CALculation Of PHAse Diagram Modeling Research Articles

CALPHAD modeling and ab initio calculations of the Np-U-Zr system

Phase diagram of Np-U-Zr, a key ternary alloy system of relevance for metallic nuclear fuels, is still largely undetermined. Here a thermodynamic model for the Np-U-Zr system is developed based on Muggianu extrapolation of our models for the U-Zr, Np-Zr, and Np-U binary systems, all employing the CALculation of PHAse Diagrams (CALPHAD) method. This model reproduces available experimental data for the high temperature phases reasonably well, but is uncertain for the lower temperature phases for which experimental data are scarce. Ab initio calculations are performed on the BCC phase of the Np-U-Zr system at 28 compositions employing density functional theory (DFT) both in its standard form and the so-called DFT plus Hubbard U (DFT + U) modification. When referencing to our CALPHAD model, standard DFT on average overestimates the enthalpy of mixing of the BCC phase by 0.093 eV/atom, while DFT + U reduces the error to 0.009–0.036 eV/atom when the effective Hubbard U parameters are in the ranges of single-structure optimized Ueff’s determined in our previous studies of the Np-Zr and U-Zr systems (0.65–0.90 for Ueff(Np) and 0.99–1.49 eV for Ueff(U), respectively). Our combined CALPHAD and ab initio modeling provides an initial attempt to determine the phase diagram of the Np-U-Zr system but further work is needed for a reliable determination.

First-principles calculations and thermodynamic modeling of the Yb-Ni binary system

A complete thermodynamic description of the Yb-Ni binary system is developed by means of the CALculation of PHAse Diagram (CALPHAD) method in combination with first-principles calculations based on density functional theory (DFT) and available experimental data in the literature. Finite temperature thermodynamic properties of the Yb-Ni intermetallic compounds are predicted using the quasi-harmonic approach, where first-principles phonon calculations are performed to calculate the lattice vibrational entropy. The associate solution model is used to describe the complex thermodynamic behavior of the liquid phase. The calculated phase diagram agrees well the experimental phase equilibrium data in the literature. By the coupling of CALPHAD modeling with first-principles calculations, the present work provides a more thermodynamically accurate model of the Yb-Ni system when compared to previous models.

Phase equilibria in equiatomic CoCuFeMnNi high entropy alloy

Phase equilibria and stability of a newly developed single phase equiatomic CoCuFeMnNi high entropy alloy (HEA) was investigated in the temperature range of 298–1573 K using in situ high temperature X-ray diffraction and thermodynamic modeling using CALPHAD (CALculation of PHAse Diagrams) approach. Complimentary characterization techniques like scanning and transmission electron microscopy with energy dispersive spectroscopy for microstructural investigation and compositional analysis, differential scanning calorimetry for thermal analysis and atom probe tomography for near-atomic scale chemical analysis were employed. It was found that the metastable FCC solid solution α phase (lattice parameter = 0.361 nm) undergoes phase transformation at 923 K and 1123 K. The α phase transforms to BCC β phase (a = 0.280 nm) at 923 K and on further heating, another FCC phase γ (a = 0.362 nm) precipitates out at 1123 K, leading to coexistence of two FCC phases and one BCC phase. Atom Probe Tomography carried out to study the three-dimensional distribution of constituent elements indicates the presence of ∼2 nm sized Cu clusters in the α phase. CALPHAD predictions indicate the tendency towards phase separation involving iron-cobalt and copper to partition out of the equiatomic solid solution to form the BCC and second FCC phase, respectively. A qualitative agreement between CALPHAD predictions and in situ high temperature X-ray diffraction accompanied with complimentary characterization tools explicitly demonstrates the fidelity of CALPHAD modeling for the design and development of novel HEA compositions.

Thermodynamic reassessment of the Ni–Si–Ti system using a four-sublattice model for ordered/disordered fcc phases supported by first-principles calculations

A thermodynamic reassessment of the ternary Ni–Si–Ti system was performed by means of CALPHAD (CALculation of PHAse Diagram) method. The fcc_A1/Ni3Si-L12 disordered/ordered transition was described using a four-sublattice model. The enthalpies of formation of the ternary compounds τ1, τ2, and τ4 and end-members of the Ti5Si3 and Ni3Ti phases at 0 K in the Ni–Si–Ti ternary system were computed via first-principles calculations to supply necessary thermodynamic data for the CALPHAD modeling. In the Ni–Si–Ti ternary system, it was clarified that the ordered Ni3Si-L12 phase is formed from the liquid phase with the addition of Ti. An optimal set of thermodynamic parameters for the Ni–Si–Ti system was obtained by taking into consideration of the experimental data from the literature and theoretic values from the present first-principles calculations. Comparisons between the calculated and measured phase diagrams indicated that almost all the reliable experimental information was satisfactorily accounted for by the present modeling.

Design of Light-Weight High-Entropy Alloys

High-entropy alloys (HEAs) are a new class of solid-solution alloys that have attracted worldwide attention for their outstanding properties. Owing to the demand from transportation and defense industries, light-weight HEAs have also garnered widespread interest from scientists for use as potential structural materials. Great efforts have been made to study the phase-formation rules of HEAs to accelerate and refine the discovery process. In this paper, many proposed solid-solution phase-formation rules are assessed, based on a series of known and newly-designed light-weight HEAs. The results indicate that these empirical rules work for most compositions but also fail for several alloys. Light-weight HEAs often involve the additions of Al and/or Ti in great amounts, resulting in large negative enthalpies for forming solid-solution phases and/or intermetallic compounds. Accordingly, these empirical rules need to be modified with the new experimental data. In contrast, CALPHAD (acronym of the calculation of phase diagrams) method is demonstrated to be an effective approach to predict the phase formation in HEAs as a function of composition and temperature. Future perspectives on the design of light-weight HEAs are discussed in light of CALPHAD modeling and physical metallurgy principles.

Lateral Versus Vertical Growth of Two-Dimensional Layered Transition-Metal Dichalcogenides: Thermodynamic Insight into MoS2.

Unprecedented interest has been spurred recently in two-dimensional (2D) layered transition metal dichalcogenides (TMDs) that possess tunable electronic and optical properties. However, synthesis of a wafer-scale TMD thin film with controlled layers and homogeneity remains highly challenging due mainly to the lack of thermodynamic and diffusion knowledge, which can be used to understand and design process conditions, but falls far behind the rapidly growing TMD field. Here, an integrated density functional theory (DFT) and calculation of phase diagram (CALPHAD) modeling approach is employed to provide thermodynamic insight into lateral versus vertical growth of the prototypical 2D material MoS2. Various DFT energies are predicted from the layer-dependent MoS2, 2D flake-size related mono- and bilayer MoS2, to Mo and S migrations with and without graphene and sapphire substrates, thus shedding light on the factors that control lateral versus vertical growth of 2D islands. For example, the monolayer MoS2 flake in a small 2D lateral size is thermodynamically favorable with respect to the bilayer counterpart, indicating the monolayer preference during the initial stage of nucleation; while the bilayer MoS2 flake becomes stable with increasing 2D lateral size. The critical 2D flake-size of phase stability between mono- and bilayer MoS2 is adjustable via the choice of substrate. In terms of DFT energies and CALPHAD modeling, the size dependent pressure-temperature-composition (P-T-x) growth windows are predicted for MoS2, indicating that the formation of MoS2 flake with reduced size appears in the middle but close to the lower T and higher P "Gas + MoS2" phase region. It further suggests that Mo diffusion is a controlling factor for MoS2 growth owing to its extremely low diffusivity compared to that of sulfur. Calculated MoS2 energies, Mo and S diffusivities, and size-dependent P-T-x growth windows are in good accord with available experiments, and the present data provide quantitative insight into the controlled growth of 2D layered MoS2.

MoNbTaV Medium-Entropy Alloy

Guided by CALPHAD (Calculation of Phase Diagrams) modeling, the refractory medium-entropy alloy MoNbTaV was synthesized by vacuum arc melting under a high-purity argon atmosphere. A body-centered cubic solid solution phase was experimentally confirmed in the as-cast ingot using X-ray diffraction and scanning electron microscopy. The measured lattice parameter of the alloy (3.208 Å) obeys the rule of mixtures (ROM), but the Vickers microhardness (4.95 GPa) and the yield strength (1.5 GPa) are about 4.5 and 4.6 times those estimated from the ROM, respectively. Using a simple model on solid solution strengthening predicts a yield strength of approximately 1.5 GPa. Thermodynamic analysis shows that the total entropy of the alloy is more than three times the configurational entropy at room temperature, and the entropy of mixing exhibits a small negative departure from ideal mixing.

Thermal conductivity of Al–Cu–Mg–Si alloys: Experimental measurement and CALPHAD modeling

In the present work, the thermal conductivities and microstructure of Al–xwt% Cu (x=1, 3, 5, 15 and 30) and Al–ywt% Si (y=2, 12.5 and 20) alloys were investigated by using laser-flash method, scanning electron microscopy (SEM) and X-ray diffraction (XRD). Besides, a CALPHAD (CALculation of PHAse Diagram) approach to evaluate the thermal conductivity of Al–Cu–Mg–Si system was performed. The numerical models for the thermal conductivity of pure elements and stoichiometric phases were described as polynomials, and the coefficients were optimized via PARROT module of Thermal-Calc software applied to the experimental data. The thermal conductivity of (Al)-based solid solutions was described by using Redlich–Kister interaction parameters. For alloys in two-phase region, the interface scattering parameter was proposed in the modeling to describe the impediment of interfaces on the heat transfer. Finally, a set of self-consistent parameters for the description of thermal conductivity in Al–Cu–Mg–Si system was obtained, and comprehensive comparisons between the calculated and measured thermal conductivities show that the experimental information is satisfactorily accounted for by the present modeling.

CALPHAD-Based Integrated Computational Materials Engineering Research for Materials Genomic Design

Due to materials genomic databases created by versatile computational tools in thermodynamics and kinetics, CALPHAD (CALculation of PHAse Diagrams) is one of the most important techniques in materials and manufacturing design. The CALPHAD method is neither empirical nor fundamental, but it plays a vital role to bridge engineering and science, industry and academia. 1,2 Evidently, CALPHAD-related models and experiments have been extensively adopted in materials and process design for both alloys and oxides. 2–4 There are three components in the materials innovation infrastructure of the Materials Genome Initiative (MGI) strategy: digital data, computational, and experimental tools. Such an idea can be well reflected in the framework of the modern CALPHAD research. As indicated in Fig. 1, modern CALPHAD modeling is based not only on experimental data but also on the combination of data with atomistic modeling, typically, quantum mechanical calculations. The integration of such techniques further extends spatial and temporal ranges of CALPHAD models. In this way, CALPHAD and its developed databases can be used in other simulation techniques for designing material properties by controlling phases and microstructure evolutions. It should be noted that experiments provide actual data resources for validating and calibrating multiscale simulation and modeling, which is indispensable in the modern CALPHAD infrastructure. Moreover, the amount of experimental needs is inversely proportional to the quality and accuracy of the computational models. Overall, the CALPHAD methodology can leverage various computational techniques to construct the integrated computational materials engineering (ICME) system design tools for materials genomic research. For the TMS 2015 Annual Meeting & Exhibition, 41 research papers were received for the dedicated MGI symposium, ‘‘CALPHAD-Based ICME Research for Materials Genomic Design,’’ sponsored by the Alloy Phases Committee and the Integrated Computational Materials Engineering Committee. Contributed talks covered (I) materials genomic design in engineering applications, (II) CALPHAD database construction and materials genomic data repository, (III) advanced processing and characterization in materials design, and (IV) CALPHADbased ICME model and tool development. Indeed, it is a formidable task for this JOM topic to represent the entire CALPHAD-based ICME research for materials genomic design. However, one may start learning the whole through seeing a part of it presented in this JOM issue. Furthermore, we hope that the MGI symposium during the TMS conference along with these papers housed in the current issue can stimulate more discussions on CALPHAD-based ICME research for materials genomic design. In the current special topic of JOM, three papers are contributed:

Material design and development: From classical thermodynamics to CALPHAD and ICME approaches

This paper presents an overview and examples of material design and development using (1) classical thermodynamics; (2) CALPHAD (calculation of phase diagrams) modeling; and (3) Integrated Computational Materials Engineering (ICME) approaches. Although the examples are given in lightweight aluminum and magnesium alloys for structural applications, the fundamental methodology and modeling principles are applicable to all materials and engineering applications. The examples in this paper have demonstrated the effectiveness and limitations of classical thermodynamics in solving specific problems (such as nucleation during solidification and solid-state precipitation in aluminum alloys). Computational thermodynamics and CALPHAD modeling, when combined with critical experimental validation, have been used to guide the selection and design of new magnesium alloys for elevated-temperature applications. The future of material design and development will be based on a holistic ICME approach. However, key challenges exist in many aspects of ICME framework, such as the lack of diffusion/mobility databases for many materials systems, limitation of current microstructural modeling capability and integration tools for simulation codes of different length scales.

Integrating computational modeling and first-principles calculations to predict stacking fault energy of dilute multicomponent Ni-base alloys

Stacking fault energy (γSF) for dilute multicomponent Ni-base alloys has been modeled using an integrating CALPHAD (calculation of phase diagram) modeling approach and first-principles alias shear deformation calculations of unary, binary, and ternary alloys. The present first-principles results of γSF from 55 Ni70X1Y1 (X and Y are 11 alloying elements of Al, Mo, Nb, Os, Re, Ru, Ta, Tc, Ti, V, and W) indicate that the more the structural similarity between X and Y, the smaller the ternary interaction of γSF; and the variation of γSF due to alloying elements is similar to that of bulk modulus.

Thermodynamic modeling of the U–Zr system – A revisit

A new thermodynamic description of the U–Zr system is developed using the CALPHAD (CALculation of PHAse Diagrams) method with the aid of ab initio calculations. Thermodynamic properties, such as heat capacity, activities, and enthalpy of mixing, are well predicted using the improved thermodynamic description in this work. The model-predicted enthalpies of formation for the bcc and δ phases are in good agreement with the results from DFT+U ab initio calculations. The calculations in this work show better agreements with experimental data comparing with the previous assessments. Using the integrated method of ab initio and CALPHAD modeling, an unexpected relation between the enthalpy of formation of the δ phase and energy of Zr with hexagonal structure is revealed and the model improved by fitting these energies together. The present work has demonstrated that ab initio calculations can help support a successful thermodynamic assessment of actinide systems, for which the thermodynamic properties are often difficult to measure.

Invited Article: Micron resolution spatially resolved measurement of heat capacity using dual-frequency time-domain thermoreflectance

A pump-probe photothermal technique - dual-frequency time-domain thermoreflectance - was developed for measuring heat capacity with a spatial resolution on the order of 10 μm. The method was validated by measuring several common materials with known heat capacity. Rapid measurement of composition-phase-property relationships was demonstrated on Ti-TiSi2 and Ni-Zr diffusion couples; experimental values of heat capacity of the intermetallic compounds in these diffusion couples were compared with literature values and CALPHAD (CALculation of PHAse Diagram) calculations. The combination of this method and diffusion multiples provides an efficient way to generate thermodynamic data for CALPHAD modeling and database construction. The limitation of this method in measuring low thermal diffusivity materials is also discussed.

First-principles calculations and thermodynamic re-modeling of the Hf–W system

An integrative approach coupling first-principles calculations and the CALculation of PHAse Diagram (CALPHAD) method provides a more thermodynamically accurate model of the Hf–W system when compared to previous models. A two-sublattice model is used for describing the solid solubility of the HfW2 Laves phase. The modeling of the Laves phase includes input from first-principles total energy calculations and predictions of finite temperature properties from the Debye–Grüneisen model. In addition, first-principles calculations performed on hcp and bcc special quasirandom structures (SQS) predicted a positive enthalpy of mixing in both solid solution phases. Predicting the finite temperature properties of bcc SQS with the Debye–Grüneisen model was necessary to balance the positive, asymmetric enthalpy of mixing found in the bcc solid solution. The model produced by the coupling of CALPHAD modeling with first-principles calculations agrees well with experimental data. It also reproduces the Hf–W phase diagram with fewer parameters than previous models, which were created without the aid of first-principles calculations.

Effect of Mg, Ca, and Zn on stability of LiBH 4 through computational thermodynamics

The effect of divalent metal-dopants, Mg, Ca, and Zn, on the stability of LiBH 4 is studied by using the first-principles calculations and CALPHAD (CALculation of PHAse Diagram) modeling. The ground states of Mg 1/2BH 4, Ca 1/2BH 4, and Zn 1/2BH 4 are shown to be I 4 ¯ m 2 , F2dd, and I 4 ¯ m 2 , respectively, through first-principles calculations. Positive enthalpy of mixing between Li and the alloying element is predicted, indicating unfavorable solubility of alloying elements in LiBH 4 and thus offering possibility to decrease the stability of LiBH 4. The ionic sublattice model of (Li +, M 2+, Va) 1(BH 4 −) 1 is adopted for the metal substituted LiBH 4 phase. It is observed that the addition of Mg or Zn has limited effect as the decomposition temperature is between those of LiBH 4 and M 1/2BH 4 for Mg and Zn substitutions. LiBH 4 is destabilized with magnesium borides or LiZn 4 formation but its decomposition temperature is higher than that of M 1/2BH 4. On the other hand, the addition of Ca significantly reduces the H 2 releasing temperature due to the formation of highly stable CaB 6.

Study of phase equilibrium of Pu2O3-PuO2 system by the first-principles calculation and CALPHAD approach

A combination of a first-principles calculation, lattice dynamics and CALPHAD (CALculation of PHAse Diagrams) modeling is proven as a powerful tool so as to evaluate the Gibbs free energy and a phase equilibrium between compounds including large amount of vacancies. In this work, non-stoichiometric PuO2−x (dioxide) and Pu2O3 (sesquioxide) has been studied. An electron cohesive energy was evaluated from a first-principles calculations to estimate total energy of the compounds and a vacancy formation energy, and the theory of statistical mechanics was applied to evaluate enthalpy/entropy change due to oxygen vacancies for the non-stoichiometry of the PuO2 (i.e. PuO2−x). Then a vacancy-vacancy interaction energy was determined by fitting to the experimental data of a quantity of non-stoichiometry of the PuO2 compounds as a function of oxygen potentials at large deviation from stoichiometry. The resulting Gibbs free energy yields phase boundary between the phases with good agreement with to the experimental data.