Entropy approximations for simple fluids.

Liquid state entropy formulas based on configurational probability distributions are examined for Lennard-Jones fluids across a range temperatures and densities. These formulas are based on expansions of the entropy in a series of n-body distribution functions. We focus on two special cases. One, which we term the "perfect gas" series, starts with the entropy of an ideal gas; the other, which we term the "dense liquid" series, removes a many-body contribution from the ideal gas entropy and reallocates it among the subsequent n-body terms. We show that the perfect gas series is most accurate at low density, while the dense liquid series is most accurate at high density. We propose empirical interpolation methods that are capable of connecting the two series and giving consistent predictions in most situations.

Vibrational Entropy of Crystalline Solids from Covariance of Atomic Displacements.

The vibrational entropy of a solid at finite temperature is investigated from the perspective of information theory. Ab initio molecular dynamics (AIMD) simulations generate ensembles of atomic configurations at finite temperature from which we obtain the N-body distribution of atomic displacements, ρN. We calculate the information-theoretic entropy from the expectation value of lnρN. At a first level of approximation, treating individual atomic displacements independently, our method may be applied using Debye-Waller B-factors, allowing diffraction experiments to obtain an upper bound on the thermodynamic entropy. At the next level of approximation we correct the overestimation through inclusion of displacement covariances. We apply this approach to elemental body-centered cubic sodium and face-centered cubic aluminum, showing good agreement with experimental values above the Debye temperatures of the metals. Below the Debye temperatures, we extract an effective vibrational density of states from eigenvalues of the covariance matrix, and then evaluate the entropy quantum mechanically, again yielding good agreement with experiment down to low temperatures. Our method readily generalizes to complex solids, as we demonstrate for a high entropy alloy. Further, our method applies in cases where the quasiharmonic approximation fails, as we demonstrate by calculating the HCP/BCC transition in Ti.

Superior High-Temperature Strength in a Supersaturated Refractory High-Entropy Alloy.

Refractory high-entropy alloys (RHEAs) show promising applications at high temperatures. However, achieving high strengths at elevated temperatures above 1173K is still challenging due to heat softening. Using intrinsic material characteristics as the alloy-design principles, a single-phase body-centered-cubic (BCC) CrMoNbV RHEA with high-temperature strengths (beyond 1000 MPa at 1273 K) is designed, superior to other reported RHEAs as well as conventional superalloys. The origin of the high-temperature strength is revealed by in situ neutron scattering, transmission-electron microscopy, and first-principles calculations. The CrMoNbV's elevated-temperature strength retention up to 1273 K arises from its large atomic-size and elastic-modulus mismatches, the insensitive temperature dependence of elastic constants, and the dominance of non-screw character dislocations caused by the strong solute pinning, which makes the solid-solution strengthening pronounced. The alloy-design principles and the insights in this study pave the way to design RHEAs with outstanding high-temperature strength.

Strength can be controlled by edge dislocations in refractory high-entropy alloys.

Energy efficiency is motivating the search for new high-temperature (high-T) metals. Some new body-centered-cubic (BCC) random multicomponent "high-entropy alloys (HEAs)" based on refractory elements (Cr-Mo-Nb-Ta-V-W-Hf-Ti-Zr) possess exceptional strengths at high temperatures but the physical origins of this outstanding behavior are not known. Here we show, using integrated in-situ neutron-diffraction (ND), high-resolution transmission electron microscopy (HRTEM), and recent theory, that the high strength and strength retention of a NbTaTiV alloy and a high-strength/low-density CrMoNbV alloy are attributable to edge dislocations. This finding is surprising because plastic flows in BCC elemental metals and dilute alloys are generally controlled by screw dislocations. We use the insight and theory to perform a computationally-guided search over 107 BCC HEAs and identify over 106 possible ultra-strong high-T alloy compositions for future exploration.

High-throughput design of high-performance lightweight high-entropy alloys.

Developing affordable and light high-temperature materials alternative to Ni-base superalloys has significantly increased the efforts in designing advanced ferritic superalloys. However, currently developed ferritic superalloys still exhibit low high-temperature strengths, which limits their usage. Here we use a CALPHAD-based high-throughput computational method to design light, strong, and low-cost high-entropy alloys for elevated-temperature applications. Through the high-throughput screening, precipitation-strengthened lightweight high-entropy alloys are discovered from thousands of initial compositions, which exhibit enhanced strengths compared to other counterparts at room and elevated temperatures. The experimental and theoretical understanding of both successful and failed cases in their strengthening mechanisms and order-disorder transitions further improves the accuracy of the thermodynamic database of the discovered alloy system. This study shows that integrating high-throughput screening, multiscale modeling, and experimental validation proves to be efficient and useful in accelerating the discovery of advanced precipitation-strengthened structural materials tuned by the high-entropy alloy concept.

2D Ising Model for Adsorption-induced Enantiopurification of Racemates.

Mechanisms for the spontaneous transformation of achiral chemical systems into states of enantiomeric purity have important ramifications in modern pharmacology and potential relevance to the origins of homochirality in life on Earth. Such mechanisms for enantiopurification are needed for production of chiral pharmaceuticals and other bioactive compounds. Previously proposed chemical mechanisms leading from achiral systems to near homochirality are initiated by a symmetry-breaking step resulting in a minor excess of one enantiomer via statistical fluctuations in enantiomer concentrations. Subsequent irreversible processes then amplify the majority enantiomer concentration while simultaneously suppressing minority enantiomer production. Herein, equilibrium adsorption of amino acid enantiomer mixtures onto chiral and achiral surfaces reveals amplification of surface enantiomeric excess relative to the gas phase; i. e. enantiopurification of chiral adsorbates by adsorption. This adsorption-induced amplification of enantiomeric excess is shown to be well-describe by the 2D Ising model. More importantly, the 2D-Ising model predicts formation of homochiral monolayers from adsorption of racemic mixtures or prochiral molecules on achiral surfaces; i. e. enantiopurification with no apparent chiral driving force.

Mysterious SiB3: Identifying the Relation between α- and ß-SiB3.

Binary silicon boride SiB3 has been reported to occur in two forms, as disordered and nonstoichiometric α-SiB3-x , which relates to the α-rhombohedral phase of boron, and as strictly ordered and stoichiometric ß-SiB3. Similar to other boron-rich icosahedral solids, these SiB3 phases represent potentially interesting refractory materials. However, their thermal stability, formation conditions, and thermodynamic relation are poorly understood. Here, we map the formation conditions of α-SiB3-x and ß-SiB3 and analyze their relative thermodynamic stabilities. α-SiB3-x is metastable (with respect to ß-SiB3 and Si), and its formation is kinetically driven. Pure polycrystalline bulk samples may be obtained within hours when heating stoichiometric mixtures of elemental silicon and boron at temperatures 1200-1300 °C. At the same time, α-SiB3-x decomposes into SiB6 and Si, and optimum time-temperature synthesis conditions represent a trade-off between rates of formation and decomposition. The formation of stable ß-SiB3 was observed after prolonged treatment (days to weeks) of elemental mixtures with ratios Si/B = 1:1-1:4 at temperatures 1175-1200 °C. The application of high pressures greatly improves the kinetics of SiB3 formation and allows decoupling of SiB3 formation from decomposition. Quantitative formation of ß-SiB3 was seen at 1100 °C for samples pressurized to 5.5-8 GPa. ß-SiB3 decomposes peritectoidally at temperatures between 1250 and 1300 °C. The highly ordered nature of ß-SiB3 is reflected in its Raman spectrum, which features narrow and distinct lines. In contrast, the Raman spectrum of α-SiB3-x is characterized by broad bands, which show a clear relation to the vibrational modes of isostructural, ordered B6P. The detailed composition and structural properties of disordered α-SiB3-x were ascertained by a combination of single-crystal X-ray diffraction and 29Si magic angle spinning NMR experiments. Notably, the compositions of polycrystalline bulk samples (obtained at T ≤ 1200 °C) and single crystal samples (obtained from Si-rich molten Si-B mixtures at T > 1400 °C) are different, SiB2.93(7) and SiB2.64(2), respectively. The incorporation of Si in the polar position of B12 icosahedra results in highly strained cluster units. This disorder feature was accounted for in the refined crystal structure model by splitting the polar position into three sites. The electron-precise composition of α-SiB3-x is SiB2.5 and corresponds to the incorporation of, on average, two Si atoms in each B12 icosahedron. Accordingly, α-SiB3-x constitutes a mixture of B10Si2 and B11Si clusters. The structural and phase stability of α-SiB3-x were explored using a first-principles cluster expansion. The most stable composition at 0 K is SiB2.5, which however is unstable with respect to the decomposition ß-SiB3 + Si. Modeling of the configurational and vibrational entropies suggests that α-SiB3-x only becomes more stable than ß-SiB3 at temperatures above its decomposition into SiB6 and Si. Hence, we conclude that α-SiB3-x is metastable at all temperatures. Density functional theory electronic structure calculations yield band gaps of similar size for electron-precise α-SiB2.5 and ß-SiB3, whereas α-SiB3 represents a p-type conductor.

First Principles Calculation of the Entropy of Liquid Aluminum.

The information required to specify a liquid structure equals, in suitable units, its thermodynamic entropy. Hence, an expansion of the entropy in terms of multi-particle correlation functions can be interpreted as a hierarchy of information measures. Utilizing first principles molecular dynamics simulations, we simulate the structure of liquid aluminum to obtain its density, pair and triplet correlation functions, allowing us to approximate the experimentally measured entropy and relate the excess entropy to the information content of the correlation functions. We discuss the accuracy and convergence of the method.

Segregation-induced ordered superstructures at general grain boundaries in a nickel-bismuth alloy.

The properties of materials change, sometimes catastrophically, as alloying elements and impurities accumulate preferentially at grain boundaries. Studies of bicrystals show that regular atomic patterns often arise as a result of this solute segregation at high-symmetry boundaries, but it is not known whether superstructures exist at general grain boundaries in polycrystals. In bismuth-doped polycrystalline nickel, we found that ordered, segregation-induced grain boundary superstructures occur at randomly selected general grain boundaries, and that these reconstructions are driven by the orientation of the terminating grain surfaces rather than by lattice matching between grains. This discovery shows that adsorbate-induced superstructures are not limited to special grain boundaries but may exist at a variety of general grain boundaries, and hence they can affect the performance of polycrystalline engineering alloys.

Generalized potentials for a mean-field density functional theory of a three-phase contact line.

We investigate generalized potentials for a mean-field density functional theory of a three-phase contact line. Compared to the symmetrical potential introduced in our previous article [Phys. Rev. E 85, 011120 (2012)], the three minima of these potentials form a small triangle located arbitrarily within the Gibbs triangle, which is more realistic for ternary fluid systems. We multiply linear functions that vanish at edges and vertices of the small triangle, yielding potentials in the form of quartic polynomials. We find that a subset of such potentials has simple analytic far-field solutions and is a linear transformation of our original potential. By scaling, we can relate their solutions to those of our original potential. For special cases, the lengths of the sides of the small triangle are proportional to the corresponding interfacial tensions. For the case of equal interfacial tensions, we calculate a line tension that is proportional to the area of the small triangle.

Mean-field density functional theory of a three-phase contact line.

A three-phase contact line in a three-phase fluid system is modeled by a mean-field density functional theory. We use a variational approach to find the Euler-Lagrange equations. Analytic solutions are obtained in the two-phase regions at large distances from the contact line. We employ a triangular grid and use a successive overrelaxation method to find numerical solutions in the entire domain for the special case of equal interfacial tensions for the two-phase interfaces. We use the Kerins-Boiteux formula to obtain a line tension associated with the contact line. This line tension turns out to be negative. We associate line adsorption with the change of line tension as the governing potentials change.

Kinetic Monte Carlo method applied to nucleic acid hairpin folding.

Kinetic Monte Carlo on coarse-grained systems, such as nucleic acid secondary structure, is advantageous for being able to access behavior at long time scales, even minutes or hours. Transition rates between coarse-grained states depend upon intermediate barriers, which are not directly simulated. We propose an Arrhenius rate model and an intermediate energy model that incorporates the effects of the barrier between simulated states without enlarging the state space itself. Applying our Arrhenius rate model to DNA hairpin folding, we demonstrate improved agreement with experiment compared to the usual kinetic Monte Carlo model. Further improvement results from including rigidity of single-stranded stacking.

Vibrational dynamics of icosahedrally symmetric biomolecular assemblies compared with predictions based on continuum elasticity.

Coarse-grained elastic network models elucidate the fluctuation dynamics of proteins around their native conformations. Low-frequency collective motions derived by simplified normal mode analysis are usually involved in biological function, and these motions often possess noteworthy symmetries related to the overall shape of the molecule. Here, insights into these motions and their frequencies are sought by considering continuum models with appropriate symmetry and boundary conditions to approximately represent the true atomistic molecular structure. We solve the elastic wave equations analytically for the case of spherical symmetry, yielding a symmetry-based classification of molecular motions together with explicit predictions for their vibrational frequencies. We address the case of icosahedral symmetry as a perturbation to the spherical case. Applications to lumazine synthase, satellite tobacco mosaic virus, and brome mosaic virus show that the spherical elastic model efficiently provides insights on collective motions that are otherwise obtained by detailed elastic network models. A major utility of the continuum models is the possibility of estimating macroscopic material properties such as the Young's modulus or Poisson's ratio for different types of viruses.

Mode-coupling approach to non-Newtonian Hele-Shaw flow.

The Saffman-Taylor viscous fingering problem is investigated for the displacement of a non-Newtonian fluid by a Newtonian one in a radial Hele-Shaw cell. We execute a mode-coupling approach to the problem and examine the morphology of the fluid-fluid interface in the weak shear limit. A differential equation describing the early nonlinear evolution of the interface modes is derived in detail. Owing to vorticity arising from our modified Darcy's law, we introduce a vector potential for the velocity in contrast to the conventional scalar potential. Our analytical results address how mode-coupling dynamics relates to tip splitting and sidebranching in both shear-thinning and shear-thickening cases. The development of non-Newtonian interfacial patterns in rectangular Hele-Shaw cells is also analyzed.