Long-range Displacement Field Research Articles

X-ray and neutron scattering by different dislocation ensembles

Dislocations cause long-range displacement fields in the crystals. In bulk crystals they belong to so-called 2nd kind defects. The results of simulations of scattering intensity on several types of dislocation distributions in bulk crystals and in thin films are presented in the paper. The presence of the surface changes both the distortions and the regularities of scattering phenomena in thin films when compared to the bulk. Diffraction phenomena on misfit dislocations have some additional peculiarities compared with the bulk crystals. The input of each system of misfit dislocations into the broadening of the rocking curve depends on the angle between the diffraction vector and the direction of dislocation lines in the system.

Investigation of β-SiC precipitation in Si1−yCy epilayers by x-ray scattering at grazing incidence

We have investigated molecular-beam-epitaxy-grown, pseudomorphic Si1−yCy epilayers (y⩽0.015) on Si(001) after ex situ annealing by x-ray scattering at grazing incidence. The diffuse intensity around the Si (220) surface reflection consists of Huang scattering due to the long-range displacement field of substitutional carbon atoms and of the form-factor-induced small angle scattering of holes created by β-SiC precipitates in the Si matrix. Even in the as-grown samples, where other methods gave no indication of β-SiC precipitates, grazing incidence diffraction clearly showed their presence. The precipitates with a mean size of 5 Å are stable against annealing up to at least 600 °C; at 800 °C carbon leaves substitutional sites and the number of precipitates increases, whereas at 1000 °C a significant increase of the precipitate size (up to ≈15 Å) is detected as well.

X-ray diffuse scattering from extended microdefects of orthorhombic symmetry for Si single crystals

The displacement field of a crystal lattice, in the continuous media approximation, caused by extended microdefects of rectangular parallelepiped shape, is considered. X-ray diffuse scattering from the defect core as well as the long-range displacement field is analyzed. A theoretical expression for the intensity of X-ray diffuse scattering resulting from randomly distributed microdefects of orthorhombic symmetry is presented using the kinematical approximation of X-ray statistical diffraction theory. The computer simulations of the isointensity contours for two sets of defect parameters are performed. A way of obtaining the defect parameters by fitting the computer simulations to the experimental data is proposed.

Vacancies and Interstitial Atoms in Irradiated Silicon

ABSTRACTDifferently doped Si-wafers were irradiated with 2.5MeV electrons and subsequently investigated by X-ray diffraction methods. We show that a high concentration of defects (>1016 cm−3) can be frozen in at 4K and that a large fraction of the defects is stabilized in the form of close Frenkel pairs. These Frenkel pairs are characterized by the nearly perfect cancellation of the long-range displacement fields of the interstitial atom and the vacancy. We discuss the absolute size of these displacements as well as the introduction rate of the defects, which is of the order of Σ = 1cm−1. Similar results are obtained for weakly doped Cz-Si or FZ-Si and for degenerate p-type Si(B) and n-type Si(As), i.e., the results are independent of the oxygen content of the samples and of the position of the Fermi level. The high defect introduction rates are at variance with the results of electrical and EPR investigations and indicate that these methods detect only a few percent of the total defect concentration which is produced and frozen in at 4K. The consequences for the understanding of the defect production in Si and for the assumption of an athermal migration of interstitial atoms are discussed. In addition we compare the defect patterns observed after 4K irradiation to those observed after room-temperature irradiations and discuss the thermally activated defect reactions up to the final annealing at 1000K.

Defect structure of ferrous oxide Fe1-xO.

We have investigated the defect structure of nonstoichiometric w\ustite ${\mathrm{Fe}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$O as a function of temperature and oxygen partial pressure by means of diffuse elastic neutron scattering of a single crystal at thermal equilibrium. Particularly for T=1423 K and x=0.08, a Fourier analysis yielded short-range order and lattice displacement parameters as well as the ratio of the numbers of vacancies to interstitials, \ensuremath{\rho}=4.0\ifmmode\pm\else\textpm\fi{}0.5. The measured short-range order showing a strong correlation between nearest interstitials and vacancies was simulated in a computer model. A further analysis yielded the size distribution of the vacancy-interstitial defect clusters exhibiting a large fraction of 30% of free vacancies, while a further 15% of the defects are bound in isolated so-called 4:1 defect clusters. The entire long-range displacement fields were modeled in a Kanzaki force approach using independent phonon data. Within the usual approach of a single-defect approximation the observed asymmetries of the diffuse scattering around the Bragg peaks were described by using Coulomb-like forces around the cation vacancies of random 4:1 defect clusters. The measured decrease of Huang scattering and the development of diffuse peaks with increasing nonstoichiometry was reproduced by a more general type of Kanzaki model for concentrated solid solutions. Therefore, we used the same defect model of the 4:1 cluster, although surrounded with two occupied cation shells to screen the long-range displacement fields.

Anomalous defect behaviour resulting from the hydriding of nanocrystalline palladium

Abstract X-ray diffraction measurements on a nanocrystalline Pd sample transformed in situ to PdH0·56 are described. Debye-Waller parameter measurements at several temperatures showed unexpected increases in both thermal and static atomic displacements caused by the hydriding. These increased displacements are associated either with the creation of new point defects on the Pd sublattice or with an increase in the magnitude of the strain fields of previously existing point defects. Substantial X-ray peak broadening due to the production of large numbers of dislocations is seen when coarse-grained Pd is hydrided. In contrast, measurable changes in the peak breadths were not observed for the nanocrystalline sample as a result of hydriding, indicating that dislocations with long-range displacement fields are not created when nanocrystalline Pd is hydrided. A preference to produce or modify short-range defects instead of dislocations during hydriding may occur as a result of the larger stresses required to gen...

Diffuse X-ray scattering from interstitial nitrogen in niobium. I. Huang diffuse scattering

The symmetry and strength of the displacement field around N atoms interstitially dissolved in Nb single crystals is determined from Huang diffuse scattering of X-rays. The measurements were performed at various temperatures from -180 to 150 degrees C. The force dipole tensor describing the long-range displacement field has tetragonal symmetry. It shows no temperature dependence within the present accuracy.

Anelastic relaxation due to single self-interstitial atoms in electron-irradiated Al

Application of a highly sensitive elastic-aftereffect technique, capable of resolving changes in strain as small as \ifmmode\pm\else\textpm\fi{} 5 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}9}$, has revealed the existence of an anelastic relaxation process due to the simultaneous migration and reorientation of single interstitials in recovery stage I of low-temperature electron-irradiated Al. Only the $〈100〉$-split interstitial configuration is consistent with the measured orientational dependence of the relaxation strength in single-crystal samples. The observed anisotropy of the interstitial dipole tensor is small, $|{P}_{11}\ensuremath{-}{P}_{22}|=1.1\ifmmode\pm\else\textpm\fi{}0.3$ eV, showing that the long-range displacement field of this defect has nearly cubic symmetry. A comparison of the annealing of the relaxation strength with that of the resistivity shows a transition from correlated to uncorrelated recovery in stage ${\mathrm{I}}_{D+E}$. The thermodynamic properties characterizing the single-interstitial relaxation process explain why it has not been observed in previous internal-friction studies.

The displacements and polarization caused by point defects in ionic crystals

Abstract The lattice statics method for the calculation of point defect properties, first proposed by Kanzaki, is here extended to discuss the polarization and displacements caused by charged point defects in ionic crystals. The method allows the determination of the exact displacement and polarization fields for a defect in a given crystal model. Detailed discussion is given for the NaCl structure using the deformation dipole model. It is shown that the long-range displacement field can be rigorously separated into pure strain and pure polarization components, the last being strictly isotropic. For a model without deformation dipoles (Szigeti effective charge e∗=e) the polarization components are exactly as assumed in the method of Mott and Littleton. Different expressions however apply when e∗≠e, as is generally the case. The elastic strengths of the cation vacancies are calculated to be much larger than those of the anion vacancies; this is also an effect of the deformation dipoles, especially of their...