Search Results (49 total)

A method for calculating free-energy differences based on a free-energy perturbation (FEP) formalism in an alloy system described by two different Hamiltonians is reported. The intended application is the calculation of solid-liquid phase equilibria in alloys with the accuracy of first-principles electronic density-functional theory (DFT). For this purpose free energies are derived with a classical interatomic potential, and FEP calculations are used to compute corrections to these reference values. For practical applications of this approach, due to the relatively high computational cost of DFT calculations, it is critical that the FEP calculations converge rapidly in terms of the number of samples used to estimate relevant ensemble averages. This issue is investigated in the current study employing two classical interatomic-potential models for Ni-Cu. These models yield differences in predicted phase-boundary temperatures of approximately 100 K, comparable to those that might be expected between a DFT Hamiltonian and a well-fit classical potential. We show that for pure elements the FEP calculations converge rapidly with the number of samples, yielding free-energy differences converged to within a fraction of a meV/atom in a few dozen energy calculations. For a concentrated equiatomic alloy similar precision requires roughly a hundred samples. The results suggest that the proposed methodology could provide a computationally tractable framework for calculating solid-liquid phase equilibria in concentrated alloys with DFT accuracy.

A detailed analysis of the structure and dynamics of the crystal-melt interface region in silicon, modeled with the Stillinger-Weber potential, is performed via molecular dynamics simulations. The focus is on the faceted (111) crystal-melt interface, but properties of the rough (100) interface are also determined. We find an intrinsic 10-90 interface width of 0.681±0.001  nm for the coarse-grained density profile at the (111) interface and a 0.570±0.005  nm width at the (100) interface. Coarse-grained profiles of a suitably defined local order parameter are found to show a smaller width anisotropy between (111) and (100) interfaces while the order profiles exhibit a 0.20–0.25  nm shift in position toward the crystal phase relative to the corresponding density profiles. The structural analysis of the layer of melt adjacent to the (111) facet of the crystal finds ordered clusters with average lifetimes of 16  ps, as determined from autocorrelations of time-dependent layer structure factors, and cluster radii of gyration from 0.2  nm for the smallest cells to as large as 1.5  nm.

The formation of nanoscale self-assembled compositional patterns in monolayer bulk-immiscible alloy films is studied from first principles within the framework of a previously proposed hybrid atomistic-continuum model [V. Ozoliņš , Phys. Rev. Lett. 88, 096101 (2002)]. The details surrounding the parametrization of the model from first-principles calculations are described for both hexagonal (0001) and bcc (110) substrates, and we demonstrate how the theoretical model can be employed in Monte Carlo simulations as a predictive framework for modeling the structure and finite-temperature stability of compositional patterns. The methodology is applied in a comparative study of equiatomic FeAg pseudomorphic alloy films on Mo(110) and Ru(0001) substrates. Stripe patterns with periodicities of a few nanometers are predicted to be stable in both systems, which is in good agreement with available experimental data for FeAg/Mo(110). The regularity of the stripe patterns and their stability with respect to disordering are found to be substantially enhanced on the anisotropic Mo(110) substrate relative to the nearly isotropic Ru(0001) surface, despite the slightly stronger ordering energetics in the latter system. A comparison of the results of the present study to the predictions of continuum theories commonly employed to describe pattern formation on crystalline surfaces serves to highlight the limitations of such models in the application to patterns with periodicities with length scales of approximately ten atomic spacings.

We resolve the structure of a c(2×2) reconstruction of the rutile TiO₂ (100) surface using a combination of transmission electron diffraction, direct methods analysis, and density functional theory. The surface structure contains an ordered array of subsurface oxygen vacancies and is in local thermodynamic equilibrium with bulk TiO₂, but not the with oxygen gas-phase environment. The transition into a bulklike (1×1) reconstruction offers insights into the time-dependent local thermodynamics of TiO₂ surface reconstruction under global nonequilibrium conditions.

A soft-phonon feature associated with the shape-memory transition in NiTi is observed in the phonon density of states (DOS) of the B2 phase of both NiTi and Ni₅₀Ti₄₇Fe₃ (with Fe substituted for Ti) using inelastic neutron scattering. In both alloys, the feature softens with decreasing temperature, but the softening occurs about 100  K lower in the Fe-substituted alloy, indicating a decreased transition temperature. Electrical resistivity and magnetic susceptibility verify the decreased transition temperature but also show that the transition develops second-order-like behavior similar to that observed by others in Ni₄₄Ti₅₀Fe₆ (with Fe substituted for Ni). First-principles calculations supported by Mössbauer spectroscopy and neutron diffraction indicate a double-defect scenario, where Fe occupies Ni sites and the displaced Ni occupies the empty Ti sites in the Ti-substituted alloys. A comparison between the current results for Ti-substituted alloys, and related experimental data for alloys featuring Fe substitution for Ni, indicates that the instability temperature is controlled by the number of Fe atoms occupying the Ni sites, while the second-order-like behavior is caused by the addition of the Ni antisite defects. We argue that this latter behavior results from percolated networks of interacting defects acting to frustrate the symmetry-breaking strains.

The c(6×2) is a reconstruction of the SrTiO₃(001) surface that is formed between 1050 and 1100  °C in oxidizing annealing conditions. This work proposes a model for the atomic structure for the c(6×2) obtained through a combination of results from transmission electron diffraction, surface x-ray diffraction, direct methods analysis, computational combinational screening, and density functional theory. As it is formed at high temperatures, the surface is complex and can be described as a short-range-ordered phase featuring microscopic domains composed of four main structural motifs. Additionally, nonperiodic TiO₂ units are present on the surface. Simulated scanning tunneling microscopy images based on the electronic structure calculations are consistent with experimental images.

Molecular-dynamics and Monte Carlo simulations have been used to compute the crystal-melt interface stress (f) in a model Lennard-Jones (LJ) binary alloy system, as well as for elemental Si and Ni modeled by many-body Stillinger-Weber and embedded-atom-method (EAM) potentials, respectively. For the LJ alloys the interface stress in the (100) orientation was found to be negative and the f vs composition behavior exhibits a slight negative deviation from linearity. For Stillinger-Weber Si, a positive interface stress was found for both (100) and (111) interfaces: f₁₀₀=(380±30)  mJ∕m² and f₁₁₁=(300±10)  mJ∕m². The Si (100) and (111) interface stresses are roughly 80 and 65% of the value of the interfacial free energy (γ), respectively. In EAM Ni we obtained f₁₀₀=(22±74)  mJ∕m², which is an order of magnitude lower than γ. A qualitative explanation for the trends in f is discussed.

The vibrational thermodynamic properties of ordered and disordered fcc-based alloys in three aluminum transition-metal (TM) systems, Al-TM (TM=Ti, Zr, and Hf), are computed by first principles methods employing supercell calculations and the transferable-force-constant (TFC) approach. In order to obtain accurate values for the high-temperature limit of the vibrational mixing entropies in these systems, it is necessary to parametrize the dependence of the force constants on both the equilibrium bond length and the TM concentration in the TFC method. Provided this concentration dependence is accounted for, the TFC approach is shown to lead to predictions for the vibrational mixing entropy accurate to within approximately 20%. The utility of the TFC method is demonstrated by its application to the calculation of vibrational entropies of mixing for approximately 30 structures in each of the three Al-TM systems, facilitating the construction of well converged vibrational-entropy cluster expansions. The calculations yield large and negative values for the vibrational mixing entropies of both ordered and disordered alloys, with an overall magnitude of up to 1.0k_B/atom, and ordering entropies (i.e., the difference between the vibrational entropy of ordered and disordered phases at the same composition) in the range of 0.2–0.3k_B/atom for concentrated alloys. Calculated results are shown to be in good agreement with experimental data available for the Al-Ti system.

In dendritic solidification, growth morphologies often display a pronounced sensitivity to small changes in composition. To gain insight into the origins of this phenomenon, we undertake an atomistic calculation of the magnitude and anisotropy of the crystal-melt interfacial free energy in a model alloy system featuring no atomic size mismatch and relatively ideal solution thermodynamics. By comparing the results of these calculations with predictions from recent phase-field calculations, we demonstrate that alloying gives rise to changes in free-energy anisotropies that are substantial on the scale required to induce changes in growth orientations.

Heteroepitaxial growth in the Ge∕Si (001) system is known to lead to the formation of pyramid-like “hut” islands with {105}-oriented facets. Recent calculations of island formation energies in this system have suggested that edge energies lead to an important contribution to the barrier to island formation at small sizes. Here we provide an independent calculation of the magnitude of the average edge energy for Ge∕Si(001) by matching the results of atomistic simulations to continuum theory for the energy of faceted surfaces. We consider an infinitely long Ge island, or wire, bounded by {105} facets with the recently proposed rebonded-step-model reconstruction, on a (001) wetting-layer terrace with the 2×8 dimer-vacancy-line reconstruction. To perform these calculations we derive models for edge structures between {105} facets and between {105} and (001) facets, leading in both cases to atomic coordinations with no more than one dangling bond per atom. For these model edge structures we obtain an average value for the edge energy on the order of 10 meV∕Å.

The kinetics of crystallization from the melt is investigated for hcp Mg employing molecular dynamics simulations based on a recently developed embedded-atom-method interatomic potential. The interface mobility (μ), defined as the constant of proportionality between interface velocity and undercooling, is calculated for the three high-symmetry orientations (0001), (101̅0), and (112̅0). The magnitudes of the interface mobilities are found to lie in the range of 40–80 cm∕s∕K. The mobilities μ_101̅0 and μ_112̅0 are found to be of comparable magnitude and approximately 1.7 times larger than μ₀₀₀₁. The calculated dependence of μ on interface normal is discussed within the framework of the kinetic density-functional theory (DFT) formulation of Mikheev and Chernov.

Recent experiments and calculations have highlighted the important role of surface-energy (γ) anisotropy in governing island formation in the Ge/Si(001) system. To further elucidate the factors determining this anisotropy, we perform atomistic and continuum calculations of the orientation dependence of γ for strained-Ge surfaces near (001), accounting for the presence of dimer-vacancy lines (DVLs). The net effect of DVLs is found to be a substantial reduction in the magnitude of the slope of γ vs orientation angle, relative to the highly negative value derived for non-DVL, dimer-reconstructed, strained-Ge(001) surfaces. The present results thus point to an important role of DVLs in stabilizing the (001) surface orientation of a strained-Ge wetting layer.

The weak anisotropy of the interfacial free energy γ is a crucial parameter influencing dendritic crystal growth morphologies in systems with atomically rough solid-liquid interfaces. The physical origin and quantitative prediction of this anisotropy are investigated for body-centered-cubic (bcc) forming systems using a Ginzburg-Landau theory where the order parameters are the amplitudes of density waves corresponding to principal reciprocal lattice vectors. We find that this theory predicts the correct sign γ₁₀₀>γ₁₁₀ and magnitude (γ₁₀₀−γ₁₁₀)∕(γ₁₀₀+γ₁₁₀)≈1% of this anisotropy in good agreement with the results of molecular dynamics (MD) simulations for Fe. The results show that the directional dependence of the rate of spatial decay of solid density waves into the liquid, imposed by the crystal structure, is a main determinant of anisotropy. This directional dependence is validated by MD computations of density wave profiles for different reciprocal lattice vectors for {110} crystal faces. Our results are contrasted with the prediction of the reverse ordering γ₁₀₀<γ₁₁₀ from an earlier formulation of Ginzburg-Landau theory [Shih , Phys. Rev. A 35, 2611 (1987)].

Crystal-melt interfacial free energies (γ) are computed for hcp Mg by employing equilibrium molecular-dynamics (MD) simulations and the capillary-fluctuation method (CFM). This work makes use of a newly developed embedded-atom-method (EAM) interatomic potential for Mg fit to crystal, liquid, and melting properties. We describe how the CFM, which has previously been applied to cubic systems only, can be generalized for studies of hcp metals by employing a parametrization for the orientation dependence of γ in terms of hexagonal harmonics. The method is applied in the calculation of the Turnbull coefficient (α) and crystalline anisotropies of γ. We obtain a value of α=0.48, with interfacial free energies for different high-symmetry orientations differing by approximately 1%. These results are compared to those obtained in previous MD-CFM studies for cubic EAM metals as well as experimental studies of solid-liquid interfaces in hcp alloys. In addition, the implications of our results for the prediction of dendrite growth directions in hcp metals are discussed.

We have measured and theoretically analyzed the diffuse scattering in the binary alloy system Au-Ni, which has been proposed as a testing ground for theories of alloy phase stability. We found strong evidence that in the alloys Au₃Ni and Au₃Ni₂, fluctuations of both ordering- and clustering-type are competing with each other. Our results resolve a long-standing controversy on the balance of relaxation and mixing energies in this alloy system and explain recent findings of ordering in thin Au-Ni films.

Atomic volumes, magnetic moments, mixing energies, and the elastic properties of bcc Fe_1−xCu_x solid solutions are studied by ab initio calculations based on the cluster expansion framework. For the calculation of concentration-dependent elastic moduli in disordered solid solutions, we introduce a generalization of the cluster expansion technique that is designed to handle tensorial quantities in high-symmetry phases. Calculated mixing energies, atomic volumes, and magnetic moments are found to be in good agreement with available measurements for metastable alloys prepared through nonequilibrium processing techniques. Additionally, the predicted variations of the bulk modulus and shear moduli C₄₄ and C^′ with respect to copper concentration are calculated for the disordered bcc phase. While the bulk modulus and C₄₄ are positive for all concentrations, C^′ is predicted to be positive only for Cu concentration less than 50 atomic %, and negative otherwise. Our results thus indicate that the mechanical instability of bcc Cu persists over a wide range of compositions. The implications of the present results are discussed in relation to the observed metastability of bcc Fe-Cu alloys, and the strengthening mechanism of nanoscale bcc precipitates in an α-Fe matrix.

Formation energies for Ge/Si(100) pyramidal islands are computed combining continuum calculations of strain energy with first-principles-computed strain-dependent surface energies. The strain dependence of surface energy is critically impacted by the presence of strain-induced changes in the Ge {100} surface reconstruction. The appreciable strain dependencies of rebonded-step {105} and dimer-vacancy-line-reconstructed {100} surface energies are estimated to give rise to a significant reduction in the surface contribution to island formation energies.

First-principles calculations based on a plane-wave pseudopotential method, as implemented in the VASP code, are presented for the formation energies of several transition-metal and non-transition-metal dopants in Ti–Al alloys. Substitution for either Ti or Al in γ‐TiAl, α₂‐Ti₃Al, Ti₂AlC, and Ti₃AlC are considered. Calculated (zero-temperature) defect formation energies exhibit clear trends as a function of the periodic-table column of transition metal solutes. Early transition metals in TiAl prefer the Ti sublattice, but this preference gradually shifts to the Al sublattice for late transition metals; the Ti sublattice is preferred by all transition metal solutes in Ti₃Al. Partitioning of solutes to Ti₃Al is predicted for mid-period transition elements, and to TiAl for early and late transition elements. A simple Ising model treatment demonstrates the plausibility of these trends, which are in excellent overall agreement with experiment. The influence of temperature on formation energies is examined with a cluster expansion for the binary TiAl alloys and a low temperature expansion for dilute ternary alloys. Results for Nb-doped alloys provide insight into the relative sensitivity of solute partitioning to individual contributions to the free energy. Whereas the calculated formation energy of Nb (substitution) at zero temperature favors partitioning to α₂‐Ti₃Al, temperature-dependent contributions to the formation free energy, evaluated at 1075 K, favor partitioning to γ‐TiAl, in agreement with experiment.

Ge deposited on Si(100) initially forms heteroepitaxial layers, which grow to a critical thickness of ∼3 MLs before the appearance of three-dimensional strain relieving structures. Experimental observations reveal that the surface structure of this Ge wetting layer is a dimer vacancy line (DVL) superstructure of the unstrained Ge(100) dimer reconstruction. In the following, the results of first-principles calculations of the thickness dependence of the wetting layer surface excess energy for the c(4×2) and 4×6 DVL surface reconstructions are reported. These results predict a wetting layer critical thickness of ∼3 MLs, which is largely unaffected by the presence of dimer vacancy lines. The 4×6 DVL reconstruction is found to be thermodynamically stable with respect to the c(4×2) structure for wetting layers at least 2 ML thick. A strong correlation between the fraction of total surface induced deformation present in the substrate and the thickness dependence of wetting layer surface energy is also shown.

Molecular-dynamics simulations have been used to compute thermodynamic and kinetic properties of the solid-liquid interface for both the fcc and bcc phases of Fe. Pure Fe was modeled using two different interatomic potentials of the embedded atom type as well as an effective pair potential. Free solidification simulations were used to determine the kinetic coefficient μ for the different models of pure Fe. The anisotropy of μ with respect to growth direction in the bcc phase is similar to that observed in fcc systems, namely μ₁₀₀>μ₁₁₀∼μ₁₁₁, and the kinetic coefficient of bcc is larger than μ for the fcc phase. The kinetic coefficient results are discussed in terms of a kinetic density-functional-theory-based model of crystal growth. In addition, results for solid-liquid interfacial free energies γ computed via the capillary fluctuation method, are summarized.

Despite decades of study, several key aspects of the Al-H system remain the subject of considerable debate. In an effort to elucidate some of these unknowns, we perform a systematic study of this system using first-principles density-functional calculations. We show that generalized gradient approximation (GGA) calculations provide an accurate picture of energetics, phase stability and structure, diffusion, and defect binding in the Al-H system. A series of calculations for hydrides in the M-H systems (M=Al, Ba, Ca, K, Mg, La, Li, Na, Ni, Pd, Sc, Sr, Ti, V, and Y) also shows that the GGA calculations are a quantitatively accurate predictor of hydride formation energies. For Al-H, we find: (i) In agreement with experiment, the observed metastable hydride, AlH₃ is found to have a small, negative formation enthalpy at ambient conditions, but a strongly positive formation free energy. (ii) Linear response calculations of AlH₃ yield vibrational frequencies, phonon densities of states (DOS), and heat capacities in excellent agreement with experimental measurements, and suggest the need for a reinterpretation of measured phonon DOS. (iii) Atomic relaxation and anharmonic vibrational effects both play an important role in the tetrahedral versus octahedral interstitial site preference of H in Al. (iv) The calculated heat of solution of H in the preferred tetrahedral site is large and positive (+0.71 eV), consistent with experimental solubility data and with Al as an endothermic hydrogen absorber. (v) Interstitial H interacts strongly with Al vacancies (□), with a calculated H-□ binding energy of 0.33 eV. (vi) In the absence of vacancies, the calculated migration energy of H between the tetrahedral and octahedral interstitial sites is 0.18 eV, but for H migrating away from an Al vacancy, the migration energy increases to 0.54 eV. Vacancy trapping of H can therefore provide an explanation for observed disparate H migration barriers.

The kinetics of isothermal crystallization and melting are studied for elemental Ni employing non-equilibrium molecular-dynamics simulations based on interatomic potentials of the embedded-atom-method form. These simulations form the basis for calculations of the magnitude and crystalline anisotropy of the kinetic coefficient μ, defined as the constant of proportionality between interface velocity and undercooling. We obtain highly symmetric rates for crystallization and melting, from which we extract the following values of μ for low index {100}, {110}, and {111} interfaces: μ₁₀₀=35.8±22, μ₁₁₀=25.5±1.6, and μ₁₁₁=24.1±4.0 in units of cm/s K. The results of the present study are discussed in the context of previous molecular-dynamics simulations for related systems, and kinetic models based upon transition-state and density-functional theories.

The structural dependence of crystal-melt interfacial free energies (γ) is investigated for fcc and bcc solids through molecular-dynamics calculations employing interatomic potentials for Fe. We compute ≈30–35 % lower values of γ for the bcc structure, and find that our results cannot be explained simply in terms of differences in latent heats (L) or densities (ρ) for bulk bcc and fcc phases. We observe a strong structural dependence of the Turnbull coefficient α=γ/Lρ^2/3, and find a trend towards lower crystalline anisotropies of γ for the bcc structure relative to fcc.

Microscopic factors governing solute partitioning in ternary two-phase Al-Sc-Mg alloys are investigated combining three-dimensional-atom-probe (3DAP) miscroscopy measurements with first-principles computations. 3DAP is employed to measure composition profiles with subnanometer-scale resolution, leading to the identification of a large enhancement of Mg solute at the coherent α-Al/Al₃Sc (fcc/L1₂) heterophase interface. First-principles calculations establish an equilibrium driving force for this interfacial segregation reflecting the nature of the interatomic interactions.

First-principles calculations are used to calculate the strain dependencies of the binding and diffusion-activation energies for Ge adatoms on both Si(001) and Ge(001) surfaces. Our calculations reveal that the binding and activation energies on a strained Ge(001) surface increase and decrease, respectively, by 0.21 and 0.12 eV per percent compressive strain. For a growth temperature of 600 °C, these strain-dependencies give rise to a 16-fold increase in adatom density and a fivefold decrease in adatom diffusivity in the region of compressive strain surrounding a Ge island with a characteristic size of 10 nm.