First-principles calculation of the Ag-Cu phase diagram

First-principles thermodynamic investigation on the α phases in TiO and TiNb binary system

O and Nb are two representative alloying elements of Ti to form high-temperature and corrosion resistance α Ti alloys. The investigation on the thermodynamic characteristics of α Ti-O and Ti-Nb has attracted much attention in recent years. However, in this regard, a satisfied experimental technique or modeling scheme is still yet to be developed due to the appearance of a variety of oxides in Ti-O and the mechanical instability present in Ti-Nb. Herein, we combined first-principles calculations with the cluster expansion method to investigate the ground-state characteristics for α Ti-O and α Ti-Nb systems. The atomic bonding interactions in these two systems were first revealed based on the calculated electronic structures. Afterward, the Debye-Grüneisen model and Monte Carlo simulations were employed together to investigate the thermodynamic properties of α phases in these two systems, and the effect of vibrational entropy on the order-disorder transition temperatures of the phases in α Ti-O system was first examined. A good agreement with experimentally reported phase boundaries is obtained in the Ti-Nb system by handling the mechanical instabilities introduced by the highly distorted structures. In addition, the cluster expansion coefficients for the Ti-O and Ti-Nb system offer a good starting point to investigate the phase equilibrium in Ti-Nb-O ternary alloy. We also believe the insights provided here would be helpful for those who would like to seek an efficient scheme they are confident with to investigate the phase thermodynamic properties of other hcp Ti-based alloys.

Study on liquid-like SiGe cluster growth during co-condensation from supersaturated vapor mixtures by molecular dynamics simulation

Based on the co-condensation processes in the Si-Ge system upon cooling, as determined by molecular dynamics (MD) simulation, we explored the mixed cluster growth dynamics and structural properties leading to the synthesis of liquid-like SiGe nanoclusters. The results indicated that the cluster size quickly increased to large clusters by the coalescence of transient small clusters in the growth stage during co-condensation. The transient clusters at different temperatures were verified to have slightly Si-rich compositions and liquid-like structures. The coalescence of such nanoclusters at high temperatures led to spherical clusters with homogeneous intermixing. However, irregularly shaped clusters with attached mixed parts were obtained owing to incomplete coalescence at low temperatures. Ge atoms tended to move to the cluster surface to exploit their energetically favorable state during the restructuring process, leading to slightly Ge-rich components on the cluster surface. The degree of intermixing for SiGe nanoclusters was related to cluster size. Generally, small clusters appeared to be more segregated during restructuring.

Finite-Temperature Structures of Supported Subnanometer Catalysts Inferred via Statistical Learning and Genetic Algorithm-Based Optimization

Single-atom catalysts (SACs) minimize noble metal utilization and can alter the activity and selectivity of supported metal nanoparticles. However, the morphology of active centers, including single atoms and subnanometer clusters of a few atoms, remains elusive due to experimental challenges. The computational cost to describe numerous cluster shapes and sizes makes direct first-principles calculations impractical. We present a computational framework to enable structure determination for single-atom and subnanometer cluster catalysts. As a case study, we obtained the low-energy structures of Pd_n (n = 1-21) clusters supported on CeO₂(111), which are critical components of automobile three-way catalysts. Trained on density functional theory data, a three-dimensional cluster expansion is established using statistical learning to describe the Hamiltonian and predict energies of supported Pd_n clusters of any structure. Low-energy stable and metastable structures are identified using a Metropolis Monte Carlo-based genetic algorithm in the canonical ensemble at 300 K. We observe that supported single atoms sinter to form bilayer clusters, and large cluster isomers share similarities in both shape and energy. The findings elucidate the significance of the support and microstructure on cluster stability. We discovered a simple surrogate structure-energy model, where the energy per atom scales with the square root of the average first coordination number, which can be used to estimate energies and compare the stability of clusters. Our framework, applicable to any metal/support system, fills an important methodological gap to predict the stability of supported metal catalysts in the subnanometer regime.

Efficient determination of solid-state phase equilibrium with the multicell Monte Carlo method

Building on our previously introduced multicell Monte Carlo (MC)^{2} method for modeling phase coexistence, this paper provides important improvements for efficient determination of phase equilibria in solids. The (MC)^{2} method uses multiple cells, representing possible phases. Mass transfer between cells is modeled virtually by solving the mass balance equation after the composition of each cell is changed arbitrarily. However, searching for the minimum free energy during this process poses a practical problem. The solution to the mass balance equation is not unique away from equilibrium, and consequently the algorithm is in risk of getting trapped in nonequilibrium solutions. Therefore, a proper stopping condition for (MC)^{2} is currently lacking. In this work, we introduce a consistency check via a predictor-corrector algorithm to penalize solutions that do not satisfy a necessary condition for equivalence of chemical potentials and steer the system toward finding equilibrium. The most general acceptance criteria for (MC)^{2} is derived starting from the isothermal-isobaric Gibbs ensemble for mixtures. Using this ensemble, translational MC moves are added to include vibrational excitations as well as volume MC moves to ensure the condition of constant pressure and temperature entirely with a MC approach, without relying on any other method for relaxation of these degrees of freedom. As a proof of concept the method is applied to two binary alloys with miscibility gaps and a model quaternary alloy, using classical interatomic potentials.

Band Edge Optical Excitation of Pyridine-Adsorbed CuAg Nanoparticles

Understanding the structure-property relationship of multielement nanoparticles is vital for developing novel nanodevices. In the present paper, via a combination of a basin hopping global sampling method, a symmetry-orbit shell optimization technique, and density functional theory reoptimizations, we determine the energetically most stable CuAg face-centered cubic nanoparticles. The calculated structures show a clear tendency toward Cu_coreAg_shell chemical ordering by populating the more cohesive Cu in the core region and of Ag in the shell region. Further, using time-dependent density functional theory (TDDFT) calculations, we analyze the band edge optical excitations of the nanoparticles with pyridine molecule on top. With the help of charge difference density plots, we found dramatic modifications in the electron density distribution of the nanoparticles. We believe that the present theoretical findings will be useful for the development of novel nanosensors.

Nanoalloy electrocatalysis: simulating cyclic voltammetry from configurational thermodynamics with adsorbates

Simulated 2-dimensional cyclic voltammetry for nanoalloys with a hybrid ensemble scheme in Monte Carlo simulation based on the cluster expansion method.

Configurational thermodynamics of alloyed nanoparticles with adsorbates

Changes in the chemical configuration of alloyed nanoparticle (NP) catalysts induced by adsorbates under working conditions, such as reversal in core-shell preference, are crucial to understand and design NP functionality. We extend the cluster expansion method to predict the configurational thermodynamics of alloyed NPs with adsorbates based on density functional theory data. Exemplified with PdRh NPs having O-coverage up to a monolayer, we fully detail the core-shell behavior across the entire range of NP composition and O-coverage with quantitative agreement to in situ experimental data. Optimally fitted cluster interactions in the heterogeneous system are the key to enable quantitative Monte Carlo simulations and design.

Phase Stability and Diagrams from First Principles

First principles theories of alloy phase equilibrium have been successfully used in recent years to compute temperature-composition phase diagrams for solid state phases. One particular approach, originating with the successful phenomenological Ising models to describe the alloy Hamiltonian, uses a cluster expansion of the configurational energy in terms of short-ranged pair and many-body interactions. The approach is deeply rooted in our ability to compute accurate total energies of relatively complex compounds, using density functional theory in the local approximation, from which effective interactions may be obtained. Fundamental aspects of the method which include convergence of the cluster expansion, treatment of the configurational entropy and description of vibrational modes are reviewed. Applications of the theory are given for binary alloys in the Ru-Zr-Nb system using the Linear Muffin Tin Orbital method for the total energy calculations, the Cluster Variation method for the description of the configurational entropy, and the Debye-Gruneisen approximation for the vibrational modes. The results are used to compute the equilibrium phase diagram for the Zr-Nb system and to assess current experimental data on phase stability in the Ru-Nb system. In the latter case, the calculations indicate that the DO19 structure is a likely candidate structure for the experimentally observed hexagonal-based compound Ru3Nb. Investigation of the energies and interactions of tetragonal structures as a function of the c/a ratio suggest the L10 structure as a likely candidate for the observed tetragonal phase near 1:1 stoichiometry.