Split Interstitials Research Articles

Temperature dependence of energy and entropy of formation of self-interstitials in Cu.

The vibrational contribution to energy of formation of self-interstitials in fcc metals is investigated with the use of the Green's-function method. The vibrational contributions to the energy, entropy, and free energy of formation of 〈100〉-split interstitials have been calculated for the case of copper so as to discuss their temperature dependence. The vibrational contribution to the formation energy at low temperatures is \ensuremath{\sim}0.045 eV. The variation in formation entropy at low temperatures is found to be more pronounced.

The Nature of Two Intense Si–H IR Stretching Bands in FZ‐Si:H

AbstractBased on the isotope effect, two H‐defect complexes: tetrahedral interstitial silane (SiH4)Td and hydrogenated 〈100〉 split interstitials (Isp · 2 H) are proposed to account for the two strong Si–H IR stretching bands in FZ‐Si grown in H atmosphere (2210 cm−1, 1946 cm−1). A series of experimental facts, including the vibration frequency, the correlation with Si–H IR bands in the bending‐wagging region, the temperature dependence of band‐width and the annealing behaviour are presented, which support the proposed model. The results coincide with the view that the self‐interstitial is the dominate thermal defect in crystalline silicon at high temperature.

Nature and diffusion of the self-interstitial in silicon

The authors exploit self-consistent, semi-empirical molecular orbital calculations (CNDO) for large silicon clusters to characterise self-interstitials. Hexagonal (I+) and split (100) forms (I- and probably I0) are favoured among the several forms investigated. Possible extended high-temperature forms are not discussed. The results imply Bourgoin-Corbett (1972) athermal diffusion in p-Si and low-activation energy classical motion in n-Si; local excitation enhanced motion is possible, though not verified, but local heating is unlikely. Results agree well with experiment, both for Si and in understanding the different behaviour of silicon and diamond. The energetic advantage of the split form predicted is also supported by the observed split impurity interstitials and unidentified defects, related to the self-interstitial, observed in structures similar to the split (100) form.

Calculation of the interaction energy between a self-interstitial and a (1/2)⟨111⟩ screw dislocation in b.c.c. transition metals moments approach

Abstract The interaction between a self-interstitial and a (1/2)⟨111⟩ screw dislocation in b.c.c. transition metals (α-Fe, Nb and W) has been investigated in detail using a tight-binding-type electronic theory. The repulsive core–core interaction energies are simulated by a Born–Mayer potential as well as by a simple power law potential. The interstitial-screw dislocation interaction energies are calculated for the ⟨110⟩ and ⟨111⟩ split interstitials as a function of their relative location and orientation with respect to the dislocation. The calculated binding energies for the ⟨110⟩ and ⟨111⟩ type interstitials in α-Fe are of the order of 0·28 and 0·66 eV respectively. In general, it is found that the interstitial-screw dislocation interaction is important for the ⟨111⟩ type interstitials and its magnitude is comparable to the double-kink nucleation energy. Furthermore, it is shown that the present results for the interstitial-screw dislocation interaction can account for the orientation dependence of the irradiation softening observed for the b.c.c. transition metals (α-Fe and Nb).

Elastic after-effect studies of self-interstitials in tungsten after fast neutron irradiation at 5 K

Abstract Elastic after-effects in Wsingle crystals with various orientations were measured below 50 K after fast neutron irradiation at about 5 K. Two prominent relaxation peaks were observed at 5.5 K and 17.6 K (relaxation time of about 2 min). These two peaks correspond, respectively, with the 8 K and 27 K internal friction peaks in previous high frequency measurements (vibrational frequency of about 500 Hz). The 5.5 K peak recovered monotonicly in recovery stage I(∼18 K). On the other hand, the 17.6 K peak showed a transieni growth in stage I and then steadily recovered in stage IIa(∼28 K). From these results, and their dependences on irradiation fluence and orientation, it was concluded that the 5.5 K and 17.6 K peaks are, respectively, associated with a stress-induced rotation (without migration) of free ⟨110⟩ split type interstitials and of di-interstitials with ⟨110⟩-symmetry. Anisotropy ratios and activation parameters of these defects were determined more accurately than in the previous work. Both activation energies for rotation and for migration showed a somewhat broad distribution for the 5.5 K and 17.6 K peaks. Further, it was found that a simple 1/T relation for relative peak heights broken down for the 5.5 K peak. Besides these peaks, many minor peaks were also observed, and their origins were discussed.

Nuclear-magnetic-resonance characterization of the defect migrating during stage III in electron-irradiated copper

Nuclear quadrupolar couplings around monovacancies created by electron irradiation in copper have been measured by the nuclear-magnetic-resonance field-cycling technique. The corresponding quadrupolar transitions disappear completely after the annealing stage III of the residual resistivity, while 17% of the initial resistivity increase remains. Consequently, this experiment shows unambiguously that all the monovacancies are annihilated or agglomerate during stage III and rules out the model in which split interstitials migrate during stage III and monovacancies during stage IV.

Application of TDPAC techniques to diffusion models: diffusion mechanism of Ag in In

The general problem of anomalous diffusion is discussed in connection with the way in which the TDPAC (time differential perturbed angular correlation) technique may help determine the relative fraction of substitutional or interstitial positions of the diffusing atoms. The TDPAC technique referred to the Ag-In system is outlined. The present measurements give a fraction of 0.89+or-0.21 of Ag solutes in In substitutional positions. This suggests a dissociative mechanism for Ag diffusion in In. The value of 0.6+or-0.5 is obtained for the electric field gradient asymmetry parameter eta 2 of the assumed interstitial positions. This value shows a low symmetry for the interstitial sites, indicating that these positions might be split interstitials of Ag solutes in In.

Dynamical theory for electron scattering from crystal defects and disorder

Dynamical diffraction calculations have been made by use of the periodic-continuation assumption for the diffuse scattering in electron diffraction patterns and for electron microscope images of single split interstitials in gold crystals for thicknesses up to 200 Å in order to demonstrate the strong fluctuations of scattering with thickness. The diffuse scattering from distributions of defects in crystals, described in terms of correlation functions, can be written in terms of 'dynamical factors' for each type of individual defect. These dynamical factors multiply the same Fourier transforms of correlation functions as are used in kinematical theory to give the effect of dynamical scattering on the diffraction intensities. Calculations of dynamical factors have been made by multi-slice dynamical diffraction methods for unit changes in atomic scattering factors and for atom displacements in gold and aluminum crystals in [001] orientation for thicknesses up to 100 Å. With increasing thickness the dynamical factors show rapidly reducing fluctuations with crystal thickness and become more nearly isotropic except for the effects of Kikuchi bands which are seen to develop.

The structure and motion of the self-interstitial in diamond

We have made self-consistent semi-empirical molecular orbital calculations for various possible self-interstitial geometries in diamond, both with and without lattice distortion. Total energies are obtained, not merely the sum of one-electron eigenvalues. The results show that the (100) split interstitial has the lowest formation energy, not the cubic, hexagonal or bond-centred forms favour previously.The nature of the interstitial does not support the local heating model of enhanced diffusion in the presence of recombination or ionisation. A Bourgoin-Corbett mechanism involving negative hexagonal and neutral split interstitials is possible, but the apparent stability of the negative hexagonal interstitial may be an artefact of the calculation. We suggest a local excitation model is appropriate in fourfold-coordinated semiconductors.

Imaging and diffraction from localized defects and disorder in crystals

The atomic arrangements in local perturbations of a crystal structure may be investigated by studying the diffuse scattering in diffraction patterns. Alternatively, for isolated perturbations the atom arrangements may well be imaged directly by high resolution electron microscopy in the near future. For either approach, realistic estimates are necessary of the nature and magnitude of dynamical effects in diffuse scattering. For neither case can the commonly used assumption of the column approximation suffice and the kinematical approximation is rarely relevant.Calculations of dynamical scattering amplitudes, for isolated defects can be made by use of an artificial super-lattice with one defect per superlattice unit cell and a multislice calculation with slice content varying in the propagation direction. Calculations of images and diffraction patterns for split interstitials in Au and A1, with and without lattice relaxation have been reported by Fields and Cowley. Figure 1 shows images and diffraction patterns calculated for a single [100] split interstitial in Au with no relaxation followed by various thicknesses of perfect crystals, with 1MeV electrons, Cs = 1.8mm and objective aperture radius uo = 0.45Å-1.

Computed electron microscope images of atomic defects in f.c.c. metals

The bright-field and dark-field electron microscope images expected for [100] split interstitials in thin crystals of gold and aluminum without and with lattice relaxation have been calculated by the method of periodic continuation including full n-beam dynamical interactions of both the Bragg reflections and the diffuse scattering. The advantage of using 1 MeV rather than 100 keV electrons is demonstrated in that, even with the same nominal resolution, the 1 MeV electrons give images in which the defect structure is more readily recognized. The conditions have been determined for which the defect images have high contrast and provide clear representations of the atom configurations.

Computer Simulation of the Imaging of Atomic Defects in Metals

Localized defects in metals, such as vacancies and interstitials, should have scattering powers for electrons comparable with those of the single heavy atoms which have been imaged in recent years by use of high resolution electron microscopes. It should therefore be possible to obtain appreciable contrast from such defects with current lOOkV electron microscopes. However in order to distinguish the intensity variations due to these defects from those due to specimen surface structure, contamination or other causes, it may be necessary to use the improved resolution of high voltage microscopes so that the characteristic shapes of the defects and their local strain fields can be recognized.In order to test these speculations, we have made computer calculations of the images and diffraction patterns to be expected from split interstitials in thin crystals of gold and aluminum for bright-field and dark-field imaging with a lOOkV microscope with an objective lens having Cs = 1.8mm and for a l000kV microscope, Cs = 1.8mm.

Free Migration of Interstitials in Tungsten

The internal friction and dynamic modulus of W single crystals were measured after neutron irradiation near liquid-helium temperature. The results on dislocation pinning and the associated relaxation peaks suggest that in W the (110) split interstitials perform a free migration at 15 K (substage I&) and the -30-K stage (substage I&) is associated with detrapping of the (110) split interstitials from impurity atoms.

Effects of self-interstitials and close pairs on the elastic constants of copper

Measurements of changes in the elastic constants of copper and their temperature dependences resulting from stage-${I}_{C}$ close pairs and stage-${I}_{D}$ isolated interstitials are used to investigate defect configurations. The relative elastic-constant changes below 4 K per unit concentration $\ensuremath{\gamma}$ of isolated interstitials, $\frac{d\mathrm{ln}C}{d\ensuremath{\gamma}}$, are found to be 0\ifmmode\pm\else\textpm\fi{}1, -30, and -15 for the bulk modulus, ${C}_{44}$, and ${C}^{\ensuremath{'}}=\frac{({C}_{11}\ensuremath{-}{C}_{12})}{2}$, respectively. These results show that the bulk effect arising from the change in number and strength of interatomic bonds is small, but that there exist polarization effects expected from 100 g split interstitials. The temperature dependence of the elastic constants provides evidence of thermally excited resonance modes of frequency $\ensuremath{\omega}=5\ifmmode\times\else\texttimes\fi{}{10}^{12}$ Hz, which are also evidence for 100 g split interstitials. An elastic relaxation due to thermally activated stress-induced ordering of ${I}_{C}$ defects is observed at 18 K in ${C}_{44}$, but not in ${C}^{\ensuremath{'}}$, providing symmetry information which leads to a model for the ${I}_{C}$ close-pair configuration.

Experimental Evidence for Split Interstitials in Copper

Experimental Evidence for Split Interstitials in Copper

Concentrated di-substitutional metallic solid solutions

Metastable solid solutions of Cu and Fe in Gd with up to ∼ 15 at. % solute were prepared by ultrarapid quenching from the liquid (splat cooling). These solid solutions are of a new type: a ratio of two solute atoms for one replaced solvent atom was found. This suggests that the solute forms di-substitutionals, S 2 (split interstitials). Conditions for simple interstitial and di-substitutional solid solution formation are discussed.

Interstitials and Vacancies inαIron

Tile migration energies and atomic configurations for mono- and di-interstitials and mono- and di-vacancies in α-iron have been calculated using a classical model. About 530 atoms surrounding the defect were treated as individual particles, each with three degrees of freedom, while the remainder of the crystal was treated as an elastic continuum with atoms imbedded in it. A two-body central force was devised which matched the elastic moduli, was sharply repulsive at close separation, and which went to zero midway between the second and third neighboring atoms. Configurations were found by choosing a starting configuration roughly approximating the situation under consideration and successively adjusting the value of each variable occurring in the energy equation so that the magnitude of the generalized force associated with it was zero until equilibrium was reached. Tile energy calculations include changes in bond energy in the discrete region, energy in the elastic field, and work done against cohesive forces, but neglect changes due to the redistribution of electrons. Calculated activation energies for motion of mono- and di-interstitials and mono- and di-vacancies were 0.33 eV, 0.18 eV, 0.68 eV and 0.66 eV respectively, and binding energies of di-interstitials and di-vacancies were 1.08 eV and 0.20 eVmore » respectively. The stable interstitial was a split configuration in which two atoms were symmetrically split in a (110) direction about a vacant normal lattice site, and the stable di-interstitial consisted of two parallel split interstitials at nearest neighbor lattice sites.with their axes perpendicular to the line joining their centers. In the vacancy configuration an atom was missing from a normal lattice site, and the di-vacancy consisted of two vacancies at second nearest neighbor lattice sites. (auth)« less

Review of internal friction due to point defects

Simple considerations lead to the expectation that point defects will cause internal friction (by a stress-induced ordering mechanism) in all cases where the introduction of the defects sets up local asymmetric distortions of the surrounding lattice. Three categories of specific examples are considered, in which the relaxation centers are believed to contain 1. (a) a single isolated elementary point defect, 2. (b) two interacting elementary point defects, 3. (c) several interacting elementary point defects. The elementary point defects considered are 1. (1) an interstitial solute atom, 2. (2) a substitutional solute atom, 3. (3) a vacancy, 4. (4) a split self-interstitial. The material for this review is taken from the existing literature with the exception of a brief account of some recent experiments by the author on cold-worked nickel, which relate to the report of a peak due to split interstitials in this metal by Seeger et et al. (17). Due to a background recovery phenomenon, it was not found possible to obtain support for the existence of the peak.