arXiv subjects

Zi-Kui Liu

Publications and source records attributed to Zi-Kui Liu.

At least 37 records · Page 2Linked to original sources

arXiv2025

Stripe Antiferromagnetic Ground-State Configuration of FeSe Revealed by Density Functional Theory

The magnetic ground-state configuration of iron selenide FeSe has been a topic of debate, with experimental evidence suggesting the stripe spin fluctuations as predominant at low temperatures, while density functional theory (DFT) calculations using exchange-correlation (XC) functional of the Generalized Gradient Approximation (GGA) have historically predicted the antiferromagnetic (AFM) dimer configuration. In this study, we utilize the $\text{r}^{2}\text{SCAN}$ functional, a variant of the Strongly Constrained and Appropriately Normed (SCAN) meta-GGA, to investigate the magnetic configurations of FeSe. It is found that $\text{r}^{2}\text{SCAN}$ predicts a stripe-AFM ground-state configuration with an anti-parallel spin alignment between layers. The energy difference between the parallel and anti-parallel inter-planar spin alignments is approximately 1.7 meV/atom, predicting a significant but previously unreported interlayer spin coupling not yet observed by experiments. The present study underscores the importance of accurate XC functionals, such as $\text{r}^{2}\text{SCAN}$, in predicting the magnetic ground-state configuration of complex materials like FeSe, highlighting its potential to predict magnetic interactions more reliably than traditional GGA functionals by adhering to exact constraints.

cond-mat.supr-con↗

arXiv2025

Deconvoluting Thermomechanical Effects in X-ray Diffraction Data using Machine Learning

X-ray diffraction is ideal for probing sub-surface state during complex or rapid thermomechanical loading of crystalline materials. However, challenges arise as the size of diffraction volumes increases due to spatial broadening and inability to deconvolute the effects of different lattice deformation mechanisms. Here, we present a novel approach to use combinations of physics-based modeling and machine learning to deconvolve thermal and mechanical elastic strains for diffraction data analysis. The method builds on a previous effort to extract thermal strain distribution information from diffraction data. The new approach is applied to extract the evolution of thermomechanical state during laser melting of an Inconel 625 wall specimen which produces significant residual stress upon cooling. A combination of heat transfer and fluid flow, elasto-plasticity, and X-ray diffraction simulations are used to generate training data for machine-learning (Gaussian Process Regression, GPR) models that map diffracted intensity distributions to underlying thermomechanical strain fields. First-principles density functional theory is used to determine accurate temperature-dependent thermal expansion and elastic stiffness used for elasto-plasticity modeling. The trained GPR models are found to be capable of deconvoluting the effects of thermal and mechanical strains, in addition to providing information about underlying strain distributions, even from complex diffraction patterns with irregularly shaped peaks.

cond-mat.mtrl-sci↗

arXiv2025

Thermodynamic modeling of the LiCl-KCl-LaCl$_3$ system with Bayesian model selection and uncertainty quantification

Chloride molten salts are increasingly used in pyroprocessing techniques for the separation of lanthanides. Understanding thermodynamic properties of these salts is essential to predict their critical characteristics and optimize the separation process. Several thermodynamic models, including the associate model, the two-sublattice ionic model, and the modified quasichemical model with quadruplet approximation (MQMQA), have been utilized in the literature to capture the complexity of molten salts. In the present work, the Bayes factor is used to guide the model selection process for thermodynamic modeling of the KCl-LaCl3 system and provide statistical comparison of various models. The results indicate that the MQMQA model is the most favorable one based on available data. The LiCl-KCl-LaCl3 system has been further modelled with uncertainty quantification (UQ) using MQMQA with the thermodynamic properties of compounds in KCl-LaCl3 predicted by the quasiharmonic approach in terms of first-principles phonon calculations as a function of temperature. The calculated phase stability shows excellent agreement with experimental data, indicating that an appropriate thermodynamic model is important for accurately predicting critical characteristics of complex molten salts.

cond-mat.mtrl-sci↗

arXiv2024

Thermodynamics and transport in molten chloride salts and their mixtures

Molten salts are important in a number of energy applications, but the fundamental mechanisms operating in ionic liquids are poorly understood, particularly at higher temperatures. This is despite their candidacy for deployment in solar cells, next-generation nuclear reactors, and nuclear pyroprocessing. We perform extensive molecular dynamics simulations over a variety of molten chloride salt compositions at varying temperature and pressures to calculate the thermodynamic and transport properties of these liquids. Using recent developments in the theory of liquid thermophysical properties, we interpret our results on the basis of collective atomistic dynamics (phonons). We find that the properties of ionic liquids well explained by their collective dynamics, as in simple liquids. In particular, we relate the decrease of heat capacity, viscosity, and thermal conductivity to the loss of transverse phonons from the liquid spectrum. We observe the singular dependence of the isochoric heat capacity on the mean free path of phonons, and the obeyance of the Stokes-Einstein equation relating the viscosity to the mass diffusion. The transport properties of mixtures are more complicated compared to simple liquids, however viscosity and thermal conductivity are well guided by fundamental bounds proposed recently. The kinematic viscosity and thermal diffusivity lie very close to one another and obey the theoretical fundamental bounds determined solely by fundamental physical constants. Our results show that recent advances in the theoretical physics of liquids are applicable to molten salts mixtures, and therefore that the evolution and interplay of properties common to all liquids may act as a guide to a deeper understanding of these mixtures.

physics.chem-ph↗

arXiv2024

Investigation of ideal shear strength of dilute binary and ternary Ni-based alloys using first-principles calculations, CALPHAD modeling and correlation analysis

In the present work, the ideal shear strength (τ_is) of dilute Ni34XZ ternary alloys (X or Z = Al, Co, Cr, Fe, Mn, Mo, Nb, Si, Ti) are predicted by first-principles calculations based on density functional theory (DFT) in terms of pure alias shear deformations. The τ_is results show that within the concentration up to 8.3% of alloying elements, τ_is increases with composition in binary systems with Mn, Fe, and Co in ascending order, and decreases with composition with Nb, Si, Mo, Ti, Al, and Cr in descending order. The composition dependence of τ_is in binary and ternary systems is modeled using the CALculation of PHAse Diagrams (CALPHAD) approach considering lattice instability, indicating that atomic bonding strength significantly influences τ_is. Correlational analyses further show that lattice constant and elastic constant C11 affect τ_is, the most out of the elemental features.

cond-mat.mtrl-sci↗

arXiv2024

Fundamentals on Dependence of Volume on Pressure and Temperature

The common wisdom that volume decreases with pressure and increases with temperature is analyzed in terms of Hillert nonequilibrium thermodynamics in the present work. It is shown that the derivative of volume to pressure in a stable system is always negative, i.e., volume decreases with the increase of pressure, when all other natural variables of the system are kept constant. This originates from the stability requirement that the conjugate variables, such as volume and negative pressure, must change in the same direction in a stable system. Consequently, since volume and temperature are not conjugate variables, they do not have to change in the same direction and thus do change in opposite directions in both natural and man-made systems. It is shown that the decrease of volume with the increase of temperature, commonly referred as negative thermal expansion (NTE) in the literature, originates from the statistical competitions of configurations in the system when the volumes of metastable configurations are smaller than that of the ground-state configuration. It is demonstrated that the zentropy theory can concisely explain and accurately predict NTE based on the density functional theory without fitting parameters.

cond-mat.mtrl-sci↗

arXiv2024

Predicting phase transitions in PbTiO$_3$ using zentropy through quasiharmonic phonon calculations

According to x-ray diffraction (XRD) measurements, PbTiO$_3$ undergoes a phase transition from a tetragonal ferroelectric (FE) phase to a cubic paraelectric phase at 763 K. However, x-ray absorption fine-structure (XAFS) measurements indicate that PbTiO$_3$ is locally tetragonal even after the phase transition. The difference in these results is because XAFS measurements can probe local features of a structure, while XRD averages over such local features. For both measurements to be consistent, PbTiO$_3$ is macroscopically cubic but locally tetragonal after the phase transition. Despite this, most models, such as the Laundau-Ginsburg-Devonshire theory and effective Hamiltonians, are still unable to explain this phenomenon. Moreover, these methods involve model parameters fitted to experimental or theoretical data and do not consider other tetragonal configurations, such as domain walls, to predict the phase transition. In our previous study, we used our zentropy approach to predict the phase transition by considering the tetragonal FE ground-state configuration and the tetragonal 90° and 180° domain wall configurations with their total energies at 0 K. In this paper, the Helmholtz energies of the three configurations are obtained from density functional theory calculations through energy-volume curves and phonon calculations. The predicted phase transition temperature using the meta-GGA $r^2\text{SCAN}$ and revised multiplicities of configurations is 716 K, showing good agreement with the experimental value of 763 K.

cond-mat.mtrl-sci↗

arXiv2024

Molecular interaction volume model of mixing enthalpy for molten salt system: An integrated calorimetry-model case study of LaCl$_3$-(LiCl-KCl)

Calorimetric determination of enthalpies of mixing ($Δ$H$_{\rm mix}$) of multicomponent molten salts often employs empirical models that lack parameters with clear physical interpretation (e.g., coordination numbers, molar volumes, and pair potentials). Although such physics informed models are not always needed, a thermodynamic understanding of the relationships between excess energies of mixing and local to intermediate solvation structures is particularly important for pyrochemical separation, as is the case for lanthanides (Ln), which are common neutron poisons and critical industrial elements found in spent nuclear fuels. Here we implement the molecular interaction volume model (MIVM) to synthesize information from experimentally measured $Δ$H$_{\rm mix}$ (using high temperature melt drop calorimetry) and the distribution of solvation structures from ab initio molecular dynamics (AIMD) simulations. This was demonstrated by a case study of molten salt system consisted of LaCl$_3$ mixing with a eutectic LiCl-KCl (58mol% to 42mol%) at 873 K and 1133 K. The parameters modelled from MIVM were used to extrapolate excess Gibbs energy ($Δ$G$_{\rm mix}$), and compositional dependence of La$^{3+}$ activity in the LaCl$_3$-(LiCl-KCl) system. In contrast, by AIMD or polarizable ion model (PIM) simulations, a significant deviation regarding the predicted $Δ$H$_{\rm mix}$ was seen if computed directly from the molecular dynamic trajectories. The integrated experimental and simulation data within the MIVM formalism are generalizable to a wide variety of molten salts and demonstrate a significant improvement over currently employed methods to study molten salts for nuclear and separations sciences.

cond-mat.mtrl-sci↗

arXiv2024

Efficient Generation of Grids and Traversal Graphs in Compositional Spaces towards Exploration and Path Planning

Many disciplines of science and engineering deal with problems related to compositions, ranging from chemical compositions in materials science to portfolio compositions in economics. They exist in non-Euclidean simplex spaces, causing many standard tools to be incorrect or inefficient, which is significant in combinatorically or structurally challenging spaces exemplified by Compositionally Complex Materials (CCMs) and Functionally Graded Materials (FGMs). Here, we explore them conceptually in terms of problem spaces and quantitatively in terms of computational feasibility. This work implements several essential methods specific to the compositional (simplex) spaces through a high-performance open-source library nimplex. Most significantly, we derive and implement an algorithm for constructing a novel n-dimensional simplex graph data structure, which contains all discretized compositions and all possible neighbor-to-neighbor transitions as pointer arrays. Critically, no distance or neighborhood calculations are performed, instead leveraging pure combinatorics and the ordering in procedurally generated simplex grids, keeping the algorithm $\mathcal{O}(N)$, so that graphs with billions of transitions take seconds to construct on a laptop. Furthermore, we demonstrate how such graph representations can be combined to express path-planning problem spaces and to incorporate prior knowledge while keeping the problem space homogeneous. This allows for efficient deployment of existing high-performance gradient descent, graph traversal search, and other path optimization algorithms.

cond-mat.mtrl-sci↗

arXiv2024

On Gibbs Equilibrium and Hillert Nonequilibrium Thermodynamics

During his time at Royal Institute of Technology (Kungliga Tekniska Hogskolan, KTH) in Sweden, the present author learned nonequilibrium thermodynamics from Mats Hillert. The key concepts are the separation of internal and external variables of a system and the definitions of potentials and molar quantities. In equilibrium thermodynamics derived by Gibbs, the internal variables are not independent and can be fully evaluated from given external variables. While irreversible thermodynamics led by Onsager focuses on internal variables though often mixed with external variables. Hillert integrated them together by first emphasizing their differences and then examining their connections. His philosophy was reflected by the title of his book "Phase Equilibria, Phase Diagrams and Phase Transformations" that puts equilibrium, nonequilibrium, and internal processes on equal footing. In the present paper honoring Hillert, the present author reflects his experiences with Hillert and his work in last 40 years and expresses his gratitude for all the wisdom and support from him in terms of "Hillert nonequilibrium thermodynamics" and discusses some recent topics that the present author has been working on.

cond-mat.stat-mech↗

arXiv2024

Circumventing cracking in grading 316L stainless steel to Monel400 through compositional modifications

In joining Fe-alloys and Cu-containing alloys to access the high strength of steels and corrosion resistance of Cu-alloy, cracking is widely observed due to the significant Cu microsegregation during the solidification process, resulting in an interdendritic Cu-rich liquid film at the end of solidification. By fabricating functionally graded materials (FGMs) that incorporate additional elements like Ni in the transition region between these terminal alloy classes, the hot cracking can be reduced. In the present work, the joining of stainless steel 316L (SS316L) and Monel400 by modifying the Ni concentration in the gradient region was studied. A new hot cracking criterion based on hybrid Scheil-equilibrium approach was developed and validated with monolithic multi-layer samples within the SS316L-Ni-Monel400 three-alloy system and an SS316L to 55/45 wt% SS316L/Ni to Monel400 FGM sample fabricated by direct energy deposition (DED) process. The new hot cracking criterion, based on the hybrid Scheil-equilibrium approach, is expected to help design FGM paths between other Fe-alloys and Cu-containing alloys as well.

cond-mat.mtrl-sci↗

arXiv2024

Efficient Structure-Informed Featurization and Property Prediction of Ordered, Dilute, and Random Atomic Structures

Structure-informed materials informatics is a rapidly evolving discipline of materials science relying on the featurization of atomic structures or configurations to construct vector, voxel, graph, graphlet, and other representations useful for machine learning prediction of properties, fingerprinting, and generative design. This work discusses how current featurizers typically perform redundant calculations and how their efficiency could be improved by considering (1) fundamentals of crystallographic (orbits) equivalency to optimize ordered cases and (2) representation-dependent equivalency to optimize cases of dilute, doped, and defect structures with broken symmetry. It also discusses and contrasts ways of (3) approximating random solid solutions occupying arbitrary lattices under such representations. Efficiency improvements discussed in this work were implemented within pySIPFENN or python toolset for Structure-Informed Property and Feature Engineering with Neural Networks developed by authors since 2019 and shown to increase performance from 2 to 10 times for typical inputs. Throughout this work, the authors explicitly discuss how these advances can be applied to different kinds of similar tools in the community.

cond-mat.mtrl-sci↗

arXiv2024

Revisiting first-principles thermodynamics by quasiharmonic approach: Application to study thermal expansion of additively-manufactured Inconel 625

An innovative method is developed for accurate determination of thermodynamic properties as a function of temperature by revisiting the density functional theory (DFT) based quasiharmonic approach (QHA). The present methodology individually evaluates the contributions from static total energy, phonon, and thermal electron to free energy for increased efficiency and accuracy. The Akaike information criterion with a correction (AICc) is used to select models and model parameters for fitting each contribution as a function of volume. Using the additively manufactured Inconel alloy 625 (IN625) as an example, predicted temperature-dependent linear coefficient of thermal expansion (CTE) agrees well with dilatometer measurements and values in the literature. Sensitivity and uncertainty are also analyzed for the predicted IN625 CTE due to different structural configurations used by DFT, and hence different equilibrium properties determined.

cond-mat.mtrl-sci↗

arXiv2024

Quantitative Predictive Theories through Integrating Quantum, Statistical, Equilibrium, and Nonequilibrium Thermodynamics

Today's thermodynamics is largely based on the combined law for equilibrium systems and statistical mechanics derived by Gibbs in 1873 and 1901, respectively, while irreversible thermodynamics for nonequilibrium systems resides essentially on the Onsager Theorem as a separate branch of thermodynamics developed in 1930s. Between them, quantum mechanics was invented and was quantitatively solved in terms of density functional theory (DFT) in 1960s. These three scientific domains operate based on different principles and are very much separated from each other. In analogy to the parable of the blind men and the elephant articulated by Perdew, they individually represent different portions of a complex system and thus are incomplete by themselves alone, resulting in the lack of quantitative agreement between their predictions and experimental observations. Over the last two decades, the author's group has developed a multiscale entropy approach (recently termed as zentropy theory) that integrates DFT-based quantum mechanics and Gibbs statistical mechanics and is capable of accurately predicting entropy and free energy of complex systems. Furthermore, in combination with the combined law for nonequilibrium systems developed by Hillert, the author developed the theory of cross phenomena beyond the phenomenological Onsager Theorem. The zentropy theory and theory of cross phenomena jointly provide quantitative predictive theories for systems from electronic to any observable scales as reviewed in the present work.

cond-mat.stat-mech↗

arXiv2024

Developments and applications of the OPTIMADE API for materials discovery, design, and data exchange

The Open Databases Integration for Materials Design (OPTIMADE) application programming interface (API) empowers users with holistic access to a growing federation of databases, enhancing the accessibility and discoverability of materials and chemical data. Since the first release of the OPTIMADE specification (v1.0), the API has undergone significant development, leading to the upcoming v1.2 release, and has underpinned multiple scientific studies. In this work, we highlight the latest features of the API format, accompanying software tools, and provide an update on the implementation of OPTIMADE in contributing materials databases. We end by providing several use cases that demonstrate the utility of the OPTIMADE API in materials research that continue to drive its ongoing development.

cond-mat.mtrl-sci↗

arXiv2024

A generalized approach for rapid entropy calculation of liquids and solids

We build a comprehensive methodology for the fast computation of entropy across both solid and liquid phases. The proposed method utilizes a single trajectory of molecular dynamics (MD) to facilitate the calculation of entropy, which is composed of three components. The electronic entropy is determined through the temporal average acquired from density functional theory (DFT) MD simulations. The vibrational entropy, typically the predominant contributor to the total entropy, even within the liquid state, is evaluated by computing the phonon density of states via the velocity auto-correlation function. The most arduous component to quantify, the configurational entropy, is assessed by probability analysis of the local structural arrangement and atomic distribution. We illustrate, through a variety of examples, that this method is both a versatile and valid technique for characterizing the thermodynamic states of both solids and liquids. Furthermore, this method is employed to expedite the calculation of melting temperatures, demonstrating its practical utility in computational thermodynamics.

physics.comp-ph↗

arXiv2024

MaterialsMap: A CALPHAD-Based Tool to Design Composition Pathways through feasibility map for Desired Dissimilar Materials, demonstrated with RSW Joining of Ag-Al-Cu

Assembly of dissimilar metals can be achieved by different methods, for example, casting, welding, and additive manufacturing (AM). However, undesired phases formed in liquid-phase assembling processes due to solute segregation during solidification diminish mechanical and other properties of the processed parts. In the present work, an open-source software named MaterialsMap, has been developed based on the CALculation of Phase Diagrams (CALPHAD) approach. The primary objective of MaterialsMap is to facilitate the design of an optimal composition pathway for assembling dissimilar alloys with liquid-phases based on the formation of desired and undesired phases along the pathway. In MaterialsMap, equilibrium thermodynamic calculations are used to predict equilibrium phases formed at slow cooling rate, while Scheil-Gulliver simulations are employed to predict non-equilibrium phases formed during rapid cooling. By combining these two simulations, MaterialsMap offers a thorough guide for understanding phase formation in various manufacturing processes, assisting users in making informed decisions during material selection and production. As a demonstration of this approach, a compositional pathway was designed from pure Al to pure Cu through Ag using MaterialsMap. The design was experimentally verified using resistance spot welding (RSW).

cond-mat.mtrl-sci↗

arXiv2024

nimCSO: A Nim package for Compositional Space Optimization

nimCSO is a high-performance tool implementing several methods for selecting components (data dimensions) in compositional datasets, which optimize the data availability and density for applications such as machine learning. Making said choice is a combinatorically hard problem for complex compositions existing in highly dimensional spaces due to the interdependency of components being present. Such spaces are encountered, for instance, in materials science, where datasets on Compositionally Complex Materials (CCMs) often span 20-45 chemical elements, 5-10 processing types, and several temperature regimes, for up to 60 total data dimensions. At its core, nimCSO leverages the metaprogramming ability of the Nim language (nim-lang.org) to optimize itself at the compile time, both in terms of speed and memory handling, to the specific problem statement and dataset at hand based on a human-readable configuration file. As demonstrated in this paper, nimCSO reaches the physical limits of the hardware (L1 cache latency) and can outperform an efficient native Python implementation over 400 times in terms of speed and 50 times in terms of memory usage (not counting interpreter), while also outperforming NumPy implementation 35 and 17 times, respectively, when checking a candidate solution. It is designed to be both (1) a user-ready tool, implementing two efficient brute-force approaches (for handling up to 25 dimensions), a custom search algorithm (for up to 40 dimensions), and a genetic algorithm (for any dimensionality), and (2) a scaffold for building even more elaborate methods in the future, including heuristics going beyond data availability. All configuration is done with a simple human-readable YAML config file and plain text data files, making it easy to modify the search method and its parameters with no knowledge of programming and only basic command line skills.

cond-mat.mtrl-sci↗