Searcharxiv⌕ Search

arXiv subjects

Zi-Kui Liu

Publications and source records attributed to Zi-Kui Liu.

At least 55 records · Page 3Linked to original sources
arXiv2024

Revisiting thermodynamics in (LiF, NaF, KF, CrF2)-CrF3 by first-principles calculations and CALPHAD modeling

The thermodynamic description of the (LiF, NaF, KF, CrF2)-CrF3 systems has been revisited, aiming for a better understanding of the effects of Cr on the FLiNaK molten salt. First-principles calculations based on density functional theory (DFT) were performed to determine the electronic and structural properties of each compound, including the formation enthalpy, volume, and bulk modulus. DFT-based phonon calculations were carried out to determine the thermodynamic properties of compounds, for example, enthalpy, entropy, and heat capacity as functions of temperature. Phonon-based thermodynamic properties show a good agreement with experimental data of binary compounds LiF, NaF, KF, CrF3, and CrF2, establishing a solid foundation to determine thermodynamic properties of ternary compounds as well as to verify results estimated by the Neumann-Kopp rule. Additionally, DFT-based ab initio molecular dynamics (AIMD) simulations were employed to predict the mixing enthalpies of liquid salts. Using DFT-based results and experimental data in the literature, the (LiF, NaF, KF, CrF2)-CrF3 system has been remodeled in terms of the CALculation of PHAse Diagrams (CALPHAD) approach using the modified quasichemical model with quadruplet approximation (MQMQA) for liquid. Calculated phase stability in the present work shows an excellent agreement with experiments, indicating the effectiveness of combining DFT-based total energy, phonon, and AIMD calculations, and CALPHAD modeling to provide the thermodynamic description in complex molten salt systems.

cond-mat.mtrl-sci↗
arXiv2024

Effects of Misorientation on Single Crystal Plasticity by Finite Element Methods

The crystal plasticity finite element method (CPFEM) is a widely used technique for resolving macroscopic stress and strain onto the physically relevant length scales of grains and slip systems in ductile crystalline materials like structural metals. Here, the calibration of a CPFEM model for single crystal applications was found to depend critically on loading orientation, with an effect significant even at an angle of 0.1 degrees. Slight misorientation from high symmetry loading affected lattice rotation during tensile deformation, changing the number of active slip systems, and, as a result, the overall stress-strain behavior. The strongest misorientation effects occurred around the multi-slip orientations of [001], [111], [101], and [102], while the single slip orientation of [213] showed a negligible effect, as expected, and the double slip orientation of [112] showed less of an effect than [102] due to its relative lattice orientation stability. The magnitude of the misorientation effect increased dramatically with the strength of slip system interaction, which, in the chosen hardening framework, is represented by the latent hardening coefficient. In a case study on [001] Cu, offsets of 0.3-2.0 degrees gave stress values at an engineering strain of 0.25 that were lower by 15-18% relative to the direct loading values, highlighting the importance of exact orientations for single crystal plasticity parameterization and application.

cond-mat.mtrl-sci↗
arXiv2024

Zentropy Theory for Quantitative Prediction of Emergent Behaviors through Symmetry-Breaking Configurations

Density functional theory (DFT) is the de facto approach for predicting self-consistent-field electronic structures of ground-state configurations of complex atoms, molecules, and solids and providing their property data for materials discovery and design. This capability is greatly enabled by the generalized gradient approximation for exchange-correlation interactions with an important set of exchange-correlation functionals developed by John Perdew and his collaborators in last several decades. The scientific community and the present author's group have greatly benefited from this capability. Over the years, the present author's group has integrated the energetics from DFT-based calculations both at zero K and finite temperature into thermodynamic modeling and developed methods to predict tracer diffusivity, elastic coefficients, interfacial energy, and a number of other properties related to the derivatives of free energy. One key outcome is the accurate prediction of free energy of a system through the consideration of both ground-state and stable symmetry-breaking non-ground-state configurations. It is articulated that phonon properties of all individual configurations can be accurately calculated by quasiharmonic approximations in the temperature and volume ranges of interest, and the emergent behaviors and anharmonicity of a system originate primarily from the statistical competition among all the configurations.

cond-mat.mtrl-sci↗
arXiv2024

Additively manufactured Ni-20Cr to V functionally graded material: computational predictions and experimental verification of phase formations

A database for the Cr-Ni-V system was constructed by modeling the binary Cr-V and ternary Cr-Ni-V systems using the CALPHAD approach aided by density functional theory (DFT)-based first-principles calculations and ab initio molecular dynamics (AIMD) simulations. To validate this new database, a functionally graded material (FGM) using Ni-20Cr and elemental V was fabricated using directed energy deposition additive manufacturing (DED AM) and experimentally characterized. The deposited Ni-20Cr was pure fcc phase, while increasing the amount of V across the gradient resulted in the formation of sigma phase, followed by the bcc phase. The experimentally measured phase data was compared with computational predictions made using a Cr-Ni-V thermodynamic database from the literature as well as the database developed in the present work. The newly developed database was shown to better predict the experimentally observed phases due to its accurate modeling of binary systems within the database and the ternary liquid phase, which is critical for accurate Scheil calculations.

cond-mat.mtrl-sci↗
arXiv2023

Zentropy theory for accurate prediction of free energy, volume, and thermal expansion without fitting parameters

Based on statistical mechanics, a macroscopically homogeneous system, i.e., a single phase in the present context, is composed of many independent configurations that the system embraces. The macroscopical properties of the system are determined by the properties and statistical probabilities of those configurations with respect to external conditions. The volume of a single phase is thus the weighted sum of the volumes of all configurations. Consequently, the derivative of the volume to temperature of a single phase depends on both the derivatives of the volumes of every configuration to temperature and the derivatives of their statistical probabilities to temperature with the latter introducing non-linear emergent behaviors. It is shown that the derivative of the volume to temperature of the single phase can be negative, i.e., negative thermal expansion (NTE), due to the symmetry-breaking non-ground-state configurations with smaller volumes than that of the ground-state configuration and the rapid increase of the statistical probabilities of the former, and NTE can be predicted without fitting parameters from the zentropy theory that combines quantum mechanics and statistical mechanics with the free energy of each configuration predicted from quantum mechanics and the partition function of each configuration calculated from its free energy.

cond-mat.stat-mech↗
arXiv2023

Building Materials Genome from Ground-State Configuration to Engineering Advance

Individual phases are commonly considered as the building blocks of materials. However, the accurate theoretical prediction of properties of individual phases remains elusive. The top-down approach by decoding genomic building blocks of individual phases from experimental observations is non-unique. The density functional theory (DFT), as the state-of-the-art solution of quantum mechanics, prescribes the existence of a ground-state configuration at zero K for a given system. It is self-evident that the ground-state configuration alone is insufficient to describe a phase at finite temperatures as symmetry-breaking non-ground-state configurations are excited statistically at temperatures above zero K. Our multi-scale entropy approach (recently terms as Zentropy theory) postulates that the entropy of a phase is composed of the sum of the entropy of each configuration weighted by its probability plus the configurational entropy among all configurations. Consequently, the partition function of each configuration in statistical mechanics needs to be evaluated by its free energy rather than total energy. The combination of the ground- and non-ground-state configurations represents the building blocks of materials and can quantitively predict free energy of individual phases with the free energies of ground- and non-ground-state configurations predicted from DFT, plus all properties derived from free energy of individual phases.

cond-mat.mtrl-sci↗
arXiv2023

Integration of Quantum, Statistical, and Irreversible Thermodynamics in A Coherent Framework

The combined law of thermodynamics derived by Gibbs laid the foundation of thermodynamics though only applicable to systems without internal processes. Gibbs further derived the classical statistical thermodynamics in terms of the probability of configurations in a system, which was extended to quantum mechanics-based statistical thermodynamics by Landau, while the irreversible thermodynamics was systemized by Onsager and expanded to chemical reactions by Prigogine. The development of density function theory (DFT) by Kohn enabled the quantitative prediction of properties of the ground-state configuration of a system from quantum mechanics. Here, we will present our theories that integrate quantum, statistical, and irreversible thermodynamics in a coherent framework by utilizing the predicative capability of DFT to revise the statistical thermodynamics (zentropy theory) and by keeping the entropy production due to irreversible processes in the combine law of thermodynamics to derive flux equations (theory of cross phenomena). The zentropy theory is shown capable of predicting the free energy landscape including singularity and instability at critical point and emergent positive or negative divergences of properties. The theory of cross phenomena can predict the coefficients of internal processes between conjugate variables (direct phenomena) and non-conjugate variables (cross phenomena) in the combined law of thermodynamics. Both are with inputs from DFT-based calculations only and without fitting parameters.

cond-mat.stat-mech↗
arXiv2023

Electronic-grade epitaxial (111) KTaO3 heterostructures

KTaO3 has recently attracted attention as a model system to study the interplay of quantum paraelectricity, spin-orbit coupling, and superconductivity. However, the high and low vapor pressures of potassium and tantalum present processing challenges to creating interfaces clean enough to reveal the intrinsic quantum properties. Here, we report superconducting heterostructures based on electronic-grade epitaxial (111) KTaO3 thin films. Electrical and structural characterizations reveal that two-dimensional electron gas at the heterointerface between amorphous LaAlO3 and KTaO3 thin film exhibits significantly higher electron mobility, superconducting transition temperature and critical current density than those in bulk single crystal KTaO3-based heterostructures owing to cleaner interface in KTaO3 thin films. Our hybrid approach may enable epitaxial growth of other alkali metal-based oxides that lie beyond the capabilities of conventional methods.

cond-mat.mtrl-sci↗
arXiv2023

Predictions and correlation analyses of Ellingham diagrams in binary oxides

Knowing oxide-forming ability is vital to gain desired or avoid deleterious oxides formation through tuning oxidizing environment and materials chemistry. Here, we have conducted a comprehensive thermodynamic analysis of 137 binary oxides using the presently predicted Ellingham diagrams. It is found that the active elements to form oxides easily are the f-block elements (lanthanides and actinides), elements in the groups II, III, and IV (alkaline earth, Sc, Y, Ti, Zr, and Hf), and Al and Li; while the noble elements with their oxides nonstable and easily reduced are coinage metals (Cu, Ag, and especially Au), Pt-group elements, and Hg and Se. Machine learning based sequential feature selection indicates that oxide-forming ability can be represented by electronic structures of pure elements, for example, their d- and s-valence electrons, Mendeleev numbers, and the groups, making the periodic table a useful tool to tailor oxide-forming ability. The other key elemental features to correlate oxide-forming ability are thermochemical properties such as melting points and standard entropy at 298 K of pure elements. It further shows that the present Ellingham diagrams enable qualitatively understanding and even predicting oxides formed in multicomponent materials, such as the Fe-20Cr-20Ni alloy (in wt.%) and the equimolar high entropy alloy of AlCoCrFeNi, which are in accordance with thermodynamic calculations using the CALPHAD approach and experimental observations in the literature.

cond-mat.mtrl-sci↗
arXiv2023

Comparing Forward and Inverse Design Paradigms: A Case Study on Refractory High-Entropy Alloys

The rapid design of advanced materials is a topic of great scientific interest. The conventional, ``forward'' paradigm of materials design involves evaluating multiple candidates to determine the best candidate that matches the target properties. However, recent advances in the field of deep learning have given rise to the possibility of an ``inverse'' design paradigm for advanced materials, wherein a model provided with the target properties is able to find the best candidate. Being a relatively new concept, there remains a need to systematically evaluate how these two paradigms perform in practical applications. Therefore, the objective of this study is to directly, quantitatively compare the forward and inverse design modeling paradigms. We do so by considering two case studies of refractory high-entropy alloy design with different objectives and constraints and comparing the inverse design method to other forward schemes like localized forward search, high throughput screening, and multi objective optimization.

cond-mat.mtrl-sci↗
arXiv2023

Thermodynamics and its Prediction and CALPHAD Modeling: Review, State of the Art, and Perspectives

Thermodynamics is a science concerning the state of a system, whether it is stable, metastable, or unstable. The combined law of thermodynamics derived by Gibbs about 150 years ago laid the foundation of thermodynamics. In Gibbs combined law, the entropy production due to internal processes was not included, and the 2nd law was thus practically removed from the Gibbs combined law, so it is only applicable to systems under equilibrium. Gibbs further derived the classical statistical thermodynamics in terms of the probability of configurations in a system. With the quantum mechanics (QM) developed, the QM-based statistical thermodynamics was established and connected to classical statistical thermodynamics at the classical limit as shown by Landau. The development of density function theory (DFT) by Kohn and co-workers enabled the QM prediction of properties of the ground state of a system. On the other hand, the entropy production due to internal processes in non-equilibrium systems was studied separately by Onsager and Prigogine and co-workers. The digitization of thermodynamics was developed by Kaufman in the framework of the CALPHAD modeling of individual phases. Our recently termed zentropy theory integrates DFT and statistical mechanics through the replacement of the internal energy of each individual configuration by its DFT-predicted free energy. Furthermore, through the combined law of thermodynamics with the entropy production as a function of internal degrees of freedom, it is shown that the kinetic coefficient matrix of independent internal processes is diagonal with respect to the conjugate potentials in the combined law, and the cross phenomena represented by the phenomenological Onsager reciprocal relationships are due to the dependence of the conjugate potential of the molar quantity in a flux on nonconjugate potentials.

cond-mat.stat-mech↗
arXiv2023

Design methodology for functionally graded materials: framework for considering cracking

In functionally graded materials (FGMs) fabricated using directed energy deposition (DED) additive manufacturing (AM), cracks may form due to interdendritic stress during solidification, the formation of intermetallics, or the buildup of residual stresses. This study builds on our previously proposed concept of three-alloy FGM system feasibility diagrams for the identification of gradient pathways that avoid deleterious phases in FGMs by also considering solidification cracking. Here, five solidification cracking criteria were integrated into the feasibility diagrams, and equilibrium simulations were carried out based on Scheil results (termed Scheil-equilibrium simulation) to predict phase formation below the solidus temperature considering solidification microsegregation. The new feasibility diagrams were applied to four previously studied FGM systems, and the newly proposed approach predicted high crack susceptibility, detrimental phase formation, or interdendritic BCC phase formation in the experimentally observed cracking region. This demonstrates the utility of the proposed framework for crack prediction in the design of future FGMs gradient pathways.

cond-mat.mtrl-sci↗
arXiv2023

Parameter-free prediction of phase transition in PbTiO3 through combination of quantum mechanics and statistical mechanics

Thermodynamics of ferroelectric materials and their ferroelectric to paraelectric (FE-PE) transitions including those in PbTiO3 is commonly described by the phenomenological Landau theory and more recently by effective Hamiltonian and various potentials, all with model parameters fitted to experimental or theoretical data. Here we show that the zentropy theory, which considers the total entropy of a system as a weighted sum of entropies of configurations that the system may experience and the statistical entropy among the configurations, can predict the FE-PE transition without fitting parameters. For PbTiO3, the configurations are identified as the FE configurations with 90- or 180-degree domain walls in addition to the ground state of the FE configuration without domain wall. With the domain wall energies predicted from first-principles calculations based on the density functional theory in the literature as the only inputs, the FE-PE transition for PbTiO3 is predicted showing remarkable agreement with experiments, unveiling the microscopic fundamentals of the transition.

cond-mat.mtrl-sci↗
arXiv2022

Silicon-doped $β$-Ga$_2$O$_3$ films grown at 1 $μ$m/h by suboxide molecular-beam epitaxy

We report the use of suboxide molecular-beam epitaxy (S-MBE) to grow $β$-Ga$_2$O$_3$ at a growth rate of ~1 $μ$m/h with control of the silicon doping concentration from 5x10$^{16}$ to 10$^{19}$ cm$^{-3}$. In S-MBE, pre-oxidized gallium in the form of a molecular beam that is 99.98\% Ga$_2$O, i.e., gallium suboxide, is supplied. Directly supplying Ga2O to the growth surface bypasses the rate-limiting first step of the two-step reaction mechanism involved in the growth of $β$-Ga$_2$O$_3$ by conventional MBE. As a result, a growth rate of ~1 $μ$m/h is readily achieved at a relatively low growth temperature (T$_{sub}$ = 525 $^\circ$C), resulting in films with high structural perfection and smooth surfaces (rms roughness of < 2 nm on ~1 $μ$m thick films). Silicon-containing oxide sources (SiO and SiO$_2$) producing an SiO suboxide molecular beam are used to dope the $β$-Ga$_2$O$_3$ layers. Temperature-dependent Hall effect measurements on a 1 $μ$m thick film with a mobile carrier concentration of 2.7x10$^{17}$ cm$^{-3}$ reveal a room-temperature mobility of 124 cm$^2$ V$^{-1}$ s$^{-1}$ that increases to 627 cm$^2$ V$^{-1}$ s$^{-1}$ at 76 K; the silicon dopants are found to exhibit an activation energy of 27 meV. We also demonstrate working MESFETs made from these silicon-doped $β$-Ga$_2$O$_3$ films grown by S-MBE at growth rates of ~1 $μ$m/h.

cond-mat.mtrl-sci↗
arXiv2022

Temperature-dependent Multi-well Free-energy Landscape for Phase Transitions: PbTiO3 as a Prototype

It has been a long challenge to analytically construct the quantitative temperature-dependent multi-well free-energy landscape over the space of order parameters describing phase transitions and associated critical phenomena. Here we propose a simple analytical model for the free energy landscape based on a priori concept of Boltzmann thermal mixing among multiple parabolic potentials representing different energetically degenerated ground states in contrast to the popular Landau theory using the high-temperature disordered state as a reference. The model recovers both the Weiss molecular field theory and the temperature dependent behaviors of the second order Landau coefficient. It is rather remarkable that such a simple analytical expression can describe a wide variety of properties across the ferroelectric phase transition in PbTiO3, including the temperature dependences of the spontaneous polarization, the heat capacities, the permittivity tensor, and the lattice parameters. The approach also allows parametrization of the free energy function across phase transitions based directly on the 0 K thermodynamics data that can be obtained from DFT calculations. We anticipate that the approach can be equally applied to other types of critical phenomena, e.g., the superconducting phase transition, the metal-insulator transition, and the magnetic transitions.

cond-mat.mtrl-sci↗
arXiv2022

Lorenz Number and Electronic Thermoelectric Figure of Merit: Thermodynamics and Direct DFT Calculations

The Lorenz number (L) contained in the Wiedemann-Franz law represents the ratio of two kinetic parameters of electronic charge carriers: the electronic contribution to the thermal conductivity (K_el) and the electrical conductivity (sigma), , and can be expressed as LT=K_el/sigma where T is temperature. We demonstrate that the Lorenz number simply equals to the ratio of two thermodynamic quantities: the electronic heat capacity (c_el) and the electrochemical capacitance (c_N) through LT=c_el/c_N , a purely thermodynamic quantity, and thus it can be calculated solely based on the electron density of states of a material. It is shown that our thermodynamic formulation for the Lorenz number leads to: i) the well-known Sommerfeld value L=pi^2/3(k_B/e)^2 at the low temperature limit, ii) the Drude value L=3/2(k_B/e)^2 at the high temperature limit with the free electron gas model, and iii) possible higher values than the Sommerfeld limit for semiconductors. It is also demonstrated that the purely electronic contribution to the thermoelectric figure-of-merit can be directly computed using high-throughput DFT calculations without resorting to the computationally more expensive Boltzmann transport theory to the electronic thermal conductivity and electrical conductivity.

cond-mat.mtrl-sci↗
arXiv2022

Thermodynamic and electron-transport properties of Ca3Ru2O7 from first-principles phonon calculations and Boltzmann transport theory

This work demonstrates a first-principles-based approach to obtaining finite temperature thermal and electronic transport properties which can be employed to model and understand mesoscale structural evolution during electronic, magnetic, and structural phase transitions. A computationally tractable model was introduced to estimate the temperature dependence of the electron relaxation time. The model is applied to Ca3Ru2O7 with a focus on understanding its electrical resistivity across the electronic phase transition at 48 K. A quasiharmonic phonon approach to the lattice vibrations was employed to account for thermal expansion while the Boltzmann transport theory including spin-orbit coupling was used to calculate the electron-transport properties, including the temperature dependence of electrical conductivity.

cond-mat.mtrl-sci↗
arXiv2022

Insight into Ideal Shear Strength of Ni-based Dilute Alloys using First-Principles Calculations and Correlational Analysis

The present work examines the effect of alloying elements (denoted X) on the ideal shear strength for 26 dilute Ni-based alloys, Ni$_{11}$X, as determined by first-principles calculations of pure alias shear deformations. The variations in ideal shear strength are quantitatively explored with correlational analysis techniques, showing the importance of atomic properties such as size and electronegativity. The shear moduli of the alloys are affirmed to show a strong linear relationship with their ideal shear strengths, while the shear moduli of the individual alloying elements were not indicative of alloy shear strength. Through combination with available ideal shear strength data on Mg alloys, a potential application of the Ni alloy data is demonstrated in the search for a set of atomic features suitable for machine learning applications to mechanical properties. As another illustration, the predicted Ni ideal shear strengths play a key role in a predictive multiscale framework for deformation behavior of single crystal alloys at large strains, as shown by simulated stress-strain curves.

cond-mat.mtrl-sci↗