Effective Interatomic Interactions Research Articles

Statistically Derived Proxy Potentials Accelerate Geometry Optimization of Crystal Structures.

The crystal structures of known materials contain the information about the interatomic interactions that produced these stable compounds. Similar to the use of reported protein structures to extract effective interactions between amino acids, that has been a useful tool in protein structure prediction, we demonstrate how to use this statistical paradigm to learn the effective inter-atomic interactions in crystalline inorganic solids. By analyzing the reported crystallographic data for inorganic materials, we have constructed statistically derived proxy potentials (SPPs) that can be used to assess how realistic or unusual a computer-generated structure is compared to the reported experimental structures. The SPPs can be directly used for structure optimization to improve this similarity metric, that we refer to as the SPP score. We apply such optimization step to markedly improve the quality of the input crystal structures for DFT calculations and demonstrate that the SPPs accelerate geometry optimization for three systems relevant to battery materials. As this approach is chemistry-agnostic and can be used at scale, we produced a database of all possible pair potentials in a tabulated form ready to use.

Phononic properties of a periodic nanostructure including vacuum gap in the presence of effective interatomic interactions.

Using the harmonic approximation and Green's function technique, we investigate the contribution of phonons to heat transport across a narrow vacuum gap by an extended mass-spring chain model. We base the investigation on the van Beest-Kramer-van Santen potential that applies to two cases of simple and alternating mass systems at a finite temperature. Employing this model, we show that in specific values of interaction strengths, incoming phonon frequency, and gap distance, the phonon transmission across the vacuum gap can be improved. Finally, the thermal conductance of the system is computed as a function of interaction strength, gap distance, and temperature. These calculations reveal a suitable fitting function that can provide valuable insight into determining the internal interaction strengths from this quantity or controlling it by variation of the gap distance.

Learning from Imperfections: Predicting Structure and Thermodynamics from Atomic Imaging of Fluctuations.

In materials characterization, traditionally a single experimental sample is used to derive information about a single point in the composition space, while the imperfections, impurities, and stochastic details of material structure are deemed irrelevant or complicating factors in the analysis. Here we demonstrate that atomic-scale studies of a single nominal composition can provide information about microstructures and thermodynamic response over a finite area of chemical space. Using the principles of statistical inference, we develop a framework for incorporating structural fluctuations into statistical mechanical models and use it to solve the inverse problem of deriving effective interatomic interactions responsible for elemental segregation in a La5/8Ca3/8MnO3 thin film. The results are further analyzed by a variational autoencoder to detect anomalous behavior in the composition phase diagram. This study provides a framework for creating generative models from a combination of multiple experimental data and provides direct insight into the driving forces for cation segregation in manganites.

Ab initio modeling of decomposition in iron based alloys

This paper reviews recent progress in the field of ab initio based simulations of structure and properties of Fe-based alloys. We focus on thermodynamics of these alloys, their decomposition kinetics, and microstructure formation taking into account disorder of magnetic moments with temperature. We review modern theoretical tools which allow a consistent description of the electronic structure and energetics of random alloys with local magnetic moments that become totally or partially disordered when temperature increases. This approach gives a basis for an accurate finite-temperature description of alloys by calculating all the relevant contributions to the Gibbs energy from first-principles, including a configurational part as well as terms due to electronic, vibrational, and magnetic excitations. Applications of these theoretical approaches to the calculations of thermodynamics parameters at elevated temperatures (solution energies and effective interatomic interactions) are discussed including atomistic modeling of decomposition/clustering in Fe-based alloys. It provides a solid basis for understanding experimental data and for developing new steels for modern applications. The precipitation in Fe–Cu based alloys, the decomposition in Fe–Cr, and the short-range order formation in iron alloys with s–p elements are considered as examples.

Effect of magnetism on the solubility of 3d elements in BCC iron: Results of first-principle investigations

The methods of quantum-mechanical simulation have been used to study alloys of bcc iron with 3d transition metals in the ferromagnetic and paramagnetic states. It has been shown that the main factor that determines the solubility of the 3d elements is their electronic structure. The energy of the solution, mixing, and effective interatomic interactions vary regularly depending on the position of the element in the Periodic Table and on the magnetic state of the matrix. In some cases, depending on the magnetic state, changes in these quantities lead to the violation of the Hume-Rothery rules that determine the solubility of substitutional elements in alloys. The results obtained help us to understand the microscopic mechanisms that determine the solubility of alloying elements and their effect on the phase stability and structural state of steels.

From electrons to materials

AbstractIn this article, we discuss how microstructural length and time scales may be reached in atomistic simulations. We bridge from electronic properties to properties of materials by employing a systematic coarse graining of the electronic structure to effective interatomic interactions. In combination with extended time scale simulations the elementary processes of microstructural evolution may then be described. We present our approach to the derivation of tight‐binding models from density functional theory, the characterization of the interatomic interaction using bond‐order potentials and extended time scale simulations based on adaptive kinetic Monte Carlo. Applications to structural stability in iron, internal interfaces in tungsten and hydrogen diffusion in iron are discussed briefly and relate our approach to Manfred Fähnle's work.

Modeling W-V and W-Ta Alloys for Fusion Applications: Phase Stability, Short-Range Order and Point Defect Properties

ABSTRACTWe have performed density-functional theory (DFT) calculations of phase stability, formation energies of radiation defects in tungsten-based binaries W-Ta and W-V. These alloys are candidate for DEMO divertor applications because of their high melting point and expected improved ductility and fracture toughness in comparison with tungsten. We have identified the lowest energy intermetallic compounds, which should form at low temperatures, and calculated the effective inter-atomic interactions. Using Monte-Carlo calculations, we calculated the temperature of order-disorder phase transformations for these alloys. The predicted temperature of order-disorder phase transformations is relatively low and at high temperature it is found that the short-range order is present for both alloys. Ab-initio calculations also show that vanadium atoms strongly trap self-interstitial atom defects in W-V alloys, whereas Ta atoms in W-Ta alloys have very little effect on either the formation energy or thermally activated mobility of self-interstitial atom defects.

Thermal conductivity of single-walled carbon nanotubes

We study numerically the thermal conductivity of single-walled carbon nanotubes for the cases of an isolated nanotube and a nanotube interacting with a substrate. We employ two different numerical methods: (i) direct modeling of the heat transfer by molecular-dynamics simulations and (ii) analysis of the equilibrium dynamics by means of the Green-Kubo formalism. For the numerical modeling of the effective interatomic interactions, we employ both the Brenner potentials and the intermolecular potentials used in the study of the dynamics of large macromolecules. We demonstrate that, quite independently of the methods employed and the potentials used, the character of the thermal conductivity depends crucially on the interaction between a nanotube and a substrate. While an isolated nanotube demonstrates anomalous thermal conductivity due to ballistic transport of long-wave acoustic phonons, the nanotube interacting with a flat substrate displays normal thermal conductivity due to both the appearance of a gap in the frequency spectrum of acoustic phonons and the absorption of long-wave acoustic phonons by the substrate. We study the dependence of the thermal conductivity on chirality, radius, and temperature of the single-walled carbon nanotubes in both the regimes and compare our findings with experimental data and earlier theoretical results for the thermal conductivity.

Semi-Empirical Parameterization of Interatomic Interactions and Kinetics of the Atomic Ordering in Ni-Fe-C Permalloys and Elinvars

Within the framework of the lattice-statics and static fluctuation-waves’ methods, the available energies of strain-induced interaction of interstitial–interstitial, interstitial–substitutional and substitutional–substitutional impurity atomic pairs are collected and analysed for f.c.c.-(Ni,Fe)–C solutions allowing for discrete atomic structure of the host-crystal lattice. The lattice spacings, elasticity moduli and/or quasi-elastic force parameters of the host-crystal lattice, and concentration coefficients of the dilatation of solid-solution lattice due to the respective solutes are selected as the input numerical experimental data used. The above-mentioned interaction energies prove to have non-monotonically decreasing (‘quasi-oscillating’) and anisotropic dependences on discrete intera-tomic radius-vector, and themselves are strong and long-range. In all f.c.c.-(Ni,Fe)-base solutions, there is strain-induced attraction in many co-ordination shells. In general, the strain-induced interaction between impurity atoms in γ-Fe is weaker than in α-Ni (but in some solid solutions, it may prove to be of the same order). The verification of applicability of the approximation of strain-induced interaction of impurities for f.c.c.-(Ni,Fe)–C alloys (by means of analysis of thermodynamic C activity and ‘short-range order’ parameters of C-atoms’ distribution revealed by Mössbauer spectroscopy) showed that it must be supplemented with additional short-range (‘electrochemical’) repulsion in the first co-ordination shell. Nevertheless, in any case, the strain-induced interaction of impurity atoms must be taken into account for analysis of structure and properties of f.c.c.-(Ni,Fe)-base solutions. The Monte Carlo simulation procedures applied for constitution of a nanoscale Fe–C-austenite crystallite and based on analysis of the dependences of numbers of the different atomic configurations on C–C interatomic-interaction energies reveal correlation between the potential energy of such a modelling system and the numbers of iterations as well as Monte Carlo steps for the approach to constrained equilibrium. As shown by the example of austenite, for adequate representation of the experimental data on thermodynamic C activity, one needs to take into account for computations the ‘electrochemical’ (direct) and strain-induced (indirect) contributions to C–C interaction. The estimated sets of energies of such a total interaction within the first several interstitial co-ordination shells with rated radii are presented, and optimal set is selected, which optimally corresponds to experimental concentration and temperature dependences of C activity and the Mössbauer-spectroscopy data on the nearest neighbourhoods of Fe atoms with octahedral C interstitials. The ‘equilibrium’ relative parts of the different atomic Fe–C and C–C configurations (depending on C–C interaction energies) are determined. The Khachaturyan–Cook microscopic approach is considered to relate the time dependence of the long-range order (LRO) or short-range order to atomic diffusion. It enables to use the data of measurements of time dependence of radiation diffraction or diffuse-scattering intensity for a Ni–Fe solid solution for calculation of both probabilities of elementary atomic-migration jumps to different lattice sites per unit time and ‘exchange’ or vacancy-controlled diffusion coefficients, respectively. By the use of quantitative experimental information about the Curie temperatures, TC, and neutron diffuse-scattering intensities for disordered f.c.c.-Ni–Fe alloys, it is possible to evaluate the Fourier components, w~tot(k), of effective Ni–Fe atomic ‘mixing’ energies (inclusive the competing exchange interactions of respective permanent magnetic moments) taking into account both long-range ‘paramagnetic’ (‘electrochemical’ + ‘strain-induced’) and Ising-type magnetic contributions that drive the long-range ordering. Magnetism and ‘chemical’ (atomic) LRO in f.c.c.-Ni1cFeFecFe alloys are analysed within the self-consistent mean-field approximation, in which the statistical thermodynamics of the non-stoichiometric L12(Ni3Fe)-type permalloy (as well as L10(NiFe)-type elinvar) is determined by several energy parameters {w~tot(k)}. There is a revealed interplay of magnetism and long-range atomic ordering with the order–disorder transformation temperatures, TK, (below TC) appreciably different from the corresponding isolated TK values (above TC). The interplay of these two phenomena is examined along two lines, i.e. through the estimation of both temperature–cFe dependence of spatial LRO parameter and magnetisations of Ni and Fe subsystems. As shown, not only the temperature-dependent phase states of such binary f.c.c. alloys can be reproduced, but also the dependence of TK vs. cFe, including the observed asymmetry of phase-diagram curves due to the T- and cFe-dependent magnetic contribution to the effective interatomic interactions etc. As revealed for f.c.c.-Ni–Fe alloy with the use of single relaxation-time kinetics approximation for calculation of equilibrium intensity values, the magnetic contribution to the ‘mixing’ energy of atoms (in low-spin states) of this alloy facilitates its atomic ordering, and the presence of atoms with essentially different spins may cause the virtually abrupt phase transition from paramagnetic state into magnetic one. The optimal sets of exchange-interaction energy parameters for f.c.c. Ni–Fe alloy are selected. As shown, the doping of small amounts of interstitial C impurities most likely increases ferromagnetic component of bond of Ni spins with Fe spins, reduces ferromagnetic component of bond of Ni spins with Ni spins, and in-creases antiferromagnetic component of bond of Fe spins with Fe spins in an f.c.c.-Ni–Fe alloy.

Amorphous materials: Properties, structure, and durability: Constrained interactions, rigidity, adaptative networks, and their role for the description of silicates

Silicate glasses can be seen as connectivity networks where specific tools are used for the understanding of the behavior with composition of their chemical and physical properties. These tools make use of the effective interatomic interactions and mechanical constraints such as those used for analyzing the stability of macroscopic trusses. We first describe how complex interactions and coordination numbers can be efficiently handled within a general framework. The ingredients of the general framework, also known as mean-field bond constraint theory, are then presented. The theory predicts flexible to stressed-rigid elastic phase transitions at threshold compositions (or mean-coordination numbers). Applications to alkali- and alkaline-earth-silicates are considered and experimental signatures of the phase transition identified. Finally, we focus on the latest development in the field, namely the appearance of a new self-organized intermediate phase between flexible and stressed-rigid phases. Experimental signatures of these phases are reviewed, and the tools of adaptative silicate networks used to understand their features.

Double-segregation effect inAgxPd1−x∕Ru(0001)thin film nanostructures

We study the structural properties of ultrathin ${\mathrm{Ag}}_{x}{\mathrm{Pd}}_{1\ensuremath{-}x}$ films on top of a Ru(0001) substrate. Effective interatomic interactions, obtained from first-principles calculations, have been used in Monte Carlo simulations to derive the distribution of the alloy components in a four-monolayer (4-ML) Ag-Pd film. Though Ag-Pd alloys show complete solubility in the bulk, the thin film geometry leads to a pronounced segregation between Ag and Pd atoms with a strong preference of Ag atoms toward the surface and Pd atoms toward the interface. The theoretical prediction of this double-segregation effect is strongly supported by photoelectron spectroscopy experiments carried out for 4-ML thin films. We also show, in an additional experiment, that even in the case where initially 1 ML Ag is buried under 6 ML Pd, the whole Ag ML segregates to the surface.

The charge excess functional theory and ordering properties of metallic alloys

Many current models of ordering phenomena in metallic alloys are based on the approximation that effective atomic interactions can be truncated by considering few-body terms only. As it has been recently shown, the charge excess functional theory (CEF) very accurately accounts for total energies and charge transfers in metallic alloys. The parameters required by the CEF theory can be easily obtained from ab initio electronic structure calculations. For binary alloys, only three CEF parameters are needed: two of them are related with the response of each atomic site to an external perturbing field, while the third is connected with the alloying species electronegativity difference. In this paper, I shall discuss the effective interatomic interactions that are implied by the CEF model. In particular, I will show that, once put in Hamiltonian form, in spite of its simplicity, the theory contains infinite body effective atomic interactions. Furthermore, in the special case in which the above responses have the same numerical values for all the alloying species, it is shown that the theory becomes equivalent to an Ising model with infinite range pair-wise interactions. The consequences for the ordering mechanisms in metallic alloys are discussed.

A microscopic theory of photonucleation: Density functional approach to the properties of a fluid of two-level atoms, a part of which is excited

The studies of equilibrium properties of a gas of identical atoms, a part of which is in an excited electronic state, have attracted attention for the last forty years [1–10]. Such atoms may appear due to the electromagnetic irradiation with the frequency, which corresponds to the excitation energy of the atom. Since the life-time of the excited state is essentially larger than the time required for establishing the equilibrium over translational degrees of freedom, the system should exhibit equilibrium properties at a given (nonequilibrium) concentration of excited atoms. Moreover, owing to new effective long-range interatomic interactions – the resonance dipole-dipole interactions – one may expect essential changes of various equilibrium characteristics due to the presence of excited atoms. The analysis performed within the framework of the cluster expansion method confirmed these expectations (see [7,8] and references therein). On the other hand, there are only a few papers which may be related to experimental observations of theoretically investigated features of the gas with excited atoms. We should mention here the papers on the effect of irradiation on the condensation of iodine and anthracene vapor [11,12] and on the photonucleation [13–21], in particular, in vapors of mercury and cesium. The latter studies reported the quantitative results of resonance irradiation effect on the nucleation rate. The main conclusion of these studies is as follows: the resonance irradiation of the nucleation zone leads to a sharp increase of the nucleation rate. The experimental results, to our best knowledge, have not been explained so far. One may

Computer simulation of morphological evolution and coarsening kinetics of δ′ (Al 3Li) precipitates in Al–Li alloys

The morphological evolution and coarsening kinetics of L1 2 ordered (Al 3Li) precipitates ( δ′) in a f.c.c. disordered matrix ( α) were investigated using computer simulations based on microscopic diffusion equations. The effective interatomic interactions were fitted to the phase diagram using a two-neighbor mean-field model whereas the kinetic parameter in the microscopic diffusion equation was fitted to the chemical diffusion coefficient in the equilibrium disordered phase. The coalescence or encounter among precipitates which belong to any one of the four different antiphase domains of the L1 2 ordered phase is automatically taken into account. Volume fractions ranging from 20 to 65% were studied. Structure, scaling and particle-size distribution (PSD) functions were calculated. It is shown that the PSDs become increasingly broad and their skewness changes sign from negative to positive with increasing precipitate volume fraction. It is found that the cube of the average particle radius varies approximately linearly with time in the scaling regime for all the volume fractions studied, with the rate constant increasing with volume fraction. During coarsening, the volume fraction is not constant, approaching the equilibrium value asymptotically with time. The results are compared with existing analytical theories and experimental measurements.

Effective Interatomic Interactions VIA The TB-LMTO Method

ABSTRACTThe energetics of metallic alloys, their surfaces or interfaces, and magnetic multilayers is studied in terms of effective interatomic (or interlayer) interactions that are determined from ab initio electronic structure calculations using the TB-LMTO method combined with the coherent potential approximation and the method of surface Green functions. First the theoretical background (force theorem, Lloyd formula, generalized perturbation method for bulk and surfaces, vertex cancellation theorem, method of infinitesimal rotations) is discussed, and then the applications to the phase stability of bulk alloys, surface segregation in disordered alloys, magnetism-induced ordering in two- and three-dimensional systems, phase diagram of two-dimensional alloys, interlayer exchange coupling in metallic multilayers, and the construction of Heisenberg-like Hamiltonians for magnetic systems are presented.

Effective Interatomic Interactions in Liquid Metals

Abstract Some liquid metals can be regarded as a binary mixture of ions and electrons interacting via binary interparticle interactions with each other. It is shown exactly on the basis of the density-functional method that a liquid metal can be taken as a quasi one-component system only via a pairwise interatomic interaction (without a many-body force) to obtain the radial distribution function, provided that a liquid metal can be thought of as an ion-electron mixture with binary interactions.

First-principles study of surface segregation in Cu-Ni alloys.

A method coupling electronic structure calculations with Monte Carlo simulations has been developed to determine surface compositions in Cu-Ni alloys. The calculations are based on an effective Ising model with parameters as defined within the framework of the generalized perturbation method and as calculated by means of the tight-binding version of the linear-muffin-tin-orbital method. Properties of Cu-Ni bulk alloys are discussed in terms of bulk effective interatomic interactions. The composition profiles are obtained for the fcc (001) surface for three bulk compositions, namely, ${\mathrm{Cu}}_{75}$${\mathrm{Ni}}_{25}$, ${\mathrm{Cu}}_{50}$${\mathrm{Ni}}_{50}$, and ${\mathrm{Cu}}_{25}$${\mathrm{Ni}}_{75}$. The major role played by the layer-dependent site-diagonal terms in the Ising model is emphasized. Our results are found to be in agreement with available experimental data.

Study of Phonon Eigenfrequencies in Metallic Glasses

AbstractThe density fluctuations in terms of phonon eigenfrequencies are studied in Ni50Zr50 and Cu66Ti34 metallic glasses using two different theoretical approaches. The calculated results of phonon eigenfrequencies show all the main characteristic features of the dispersion curves. The effective interatomic interactions are studied in terms of a pair potential using the extended theory of the Wills‐Harrison potential which includes the effect of d‐band electrons. Finally, from the low wave‐vector transfer region of the dispersion curves, some thermodynamical properties are also calculated which are in agreement with each other.

Atomistic modeling of materials properties by Monte Carlo Simulation

AbstractIn order to optimize materials properties, in many cases a deeper understanding of the relationship between the chemical‐atomistic structure and the physical properties of the solid and fluid phases of the material is necessary. Monte Carlo simulation is a tool that allows the reliable calculation of thermodynamic properties of strongly interacting many‐body condensed matter systems. Given a model of effective interatomic or intermolecular interactions (drawn either from quantum‐chemical‐type interactions or from analysis of suitable experimental data), macroscopic bulk properties of a material can be simulated, as well as interfacial phenomena and certain kinds of slow dynamic processes (of relaxational or diffusive type). After a brief review of the foundations of this approach in statistical mechanics, the wide potential of this method is illustrated with examples taken from magnetism, metallurgy and amorphous polymeric materials. Strengths and limitations of this atomistic approach towards modeling materials properties are discussed and directions of future research are spelled out.

A theoretical study of the structure and dynamics of amorphous Fe

The extended theory of transition-metal potential, which includes the transition-metal d states, is used to obtain the effective interatomic interactions in terms of pair potential for amorphous Fe. Pair potential for amorphous Fe is also computed using a simple approach for liquid metals given by de-Angelis and March. We employ the so obtained pair potentials to calculate the longitudinal- and transverse-phonon eigenfrequencies using the theory of phonons in amorphous solids. The results for the phonon eigenfrequencies obtained from these potentials are in good qualitative agreement with the molecular-dynamics results as well as with the theoretical results of Bhatia and Singh. Computation of the Debye temperature and the isothermal bulk modulus also shows a close agreement with other results.