Dilute Defects Research Articles

Modeling Charged Defects Using the Defect Energy Formalism With a Charge Sublattice Within a CALPHAD Framework

AbstractThe non‐stoichiometry of material compounds significantly influences their functional properties. In semiconductors, point defects determine whether a material is n‐type or p‐type and the concentration of charge carriers. Even in structural alloys and ion conductors used in batteries and fuel cells, non‐stoichiometry and dilute defects play an integral role in their function. The design of metal alloys has advanced rapidly with the aid of thermodynamic modeling using calculation of phase diagrams (CALPHAD) to predict the phases produced during different processing conditions. While thermodynamic modeling has been done previously by fitting experimental data, the advent of first‐principle techniques has enabled the computational prediction of material properties. The defect energy formalism (DEF) is described for modeling charged and uncharged defects in compounds, showing that it accurately predicts non‐stoichiometry using density functional theory (DFT), without fitting experiments. The model reproduces the expected defect and free‐charge carrier concentrations using the statistical mechanics approach commonly used in most DFT defect studies. Finally, the model is used to accurately predict the single‐phase region of PbTe with no fitting to measured defect concentrations. This method can revolutionize materials development of insulators, semiconductors, and even metals by allowing rapid DFT calculations to replace laborious experiments when dilute defects are involved.

High-resolution real-space evaluation of the self-energy operator of disordered lattices: Gade singularity, spin–orbit effects and p-wave superconductivity

Disorder is a key factor influencing the behavior of condensed states of matter, however the true extent of its impact is generally difficult to determine due to the prominent roles played by quantum interference, entanglement between spin and orbital degrees of freedom and proximity to quantum critical points. Here we show that the one-particle disorder self-energy—a direct probe of the renormalization of low-energy excitations due to defects and impurities distributed randomly in a crystal—can be obtained by means of unbiased spectral expansions of lattice Green’s functions in a computationally expedient manner. Our scheme provides a powerful framework to map out the frequency and wavevector dependence of electronic excitations in unprecedented large tight-binding systems, up to 109 orbitals, with energy resolution only limited by the mean level spacing. We demonstrate the versatility of our approach in three distinct problems: (i) the Gade singularity in honeycomb layers with dilute topological defects; (ii) the rich landscape of impurity resonances in a spin–orbit-coupled ferromagnet; and (iii) the tailoring of emergent s-wave and p-wave superconducting phases in graphene via atomic defects. These examples reveal rich features in the disorder self-energy that are absent from the self-consistent T-matrix approach and other common approximation schemes, which include regimes of nontrivial wavevector dependence and anomalous dependence upon the impurity concentration. Our study unravels puzzling, and so far largely inaccessible, manifestations of strong nonperturbative quantum interference effects in quantum materials and disordered phases of matter.

Dependence of the contact line roughness exponent on the contact angle on substrates with dilute mesa defects: numerical study.

We compute the roughness exponent of the averaged contact line width of a liquid on heterogeneous substrates with randomly distributed dilute defects in statics. We study the case of circular "mesa"-type defects placed on homogeneous base. The shape of the liquid meniscus and the contact line are obtained numerically, using the full capillary model when a vertical solid plate, partially dipped in a tank of liquid, is slowly withdrawing from the liquid. The obtained results imply that the contact line roughness exponent depends on the contact angle [Formula: see text], which the liquid meniscus forms with the solid homogeneous base. The roughness exponent grows when [Formula: see text] decreases, and it changes from 0.5 at [Formula: see text] to 0.67 at [Formula: see text]. A wide range of contact angles ([Formula: see text]-[Formula: see text]) is present, where the roughness exponent is practically constant, equal to previously obtained experimental results on the magnitude of the roughness exponent and its dependence on [Formula: see text].

Tracking the evolution from isolated dimers to many-body entanglement in NaLuxYb1−xSe2

We synthesize homogeneous compositions of NaLu$_x$Yb$_{1-x}$Se$_2$, connecting non-magnetic NaLuSe$_2$ to the triangular lattice spin liquid candidate NaYbSe$_2$. Thermal and magnetic properties are studied as the system evolves from one with dilute magnetic defects to one of a dense magnetic lattice. The field and temperature dependent heat capacity show the carriers of entropy crossover from isolated magnetic ions to a correlated lattice borne from spin dimers. For the dilute system we estimate the single ion anisotropy $(g_\perp/g_\parallel =3.13)$ and also the dimer exchange couplings $J_\parallel(=5.4$~K) and $J_\perp(=9.6$~K), in order to draw comparison to the half-doped and full magnetic compounds.

Ab initio investigations of point and complex defect structures in B2-FeAl

We study single-site and two-site defect structures in B2-type Fe-Al alloys by means of density functional theory supercell calculations. The defect formation energies are calculated as functions of the chemical potential, which are used to obtain the dependence of the defect concentrations on Al content at different temperatures. We also examine the converging behavior of the formation energies with respect to the supercell size to study the corresponding limit of dilute defects. The effect of magnetism is investigated by considering nonmagnetic, ferromagnetic, and paramagnetic states, calculations for the latter showing that the magnitude of the local magnetic moments strongly impacts the defect formation energies. The methodological studies are used to provide explanations for the wide spread of defect formation energies reported by experiments and other theoretical investigations. Based on these insights, the stability of the B2-FeAl structure as a function of Al concentration is obtained and discussed.

Study of the Droplet Pinning Force in the Transition from Dry to Liquid-Infused Thin Polymer Films.

The change in the pinning force during the transition from dry to oil-impregnated thin polymer films is studied for droplets of water and hexadecane. A careful variation of the oil amount in the films is performed by means of supercritical impregnation. The film thickness dependence on the oil content is measured using ellipsometry and compared to gel swelling theory estimates. Depending on the oil content, two cases of pinning force behavior have been identified. For each case, the factors that determine the pinning force are discussed. The pinning force in the transition from dry to equilibrium swollen gel films is well approximated by the Joanny and de Gennes hysteresis model of dilute defects.

Direct Visualization of Native Defects in Graphite and Their Effect on the Electronic Properties of Bernal-Stacked Bilayer Graphene.

Graphite crystals used to prepare graphene-based heterostructures are generally assumed to be defect free. We report here scanning tunneling microscopy results that show graphite commonly used to prepare graphene devices can contain a significant amount of native defects. Extensive scanning of the surface allows us to determine the concentration of native defects to be 6.6 × 108 cm-2. We further study the effects of these native defects on the electronic properties of Bernal-stacked bilayer graphene. We observe gate-dependent intravalley scattering and successfully compare our experimental results to T-matrix-based calculations, revealing a clear carrier density dependence in the distribution of the scattering vectors. We also present a technique for evaluating the spatial distribution of short-scale scattering. Finally, we present a theoretical analysis based on the Boltzmann transport equation that predicts that the dilute native defects identified in our study are an important extrinsic source of scattering, ultimately setting the charge carrier mobility at low temperatures.

Defects in Li4Ti5O12induced by carbon deposition: an analysis of unidentified bands in Raman spectra

Lithium titanate (Li4Ti5O12, LTO) has already occupied its niche as an anode material for high-power and long-lifespan lithium batteries, but some novel directions for basic and applied research are still open. One of the most promising approaches in improving its properties, e.g., electronic conductivity and rate capability, is based on controllable defect engineering. The "defects" may be intentionally introduced into LTO via doping, surface modifications, and the synergy between them. However, the defects, which have significant effects to the electrical and electrochemical properties, are usually extremely dilute. Reliable material characterizations are essential and challenging, but the instrumental tools for revealing dilute defects are still insufficient. Herein, detailed analyses on the surface or subsurface defects of carbon-coated LTO were performed using various material characterization methods. Raman spectroscopy has been identified as a unique tool for the probing of structural defects.

Single-crystal diffuse scattering for analysing structures of dilute defects

Single-crystal diffuse scattering for analysing structures of dilute defects

(Invited) Computing the Anisotropic Chemical Strain in Non-Stoichiometric Oxides for Solid Oxide Fuel Cell and Li-Ion Battery Applications

Accurate characterization of chemical strain is required to study a broad range of chemical-mechanical coupling phenomena. By combining density functional theory (DFT) calculations and elastic dipole tensor theory, it is readily to predict the long-range chemical strain tensor and the chemical expansion coefficient tensor induced by dilute point defects in a crystal structure. First, we demonstrate that, even in cubic CeO2-δ, both the short-range deformation surrounding an oxygen vacancy and the long-range chemical strain (or the expansion coefficient) are anisotropic. The origin of this anisotropy is the charge disproportionation between the four cerium atoms surrounding each oxygen vacancy (two become Ce3+ and two become Ce4+) when a neutral oxygen vacancy is formed. While the short-range deformation agrees with experimentally determined Ce-O bond lengths, the predicted maximum and average chemical strains successfully bound the variety of CeO2-δ chemical strain behavior previously reported in the literature. Normally, since there are six possible disproportionation configurations, the average chemical strain is isotropic. Only under an external bias, such as an applied electric field, the chemical strain can be oriented to show the anisotropic effect. This successfully explained the giant electrostriction effect reported in doped and un-doped CeO2-δ. Next, we show strains induced by coupled vacancies in layered Li-intercalation compounds for battery applications. Li2MnO3 was investigated as Li-excess intercalation compounds containing Li2MnO3 need to be “activated” to deliver the high capacity. This activation process during the first delithiation cycle at a high voltage is believed to introduce oxygen vacancies into the system. Due to the large amount Li vacancy generated, a large number of defect configurations were sampled and the average chemical strain induced by Li vacancy concentration is obtained by Boltzmann average. Previously, we have demonstrated that it is energetically favorable to create a Li-O-Li vacancy dumbbell structure (VLi - VO - VLi) in Li2MnO3. The chemical strain of the vacancy dumbbell structure is smaller than the sum of the chemical strain of one Vo and two VLis. The chemical expansion coefficient averaged for the polycrystalline samples and the experimentally measured stress change provided a novel method to in situ track the irreversible chemical changes in Li-excess cathode materials.

Sputtering-induced reemergence of the topological surface state inBi2Se3

We study the fate of the surface states of Bi$_2$Se$_3$ under disorder with strength larger than the bulk gap, caused by neon sputtering and nonmagnetic adsorbates. We find that neon sputtering introduces strong but dilute defects, which can be modeled by a unitary impurity distribution, whereas adsorbates, such as water vapor or carbon monoxide, are best described by Gaussian disorder. Remarkably, these two disorder types have a dramatically different effect on the surface states. Our soft x-ray ARPES measurements combined with numerical simulations show that unitary surface disorder pushes the Dirac state to inward quintuplet layers, burying it below an insulating surface layer. As a consequence, the surface spectral function becomes weaker, but retains its quasiparticle peak. This is in contrast to Gaussian disorder, which smears out the quasiparticle peak completely. At the surface of Bi$_2$Se$_3$, the effects of Gaussian disorder can be reduced by removing surface adsorbates using neon sputtering, which, however, introduces unitary scatterers. Since unitary disorder has a weaker effect than Gaussian disorder, the ARPES signal of the Dirac surface state becomes sharper upon sputtering.

From solid solution to cluster formation of Fe and Cr in α-Zr

To understand the mechanisms by which the re-solution of Fe and Cr additions increase the corrosion rate of irradiated Zr alloys, the solubility and clustering of Fe and Cr in model binary Zr alloys was investigated using a combination of experimental and modelling techniques — atom probe tomography (APT), x-ray diffraction (XRD), thermoelectric power (TEP) and density functional theory (DFT). Cr occupies both interstitial and substitutional sites in the α-Zr lattice; Fe favours interstitial sites, and a low-symmetry site that was not previously modelled is found to be the most favourable for Fe. Lattice expansion as a function of Fe and Cr content in the α-Zr matrix deviates from Vegard's law and is strongly anisotropic for Fe additions, expanding the c-axis while contracting the a-axis. Matrix content of solutes cannot be reliably estimated from lattice parameter measurements, instead a combination of TEP and APT was employed. Defect clusters form at higher solution concentrations, which induce a smaller lattice strain compared to the dilute defects. In the presence of a Zr vacancy, all two-atom clusters are more soluble than individual point defects and as many as four Fe or three Cr atoms could be accommodated in a single Zr vacancy. The Zr vacancy is critical for the increased apparent solubility of defect clusters; the implications for irradiation induced microstructure changes in Zr alloys are discussed.

Water drop impingement on graphite substrates with random dilute defects

Droplet impingement experiments for a wide range of Weber numbers were conducted by digitizing silhouettes of impacting water drops onto a tailored grinded graphite substrate, typified by randomly distributed cavities on a generally smooth surface. The aim was to investigate if the anchoring of the triple line, due to friction forces generated by dilute superficial defects, could be observed for drop impingement experiments. During the early inertially dominated spreading phase, the drops showed similar behaviors independently of the initial impact velocities. However, just after this phase, droplets impacting at low Weber numbers indeed exhibited this peculiar friction-induced pinned configuration.

Residual resistivity of FeGe under pressure

Residual resistivity of FeGe under pressure exhibits an anomaly at a critical pressure ${p}_{c}\ensuremath{\approx}19$ GPa whose origin is not understood. In previous theoretical work, it has been suggested that at the critical pressure a minority spin band starts to become occupied in FeGe. Here we provide further support for this scenario by studying, within the standard Boltzmann-type transport theory combined with a $T$-matrix treatment of scattering on dilute point defects, how the residual resistivity of a helical ferromagnet changes with exchange splitting.

Spin Pseudogap in Ni-DopedSrCuO2

The S=1/2 spin chain material SrCuO2 doped with 1% S=1 Ni impurities is studied by inelastic neutron scattering. At low temperatures, the spectrum shows a pseudogap Δ≈8 meV, absent in the parent compound, and not related to any structural phase transition. The pseudogap is shown to be a generic feature of quantum spin chains with dilute defects. A simple model based on this idea quantitatively accounts for the experimental data measured in the temperature range from 2 to 300 K, and allows us to represent the momentum-integrated dynamic structure factor in a universal scaling form.

First principles calculations for defects in U

Uranium (U) exhibits a high temperature body-centered cubic (bcc) allotrope that is oftenstabilized by alloying with transition metals such as Zr, Mo, and Nb for technologicalapplications. One such application involves U–Zr as nuclear fuel, where radiation damageand diffusion (processes heavily dependent on point defects) are of vital importance.Several systems of U are examined within a density functional theory frameworkutilizing projector augmented wave pseudopotentials. Two separate generalizedgradient approximations of the exchange-correlation are used to calculate defectproperties and are compared. The bulk modulus, the lattice constant, and theBirch–Murnaghan equation of state for the defect free bcc uranium allotrope are calculated.Defect parameters calculated include energies of formation of vacancies in theα andγ allotropes, as well as self-interstitials, Zr interstitials, and Zr substitutional defects for theγ allotrope. The results for vacancies agree very well with experimental andprevious computational studies. The most probable self-interstitial site inγ-U isthe ⟨110⟩ dumbbell, and the most probable defect location for dilute Zr inγ-U is the substitutional site. This is the first detailed study of self-defects in thebcc allotrope of U and also the first comprehensive study of dilute Zr defects inγ-U.

ChemInform Abstract: Dilute Doping, Defects, and Ferromagnetism in Metal Oxide Systems

AbstractReview: 184 refs.

Dilute Doping, Defects, and Ferromagnetism in Metal Oxide Systems

Over the past decade intensive research efforts have been carried out by researchers around the globe on exploring the effects of dilute doping of magnetic impurities on the physical properties of functional non-magnetic metal oxides such as TiO(2) and ZnO. This effort is aimed at inducing spin functionality (magnetism, spin polarization) and thereby novel magneto-transport and magneto-optic effects in such oxides. After an early excitement and in spite of some very promising results reported in the literature, this field of diluted magnetic semiconducting oxides (DMSO) has continued to be dogged by concerns regarding uniformity of dopant incorporation, the possibilities of secondary ferromagnetic phases, and contamination issues. The rather sensitive dependence of magnetism of the DMSO systems on growth methods and conditions has led to interesting questions regarding the specific role played by defects in the attendant phenomena. Indeed, it has also led to the rapid re-emergence of the field of defect ferromagnetism. Many theoretical studies have contributed to the analysis of diverse experimental observations in this field and in some cases to the predictions of new systems and scenarios. In this review an attempt is made to capture the scope and spirit of this effort highlighting the successes, concerns, and questions.

Effects of dilute columnar defects on the vortex matter in Bi 2Sr 2CaCu 2O 8+δ near the disorder-driven phase transition

Magneto-optical measurements are employed to characterize the disorder-driven vortex phase transition and the metastable disordered vortex state in heavy-ion irradiated and pristine regions of the same Bi 2Sr 2CaCu 2O 8+δ crystal. We find that dilute columnar defects, while hardly affect the disorder-driven phase transition line, significantly increase the lifetime of the metastable state created in the vicinity of this line. Study of flux injection from the pristine region into the irradiated region suggests that in presence of columnar defects a metastable disordered state may be created in the bulk, in addition to being injected from the edges.

Contact Angle Hysteresis Generated by Strong Dilute Defects

Water on solid decorated with hydrophobic defects (such as micropillars) often stays at the top of the defects in a so-called fakir state, which explains the superhydrophobicity observed in such case, provided that the density of defects is small enough. Here we show that this situation provides an ideal frame for studying the contact angle hysteresis; the phase below the liquid is "perfect" and slippery (it is air), contrasting with pillars' tops whose edges form strong pining sites for the contact line. This model system thus allows us to study the hysteresis as a function of the density of defects and to compare it to the classical theory by Joanny and de Gennes, which is based on very similar hypothesis.