First-principles Molecular Dynamics Research Articles

Atomic Structure of Glassy GeTe4 as a Playground to Assess the Performances of Density Functional Schemes Accounting for Dispersion Forces.

The atomic structure of glassy GeTe4 is obtained in the framework of first-principles molecular dynamics (FPMD) by considering five different approaches for the description of the electronic structure within density functional theory (DFT). Among these schemes, one is not corrected by accounting for the dispersion forces and it is based on the BLYP exchange-correlation (XC) functional, while all of the others consider the dispersion forces according to different theoretical strategies. In particular, by maintaining the BLYP expression for the XC functional, two of them (BLYP-D2 and BLYP-D3) exploit the Grimme expressions for the dispersion forces, while the fourth scheme is based on the maximally localized Wannier functions (MLWFs). Finally, we also considered the rVV10 functional constructed to include seamlessly the dispersion part. Our results point out the better performances of BLYP-D3 and MLWF in terms of comparison with experimental data for the total pair correlation functions, with BLYP-D2 and rVV10 being closer to the uncorrected BLYP data. The implications of such findings are discussed by considering the overall limited impact of dispersion forces on the atomic structure of glassy GeTe4.

Static and dynamic ionic structure of molten CaCl2 via first-principles molecular dynamics simulations

Molten CaCl2 could further broaden and open up new solar power applications due to its high melting point and chemical stability. However, few studies have focused on the ionic structure of molten CaCl2 with the experimental limitations such as extremely high temperature, high corrosiveness, and water absorbency, so that static and dynamic structure of molten CaCl2 has not been well understood. In this work, the static and dynamic ionic structure of molten salts was investigated by conducting first-principles molecular dynamics simulations. Structural features like short-range order and intermediate-range order are observed in molten CaCl2. The 6-coordinated structure stays dominant in the CaCl2 melt among the temperature range of 1100–1500 K. The network structure is filled with distorted octahedron which tends to be rutile structure, and these octahedrons are linked via corner-sharing and edge-sharing models. Among the temperature range of 1100–1500 K, the increase of temperature can accelerate the movement of ions, but there is no obvious effect on the local ionic structure of molten CaCl2. Analysis in this paper may be supportive to fill the gap in understanding the ion behavior of molten CaCl2 and other divalent chlorides.

Stability of CH4, CO2, and H2S in two-dimensional clathrate hydrates

The stability of CH4, CO2, and H2S in four two-dimensional hydrates, denoted as 2D-I, 2D-II, 2D-III, and 2D-IV, was investigated by the first-principle calculations and molecular dynamics simulations. The result shows that two-dimensional CH4 hydrates are thermodynamically and dynamically stable. CO2 can only form the 2D-I and 2D-II hydrates, while these structures are dynamically unstable. Four two-dimensional H2S hydrates are thermodynamically stable, but only the 2D-I structure is dynamically stable. Further, simulation result suggests that the stability of the two-dimensional hydrate can be increased at low temperatures or in the confined environments (for example, nano-slits). As for the 2D-I binary hydrate, its thermodynamic stability is in between two corresponding pure hydrates, and only the CH4-H2S binary hydrate is dynamically stable. The CH4-CO2-H2S ternary hydrate is dynamically unstable because of the overflow of CO2.

First-principles molecular dynamics study for S[formula omitted]O bond dissociation of sulfolane on Li-metal negative electrode

Sulfolane (SL) has attracted a great deal of interest as an electrolyte solvent in Li-metal batteries owing to its suitable properties. In this study, we performed a first-principles molecular dynamics simulation involving an Li metal | LiBF4-SL liquid interface. It was found that two S−O bonds of SL preferentially dissociate on the Li surface, while decomposition of BF4 was not observed. Since the dissociated O atoms dissolved into the Li surface, our results indicate that an Li-oxide layer formed on the Li surface, which suggests that a preferable performance of the Li-metal negative electrode can be expected for this system.

First-principles investigations of the pressure-induced phase transformations and properties of crystalline and amorphous AlN

One-step first principles molecular-dynamics (FPMD) simulations were carried out to investigate structural transformations in wurtzite-type AlN under compression and decompression. The hexagonal transformation path $P{6}_{3}mc\text{\ensuremath{-}}P{6}_{3}/mmc\text{\ensuremath{-}}Cmmm\text{\ensuremath{-}}Fm\overline{3}m$ was identified during compression at $P=50$ GPa and $T=500$ K. The inversion of this path of transformation was established at the decompression of compressed rock-salt AlN at 1500 K. The plausible origin of these transformations is established. The occurrence of intermediate and metastable phases was predicted by taking into account their dynamical and elastic instability, and for this purpose, phonon spectra and elastic constant calculations were performed. FPMD simulations were used to generate amorphous AlN and to investigate its behavior under pressure. The sequence of phase transitions: low-density amorphous---high-density amorphous---rock-salt type was revealed at $P=40$ GPa, and the thermodynamic and mechanical properties of crystalline and amorphous AlN were compared. It was found that the one-step FPMD simulations is a viable scheme to predict phase transitions in crystalline and amorphous AlN with higher precision compared with other FPMD approaches with step-wise pressure changes.

Validating first-principles molecular dynamics calculations of oxide/water interfaces with x-ray reflectivity data

Metal oxide/water interfaces play a crucial role in many electrochemical and photocatalytic processes, such as photoelectrochemical water splitting, the creation of fuel from sunlight, and electrochemical $\mathrm{C}{\mathrm{O}}_{2}$ reduction. First-principles electronic structure calculations can reveal unique insights into these processes, such as the role of the alignment of the oxide electronic energy levels with those of liquid water. An essential prerequisite for the success of such calculations is the ability to predict accurate structural models of these interfaces, which in turn requires careful experimental validation. Here we report a general, quantitative validation protocol for first-principles molecular dynamics simulations of oxide/aqueous interfaces. The approach makes direct comparisons of interfacial x-ray reflectivity (XR) signals from experimental measurements and those obtained from ab initio simulations with semilocal and van der Waals functionals. The protocol is demonstrated here for the case of the ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}(001)$/water interface, one of the simplest oxide/water interfaces. We discuss the technical requirements needed for validation, including the choice of the density functional, the simulation cell size, and the optimal choice of the thermodynamic ensemble. Our results establish a general paradigm for the validation of structural models and interactions at solid/water interfaces derived from first-principles simulations. While there is qualitative agreement between the simulated structures and the experimental best-fit structure, direct comparisons of simulated and measured XR intensities show quantitative discrepancies that derive from both bulk regions (i.e., alumina and water) as well as the interfacial region, highlighting the need for accurate density functionals to properly describe interfacial interactions. Our results show that XR data are sensitive not only to the atomic structure (i.e., the atom locations) but also to the electron-density distributions in both the substrate and at the interface.

First-principles adaptive-boost accelerated molecular dynamics simulation with effective boost potential construction methods: a study of Li diffusion in Si crystal

First-principles molecular dynamics (FPMD) simulation is a powerful tool for studying the mechanical, chemical, and thermal properties of materials. However, because of the fundamental time-scale limitation of molecular dynamics and the high computational cost of density functional theory, many of the rare events that dominate these properties cannot be directly investigated. Several methods of accelerating FPMD calculations have been developed to analyze these rare events, but to the best of the authors’ knowledge, no quantitative computation of event rate and activation free energy has been achieved. Here, we have developed an accelerated FPMD based on FPMD and the adaptive boost method (Ishii et al. Phys. Rev. B 85, 064303 (2012)), which remove the fundamental drawback of FPMD: time-scale limitation. We also propose a novel boost potential construction algorithms that allows an accurate boost potential to be constructed with a limited number of FPMD samplings. In this study, to confirm the validity of the method, we compute the diffusion of a Li atom in a Si crystal. The temperature-dependent diffusivity was obtained and the activation enthalpy was calculated from an Arrhenius plot and compared with reported experimental diffusivities.

Oxygen depletion in FLASH ultra-high-dose-rate radiotherapy: A molecular dynamics simulation.

We present a first-principles molecular dynamics (MD) simulation and expound upon a mechanism of oxygen depletion hypothesis to explain the mitigation of normal tissue injury observed in ultra-high-dose-rate (UHDR) FLASH radiotherapy. We simulated damage to a segment of DNA (also representing other biomolecules such as RNA and proteins) in a simulation box filled with O and molecules. Attoseconds physical interactions (ionizations, electronic, and vibrational excitations) were simulated by using the Monte Carlo track structure code Geant4-DNA. Immediately after ionization, ab initio Car-Parrinello molecular dynamics (CPMD) simulation was used to identify which O and molecules surrounding the DNA molecule were converted into reactive oxygen species (ROS). Subsequently, the femto- to nanosecond reactions of ROS were simulated by using MD with reactive force field (ReaxFF), to illustrate ROS merging into new types of non-reactive oxygen species (NROS) due to strong coupling among ROS. A coarse-grained model was constructed to describe the relevant collective phenomenon at the macroscopic level on ROS aggregation and formation of NROS agglomerates consistent with the underlying microscopic pathways obtained from MD simulations. Time-dependent molecular simulations revealed the formation of metastable and transient spaghetti-like complexes among ROS generated at UHDR. At the higher ROS densities produced under UHDR, stranded chains (i.e., NROS) are produced, mediated through attractive electric polarity forces, hydrogen bonds, and magnetic dipole-dipole interactions among hydroxyl radicals. NROS tend to be less mobile than cellular biomolecules as opposed to the isolated and sparsely dense ROS generated at conventional dose rates (CDR). We attribute this effect to the suppression of biomolecular damage induced per particle track. At a given oxygen level, as the dose rate increases, the size and number of NROS chains increase, and correspondingly the population of toxic ROS components decreases. Similarly, at a given high dose rate, as the oxygen level increases, so do the size and number of NROS chains until an optimum level of oxygen is reached. Beyond that level, the amount of oxygen present may be sufficient to saturate the production of NROS chains, thereby reversing the sparing effects of UHDRs. We showed that oxygen depletion, hypothesized to lead to lower normal-tissue toxicity at FLASH dose rates, takes place within femto- to nanoseconds after irradiation. The mechanism is governed by the slow dynamics of chains of ROS complexes (NROS). Under physoxic (≈ 4-5% oxygen) conditions (i.e., in normal tissues), NROS are more abundant than in hypoxic conditions (e.g., <0.3% in parts of tumors), suggesting that biomolecular damage would be reduced in an environment with physoxic oxygen levels. Hence irradiation at UHDRs would be more effective for sparing physoxic normal tissues but not tumors containing regions of hypoxia. At much higher levels of oxygen (e.g., >10-15%), oxygen depletion by UHDRs may not be sufficient for tissue sparing.

Buckling of boron nanotubes under axial compression: Insights from molecular mechanics and continuum mechanics

The buckling behaviours of boron nanotubes (BNTs) are investigated in this paper by using molecular structural mechanics (MSM) simulations and elastic shell models. Two types of BNTs (α and χ-BNTs) whose structures are proven to be thermally stable in first-principles molecular dynamics simulations are considered in the study. Our MSM results show a shell-to-column buckling mode transition occurring in BNTs with increasing aspect ratio. The critical buckling force of the column buckling of long BNTs significantly decreases as the aspect ratio grows, while that of the shell buckling of short BNTs is almost independent of the aspect ratio. MSM simulations also show that α and χ-BNTs both have anisotropic elastic properties. As a result, the simple Donnell shell model previously employed in other tubular nanomaterials becomes inapplicable in describing the buckling behaviours of the present BNTs. Under this circumstance, we propose an orthotropic elastic shell model to consider the anisotropy of elastic properties in the continuum mechanical modelling of BNTs. Through the orthotropic elastic shell model, the buckling behaviours of α and χ-BNTs are found to have different relations with their chirality, which is attributed to different anisotropy features observed in the elastic properties of these two BNTs.

Tuning CO2 Capture at the Gas/Amine Solution Interface by Changing the Solvent Polarity.

Carbon dioxide scrubbing by aqueous amine solution is considered as a promising technology for post-combustion CO2 capture, while mitigating climate change. The lack of physicochemical details for this process, especially at the interface between the gas and the condensed phase, limits our capability in designing novel and more cost-effective scrubbing systems. Here, we present classical and first-principles molecular dynamics results on CO2 capture at the gas/amine solution interfaces using solvents of different polarities. Even if it is apolar, carbon dioxide is absorbed at the gas/monoethanolamine (MEA) aqueous solution interface, forming stable and interfacial [CO2·MEA] complexes, which are the first reaction intermediate toward the chemical conversion of CO2 to carbamate ions. We report that the stability of the interfacial [CO2·MEA] precomplex depends on the nature and polarity of the solution, as well as on the conformer population of MEA. By changing the polarity of the solvent, using chloroform, we observed a shift in the interfacial MEA population toward conformers that form more stable [CO2·MEA] complexes and, at the same time, a further stabilization of the complex induced by the solvent environment. Thus, while lowering the polarity of the solvent could decrease the solubility of MEA, at the same time, it favors conformers that are more prone to CO2 capture and mineralization. The results presented here offer a theoretical framework that helps in designing novel and more cost-effective solvents for CO2 scrubbing systems, while shedding further light on the intrinsic reaction mechanisms of interfacial environments in general.

Molecular Dynamics Simulations of Molten Magnesium Chloride Using Machine‐Learning‐Based Deep Potential

AbstractIn previous work, molten magnesium chloride has been investigated using first‐principles molecular dynamics (FPMD) simulations based on density functional theory (DFT). However, such simulations are computationally intensive and therefore are restricted in terms of simulated size and time. In this work, a machine learning‐based deep potential (DP) is trained to accelerate the molecular dynamics simulation of molten magnesium chloride. The trained DP can accurately describe the energies and forces with the prediction errors in energy and force being 1.76 × 10−3 eV/atom and 4.76 × 10−2 eV Å−1, respectively. Applying the deep potential molecular dynamics (DPMD) approach, simulations can be performed with more than 1000 atoms, which is infeasible for FPMD simulations. Additionally, the partial radial distribution functions, angle distribution functions, densities, and self‐diffusion coefficients predicted by DPMD simulations are also in reasonable agreement with FPMD or experimental results. This work shows that the DP enables higher efficiency and similar accuracy relative to DFT, exhibiting a bright application prospect in modeling molten salt systems.

LaO1.5 surface modification of titanium-substituted hydroxyapatite photocatalyst and effects on 2-propanol photocatalytic decomposition mechanisms

After using impregnation to prepare LaO1.5 cluster modified titanium-substituted hydroxyapatites (Ti-HAps), photocatalytic decomposition activity on gaseous 2-propanol (IPA) under UV illumination was increased by three times through LaO1.5 modification while preserving its high adsorption capability for organic compounds. First-principles molecular dynamics simulations and electronic structure investigations revealed that photo-excited electron transfer from Ti to La does not occur in LaO1.5-modified Ti-HAp. Rather, the results implied that its photocatalytic activity increase is related to gaseous IPA and O2 adsorption properties. The IPA dissociative adsorption at Ca sites was observed in LaO1.5-modified Ti-HAp. The obtained electronic structure suggests that the adsorbed IPA molecule can be oxidized easily and directly. Moreover, O2 molecule adsorption and desorption were observed, which implies charge recombination suppression and that O2●- radical can be involved in IPA decomposition. Results demonstrate that control of the adsorption properties of target molecules by cluster modification can enhance photocatalytic decomposition activity.

Bathochromic Shift in the UV-Visible Absorption Spectra of Phenols at Ice Surfaces: Insights from First-Principles Calculations.

Some organic pollutants in snowpacks undergo faster photodegradation than in solution. One possible explanation for such effect is that their UV-visible absorption spectra are shifted toward lower energy when the molecules are adsorbed at the air-ice interface. However, such bathochromic shift is difficult to measure experimentally. Here, we employ a multiscale/multimodel approach that combines classical and first-principles molecular dynamics, quantum chemical methods, and statistical learning to compute the light absorption spectra of two phenolic molecules in different solvation environments at the relevant thermodynamic conditions. Our calculations provide an accurate estimate of the bathochromic shift of the lowest-energy UV-visible absorption band when these molecules are adsorbed at the air-ice interface, and they shed light into its molecular origin.

Chemical and Structural Variety in Sodium Thioarsenate Glasses Studied by Neutron Diffraction and Supported by First-Principles Simulations.

Sodium-conducting sulfide glasses are promising materials for the next generation of solid-state batteries. Deep insight into the glass structure is required to ensure a functional design and tailoring of vitreous alloys for energy applications. Using pulsed neutron diffraction supported by first-principles molecular dynamics, we show a structural diversity of Na2S-As2S3 sodium thioarsenate glasses, consisting of long corner-sharing (CS) pyramidal chains CS-(AsSS2/2)k, small AspSq rings (p + q ≤ 11), mixed corner- and edge-sharing oligomers, edge-sharing (ES) dimers ES-As2S4, and isolated (ISO) pyramids ISO-AsS3, entirely or partially connected by sodium species. Polysulfide S-S bridges and structural units with homopolar As-As bonds complete the glass structure, which is basically different from structural motifs predicted by the equilibrium phase diagram. In contrast to superionic silver and sodium sulfide glasses, characterized by a significant population of isolated sulfur species Siso (0.20 < Siso/Stot < 0.28), that is, sulfur connected to only mobile cations M+ with a usual M/Siso stoichiometry of 2, poorly conducting Na2S-As2S3 alloys exhibit a modest Siso fraction of 6.2%.

Catalytic Mechanism of Liquid-Metal Indium for Direct Dehydrogenative Conversion of Methane to Higher Hydrocarbons.

There is a great interest in direct conversion of methane to valuable chemicals. Recently, we reported that silica-supported liquid-metal indium catalysts (In/SiO2) were effective for direct dehydrogenative conversion of methane to higher hydrocarbons. However, the catalytic mechanism of liquid-metal indium has not been clear. Here, we show the catalytic mechanism of the In/SiO2 catalyst in terms of both experiments and calculations in detail. Kinetic studies clearly show that liquid-metal indium activates a C–H bond of methane and converts methane to ethane. The apparent activation energy of the In/SiO2 catalyst is 170 kJ mol–1, which is much lower than that of SiO2, 365 kJ mol–1. Temperature-programmed reactions in CH4, C2H6, and C2H4 and reactivity of C2H6 for the In/SiO2 catalyst indicate that indium selectively activates methane among hydrocarbons. In addition, density functional theory calculations and first-principles molecular dynamics calculations were performed to evaluate activation free energy for methane activation, its reverse reaction, CH3–CH3 coupling via Langmuir–Hinshelwood (LH) and Eley–Rideal mechanisms, and other side reactions. A qualitative level of interpretation is as follows. CH3–In and H–In species form after the activation of methane. The CH3–In species wander on liquid-metal indium surfaces and couple each other with ethane via the LH mechanism. The solubility of H species into the bulk phase of In is important to enhance the coupling of CH3–In species to C2H6 by decreasing the formation of CH4 though the coupling of CH3–In species and H–In species. Results of isotope experiments by combinations of CD4, CH4, D2, and H2 corresponded to the LH mechanism.

Intrinsic molecular vibration and rigorous vibrational assignment of benzene by first-principles molecular dynamics

Vibrational assignment, which establishes the correspondence between vibrational modes and spectral frequencies, is a key step in any spectroscopic study. Due to the lack of experimental technique to directly observe the thermal vibration of atoms, the assignment is usually done by empirical trial-and-error method with considerable uncertainty. Here we demonstrate a successful study of intrinsic molecular vibration property based on first-principles molecular dynamics trajectory. A unified approach for calculating and assigning vibrational frequencies is developed and applied to solve some historical issues of benzene vibration. As a major achievement, the experimental frequencies of benzene a2g and b2u vibrations are reassigned, which breaks a deadlock in contemporary spectroscopic science and removes a cloud over the application of density-functional theory in organic chemistry. This work paves the way for the comprehensive realization of the first-principles spectroscopic research, and provides crucial clues to solve the century-old problems of Kekule resonance, π-deformation, and aromaticity.

Lithium Cluster Segregation in Coherent Contraction Twin Boundaries of Magnesium Alloys

Modification of twin boundaries has been deemed as a potential strategy to achieve high strength in combination with good ductility for many engineering alloys. Herein, we report a unique Li cluster segregation phenomenon in coherent contraction twin boundaries of Mg alloys. The structures at the atomic scale have been investigated by transmission electron microscopy. Meanwhile, the driving force for segregation and strengthening mechanisms have been elucidated by first-principles calculations and molecular dynamics simulations, respectively. Experimental results show that the segregated Li cluster with a hexagonal close-packed structure is coherent with a contraction twin. Subsequently, theoretical calculations reveal that the Li cluster is prone to occupy the interface vacancy in the contraction twin boundaries, following which it grows along the twin boundaries preferentially. Finally, both dynamics simulations and experimental observations demonstrate that the formation of Li cluster in contraction twin boundaries can not only directly pin dislocation movement analogous to precipitation strengthening, but also improve the critical shear strain of contraction twin boundaries, inhibiting their deformation or widening. The finding of cluster segregation in twin boundaries also occurs in other systems, which might open an avenue for twin boundary engineering to tune the mechanical properties of metals and ceramics.

A parallel strategy for density functional theory computations on accelerated nodes

Using the Löwdin orthonormalization of tall-skinny matrices as a proxy-app for wavefunction-based Density Functional Theory solvers, we investigate a distributed memory parallel strategy focusing on Graphics Processing Unit (GPU)-accelerated nodes as available on some of the top ranked supercomputers at the present time. We present numerical results in the strong limit regime, as it is particularly relevant for First-Principles Molecular Dynamics. We also examine how matrix product-based iterative solvers provide a competitive alternative to dense eigensolvers on GPUs, allowing to push the strong scaling limit of these computations to a larger number of distributed tasks. Our strategy, which relies on replicated Gram matrices and efficient collective communications using the NCCL library, leads to a time-to-solution under 0.5 s for the Löwdin orthonormalization of a tall-skinny matrix of 3000 columns on Summit at Oak Ridge Leadership Facility (OLCF). Given the similarity in computational operations between one iteration of a DFT solver and this proxy-app, this shows the possibility of solving accurately the DFT equations well under a minute for 3000 electronic wave functions, and thus perform First-Principles molecular dynamics of physical systems much larger than traditionally solved on CPU systems.

An Atomic-Scale Understanding of the Solution Chemistry of Antimony(V): Insights from First-Principles Molecular Dynamics Simulation.

In this study, the structure, hydrolysis, and complexation of Sb(V) in aqueous solution has been elucidated by using first-principles molecular dynamics (FPMD) simulations. The results show that both antimonic acid and its deprotonated form have an octahedral configuration, with average Sb-OH2 and Sb-OH distances of 2.25 and 2.05 Å, respectively. The computed pKa of [Sb(OH)5(OH2)] is 1.8, while [Sb(OH)6]- has an extremely high pKa. Consequently, [Sb(OH)6]- is the most dominant species of Sb(V) under common environmental conditions. A stable aqueous complex can form between [Sb(OH)6]- and common cations, and an Sb-Al bidentate complex has the largest dissociation free energy, followed by a Sb-Mg bidentate complex, indicating that they have significantly higher stabilities. For Na+ and Ca2+, their respective monodentate and bidentate complexes have similar dissociation free energies, indicating very close possibilities. These findings provide a comprehensive understanding of the solution chemistry of Sb(V) from a quantitative and microscopic perspective.

Equilibrium barium isotope fractionation between minerals and aqueous solution from first-principles calculations

Barium isotopes could be a novel tracer in low-temperature geochemical processes such as the Ba cycle in rivers and oceans. Equilibrium Ba isotope fractionation between Ba-hosting minerals and aqueous solution is of great importance for the applications of Ba isotopes in geochemistry, but it remains poorly constrained. In this study, we performed first-principles calculations based on the density functional theory (DFT) to determine the equilibrium Ba isotope fractionation between minerals and aqueous solution (103lnαmineral-Ba_aq of 137Ba/134Ba). The structural properties of aqueous Ba2+ are well predicted by the first-principles molecular dynamics (FPMD) simulation and 121 snapshots are extracted from FPMD trajectories to estimate the reduced partition function ratio (β factor or 103lnβ of 137Ba/134Ba) of aqueous Ba2+. The 103lnβ decreases in the sequence of aragonite > calcite > aqueous Ba2+ ∼ witherite > barite. The β factor is dominantly determined by the force constant, which is affected by both the average BaO bond length and the coordination number.Our results show that 103lnαaragonite-Ba_aq and 103lnαwitherite-Ba_aq are 0.36‰ and −0.02‰ at 300 K, respectively, consistent with results of experimental studies at equilibrium. The depletion of heavy Ba isotopes observed in natural corals relative to seawater suggests that kinetic effects play an important role in Ba isotope fractionation during coral growth. The 103lnαbarite-Ba_aq is only −0.17‰ at 300 K, indicating limited Ba isotope fractionation caused by the Ba removal stemmed from inorganic barite precipitation. Overall, the equilibrium Ba isotope fractionation factors between minerals and aqueous Ba2+ calculated in this study provide a guideline for the applications of Ba isotopes in low-temperature geochemistry.