Predicted Phase Diagram Research Articles

First principles prediction of the Al-Li phase diagram including configurational and vibrational entropic contributions

The whole Al-Li phase diagram is predicted from first principles calculations and statistical mechanics including the effect of configurational and vibrational entropy. The formation enthalpy of different configurations at different temperatures was accurately predicted by means of cluster expansions that were fitted from first principles calculations. The vibrational entropic contribution of each configuration was determined from the bond length vs. bond stiffness relationships for each type of bond and the Gibbs free energy of the different phases was obtained as a function of temperature from Monte Carlo simulations. The predicted phase diagram was in excellent agreement with the currently accepted experimental one in terms of the stable (AlLi, Al2Li3, AlLi2, Al4Li9) and metastable (Al3Li) phases, of the phase boundaries between them and of the maximum stability temperature of line compounds. In addition, it provided accurate information about the gap between Al3Li and AlLi solvus lines. Finally, the influence of the vibrational entropy on the correct prediction of the phase diagram is discussed. Overall, the methodology shows that accurate phase diagrams of alloys of technological interest can be predicted from first principles calculations.

A solidification mode selection process map for laser powder bed fusion additive manufacturing of B-modified Ti6Al4V

The unique solidification kinetics of laser powder bed fusion (LPBF) additive manufacturing tend to result in solidification modes deviating from the phase diagram predictions. This study documents an approach for developing LPBF solidification mode selection process map based on an analytical equation model which determines the solidification mode transition criteria as a function of laser power ( P ), scan velocity ( V ) and material properties. As case studies, solidification mode selection process maps were developed for three Ti6Al4V-xB alloys (x = 1, 2, 5 wt% B), presenting primary β , primary TiB, and coupled eutectic solidification modes. To validate the proposed approach, laser deposition experiments were conducted to fabricate single-tracks, single-layer and two-layer pads on arc-melted Ti6Al4V-xB alloy buttons with different P-V parameters. The model-developed process maps agreed with the experimental results. P-V windows were found to allow coupled-eutectic solidification for off-eutectic Ti6Al4V-1, 2, 5 % B and primary- β solidification for hyper-eutectic Ti6Al4V-5 %B, producing a microstructure with a continuous TiB network and a microstructure with a discontinuous network of nano-scale TiB whiskers respectively. Single-layer and two-layer pads showed consistent microstructure features of the tracks, except for the narrow region that was remelted during pad deposition. Melt pool hardness was measured, which increases with scan velocity and shows a sudden change when solidification mode was altered. The potential and limitations of the proposed method for LPBF microstructure investigation are discussed. • An approach based on analytical models was used to develop a solidification mode selection process map for LPBF. • Solidification process maps were constructed for LPBF of Ti6Al4V-1, 2, 5%B, showing windows for coupled eutectic mode. • By varying P-V parameters, high-B% Ti6Al4V-xB solidification alters from primary TiB to eutectic to primary β-Ti mode. • LPBF with Ti6Al4V-xB could render four TiB morphologies after solidification

Compatibility of selected active pharmaceutical ingredients with poly(D, L-lactide-co-glycolide): Computational and experimental study

Biodegradable polyesters have emerged as a promising class of polymers for the development of efficient drug delivery systems for various treatments (including cancer treatment) due to their biocompatibility, low toxicity, and controlled drug release. This study presents a computational and experimental evaluation of the compatibility of selected model active pharmaceutical ingredients (APIs) with poly(D, L-lactide-co-glycolide) (PLGA), which is a key parameter to designing drug delivery systems based on amorphous solid dispersions (ASDs) and polymeric micro- or nanoparticles. PLGA with different molar ratios of the monomer units, i.e., lactide to glycolide ratio of 50:50 (PLGA50) or 75:25 (PLGA75), were investigated as polymeric carriers for the following model APIs: ibuprofen (IBU), paracetamol (PARA), naproxen (NAP), and indomethacin (IND). The phase diagrams obtained by a combination of calorimetric measurements and modeling using the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EOS) demonstrated low solubility of the model APIs in the studied copolymers at storage temperature (25 °C). The amorphous-amorphous phase separation was predicted by the PC-SAFT EOS for all API–PLGA systems and experimentally detected for the IBU–PLGA50, IBU–PLGA75, and NAP–PLGA75 systems. To investigate the physical stability of the API–PLGA systems and their link to the constructed phase diagrams, API–PLGA75 formulations were prepared using a melting process, and their solid-state properties were monitored over time. Of the analyzed API–PLGA75 formulations, only IND–PLGA75 remained in the amorphous state after 20 weeks of storage under dry conditions at 25 °C, while the other formulations recrystallized rapidly after preparation (IBU–PLGA75 and NAP–PLGA75) or after a limited storage period (PARA–PLGA75), reflecting poor compatibility of the investigated APIs with the PLGA copolymers and limited kinetic stabilization, as predicted from the constructed phase diagrams. Another important output of this work is the evaluation of the pure predictions of phase diagrams using the PC-SAFT EOS and its performance in ranking API–polymer compatibility.

Machine learning assisted predictions of multi-component phase diagrams and fine boundary information

A phase diagram is a critical tool in materials science, but establishing it often requires a large number of experiments, especially for multi-component systems. In this work, we propose a machine learning strategy to accurately predict the phase diagram for the multi-component ferroelectric system (Ba1−x−yCaxSry)(Ti1−u−v−wZruSnvHfw)O3 by combining classification and regression methods. Based on literature data, we construct by classification a diagram that maps composition and temperature to the phase, and identify octahedral factor, Matyonov-Batsanov electronegativity, the ratio of valence electron number to nuclear charge and core electron distance (Schubert) for the A site and B site cations as the dominant physical descriptors. A neural network (NN) regression model is adopted to accurately predict phase transition temperatures, i.e. the phase boundaries, so that a phase diagram can be established in composition space. In the region of phase boundaries, the relative proportions of coexisting phases are also estimated by their prediction probability. The predicted phase labels, location boundaries and coexisting phase proportions are experimentally validated for the ceramic (Ba0.96Ca0.02Sr0.02)(Ti0.98−xZr0.02Hfx)O3. Our work provides an effective approach to establish phase diagrams for multi-component systems and also predict fine boundary information.

Formation of hypoeutectic structure and strengthening mechanism of Co4Cr1.5Fe1.5Ni5 high entropy alloy alloyed by Al

To reveal the phase formation mechanism and the strengthening mechanism, the AlxCo4Cr1.5Fe1.5Ni5 alloys (x = 1.0, 1.2, 1.4, 1.6, 1.8, 2.0) were prepared by arc melting. Phase formation and prediction, tensile properties, strengthening mechanism and deformation mechanism were researched in detail. Results show that the microstructure of AlxCo4Cr1.5Fe1.5Ni5 alloys changes from single FCC phases (x ≤ 1.4)) to FCC and BCC phases (x＞1.4), which was in good agreement with the calculated phase diagram (CALPHAD) prediction. The lower mixing enthalpy of Ni-Al leads to the segregation of Al element at the inter-dendritic region, which promotes the formation of BCC and FCC lamellar structure in hypoeutectic Al2Co4Cr1.5Fe1.5Ni5 alloy. The ultimate tensile strength of Al2Co4Cr1.5Fe1.5Ni5 alloy is 835 MPa, meanwhile the fracture strain is 31.8 %. The tensile strength of Al2Co4Cr1.5Fe1.5Ni5 alloy is attributed to the interface strengthening and the solid solution strengthening. The massive cross slip of dislocations in primary FCC phases and the dense dislocations blocked by the FCC-BCC interface increase the tensile strength. The interface barrier strength of the BCC-FCC interface in Al2Co4Cr1.5Fe1.5Ni5 alloy was estimated to be 3.9 GPa, which shows the higher barrier strength than conventional BCC-FCC interfaces. Coupled effects of the primary FCC and the lamellar structure of FCC and BCC phases will maintain good mechanical properties.

Thermodynamic analysis of polymeric membrane formation by non-solvent induced phase separation in the presence of different nanoparticles

Thermodynamic phase diagrams are powerful tools for predicting the thermodynamic behavior and finally, the morphology of phase inversion membranes. Addition of nanoparticles into a polymeric membrane forming system significantly affects the system phase diagram. Using a lattice-based thermodynamic model, we study the phase diagram of polymeric membrane formation by non-solvent induced phase separation (NIPS) in the presence of three types of nanoparticles (spherical, rod-like or sheet-like). The concept of “nanoparticle-out effect” is introduced to justify the influence of nanoparticles on the binodal curves of the systems. Due to this effect, nanoparticles attract the solvent molecules and reduce the polymer solubility, thereby increasing the thermodynamic instability of the system and moving the binodal curves toward the polymer–solvent axis. This effect is found to be more pronounced for nanorods and nanosheets than for nanospheres. The effect is intensified with increasing the nanoparticles size faster for anisotropic nanosheet and nanorod than for isotropic nanospheres, which results from their different surface fraction values. The system thermodynamic instability gradually rises with decreasing the binary interaction parameters between nanorods or nanosheets and other components while it is nearly unchanged by varying the interaction parameters for nanospheres, which is consistent with their smaller surface fraction value. The accuracy of the phase diagram predictions is demonstrated by comparison with published experimental data on related systems. This thermodynamic description along with the governing kinetic features of membrane forming systems containing nanoparticles could be applied for fabricating polymeric membranes with the desired morphology and function.

Prediction of Phase Diagrams and Associated Phase Structural Properties

The knowledge of phase diagrams is crucial to understand materials and to design new ones with better properties. However, elucidating phase diagrams is a difficult task, both experimentally and theoretically. In this work, we address the problem of predicting phase diagrams and crystal structures using a data-driven approach. We used machine learning methods to predict the stable phases using composition, temperature, and pressure extracted from a set of diagrams contained in the NIST database. We used the extracted data to train machine learning algorithms to predict the stable phases and the chemical formula of the stable compounds, including structural features such as Bravais lattices, crystal types, and the local atomic environments of the inorganic compounds contained in the ICSD database. The computationally efficient data-driven methods presented in this paper will aid material scientists in estimating the structure of virtually any mixture of elements in any proportion over a wide temperature range.

A machine learning–based classification approach for phase diagram prediction

Knowledge of phase diagrams is essential for material design as it helps in understanding microstructure evolution during processing. The determination of phase diagrams is thus one of the central tasks in materials science. When exploring new materials for which the phase diagram is unknown, experimentalists often try to determine the key experiments that should be performed by referencing known phase diagrams of similar systems. To enhance this practical strategy, we attempted to estimate unknown phase diagrams based on known phase diagrams using a machine learning–based classification approach. As a proof of concept, we focused on predicting the number of coexisting phases across the 800 K isothermal section of each of the 10 ternaries of the Al-Cu-Mg-Si-Zn system from the other 9 sections. To increase the prediction accuracy, we introduced new descriptors generated from the thermodynamic properties of the elements and CALPHAD extrapolations from lower-order systems. Using the random forest method, the presence of single-, two-, and three-phase domains was predicted with an average accuracy of 84% across all 10 considered sections with a standard deviation of 11%. The proposed approach represents a promising tool for assisting the investigator in developing new materials and determining phase equilibria efficiently.

Block copolymer self-assembly: Melt and solution by molecular density functional theory.

The self-assembly of block copolymer melts and solutions with two-dimensional density inhomogeneity is studied using modified inhomogeneous statistical associating fluid theory (iSAFT). A real-space combinatorial screening method under density functional theory formalism is proposed and used to map out the phase diagram of block copolymer melts including order-disorder transitions and order-order transitions. The predicted phase diagram agrees well with molecular dynamics simulation and self-consistent field theory. The compressibility effect on order-disorder transition temperature for block copolymer melts is modeled using iSAFT. The pressure induced temperature change by theory has a similar trend to experimental studies. Then, the lyotropic and thermotropic self-assembly phase behavior of block copolymer solutions is investigated. Detailed density distributions by iSAFT provide insight into the lyotropic properties of the block copolymer solutions at the molecular level. The effect of the block copolymer molecular architecture is studied by comparing block copolymers with different molecular packing parameters. Block copolymer solutions in the inverted hexagonal phase are predicted by theory for the block copolymer having a large molecular packing parameter. Finally, solvent selectivity is studied by modeling the block copolymers in a neutral good solvent. The enhanced local solvent concentration predicted by theory explains the reason for fewer ordered phases found in experiments.

Mean activity coefficients of KCl in the KCl + SrCl2 + H2O solutions at 278.15 K determined by cell potential method and their application to the prediction of solid-liquid equilibria of the KCl + SrCl2 + H2O system

The cell potentials were determined by the cell without liquid junction K-ISE |KCl (m0) |Cl-ISE firstly. Using Nernst equation and the measured cell potentials, the response slope κ of the single-salt electrode and the standard cell potential E0 were fitted well. The total ionic strengths range from 0.0100 to 1.0000 mol·kg−1, the cell without liquid junction K-ISE |KCl (m1), SrCl2 (m2) |Cl-ISE is used to determine the mean activity coefficients of KCl in the KCl + SrCl2 + H2O solutions, the ionic strength fractions yb of SrCl2 are 0.8, 0.6, 0.4, 0.2 and 0. According to the measured cell potentials, the mean activity coefficients of KCl in the KCl + SrCl2 + H2O solutions were calculated by Nernst equation, and the relationship diagrams between the mean activity coefficients and total ionic strengths of the mixed solutions are drawn at 278.15 K. The mixed interaction parameters θK,Sr, and ψK,Sr,Cl in the Pitzer model were also obtained by regression of the mean activity coefficients of KCl in the mixed solutions. The mean activity coefficients of SrCl2, the osmotic coefficients, the water activities, and the excess Gibbs free energies of the mixed solutions were also calculated by Pitzer equations. Additionally, in order to verify the mixed ion parameters of Pitzer model fitted in this work, the isothermal dissolution equilibrium method is used to measure experimentally the phase equilibria of the mixed solutions at 278.15 K, and then the Pitzer equations and the mixed ion parameters are used to predict the solubilities of the salts in the mixed solutions at 278.15 K. The experimental and predicted phase diagrams are good agreement.

Ab initio free energies of liquid metal alloys: Application to the phase diagrams of Li-Na and K-Na

Comparison of free energies between different phases and different compositions underlies the prediction of alloy phase diagrams. To allow direct comparison, consistent reference points for the energies or enthalpies are required, and the entropy must be placed on an absolute scale, yielding absolute free energies. Here we derive absolute free energies of liquids from ab initio molecular dynamics by combining the directly simulated enthalpies with an entropy derived from simulated densities and pair correlation functions. As an example of the power of this method we calculate the phase diagrams of two binary alkali metal alloys, Li-Na and K-Na, revealing a critical point and liquid-liquid phase separation in the former case, and a deep eutectic in the latter. Good agreement with experimental data demonstrates the power of this simple method.

Phase diagram prediction and high pressure melting characteristics of GaN

The III-V compound semiconductor, GaN, has become an excellent semiconductor material for developing the high-frequency and high-power electronic devices because of its excellent characteristics, including large band width, high thermal conductivity and fast electron saturation rate, and has received extensive attention in recent years. However, the decomposition temperature of GaN is lower than the melting temperature, some of its fundamental properties, such as melting temperature and high temperature phase transition pressure, are still unclear, and so, now the investigation of fundamental properties dominates the whole process of this material from development to mature applications. In the present work, the classical molecular dynamics simulations combined with the first-principles calculations and lattice dynamics methods are adopted to predict the phase diagrams of GaN with wurtzite and rocksalt structures in a pressure range of 0–80 GPa. The phase transition pressures, 44.3 GPa and 45.9 GPa, obtained from the first-principles calculations and molecular dynamics simulations from wurtzite to rocksalt structure in GaN at zero temperature, are in agreement with the available experimental results (Sadovyi B, et al. <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="http://doi.org/10.1103/PhysRevB.102.235109">2020 <i>Phys. Rev. B</i> <b>102</b> 235109</ext-link>). The melting temperature at 0 GPa is 2295 K obtained by extrapolating the GaN melting curve of the wurtzite structure. With the pressure increasing to 33.3 GPa, the melting curve of wurtzite structure in GaN intersects with the melting curve of rocksalt structure, and the melting temperatures of both structures increase with pressure increasing. It is found that GaN may have a superionic phase and the superionic phase transition occurs in the wurtzite structure at pressures greater than 2.0 GPa and temperatures above 2550 K, whereas the rocksalt structure undergoes a superionic phase transition at pressures and temperatures higher than 33.1 GPa and 4182 K, respectively, and both of the phase transition temperatures increase with pressure increasing. The slope of the phase boundary line of GaN is positive at high temperatures and gradually changes into a curve with a negative slope as the temperature decreases.

Machine Learning Assisted Predictions of Multi-Component Phase Diagrams and Fine Boundary Information

Machine Learning Assisted Predictions of Multi-Component Phase Diagrams and Fine Boundary Information

Ordered Oxygen Vacancies in the Lithium-Rich Oxide Li4CuSbO5.5, a Triclinic Structure Type Derived from the Cubic Rocksalt Structure.

Li-rich rocksalt oxides are promising candidates as high-energy density cathode materials for next-generation Li-ion batteries because they present extremely diverse structures and compositions. Most reported materials in this family contain as many cations as anions, a characteristic of the ideal cubic closed-packed rocksalt composition. In this work, a new rocksalt-derived structure type is stabilized by selecting divalent Cu and pentavalent Sb cations to favor the formation of oxygen vacancies during synthesis. The structure and composition of the oxygen-deficient Li4CuSbO5.5□0.5 phase is characterized by combining X-ray and neutron diffraction, ICP-OES, XAS, and magnetometry measurements. The ordering of cations and oxygen vacancies is discussed in comparison with the related Li2CuO2□1 and Li5SbO5□1 phases. The electrochemical properties of this material are presented, with only 0.55 Li+ extracted upon oxidation, corresponding to a limited utilization of cationic and/or anionic redox, whereas more than 2 Li+ ions can be reversibly inserted upon reduction to 1 V vs Li+/Li, a large capacity attributed to a conversion reaction and the reduction of Cu2+ to Cu0. Control of the formation of oxygen vacancies in Li-rich rocksalt oxides by selecting appropriate cations and synthesis conditions affords a new route for tuning the electrochemical properties of cathode materials for Li-ion batteries. Furthermore, the development of material models of the required level of detail to predict phase diagrams and electrochemical properties, including oxygen release in Li-rich rocksalt oxides, still relies on the accurate prediction of crystal structures. Experimental identification of new accessible structure types stabilized by oxygen vacancies represents a valuable step forward in the development of predictive models.

The phase diagram prediction and experimental study of ternary same cation systems

The phase diagram prediction and experimental study of ternary same cation systems

Phase diagrams for the ternary system (NH4NO3 + CsNO3 + H2O) at 298.15 and 348.15 K and its application to cesium nitrate recovery from the eluent aqueous solution of ammonium nitrate

A novel green process for CsNO3 separation from the eluent solution of NH4NO3 was developed based on the predictive phase diagrams of (NH4NO3 + CsNO3 + H2O) at 298.15 and 348.15 K, which were drawn using the Pitzer and its extended HW model. These single-salt parameters and the mixing ion parameters obtained either from the literature or fitted with the relevant experimental data in the literature were used to calculate the solubilities of the ternary system (NH4NO3 + CsNO3 + H2O) at two temperatures successfully. Based on phase diagrams at 298.15 and 348.15 K, a comparison of the ternary system diagrams shows that area of CsNO3 crystallized region is decreased obviously with the increasing temperature, which accounts for separating cesium nitrate from eluent by raising the temperature. Under the guidance of the predictive phase diagram at 298.15 and 348.15 K, the separating process of cesium nitrate from the eluent solution of ammonium nitrate by three fractional crystallization operations was established for the first time, and the material balance of the cyclic process is presented.

Rapid screening of high-throughput ground state predictions

High-throughput computational thermodynamic approaches are becoming an increasingly popular tool to uncover novel compounds. However, traditional methods tend to be limited to stability predictions of stoichiometric phases at absolute zero. Such methods thus carry the risk of identifying an excess of possible phases that do not survive to temperatures of practical relevance. We demonstrate how the Calphad formalism, informed by simple first-principles input can be simply used to overcome this problem at a low computational cost and deliver quantitatively useful phase diagram predictions at all temperatures. We illustrate the method by re-assessing prior compound formation predictions and reconcile these findings with long-standing experimental evidence to the contrary.

Generic energy formalism for reciprocal quadruplets within the two-sublattice quasichemical model

Ever-increasing interests for more accurate thermodynamic predictions of phase diagrams motivate the development of more reliable thermodynamic models. The Modified Quasichemical Model within the two-sublattice Quadruplet Approximation (MQMQA) was thus established in well response to these interests and motivations. However, the model still needs to be further improved in order to have better thermodynamic predictions of general reciprocal solutions. The present paper proposes a new and generic formalism to characterize the Gibbs energy of the ternary reciprocal quadruplet within the framework of the MQMQA. The new formalism is developed by circumventing the problem spawned from solving the singular matrix of mass equations. As a result, energy landscapes of reciprocal solutions can be better defined everywhere in reciprocal composition spaces. With the current improvement, the MQMQA is believed to be one of the most reliable thermodynamic models for various types of solutions with or without short-range ordering.

Dynamic contact line lithography: Template-less complex Meso-patterning with polystyrene and poly(methyl methacrylate)

HypothesisMicro/nanopatterning on a 2D surface is apt for cutting-edge miniaturization technology, which directly or indirectly requires high-end expensive lithographic tools. The evaporative deposition at the receding contact-line of a polymer solution, termed as Dynamic Contact Line Lithography (DCLL), can be a potential inexpensive technique for template-less meso-patterning if the deposition patterns from DCLL can be predicted a priori. ExperimentsA deposition map (morphological phase diagram) from the myriads of patterns is constructed in terms of contact-line velocity and the polymer concentration. Specifically, two combinations: polystyrene (PS)/cyclohexane and poly (methyl methacrylate) (PMMA)/toluene are used to show the generic nature of the phase diagrams. The surface wettability of Si (water contact angle, CA ~15°) is tuned from CA ~35° to ~98° by patterning with DCLL. FindingsDirected by the phase diagrams, fabrication of a complex rectangular cross-pattern of PS and PMMA micro-threads with a periodicity of ~65 μm and ~50 μm respectively on a Si surface is demonstrated to establish the robustness and potential of the DCLL and predictive phase diagram.

Stability of Pharmaceutical Co-Crystals at Humid Conditions Can Be Predicted.

Knowledge of the stability of pharmaceutical formulations against relative humidity (RH) is essential if they are to become pharmaceutical products. The increasing interest in formulating active pharmaceutical ingredients as stable co-crystals (CCs) triggers the need for fast and reliable in-silico predictions of CC stability as a function of RH. CC storage at elevated RH can lead to deliquescence, which leads to CC dissolution and possible transformation to less soluble solid-state forms. In this work, the deliquescence RHs of the CCs succinic acid/nicotinamide, carbamazepine/nicotinamide, theophylline/citric acid, and urea/glutaric acid were predicted using the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT). These deliquescence RH values together with predicted phase diagrams of CCs in water were used to determine critical storage conditions, that could lead to CC instability, that is, CC dissolution and precipitation of its components. The importance of CC phase purity on RH conditions for CC stability is demonstrated, where trace levels of a separate phase of active pharmaceutical ingredient or of coformer can significantly decrease the deliquescence RH. The use of additional excipients such as fructose or xylitol was predicted to decrease the deliquescence RH even further. All predictions were successfully validated by stability measurements at 58%, 76%, 86%, 93%, and 98% RH and 25 °C.