ions. The preexponential factors for the conductivity are used to determine relative values of the physical correlation factor. The changes in the physical correlation factor with the rubidium-rubidium spacing suggest that as the spacing decreases ordering sets in and ƒ I is reduced.

Temperature effects in atomic diffusion in silicon.

When an intrinsic defect (e.g., vacancy or self-interstitial) mediates self-diffusion, the activation enthalpy is equal to the sum of the defect's formation and migration enthalpies. If the migration enthalpy is small and the migration entropy is large, however, at some critical temperature the saddle point becomes the stable configuration, whereby a totally different path may become dominant. It is, therefore, possible that paths with higher activation enthalphies may dominate at high temperatures, giving rise to a curvature in the Arrhenius plot of the diffusion coefficient. These effects are very likely to occur in crystalline Si and may account for the observed large entropy in high-temperature self-diffusion.

The influence of scandium on the anomalous self-diffusion in b.c.c.-zirconium

For further information on the origin of the anomalous self-diffusion in the b.c.c. phase of IVb metals and alloys the temperature dependence of 95Zr-diffusion and of the isotope effect of 88Zr and 95Zr were measured in Zr-Sc alloys with 6.7 and 13.6 at.% scandium. The Arrhenius plots are more strongly curved than that for self-diffusion in pure β-Zr, quite the opposite to our previous findings over Zr-Nb alloys. The results of the isotope effect are consistent with a predominant monovacancy mechanism in the whole stability range of the b.c.c. structure. The diffusion anomaly is explained by phonon assisted diffusion jumps induced by the softening of the LA 2 3 〈111〉 phonon mode, which results in a continuous decrease of the free enthalpy of migration with decreasing temperature. With this assumption values of the frequency factor and the activation enthalpy representing normal diffusion behaviour in these alloys are calculated. A systematic variation in the electronic structure when alloying Vb and IIIb metals, respectively, to IVb metals is regarded to be responsible for the observed continuous change in the diffusion anomaly of β-Zr-Nb alloys, pure β-Zr and β-Zr-Sc alloys.

Vacancy Migration Enthalpy in Tungsten at High Temperatures

The curvature found in the Arrhenius plot for tungsten self-diffusion has been commonly interpreted in terms of simultaneous diffusion by two different defect processes. An alternative interpretation has been made in terms of the temperature dependence of the migration enthalpy and/or the formation enthalpy for single vacancies. In order to study the magnitude of the temperature dependence for the migration enthalpy, the present interrupted quenching experiments studied the annealing of a supersaturation of vacancies at high temperatures in tungsten. The temperature dependence of H/sup m//sub 1v/ found in the present experiments is insufficient to explain the Arrhenius curvature found for self-diffusion in tungsten. However, the curvature could be explained if the formation enthalpy, H/sup f//sub 1v/ had a temperature dependence of similar magnitude.

Ionic transport in sodium aluminogermanate glasses

Measurements of the electrical conductivity and tracer diffusion coefficient have been made in a series of XNa 2O : YAl 2O 3 : (1− X− Y) GeO 2 glasses where X ≈ 0.01, 0.05, 0.10, 0.15, 0.19 and 0.29 and Y/ X ≈ 0, 0.33 and 1.0. The dc conductivities of the sodium germanate glasses show a minimum in sodium ion mobility at X ∼ 0.09, that is a result of a maximum in the activation enthalpy for ion migration. The maximum in the activation enthalpy appears to be directly related to the packing density of the glass network forming ions. Measurements of the activation enthalpy for the sodium aluminogermanate glasses confirm this relationship between enthalpy and the packing density of the network forming ions. Examination of the pre-exponential factors for the present glasses (with or without alumina) show a strong dependence on sodium content. This dependence appears to be a direct result of the changes in the physical correlation factor, ƒ I, that ensue when the spacing between the sodium ions is changed. At low X the sodium ions are far apart and ƒ I is close to unity but as X increases and sodium ion separation decreases, ordering sets in and ƒ I is reduced.

Magnetic circular dichroism, electric conductivity and mobility of anion vacancies in KBr:Se2-

The mobility of anion vacancies has been investigated by parallel measurements of ultraviolet absorption and electric conductivity on KBr:Se2- crystals subjected to various heat treatments. The MCD A-terms in the absorption spectra of samples freshly quenched from near the melting point are ascribed to unassociated Se2- ions. On annealing, the MCD A-terms and the electric conductivity decay in an identical fashion. This is attributed to pairing of the Se2- ions and vacancies. The activation energy of this pairing reaction is 1.10 eV which may be equal to the enthalpy of migration of anion vacancies although the order of the kinetics (first-order) raises some uncertainty about this assignment.

Electrical properties of non-irradiated and X-irradiated LiH and LiD

Abstract Various electrical properties of LiH have been experimentally studied by means of the following techniques: (1)d.c. conductivity, (2)dielectric loss and (3)ionic thermocurrents (ITC). 1) The study of d.c. conductivity has been extended up to the corresponding melting points of LiH and LiD. The migration enthalpies of the cation vacancy motion and the formation enthalpies per Schottky defect have been determined. 2) The dielectric loss spectrum of O2 X-irradiated LiD crystal doped with Mg+2 is studied and compared with the spectrum of the non-irradiated crystal. It is found that the X-irradiation produces a decrease of the d.c. conductivity but it does not affect the dipolar contribution to the imaginary part of the dielectric constant. The results are discussed in the frame of various centers that are possibly formed upon irradiation. 3) The ITC-spectra of LiH doped with Ca+2 and LiD doped with Mg+2 were measured from liquid nitrogen to room temperature. A computer analysis of the depolarization ...

Magnetic Anomalies of59Fe and60Co Diffusion in Iron and of48V Diffusion in Cobalt Quasi-Chemical Model

The measurements of V hetero-diffusion in f.c.c. cobalt, which reveal an evident magnetic diffusion anomaly (MDA), are reported. With respect to the fact that the equations derived in a previous work on the basis of Kirkwood's method (KM) cannot be applied when analysing MDA in trian-gular or honeycomb plane lattices, or in f.c.c. lattices, equations based on quasi-chemical approxima-tion (QCHM) are introduced. These equations are applied in 48V/Co hetero-diffusion analysis and in 59Fe/α-Fe and in 60Co/α-Fe [1]re-analysis, which yield: diffusion characteristics D0 and H in paramagnetic and in ferromagnetic matrices; exchange integrals J/k for α-Fe and Co, para-magnetic temperatures Tp, ratios ΔHM/ΔHM of the excess activation enthalpies of vacancy migra-tion (M) and formation (F), and experimental constants K1 The results obtained for α-Fe are compared with the parameters published in a previous work obtained by Hie use of KM. Es wird über Messungen der V-Heterodiffusion in k.f.z.-Kobalt berichtet, die auf eine deutliche magnetische Diffusionsanomalie (MDA) hinweisen. Da die in einer früheren Arbeit auf der Grund-lage der Methode von Kirkwood (KM) abgeleiteten Gleichungen nicht zur Analyse der MDA in dreieckigen oder wabenförmigen ebenen Gittern oder k.f.z.-Gittem benutzt werden können, werden Gleichungen eingeführt, die auf der quasi-chemischen Näherung (QCHM) beruhen. Diese Gleichungen werden für die 48V/Co-Heterodiffusionsanalyse und erneute Analyse von 59Fe/α-Fe und 60Co/α-Fe angewendet. die folgende Parameter ergeben: Diffusionscharakteristiken D0 und H in paramagnetischen und ferromagnetischen Matrizen; Austauschintcgrale J/k für α-Fe und Co, paramagnetische Temperaturen Tp, die Verhältnisse ΔHM/ΔHF der überschüssigen Aktivierungs-enthalpien der Leerstellenwanderung (M) und -bildung (F) und die experimentelle Konstante K1. Die erhaltenen Ergebnisse für α-Fe werden mit früher publizierten und mit KM erhaltenen Parametern verglichen.

Ion irradiation induced mass transport of Ni in Ni and Fe-20Cr-20Ni

Diffusion coefficients of 63Ni in Ni and Fe-20Cr-20Ni were measured with SIMS after 300 keV Ni + irradiation at temperatures between 293 and 1000 K with an ion flux of 6.3 × 10 12 cm −2s −1. At lower temperatures up to about 600 K a temperature independent diffusion coefficient of about 1.4 × 10 −16 cm 2s −1 was observed, which indicates that transport is dominated at these temperatures by athermal recoil mixing. At higher temperatures the diffusion coefficients are temperature dependent. These results are discussed with respect to point defect reactions and diffusion. The activation energies of the thermally activated process of 0.58 eV for Ni and 0.67 eV for Fe-20Cr-20Ni are determined by half the respective vacancy migration enthalpies. The production rate of freely migrating defects is estimated to be about 2.5% of the calculated damage rate per atom in self-ion irradiated nickel.

Diffusion of heterovalent ions in ionic crystals

Diffusion of divalent and trivalent cations is investigated in NaCl and KCl under conditions of heterodiffusion at infinite dilution. This purpose is achieved by letting radiotracers of very strong specific activity diffuse in the intrinsic range of highly pure single crystals. The importance of the experimental procedures in yielding reliable results is emphasized. Thus, Co ++, although supposedly characterized by an anomalous diffusion in NaCl and KCl, gives very good diffusion profiles with the carrier-free isotope Co-58. Also Fe +++, whose diffusion was considered impossible, gives good diffusion profiles with certain experimental precautions. Analysis of the data gives, for the diffusion of Co ++, the migration enthalpy of 0.76 eV in NaCl and 0.66 eV in KCl and the migration entropy of −2.84 k in NaCl and −1.45 k in KCl. These results are in good agreement with the values for the full set of divalent cations.