Quantified Uncertainty in Thermodynamic Modeling for Materials Design

Phase fractions, compositions and energies of the stable phases as a function of macroscopic composition, temperature, and pressure (X-T-P) are the principle correlations needed for the design of new materials and improvement of existing materials. They are the outcomes of thermodynamic modeling based on the CALculation of PHAse Diagrams (CALPHAD) approach. The accuracy of CALPHAD predictions vary widely in X-T-P space due to experimental error, model inadequacy and unequal data coverage. In response, researchers have developed frameworks to quantify the uncertainty of thermodynamic property model parameters and propagate it to phase diagram predictions. In previous studies, uncertainty was represented as intervals on phase boundaries (with respect to composition) or invariant reactions (with respect to temperature) and was unable to represent the uncertainty in eutectoid reactions or in the stability of phase regions. In this work, we propose a suite of tools that leverages samples from the multivariate model parameter distribution to represent uncertainty in forms that surpass previous limitations and are well suited to materials design. These representations include the distribution of phase diagrams and their features, as well as the dependence of phase stability and the distributions of phase fraction, composition activity and Gibbs energy on X-T-P location - irrespective of the total number of components. Most critically, the new methodology allows the material designer to interrogate a certain composition and temperature domain and get in return the probability of different phases to be stable, which can positively impact materials design

Suitability of binary oxides for molecular-beam epitaxy source materials: A comprehensive thermodynamic analysis

We have conducted a comprehensive thermodynamic analysis of the volatility of 128 binary oxides to evaluate their suitability as source materials for oxide molecular-beam epitaxy (MBE). 16 solid or liquid oxides are identified that evaporate nearly congruently from stable oxide sources to gas species: As2O3, B2O3, BaO, MoO3, OsO4, P2O5, PbO, PuO2, Rb2O, Re2O7, Sb2O3, SeO2, SnO, ThO2, Tl2O, and WO3. An additional 24 oxides could provide molecular beams with dominant gas species of CeO, Cs2O, DyO, ErO, Ga2O, GdO, GeO, HfO, HoO, In2O, LaO, LuO, NdO, PmO, PrO, PuO, ScO, SiO, SmO, TbO, Te2O2, U2O6, VO2, and YO2. The present findings are in close accord with available experimental results in the literature. For example, As2O3, B2O3, BaO, MoO3, PbO, Sb2O3, and WO3 are the only oxides in the ideal category that have been used in MBE. The remaining oxides deemed ideal for MBE awaiting experimental verification. We also consider two-phase mixtures as a route to achieve the desired congruent evaporation characteristic of an ideal MBE source. These include (Ga2O3 + Ga) to produce a molecular beam of Ga2O(g), (GeO2 + Ge) to produce GeO(g), (SiO2 + Si) to produce SiO(g), (SnO2 + Sn) to produce SnO(g), etc.; these suboxide sources enable suboxide MBE. Our analysis provides the vapor pressures of the gas species over the condensed phases of 128 binary oxides, which may be either solid or liquid depending on the melting temperature. © 2020 Author(s)

DFTTK: Density Functional Theory Tool Kit for High-throughput Calculations of Thermodynamic Properties at Finite Temperatures

In this work, we present a software package in Python for high-throughput first-principles calculations of thermodynamic properties at finite temperatures, which we refer to as DFTTK (Density Functional Theory Tool Kit). DFTTK is based on the atomate package and integrates our experiences in the last decades on the development of theoretical methods and computational software. It includes task submissions on all major operating systems and task execution on high-performance computing environments. The distribution of the DFTTK package comes with examples of calculations of phonon density of states, heat capacity, entropy, enthalpy, and free energy under the quasi-harmonic phonon scheme for the stoichiometric phases of Al, Ni, Al3Ni, AlNi, AlNi3, Al3Ni4, and Al3Ni5, and the fcc solution phases treated using the special quasirandom structures at the compositions of Al3Ni, AlNi, and AlNi3.Comment: 49 pages, 18 figure

Quantified Uncertainty in Thermodynamic Modeling for Materials Design

Phase fractions, compositions and energies of the stable phases as a function of macroscopic composition, temperature, and pressure (X-T-P) are the principle correlations needed for the design of new materials and improvement of existing materials. They are the outcomes of thermodynamic modeling based on the CALculation of PHAse Diagrams (CALPHAD) approach. The accuracy of CALPHAD predictions vary widely in X-T-P space due to experimental error, model inadequacy and unequal data coverage. In response, researchers have developed frameworks to quantify the uncertainty of thermodynamic property model parameters and propagate it to phase diagram predictions. In most previous studies, uncertainty was represented as intervals on phase boundaries (with respect to composition or temperature) and was unable to represent the uncertainty in invariant reactions or in the stability of phase regions. In this work, we propose a suite of tools that leverages samples from the multivariate model parameter distribution to represent uncertainty in forms that surpass previous limitations and are well suited to materials design. These representations include the distribution of phase diagrams and their features, as well as the dependence of phase stability and the distributions of phase fraction, composition, activity and Gibbs energy on X-T-P location - irrespective of the total number of components. Most critically, the new methodology allows the material designer to interrogate a certain composition and temperature domain and get in return the probability of different phases to be stable, which can positively impact materials design

Computational discovery of ultra-strong, stable, and lightweight refractory multi-principal element alloys. Part I: design principles and rapid down-selection

Abstract Refractory metal-based multi-principal element alloys (MPEAs) are compelling materials for high-temperature (1000–2000 K) structural applications. However, only a minuscule fraction of their vast and heterogeneous compositional design space has been explored, leaving many potentially interesting alloys undiscovered. In this two-part work, a large region of the 11-element Al-Cr-Fe-Hf-Mo-Nb-Ta-Ti-V-W-Zr design space is computationally explored to identify refractory MPEAs with simultaneously high yield strength or specific yield strength and body-centered cubic (BCC) solid solution stability. In Part I, two case studies illuminate key factors and considerations in the yield strength versus phase stability tradeoff, provide guidelines for narrowing the expansive design space, and identify many candidates predicted to be stronger than refractory MPEAs reported to date, with BCC phase stability. Our findings indicate that medium entropy ternary alloys can outperform alloys with more elements and highlight the importance of exploring regions away from the equiatomic center of composition space

Design of an additively manufactured functionally graded material of 316 stainless steel and Ti-6Al-4V with Ni-20Cr, Cr, and V intermediate compositions

This study presents a method for designing a computationally informed gradient pathway to fabricate a functionally graded material (FGM) with terminal alloys of 316 stainless steel (SS316) and Ti-6Al-4V via directed energy deposition additive manufacturing with powder feedstock. In this work, the grading is accomplished through the introduction of intermediate elements and alloys (Ni-20Cr, Cr, and V) to avoid the brittle Fe-Ti intermetallic phases that form in the direct liquid phase joining of Ti-alloys and stainless steels. Using a combination of equilibrium calculations and Scheil-Gulliver simulations, a compositional pathway was designed to avoid deleterious phases. FGM samples were fabricated and experimentally characterized to determine the viability of the pathway. A change in phases from fcc to bcc was predicted to occur within the Ni-20Cr/Cr gradient region, and this was validated through experimental characterization. No detrimental phases (intermetallic, Laves, or σ phases) formed along the gradient path, demonstrating a successful computationally-informed design and fabrication of an FGM from SS316 to Ti-6Al-4V.This is a manuscript of an article published as Bobbio, Lourdes D., Brandon Bocklund, Emrah Simsek, Ryan T. Ott, Matt J. Kramer, Zi-Kui Liu, and Allison M. Beese. "Design of an additively manufactured functionally graded material of 316 stainless steel and Ti-6Al-4V with Ni-20Cr, Cr, and V intermediate compositions." Additive Manufacturing 51 (2022): 102649. DOI: 10.1016/j.addma.2022.102649. Copyright 2022 Elsevier B.V. Posted with permission. DOE Contract Number(s): AC02-07CH11358; 90NSSC18K1168; DGE-1449785; CMMI-205006