First-principles statistical mechanics of structural stability of intermetallic compounds

Temperature-driven phase transition of Ti2CN from first-principles calculations

First-principles evolutionary simulations are used to predict the stable compound of Ti2CN. Body-centered tetragonal I41/amd-Ti2CN is found to be more energetically favorable than other Ti2CN compounds at 0 K. The...

DFT-CEF Approach for the Thermodynamic Properties and Volume of Stable and Metastable Al–Ni Compounds

The Al–Ni system has been intensively studied both experimentally and theoretically. Previous first-principles calculations based on density-functional theory (DFT) typically investigate the stable phases of this system in their experimental stoichiometry. In this work, we present DFT calculations for the Al–Ni system that cover stable and metastable phases across the whole composition range for each phase. The considered metastable phases are relevant for applications as they are observed in engineering alloys based on Al–Ni. To model the Gibbs energies of solid phases of the Al–Ni system, we combine our DFT calculations with the compound energy formalism (CEF) that takes the Bragg–Williams–Gorsky approximation for the configurational entropy. Our results indicate that the majority of the investigated configurations have negative energy of formation with respect to Al fcc and Ni fcc. The calculated molar volumes for all investigated phases show negative deviations from Zen’s law. The thermodynamic properties at finite temperatures of individual phases allow one to predict the configurational contributions to the Gibbs energy. By applying a fully predictive approach without excess parameters, an acceptable topology of the DFT-based equilibrium phase diagram is obtained at low and intermediate temperatures. Further contributions can be added to improve the predictability of the method, such as phonons or going beyond the Bragg–Williams–Gorsky approximation that overestimates the stability range of the ordered phases. This is clearly demonstrated in the fcc order/disorder predicted metastable phase diagram.

Cluster expansion Monte Carlo study of indium–aluminum segregation and homogenization in CuInSe2–CuAlSe2 pseudobinary alloys

Systematic cluster expansion Monte Carlo simulations of CuIn_1−xAl_xSe₂ alloys probe the origin and evolution of In–Al segregation behavior comprehensively.

Investigation of compound formation sequence in Al/Ni/…/Al/Ni multilayer system under conditions of an excessive amount of one component and its prediction using the analogy with gas system behavior

Interaction processes in Al/Ni/.../Al/Ni multilayer systems with an excess of one of the components are studied by of DSC, XRD and TEM methods. It is shown that the compounds formation sequence differs depending on which component is excessive. There is proposed a rule for compounds formation sequence in systems with an excess of one of the initial phases. It is based on the assumption that behaviour of two contacting solid phases system is analogical to that of a gas system: energy density change in a solid-state system is analogical to pressure change in gas system. The prediction is built on the calculation of parameter ΔH⁰/νV, where ΔH⁰ and νV are enthalpy change and volume of new phase forming as a result of the reaction.

Configurational Entropy in Multicomponent Alloys: Matrix Formulation from Ab Initio Based Hamiltonian and Application to the FCC Cr-Fe-Mn-Ni System

Configuration entropy is believed to stabilize disordered solid solution phases in multicomponent systems at elevated temperatures over intermetallic compounds by lowering the Gibbs free energy. Traditionally, the increment of configuration entropy with temperature was computed by time-consuming thermodynamic integration methods. In this work, a new formalism based on a hybrid combination of the Cluster Expansion (CE) Hamiltonian and Monte Carlo simulations is developed to predict the configuration entropy as a function of temperature from multi-body cluster probability in a multi-component system with arbitrary average composition. The multi-body probabilities are worked out by explicit inversion and direct product of a matrix formulation within orthonomal sets of point functions in the clusters obtained from symmetry independent correlation functions. The matrix quantities are determined from semi canonical Monte Carlo simulations with Effective Cluster Interactions (ECIs) derived from Density Functional Theory (DFT) calculations. The formalism is applied to analyze the 4-body cluster probabilities for the quaternary system Cr-Fe-Mn-Ni as a function of temperature and alloy concentration. It is shown that, for two specific compositions (Cr 25Fe 25Mn 25Ni 25 and Cr 18Fe 27Mn 27Ni 28), the high value of probabilities for Cr-Fe-Fe-Fe and Mn-Mn-Ni-Ni are strongly correlated with the presence of the ordered phases L1 2 -CrFe 3 and L1 0-MnNi, respectively. These results are in an excellent agreement with predictions of these ground state structures by ab initio calculations. The general formalism is used to investigate the configuration entropy as a function of temperature and for 285 different alloy compositions. It is found that our matrix formulation of cluster probabilities provides an efficient tool to compute configuration entropy in multi-component alloys in a comparison with the result obtained by the thermodynamic integration method. At high temperatures, it is shown that many-body cluster correlations still play an important role in understanding the configuration entropy before reaching the solid solution limit of high-entroy alloys (HEAs).

Synthesis of Xenon and Iron-Nickel Intermetallic Compounds at Earth's Core Thermodynamic Conditions

Using in situ synchrotron x-ray diffraction and Raman spectroscopy in concert with first principles calculations we demonstrate the synthesis of stable Xe(Fe,Fe/Ni)_{3} and XeNi_{3} compounds at thermodynamic conditions representative of Earth's core. Surprisingly, in the case of both the Xe-Fe and Xe-Ni systems Fe and Ni become highly electronegative and can act as oxidants. The results indicate the changing chemical properties of elements under extreme conditions by documenting that electropositive at ambient pressure elements could gain electrons and form anions.

Exchange-Correlation Catastrophe in Cu-Au: A Challenge for Semilocal Density Functional Approximations

Semilocal density functional approximations occupy the second rung of the Jacob's ladder model and are thus expected to have certain limits to their applicability. A recent study [Y. Zhang, G. Kresse, and C. Wolverton, Phys. Rev. Lett. 112, 075502 (2014)] hypothesizes that the formation energy, being one of the key quantities in alloy theory, would be beyond the grasp of semilocal density functional theory (DFT). Here, we explore the physics of semilocal DFT formation energies and shed light on the connection between the accuracy of the formation energy and the ability of a semilocal approximation to produce accurate lattice constants. We demonstrate that semilocal functionals designed to perform well for alloy constituents can concomitantly solve the problem of alloy formation energies.

A basin-hopping Monte Carlo investigation of the structural and energetic properties of 55- and 561-atom bimetallic nanoclusters: the examples of the ZrCu, ZrAl, and CuAl systems

We report a basin-hopping Monte Carlo investigation within the embedded-atom method of the structural and energetic properties of bimetallic ZrCu, ZrAl, and CuAl nanoclusters with 55 and 561 atoms. We found that unary Zr55, Zr561, Cu55, Cu561, Al55, and Al561 systems adopt the well known compact icosahedron (ICO) structure. The excess energy is negative for all systems and compositions, which indicates an energetic preference for the mixing of both chemical species. The ICO structure is preserved if a few atoms of the host system are replaced by different species, however, the composition limit in which the ICO structure is preserved depends on both the host and new chemical species. Using several structural analyses, three classes of structures, namely ideal ICO, nearly ICO, and distorted ICO structures, were identified. As the amounts of both chemical species change towards a more balanced composition, configurations far from the ICO structure arise and the dominant structures are nearly spherical, which indicates a strong minimization of the surface energy by decreasing the number of atoms with lower coordination on the surface. The average bond lengths follow Vegard's law almost exactly for ZrCu and ZrAl, however, this is not the case for CuAl. Furthermore, the radial distribution allowed us to identify the presence of an onion-like behavior in the surface of the 561-atom CuAl nanocluster with the Al atoms located in the outermost surface shell, which can be explained by the lower surface energies of the Al surfaces compared with the Cu surfaces. In ZrCu and ZrAl the radial distribution indicates a nearly homogeneous distribution for the chemical species, however, with a slightly higher concentration of Al atoms on the ZrAl surface, which can also be explained by the lower surface energy.

Nonlocal first-principles calculations in Cu-Au and other intermetallic alloys

Cu-Au is the prototypical alloy system used to exemplify ordering and compound formation, and it serves as a testbed for all new alloy theory methods. Yet, despite the importance of this system, conventional density functional theory (DFT) calculations with semilocal approximations have two dramatic failures in describing the energies of this system: (1) DFT formation energies of the observed Cu3Au and CuAu compounds are nearly a factor of 2 smaller in magnitude than experimental values, and (2) DFT predicts incorrect ordered ground states ground states for Au-rich compositions. Here, we show how modern extensions of DFT based on nonlocal interactions can rectify both of these failures. Our corrections shed light on improving the theoretical predictions for alloy systems to determine accurate formation energies, order-disorder critical temperatures, phase diagrams, and high-throughput computations.

Phase relationships and structures of inorganic crystals by a combination of the cluster expansion method and first principles calculations

Properties of crystalline solutions are generally dependent not only on their chemical composition but also on the configurations of solute atoms and/or point defects. Quantitative knowledge of the configuration-dependent properties is therefore essential for materials design. The cluster expansion (CE) method has been widely used to describe the configurational properties. Increases in computational power and advances in numerical techniques enable us to perform a large set of systematic first principles calculations based on density functional theory (DFT) to be combined with CE calculations. In this paper, our procedure of CE with optimal selections of clusters and DFT structures is described. Two examples of such calculations are then shown. One is the cation arrangement in a series of spinel oxides. The other is arrangement of the oxygen vacancy in a series of tin sub-dioxides.

First-principles study of phase equilibria in Cu-Pt-Rh disordered alloys

Phase stability of Cu-Pt-Rh ternary disordered alloys is examined by a combination of cluster expansion techniques and Monte Carlo statistical simulation based on first-principles calculation. The sign of pseudo-binary ECIs indicates that neighboring Cu and Pt strongly prefer unlike-atom pairs, Pt and Rh weakly prefer unlike-atom pairs, and Cu and Rh atoms prefer like-atom pairs, indicating that the ternary alloy retains the ordering tendency of the constituent binary alloys. The formation energy of a random alloy at T = 1200 K exhibits a negative sign for a wide range of Pt-rich compositions, while at Pt-poor compositions of x≤0.25, the formation energy has a positive value. Calculated affinities for the random alloy show the variety of energetically favored bonds for the alloy: Cu-Pt bonds in both first-and second-nearest neighbor (1-NN and 2-NN) are energetically preferred for all the composition range, the Pt-Rh bond in 1-NN is preferred at Pt-rich compositions, the Pt-Rh in 2-NN and Rh-Cu in 1-NN bonds are unfavored for all compositions, and the Rh-Cu bond in 2-NN is unfavored for Pt-poor compositions. We elucidate that the ordering tendency of 1-NN and 2-NN Cu-Pt, 2-NN Pt-Rh and 1-NN Cu-Rh atoms in constituent binary alloys is retained for the whole composition range of Cu-Pt-Rh ternary alloys, while that of 1-NN Pt-Rh and 2-NN Cu-Rh atoms significantly depends on composition.

First-principles theory of competing order types, phase separation, and phonon spectra in thermoelectric AgPbmSbTe(m+2) alloys

Using a first-principles cluster expansion, we shed light on the solid-state phase diagram and structure of the recently discovered high-performance Pb-Ag-Sb-Te thermoelectrics. The calculated bulk thermodynamics favors the formation of coherent precipitates of ordered Ag(m)Sb(n)Te(m+n) phases immiscible with rocksalt PbTe, such as AgSbTe2. The solubility is high for Pb in AgSbTe2 and low for (Ag,Sb) in PbTe (8% vs 0.6% at 850 K). The differences in the phonon spectra of PbTe and AgSbTe2 suggest that these precipitates enhance the thermoelectric performance by lowering thermal conductivity.

Ordering and magnetism in Fe-Co: dense sequence of ground-state structures

We discover that Fe-Co alloys develop a series of ordered ground-state structures in addition to the known CsCl-type structure. This new set of structures is found from a combinatorial ground-state search of 1.5 x 10(10) bcc-based structures. The energies of the searched bcc structures are constructed with the cluster expansion method from few first-principles calculations of ordered Fe-Co structures. The set of new ground-state structures is explained from the decay behavior of the cluster expansion coefficients which allows us to identify a simple geometric motif common to all structures. The appearance of these FeCo superstructures offers a broader view of the ordering reactions in bipartite-lattice based binary alloys.

Ab initio study of phase equilibria in TiC(x)

The phase diagram for the vacancy-ordered structures in the substoichiometric TiC(x) (x = 0.5-1.0) has been established from Monte Carlo simulations with the long-range pair and multisite effective interactions obtained from ab initio calculations. Three ordered superstructures of vacancies (Ti(2)C, Ti(3)C(2), and Ti(6)C(5)) are found to be ground state configurations. Their stability has been verified by full-potential total energy calculations of the fully relaxed structures.

Spontaneous L1(2) order at Ni(90)Al(10)(110) surfaces: an x-ray and first-principles-calculation study

We have combined x-ray diffraction studies with first-principles calculations to study the interplay between segregation and ordering at the (110) surface of Ni(90)Al(10). We find a L1(2)-ordered monolayer at the surface. The observed ordering as well as recently reported Al segregation at the surface are explained in a consistent picture. A delicate competition between the tendency for Al segregation and ordering in the Ni-Al system induced by the symmetry break at the surface stabilizes a long-range ordered surface in the entire concentration range c(Ni)>0.75.