arXiv subjects
Publications and source records attributed to Koretaka Yuge.
In this study, we confirm the universality of density of microscopic states in non-interacting system; this means statistical interdependence is vanished in any lattices. This enable one to obtain information of configuration of solute atoms, free energy, phase diagram with performing first-principles calculation on few special microscopic states combined with our established theory.
Our recent study elucidate that information of density of states in configuration space (CDOS) for non-interacting system, characterized by spatial constraint on the system, plays essential role to determine thermodynamically equilibrium properties for interacting systems. Particularly for disordered states, variance of CDOS along all possible coordinations plays significant role. Despite this fact, even for binary system of crystalline solids, analytic expression for variance of CDOS as a function of composition has not been clarified so far. Here we successfully derive variance of CDOS as a function of composition for pair correlations, whose validity is demonstrated by comparing the results with uniform sampling of CDOS on real lattices. The present result certainly advances determining special microscopic state to characterize Helmholtz free energy in classical systems, whose structure is difficult to determine by numerical simulation.
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.
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.
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.
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.
To investigate the formation of Mg-based long-period stacking ordered (LPSO) structure, we systematically study the preference of the short-range order (SRO) in metastable disordered phases of Mg-RE-Zn (RE = Y, La, Er, Ho, Dy, Tb) and Mg-Gd-Al ternary alloy systems through first-principles calculation. RE-Zn (RE = Y, Er, Ho, Dy, Tb) and Gd-Al pair clusters' probability showed the tendency of increasing. In contrast, La-Zn pair clusters' probability is not increasing, whose system dose not form LPSO structure. This preference of SRO in disordered phases of Mg-based ternary alloys certainly indicates that peculiar L12-type ordering in LPSO as well as possibility of LPSO formation should have strong correlation with SRO tendency of energetically competitive disordered phases.
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.
When non-solid matter (e.g., liquids or gas) is under constant volume V and density rho (e.g., in rigid box), spatial positions for their constituents are restricted by these conditions. We recently focus on the role of constraint in classical statistical thermodynamics, and find how spatial constraint connects with equilibrium properties for crystalline solids, which has not been clarified so far. The present study extend the idea to non-solid matter under NVT ensemble in classical systems. We provide explicit representation of canonical average of radial distribution function in terms of spatial constraint, which can be well characterized by a single special microscopic state on configuration space called projection state for non-solid matter. We demonstrate that the special microscopic state can be numerically constructed for a finite number of particles.
Recently, we clarify connection of spatial constraint and equilibrium macroscopic properties in disordered states of classical system under the fixed composition; namely few special microscopic states, independent of constituent elements, can describe macroscopic properties. In this study, we extend our developed approach to composition-unfixed system. Through this extension in binary system, we discover a single special microscopic state to determine not only composition but also Helmholtz free energy measured from unary system, which has not been described by a single state.
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.
We investigate segregation behavior of additive elements M (= Ni, Cr) at the C11b/D8m interface for MoSi2- Mo5Si3 alloys, based on first-principles calculation. We first find energetically stable interface structure with interface energy of 0.08 eV/A^2. Based on the stable interface, segregation energy for additive elements is calcu- lated 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 capture the characteristics in measured segregation tendency of (i) Similarity in strong segregation at interface both for Ni and Cr compared with bulk composition, and (ii) stronger segregation for Ni than for Cr, which can be mainly attributed to differences in calculated segregation energy. The present results indicate that measured segregated interface for MoSi2-Mo5Si3 alloys can be thermodynamically stable.
We propose a new approach, "structure integration", enabling direct evaluation of configurational free energy for large systems. The present approach is based on the statistical information of lattice. Through first-principles-based simulation, we find that the present method not only evaluates configurational free energy accurately in disorder states above critical temperature but also clarify importance of lattice to determine configurational free energy at high temperature.
In classical systems, our recent theoretical study provides new insight into how spatial constraint on the system connects with macroscopic properties, which lead to universal representation of equilibrium macroscopic physical property and structure in disordered states. These important characteristics rely on the fact that statistical interdependence for density of microscopic states (DOMS) in configuration space appears numerically vanished at thermodynamic limit for a wide class of spatial constraints, while such behavior of the DOMS is not quantitatively well-understood so far. The present study theoretically address this problem based on the Random Matrix with Gaussian Orthogonal Ensemble, where corresponding statistical independence is mathematically guaranteed. Using the generalized Ising model, we confirm that lower-order moment of density of eigenstates (DOE) of covariance matrix of DOMS shows asymptotic behavior to those for Random Matrix with increase of system size. This result supports our developed theoretical approach, where equilibrium macroscopic property in disordered states can be decomposed into individual contribtion from each generalized coordinate with the sufficiently high number of constituents in the given system, leading to representing equilibrium macroscopic properties by a few special microscopic states.
We extend our previously developed method, "structure integration", to evaluate free energy directly for magnetic large systems on given lattice. The present method express the density of states(DOS) as the parameters independent of system but depend on lattice, and replace the DOS unknown a priori as that known a priori. Through two-dimensional square lattice Ising model, we find that the present method can evaluate magnetic free energy efficiently and accurately above critical temperature without iterative method like Monte Carlo simulation.
In classical systems, we reexamine how macroscopic structures in equilibrium state connect with spatial con- straint on the systems: e.g., volume and density as the constraint for liquids in rigid box, and crystal lattice as the constraint for crystalline solids. We reveal that in disordered states, equilibrium macroscopic structure, depend- ing on temperature and on multibody interactions in the system, is characterized by a single special microscopic structure independent of temperature and of interactions. The special microscopic structure depends only on the spatial constraint. We demonstrate the present findings providing (i) significantly efficient and systematic prediction of macroscopic structures for possible combination of constituents in multicomponent systems, and (ii) unique and accurate determination of multibody interactions in given system from measured macroscopic structure, without performing trial-and-error simulation.
In order to clarify thermodynamic stability of Mg-based long-period stacking ordered (LPSO) structure, we systematically study energetic preference for alloys on multiple stacking with different composition for random mixing of constituent elements, Mg, Y, and Zn based on special quasirandom structure (SQS). Through calculation of formation free energy of SQS, Mg-Y-Zn alloy exhibits phase separation into Mg- and Y-Zn rich phase, which is consistent with previous theoretical studies. Bulk modulus of SQSs for multiple compositions, stacking sequences, and atomic configuratons ranges around 35 GPa, i.e., they do not show significant dependence of Mg concentration, which therefore means that the effects of phonon do not play significant role on LPSO phase stability. Introducing stacking fault to hcp stacking gains "negative" energy, which indicates profound relationship between introducing stacking faults and the formation of long-period stacking ordering.
Based on classical statistical thermodynamics, we develop a theoretical approach that provides new insight into how macroscopic and microscopic physical properties are bridged via crystal lattice for condensed mat- ters. We find that in order to determine macroscopic physical properties and their temperature dependence in equilibrium disordered state, information about a few specially selected microscopic states, established from geometrical characteristics of the crystal lattice, is sufficient. These special states are found to be independent of constitument elements as well as of temperature, which is in contrast to the standard conception in statistical thermodyanamics where a set of microscopic states mainly contributing to determining macroscopic physical properties depend on temperature and constituent elements. Validity and applicability of the theoretical ap- proach is confirmed through prediction of macroscopic physical properties in practical alloys, compared with prediction by full thermodynamic simulation. The present findings provide efficient and systematic prediction of macroscopic physical properties for equilibrium disordered states based on those for special microscopic states without any information of interactions for given system.