Calculated Phase Diagram Research Articles

Toward the Equiaxed Grain Microstructure in CrMnFeCoNi High‐Entropy Alloy Fabricated by Directed‐Energy Deposition

The columnar grains in additively manufactured alloys increase the tendency to form solidification cracks and cause anisotropy. Studying the effect of process parameters on microstructure development helps to guide the manufacturing of the equiaxed grain microstructure. First, the effect of process conditions on the melt pool dimensions using in situ synchrotron X‐ray imaging and thermal profile and solidification condition using finite element simulation and calculation of thermodynamics phase diagrams of CrMnFeCoNi high‐entropy alloy fabricated by directed energy deposition is studied. Increasing the laser power reduces the thermal gradient to solidification rate ratio, pushing the solidification closer to the columnar‐equiaxed transition. Nevertheless, the simulations still indicate the columnar microstructure for all scan conditions in contrast to the experimental observation that shows single‐wall samples built at 200 W consisted of dominantly equiaxed grains, whereas columnar grains are dominant in samples built at 100 W. It is believed that in addition to the effect of thermal gradient and solidification rate, the chemical segregation (Mn and Ni) during solidification may promote dendrite detachment, hence assisting the transition to equiaxed grains. The multitrack deposition results in more solid beneath a new melt pool, increasing the thermal gradient that promotes more columnar grains in comparison to single tracks.

Solid-state diffusion bonding for INCONEl 617 superalloy using field-assisted sintering technology (FAST) guided by CALPHAD approach

This study investigates solid-state diffusion bonding between two INCONEL 617 alloy samples using field-assisted sintering technology (FAST). The study focuses on analyzing the faying surface validating the theoretical alloy design modeling done by the CALculation of PHAse Diagrams (CALPHAD) approach followed by experimental validation. Varying kinetics’ limitations enabled phase stability and phase control governed by the CALPHAD approach alloy design. The alloy design contains a pseudo-binary phase diagram assisted with thermal mapping of a property phase diagram to obtain the optimum temperature of solid-state diffusion bonding while understanding phase fields and their evolution through Molybdenum (Mo) increasing content and temperature increase. The FAST parameters recommended by CALPHAD were 800 °C under 10 MPa pressure with a holding time of 30 min. The investigation observations were promising in a way that the faying surface contains gamma (γ) only, while the further region on the alloy contains γ and gamma prime (γ′). It is worth mentioning that FAST joining resulted in fine faying surface thickness of around 10 μm and a controlled heat affected zone (HAZ) leading to relevant reduction in the recrystallization zone yielding an average grain size of 60–100 μm before and after diffusion bonding. Furthermore, two modes of metal carbide (MC) have been found; MC formed under the faying surface and micro-MC pools formed around the faying surface.

Critical evaluation and thermodynamic assessment of the Al2O3–TiO2–CaO ternary system

Knowledge about the thermodynamic equilibria of the Al2O3–TiO2–CaO system is important for the design of refractory and ceramic materials. The Al2O3–TiO2, Al2O3–CaO and CaO–TiO2 binary systems were reoptimized and the Al2O3–TiO2–CaO ternary system was assessed by CALPHAD (CAlculation of PHAse Diagram) approach due to the reliability of phase diagram and thermodynamic property data. The liquid phase was described by the ionic two-sublattice model with the formula (Al+3,Ti+2,Ti+3,Ca+2)P(O−2,AlO1.5,Va,O,TiO2)Q. A set of self-consistent thermodynamic parameters for the Al2O3–TiO2–CaO ternary system was finally obtained, reproducing well the phase diagram and thermodynamic properties, predicting the Ca4Ti3O10 primary crystallization field. The present thermodynamic description is of interest for the design of refractory and ceramic materials as well as the development of thermodynamic databases for multicomponent aluminosilicate system.

New lightweight high-entropy alloy coatings: Design concept, experimental characterization, and high-temperature oxidation behaviors

Lightweight high-entropy alloy (HEA) coatings by laser cladding (LC), which combines the advantages of high-entropy alloys and laser cladding, are potential materials for high-temperature applications. Al20Cr5Fe50Mn20Ti5 and Al25Cr20Fe20Mn15Ti20 HEAs were designed, and the calculated thermal parameters were close to the Ni-based alloy substrate (Inconel 718). Based on this, Al20Cr5Fe50Mn20Ti5 and Al25Cr20Fe20Mn15Ti20 HEA coatings were fabricated by LC on the substrates. The main phase structures of the two designed HEAs are the BCC + L21 phase, as revealed by the CALculation of PHAse Diagrams (CALPHAD). The high-temperature oxidation properties of the coatings were systematically investigated using isothermal oxidation tests. The oxidation activation energies of both coatings were 154.8 and 133.4 kJ/mol. Combined with molecular dynamics (MD) simulation, the clustering mechanism of Al and Ti elements was revealed in the formation of the L21 phase, whereas the high proportion of Ti elements increased the vacancy concentration, which was not conducive to oxidation resistance. Through this study, lightweight HEA coatings with excellent high-temperature performance can be designed and developed in the Al-Cr-Fe-Mn-Ti HEA system.

Effect of Nb and B on the Precipitation Behaviors in Al-Ti-Nb Balanced-Ratio Ni-Based Superalloy: A Phase-Field Study

In this paper, quantitative two-dimensional (2-D) phase-field simulations were performed to gain insight into the effects of B and Nb for Al-Ti-Nb balanced-ratio GH4742 alloys. The microstructure evolution during the precipitation process was simulated using the MICRESS (MICRostructure Evolution Simulation Software) package developed in the formalism of the multi-phase field model. The coupling to CALPHAD (CALculation of PHAse Diagram) thermodynamic databases was realized via the TQ interface. The morphological evolution, concentration distribution, and thermodynamic properties were extensively analyzed. It is indicated that a higher Nb content contributes to a faster precipitation rate and higher amounts and the smaller precipitate size of the γ′ phase, contributing to better mechanical properties. The segregation of the W element in γ′ precipitate due to its sluggish diffusion effect has also been observed. Higher temperatures and lower B contents accelerate the dissolution of boride and reduce the precipitation of borides. With the increased addition of B, the formation of borides may have a pinning effect on the grain boundary to hinder the kinetic process. In addition, borides are prone to precipitate around the interface rather than in the bulk phase. Once the M3B2 borides nucleate, they grow in the consumption of γ′ phases.

Accelerating the Exploration of High‐Entropy Alloys: Synergistic Effects of Integrating Computational Simulation and Experiments

High‐entropy alloys (HEAs) are novel materials composed of multiple elements with nearly equal concentrations and they exhibit exceptional properties such as high strength, ductility, thermal stability, and corrosion resistance. However, the intricate and diverse structures of HEAs pose significant challenges to understanding and predicting their behavior at different length scales. This review summarizes recent advances in computational simulations and experiments of structure‐property relationships in HEAs at the nano/micro scales. Various methods such as first‐principles calculations, molecular dynamics simulations, phase diagram calculations, and finite element simulations are discussed for revealing atomic/chemical and crystal structures, defect formation and migration, diffusion and phase transition, phase formation and stability, stress‐strain distribution, deformation behavior, and thermodynamic properties of HEAs. Emphasis is placed on the synergistic effects of computational simulations and experiments in terms of validation and complementarity to provide insights into the underlying mechanisms and evolutionary rules of HEAs. Additionally, current challenges and future directions for computational and experimental studies of HEAs are identified, including accuracy, efficiency, and scalability of methods, integration of multiscale and multiphysics models, and exploration of practical applications of HEAs.

Thermodynamic stability of selected ASb2O6 and A2Sb2O7 phases (A = Ca, Ba, Cd, Sr, Zn)

– Antimonates with the stoichiometry ASb2O6 and A2Sb2O7 have a wide range of applications in many areas of materials sciences and geosciences. In this work, we have derived thermodynamic properties of ASb2O6 (A = Ba, Ca, Sr, Zn, Na2, Cd) and A2Sb2O7, (A = Ca, Cd) with a combination of high-temperature oxide-melt calorimetry, relaxation calorimetry, differential scanning calorimetry (DSC), and density-functional theory (DFT) calculations. The samples were synthesized by solid-state techniques, characterized by powder X-ray diffraction, and found to belong to different structural types (rosiaite, trirutile, ilmenite, pyrochlore, and weberite). The Gibbs free energies of formation at T = 298.15 K from elements are (all data in kJ·mol−1) −1691.7 ± 4.8 (BaSb2O6), −1710.8 ± 4.7 (CaSb2O6), −1219.3 ± 4.1 (CdSb2O6), −1674.4 ± 4.9 (SrSb2O6), −1302.0 ± 3.4 (ZnSb2O6), −1596.9 ± 5.4 (Na2Sb2O6), −2407.6 ± 8.0 (Ca2Sb2O7), −1497.6 ± 7.5 (Cd2Sb2O7). The DFT calculations allowed to extrapolate the experimental heat capacity up to T = 1000 K and to calculate phase diagrams. They show that the syntheses of these compounds should be feasible either by hydrothermal treatment or solid-state reaction (using carbonates) with Na2Sb2O6 as a precursor at relatively low temperatures. The only exception seems to be the phase SrSb2O6 that is predicted to be unstable in a solid-state reaction involving Na2Sb2O6 and SrCO3.

A cluster-based computational thermodynamics framework with intrinsic chemical short-range order: Part I. Configurational contribution

Exploiting Chemical Short-Range Order (CSRO) is a promising avenue for manipulating the properties of alloys. However, existing modeling frameworks are not sufficient to predict CSRO in multicomponent alloys (>3 components) in an efficient and reliable manner. In this work, we developed a hybrid computational thermodynamics framework by combining unique advantages from Cluster Variation Method (CVM) and CALculation of PHAse Diagram (CALPHAD) method. The key is to decompose the cumbersome cluster variables in CVM into fewer site variables of the basic cluster using the Fowler-Yang-Li (FYL) transform, which considerably reduces the number of variables that must be minimized for multicomponent systems. CSRO is incorporated into CALPHAD with a novel cluster-based solution model called FYL-CVM. This new framework brings more physics into CALPHAD while maintaining its practicality and achieves a good balance between accuracy and computational cost. It leverages statistical mechanics to yield a more physical description of configurational entropy and opens the door to cluster-based CALPHAD database development. The application of the FYL-CVM model in a prototype fcc AB alloy demonstrates its capability to calculate the phase diagram and thermodynamic properties with remarkable accuracy comparable to CVM. The hybrid CVM-CALPHAD framework represents a new methodology for thermodynamic modeling that enables atomic-scale order to be exploited for materials design.

Microstructural evolution, mechanical behavior, and deformation mechanisms of a lightweight Ti–Nb–Cr–V refractory high-entropy alloy at room and elevated temperatures

Refractory high-entropy alloys (RHEAs) have emerged as promising candidates for high-temperature applications owing to their distinctive mechanical properties. However, their limited tensile ductility and high density pose hurdles for further engineering utilization. In this study, we introduce a novel RHEA composition, Ti45Nb30Cr15V10 (at.%), distinguished by its reduced density (∼6.2 g/cm3), achieved through the assistance of CALPHAD (CALculation of PHAse Diagrams) modeling. The as-cast RHEA exhibits a single body-centered cubic (BCC) structure, demonstrating a tensile yield strength of ∼904 MPa along with a total elongation of ∼9.7 %. By employing cold rolling followed by recrystallized annealing (designated as the CRRA sample), we achieve notable enhancements in both strength and ductility. Specifically, the CRRA sample manifests an impressive tensile yield strength of ∼1010 MPa and a total elongation of ∼20.6 % at room temperature. Remarkably, even at an elevated temperature of 700 °C, the CRRA sample maintains notable strength, displaying a yield strength of ∼695 MPa. The observed dislocation behavior, transitioning from dual-system slip to multi-system slip, along with the intricate interactions of dislocation substructures (e.g., loops, tangles, networks, bands, and cells) and kink bands, are identified as the principal deformation mechanisms contributing to the exceptional tensile properties of the CRRA sample at room temperature. At 700 °C, the presence of wavy-slipping dislocations, induced by the strong pinning effect of component fluctuations, predominantly contributes to the strength of the CRRA sample. However, the emergence of Cr2(Ti, Nb, V) Laves phase at grain boundaries results in premature fracture. The extraordinary tensile properties exhibited by the CRRA sample at both room and elevated temperatures underscore its potential for advanced engineering applications.

Study of Phase Transformations and Interface Evolution in Carbon Steel under Temperatures and Loads Using Molecular Dynamics Simulation

Carbon steel materials are widely used in mechanical transmission. Under different temperature and pressure service conditions, the microscopic changes of stress and strain that are difficult to detect and analyze by experimental means will lead to failure deformation, thus affecting their operational stability and life. In this study, the molecular dynamics method is used to simulate the heating–cooling phase transition process of common carbon steel materials. Austenite transformation temperatures of 980 K (0.2 wt.%) and 1095 K (0.5 wt.%) are acquired which is determined by the volume hysteresis before and after transformation, which is consistent with the results of JMatPro phase diagram analysis. The internal stress state of the material varies between compressive stress and tensile stress due to the change of phase structure, and the dislocation characteristics during the phase transition period are observed to change significantly. Then, an α/γ two-phase interface model is constructed to study the migration of the phase interface and the change of the phase structure by applying a continuously changing external load. At the same time, the transition pressure of α→ϵ is obtained with a value of 37 GPa under three different initial loads showing the independence of the initial load and the historical path. Based on the molecular dynamics simulation and the phase diagram calculation of the carbon steel, the analysis method for the microstructure transformation and the stress–strain behavior of the phase interface under the external load can provide a reference for the design of microstructure and mechanical properties of alloy steel in the future.

Effect of Cu Addition Above the Solubility Limit on Microstructure Formation and Cu Segregation in 800 MPa Grade Ductile Cast Iron During Solidification

In this study, the effect of 3 mass%Cu additions on microstructure formation and Cu segregation in 800 MPa grade ductile cast iron during solidification was investigated. The calculated phase diagram showed that after the addition of 3 mass%Cu, the Cu phase with a negligible amount appeared below 1000°C, and most Cu was included in the matrix. Based on optical microstructure, after the addition of 3 mass%Cu, the size of graphite nodules became finer, and the microstructure rarely had an area with α-ferrite. Image analysis showed that the fraction of pearlite increased significantly, indicating that Cu greatly promoted the formation of pearlite. Compositional analysis by scanning electron microscopy indicated that the pearlitic area also contained approximately 3 mass%Cu, which corresponds to those of primary and secondary austenite calculated. A small and bright phase particle containing a large amount of Cu was observed at the interface of graphite and matrix.

Ways to improve the properties of high-entropy alloys Cantor CoCrFeNiMn and CoCrFeNiAl

Created one of the first and studied more than 20 years ago, high-entropy five-component alloys CoCrFeNiMn (Cantor alloy) and CoCrFeNiAl still attract the attention of researchers in the field of physical materials science due to their possible application in various industries because of their successful combination of strength and plastic properties. To date, a large amount of experimental materials has been accumulated on the ways to control the properties of these alloys. This article reviews the publications of domestic and foreign authors in two areas of improving the properties of these alloys: alloying, precipitation and heat treatment, and the use of CALPHAD phase diagrams. In the first direction, the role of alloying with B, Al, V, Si, Nb is analyzed; γ and γ′ nanoprecipitations, various modes of thermal and deformation processing. It was concluded that it is necessary to conduct experiments on the alloying of HEAs with Zr and Nb, which have proven themselves well in hardening steels. Creation and modification of the properties of five-component HEAs is possible using the CALPHAD computer programs developed for calculating state diagrams. The results of publications on the thermodynamic description of five-component alloys analyzed in the article are confirmed by comparing the phase diagrams with the available experimental data. In one of the analyzed works on the phase formation of five-component HEAs consisting of Co, Cr, Fe, Ni, Al, Mn, Cu, 2436 compositions were considered, which made it possible to determine 1761 variants of reliab­le prediction of the formation of bcc/B2 and fcc phases, bypassing amorphous phases and intermetallic compounds, thereby designing a certain level of mechanical properties. It is shown that the design of a new generation of HEAs is possible based on calculation of the CALPHAD phase diagrams.

Achievement of heat treatment strengthening in phosphor bronze through semi-coherent precipitation

Traditional phosphor bronzes have faced difficulties in terms of strengthening via heat treatment. In this study, a Cu-Sn-P-Ni-Si alloy with capability of precipitation strengthening was designed based on phase diagram calculations. After direct aging treatment, the mechanical properties of the Cu-8Sn-0.1P alloy exhibit minimal changes. However, significant strengthening was achieved in the Cu-Sn-P-Ni-Si alloy. Experimental results demonstrate that during the direct aging process, semi-coherent interfaces are formed between the precipitate phases and the matrix in Cu-8Sn-0.1P-1Ni-0.227Si alloy, resulting in significant performance enhancement. Specifically, the yield strength of the alloy was increased by approximately 39% after aging treatment. Crucially, the strengthening mechanism of the Cu-Sn-P-Ni-Si alloy and the formation mechanism of semi-coherent interfaces were elucidated. This work provides a method to significantly enhance the comprehensive performance of phosphor bronze without requiring any special additional manufacturing processes. The achievement of heat treatment strengthening of phosphor bronze without undergoing deformation processing will enhance its potential for application.

MaterialsMap: A CALPHAD-based tool to design composition pathways through feasibility map for desired dissimilar materials, demonstrated with resistance spot welding 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).

Thermodynamic modeling of the Hf-Ta-O system for the design of oxidation resistant HfC-TaC ceramics

An improved understanding of the oxidation resistance of HfC-TaC ultra-high temperature ceramics (UHTCs) is developed through modeling of the phase equilibria in the Hf-Ta-O system and HfO2-Ta2O5 isoplethal section. CALculation of PHAse Diagrams (CALPHAD) thermodynamic models of the systems are developed in conjunction with experimental data from the literature and first-principles calculations. Density functional theory (DFT) calculations accurately describe thermodynamic properties of binary oxides in the Hf-Ta-O system and predict cation disorder in Hf(n-5)/2Ta2On. The ternary modeling includes revised models of the Hf–O system and existing models of the Ta–O and Hf–Ta systems. The Hf(n-5)/2Ta2On ternary oxide series is modeled as three entropically stabilized solid solutions with disordered cation sublattices that increase in stability with structure size. Hf4Ta2O13 is considered a metastable phase based on the present models and phase diagram, consistent with the lack of experimental data supporting its stability. The calculated phase diagrams improve upon prior ones and predict optimal thermal resistance of HfC-TaC ceramics at compositions between 3HfC-1TaC and 4HfC-1TaC.

Clorine Solubility in Silicate Melts: New Experiments and Thermodynamic Mixing Model

We present new experimental data on Cl solubility in model basalt melts of eutectic compositions diopside (Di)–albite (Ab) and Di–anorthite ± quartz (Qtz). The starting glasses were equilibrated with aqueous fluid H₂O-NaCl-CaCl₂ at 4 kbar in the temperature range 900–1200°C. The experiments show that the Cl solubility decreases with increasing NaCl in the fluid. Ca-Na partitioning between melts and fluid is weekly temperature dependent and resembles that of the plagioclase-fluid system. The new experimental data, along with the previously published results on the model granite melting in the presence of (Na, K)Cl brines (Aranovich et al., 2013) are used to calibrate an empirical thermodynamic model for the salt species (NaCl, KCl, CaCl₂) in silicate melt. Calculations show that Cl solubility in the haplogranite melt decreases with increasing K/Na ratio in the fluid (and, correspondingly, melt). At high pressure (10 kbar) Cl solubility in the granite increases with increasing H₂O content. Calculated phase diagram for a simple pseudo-ternary system Ab–H₂O–NaCl demonstrates complex phase relations and, correspondingly, evolution of the H₂O and NaCl concentrations in the melt. Literature data on the variations of H₂O and NaCl in the melt and fluid inclusions in Qtz from the granite of Badzhal tin deposit is used to illustrate complex evolution of a fluid-magmatic system.

Phase equilibria study and thermodynamic assessment of CaO–MgO–P2O5 system

The phase diagram of the CaO–MgO–P2O5 system was established by both experimental investigation and thermodynamic assessment. The presence of the contentious binary compound Ca4P6O19 in the CaO–P2O5 system was confirmed. The phase relationships in the CaO–MgO–P2O5 system at temperature 1150 °C and 1200 °C were studied via high-temperature quenching experiments in conjunction with X-ray diffraction (XRD) and electron probe micro-analyzer (EPMA) techniques. The CaO–MgO–P2O5 system was critically evaluated and optimized by means of the CALPHAD (CALculation of PHAse Diagrams) methodology. The ionic two-sublattice model (Ca+2, Mg+2)P (O−2,PO3−1,PO4−3,PO7/2−2,PO5/2)Q is used to describe the liquid phase in the CaO–MgO–P2O5 system due to the ionic nature of oxide melts and the presence of ions with different charges. A set of self-consistent thermodynamic parameters were obtained, showing good agreement between the experimental data and the calculated results. This study holds significant implications for guiding the manufacturing processes of phosphate ceramics.

Critical Experiments and Thermodynamic Modeling of the Li2O-SiO2 System

Phase equilibria studies were performed in the Li2O-SiO2 system for heat-treated samples using Scanning Electron Microscope (SEM) and X-Ray Diffraction (XRD). The temperature of the eutectic reaction (Liq. ⇌ Li4SiO4 + Li2SiO3) was experimentally determined at 1289 K using Differential Thermal Analysis (DTA). No evidences of the Li6Si2O7 formation was found by the experimental investigation and therefore, it was not considered. Heat capacity of the Li8SiO6 phase was measured using Differential Scanning Calorimetry (DSC). Solid phases of the Li2O-SiO2 system were described as stoichiometric compounds and liquid phases by two-sublattice partially ionic liquid model. Four stoichiometric intermediate compounds were considered to be stable (Li8SiO6, Li4SiO4, Li2SiO3 and Li2Si2O5). The polymorphic transformation in Li2Si2O5 phase was accounted and the metastable liquid miscibility gap on SiO2-rich side was reproduced. The calculated phase diagram satisfactorily agrees with the experimental phase equilibria as well as calculated thermodynamic properties reproduces experimental values within uncertainty limits.

Design method of immiscible dissimilar welding (Mg/Fe) based on CALPHAD and thermodynamic modelling

Joining dissimilar metals is a major challenge in joining technology; the weldability of immiscible systems is especially challenging. In this study, a design methodology for dissimilar welding is suggested. The Miedema model and Toop model are developed to calculate the thermodynamics of quaternary alloy systems (Mg-Fe-Al-Cu). Finite element modelling (FEM) of temperature fields and the calculation of phase diagrams (CALPHAD) are combined to provide prerequisite information for modelling. As a test subject, laser welded lap configuration joints of AZ31B magnesium alloy and DP590 steel with a copper coating were put into the design scheme. The interfacial elemental diffusion and formation of intermetallics (IMCs) along the interface during the welding process are predicted. This simulation design scheme predicts the interfacial reaction kinetics and identifies whether the intermediate element works or not. The effects of the Cu coating thickness on the weld constitution, interfacial microstructures and mechanical properties were studied. Cu coating promotes the weld formation fostering the metallurgical reaction of the fusion zone (FZ) with the steel brazing interface. The mechanism of interfacial reactions during the welding-brazing process has been clarified. The Vickers hardness distribution across the interface shows that the Cu-IMCs are ductile.

Modeling Charged Defects Using the Defect Energy Formalism With a Charge Sublattice Within a CALPHAD Framework

AbstractThe non‐stoichiometry of material compounds significantly influences their functional properties. In semiconductors, point defects determine whether a material is n‐type or p‐type and the concentration of charge carriers. Even in structural alloys and ion conductors used in batteries and fuel cells, non‐stoichiometry and dilute defects play an integral role in their function. The design of metal alloys has advanced rapidly with the aid of thermodynamic modeling using calculation of phase diagrams (CALPHAD) to predict the phases produced during different processing conditions. While thermodynamic modeling has been done previously by fitting experimental data, the advent of first‐principle techniques has enabled the computational prediction of material properties. The defect energy formalism (DEF) is described for modeling charged and uncharged defects in compounds, showing that it accurately predicts non‐stoichiometry using density functional theory (DFT), without fitting experiments. The model reproduces the expected defect and free‐charge carrier concentrations using the statistical mechanics approach commonly used in most DFT defect studies. Finally, the model is used to accurately predict the single‐phase region of PbTe with no fitting to measured defect concentrations. This method can revolutionize materials development of insulators, semiconductors, and even metals by allowing rapid DFT calculations to replace laborious experiments when dilute defects are involved.