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DOE OSTI2014

High resolution measurements supported by electronic structure calculations of two naphthalene derivatives: [1,5]- and [1,6]-naphthyridine—Estimation of the zero point inertial defect for planar polycyclic aromatic compounds

Polycyclic aromatic hydrocarbons (PAHs) molecules are suspected to be present in the interstellar medium and to participate to the broad and unresolved emissions features, the so-called unidentified infrared bands. In the laboratory, very few studies report the rotationally resolved structure of such important class of molecules. In the present work, both experimental and theoretical approaches provide the first accurate determination of the rotational energy levels of two diazanaphthalene: [1,5]- and [1,6]-naphthyridine. [1,6]-naphthyridine has been studied at high resolution, in the microwave (MW) region using a Fourier transform microwave spectrometer and in the far-infrared (FIR) region using synchrotron-based Fourier transform spectroscopy. The very accurate set of ground state (GS) constants deduced from the analysis of the MW spectrum allowed the analysis of the most intense modes in the FIR (ν{sub 38}-GS centered at about 483 cm{sup −1} and ν{sub 34}-GS centered at about 842 cm{sup −1}). In contrast with [1,6]-naphthyridine, pure rotation spectroscopy of [1,5]-naphthyridine cannot be performed for symmetry reasons so the combined study of the two intense FIR modes (ν{sub 22}-GS centered at about 166 cm{sup −1} and ν{sub 18}-GS centered at about 818 cm{sup −1}) provided the GS and the excited states constants. Although the analysis of the very dense rotational patterns for such large molecules remains very challenging, relatively accurate anharmonic density functional theory calculations appeared as a highly relevant supporting tool to the analysis for both molecules. In addition, the good agreement between the experimental and calculated infrared spectrum shows that the present theoretical approach should provide useful data for the astrophysical models. Moreover, inertial defects calculated in the GS (Δ{sub GS}) of both molecules exhibit slightly negative values as previously observed for planar species of this molecular family. We adjusted the semi-empirical relations to estimate the zero-point inertial defect (Δ{sub 0}) of polycyclic aromatic molecules and confirmed the contribution of low frequency out-of-plane vibrational modes to the GS inertial defects of PAHs, which is indeed a key parameter to validate the analysis of such large molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2013

Effects of defect clustering on optical properties of GaN by single and molecular ion irradiation

The effects of irradiation by F, P, and PF{sub 4} on optical properties of GaN were studied experimentally and by atomistic simulations. Additionally, the effect of Ag was studied by simulation. The irradiation energy was 0.6 keV/amu for all projectiles. The measured photoluminescence (PL) decay time was found to be decreasing faster when irradiation was done by molecular ion compared to light ion irradiation. The PL decay time change is connected with the types of defect produced by different projectiles. Simulation results show that the light ions mainly produce isolated point defects while molecular and heavy ions produce clusters of point defects. The total amount of defects produced by the PF{sub 4} projectile was found to be very close to the sum of all defects produced in five individual cascades started by one P and four F single ions. This and the similar depth profiles of damage produced by molecular and light ion irradiations suggest that the defect clusters are one of the important reasons for fast PL decay. Moreover, the simulations of irradiation by Ag ions, whose mass is close to the mass of the PF{sub 4} molecule, showed that the produced defects are clustering in even bigger conglomerates compared to PF{sub 4} case. The latter has a tendency to split in the pre-surface region, reducing on average the density of the collision cascade.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Imaging dark charge emitters in diamond via carrier-to-photon conversion

The application of color centers in wide-bandgap semiconductors to nanoscale sensing and quantum information processing largely rests on our knowledge of the surrounding crystalline lattice, often obscured by the countless classes of point defects the material can host. Here, we monitor the fluorescence from a negatively charged nitrogen-vacancy (NV – ) center in diamond as we illuminate its vicinity. Cyclic charge state conversion of neighboring point defects sensitive to the excitation beam leads to a position-dependent stream of photo-generated carriers whose capture by the probe NV – leads to a fluorescence change. This “charge-to-photon” conversion scheme allows us to image other individual point defects surrounding the probe NV, including nonfluorescent “single-charge emitters” that would otherwise remain unnoticed. Given the ubiquity of color center photochromism, this strategy may likely find extensions to material systems other than diamond.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

The Defects Genome of Janus Transition Metal Dichalcogenides

2D Janus Transition Metal Dichalcogenides (TMDs) have attracted much interest due to their exciting quantum properties arising from their unique two-faced structure, broken-mirror symmetry, and consequent colossal polarization field within the monolayer. While efforts are made to achieve high-quality Janus monolayers, the existing methods rely on highly energetic processes that introduce unwanted grain-boundary and point defects with still unexplored effects on the material's structural and excitonic properties Through high-resolution scanning transmission electron microscopy (HRSTEM), density functional theory (DFT), and optical spectroscopy measurements; this work introduces the most encountered and energetically stable point defects. It establishes their impact on the material's optical properties. HRSTEM studies show that the most energetically stable point defects are single (V S and V Se ) and double chalcogen vacancy (V S −V Se ), interstitial defects (Mi), and metal impurities (MW) and establish their structural characteristics. DFT further establishes their formation energies and related localized bands within the forbidden band. Cryogenic excitonic studies on h-BN-encapsulated Janus monolayers offer a clear correlation between these structural defects and observed emission features, which closely align with the results of the theory. Finally, the overall results introduce the defect genome of Janus TMDs as an essential guideline for assessing their structural quality and device properties.

2D materials↗

DOE OSTI2016

Kinetic Interaction of Uranium Vacancies and Dislocations in UO 2

Understanding how point defects and defect clusters interact with dislocations in urania is important for a number of phenomena. For example, dislocations are one (of many) trap sites in the fuel where fission gases may accumulate and ultimately nucleate fission gas bubbles. Further, some creep mechanisms are governed by the flow of point defects to dislocations. Thus, for a variety of reasons, it is important to examine how dislocations attract and accelerate the kinetics of point defects.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

First-principles study of quantum defect candidates in beryllium oxide

Beryllium oxide (BeO) is a promising host for quantum defects because of its ultrawide band gap. We conducted comprehensive first-principles investigations of the native point defects in BeO using density functional theory with a hybrid functional. We found that the beryllium and oxygen vacancies are the most stable defects, whereas other native defects such as interstitials or antisites have high formation energies. We investigate the point defects as candidates for quantum defects by examining spin states and internal optical transitions. Here, the oxygen vacancy ($V$$^{+}_{O}$) emerges as a suitable spin qubit or single-photon emitter; we also find its stability can be enhanced by forming a (V O – Li Be ) 0 complex with a Li acceptor. The $O$$^{–}_{Be}$ antisite also has desirable optical and spin properties. Overall, because of its desirable properties as a host material, BeO could be an excellent host for quantum defects, with $V$$^{+}_{O}$, (V O – Li Be ) 0 , and $O$$^{–}_{Be}$ as prime candidates.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Radiation Effects in Innovative Structural Materials

The extreme radiation environments and demanding structural conditions of next-generation fission and proposed fusion reactors will require high performance materials with very high radiation resistance. Although conventional structural materials such as ferritic/ martensitic steels offer several attractive features, there is value in exploring alternative materials systems that may offer unprecedented radiation stability while also offering good thermomechanical properties. As noted elsewhere, options for designing radiation resistance include (a) the traditional approach of introducing a very high sink strength for recombination of radiation-induced vacancies and interstitials (e.g., Ti-modified stainless steels or 'nano-cluster-strengthened ferritic alloys', (b) utilizing materials with immobile vacancies at the operating temperature (e.g., silicon carbide), and (c) utilizing certain classes of materials that inherently exhibit superior resistance to radiation defect retention and accumulation (e.g., ferritic steels). Three relatively new but promising structural materials systems were selected for investigation, based on their favorable unirradiated mechanical properties and potential for good stability under irradiation: High entropy alloys (HEAs), bulk metallic glass (BMG), and MAX phase ceramics. The high configurational entropy in HEAs might alter point defect (solute and radiation defects) diffusion processes, thus potentially enhancing the recombination of radiation-produced damage. Therefore, HEAs offer the potential of a new class of materials for radiation resistance category (c) mentioned previously. A variety of BMGs such as Zr{sub 52.5}Cu{sub 17.9}Ni{sub 14.6}Al{sub 10}Ti{sub 5} offer good mechanical properties including fracture toughness values that may exceed 100 MPa-m{sup 1/2} and near net shape fabrication potential. The lack of crystallinity in BMGs prohibits the formation of conventional Frenkel pair defects under irradiation and therefore offer the possibility of another new material system for radiation resistance category (c). MAX phase ceramics (e.g., Ti{sub 3}SiC{sub 2}, Ti{sub 3}AlC{sub 2}, Ti{sub 2}AlC) have good mechanical properties and contain a nano-laminate structure that could provide a very high point defect sink strength. Due to their refractory nature, many of the MAX phase ceramics may exhibit negligible vacancy mobility up to high temperatures. Therefore, MAX phase ceramics offer the potential to provide radiation resistance in either categories (a) and (b), depending on the operating temperature. For this study, a novel 27%Fe-27%Mn-28%Ni-18%Cr single phase face centered cubic high entropy alloy was synthesized that exhibited good strength and ductility over a wide temperature range. Zr{sub 52.5}Cu{sub 17.9}Ni{sub 14.6}Al{sub 10}Ti{sub 5} (BAM-11) was selected as a prototypic advanced BMG. Several MAX phase ceramics (e.g., Ti{sub 3}SiC{sub 2}, Ti{sub 3}AlC{sub 2}, Ti{sub 2}AlC) that have good unirradiated thermal and mechanical properties were also investigated. The irradiation damage behaviors of these three novel materials systems have been studied after fission neutron at ∼75 deg. C up to 1 dpa and Ni ion irradiation at 25- 700 deg. C up to 30 dpa (lower temperatures and doses for the BMGs). All three sets of materials generally exhibited good radiation stability within certain temperature regimes. For example, the BMG exhibited only minor (<10%) change in strength that appeared to saturate after a dose of ∼1 dpa. A key shortcoming of current BMGs are that they can not be used at temperatures >>300 deg. C due to glass to crystalline transition at elevated temperature. The MAX phase ceramics irradiated at 400-700 deg. C appeared to be in the 'low temperature' regime where vacancies are immobile and therefore the radiation hardening saturated at relatively low doses. The Ti{sub 3}SiC{sub 2} MAX phase exhibited the best overall radiation stability over a wide temperature range. The HEA exhibited fine scale dislocation loop formation, no observable cavity swelling and reduced amounts of Cr depletion compared to traditional austenitic Fe-Cr-Ni alloys after ion irradiation, which suggests suppressed point defect and solute diffusion behavior. (authors)

36 MATERIALS SCIENCE↗

DOE OSTI2019

Photoluminescence of Amorphous SiO{sub 2} with Implanted Ar{sup +} Ions

Implantation of ions into amorphous silicon dioxide (a-SiO{sub 2}) is widely used in microelectronics (mainly, using Si ions) and in the production of light-guiding components of optical fibers (Ge, P, B ions). All of these elements interact with the matrix oxygen, so the point defects that occur during implantation are not only the result of the displacement of the silicon–oxygen frame atoms from their equilibrium positions, but also reflect the specific chemical interaction in the material. In this study, inert argon ions were implanted into silicon dioxide plates, which excluded chemical reactions. It is demonstrated using photoluminescence (PL) that the highest concentration of point defects in the damaged silicate network belongs to neutral oxygen vacancies (NOVs). The concentration of these and some other induced defects increased with an increase in fluence up to 5 × 10{sup 15} Ar{sup +}/cm{sup 2}, and, with a further increase in dose, the concentration dropped due to annealing of defects in the layer heated by the introduction of ions. The NOV defects appeared in the photoluminescence spectrum in the form of doublets, that is, pairs of bands belonging to the same optical transition. The appearance of doublets is explained by the dependence of the optical transition energy on the localization of identical point defects in zones of different distortions of the matrix structure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2016

Modification of the G-phonon mode of graphene by nitrogen doping

The effect of nitrogen doping on the phonon spectra of graphene is analyzed. In particular, we employ first-principles calculations and scanning Raman analysis to investigate the dependence of phonon frequencies in graphene on the concentration of nitrogen dopants. We demonstrate that the G phonon frequency shows oscillatory behavior as a function of nitrogen concentration. We analyze different mechanisms which could potentially be responsible for this behavior, such as Friedel charge oscillations around the localized nitrogen impurity atom, the bond length change between nitrogen impurity and its nearest neighbor carbon atoms, and the long-range interactions of the nitrogen point defects. We show that the bond length change and the long range interaction of point defects are possible mechanisms responsible for the oscillatory behavior of the G frequency as a function of nitrogen concentration. At the same time, Friedel charge oscillations are unlikely to contribute to this behavior.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Atomistic simulation of defect-dislocation interactions in concentrated solid-solution alloys

The interaction between point defects and dislocations plays a crucial role in governing material properties and microstructural evolutions under external stimuli, such as mechanical deformation and irradiation. Here, we present an atomistic study of the interactions between point defects and dislocations in concentrated solid-solution alloys (CSAs). Using molecular statics and kinetic Monte Carlo methods, we demonstrate that the strain energy and stress field distribution induced by a dislocation in CSAs are highly inhomogeneous along the dislocation line, which leads to heterogeneity of defect-dislocation interactions. Specifically, the interactions are spatially different and screened by the random arrangement of different elemental species. Furthermore, such localization of defect-dislocation interaction indicates that the “dislocation-bias” mechanism that is a driving force for radiation-induced void swelling can be suppressed in concentrated alloys.

36 MATERIALS SCIENCE↗

DOE OSTI2015

Multiscale modeling of thermal conductivity of high burnup structures in UO 2 fuels

The high burnup structure forming at the rim region in UO 2 based nuclear fuel pellets has interesting physical properties such as improved thermal conductivity, even though it contains a high density of grain boundaries and micron-size gas bubbles. To understand this counterintuitive phenomenon, mesoscale heat conduction simulations with inputs from atomistic simulations and experiments were conducted to study the thermal conductivities of a small-grain high burnup microstructure and two large-grain unrestructured microstructures. We concluded that the phonon scattering effects caused by small point defects such as dispersed Xe atoms in the grain interior must be included in order to correctly predict the thermal transport properties of these microstructures. In extreme cases, even a small concentration of dispersed Xe atoms such as 10 -5 can result in a lower thermal conductivity in the large-grain unrestructured microstructures than in the small-grain high burnup structure. The high-density grain boundaries in a high burnup structure act as defect sinks and can reduce the concentration of point defects in its grain interior and improve its thermal conductivity in comparison with its large-grain counterparts. Furthermore, an analytical model was developed to describe the thermal conductivity at different concentrations of dispersed Xe, bubble porosities, and grain sizes. Upon calibration, the model is robust and agrees well with independent heat conduction modeling over a wide range of microstructural parameters.

36 MATERIALS SCIENCE↗

DOE OSTI2015

Photocatalytic characteristics of single phase Fe-doped anatase TiO{sub 2} nanoparticles sensitized with vitamin B{sub 12}

Highlights: • Anatase TiO{sub 2}/B{sub 12} hybrid nanostructured catalyst was successfully synthesized by sol–gel technique. • The nanoparticle catalyst was doped with iron at several concentrations. • Nanoparticles were characterized in detail by XRD, Raman, TEM, EDS, and spectroscopy techniques. • The formation mechanism and role of point defects on photocatalytic properties were discussed. • A structure-property-processing correlation was established. - Abstract: We report a processing-structure-property correlation in B{sub 12}-anatase titania hybrid catalysts doped with several concentrations of iron. Our results clearly show that low-level iron doping alters structure, defect content, and photocatalytic characteristics of TiO{sub 2}. XRD and Raman studies revealed formation of a single-phase anatase TiO{sub 2} where no iron based segregation in particular iron oxide, was detected. FT-IR spectra clearly confirmed sensitization of TiO{sub 2} nanoparticles with vitamin B{sub 12}. TEM micrographs and diffraction patterns confirmed crystallization of anatase nanoparticles with a radius of 15–20 nm. Both XRD and Raman signals showed a peak shift and a peak broadening which are surmised to originate from creation of point defects, namely oxygen vacancy and titanium interstitial. The doped samples revealed a narrower band gap as compared to undoped samples. Photocatalytic activity of the samples was assessed through measuring the decomposition rate of rhodamine B. It was found that sensitization with vitamin B{sub 12} and Fe-doping significantly enhances the photocatalytic efficiency of the anatase nanoparticles. We also showed that there is an optimum Fe-doping level where the maximum photocatalytic activity is achieved. The boost of photocatalytic activity was qualitatively understood to originate from a more effective use of the light photons, formation of point defects, which enhance the charge separation, higher carrier mobility.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Illuminating the Material World: Autonomous Microscopy to Understand Order, Disorder, and Everything In Between

Artificial intelligence (AI) holds immense promise for revolutionizing microscopy, yet its widespread adoption has been hindered by challenges ranging from user inexperience to limited model transferability and difficulties in operationalizing machine learning. This presentation showcases our approach to developing practical autonomy for materials discovery, aiming to accelerate the integration of AI into everyday microscopy workflows. As shown in Fig. 1, I will focus on three key areas: understanding order-disorder transitions, quantifying point defects, and achieving truly device-scale microscopy. First, I will demonstrate the power of multi-modal knowledge graphs for integrating diverse microscopy data. By combining imaging, spectroscopy, and diffraction data, these graphs provide a holistic view of material behavior, capturing the intricate relationships between different modalities [1,2]. I will present a case study on how these models illuminate the structural and chemical changes associated with irradiation in oxide thin films, revealing critical insights for designing materials for extreme environments like spaceflight and nuclear energy. Specifically, I will show how multi-modal analysis clarifies the evolution of order-disorder transitions under irradiation, a key factor influencing material performance in these applications. Next, I will address the challenge of quantifying point defects in 2D materials. We demonstrate the application of computer vision and transfer learning to accurately identify and classify various defect types, such as vacancies and substitutional atoms, and to quantify their concentrations. This information is crucial for understanding and tailoring the properties of 2D materials for applications in electronics, optoelectronics, and catalysis. For example, I will show how our models can characterize the topological distribution of point defects in MXene transition metal carbides, providing valuable insights for optimizing their performance in energy storage and separation science. Finally, I will discuss our progress toward autonomous device-scale microscopy [3,4]. We are fundamentally redesigning electron microscopes around the principles of machine reasoning, enabling automation beyond basic tasks like sample navigation and data acquisition to include sophisticated experimental design. This approach paves the way for truly reproducible and massively scaled analysis campaigns. I will emphasize the importance of autonomous microscopy platforms for high-throughput materials discovery and characterization, facilitating the rapid screening of materials for a broad range of applications and accelerating the development of next-generation technologies.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Defect Stability in CdTe Based on Formation Energies and Migration Barriers

Native point defects are thought to play a key role in CdTe, either as compensation centers in intentionally doped material, as a source of conductivity in nominally undoped material, or as electron–hole recombination centers. Here, the discussion of their concentration and impact has often centered only on formation energies and transition levels. Using hybrid density functional calculations, including the effects of spin–orbit coupling (SOC), we discuss the stability of native point defects in CdTe based on their formation energies and migration barriers. We show that although Cd interstitials are the lowest energy donor defects, they are unstable at room temperature due to a low migration barrier. They are important for maintaining charge neutrality during growth or annealing at high temperatures, but once the material is brought to room temperature, they are not frozen in as often assumed and are expected to anneal out, leaving the other more stable defects to determine the conductivity. Taking this into account in the solution of the charge neutrality equation, we are able to predict the conductivity type and carrier concentrations that are in good agreement with experimental observations.

14 SOLAR ENERGY↗

DOE OSTI2014

Competing effects of electronic and nuclear energy loss on microstructural evolution in ionic-covalent materials

Ever increasing energy needs have raised the demands for advanced fuels and cladding materials that withstand the extreme radiation environments with improved accident tolerance over a long period of time. Ceria (CeO2) is a well known ionic conductor that is isostructural with urania and plutonia-based nuclear fuels. In the context of nuclear fuels, immobilization and transmutation of actinides, CeO2 is a model system for radiation effect studies. Covalent silicon carbide (SiC) is a candidate for use as structural material in fusion, cladding material for fission reactors, and an inert matrix for the transmutation of plutonium and other radioactive actinides. Understanding microstructural change of these ionic-covalent materials to irradiation is important for advanced nuclear energy systems. While displacements from nuclear energy loss may be the primary contribution to damage accumulation in a crystalline matrix and a driving force for the grain boundary evolution in nanostructured materials, local non-equilibrium disorder and excitation through electronic energy loss may, however, produce additional damage or anneal pre-existing defects. At intermediate transit energies where electronic and nuclear energy losses are both significant, synergistic, additive or competitive processes may evolve that affect the dynamic response of materials to irradiation. The response of crystalline and nanostructured CeO2 and SiC to ion irradiation are studied under different nuclear and electronic stopping powers to describe some general material response in this transit energy regime. Although fast radiation-induced grain growth in CeO2 is evident with no phase transformation, different fluence and dose dependence on the growth rate is observed under Si and Au irradiations. While grain shrinkage and amorphization are observed in the nano-engineered 3C SiC with a high-density of stacking faults embedded in nanosize columnar grains, significantly enhanced radiation resistance is attributed to stacking faults that promote efficient point defect annihilation. Moreover, competing effects of electronic and nuclear energy loss on the damage accumulation and annihilation are observed in crystalline 4H-SiC. Systematic experiments and simulation effort are needed to understand the competitive or synergistic effects.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Defect-Induced (Dis)Order in Relaxor Ferroelectric Thin Films

The effect of intrinsic point defects on relaxor properties of 0.68 $\mathrm{PbMg_{1/3}Nb_{2/3}O_{3}-0.32 PbTiO_{3}}$ thin films is studied across nearly 2 orders of magnitude of defect concentration via ex post facto ion bombardment. A weakening of the relaxor character is observed with increasing concentration of bombardment-induced point defects, which is hypothesized to be related to strong interactions between defect dipoles and the polarization. Finally, although more defects and structural disorder are introduced in the system as a result of ion bombardment, the special type of defects that are likely to form in these polar materials (i.e., defect dipoles) can stabilize the direction of polarization against thermal fluctuations, and in turn, weaken relaxor behavior.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Molecular dynamics studies of lattice defect effects on tritium diffusion in zirconium

Tritium diffusion in α-Zr containing point defects such as vacancies or self-interstitial atoms (SIAs) is simulated using molecular dynamics. Point defects rapidly aggregate to form extended defects, such as 3D nanoclusters and Frank loops. The geometry of extended defects is affected by the presence of tritium. At low temperature and in the absence of tritium, vacancies aggregate to form stacking fault pyramids. Addition of tritium at these temperatures promotes aggregation of vacancies to form 3D nanoclusters, within which the tritium concentration can be sufficiently high to suggest that these defects may serve as nucleation sites for hydride precipitation. Trapping of tritium in vacancy nanocluster reduces the calculated bulk diffusivity by an amount proportional to the vacancy concentration. At high temperature, vacancy clusters change shape to form planar basal dislocation loops, which bind tritium less strongly, leading to a sharp reduction in the fraction of trapped tritium and a corresponding increase in tritium diffusivity at high temperature. In contrast, SIAs increase tritium diffusion through α-Zr. Analysis of atomic trajectories shows that tritium does not interact directly with SIAs. In conclusion, diffusion enhancement is instead related to expansion of the lattice.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Development of the Local (Site) Symmetry Method in the Supercell Model for a Crystal with an Impurity

Symmetry aspects of the periodic model of a crystal with a point defect (a supercell model or a extended unit cell (EUC) model) are considered; splitting of the Wyckoff positions in a primitive crystal cell with the introduction of supercell and the change of the one-electron states classification over k-vector (Brillouin zone folding) are discussed. When considering a point defect in a crystal in the supercell model, it is necessary to take into account the symmetry of the one-electron states of the original crystal at the top of the valence band and at the bottom of the conduction band. The selected supercell should reproduce these states. Each specific selection of a supercell corresponds to a specific splitting of the Wyckoff positions of the original crystal and, as a result, the possibility to place a defect in positions with different point symmetry and to perform a calculation without taking into account the point symmetry of the crystal with a defect at all (site symmetry method). By the results of the calculation of a crystal with a defect in the supercell model, taking into account site symmetry, it is possible to determine the real symmetry of the crystal with a defect, which is essential for the interpretation of experimental data. A copper impurity in a lithium node in a LiCl crystal retains the cubic symmetry of the atom being replaced; the impurity of an iron atom in a titanium site with cubic local symmetry in a SrTiO{sub 3} crystal lowers the symmetry to tetragonal; and the H site in the CsPbI{sub 3} crystal is characterized by the complete removal of point symmetry with the formation of an I{sub 2}{sup −} ion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗