Ab initio pseudopotential study of vacancies and self-interstitials in hcp titanium

By means of an ab initio plane-wave pseudopotential method, monovacancy, divacancy and self-interstitials in hcp titanium are investigated. The calculated monovacancy formation energy is 1.97 eV, which is in excellent agreement with other theoretical calculations, and agrees qualitatively with published experimental results. The relaxation of the atoms around a single vacancy is observed to be small. Two divacancy configurations, the in-plane and the off-plane, have also been shown to be equally stable. With regards to the interstitials, of the eight configurations studied, two (octahedral and basal octahedral) have relatively lower formation energies and are, thus, the most likely stable configurations. We find small energy differences between them, suggesting their possible co-existence. It is also observed that the tetrahedral configuration decays to a split dumbbell configuration, whereas both the basal tetrahedral and the basal pseudocrowdion interstitials decay to the basal octahedral configuration. Using the nudged elastic band method (NEB), we determine a possible minimum energy path (MEP) for the diffusion of self-interstitial titanium atoms from an octahedral site to the nearest octahedral site. The energy barrier for this migration mechanism is shown to be about 0.20 eV.     

High-temperature diffusion of phosphorus and boron in silicon via vacancies or via self-interstitials?

The paper re-examines the effect of oxidation on the diffusion of phosphorus and boron in silicon as well as recent results on redistribution phenomena of these dopants under irradiation and on the emitter-push effect. It is shown that at high temperatures phosphorus and boron diffuse via a defect mechanism involving silicon self-interstitials. These results support the view-point that self-interstitials are the dominating point defects in silicon under thermal equilibrium conditions. Possible generation mechanisms for the self-interstitial supersaturation causing the emitter-push effect are suggested.     

Resistometric and anelastic approaches to the determination of the mobility of vacancies and self-interstitials in concentrated alloys

Analysis of the kinetics for local ordering to probe the atomic mobility in concentrated alloys is considered. Some recent applications in -AgZn solid solutions are reported to show the potentials and limitations of this method for the investigation of point defect properties. They are based on the use of mechanical after-effect and resistivity measurements to monitor the ordering rates in conditions of permanent irradiation or after quenching.     

Relaxation round vacancies in the alkali metals

The long-range ionic displacements round a vacancy are shown to come from both the elastic, long-wavelength, limit and from the Kohn anomaly. The effect of the topology of the Fermi surface is stressed.Attention is then focussed on the alkali metals with almost spherical Fermi surfaces, where it can reasonably be assumed that the elastic displacements dominate. Complete relaxation around a vacancy relates formation energy E_v, bulk modulus B and atomic volume Ω through E_v = αBΩ where α is a constant. The formation volume follows as a balance between a negative harmonic contribution and a positive and larger anharmonic term.     

Quantum tunnelling of vacancies in light metals

Summary The usefulness of the WKB method is illustrated by calculating characteristic tunnelling rates in several elemental solids and establishing the temperatures at which the tunnelling becomes of comparable importance to the thermally activated processes. In this way we have verified the importance of tunnelling which dominates the low-temperature region, while it becomes negligible above a temperature value depending on the mass and the barrier thickness. In studying vacancy migration in lithium metal we have considered various pathways in the configuration space of Li atoms. A (1, 1, 1)-jump of the vacancy, accompanied by the simultaneous outward movement of between 4 to 12 lithium atoms, is shown to be most efficient. In this model the lithium motion achieves a 10⁴-fold increase in the jump probability and a reduction of the activation energy from ∼0.25 to ∼0.16 eV.

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Riassunto L’utilità del metodo WKB è illustrata calcolando la probabilità di transizione per tunnelling in diversi solidi elementari e stabilendo la temperature alla quale il contributo del tunnelling diviene confrontabile con quello dovuto ai processi termicamente attivati. In tal modo si stabilisce l’importanza del tunnelling che domina la regione delle basse temperature, mentre divience trascurabile a temperature piú alte, dipendenti dalla massa e dallo spessore della barriera. Studiando il moto di vancaze nel litio, sono stati considerati diversi cammini nello spazio delle configurazioni degli atomi Li. Un salto della vacanza nella direzione (1, 1, 1), accompagnato dal simultaneo spostamento di 4÷12 atomi di litio, è dimostrato essere il piú efficiente. In questo modello la probabilità di moto delle vacanze aumenta di un fattore 10⁴ con una riduzione dell’energia di attivazione da ∼0.25 a ∼0.16 eV.

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Резюме Метод ВКБ применяется для вычисления характеристических вероятностей туннельных переходов в некоторых злементарных твердых телах. Определяются температуры, при которых туннелирование дает сравнимый вклад в термически активированные процессы. Мы показываем важность туннелирования, которое доминирует в области низких температур, но становится пренебрежимо малым при более высоких температурах, которые зависят от массы и толщины барьера. Исследуя движение вакансий в литии, мы рассматриваем различные траектории в конфигурационном пространстве атомов лития. Показывается, что скачок вакансии в направлении (1, 1, 1), который сопровождается одновременно смещением от 4 до 12 атомов лития, является наиболее эффективным. В этой модели вероятность движения вакансии увеличивается в 10⁴ раз при уменьшении энергии активации от ∼0.25 эВ до ∼0.16 эВ.

     

Residual resistivity of vacancies in simple metals

The residual resistivities of vacancies in simple metals are estimated by using the Kohn-Sham method to calculate a self-consistent scattering potential for free electrons. The results are compared to other calculations and experimental resistivities.     

Radiation-induced diffusion of quenched-in vacancies in metals

It is shown that the plateau observed by Lucasson and coworkers in the resistivity versus fluence curve during electron irradiation of pre-quenched metals can be explained in terms of radiation-induced diffusion of vacancies.     

Positrons in metals with voids,vacancies and surfaces

The behaviour of positrons near monovacancies and voids in a metal is discussed in terms of three contributions to the positron work function for the metal, namely the positron zero-point energy, the positron-electron correlation energy and the surface dipole barrier. The image potential when a positron comes near to a metal surface leads to a deep potential ‘trough’ just outside an exterior metal surface or just inside a void surface. Calculations indicate positron bound states localized at metal surfaces for most metals which should be manifested in a long lived positron lifetime component. The behaviour of positronium near metal surfaces is also discussed.     

Atomic simulation of the vacancies in BCC metals with MAEAM

The formation energy of the mono-vacancy and both the formation energy and binding energy of the di-and tri-vacancy in BCC alkali metals and transition metals have been calculated by using the modified analytical embedded-atom method (MAEAM). The formation energy of each type of configuration of the vacancies in the alkali metals is much lower than that in the transition metals. From minimum of the formation energy or maximum of the binding energy, the favorable configuration of the di-vacancy and tri-vacancy respectively is the first-nearest-neighbor (FN) or second-nearest-neighbor (SN) di-vacancy and the [112] tri-vacancy constructed by two first-and one second-nearest-neighbor vacancies. It is indicated that there is a concentration tendency for vacancies in BCC metals.     

The loss of single vacancies in metals during quenching

The Lomer equation, describing the rate of change of single vacancy concentration in a metal specimen during exponential quenching, was numerically solved for different quenching temperatures and different quenching rates. A relation has been found between the constantb, which characterizes the initial quenching rate, and the quenching temperature leading to the same percentual loss of vacancies. This relation enables us to determine the conditions of quenching, yielding the predetermined percentage of retained vacancies.The possibility is discussed of applying the above results in measurements of the formation energyEf^F, to estimate the migration energyE ^M and to determine the change of the mean number of jumps during quenching.The author would like to express his gratitude to Dr. K. Míek, head of the Metal Physics Department, for his interest and useful comments.     

Positron annihilation in vacancies at grain boundaries in metals

The behavior of vacancies in selected coherent grain boundaries (GBs) in Fe and Ni is studied by means of molecular dynamics simulations. Corresponding positron lifetimes are calculated using the atomic superposition method. There is a difference between the vacancy behavior in Fe and Ni in dependence on temperature. In Ni, vacancies at GBs appear to diminish substantially their free volume (and lifetime) with the increasing temperature, which can be attributed to ‘vacancy delocalization’. Contrary, GB vacancies remain stable up to apparently higher temperatures in Fe.     

Effects of simple vacancies and divacancies on the physical properties of metals

The effects of simple vacancies and divacancies on the electrical and thermal conductivities of metals are calculated. It is shown that, although the concentration of divacancies is usually less than that of simple vacancies, the changes caused in the kinetic coefficients by the two types of vacancies can be comparable.Translated from Izvestiya VUZ. Fizika, No. 10, pp. 88–93, October, 1969.     

Trap-centers of self-interstitials in silicon

Deep-level profiles were measured radially acrossn-type FZ silicon wafers containing A-swirl defects by applying DLTS to an array of Schottky contacts. The trapparameters were obtained very accurately using a computer-fit procedure for the full DLTS peaks. Two acceptor levels atE _c −0.49 eV (σ _n =6.6×10⁻¹⁶cm²) andE _c −0.07 eV (σ _n =4.6×10⁻¹⁶cm²) were observed, which varied oppositely to the A-swirl defect density. At short ranges (1–2mm) the trap concentration-profile was smeared out and did not follow the strong fluctuations in the etch pattern. Both levels were measured together with the same concentration. The profiles indicate outdiffusion. A level atE _c −0.14 eV (σ _n =1.1×10⁻¹⁶cm²) was not related to A-swirl defects. A level atE _c −0.11 eV (σ _n =1.1×10⁻¹⁵cm²) was only detected in one ingot. The properties of the deep level atE _c −0.49 eV are discussed in the light of published DLTS results reported for γ-irradiation, laser annealing after self-implantation, annealing under pressure and oxidation of silicon samples. It is concluded, that this level is related to interstitial silicon rather than to an impurity.     

Pseudopotential calculations of electrical resistivities due to vacancies in noble metals

Electrical resistivities due to vacancies in noble metals are calculated using the pseudopotential form factors given by Moriarty and Animalu. On the whole the values using the Moriarty's potentials are in good agreement with those calculated from phase shift except for Cu, but the Animalu's potentials do not produce reasonable values for these metals.     

Electric quadrupole interaction due to vacancies and interstitials in cubic host metals

A procedure has been developed to evaluate from first principle the electric field gradient (efg) due to vacancies and interstitials in cubic host metals. For this purpose the screening charge distribution in the valence-effect has been constructed in scattering theory using appropriate muffin-tin potential. In the size-effect, the efg has been evaluated in a more realistic model of the lattice than the commonly used elastic continuum. Unlike other calculations, no adjustable parameter has been used in the present procedure.     

Interaction between cation vacancies in pyrrhotite

Measurements of the sulphur fugacity of pyrrhotite [Fe_(1−Δ)S] are interpreted in terms of a model which involves interaction between cation vacancies. Good agreement is found between theory and experiment.     

Effect of vacancies in the lattice of an oxide on interaction with films of metals

It is shown that oxygen vacancies in the lattice of an oxide, being acceptor centers, facilitate ionic interaction in contact with films of metallic condensates and increase adhesion at the interface.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 45–49, October, 1986.     

Resonant vibrations of self-interstitials in fcc-metals

Some aspects of resonant vibrations of self-interstitials in the 100-dumbbell configuration are discussed by using a simple defect model incorporating nearest-neighbour interactions, with parameters fitted to the results of computer simulation. Especially we calculate the change of the lattice specific heat due to interstitials. An appreciable increase of the specific heat is obtained yielding a peak at 9–10 K in C/C for Cu. Following a recent suggestion of W. Schilling the diffuse inelastic one-phonon scattering is calculated in the range of the resonance frequencies forq-values away from the phonon-line. In particular, an appreciable diffuse intensity is obtained for theE _g-mode making an experimental observation by neutron scattering feasible.     

The influence of atomic displacements on the electrical resistivity due to vacancies in simple metals

The influence of atomic displacements around a vacancy on the electrical resistivity due to vacancies in simple metals has been calculated by the pseudopotential method. The influence of atomic displacements on the electrical resistivity was very large and the resistivity has a minimum at an appropriate relaxation. Therefore it is very important to take into account the effect of the lattice distortions considering the individual atomic displacements around vacancies in the calculation of the electrical resistivity due to vacancies.