Impurity Clusters Research Articles

Extended x-ray-absorption fine-structure and perturbed-angular-correlation study of impurity clustering in dilute nickel alloys.

We report on an experimental study of indium and niobium impurity distributions in NiNbIn dilute alloys by combining the perturbed-angular-correlation (PAC) technique with extended x-ray-absorption fine-structure (EXAFS) measurements on both the indium and niobium K edges at room temperature. Our EXAFS results show that around the indium or niobium central atom, the first-shell coordination number is strongly reduced with respect to a pure nickel environment. Whereas niobium is found in the first shell around niobium in small cluster configurations, indium is found at larger distances from indium indicating a repulsive In-In interaction. No close mixing between these two impurities was detected, confirming the strong In-Nb repulsion. These findings are fully consistent with the conclusions drawn from the data obtained in an earlier as well as the present PAC study.

Thermomechanical detwinning of YBa 2Cu 3O 7− x single crystals under reduced oxygen partial pressure

The kinetics of the thermomechanical detwinning of YBa 2Cu 3O 7− x crystals is studied as the influence of the starting domain structure, the oxygen content and the temperature on the detwinning process. We observed that after the release of uniaxial pressure at the detwinning temperatures or when detwinned crystals are heated again up to 120–150°C, nearly the same twin patterns as before the detwinning can reappear spontaneously (memory effect). If appropriate times and temperatures for the detwinning process are used the memory can be cleared. This memory effect is attributed to the presence of impurity and atomic defect clusters near former twin boundaries or to remaining minute twin domains which cannot be detected by optical methods. The time during which the uniaxial pressure has to be applied for clearing the memory follows an Arrhenius relation with an activation energy of 1.09 ± 0.10 eV. This value is close to the activation energy diffusion in YBa 2Cu 3O 7− x . The detwinning was found to be easy and complete when the crystal initially was reduced into the tetragonal phase at 560–600°C followed by the application of a uniaxial pressure along 〉100〈. After changing the atmosphere to pure oxygen the crystal transformed again into the orthorhombic phase without dividing into domains.

Effect of previous heat treatment on ionic conductivity of yttrium-doped KBr crystals

Ionic conductivity studies have been carried out on KBr:Y crystals at different temperatures. The conductivity temperature plot of KBr:Y exhibits a well-known three-stage conductivity in the temperature range 100–560 °C. From the analysis of these plots activation energies for the migration of cation vacancies, the formation of Schottky pairs, the association of yttrium ion with a cation vacancy etc. are calculated. The conductivity of KBr:Y after quenching from elevated temperature is found to decrease. This result in comparison with optical absorption results is explained on the basis of formation of impurity vacancy dipoles, precipitates and clusters.

Some Observations of the Effect of Porous Silicon on Oxidation‐Induced Stacking Faults

Experiments have been carried out to determine the influence of a porous silicon patch (located on the back surface of a silicon wafer) on the formation of stacking faults during oxidation typically encountered in the manufacture of integrated circuits. The porous silicon was found to reduce the incidence of stacking faults. A possible explanation is that the porous silicon serves as a gettering center which reduces the number of impurity clusters that would otherwise nucleate stacking faults.

Development of etch pit size distributions on dissolving minerals

We have applied the theory of crystal size distributions to the evolution of etch pit size distributions (PSD's) on dissolving minerals. Population-balance equations are derived based on nucleation, growth and annihilation of etch pits. PSD plots of log n (number of pits per size per area) vs. W (etch pit width) are used to compare etch pit populations. We have used PSD analysis to study the development of etch pits on calcite dissolved in a rotating disk experiment (far from equilibrium, 25°C, initial pH = 8.6, 0.7 M KCl). A maximum is present on the PSD plot in the early stages of dissolution and appears to result from nucleation of pits at all available sites on the initial cleaved surface over a finite time interval. As pits grow larger, become flat-bottomed and annihilate, the peak moves to larger sizes and decreases in magnitude to become insignificant after 17.5 hr. After 0.5 hr, the PSD plots become linear at small pit widths marking a population balance as new pits nucleate within flat pits, grow larger, become flat-bottomed and finally annihilate. This population of short-lived, small (< 100 μm) etch pits possibly results from nucleation at point-defect or impurity clusters. A linear PSD for long-lived, larger pits appears at 17.5 hr, possibly reflecting etch pits at dislocations. The overall PSD plot at 17.5 hr is kinked due to these two populations. Calcite dissolution rates calculated from the coefficients of the PSD are within a factor of two of the dissolution rate measured from solution chemistry. Such estimates will be more accurate if the duration of dissolution does not greatly exceed the mean lifetime of etch pits. PSD plots for hornblende and microcline grains from a loess soil that has weathered for 12,500 yr show similarities to the PSD's from our calcite experiments. The hornblende PSD shows a peak and the microcline PSD is linear or possibly kinked. Bulk dissolution rates for the grains calculated from the PSD's are slower than rates measured for these minerals in the laboratory. Dissolution rates estimated from the PSD coefficients for the hornblende and microcline soil grains are 3–4 and 1–2 orders of magnitude slower, respectively, than the corresponding laboratory rates.

Effect of impurities on the processes of crystal growth

The influence of impurities inherently present in growth media and deliberately added to them on crystal growth is manifested during the process of crystallization in a number of ways. Impurities change growth rates, shape and thickness of growth layers and growth habit, and are trapped as impurity striations and large clusters of impurities and inhomogeneities. Some of these effects of impurities are reviewed for growth of bulk single crystals.

Phonons in a medium with correlated substitutional disorder: a one-dimensional study

1D lattice dynamics are considered for a pseudo-binary atomic chain in order to investigate the effects of thermodynamical clustering due to non-ideality of the solid solution AxB1-xC on the phonon density of states (DOS). Using an exact dimensional distribution function for impurity clusters, phonon spectra are calculated numerically for 1D models of (Cd,Hg)Te and (Al,Ga)As of different compositions and temperatures of alloy preparation. The phonon DOS is also obtained analytically near the limits of the frequency range, and in the vicinity of the local mode. It is shown that clustering strongly suppresses the local mode. Moreover, for the decaying alloy where impurity clusters can be quite long, the DOS looks like a superposition of the phonon DOSs of pure materials, and positions of the maxima of the alloy DOS with respect to those in pure materials are sensitive to the degree of clustering.

A unified mobility model for device simulation—I. Model equations and concentration dependence

The first physics-based analytical model is presented that unifies the descriptions of majority and minority carrier mobility and that includes screening of the impurities by charge carriers, electron-hole scattering, clustering of impurities and the full temperature dependence of both majority and minority carrier mobility. Using this model, excellent agreement is obtained with published experimental data on Si. The model is especially suited for device simulation purposes, because the carrier mobility is given as an analytical function of the donor, acceptor, electron and hole concentrations and of the temperature.

A unified mobility model for device simulation—II. Temperature dependence of carrier mobility and lifetime

In Part I we presented the first physics-based analytical model that unifies the descriptions of majority and minority carrier mobility and that includes screening of the impurities by charge carriers, electron-hole scattering and clustering of impurities. Here the model is extended to include the full temperature dependence of both majority and minority carrier mobility. Based on our model and experimental data on the minority carrier diffusion length as a function of temperature, the temperature dependence of the carrier lifetime is determined. The model is especially suited for device simulation purposes, because the carrier mobility is given as an analytical function of the donor, acceptor, electron and hole concentrations and of the temperature.

Inter-Impurity Interaction in Doped Conjugated Polymers: Two Impurity Problem and Dependence on Impurity-Potential Forms

Abstract Effects of inter-impurity interaction in conjugated polymers are numerically investigated. The Su-Schrieffer-Heeger (SSH) hamiltonian is used for the polymer chain. There are two acceptor-type long-ranged impurities, with anisotropic dielectric constants and a screening factor. Direct inter-impurity repulsion is taken into account. Impurity arrangements as well as lattice and electron configurations are determined so as to minimize the total energy. Impurity clustering occurs when the range of the impurity potential is long enough. Impurities are isolated each other when the range becomes shorter. In order to look at how the clustering would be observed, optical absorption is calculated. There exists only one mid-gap absorption peak. This is the consequence of the strong impurity potential.

Formation of impurity clusters in CdS:Ag:Cl

The Kröger-Brouwer-type analysis of integral intensities of R- and O-luminescence emission bands as a function of the reciprocal temperature of the previous thermal treatment of powder samples under well-defined component vapour conditions has been used for the determination of the enthalpies of impurity cluster formation reactions in CdS:Ag:Cl. The following enthalpies were found 2 Ag Cd'Cl S . = (Ag Cd'Cl S .) 2 − (0.10 ± 0.02) eV , 2 Ag Cd'Ag i . = (Ag Cd'Ag i .) 2 − (0.22 ± 0.06) eV.

The role of dislocations and surface morphology in calcite dissolution

We have measured the dissolution rate for undeformed (ρ ~ 10 3 dislocations · cm −2 ) calcite to be 3.1 × 10 −10 mol · cm −2 · s −1 in free-drift rotating disk experiments at 1160 rpm, 25°C and pH 8.6 in 0.7 M KCl solution far from equilibrium. The rate increased by a factor of ~2.3 for a strained sample (ρ = 6 × 10 8 · cm −2) . Dissolution rates of calcite far from equilibrium were observed to depend on surface preparation and surface morphology resulting from defects outcropping at the crystal surface, but large rate increases due to surface roughness were not observed. The high dissolution rate for mechanically polished surfaces is attributed to enhanced dissolution at cracks and dislocation loops produced in the grinding process. The initial dissolution rate for cleaved surfaces depends on the surface morphology, but reaches a reproducible steady state value when a constant bimodal size distribution of intersecting pits with time-independent wall slope (θ ~ 3°) is achieved (t > 3 h). Steady state is also characterized by a constant ratio of sloped to relatively flat surface. The two populations of etch pits consist of abundant, short-lived, small etch pits (attributed to nucleation at impurity or point defect clusters) and long-lived, larger point-bottomed pits (attributed to dislocations). Consistent with this interpretation, significant dissolution at an abundance of nondislocation nucleation sites in undeformed calcite explains the relatively small increase in dissolution rate for strained samples. Simulation of bulk crystal dissolution based on etch pit growth rates is in reasonable agreement with observed dissolution rates and surface morphology and indicates that discontinuous dissolution at dislocations is necessary to explain the observed steady state surface morphology. Activation energies for pit deepening and widening were measured between 5 and 50°C as 27 ± 5 and 37 ± 3 kJ · mol −1 , respectively. These values are lower than the measured activation energy for bulk dissolution (59 ± 12 kJ · mol −1) .

Trapped bipolaron due to interimpurity interactions in doped conjugated polymers: Two-impurity problem and dependence on impurity-potential forms.

Effects of interimpurity interaction in conjugated polymers are numerically investigated. The Su-Schrieffer-Heeger Hamiltonian is studied with two acceptor-type long-ranged impurities that have anisotropic dielectric constants and a screening factor. Direct interimpurity repulsion is taken into account. Impurity clustering occurs and a trapped bipolaron is formed when the range of the impurity potential is long enough. Optical absorption has only one midgap absorption peak due to the strong impurity potential. Impurities are isolated from one another when the range becomes shorter.

Hot Spot Heating from Impurities and Vacancies in a Crystalline Solid Under Rapid Compression

AbstractThe role of impurity atoms and vacancy defects in the heating of hot spots in a 2D, fcc, monatomic lattice, subjected to rapid, 1D compression, has been studied by means of molecular dynamics. The interaction potential of the impurity atoms, their mass, and size were allowed to differ from those of the atoms in the host lattice. Several configurations of impurity and vacancy clusters were examined. The mechanisms of heating observed here were similar to those found earlier in a bcc lattice with vacancy defects but without impurities.

Amorphous clusters. II. Electronic structure of Ge clusters with N, P, and As impurities

The electronic structure of random clusters has been used in the literature to qualitatively understand the properties of amorphous solids. Here impurity clusters of the type XGe20H28 with X = N, P, and As are studied using the pseudopotential SCF Hartree-Fock Method and the HONDO Program. The charge distribution and local density of states are calculated both for pure germanium and for clusters with each of the three impurities mentioned above. It is found that even though the covalent nature of the bonding of pure germanium is still present, its relevance is greatly diminished due to the presence of ionic components and shielding effects caused by the impurities. The charge distribution of the half-filled 57th orbitals clearly shows these effects. The LDOS exhibits the s- and p-components expected for the molecular orbitals of the clusters as well as two types of localized states; one is due to states localized at the bottom of the conduction band whose energies decrease as the mass of the dopants increases, and the other is due to deep states whose energies increase as the mass of the dopants increases. The top of the valence band is practically unaltered by the introduction of the impurities. A comparison is made of these results with experiment, and with those previously reported for amorphous Si clusters.

Amorphous clusters I. Electronic structure of Si clusters with N, P and As dopants

Amorphous impurity clusters of the type XSi 20 H 28 with X = N, P and As have been studied using the well-known pseudopotential SCF Hartree-Fock method (and the HONDO Program). The local electronic density of states and charge density contours have been obtained. It is found that the covalent nature of the bonding in undoped silicon is altered by the presence of the dopants and both an ionic component and a shielding effect appear when N, P and As are substituted in the center of the amorphous cluster. Also, the local density of states in the neighborhood of a Si atom, nearest neighbor to the center of the cluster, indicates the presence of a new p-state in the band gap. There are quantitative differences in the electronic structure of the clusters as a function of the dopants. These results are analyzed in the light of the local changes and their relevance to the amorphous solid state properties.

Inter-impurity interaction and structure of a trapped bipolaron in doped conjugated polymers

The effects of an inter-impurity interaction are studied by the extended Peierls-Hubbard model. The Coulomb interactions in the chain are treated by the Hartree-Fock approximation. There are two acceptor-type impurities expressed by long-ranged Coulomb potentials with anisotropic dielectric constants. Stationary positions of the impurities as well as stationary lattice configurations and electronic wave functions are numerically determined self-consistently. Trapping of a bipolaron around impurities is found. The distance between impurities is of the order of the coherence length. Two mid-gap levels, which would exist for a free bipolaron, move to higher energies due to the strong dopant potential. The Coulomb interactions in the chain effectively weaken the strength of the dopant potential. The energy levels shift to lower energies with increasing interaction strengths. Dynamical conductivity (optical absorption) is calculated. The isolated peak in the lower frequencies is associated with the position of the localized level in the energy gap. The consequences for experimental observation of the impurity clustering are discussed.

Electromigration in transition metals. III. Substitutional impurities in Cu, Ag, Al and Nb

For pt.II see ibid., vol.3, p.7331 (1991). Using the KKR Green function method, the electromigration wind valences of several substitutional impurities in Al and in the transition metals Cu, Ag and Nb have been calculated. In a complete migration jump the migrating ion exchanges position with a neighbouring vacancy. The present study is limited to the initial position in such a migration and to points along the migration path near to it. The complete band structure as well as all multiple scattering effects for the impurity cluster embedded in a crystal have been accounted for. For self-electromigration in Cu, Ag and Nb a positive wind valence is calculated while in Al the wind valence is negative. Sb in Ag has a large negative wind valence at the initial position. The constructed potentials for Cr and Fe in Nb yield negative wind valences for the impurities. It is concluded that the saddle-point configuration, where the impurity is midway along the path, generally will provide a large contribution to the average wind valence along the path.

Electromigration in transition metals. II. Light interstitials in Cu, Ag, Ni, Pd, Al, V, Nb and Ta

For pt.I see ibid., vol.3, p.7307 (1991). The electromigration wind valence of interstitial hydrogen in a series of transition metals is calculated using a state-of-the-art computational scheme accounting for the real band structure and local lattice deformation plus charge transfer in the impurity cluster. A microscopic picture of the oscillatory motion and the mobility of the proton explains the remarkable difference between the wind valence of hydrogen in Nb and Ta. A zero-point motion model explains the H/D isotope effect in the effective valence as observed in many systems. From a comparison of experimental effective valences with calculated wind valences, it is concluded that the direct valence, in systems where the wind valence is not dominant, has a value close to unity. Thermal effects are investigated and shown to be unimportant at moderate temperatures. In addition wind valences of interstitial boron in Pd, carbon in Pd and Nb and oxygen in Nb are presented.

Residual resistivity of interstitial and substitutional impurities in transition metals

Residual resistivities for interstitial H in the face-centred cubic metals Cu, Ag, Ni, Pd and Al as well as in the body-centred cubic metals V, Nb and Ta are calculated using the Korringa-Kohn-Rostoker Green function description of Bloch electron scattering by impurity clusters. Heavier interstitials like B and C in Pd and C and O in Nb are also investigated. Inclusion of environmental effects, especially local lattice deformation of the first shell of surrounding atoms, turned out to be of crucial importance in order to obtain agreement with experimental residual resistivities. The firmly established absence of a H/D isotope effect in Pd, V. Nb and Ta can be explained. Measured residual resistivities due to substitutional impurities in Cu, Ag, Pd. Al and Nb are reproduced with varying success, depending on the complexity of the electronic structure of the defect potential. A first shell of surrounding metal atoms improves the calculated results, while lattice distortion is not as important as it is for the interstitial alloys.