Formation Energies Of Clusters Research Articles

The potential application of Ru in aluminide coatings with reduced Al contents: A combined experimental and theoretical study

Aluminide coatings are widely used on turbine blades due to their excellent oxidation resistance. However, the interdiffusion between these coatings and superalloy substrates can lead to a deterioration of mechanical properties in the coated alloys. In the present study, Ni-Al alloys (Ni-50Al, Ni-40Al, and Ni-30Al), both with and without the addition of 10 at. % Ru, are prepared and used to form diffusion couples with a single crystal superalloy SCA21. After a diffusion process at 1150 ℃ for 100 h, interdiffusion layers with the matrix of β-NiAl or γ ′-Ni3Al form at the diffusion couple interfaces. The formation of L12-ordered Ni3Al phases is found to impede elemental interdiffusion. Consequently, Ni-30Al/SCA21, which exhibits only Ni3Al-based interdiffusion layers, displays the lowest interdiffusion coefficients among the diffusion couples without Ru addition. Furthermore, first-principles studies reveal that the addition of Ru increases the formation energies of point defects and defect clusters involved in elemental interdiffusion in stoichiometric NiAl, Ni-rich NiAl, and Ni3Al phases, particularly when Ru occupies the Al site of Ni3Al phases at high temperatures. The remarkable diffusion barrier effects of Ru in Ni-30Al coatings have the potential to significantly enhance their performance and broaden their application prospects.

Structure and Migration Mechanisms of Small Vacancy Clusters in Cu: A Combined EAM and DFT Study.

Voids in face-centered cubic (fcc) metals are commonly assumed to form via the aggregation of vacancies; however, the mechanisms of vacancy clustering and diffusion are not fully understood. In this study, we use computational modeling to provide a detailed insight into the structures and formation energies of primary vacancy clusters, mechanisms and barriers for their migration in bulk copper, and how these properties are affected at simple grain boundaries. The calculations were carried out using embedded atom method (EAM) potentials and density functional theory (DFT) and employed the site-occupation disorder code (SOD), the activation relaxation technique nouveau (ARTn) and the knowledge led master code (KLMC). We investigate stable structures and migration paths and barriers for clusters of up to six vacancies. The migration of vacancy clusters occurs via hops of individual constituent vacancies with di-vacancies having a significantly smaller migration barrier than mono-vacancies and other clusters. This barrier is further reduced when di-vacancies interact with grain boundaries. This interaction leads to the formation of self-interstitial atoms and introduces significant changes into the boundary structure. Tetra-, penta-, and hexa-vacancy clusters exhibit increasingly complex migration paths and higher barriers than smaller clusters. Finally, a direct comparison with the DFT results shows that EAM can accurately describe the vacancy-induced relaxation effects in the Cu bulk and in grain boundaries. Significant discrepancies between the two methods were found in structures with a higher number of low-coordinated atoms, such as penta-vacancies and di-vacancy absortion by grain boundary. These results will be useful for modeling the mechanisms of diffusion of complex defect structures and provide further insights into the structural evolution of metal films under thermal and mechanical stress.

Insights into structural and electronic properties of (LiH)n (n = 5–25) clusters: Density functional calculations

First principles calculations have been performed to analyze the structural and electronic properties of (LiH)n clusters by combining an artificial bee colony algorithm within the framework of Density Functional Theory (DFT). The structural analysis shows that with an increase in cluster size, the structural shape tends to become more amorphous in which the lithium (Li) atom occupies the central position, surrounded by hydrogen (H) atoms at the vertex sites. The bond length between Li and H was found to be 1.77–2.01 Å, which is in good agreement with the previous study. Through stability analysis, the calculated formation energy of LiH clusters increase from n = 5 through n = 25. The projected density of states was calculated and analyzed to get deeper insight of the electronic structure. The charge density distribution and results of density derived electrostatic and chemical (DDEC6) analysis revealed ionic bonding characteristics between Li and H atoms, and charge density difference analysis concludes electron transfers from Li to H atoms.

Unconventional energetics of small vacancy clusters in BCC high-entropy alloy Nb0.75ZrTiV0.5

The stability of small vacancy clusters including divacancy, trivacancy and tetravacancy has been studied in body-centered cubic high-entropy alloy Nb0.75ZrTiV0.5 in structures of random solid solution and short-range order by first-principles calculations and molecular dynamics simulations. Different from conventional body-centered cubic metals, the tightly bound configurations have a lower structural stability and are not preferred energetically in the studied high-entropy alloy. Instability of vacancy configurations leads to vacancy-atom exchanges that favor less compact configurations. The formation energy of small vacancy clusters is much smaller than its constituent elements of Nb and V due to the large structural adjustment induced by severe local lattice distortion. The difference in local lattice distortion and elemental arrangement in the vacancy neighborhood leads to significant site-to-site variation in vacancy cluster energy and configuration. The formation energy has a strong correlation with the local energy state of the vacancy configuration and the extent of structural relaxation. Compared to random solid solution, the structure of short-range order has a higher stability for the most compact cluster configurations and tends to have higher vacancy cluster formation energy. According to classical molecular dynamics simulations of cluster diffusion at high temperature, the studied high-entropy alloy has a higher probability of cluster dissociation compared to Nb and V. The unconventional energetics of small vacancy clusters is expected to have a profound impact on their generation, diffusion, dissociation, coalescence, as well as the defect microstructure evolution during irradiation.

Interactions of alloying Cr/Ti with substitutional solutes and self-interstitial atoms in vanadium

The interactions between alloying Ti/Cr and 14 substitutional solutes/self-interstitial atoms (SIAs) and stability of small interstitial Crm/Tim clusters and Ti/Cr-SIA mixed clusters in vanadium (V) were investigated by first-principles calculations. We calculated the binding energy between Cr/Ti and substitutional solute atoms (Al, Fe, Y, Ta, Cu, Mn, Ni, Nb, Mo, Zr, W, Si, S and P). The Ti can attract most substitutional solutes while Cr repel most of them. For two interstitials, the formation orders of stable configurations are <111>Cr-Cr, mixed <111>Cr-V, <111>SIA, mixed <111>Cr-Ti and <111>Ti-Ti dumbbells. For interstitial Crm, (Cr-Ti)m/2 and Tim clusters with m = 4–12, the most stable configurations are always the parallel 〈111〉 dumbbell, the formation energies of Cr clusters are lower than other clusters. Finally, we explored the interactions between two Cr/Ti atoms and <111>SIA dumbbell as well as the interactions between <111>Cr-Cr dumbbell and solutes. The Ti/Y/Zr/Nb/Ta solutes can attract <111>Cr-Cr dumbbell in similar with the cases of <111>SIA and <111>Cr-V, reducing the mobility of them.

Vacancy clustering behaviors and stable configurations in vanadium metal: First-principles investigations

• We calculate energetics and configurations of vacancy clusters with the size up to 30 in vanadium. • The average formation energies of vacancy clusters decrease with the size. • We determined the relationship between energetics of vacancy clusters and Wigner-Seitz area in vanadium. • We establish a model by machine learning to predict formation energies of vacancy clusters. The clustering behaviors and stable configurations of vacancies with the size up to 30 in vanadium were studied by first-principles investigations. The average formation energies per vacancy of vacancy clusters decreases with the sizes. When V n cluster with the odd size forms V n +1 cluster, the average formation energy per vacancy has a lager reduction relative to the case of even size. The stabilities of vacancy clusters increase with the sizes in terms of the total binding energy ( n =2-30), the incremental binding energies of vacancy clusters show an increasing trend of fluctuation with the sizes, which can be explained by both the size characteristics and terrace-ledge-kink model. We also estimated the relationship between vacancy formation/incremental binding energy and Wigner-Seitz area. Finally, we established a machine learning model based on Linear-SVM to predict formation energies of larger vacancy clusters. These results deepened the understanding of the formation and evolution of nanovoids in vanadium metal under irradiation.

A two-step optimization approach for structures investigation of Pd-Ir bimetallic nanoclusters

The structures of nanoalloys are crucial for understanding their catalytic performance because the stable structures can affect the activity and selectivity of nanocatalysts. Therefore, investigating the stable structures of nanoalloys is important to understand their catalytic activities. In this article, a two-step optimization approach by combining a basin hoping genetic algorithm (BHGA) and DFT calculation is employed to investigate the structural stability of Pd-Ir alloy nanoclusters. Different compositions (Pd and Ir atoms proportion) and different initial configurations of 38-atom Pd-Ir alloys are considered. The combination of BHGA and DFT method can effectively find the stable structures of truncated octahedral (TO) configurations for 38-atom Pd-Ir alloys with high accuracy and low time complexity. Furthermore, the formation energy and bond energy of Pd-Ir clusters are calculated and analyzed, the results show the bond strength follows Pd-Pd > Pd-Ir > Ir-Ir. The most stable configuration is Pd6Ir32 with all the core sites are occupied by Pd, which shows better electrochemical performance.

Thermodynamic analysis of nucleation of alcohol molecules with the varied alkyl chain length in nanoconfined solution

Combining the molecular dynamics (MD) simulations and the free-energy-based thermodynamic analysis, we analyze the role of alkyl chain length on the nucleation of alcohol molecules with the mono-hydroxyl in nanoconfined solution. The free energy formulae and thermodynamic equilibrium equation are parameterized by fitting the theoretical equilibrium equation to MD simulation results. We find that alcohol molecules with the varied alkyl chain length show different nucleation states, i.e., dispersion, reversible and aggregation states, corresponding to the total free energy Gconfine(n, N) with a single minimum at n∼ 1, two minima at n∼ 1 and N separated by a maximum, and a local minimum at n∼N, respectively. The alcohol molecule with a longer alkyl chain tends to aggregate into a cluster at a lower solute number in nanoconfined solution. Besides, the free energy of cluster formation in nanoconfined solution Gcluster(n) also depends on the alkyl chain length, and three regions can be identified: For the shorter alkyl chain, such as ethanol, there is no local maximum on Gcluster(n), indicating that alcohol molecules tend to be dispersed in water; For the intermediate alkyl chain length, such as 1-propanol, 1-butanol, 1-pentanol, and 1-hexanol, the critical nucleation number nc and nucleation barrier Gb monotonically decrease with the increase of alkyl chain length; For the longer alkyl chain, nc∼ 1 and Gb∼0kBT suggest that alcohol molecules, such as 1-heptanol, can aggregate into clusters easily. Our work deepens the understanding of the alkyl chain length effect on the nucleation behavior of alcohol molecules in nanoconfined solution.

Molecular Dynamics Simulations of Xe Behaviors at the Grain Boundary in UO2

In this study, we investigated the behavior of xenon (Xe) bubbles in uranium dioxide (UO2) grain boundaries using molecular dynamics simulations and compared it to that in the UO2 bulk. The results show that the formation energy of Xe clusters at the Σ5 grain boundaries (GBs) is much lower than in the bulk. The diffusion activation energy of a single interstitial Xe atom at the GBs was approximately 1 eV lower than that in the bulk. Furthermore, the nucleation and growth of Xe bubbles in the Σ5 GBs at 1000 and 2000 K were simulated. The volume and pressure of bubbles with different numbers of Xe atoms were simulated. The bubble pressure dropped with increasing temperature at low Xe concentrations, whereas the volume increased. The radial distribution function was computed to explore the configuration evolution of Xe bubbles. The bubble structures in the GB and bulk material at the same temperature were also compared. Xe atoms were more regular in the bulk, whereas multiple Xe atoms formed a planar structure at the GBs.

Formation of ice particles through nucleation in the mesosphere

Abstract. Observations of polar mesospheric clouds have revealed the presence of solid ice particles in the upper mesosphere at high latitudes; however, their formation mechanism remains uncertain. In this study, we investigated the formation process of ice particles through nucleation from small amounts of water vapor at low temperatures. Previous studies that used classical nucleation theory have shown that amorphous solid water particles can nucleate homogeneously at conditions that are present in the mesosphere. However, the rate predictions for water in classical nucleation theory disagree with experimental measurements by several orders of magnitude. We adopted a semi-phenomenological model for the nucleation process, which corrects the evaluation of the molecular cluster formation energy using the second virial coefficient, which agrees with both experiments and molecular dynamics simulations. To calculate the nucleation process, we applied atmospheric conditions for the temperature, pressure, numerical density of dust grains, and cooling rate. The results indicate that homogeneous water nucleation is extremely unlikely to occur in the mesosphere, while heterogeneous nucleation occurs effectively. Dust grains generated by meteor ablation can serve as nuclei for heterogeneous nucleation. We also showed that the ice can form directly in a crystalline state, rather than an amorphous state.

Theoretical study on the influence of Cr, Mo, and W alloying additions on the helium behavior in nickel

In nuclear reactors, the helium (He) production and retention from intensity particle irradiation can degrade the physical and mechanical properties of Ni-based alloys. Understanding the fundamental behaviors of He in metals is a critical issue in the development of nuclear materials. In this research, the influence of Cr/Mo/W additions on the stability, migration, and clustering of He in face-centered cubic (fcc) nickel were systematically studied by using density functional theory (DFT). The formation and binding energies show that Cr and Mo/W atoms affect the occupying priority of tetrahedral interstitial He in Ni lattice. The interstitial He prefers to occupy the first nearest neighbor octahedral site with the presence of Cr, while it would locate far away from Mo/W addition. For He migration around alloying elements, the barrier of interstitial He in NiCr is slightly higher than that of pure Ni, while NiMo and NiW systems have a relatively lower barrier. The effective diffusivity of interstitial He atom in Ni-based alloys significantly decreases with the increase of the temperature and Cr/Mo/W concentration. Moreover, when He aggregates at vacancy, the Cr/Mo/W can weaken the formation energy of He clusters and hamper their growth to larger sizes. All these results provide microscopic insights into Cr/Mo/W alloying effect on helium behaviors in Ni-based materials.

A theoretical study of the monolayer-protected gold cluster Au317(SR)110.

Significant efforts have been made to uncover the structures of monolayer-protected gold nanoclusters. However, the synthesis, crystallization, and structural analysis of gold nanoclusters with over 300 metal atoms is a grand challenge. In this work, a new gold nanocluster containing 317 gold atoms and 110 thiolate (SH) ligands (referred to as Au317(SH)110) is theoretically studied, which is larger in size than the formerly reported Au279(SR)84 cluster. The stability of the Au317(SH)110 cluster is studied based on calculations of the averaged cluster formation energy (Eave), indicating that Au317(SH)110 has good structural stability and that the SPhCOOH (p-MBA) ligand is a good candidate for stabilizing the cluster. The calculation of density of state and the time-dependent density functional theory (TD-DFT) calculations of the optical absorption properties show that Au317(SH)110 is in a metallic state.

Density Functional Theory Study of Metal and Metal-Oxide Nucleation and Growth on the Anatase TiO2(101) Surface

Experimental studies have shown the possible production of hydrogen through photocatalytic water splitting using metal oxide (MOy) nanoparticles attached to an anatase TiO2 surface. In this work, we performed density functional theory (DFT) calculations to provide a detailed description of the stability and geometry of MxOy clusters M = Cu, Ni, Co, Fe and Mn, x = 1–5, and y = 0–5 on the anatase TiO2(101) surface. It is found that unsaturated 2-fold-coordinated O-sites may serve as nucleation centers for the growth of metal clusters. The formation energy of Ni-containing clusters on the anatase surface is larger than for other M clusters. In addition, the Nin adsorption energy increases with cluster size n, which makes the formation of bigger Ni clusters plausible as confirmed by transition electron microscopy images. Another particularity for Ni-containing clusters is that the adsorption energy per atom gets larger when the O-content is reduced, while for other M atoms it remains almost constant or, as for Mn, even decreases. This trend is in line with experimental results. Also provided is a discussion of the oxidation states of M5Oy clusters based on their magnetic moments and Bader charges and their possible reduction with oxygen depletion.

Machine-learning interatomic potential for radiation damage effects in bcc-iron

We introduce a machine-learning interatomic potential for bcc iron based on the moment tensor potential framework and a hybridization scheme of distinct sub-potentials. With an orientation on radiation damage effects, the potential shows good transferability from properties relevant to collision cascade to those relevant to plasticity. Specifically, the potential accurately reproduces the short-range repulsive interactions, the generalized stacking fault energies, the dislocation core structures and the formation energies of defect clusters. The general purposed applicability of the potential enables simulation of radiation damage effects in bcc iron with an accurate and an unprecedentedly unified theoretical model.

Synergistic Effect of FeNi Bimetallic Clusters for the Catalytic of Hydrogen Dissociation and Desorption: A Density Functional Theory Study

Cognition to the metal-metal interactions is of vital importance for the catalytic process and would help exploring novel catalysts. In the present study, the model system of FexNiy (x + y = 6) bimetallic clusters was utilized to study how metal-metal interactions influence the catalytic performance. The formation energies of different FeNi clusters, the hydrogen chemisorption energies together with the maximum hydrogen capacity and the saturated hydrogen atoms desorption energies were calculated. Bimetallic clusters exhibit a superior performance than pure clusters. Especially, Fe2Ni4 cluster has the highest hydrogen loading capacity, the most facile hydrogen molecule dissociation activation energy barrier and the lowest hydrogen atom desorption energy, suggesting that it is easier to dissociate H2 and release the H atoms. As a consequence, by adjusting appropriate metal/metal ratios, it is possible to design bimetallic catalysts with excellent catalytic performance.

Vacancy-cluster and off-lattice metal-atom diffusion mechanisms in transition metal carbides

Using ab initio simulations, we report potential metal atom diffusion mechanisms in the group IVB and VB transition metal carbides. By computing the metal vacancy formation energies of vacancy clusters, we find that a metal vacancy surrounded by six carbon vacancies is the lowest metal vacancy formation energy structure for the group IVB carbides while the lowest energy for the group VB carbides is a metal vacancy surrounded by two carbon vacancies. The vacancy cluster mechanisms reveal activation energies that are consistent with experiments in both TiC (group IVB) and TaC (group VB). We also report that an off-lattice diffusion mechanism, that is only energetically favorable in the group IVB transition metal carbides, has a lower formation energy than the regular vacancy cluster mechanism. This new mechanism shows lower formation energies for a given carbon vacancy concentration which indicates this off-lattice mechanism might be the most dominant metal-atom diffusion mechanism among the existing mechanisms proposed for the group IVB metal carbides.

Towards understanding the trapping, migration and clustering of He atoms in W–Ta alloy

We investigated the properties of He defects, the migration of a single He atom and the formation of He clusters in W–Ta (atomic ratio 1:1) alloy via first-principles density functional theory calculations. Results showed that He most preferred to occupy the substitutional site first and then the tetrahedral and octahedral interstitial sites . The formation energies of interstitial He in W–Ta alloy are between in bulk W and Ta. While the formation energies of substitutional He in W–Ta alloy were higher than those in bulk W and Ta. Structural relaxation and energy calculations revealed that the formation energies of He clusters linearly increased with cluster size. The binding energies of even-numbered He clusters were lower than those of their neighbouring odd-numbered He clusters. The migration calculation showed that the energy of Sub Ta was lower, and it had stronger attraction to He atom. Density of state and electronic structure were analysed to reveal the underlying mechanisms governing cluster formation. Results demonstrated that the hybridizations of p -projected DOS of He and its neighbouring metal atoms were responsible for the site-preference order of He in DOS. Moreover, the differences in charge density between He and W(Ta) were negative under all conditions, suggesting the repulsive interaction of He and W(Ta) in W–Ta alloy. This study provides a good reference for evaluating the influence of He on the performance of W–Ta alloy for plasma-facing materials.

First-principle calculations of vacancy clustering in zirconium-based alloys

In this article we study stability of small vacancy clusters in zirconium-based Zr−Nb and Zr−Sn alloys with small concentration of alloying additions in the framework of ab-initio calculations. By varying the distance between solute and vacancy cluster we discuss formation energy of vacancy clusters of different size and the binding energy between solute and vacancy clusters in order to analyze an ability of alloying element to localize small vacancy clusters containing different number of vacancies. We discuss a change in both vacancy cluster formation and vacancy-cluster binding energies with an increase in the number of vacancies in a cluster. This study provides insight into details of the effect of alloying elements for vacancies clustering in zirconium-based alloys.

Shape transition and coalescence of Au islands on Ag (110) by molecular dynamics simulation.

We have used molecular dynamics simulations based on many body semi-empirical potentials described by the embedded atom method, to analyze and understand the diffusion and coalescence phenomena of Au-clusters during the heteroepitaxial growth on Ag (110) surface. Temperature ranging from 300 to 700K were considered. In this study, we examined the heterogeneous system Aun/Ag(110), where n is the number of atoms in each cluster/island (withn = 15, ….35). Our results show that the clusters diffuse on the Ag (110) surface via different diffusion processes, namely, the exchange mechanism and the simple jump, which generate a 2D to 3D transition. Formation and adsorption energies of clusters with different sizes have been computed using static simulations. The dynamic study of coalescence for two islands of system Au15; Au0 - 9/Ag(110) at different temperatures makes it possible to deduce the detail of cluster shape and the influence of its temperature on the stability of the system and its growth during this evolution.

Accurate prediction of vacancy cluster structures and energetics in bcc transition metals

Knowledge on structures and energetics of vacancy clusters is fundamental to understand defect evolution in metals. Yet there remain no reliable methods able to determine essential structural details or to provide accurate assessment of energetics for general vacancy clusters. Here, we performed systematic first-principles investigations to examine stable structures and energetics of vacancy clusters in bcc metals, explicitly demonstrated the stable structures can be precisely determined by minimizing their Wigner-Seitz area, and revealed a linear relationship between formation energy and Wigner-Seitz area of vacancy clusters. We further developed a new physics-based model to accurately predict stable structures and energetics for arbitrary-sized vacancy clusters. This model was well validated by first-principles calculations and recent vacancy cluster annealing experiments, and showed distinct advantages over the widely used spherical approximation. The present work offers mechanistic insights that crucial for understanding vacancy cluster formation and evolution, provides crucial benchmarks for assessing empirical interatomic potentials, and enables a critical step towards predictive control and prevention of vacancy cluster related damage processes in structural metals.