Vacancy Formation Process Research Articles

Temperature dependence of iodine vacancies concentration in [formula omitted] perovskite: A theoretical analysis

In this study, we investigate the temperature dependence of iodine vacancies in the organic-inorganic hybrid perovskite CH3NH3PbI3 through theoretical analysis. Iodine vacancies, as point defects, play a crucial role in the instability of perovskite solar cells. By employing molecular dynamics (MD) simulations, we calculate the formation energy of vacancies and examine its relationship with temperature. Our results reveal that the formation energy remains constant irrespective of temperature. However, elevated temperatures facilitate the provision of energy necessary for vacancy formation. To accurately determine the vacancy concentration, it is essential to consider the associated entropy changes. Analytical methods are employed to assess these entropy changes, offering valuable insights into the vacancy formation process. Utilizing the derived values, we quantify the concentration of vacancies and analyze their dependence on temperature. The findings obtained from this research contribute significant insights into the behavior of iodine vacancies within the studied CH3NH3PbI3 perovskite system.

Parameters of the vacancy formation and self-diffusion in the iron

The parameters of the electroneutral vacancy formation and self-diffusion of atoms in iron have been calculated by the analytical method based on the paired four-parameter Mie–Lennard-Jones interatomic interaction potential. For the first time, all activation process parameters were calculated within the framework of a single method: Gibbs energy, enthalpy, entropy and volume for both the vacancy formation process and the self-diffusion process. The isobaric temperature dependences of the indicated activation parameters for bcc and fcc iron structures from T = 10 K–1810 K along two isobars: P = 0 and 10 GPa were calculated. It is shown that, at low temperatures, due to quantum regularities, activation parameters strongly depend on temperature, and the entropy of activation processes in this region is negative. In the high temperature region, a good agreement has been obtained with the experimental estimates of activation parameters for different iron structures known from the literature. It is shown that at the α-γ transition temperature (1184 K), the activation parameters decrease during the isobaric transition from the bcc to the fcc structure. At the γ-δ transition temperature (1667 K), the activation parameters increase during the isobaric transition from the fcc to the bcc structure. With increasing pressure, the jumps magnitude for the Gibbs energy and the enthalpy of the activation process increases, and for the entropy and volume of the activation process decreases.

Dependencies of the parameters of vacancy formation and self-diffusion in a single-component crystal on temperature and pressure

An analytical method for calculating the parameters of electroneutral vacancy formation and self-diffusion of atoms in a single-component crystal is proposed. The method is based on the four-parameter pairwise Mie–Lennard-Jones interatomic interaction potential. The method allows calculation of all activation process parameters, that is, Gibbs energy, enthalpy, entropy, and volume, for both the vacancy formation process and the self-diffusion process. The method is applicable at any pressure (P) and temperature (T). The temperature dependences of the activation process parameters for gold have been calculated from T = 10 K–1330 K along two isobars, P = 0 and 24 GPa. It is shown that, at low temperatures, due to quantum regularities, activation parameters strongly depend on temperature, and the entropy of activation processes in this region has a negative value. In the high-temperature region, the probability of vacancy formation and the self-diffusion coefficient pass into classical Arrhenius dependences, with a weakly temperature-dependent enthalpy and a positive value of the activation process entropy. Good agreement has been obtained with estimated activation parameters for gold in the literature. It is shown that at T = 0 K the activation process parameters reach their minima: the Gibbs energy, enthalpy, and volume of the activation process all become zero, and the minimum of the activation process entropy lies in the negative region. The connection of the proposed calculation method with the Varotsos cBΩ model is discussed.

Changing the Parameters of Vacancy Formation and Self-Diffusion in a Crystal with Temperature and Pressure

An analytical method for calculating the parameters of the electroneutral vacancies formation and self-diffusion of atoms in a single-component crystal is proposed. The method is based on the 4-parameters pairwise Mie--Lennard-Jones interatomic interaction potential. The method allows calculating all the activation processes parameters: Gibbs energy, enthalpy, entropy and volume for both the vacancy formation process and the self-diffusion process. The method is applicable at any pressure (P) and temperature (T). The temperature dependencies of the activation processes parameters for gold are calculated from T=10 K to 1330 K along two isobars P=0 and 24 GPa. It is shown that at low temperatures, due to quantum regularities, activation parameters strongly depend on temperature, and the entropy of activation processes in this region has a negative value. In the high temperature region, the probability of vacancy formation and the self-diffusion coefficient pass into classical Arrhenius dependencies with a weakly temperature-dependent enthalpy and with a positive value of the activation process entropy. Good agreements were obtained with the estimates of activation parameters for gold known from the literature. The values of activation parameters at T=0 K were discussed. Keywords: vacancy, self-diffusion, interatomic potential, gold, state equation, thermal expansion.

Изменение параметров образования вакансий и самодиффузии в кристалле с температурой и давлением

An analytical method for calculating the parameters of the electroneutral vacancies formation and self-diffusion of atoms in a single-component crystal is proposed. The method is based on the 4-parameters pairwise Mie–Lennard-Jones interatomic interaction potential. The method allows calculating all the activation processes parameters: Gibbs energy, enthalpy, entropy and volume for both the vacancy formation process and the self-diffusion process. The method is applicable at any pressure (P) and temperature (T). The temperature dependencies of the activation processes parameters for gold are calculated from T = 10 K to 1330 K along two isobars P = 0 and 24 GPa. It is shown that at low temperatures, due to quantum regularities, activation parameters strongly depend on temperature, and the entropy of activation processes in this region has a negative value. In the high temperature region, the probability of vacancy formation and the self-diffusion coefficient pass into classical Arrhenius dependencies with a weakly temperature-dependent enthalpy and with a positive value of the activation process entropy. Good agreements were obtained with the estimates of activation parameters for gold known from the literature. The values of activation parameters at T = 0 K were discussed.

Influence of vacancy defects on the thermoelectric performance of SnSe sheet

Native defects are present in materials under various growth conditions. A fundamental understanding of the effect and nature of these defects in the lattice is crucial to optimize its thermoelectric performance. In this paper, we investigate the influence of the vacancy defects on the thermoelectric performance of the SnSe sheet. The results indicate that the process of vacancy formation is endothermic in nature. The calculated electronic structure shows that the band gap in case of sheet containing one Se vacancy decreases whereas the band gap in case of sheet containing a pair of Sn & Se vacancies increases with respect to the pristine sheet. However, in case of the sheet containing one Sn vacancy, the formation of a lone pair state near the valance band maximum results in the disappearance of band gap in the sheet. The calculated relaxation time of charge carriers shows higher values for the pristine sheet as compared to the sheet containing vacancies. The transport calculations show that the introduction of vacancies in the lattice deteriorates the thermoelectric performance of the sheet. • Systematic investigations of influence of vacancies on the thermoelectric properties has been performed. • Introduction of vacancies in the sheet results in dangling states formation in the gap region between VBM and CBM. • The bandgap for sheet containing Se vacancy decreases whereas bandgap for sheet containing a pair of Se & Sn vacancies increases w.r.t. pristine sheet. • In case of Sn vacancy, the bandgap of the sheet is disappeared due to formation of dangling states. • The transport coefficients of the sheet are deteriorated with the introduction of vacancies in the sheet.

Improved Negative Bias Stress Stability of Sol–Gel-Processed Li-Doped SnO2 Thin-Film Transistors

In this study, sol–gel-processed Li-doped SnO2-based thin-film transistors (TFTs) were fabricated on SiO2/p+ Si substrates. The influence of Li dopant (wt%) on the structural, chemical, optical, and electrical characteristics was investigated. By adding 0.5 wt% Li dopant, the oxygen vacancy formation process was successfully suppressed. Its smaller ionic size and strong bonding strength made it possible for Li to work as an oxygen vacancy suppressor. The fabricated TFTs consisting of 0.5 wt% Li-doped SnO2 semiconductor films delivered the field-effect mobility in a 2.0 cm2/Vs saturation regime and Ion/Ioff value of 1 × 108 and showed enhancement mode operation. The decreased oxygen vacancy inside SnO2 TFTs with 0.5 wt% Li dopant improved the negative bias stability of TFTs.

Atomistic Approximation of Solid Surface Energy and Its Anisotropy

The anisotropic surface energy of solid surfaces is mainly calculated using electron-based analyses. Experimental measurements are both difficult and subject to numerous errors. In this communication, by quantifying the surface area increment accompanying a vacancy formation process on solid surfaces, the anisotropic solid surface energy is approximated. Further analyses on the dependence of solid surface energy on planar packing fraction show that, however, the electron-based data may seem unrealistic in some cases.

Low Valence Cation Doping of Bulk Cr2O3: Charge Compensation and Oxygen Vacancy Formation

The different oxidation states of chromium allow its bulk oxide form to be reducible, facilitating the oxygen vacancy formation process, which is a key property in applications such as catalysis. Similar to other useful oxides such as TiO2, and CeO2, the effect of substitutional metal dopants in bulk Cr2O3 and its effect on the electronic structure and oxygen vacancy formation are of interest, particularly in enhancing the latter. In this paper, density functional theory (DFT) calculations with a Hubbard + U correction (DFT+U) applied to the Cr 3d and O 2p states, are carried out on pure and metal-doped bulk Cr2O3 to examine the effect of doping on the electronic and geometric structure. The role of dopants in enhancing the reducibility of Cr2O3 is examined to promote oxygen vacancy formation. The dopants are Mg, Cu, Ni, and Zn, which have a formal +2 oxidation state in their bulk oxides. Given this difference in host and dopant oxidation states, we show that to predict the correct ground state two metal ...

Research of vacancy defect formation on the surface of two-dimensional boron sheets

Mechanism of vacancy defect formation on the surface of two types of BS: triangular BS (TBS), α-sheet (αBS) have been calculated within the model of molecular cluster with the use of quantum chemical MNDO scheme. The process of atomic vacancy formation of BS has been modeled by step-by-step abstraction of one central boron atom. Incremental method allowed us to build energy curves for vacancy formation process. The process of vacancy migration on the BS surface has also have been investigated, and more probable paths of migration have been found.

Mechanism of Sulfur Poisoning of Sr2Fe1.5Mo0.5O6-δPerovskite Anode under Solid Oxide Fuel Cell Conditions

The interactions between sulfur and the Sr2Fe1.5Mo0.5O6-δ (SFMO) perovskite anode are investigated using periodic density functional theory (DFT) calculations and constrained ab initio thermodynamic analysis under anodic solid oxide fuel cell conditions. Three surface models with different Fe:Mo ratios in the topmost layer are used to investigate the mechanism of sulfur poisoning. Sulfur prefers to interact with these surfaces by replacing existing oxygen rather than adsorbing on a metal or oxygen vacancy. Constructed phase diagrams suggest that the surface with higher Mo content on the gas exposed surface layer is highly resistant toward sulfur poisoning, whereas the FeO2 terminated surface is more susceptible to sulfur poisoning. The presence of S in the surface has also a negative impact on the surface vacancy formation process, which is the rate-controlling step in the H2 electro-oxidation. Adding a small Ni3 cluster to the least active FeO2 terminated surface promotes the oxygen vacancy formation; ho...

In situ study of emerging metallicity on ion-bombarded SrTiO3 surface

We report how argon bombardment induces metallic states on the surface of insulating SrTiO3 at different temperatures by combining in situ conductance measurements and model calculations. At cryogenic temperatures, ionic bombardment created a thin–but much thicker than the argon-penetration depth–steady-state oxygen-vacant layer, leading to a highly-concentric metallic state. Near room temperatures, however, significant thermal diffusion occurred and the metallic state continuously diffused into the bulk, leaving only low concentration of electron carriers on the surface. Analysis of the discrepancy between the experiments and the models also provided evidence for vacancy clustering, which seems to occur during any vacancy formation process and affects the observed conductance.

Healing of oxygen vacancies on reduced surfaces of gold-doped ceria

As an oxidation-reduction catalyst, ceria can catalyze molecular oxidation and reduction. There has been a focus on understanding and enhancing the vacancy formation process to improve the oxidative power of ceria. However, it is important to also address healing of the surface vacancy. To investigate healing of oxygen vacancies in ceria, we study the interaction of atomic and molecular oxygen and NO(2) with oxygen vacancies on gold-doped (110) and (100) surfaces using density functional theory, corrected for on-site Coulomb interactions (DFT+U). For atomic and molecular oxygen, adsorption at the reduced surface is favorable and results in an oxygen atom sitting in an oxygen lattice site, healing the oxygen vacancy. On undoped surfaces, O(2) adsorbs as a peroxo (O(2)(2-)) species. However, on the doped (110) surface a superoxo (O(2)(-)) species is present. When NO(2) adsorbs (exothermically) at a divacancy surface, one oxygen of the molecule sits in the vacancy site and the N-O distances are elongated and an [NO(2)](-) anion forms, similar to the undoped surface. Vacancy healing of ceria surfaces is favorable, even if vacancy formation is enhanced, justifying the current focus on improving the oxidative power of ceria. We briefly examine a catalytic cycle: the reaction of CO with adsorbed O(2) on the undoped and doped surfaces, and find that the doped (110) surface facilitates CO oxidation.

Vacancy Formation Process in Carbon Nanotubes: First-Principles Approach

The electronic and structural properties of a single-walled carbon nanotube (SWNT) under mechanical deformation are studied using first-principles calculations based on the density functional theory. A force is applied over one particular C-atom with enough strength to break the chemical bonds between the atom and its nearest neighbors, leading to a final configuration represented by one tube with a vacancy and an isolated C-atom inside the tube. Our investigation demonstrates that there is a tendency that the first bond to break is the one most parallel possible to the tube axis and, after, the remaining two other bonds are broken. The analysis of the electronic charge densities, just before and after the bonds breaking, helps to elucidate how the vacancy is formed on an atom-by-atom basis. In particular, for tubes with a diameter around 11 angstroms, it is shown that the chemical bonds start to break only when the externally applied force is of the order of 14 nN and it is independent of the chirality. The formation energies for the vacancies created using this process are almost independent of the chirality, otherwise the bonds broken and the reconstruction are dependent.

Elucidation by computer simulations of the CUS regeneration mechanism during HDS over MoS2 in combination with 35S experiments

The first part of this paper is a short review of the 35S radioactive tracer methods developed in recent years. Then, the experimental results obtained so far on Mo/Al2O3 catalysts are compared with computer simulation results recently claimed in order to elucidate the coordinatively unsaturated site (CUS) creation/replenishment/ regeneration mechanism over MoS2 crystallites. The computer simulations allowed us to pre-select thermodynamically acceptable mechanisms among a set of suggested ones. Then, by comparison of the calculated activation energies with the 35S experiments results we could further validate the most probable mechanism. This mechanism involved the dissociative adsorption of an H2 molecule on the metallic edge of a MoS2 crystallite surface with further creation of a CUS by release of one H2S molecule in the gas phase. Both laboratory and computer simulated experiments permitted to calculate the activation energy for the H2S liberation reaction. In both cases, this energy was about 10- 12 kcal/mol, confirming the accuracy of the proposed mechanism. Moreover, the calculated activation energy of the rate-limiting step for the creation of one CUS by the proposed mechanism was about 23 kcal/mol, which was also in good agreement with the experimental activation energy of the dibenzothiophene (DBT) hydrodesulphurisation (HDS) reaction (typically about 20- 22 kcal/mol). This correlation indicated that the DBT HDS reaction rate might be intrinsically governed by the CUS formation/replenishment process, i.e. that the vacancy formation process is a crucial parameter in the global HDS reaction mechanism. Nevertheless, in the case of the 4,6-dimethyl DBT (4,6-DMDBT) HDS reaction, the experimental activation energy is higher (approx. 30 kcal/mol), confirming that external parameters induced by the 4,6-DMDBT-specific properties themselves are likely to play an important role in the reaction process, in addition to the ones intrinsic to the catalytic phase.

Effect of charge carriers on the barrier height for vacancy formation on InP(110) surfaces

We determine the energy barrier height for the formation of positively charged phosphorus vacancies in InP(110) surfaces using the rate of formation of vacancies measured directly from scanning tunneling microscope images. We found a barrier height in the range of 1.15–1.21 eV. The barrier height decreases with increasing carrier concentration. These results are explained by a charge separation during the vacancy formation process.

Melting of the condensed inert gases

The melting of a macroscopic system of bound atoms with a pairwise interaction is examined as a vacancy formation process. It is found that the existence of a liquid state is related to a double-humped dependence of the partition function on the number of vacancies, where the peaks correspond to the solid and liquid states and the heights of the peaks are equal at the melting point. In order for the liquid state to form, the derivative of the vacancy interaction with respect to energy must have a maximum. The vacancies are compressed as a result of the interaction. In the condensed inert gases, the specific energy of vacancy formation is proportional to the resulting empty space per atom.

Thermal vacancies in B2 and L1 2 ordering alloys

Equilibrium configurations in L1 2- and B2-ordering ternary alloys A 3B 1 − x C x and AB 1 − x C x (0 ⩽ x ⩽ 1) containing thermal vacancies are studied within the Bragg-Williams approximation. A new approach proposed for the estimation of vacancy concentration in a crystal consists of analysing a state of equilibrium with respect to vacancy migration between the crystal and its surroundings considered as an infinite “vacant” crystalline lattice. Direct numerical minimisation of the alloy free energy yields a full overview of an interplay between vacancy formation, vacancy ordering and atomic ordering in alloys characterised by particular interrelations between pair interaction energies of atoms. It is found out that, without affecting the character of chemical ordering, various relations between atomic pair interaction energies control the vacancy formation process and lead to qualitatively different vacancy configurations. The origin of considerable discrepancies between the present results and some of the literature data is discussed.

Pseudopotential theory for self-diffusion and impurity diffusion: Defect-energy calculations for fcc metals.

Generalized formulations for the calculation of energies of multivacancy formation and migration in pure and impure lattices and a multi-interstitial formation in otherwise pure lattices have been obtained with use of a pseudopotential scheme. The energies caused by relaxations of the surrounding neighbors are incorporated in these processes. Formulas relating self-diffusion and impurity diffusion via a vacancy mechanism have been discussed. Calculations of the vacancy-formation energy, the migration energy, and hence the activation energy for self-diffusion and impurity diffusion and their changes have been done with use of standard model potentials. My calculations show that the effect of relaxations of the surrounding neighbors of the migrating atom at its activated position is significant while it has negligible effect in vacancy-formation process. The calculations also show that a Heine-Abarenkov model explains successfully all the defect parameters but the Aschroft model does not. A more sophisticated multiparameter model or the Heine-Abarenkov two-parameter model with approximate explanation of all the atomic properties is perhaps a better choice. It is also noted that careful numerical computation is essential for achieving satisfactory agreement with experiment.

Ferroelectricity associated with the metastable phase ?III? of AgNO3

The dielectric constant, dc resistance, D-E ferroelectric hysteresis loop and dilatometric analysis of the three phases I, II, and III of AgNO3 single crystals has been studied over the temperature range 100–200° C. A ferroelectric behaviour of the metastable phase III was detected here for the first time similar to what happened in KNO3. The ferroelectric is attributed here to Ag+-ion vacancy formation in the unit cell of AgNO3. The energy activating the process of vacancy formation was found to beEv=2.6 eV. It was found that an ionic shift from one lattice point to another requires an amount of energy to overcome a potential barrierEm=0.1 eV. A model is suggested to explain such behaviour. Dilatometric analysis indicated that this metastable phase transition I→II is accompanied by an expansion of the unit cell.