Theory of impurity scattering: Interstitial impurities

A framework for studying impurity scattering in dilute, non-magnetic, metal alloys can be developed from a knowledge of the exact electronic eigenstates of a single impurity in an otherwise perfect lattice of muffin tin potentials. Such an approach has been developed for systems in which the impurity occupies a substitutional site of the lattice, as will be discussed by Coleridge, Lee, Harris, and other speakers of this conference. In this paper, motivated by recent experimental studies of Dingle temperature anisotropies induced by hydrogen impurities in copper, we will discuss the analogous treatment of scattering by interstitial impurities. In contrast to a substitutional impurity, an interstitial impurity introduces an additional scattering site into the lattice. Whereas the substitutional impurity wavefunctions can be described in terms of the same structure factors as can the Bloch wavefunctions for the pure host lattice, the interstitial impurity wavefunctions depend upon additional structure factors appropriate to the new scattering geometry. These additional structure factors appear in the transition matrix for impurity-induced scattering between Bloch states of the host lattice, and consequently in the weight factors involved in a partial wave analysis of the Dingle temperature anisotropies.     

Theory of impurity scattering: Interstitial impurities

A framework for studying impurity scattering in dilute, non-magnetic, metal alloys can be developed from a knowledge of the exact electronic eigenstates of a single impurity in an otherwise perfect lattice of muffin tin potentials. Such an approach has been developed for systems in which the impurity occupies a substitutional site of the lattice, as will be discussed by Coleridge, Lee, Harris, and other speakers of this conference. In this paper, motivated by recent experimental studies of Dingle temperature anisotropies induced by hydrogen impurities in copper, we will discuss the analogous treatment of scattering by interstitial impurities. In contrast to a substitutional impurity, an interstitial impurity introduces an additional scattering site into the lattice. Whereas the substitutional impurity wavefunctions can be described in terms of the same structure factors as can the Bloch wavefunctions for the pure host lattice, the interstitial impurity wavefunctions depend upon additional structure factors appropriate to the new scattering geometry. These additional structure factors appear in the transition matrix for impurity-induced scattering between Bloch states of the host lattice, and consequently in the weight factors involved in a partial wave analysis of the Dingle temperature anisotropies.This work was supported by the National Science Foundation through the Materials Research Laboratory at the University of Chicago.     

Sites and diffusion for muons and hydrogen in titanium hydrides

Low temperature sites for muons implanted in TiHx have been found to be a mixture of interstitial and substitutional sites, with substitutional occupancy determined by the probability that a muon in an interstitial site will have a vacant nearest neighbor substitutional site. As with ZrHx, activation from the interstitial site is observed below 300 K. From the depolarization rate in the substitutional site, the muon likely displaces the neighboring H atoms by about 0.1 A. Diffusion for the substitutional muons occurs above room temperature with an activation of about 0.38 eV, which is less than the 0.505 eV for hydrogen vacancy motion observed by NMR. To explain this the muon transition rate to a vacancy must be less than that of hydrogen.     

P掺杂锐钛矿相TiO2的第一性原理计算

利用基于密度泛函理论的第一性原理对不同P掺杂形式(P替位Ti, P替位O, 间隙P)的锐钛矿相TiO₂的晶格常数、电荷布居、能带结构、分态密度和吸收光谱进行了计算. 结果表明, P替位Ti时, TiO₂体积减小, P替位O和间隙P的存在使TiO₂的体积膨胀; 替位Ti的P和间隙P均有不同程度的氧化, 而替位O的P带有负电荷. 三种P掺杂形式均导致锐钛矿相TiO₂禁带宽度的增大, 并在TiO₂禁带之内引入了掺杂局域能级. P掺杂导致TiO₂禁带宽度增大的程度依次为: 间隙P>P替位Ti>P替位O. 吸收光谱的计算结果表明, P替位Ti并不能增强TiO₂的可见光吸收能力, 但间隙P的存在大幅提高了TiO₂的可见光光吸收能力, 间隙P有可能是造成实验上P掺杂增强锐钛矿相TiO₂光催化活性的重要原因. 关键词： P掺杂 2')" href="#">锐钛矿相TiO₂ 第一性原理     

Anionic and hidden hydrogen in ZnO

First-principles calculations are performed to study energetics and kinetics of hydrogen in ZnO, in particular, the H(-) anion and the H(2) molecule on the interstitial site and in the oxygen vacancy. We show that the H(2) molecule kinetically trapped in the oxygen vacancy, rather than interstitial H(2), can explain a variety of experimental observations on "hidden" hydrogen in ZnO. The accumulation of shallow donors, especially the substitutional H, near the ZnO surface is important to the formation of hidden hydrogen in the ZnO bulk and can also lead to persistent photoconductivity.     

Orientational (EPR) study of vanadyl ion in potassium hydrogen oxalate lattice

The EPR spectra of VO²⁺ doped KHC₂O₄ crystals revealed two sites with intensity ratio 2:1 and indicated two nearly parallel orientations of the ion in the lattice. On the basis of comparison of the experimentally determined and the calculated direction cosines, only one of the sites could be identified as the substitutional. The other site is suggested to be due to the interstitial occupation of VO²⁺ in the lattice. While the g? tensor is axially symmetric, the à tensor does not show such perfect axial character. The features are explained in terms of the covalency effects arising from hydrogen bonding in the lattice.     

The thermodynamics of palladium-based solid solutions containing a noble-metal substitutional solute and hydrogen

A cell model for tenary solid solutions containing a substitutional and an interstitial solute species is considered. The interstitial solute is restricted to cells (interstitial sites) in the f.c.c. solvent lattice in which it has either zero or one nearest neighbor substitutional solute atom. The effects of the dilation of the solvent lattice by the substitutional solute are taken into account in an appropriate manner using the currently limited elastic data available.It is shown that the model is in good accord with the measured partial enthalpies and excess entropies in the Pd-Ag-H system, in which the Ag atoms cause a positive lattice dilation, but not for the case of Pd-Cu-H, where there is a contraction.     

Quadrupole interaction at181Ta in tellurium

The quandrupole interaction at¹⁸¹Ta in tellurium measured at various temperatures revealed two unique sites with an axially symmetric electric field gradient. These are interpreted as a near substitutional site with almost octahedral symmetry and a pure interstitial site in the tellurium lattice. The temperature dependence observed for QI frequencies corresponding to these sites supports this conclusion.     

Diffusion and lattice location of lithium in zinc telluride

The diffusion of Li in ZnTe has been investigated in the temperature range 400–700°C by use of nuclear analysis and chemical or ion beam etching techniques. The penetration profiles are complex and most of them were found to show three regions. The experimental results are interpreted as a superposition of different diffusion mechanisms: one where the impurity diffuses simultaneously in substitutional and interstitial forms, the interstitial form being trapped at defects, and the other which involves short-circuit paths. Activation energies and diffusion constants D_o were measured. Furthermore the channeling technique was used for lattice location. This revealed that (60–80)% of the lithium atoms occupy the zinc substitutional site following annealing at 500°C.     

Dopant-assisted concentration enhancement of substitutional Mn in Si and Ge

The influence of p- and n-type electronic dopants on Mn incorporation in bulk Si and Ge is studied using first-principles calculations within density functional theory. In Si, it is found that the site preference of a single Mn atom is reversed from interstitial to substitutional in the presence of a neighboring n-type dopant. In Ge, a Mn atom is more readily incorporated into the lattice when an n-type dopant is present in its immediate neighborhood, forming a stable Mn-dopant pair with both impurities at substitutional sites. A detailed analysis of the magnetic exchange interactions between such pairs reveals a new type of magnetic anisotropy in both systems.     

The effect of substitutional impurity atoms on the diffusivity of an interstitial species

A model has been developed to treat the problem of the effect of substitutional solute elements on the diffusion of an interstitial species. The calculation applies only to cases where the substitutional solute creates “antitrapping” sites, whose energies are higher than the “normal” interstitial sites in the defect-free solvent lattice.The model predicts that, for sufficiently “high” antitrapping sites, there will be substantially no effect of composition or even solute atom type on the mobility of the interstitial species even up to about 20 atm% of substitutional solute.It is also possible for a given substitutional solute to act both as an accelerator or retarder with respect to the diffusivity of the interstitial species, depending upon temperature.     

A simple method of calculation of the configurational entropy for interstitial solutions with short range repulsive interactions

A simple method has been proposed to calculate the partial molar entropy for interstitial solid solution with exclusion of nearest neighbor sites. Its accuracy has been tested by comparing its results with exact results known for hard sphere lattice gases. This method has been applied to solutions of hydrogen in b.c.c. metals (vanadium, niobium and tantalum) and it has been shown that experimental results are consistent with the exclusion of first and second nearest neighbors of occupied sites.     

Application of a solvation shell analysis to the diffusivity of an interstitial species in binary substitutional solutions

A model is presented for the effect of substitutional solute elements on the diffusion coefficient of an interstitial species for low concentrations of both solutes. The model is based on the theory of absolute reaction rates and a Wagner random, noninteractive model for the substitutional solution, with Maxwell-Boltzmann statistics for the distribution of the interstitial atoms. Simplifying assumptions are made concerning the configuration of activated complexes, treating them as formed by the interstitial atom and the two nearest lattice atoms. The calculations are compared with experimental data reviewed for the diffusivity of carbon in Fe-Cr, Fe-Mn, Fe-Co and Fe-Ni alloys.     

Ground-state properties of boron-doped diamond

Boron-doped diamond undergoes an insulator-metal or even a superconducting transition at some critical value of the dopant concentration. We study the equilibrium lattice parameter and bulk modulus of boron-doped diamond experimentally and in the framework of the density functional method for different levels of boron doping. We theoretically consider the possibility for the boron atoms to occupy both substitutional and interstitial positions and investigate their influence on the electronic structure of the material. The data suggest that boron softens the lattice, but softening due to substitutions of carbon with boron is much weaker than due to incorporation of boron into interstitial positions. Theoretical results obtained for substitution of carbon are in very good agreement with our experiment. We present a concentration dependence of the lattice parameter in boron-doped diamond, which can be used for to identify the levels of boron doping in future experiments. The text was submitted by the authors in English.     

Dynamical theory of diffraction of plane and spherical waves by a periodic system of scatterers with isolated defects

Using the T-matrix formalism a method known from the crystal lattice dynamics is applied to the study of the diffraction of radiation by a crystal with isolated defects. The following cases are discussed: substitutional foreign atoms or vacancies without lattice deformation, lattice deformation, interstitial atoms. Plane or spherical primary incident scalar waves are considered.     

金属Fe与间隙H原子相互作用的密度泛函研究

采用基于密度泛函理论的第一性原理方法, 研究了不同摩尔比下H在α-Fe和γ-Fe晶格中的间隙占位情况, 计算了稳态晶体的总能量、结合能、溶解热、电子态密度、电荷差分密度和电荷布居, 分析了间隙H原子和Fe晶格之间的相互作用, 讨论了H溶解对α-Fe和γ -Fe晶体电子结构的影响. 结果表明: H溶解引起α-Fe和γ-Fe晶体点阵晶格畸变, 体积膨胀率随着溶氢量的增加而增加. 从能量角度分析发现, H优先占据α-Fe的四面体间隙位, 而在γ -Fe中优先 占据八面体间隙位. 态密度、电荷差分密度以及电荷布居分析发现, 间隙H原子与Fe晶格的相互作用仅由H的1s轨道电子和Fe的4s轨道电子所贡献, 二者作用力相对较弱, 这是造成H在Fe晶格中固溶度较低的主要原因之一. 关键词： 金属Fe 间隙H原子 第一性原理 溶解热     

Effects of hydrogen and impurities on void nucleation in copper: simulation point of view

The mechanisms of hydrogen influence on vacancy cluster formation in copper are studied using numerical simulations. Vacancy agglomeration in clusters larger than divacancies is found to be energetically favourable, but in pure copper the cluster creation is prevented by the lack of binding between single vacancies. Hydrogen dissolved in the lattice readily accumulates in vacancy-type defects, changing their properties. A single vacancy can accommodate up to six hydrogen atoms. Hydrogen stabilizes divacancies and promotes vacancy cluster nucleation. In larger vacancy clusters, accumulated hydrogen prevents cluster collapse into stacking fault tetrahedra. In small voids, hydrogen prefers to remain in atomic form at the void surface, but when voids become sufficiently large, hydrogen molecules in the void interior can also be formed. Some common impurities in copper (O, S, P and Ag) contribute to void formation by capturing vacancies in their vicinity. In contrast, substitutional Ni has little effect on vacancy clustering but tends to capture interstitial hydrogen.     

Effect of thermal annealing on sub-band-gap absorptance of microstructured silicon in air

The optical absorption properties of femtosecond-laser-made “black silicon” as a function of the annealing conditions were investigated. We found that the annealing process changes the surface morphology and absorption spectroscopy of the “black silicon” samples, and obtained a maximum sub-band-gap absorptance value of approximately 30% by annealing at 1000 °C for 30 min. The thermal relaxation and atomic structural transformation mechanisms are used to describe the lattice recovery and the increase and decrease of the substitutional dopant atom concentration in the microstructured surface during the annealing. Our results confirm that: i) owing to the thermal relaxation, the lattice defects decrease with the increase of the annealing temperature; ii) the quasi-substitutional and interstitial configurations of the doped atoms transform into substitutional arrangements when the annealing temperature increases; iii) the quasi-substitutional and interstitial configurations with higher energies of the doped atoms transform into interstitial configurations with the lowest energy after high-temperature annealing for a long period of time, causing the deactivation or reactivation of the sub-band-gap absorptance by diffusion. The results demonstrate that the annealing can improve the properties of “black silicon”, including defects repairing, carrier lifetime lengthening, and retention of a high absorptive performance.     

μ+ diffusion and trapping in high purity and oxygen-doped Nb

Data are presented for the temperature dependence of the muon depolarization rate between 10 K and 120 K for three samples of niobium of varying. purity. Two samples, each containing approximately 200 ppm substitutional Ta and interstitial concentrations of 10 ppm and 560 ppm (mostly O), respectively, were studied. A third sample containing only 3 ppm Ta and an estimated 10 ppm total interstitial impurities was also measured. The results indicate that even at the lowest temperatures studied the depolarization of the muon is dominated by traps associated with impurities.This work was supported by the U. S. Department of Energy     

Formation and migration properties of the rare gases He,Ne, Ar,Kr, and Xe in nickel

The energies of formation and migration of various rare gas-point defect complexes in an f.c.c. nickel lattice have been calculated for He, Ne, Ar, Kr, and Xe. Formation energies of rare gas atoms at interstitial sites are compared with those in substitutional sites. Binding energies are presented for self-interstitials and vacancies trapped to the various rare gas substitutionals. We also present migration energies and migration paths for various rare gas interstitials and substitutionals with and without trapped vacancies and self-interstitials. The migration energies are compared with the breakup energies for the corresponding complexes. We find that divacancy-rare gas complexes are rather stable and will migrate at relatively low energies compared to other substitutional rare gas migration processes.