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A new route to achieve high strength and high ductility compositions in the Cr-Co-Ni medium entropy alloys (MEAs) is proposed, by controlling the solid solution hardening parameter (Mean Square Atomic Displacement, MSAD) and twinning propensity parameter (Stacking Fault Energy, SFE), respectively. The MSAD is calculated to increase with the increase in the Cr content and with the increase in the Ni/Co ratio at high Cr concentrations, while the SFE is calculated to decrease with the increase in the Cr content and with the increase in the Co/Ni ratio at high Cr concentrations. In experiment, the strength at 0 K (derived from the temperature dependence of yield stress) increases as the Cr content increases and/or as the Ni content increases for a given high Cr content, so that a linear correlation is found between the yield strength at 0 K and MSAD. The SFE also decreases as the Cr content increases and as the Co content increases for a given high Cr content. However, while the tensile elongation increases with the decrease in SFE down to SFE values of 10–12 mJ/m2, it abruptly decreases once the SFE decreases below this value due to a change in major deformation mode from deformation twinning to deformation-induced ε-martensite transformation. Based on the established connection between the theoretical calculation and experimental measurement, outstanding combinations of strength and ductility are predicted and experimentally confirmed at high Cr compositions and at a bit Ni-rich side of the Co/Ni equi-composition line. The proposed composition (around 45Cr-20Co-35Ni) exhibits a greater 0 K strength and a superior 77 K tensile ductility by 32 % and 13 %, respectively, compared to those of the equiatomic Cr-Co-Ni alloy., 新規高強度高延性合金の開発に成功 --計算と実験の融合による合金設計法の確立--. 京都大学プレスリリース. 2023-05-25.

MoSi2/Mo5Si3 eutectic composites have been considered as one of the promising candidates for ultra-high temperature structural applications owing to their high melting point, good oxidation resistance, and low mass density. Their mechanical properties can be improved by controlling the eutectic structure (i.e. script lamellar structure) in directional solidification. It is important to elucidate the dominant factors underlining the unique pattern formation. We conducted a comprehensive phase field study to examine the influence of various factors on the MoSi2/Mo5Si3 eutectic microstructure with complicated morphology. First, the inclined lamellae have been attributed to the minimization of elastic strain energy due to the lattice mismatch between MoSi2 and Mo5Si3, which are partially relaxed by forming semi-coherent phase boundaries. Second, the maze-like pattern on the horizontal cross-section appeared when a two-fold anisotropy of interfacial energy is superimposed on the MoSi2/Mo5Si3 boundary. Third, the random and intersected lamellae have been obtained by assuming the instability of the solid-liquid interface and introducing successive nucleation of Mo5Si3 phase. These findings provide guidance for manipulating the eutectic structure and act as footsteps for further theoretical investigation.

In order to predict the potential energy surface (PES) from measured structure in equilibrium state, one should typically perform trial-and-error statistical thermodynamic simulation with assumed multibody interactions. Very recently, we derive map from a set of equilibrium structure in crystalline solids to that of corresponding PES in explicit matrix form, where the PES can be inversely determined from the measured structure. The practical problem to construct the map appears when system size of measured structure is not sufficiently large, which results in non-trivial treatment of asymmetry problem in the map. The present study proposes alternative approach to avoiding treatment of the asymmetry problem, demonstrating more accurate prediction of the PES than the map constructed by explicitly treating the asymmetry., 3pages, 3figures

We propose theoretical approach based on combination of graph theory and generalized Ising model (GIM), which enables systematic determination of extremal structures for crystalline solids without any information about interactions or constituent elements. The conventional approach to find such set of structure typically employs configurational polyhedra (CP) on configuration space based on GIM description, whose vertices can always be candidates to exhibit maximum or minimum physical quantities. We demonstrate that the present approach can construct extended CP whose vertices not only include those found in conventional CP, but also include other topologically and/or configurationally characteristic structures on the same dimensional configuration space with the same set of figures composed of underlying lattice points, which therefore has significant advantage over the conventional approach., 4 pages, 4 figures

For classical discrete systems with constant composition (typically referred to substitutional alloys) under thermodynamically equilibrium state, macroscopic structure should in principle depend on temperature and many-body interaction through Boltzmann factor, exp(-bE). Despite this fact, our recently find that (i) thermodynamic average for structure can be characterized by a set of special microscopic state whose structure is independent of energy and temperature, and (ii) bidirectional-stability character for thermodynamic average between microscopic structure and potential energy surface is formulated without any information about temperature or many-body interaction. These results strongly indicates the significant role of configurational geometry, where anharmonicity in structural degree of freedom (ASDF) that is a vector field on configuration space, plays central role, intuitively corresponding to nonlinearity in thermodynamic average depending only on configurational geometry. Although ASDF can be practically drawn by performing numerical simulation based on such as Monte Carlo simulation, it is still unclear how its entire character is dominated by geometry of underlying lattice. We here show that by applying the limit in tropical geometry (i.e., tropical limit) with special scale-transformation to discrete dynamical system for ASDF, we find tropical relationships between how nonlinearity in terms of configurational geometry expands or shrinks and geometric information about underlying lattice for binary system with a single structural degree of freedom (SDF). The proposed tropical limit will be powerful procedure to simplify analyzation of complicated nonlinear character for thermodynamic average with multiple SDF systems., Comment: 5 pages, 3 figures (More accurate expression for series expansion is applied)

A phase-field study has been conducted to obtain an understanding of the formation mechanism of the script lamellar pattern of MoSi2/Mo5Si3 eutectic composite, which is a promising candidate for high-temperature structural application. The spacing of the lamellar pattern in the simulation results shows good agreement with that of experimental observations and analytical solutions under three growth rates: 10 mm/h, 50 mm/h, and 100 mm/h. The discontinuity of Mo5Si3 rods, in contrast to the regular eutectic with a continuous pattern, is claimed to be caused by the instability of the solid-liquid interface. In this study, the implementation of Mo5Si3 nucleation over the solid-liquid interface has been proposed and successfully reproduced the characteristic of discontinuity. A highly random and intersected lamellar pattern similar to that observed in the ternary MoSi2/Mo5Si3 eutectic alloyed with 0.1at% Co has been obtained in simulation owing to the increase in the frequency of nucleation. In addition, it has been demonstrated that the inclination of the Mo5Si3 rod can be reproduced by taking into account the strong relaxation of lattice strain energy, which is generally considered to be negligible in eutectic reaction, as the result of the formation of ledge-terrace structure., Comment: 19 pages, 13 figures

For substitutional alloys typically referred to as classical discrete systems under constant composition, a set of microscopic states dominantly contributing to thermodynamically equilibrium struct...

Variations in the fracture toughness of lamellar-structured C40/C11b silicides as a function of the microstructure were examined by using Cr-, Zr-, and Ir-added (Mo0.85Nb0.15)Si2 crystals. Fracture toughness variation showed strong orientation dependence, governed by the occurrence frequency of delamination and crack deflection. The refinement of the lamellar microstructure by Ir-addition led to an increase in fracture toughness when the lamella boundary was laid perpendicular to the loading axis, although it decreased at other orientations. The variation in fracture toughness when the alloyed crystal was loaded parallel to the lamellar boundary qualitatively showed good agreement with the predictions by first-principles calculations on the cohesive energy of the C40/C11b interface.

Sum peaks, escape peaks, and diffraction peaks are considered artificial or spurious peaks in energy dispersive X-ray spectrometry. Experimental examples are given, which showed that escape and diffraction peaks can add up to become sum peaks. These artificial peaks are not weak, and great care must be taken to differentiate them from peaks due to impurity or trace elements. The relationship between the intensity of a sum peak and the original peaks is illustrated using computer simulation as well as probability theory. Copyright © 2016 John Wiley & Sons, Ltd.

To clarify the thermodynamic stability of a Mg-based long-period stacking ordered (LPSO) structure, we systematically study the energetic preference for alloys on multiple stacking sequences with different compositions for random mixing of constituent elements, Mg, Y, and Zn, based on special quasirandom structure (SQS). Through calculation of the formation free energy of SQSs, it was found that the Mg–Y–Zn alloy exhibits phase separation into Mg- and Y–Zn- rich phases, which is consistent with previous theoretical studies. The bulk modulus of SQSs for various compositions, stacking sequences, and atomic configurations is approximately 35 GPa, i . e ., it does not show significant dependence on the atomic arrangements, which therefore means that there are not significant differences among the effects of phonon on the stability of each structure in the LPSO structure. Introducing a stacking fault into hcp stacking sequence results in the acquisition of a “negative” energy, which indicates the profound relationship between the introduction of stacking faults and the formation of an LPSO structure.

Configurational polyhedora (CP) is a hyperpolyhedra on multidimensional configuration space, whose vertex (and edges) corresponds to upper or lower limit value of correlation functions for all possible atomic configuration on given lattice. In classical systems where physical property including internal energy and elastic modulus can be a linear map for structures considered, it is known that atomic configuration having highest (or lowerst) physical quantity should always locate on one of the vertices at absolute zero temperature. The present study extend the idea of CP to finite-temperature property (especially, focusing on internal energy), and successfully provides demonstration of how temperature dependence of internal energy in equilibrium state for alloys is interpreted in terms of the density of states for non-interacting system along specially selected direction on cofiguration space., 4 figures

For a classical discrete system under constant composition, the macroscopic structure in a thermodynamically equilibrium state can be typically determined through the so-called canonical average, i...

Short-range ordering (SRO) tendency for disordered alloys is considered as competition between chemical ordering and geometric (mainly, difference in atomic radius for constituents) effects. Especially for multicomponent (including the so-called high entropy alloys (HEAs) near equiatomic composition), it has been considered as difficult to systematically characterize the SRO tendency only by geometric effects, due mainly to the fact that (i) chemical effects typically plays significant role, (ii) near equiatomic composition, we cannnot classify which elements belong to solute or solvent, and (iii) underlying lattice for pure elements can typically differ from each other. Despite these facts, we here show that SRO tendency for seven fcc-based alloys including subsystems of Ni-based HEAs, can be well characterized by geometric effects, where corresponding atomic radius is defined based on atomic configuration with special fluctuation, measured from ideally random structure. The present findings strongly indicate the significant role of geometry in underlying lattice on SRO for multicomponent alloys., Comment: 5 pages, 3 figures

We developed a phase-field model of C11b-MoSi2/C40-NbSi2 duplex silicide incorporating elastic inhomogeneity, and simulated microstructure formation and interface segregation. We examined the effect of elastic inhomogeneity on the morphology, volume fraction of the C11b-precipitate, stress distribution, and solute partitioning. In the simulations, parameters evaluated by first-principles calculation are used for the experimentally unknown parameters. The lamellar structure was not formed in the case incorporating the elastic strain energy only and ignoring the anisotropy of the interfacial energy. When the anisotropy of the interfacial energy was taken into account, the lamellar structure was formed parallel to (0 0 0 1)C40 as observed in the experiment. It was also found that the elastic strain energy changes the equilibrium concentrations by >0.2 at%, but the difference between the equilibrium concentrations in homogeneous and inhomogeneous systems was

Based on the first-principle calculation combined with cluster expansion technique and Monte Carlo statistical simulation, we propose an optimization of local electronic structure in bimetallic nanoparticles. We apply the proposed optimization to Pt-Rh nanoparticles, and find that Pt d -band center can be quantitatively described by finite set of basis functions in terms of atomic arrangements. Consequently, electronic structures of Pt d -band at specific site can be reasonably controlled by changing surrounding atomic arrangements, which enables systematic changes in molecular adsorption energy.

We propose a new approach to constructing a phase diagram using the effective Hamiltonian derived only from a single real-space image produced by scanning tunneling microscopy (STM). Currently, there have been two main methods to construct phase diagrams in material science: ab initio calculations and CALPHAD with thermodynamic information obtained by experiments and/or theoretical calculations. Although the two methods have successfully revealed a number of unsettled phase diagrams, their results sometimes contradicted when it is difficult to construct an appropriate Hamiltonian that captures the characteristics of materials, e.g., for a system consisting of multiple-scale objects whose interactions are essential to the system’s characteristics. Meanwhile, the advantage of our approach over existing methods is that it can directly and uniquely determine the effective Hamiltonian without any thermodynamic information. The validity of our approach is demonstrated through an Mg–Zn–Y long-period stacking-ordered structure, which is a challenging system for existing methods, leading to contradictory results. Our result successfully reproduces the ordering tendency seen in STM images that previous theoretical study failed to reproduce and clarifies its previously unknown phase diagram. Thus, our approach can be used to clear up contradictions shown by existing methods.

Short-range order (SRO) in disordered alloys is typically interpreted as competition between chemical effect of negative (or positive) energy gain by mixing constituent elements and geometric effects comes from difference in effective atomic radius. Although we have a number of theoretical approaches to quantitatively estimate SRO at given temperatures, it is still unclear to systematically understand trends in SRO for binary alloys in terms of geometric character, e.g., effective atomic radius for constituents. Since chemical effect plays significant role on SRO, it has been believed that purely geometric character cannot quantitatively explain the SRO trends. Despite these considerations, based on the density functional theory (DFT) calculations on fcc-based 28 equiatomic binary alloys, we find that while convensional Goldschmidt or DFT-based atomic radius for constituents have no significant correlation with SRO, atomic radius for specially selected structure, constructed purely from information about underlying lattice, can successfully capture the magnitude of SRO. These facts strongly indicate that purely geometric information of the system plays central role to determine characteristic disordered structure., Comment: 4pages, 4figures

Cr segregation at lamellar interfaces in the MoSi 2 /NbSi 2 duplex silicide was examined using a newly developed phase-field model to elucidate the mechanism of interfacial segregation, which is believed to improve the thermal stability of lamellar structures as well as creep resistance. This is because lamellar structures can improve the high-temperature strength, and the stabilization of the lamellar structures improves creep resistance. The model takes into account the segregation energy determined using first-principles calculations to reflect the chemical interaction between the solute atoms and the interface, in addition to the elastic interaction. Cr segregation occurs at the interface when the segregation energy is considered, whereas no segregation occurs in the case where only the elastic interaction is considered. However, the extent of segregation was much smaller than that observed experimentally when the segregation energy was evaluated using first-principles calculations without considering lattice vibrations (i.e., the calculations were performed for 0 K). A simulation that took into consideration the segregation energy with the lattice vibrations at 1673 K resulted in segregation similar to that observed experimentally, where the Cr-added MoSi 2 /NbSi 2 duplex silicide was equilibrated at 1673 K, namely, the temperature at which the segregation energy was calculated. Thus, it was revealed that the solute-interface chemical interaction and its temperature dependence are responsible for the interfacial segregation of Cr. These results suggest that the segregation energy needs to be taken into account in the search for more effective additive elements for improving the thermal stability of lamellar structures as well as the creep resistance.

NbSi2/MoSi2 duplex silicide crystals are potentially a new-class of ultra-high temperature structural materials. Improvement in the thermal stability of their lamellar microstructure was accomplished by the addition of a minute amount of either Cr or Zr. The mechanical properties of the duplex silicide, such as fracture toughness and high temperature strength, show strong orientation dependence, thereby suggesting the importance of the control of microstructure to improve their properties.

MoSi2–based alloys are attracting attention as ultra-high temperature structural material for super-high efficiency gas turbine power generation systems. In this study, the effects of Cr-and Zr-addition on interface migration in MoSi2/NbSi2 lamellar silicide were examined by phase field simulations employing the segregation energies evaluated by the first principles calculation in addition to thermodynamic free energy in order to take into account the chemically-driven interfacial segregation. The simulation results indicate that both Cr and Zr can segregate at the lamellar interface to suppress its migration, and the Zr-addition is more effective to lower the interface migration rate than the Cr-addition owing to its higher segregation energy.

We demonstrate applicability of the proposed extended cluster expansion (CE) technique, enabling complete representation of strain effects on alloy configurational energy on single and multiple lattices. Complete and orthonormal basis function to describe configurational energy is constructed in terms of spin variable ω on virtual lattice and σ on base lattice, where the former specifies the strain of a given cell from the base cell. We estimate formation energy of superlattice composed of alternate stacking of ordered structures for Cu–Au binary alloys where the strain effects should play significant role. The proposed CE is shown to precisely estimate the strain effects on total energy for alloys, which cannot be essentially handled by the current CE.

For classical systems, expectation value of macroscopic property in equilibrium state can be typically provided through thermodynamic (so-called canonical) average, where summation is taken over possible states in phase space (or in crystalline solids, it is typically approximated on cofiguration space). Although we have a number of theoretical approaches enabling to quantitatively estimate equilibrium properties by applying given potential energy surface (PES) to the thermodynamic average, it is generally unclear whether PES can be stablly, inversely determined from a given set of properties. This essentially comes from the fact that bidirectional stability characters of thermodynamic average for classical system is not sufficiently understood so far. Our recent study reveals that for classical discrete system, this property for a set of microscopic states satisfying special condition can be well-characterized by a newly-introduced concept of anharmonicity in the structural degree of freedom of D, where these states are expected to be stably inversed to underlying PES, known without any thermodynamic information. However, it is still quantitatively unclear how the bidirectional stability character is broken inside the configuration space. Here we show that the breaking in bidirectional stability for thermodynamic average is quantitatively formulated: We find that the breaking is mainly dominated by the sum of divergence and Jacobian of vector field D in configuration space, which can be fully known a priori only from geometric information of underlying lattice, without using any thermodynamic information such as energy or temperature., Comment: 4 pages,1 figure

Our recent study reveals that macroscopic structure in thermodynamically equilibrium state and its temperature dependence for classical discrete system can be well-characterized by a single specially-selected microscopic state (which we call projection state: PS), whose structure can be known a priori without any information about energy or temperature. Although PS can be universally constructed for any number of components R, practical application of PS to systems with R >= 3 is non-trivial compared with R = 2 (i.e., binary system). This is because (i) essentially, multicomponent system should inevitably requires linear transformation from conventional basis functions to intuitively-interpreted cluster probability basis, i.e., multiple PS energies are required to predict one chosen pair probability, leading to practically accumulating numerical errors, and (ii) additionally, explicit formula for the transformation from basis functions to pair probabilities should be required, which has been explicitly provided up to ternary (R = 3) system so far. We here derive modified formulation to directly determine probability for likeand unlike-atom pair consisting of any chosen elements by using a single PS energy, with providing explicit relationship between basis functions and pair probabilities up to quinary (R = 5) systems. We demonstrate the validity of the formulation by comparing temperature dependence of pair probabilities for multicomponent systems from thermodynamic simulations., 8 pages. Detailed derivation of the proposed formulation of pair probability is added. Application to practical ternary system is added to demonstrate the validity of the present approach

For a classical discrete system on a periodic lattice under a constant composition, we show that the multivariate any-order moment for the configurational density of states (CDOS) before applying p...

Based on the first-principles calculation, we investigated Cr segregation behavior at the C11 b /C40 lamellar interface for MoSi 2 -based alloys. We first elucidated the energetically stable interface structure among possible contacts between C11 b and C40, where the interface energy is 1.7 meV/A 2 . Without inclusion of lattice vibrational contribution to segregation energy, Cr composition at the interface was lower than that at C40 phase, which was inconsistent with the early experimental result. Inclusion of the vibrational contribution successfully resulted in strong Cr segregation at the interface over that at C11 b as well as C40 phase. This indicates that Cr segregation at the most stable interface is a thermodynamically stable state, in which lattice vibration plays a significant role.

The effect of including an additional element, like Re, Cr, V, Zr or Ir, in (Mo0.85Nb0.15)Si2 crystals, carried out with the aim of improving the thermal stability of the fine lamellar microstructures of the crystals, was examined with the help of first-principles calculations. The addition improved the thermal stability of the microstructures at 1400 °C in all cases, and the effect was especially significant in crystals containing Cr and Zr additives. Quantitative evaluation by Moire fringe analysis revealed that the misfit strain at the interfaces in crystals with added Cr and Zr was smaller than those in crystals with other elements added. The reduced misfit strain resulted in the suppression of the rapid growth of the C11b phase precipitates that did not possess the variant orientation relationship with the C40 matrix, and hence the thermal stability of the fine lamellar microstructures improved. The results further revealed that the ratio of the atomic size of the additive element to that of Mo, which is the main constituent element in the C11b phase, is an important factor that controlled the misfit strain at the lamellar interface by the result of Cr addition. However, the addition of Zr was found to result in a significant improvement in the thermal stability of the lamellar microstructure, despite the markedly larger atomic radius of Zr compared with that of Mo. This indicates that there may be other factors, in addition to the atomic radius of the additive, contributing to the thermal stability.

We conducted phase-field simulations of microstructural evolution in C11b-MoSi2 / C40-NbSi2 dual phase alloy with and without Cr-addition to examine the factors responsible for the formation and stability of the lamellar structure on the basis of thermodynamics, micromechanics and first-principles calculations. The first principles calculation was used for evaluating the interfacial energy, segregation energy of solute Cr-atoms and lattice parameters of imaginary disilicides for estimating the effects of solute distribution on the lattice misfit. When both of lattice misfit and the anisotropy of interfacial energy is taken into account, a lamellar structure similar to that observed experimentally is formed. In the absence of Cr-addition, the straightness of lamellar structure decreased slightly. When an isotropic interfacial energy is assumed, lamellar structure is not formed. Instead, a microstructure with habit planes parallel to {1 0 $\bar 1$ 1} plane of C40-phase is formed. Thus, the anisotropy of interfacial energy is crucial for the lamellar structure formation rather than the elastic energy due to lattice misfit.

We have examined segregation behavior of various alloying elements at lamellar interfaces of C40-NbSi2/C11b-MoSi2 duplex silicide by a phase-field simulation, which takes into account not only bulk chemical free energy but also segregation energy evaluated by the first principles calculation to reflect interaction between solutes and interface. The simulation suggests that segregation behaviors greatly depend on additive elements. In the case of Cr-addition, the C40-phase becomes enriched with Nb and Cr, while the C11b-phase becomes enriched with Mo, which agrees with the equilibrium phase diagram. Slight segregation of Cr atoms is observed at the interface, whereas Nb and Mo concentrations monotonically change across the diffuse interface between C11b and C40 phases. Significant segregations of Zr and Hf are formed at static interfaces, which are attributed to the chemical interaction between solute atoms and the static interface.

We investigate the formation of long-period stacking ordered (LPSO) structure for Mg-Y-Zn ternary alloys based on the short-range order (SRO) tendency of energetically competitive disordered phases. We find that unisotropic SRO tendencies for structures with stacking faults cannot be simply interpreted by arithmetic average of SRO for constituent fcc and hcp stackings, indicating that the SRO should be significantly affected by periodically-introduced stacking faults. We also find that SRO for neighboring Y-Zn pair, which should have positive sign to form specific L12 type cluster found in LPSO, is strongly affected by the distance between stacking faults: e.g., five atomic layer distance does not prefer in-plane Y-Zn pair, while seven atomic layer distance prefer both in- and inter-plane Y-Zn pair. These facts strongly indicate that ordering tendency for the Mg-Y-Zn alloy is significantly dominated by the stacking faults as well as their periodicity. We also systematically investigate correlation between SRO for other Mg-RE-Zn (RE = La, Tb, Dy, Ho, Er) alloys and the physical property of RE elements. We find that while SRO for RE-Zn pair does not show effective correlation with atomic radius, it has strong quadratic correlation with atomic radius considering unisotoropy along in- and inter-plane directions., 4 pages, 3 figures

We investigate segregation behavior of additional elements M (=Ni, Co, Ta) at the C11 b /D8 m interface for MoSi 2 –Mo 5 Si 3 alloys, based on first-principles calculation. We first find energetically stable interface structure with interface energy of 0.08 eV/A 2 (1.3 J/m 2 ). Based on the stable interface, segregation energy for additional elements is calculated for individual atomic layer, which is applied to Monte Carlo statistical simulation under grand-canonical ensemble to quantitatively predict interface segregation profile. We find that our simulation successfully captures the characteristics in measured segregation tendency of (i) similarity in strong segregation at interface both for Ni and Co compared with bulk composition while Ta does not exhibit interface segregation and (ii) stronger segregation for Ni than for Co. The present results indicate that measured segregated interface for MoSi 2 –Mo 5 Si 3 alloys can be thermodynamically stable.

When spatial constraint for the constituents (e.g., atom or particle) of system is once given, disordered structure for non-interacting system in equilibrium states is symmetric with respect to equiatomic composition. Meanwhile, when the interaction between constituents is introduced, this symmetry is typically broken, naturally appearing compositional asymmetry. Although this asymmetry, depending on temperature, comes from multibody interactions in the system, we here clarify that the asymmetry near equiatomic composition can be universally well-characterized by two specially selected microscopic structure, which can be known a priori without any information about interactions or temperature: The key role is the class of spatial constraint. Based on the facts, we provide analytical expression of temperature dependence of disordered structure, and demonstrate its validity and applicability by predicting short-range order parameters of practical alloys compared with full thermodynamic simulation., Comment: 3pages, 2figures

We propose representation of configurational physical quantities and microscopic structures for multicomponent system on lattice, by extending a concept of generalized Ising model (GIM) to graph theory. We construct graph Laplacian (and adjacency matrix) composed of symmetry-equivalent neighboring edges, whose landscape of spectrum explicitly represents GIM description of structures as well as low-dimensional topological information in terms of graph. The proposed representation indicates the importance of linear combination of graph to further investigate the role of spatial constraint on equilibrium properties in classical systems. We demonstrate that spectrum for such linear combination of graph can find out additional characteristic microscopic structures compared with GIM-based descriptions for given set of figures on the same low-dimensional configuration space, coming from the proposed representation explicitly having more structural information for e.g., higher-order closed links of selected element. Statistical interdependence for density of microscopic states including graph representation for structures is also examined, which exhibits similar behavior that has been seen for GIM description of the microscopic structures., Comment: 8 pages, 6 figures. Interpretation of the proposed graph spectrum and intuitions for the proposed approach are added

We develop an approach to apply Wang-Landau algorithm to multicomponent alloys in semi-grand-canonical ensemble. Although the Wang-Landau algorithm has great advantages over conventional sampling methods, there are few applications to alloys. This is because calculating compositions in semi-grand-canonical ensemble using the Wang-Landau algorithm requires a multi-dimensional density of states in terms of total energy and compositions. However, constructing the multi-dimensional density of states is difficult. In this study, we develop a simple approach to calculate the alloy phase diagram using Wang-Landau algorithm, and show that compositions in semi-grand-canonical ensemble require just some one-dimensional densities of states. Finally, we applied the present method to Cu-Au and Pd-Rh alloys and confirmed that the present method successfully describes the phase diagram with high validity and accuracy., Comment: 6 pages, 6 figures

We propose a cluster expansion (CE) technique that can be applied to any atomic arrangement on alloy systems in their polymorphs. The proposed CE introduces virtual vacancy sites in the starting structure in order to describe the atomic positions for a variety of lattices. We derive the general condition for obtaining effective interactions in the present CE, which results in rigorous expansion of any properties on polymorphs in alloys. As an example, the proposed CE is combined with a density functional theory (DFT) calculation, applied to the description of internal energy for the Al–Na binary alloy system, which clarifies the concept and practical application of the CE to real systems. We successfully predict the tendency of phase separation as well as the most stable structures for Al (fcc) and Na (bcc) from information about the internal energy for structures other than fcc or bcc.

Based on a first-principles calculation, the effects of lattice vibration on the segregation behavior of Pt–Rh alloy nanoparticles is examined. Pt atoms naturally have lower vibrational free energy for sites with lower coordination number, while Rh atoms neighboring to the Pt atoms also have lower vibrational free energy with respect to Rh metal nanoparticles. Due to the substantial decrease in vibrational free energy for the Rh atoms neighboring Pt at the core site, lattice vibration increases the Pt on-site segregation energy from the core site to subsurface or surface sites. A significant difference in the temperature dependence of the on-site segregation energy between vertex and edge sites would lead to a reversal of segregation induced by lattice vibration, which is confirmed by cluster expansion and Monte Carlo statistical simulation.

We investigate the energetic stability and electronic structures of Pt-Rh icosahedral nanoparticles based on first-principles calculations. We find that Pt atom energetically prefers vertex and edge sites at the surface rather than subsurface and core sites, which is a tendency similar to PtRh cuboctahedral nanoparticles. This can be attributed to lower surface energy of Pt compared with Rh. Edges of nanoparticles with secondlowest coordination number are the most favorable sites for Pt atom. This could be attributed to the enhanced interatomic distance at the edge site. 1st order moment of d-state electronic contribution for Pt atom exhibits almost negative dependence in terms of Pt coordination number. This can be qualitatively interpreted by positive dependence of 2nd order moment of the density of states for the Pt atom on the coordination number. Pt surface segregation is expected mainly due to contribution from Pt on-site segregation energy compared with weak ordering tendency of Pt-Rh unlike-atom pairs. [doi:10.2320/matertrans.M2011055]

Potential energy landscape (PEL) is essential to determine phase stability, reaction path, and other important physical as well as chemical properties. Whereas given PEL can reasonably determine the properties in thermodynamically equilibrium state, it is generally unclear whether a set of known property can uniquely and/or stably determines PEL, i.e., understandings of property/PEL correspondence is basically unidirectional in the current statistical mechanics. Here we make significant advance toward bidirectional bridging of this gap for classical discrete systems under many-body interactions. Our idea is to focus on characteristic microscopic geometry in configuration space for an exactly solvable system, resulting in a new, important quantity of "harmonicity in the structural degree of freedom". This quantity reasonablly characterizes which structures in equilibrium state have practically unique and stable correspondence to PEL, without requiring any thermodynamic information such as energy or temperature. The present findings will open a gate to constructing reliable PEL, where its predictive uncertainty can be a priori known. A significant role of microscopic geometry for non-interacting system should be re-emphasized in statistical mechanics., Comment: 7 pages, 4 figures

Energetic stability and electronic structures of Pt atoms in Pt-Rh nanoparticle is investigated by first-principles calculation. Pt atom energetically prefer surface sites (vertex, edge, and (100)) rather than subsurface and core site, which is attributed to lower Pt surface energy compared with Rh. Vertex of nanoparticle is the most favorable site for Pt atom, which has lowest coordination numbers. Band center of d-state electronic contribution for Pt atom measured from the Fermi energy exhibit negative dependence with respect to Pt coordination number. This can be attributed to positive dependence of second-order moment of density of states for the Pt d-band on the coordination number. Pt segregation to the surface is expected due mainly to contribution from Pt on-site segregation energy compared with weak ordering tendency of Pt-Rh unlike-atom pairs. [doi:10.2320/matertrans.M2009295]