arXiv subjects

Koretaka Yuge

Publications and source records attributed to Koretaka Yuge.

At least 37 records · Page 2Linked to original sources

arXiv2019

Optimal Selection of Structural Degree of Freedoms for Spceial Microscopic States to Characterize Disordered Structures

For classical discrete systems under constant composition, statistical mechanics tells us that a set of microscopic state dominantly contributing to thermodynamically equilibrium state should depend on temperature as well as on many-body interaction (i.e. thermodynamic information), through Boltzamann factor of exp(-bE). Despite this fact, our recent study reveals that a single (and a few additional) microscopic state (called projection state: PS), whose structure can be known a priori without r equiring thermodynamic information, can universally characterize equiibrium properties for disordered states, where their sturctures depends on configurational geometry before applying many-body interaction to the system. Although mathematical condition for the structures of PS have been rigorously established, practically effective condition for constructing the stuructures, especially for which set of a finite structural degree of freedoms (SDF) should be selected for considered coordination has not been clarified so far. We here tuckle this problem, proposing a quantitative and systematic criteria for an optimal set of SDFs. The present proposal enables to effectively constructing PSs for a limited system size, and also providing new insight into which set of SDFs should generally affects equilibrium properties along a chosen coordination, without using any thermodynamic information.

cond-mat.stat-mech↗

arXiv2019

Configurational Geometry Bridges Equilibrium Structure Information from a Single to Multiple Compositions

For classical discrete systems under constant composition, a set of microscopic state dominantly contributing to thermodynamically equilibrium structure should depend on temperature and energy through Boltzmann factor, exp(-bE). Despite this fact, our recent study find a set of special microscopic state that can characterize equilibrium properties, where these structures can be know a priori without any thermodynamic information. Here, for binary system, we extend the theoretical approach to develop a new formulation, where the special microscopic states at a given, single composition can characterize equilibrium structure over whole composition. We demonstrate the validity of the proposed formulation by comparing with results by conventional thermodynamic simulaton. The results strongly indicate that most information about composition- and temperature- dependence of thermodynamically equilibrium structure for disordered state on multiple compositions can be concentrated to a set of special microscopic state on any single composition.

cond-mat.stat-mech↗

arXiv2019

Where Nonlinearity in Thermodynamic Average Comes from? Configurational Geometry Revisited

For classical discrete system under constant composition, we theoretically examine origin of nonlinearity in thermodynamic (so-called canonical) average w.r.t. many-body interactions, in terms of geometrical information in configuratin space. We clarify that nonlinearity essentially comes from deviation in configurational density of states (CDOS) before applying many-body interactions to the system, from multidimensional gaussian distribution. The present finding strongly suggest the significance to investigate how the deviation in CDOS bridges bidirectional stability relationships between equilibrium structure and potential energy in thermodynamic average.

cond-mat.stat-mech↗

arXiv2019

Modified Representation of Canonical Average by Special Microscopic States for Classical Discrete Systems

For substitutional crystalline solids typically referred to classical discrete system under constant composition, macroscopic structure in thermodynamically equilibrium state can be typically obtained through canonical average, where a set of microscopic structure dominantly contributing to the average should depend on temperature and many-body interaction through Boltzmann factor, exp(-bE). Despite these facts, our recent study reveals that based on configurational geometry, a few specially-selected microscopic structure (called projection state PS) independent of temperature and many-body interaction can reasonably characterize temperature dependence of macroscopic structure. Here we further modify representation of canonical average by using the same PSs, based on (i) transformation of multivariate 3-order moment matrix by one of the PS, and (ii) Pade approximation. We prove that the former can always results in better representation of canonical average than non-transformation one, confirmed by performing hypershere integration, while the latter approximation can provide better representaion except for e.g., inclusion of its own singular point within considered temperature, which can be known a priori.

cond-mat.stat-mech↗

arXiv2019

Pattern Formation Mechanism of Directionally-Solidified MoSi2/Mo5Si3 Eutectic by Phase-Field Simulation

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.

cond-mat.mtrl-sci↗

arXiv2019

Bidirectional-Stability Breaking in Thermodynamic Average for Classical Discrete Systems

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.

cond-mat.stat-mech↗

arXiv2018

Microscopic Geometry Rules Ordering Tendency for Multicomponent Disordered Alloys

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.

cond-mat.mtrl-sci↗

arXiv2018

Does Stochastic Disorder Conform to Configurational Disorder?

In alloy thermodynamics, stochastically disordered state (SDS), where each lattice point is stochastically occupied by constituents according to given composition, is typically referred to investigating physical properties for homogeneously substitutional state: The so-called special quasirandom structure (SQS) of a single microscopic structure, that mimics multisite correlation function for SDS, is amply, widely used for bulk, surface, interface and nano-cluster properties. Despite the widely-used concept for SDS, it has not been clear whether the SDS should conform to configurationally disordered state (CDS) for discrete system, i.e., average over all possible configuration. Here we quantitatively discuss the difference between SDS and CDS for multisite correlation, and show the condition where SDS conforms to CDS. The results show that when practical system size contains below around 100,000 atoms, differences in multisite correlation between SDS and CDS remains few percent depending on the geometry of lattice as well as of figure, indicating that SQS for subsystem of surface and interface, and for isolated clusters, should be carefully applied to investigate high-temperature properties as CDS.

cond-mat.stat-mech↗

arXiv2018

A Single Microscopic State to Characterize Ordering Tendency in Discrete Multicomponent System

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.

cond-mat.mtrl-sci↗

arXiv2018

Formulation of Genuine Thermodynamic Variables from Special Microscopic States

For classical discrete systems under constant composition, it has been considered that genuine thermodynamic variables such as free energy cannot be generally determined from information about a single or a few selected microscopic states. Despite this fact, we here show that Helmholtz free energy for any given composition for disordered states can be well characterized by information about a few (R+3, where R denotes number of components) specially selected microscopic states, whose structure can be known a priori without requiring any thermodynamic information. The present study is a non-trivial extension of our recently-developed theoretical approach for special microscopic states in canonical ensemble to semi-grand canonical ensemble, which additionally enables to characterize temperature dependence of other thermodynamic variables such as internal energy and entropy.

cond-mat.stat-mech↗

arXiv2018

Special Microscopic-states-basis Formulation of Macroscopic Structure for Thermodynamic Systems

For classical system under constant composition, macroscopic structure in thermodynamically equilibrium state can be determined through the so-called canonical average, including sum over possible microscopic states on phase space. Although a set of microscopic structure dominantly contributing to equilibrium properties should depend on temperature and many-body interactions, we recently clarify that at high temperature, they are universally characterized by a single special microscopic state (which we call projection state: PS), whose structure can be known a priori without any thermodynamic information. Here we extend this approach to find additional special microscopic states, enabling us to characterize equilibrium structures for lower-temperature region above transition temperature. The concept of our approach will lead to a new paradigm; the formulation of macroscopic properties by special microscopic states basis.

cond-mat.stat-mech↗

arXiv2018

Microscopic Geometry Characterizes Structure/Potential-Energy Correspondence in a Thermodynamic System

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.

cond-mat.dis-nn↗

arXiv2018

Exact Determination of Moments for Density of States in Multidimensional Configuration Space

For classical discrete systems on periodic lattice under constant composition x, we derive explicit expression of any-order moments for configurational density of states (CDOS). The derived expression clarifies that any-order moments can always be given by linear combination of the first-order moments, whose coefficient depends on geometric information of lattice. The expression enables us to exactly determine system-size (N) dependence of moments, where analytic representation in terms of N and x is explicitly given up to lower-order generalized moment. Validity of the derived expression is confirmed by exact estimation of moments for binary system bcc with finite system size, considering all possible atomic configuration.

cond-mat.stat-mech↗

arXiv2018

Analytic Representation of Canonical Average From Fine Structure of Density of States

Expectation value of dynamical variables in thermodynamically equilibrium state can be typically provided through well-known canonical average. The average includes tremendous number of possible states considered far beyond practically handled, which makes it difficult to obtain analytic representation of the average to clarify how the expectation value connects with given interaction: i.e., the relationship is generally understood in phonomenological manner except for modest, simple models. Here we show that the relationship is explicitly clarified for discrete large systems, where the configurational density of states for any single pair correlation is represented in terms of linear combination of Dirac delta function and its derivatives. The significant advantage of the present representation is that it can decompose contributions to macroscopic dynamical variables into harmonicity and anharmonicity in terms of their underlying structural degree of freedom, which will lead to find a set of special microscopic state to characterize macroscopic properties in equilibrium state for classical many-body systems.

physics.gen-ph↗

arXiv2017

Accurate estimation of interface phase diagram from STM images

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.

cond-mat.mtrl-sci↗

arXiv2017

Accurate Prediction of Potential Energy Surface via Thermodynamically Equilibrium Structure

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.

cond-mat.dis-nn↗

arXiv2017

Short-Range-Order for fcc-based binary alloys Revisited from Microscopic Geometry

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.

cond-mat.dis-nn↗

arXiv2017

Landscape of Configurational Density of States for Discrete Large Systems

For classical many-body systems, our recent study reveals that expectation value of internal energy, structure, and free energy can be well characterized by a single specially-selected microscopic structure. This finding relies on the fact that configurational density of states (CDOS) for typical classical system before applying interatomic interaction can be well characterized by multidimensional gaussian distribution. Although gaussian distribution is an well-known and widely-used function in diverse fields, it is quantitatively unclear why the CDOS takes gaussian when system size gets large, even for projected CDOS onto a single chosen coordination. Here we demonstrate that for equiatomic binary system, one-dimensional CDOS along coordination of pair correlation can be reasonably described by gaussian distribution under an appropriate condition, whose deviation from real CDOS mainly reflects the existence of triplet closed link consisting of the pair figure considered. The present result thus significantly makes advance in analytic determination of the special microscopic states to characterized macroscopic physical property in equilibrium state.

cond-mat.dis-nn↗