Model Alloy System Research Articles

A secondary high-temperature precursor of the θ′-phase in Al-Cu-(Sc) alloys

The Al-Cu alloy is a historical model alloy system in the physical metallurgy of engineering aluminum alloys. Nevertheless, a few fundamental phenomena of phase transformation occurring in this simple alloy are still not adequately understood. Among all, for instance, the formation mechanisms of its key hardening θ′-phase remain mysterious. There is strong evidence that θ′-precipitates can form from a different high-temperature precipitation pathway, while their formation mechanism via the conventional pathway well-known since 1938 remains to be clarified. Using state-of-the-art electron microscopy, here we report a secondary high-temperature precipitation pathway of θ′-precipitates. It is demonstrated that led by a secondary high-temperature precursor, named θ′S-HTP, very fine θ′-precipitates can form in the undeformed bulk Al-Cu alloys at elevated temperatures (≥ 250 °C). Interestingly is that with Sc-microalloying the surviving rate of meta-stable θ′S-HTP precipitates increases drastically and the formed θ′-precipitates become much finer, significantly enhancing the alloys’ strength and thermal stability. It is also revealed that a θ′S-HTP precipitate can genetically evolve into a θ′-precipitate without having to change its morphology and orientation. Our study provides new insights into understanding the industry bulk alloys’ microstructures and properties.

Effect of structural disorder on the oxidation of Zr-based amorphous alloys: A focused review

Structural disordering leads to outstanding mechanical properties of amorphous alloys. Many properties are strongly related to formation of surface oxide layers. An in-depth understanding of effect of structural disordering of amorphous alloys on oxide evolution is essential for applications. This paper presents a review of recent comparative oxidation studies of Zr-based amorphous and single-phase crystalline counterpart alloys. Three representative model alloy systems are selected: Zr–Cu and Zr–Al representing alloys with components of different and similar oxygen affinities, respectively, and Zr–Cu–Al representing multi-component alloys. In combination with molecular dynamic simulations, the fundamental role of the structural disordering of parent alloys in the oxidation processes is revealed. The oxidation of Zr–Cu–Al–Ni amorphous alloys at the supercooled liquid temperature region is further reviewed to clarify the relationship between oxidation and substrate crystallization.

Casting microstructure and phase-specific deformation behavior of Ti–20Ni alloy containing Ti2Ni phase

Understanding the microstructural formation mechanisms and phase-specific deformation behaviors is essential for optimizing the mechanical properties of Ti alloys containing intermetallic phases. Thus, the present study investigated Ti-20 wt% Ni as a model alloy system and elucidated the formation of casting microstructure and the phase-specific deformation behavior. The as-cast microstructure reveals a dendritic region consisting of a mixture of lamellar α-Ti and Ti2Ni and an interdendritic region consisting of Ti2Ni, TiC, and a mixture of α-Ti phase and a small amount of Ti2Ni. The dendritic region displayed lower and relatively more uniform hardness than that of the interdendritic region. The phase-specific hardness decreased in the following order: dendritic region < dendritic region/Ti2Ni interface < Ti2Ni < TiC. After 6% cold-rolling, the fractured sample showed that the density of cracks in the interior of Ti2Ni and TiC was much higher than that at the α-Ti/Ti2Ni interfaces. Thus, the dispersion of the Ti2Ni and TiC phases inside the α-Ti phase is essential for achieving high-strength and high-formability Ti–Ni alloys.

Heterogeneous phase transformation pathways in additively manufactured Al-Ce-Mn alloys

Heat treatment of additively manufactured Al-Ce based multicomponent alloys leads to complex microstructure evolution. In this research, the ability to extend the phase transformation theories involving nucleation of a product phase from a heterogeneous multi-phase microstructure typical to that of additively manufactured samples is explored. The Al-10Ce-8Mn (wt%) was used as a model alloy system. Under additive manufacturing conditions different solidification microstructures were obtained due to spatial and temporal variations of thermal gradients (G) and liquid-solid interface velocities (R) within a given melt pool. Near the melt pool boundary (high G and low R, referred as MPB region), initially, Al20Mn2Ce forms from the liquid followed by a eutectic of FCC Al and Al11Ce3. In the melt pool interiors (low G and high R referred as ES region) a eutectic structure between FCC Al and Al20Mn2Ce is observed. During subsequent heat treatments, the MPB and ES regions transform into different sets of microstructures. In the MPB region, a fine globular microstructure containing FCC Al, Al11Ce3, Al6Mn, and Al12Mn results from the decomposition of Al20Mn2Ce. In the ES region a faceted Al51Mn7Ce4 plate phase results from the decomposition of Al20Mn2Ce. The formation of the Al51Mn7Ce4 phase within the eutectic microstructure at the boundaries of FCC Al and Al20Mn2Ce has not been reported in the literature. These two distinct phase transformation pathways are rationalized based on the role of driving force on the nucleation of (Al6Mn) and/or metastable intermetallic (Al51Mn7Ce4) phases at the interface of aluminum (FCC) and the non-equilibrium intermetallic (Al20Mn2Ce) phases.

On the energetics of the cubic‐to‐hexagonal transformations in TiAl+Mo alloys

Diffusionless transformations allow access to metastable phases and enrich the materials design portfolio. They are well suited for atomistic modeling; nonetheless, they are challenging when involving disordered systems or alloys with complex compositions. This work presents a comprehensive study of transformation energetics between bcc and hcp ordered and disordered phases in the TiAl+Mo model alloy system. By employing two complementary techniques I. VASP-SQS, and II. EMTO-CPA, we can show that chemical disorder flattens the energy landscape but may introduce a small barrier. Unlike that, the energetics of ordered phases are barrier-less and hence would suggest a spontaneous transformation. Finally, we show that Mo stabilizes the bcc phases, leading to a barrier-less transformation hcp→bcc for both ordered and disordered states when Mo content exceeds ≈12 at.%.

Atomistic study on simultaneous achievement of partial crystallization and rejuvenated glassy structure in thermal process of metallic glasses

ABSTRACT The relaxation state and partial crystallization are crucial factors that affect the material properties of metallic glasses. Rejuvenation induces a less relaxed glass state and hence facilitates the control of the relaxation state. The rejuvenation and crystallization during thermal processing are associated closely with the phase changes of metallic glasses upon heating. Most nanocrystalline metallic glasses formed via conventional thermal annealing have a relaxed glassy matrix. In this molecular dynamics study, we investigate the feasibility of thermal processing to simultaneously realise both partial crystallization and rejuvenation using model alloy system. Dynamic mechanical analyses reveal relaxation behaviours and local deformation features of metallic glasses composed of a crystalline phase and a rejuvenated glass matrix. The crystalline phase increases the macroscopic shear stiffness of the composite model over a wide temperature range, whereas it does not significantly affect the internal friction of the rejuvenated glass matrix. In addition, dispersed nanocrystals suppress the development of sharp and concentrated shear localisation in the rejuvenated glass matrix. The simultaneous adjustment of the relaxation state and crystalline phase in the glass matrix is discussed from a viewpoint of the microstructure design of metallic glasses.

Inverse analysis of anisotropy of solid-liquid interfacial free energy based on machine learning

A machine leaning-based approach is proposed for the inverse analysis of the anisotropy parameters of solid–liquid interfacial free energy. The interface shape distribution (ISD) map, which characterizes the details of the dendrite morphology, was selected as the input of a convolutional neural network (CNN). The ISD maps for a free-growing dendrite during the isothermal solidification of a model alloy system were obtained by quantitative phase-field simulations and used as the training and test data for the CNN. Two anisotropy parameters were estimated with errors of less than 5%, which can be further improved by increasing the size of the training dataset.

Influence of the Co/Ni Ratio and Dendritic Segregations on the High-Temperature Oxidation Resistance of Multinary Co-Rich Superalloys at 850\xa0\xb0C and 1050\xa0\xb0C

Excellent inherent oxidation resistance is a prerequisite for the use of superalloys in many high-temperature applications. To achieve this goal, typically continuous alumina and chromia scale growths are assured through sufficient Cr and Al additions. Since the intended γ/γ′-microstructure of superalloys is only stable within a certain compositional window, the maximum concentrations of these protective scale forming elements are, however, dependent on the overall alloy composition. The latter is a severe drawback, especially for Co-rich superalloys, as for these the maximum content often is insufficient for reaching the desired continuous scale growth. In recent years, the addition of significant Ni levels was identified to improve the high-temperature oxidation properties in the case of simple model alloy systems. In this study, we compare the high-temperature oxidation behavior of two complex Co-rich multinary single-crystalline γ/γ′-strengthened superalloys that only differ regarding their Co/Ni ratios to the commercial Ni-base superalloy CMSX-4. Therefore, time-resolved isothermal gravimetric analysis (TGA) in synthetic air at 850 °C and 1050 °C for 100 hours, scanning electron microscopy analysis (SEM), and electron probe microanalysis (EPMA) were conducted. The results point out that a high Co-content beneficially affects the oxidation resistance at 850 °C, meaning that the Ni-base CMSX-4 is slightly outmatched by the Co-rich competitors. In contrast, at 1050 °C, the commercial (most Ni-rich) alloy performed best and, clearly, an increasing Co-content was identified to deteriorate the oxidation resistance. This temperature-dependent influence of the nominal Co/Ni ratio on oxidation resistance is shown to be especially pronounced for dendritic regions. Consequently, the latter could be identified to especially determine the overall oxidation kinetics.

Radiation-resistant binary solid solutions via vacancy trapping on solute clusters

Additions of solute that trap vacancies slow down vacancy diffusion and promote point-defect recombination in alloys subjected to irradiation. Such selective alloying can thus help to minimize the detrimental consequences resulting from point defect fluxes. The current work investigates the effect of solute additions on the recombination rate using kinetic Monte Carlo simulations for a model alloy system, which was parametrized to Cu-Ag in the dilute limit, but with an increased solubility limit, ≈ 0.86 at.% at 300 K. As the solute concentration was increased above 0.1 at.%, solute clustering was observed and led to a strong increase in recombination rate. The beneficial effects of solute clustering on reducing vacancy mobility, and reducing solute drag, were analyzed by calculating relevant transport coefficients using the KineCluE code (Schuler et al., Computational Materials Science (2020) 172,109,191). Moreover, it was observed in the KMC simulations that large recombination rates resulted in a shift of steady-state distributions of solute cluster sizes to smaller clusters compared to equilibrium distributions in the solid solution. This shift is rationalized as resulting from the irreversible character of the interstitial-vacancy recombination reaction. These results suggest a novel irradiation effect on phase stability where a high recombination rate increases the solubility limit of a solute at steady state over its equilibrium value.

Traceable quantitative analysis of Ag x Cu1−x alloy films by ID ICP-MS, RBS and MEIS

The measurement traceability of Rutherford backscattering spectroscopy (RBS), medium energy ion scattering spectroscopy (MEIS) and isotope dilution inductively coupled plasma mass spectrometry (ID ICP-MS) was compared for the quantitative analysis of alloy thin films. A set of thin Ag x Cu1−x alloy films were selected as a model alloy system for the quantitative analysis of MEIS and ID ICP-MS. Two sets of five Ag x Cu1−x alloy films with different mole fractions were grown on Si (100) wafers by ion beam sputter deposition. The mole fractions of thick Ag x Cu1−x alloy films (100 nm) measured by RBS and ID ICP-MS showed a great agreement within 0.4% difference. The mole fractions of thin Ag x Cu1−x alloy films (10 nm) measured with MEIS and ID ICP-MS also showed a small difference of about 1.0%. As a result, ID ICP-MS, RBS and MEIS can be used to certify the mole fractions of thin alloy reference films. ID ICP-MS is an absolute method for the mole fraction analysis of thin Ag x Cu1−x alloy films. Although the contribution of sample homogeneity was included, the uncertainties of ID ICP-MS results were much smaller than those of RBS and MEIS.

Experimental and modelling assessment of ductility in a precipitation hardening AlMgScZr alloy

Precipitation hardening is the most effective strategy to enhance the mechanical properties of metals. Dislocation mechanisms to control strengthening during precipitation have been demonstrated extensively. However, owing to the complexity of different precipitates in alloys, variations in ductility caused by precipitation are complex and have not been clarified so far. In this study, the effects of precipitation on ductility in precipitation hardening aluminium alloys are investigated based on a modified dislocation-based approach and experimental characterisation. The AlMgScZr alloy with spherical Al3(Sc, Zr) precipitates is used as a model alloy system to understand the effects of precipitation on ductility. Via heat treatment, shearable and nonshearable Al3(Sc, Zr) precipitates are introduced in the AlMg matrix. The results show that the ductility of AlMgScZr alloy decreases when shearable precipitates occur, while it increases with shearable precipitates being replaced by nonshearable precipitates. The variation in ductility of AlMgScZr alloy is mainly controlled by the dynamic recovery rate of the dislocations. Finally, by analysing the different precipitate–dislocation interactions and evaluating the dislocation density evolution during deformation, the dislocation mechanisms of ductility during precipitation for AlMgScZr alloy are demonstrated. This study reveals the dislocation mechanism for controlling ductility during precipitation for AlMgScZr alloy which can provide a theoretical foundation for the design of high-performance structural materials.

Diffusional-displacive transformation mechanism for the β1 precipitate in a model Mg-rare-earth alloy

The β1 precipitate is a key strengthening-phase in Mg-rare-earth alloys, however, the formation mechanism concerning it has not yet been addressed. Herein, we have uncovered a diffusional-displacive dominated formation mechanism for the β1 phase, using aberration-corrected scanning transmission electron microscopy observation combined with first-principles calculations, in an aged MgSm model alloy system. Shear of the nucleated {101¯0}hcp zig-zag monolayers along a direction parallel to <001>fcc with a shear angle of ~5.26°, followed by atoms shuffling on the non-close-packed {101¯0}hcp planes, can transform the hexagonal close-packed Mg3Sm structure (β” or βH’ intermediate phase) to the face-centered-cubic structure Mg3Sm (β1 phase). Besides, the formation of the β1 phase can also be realized from the other βS’ or βL’ intermediate phase (c-bco, Mg7Sm) via solute diffusion coupled with shuffle transformation manner. A new habit plane of {101¯0}hcp // {11¯0}fcc and [0001]hcp // [110]fcc on the non-closed packed plane has been identified, which is completely different from the traditional displacive transformation mechanism usually happened on the closed-packed plane. This finding enriches the diffusional-displacive transformations.

On the High-Temperature Oxidation Behavior of a Ta-Containing Quaternary Co-Base Model Alloy System with \u03b3/\u03b3\u2032-Microstructure - Influence of \u03b3\u2032-Volume Fraction, Surface State, and Heating Condition on Alumina Growth

The improvement of the high-temperature oxidation resistance remains an ambitious goal for the design of new γ/γ′-strengthened Co-base superalloys, since their oxidation resistance beyond 800 °C still ranks behind their Ni-base counterparts. To better understand the origin of the poor oxidation resistance at higher temperatures, this study focuses on early stages of oxidation of four quaternary (Co-Al-W-Ta system) Co-base model alloys with a two-phase γ/γ′-microstructure and varying γ′-volume fraction at 800 °C, 850 °C and 900 °C. Based on time-resolved isothermal gravimetric analysis (TGA) in synthetic air and detailed electron microscopic analysis, the role of the γ-channel width (or γ′-volume fraction), the surface preparation prior to exposure (polishing versus shot-peening), and the heating conditions (synthetic air versus argon) on protective alumina growth is elucidated. Firstly, for alloys of increased γ′-volume fractions slower oxidation kinetics prevailed. Secondly, the two-phase microstructure was found to decisively affect the propagation of the internal oxidation front at the early stages of oxidation. Thirdly, shot-peening prior to exposure together with a lack of oxygen availability during heating was identified to foster protective alumina growth, accompanied by TCP-phase formation in the substrate. The critical role of a high Al availability in the alloy for a rapid growth of protective alumina and the relating challenges in alloy development regarding, for example, phase stability in this relatively novel Co-base alloy class are discussed in detail.

Mechanistic Origin of Ductility in Precipitation Hardening AlMgScZr Alloys

Precipitation hardening is the most effective strategy to enhance the mechanical properties of metals. Dislocation mechanisms to control strengthening during precipitation have been demonstrated extensively. However, owing to the complexity of different precipitates in alloys, variations in ductility caused by precipitation are very complex and have not been clarified so far. In this study, the effects of precipitation on ductility in precipitation hardening aluminium alloys are investigated based on a modified dislocation-based approach and experimental characterisation. The AlMgScZr alloy with spherical Al3(Sc, Zr) precipitates is used as a model alloy system to understand the effects of precipitation on ductility. Via heat treatment, shearable and non-shearable Al3(Sc, Zr) precipitates are introduced in the AlMg matrix. The results show that the ductility of AlMgScZr alloy decreases when shearable precipitates occur, while it increases during the shearable–non-shearable transition. The variation in ductility is mainly controlled by the dynamic recovery rate of the dislocations. This dislocation mechanism is supported by analysing the different precipitation–dislocation interactions and evaluating the dislocation density evolution during deformation. This study reveals the dislocation mechanism for controlling ductility during precipitation, which can provide a theoretical foundation for the design of high-performance structural materials.

Precipitation-site competition in duplex stainless steels: Cu clusters vs spinodal decomposition interfaces as nucleation sites during thermal aging

Competing microstructural evolution mechanisms can exist simultaneously when duplex stainless steels are operating for several decades in a high temperature service environment. Such competition between different microstructural evolution pathways can be difficult to ascertain using simple model alloy systems necessitating detailed microstructural analysis of phase transformation mechanisms in complex alloys. Thus, duplex stainless steels with complex but well understood chemistries were used to investigate the relative importance of different heterogeneous nucleation sites – specifically, spinodal decomposition and Cu clustering – on Ni-Si-Mn precipitation during thermal aging. Precipitation of Ni-Si-Mn particles in ferrite-bearing steels during thermal aging and irradiation can greatly change mechanical properties. Using duplex stainless steels with custom-modified compositions along with advanced microstructural characterization and first-passage kinetic Monte Carlo simulations, it is revealed that while the interface between Cr and Fe formed during spinodal decomposition can be a pathway for solute diffusion, it is not a preferred site for Ni-Si-Mn precipitation. Instead, the presence of a higher concentration of Cu leads to the formation of small Cu-rich clusters with high energy interfaces that act as nucleation sites for Ni-Si-Mn particles. These results will inform predictive models for the use of precipitation-hardened alloys for extended operation at high temperatures.

A simulation study on the orientational phase transformation behavior of Au-Pt alloy for different concentration of Pt

In this study, the AuxPt100-x (x = 90, 50, 10) model alloy system was modelled molecular dynamic (MD) simulation for different atomic concentration percentage of platinum (Pt). The potential energy function was used the Embedded Atom Method (EAM). The bond-type index method of Honeycutt–Andersen (HA) and cluster-type index methods (CTIM-1 and CTIM-2) was used to detect the crystal/amorphous-type polyhedrons. The phase transformation behavior of the model alloy system was examined by using local order symmetry based on bond orientational parameter. In addition, the structural development of system at a defined temperature was investigated by radial distribution function (RDF). The melting point of system was obtained by potential energy function and HA method during the heating. In this process, the α′, the α″ and the α′+ α″ phase regions for Au-Pt system was determined by bond orientational order parameter. The modelling results were compared with experimental results and the results demonstrate that the simulation calculations are in reasonable agreement with the experimental data.

The effect of through thickness texture variation on the anisotropic mechanical response of an extruded Al-Mn-Fe-Si alloy

There is currently a significant scientific and industrial interest in developing material models for the simulation of plastic deformation of aluminum extrusions relevant to their forming and their response during in service events such as vehicle crash. The objective of this work is to evaluate the effect of through thickness crystallographic texture gradients on material mechanical behaviour. This has been studied using a combination of experiments (i.e. pilot scale extrusions and stress-strain curves with the R-value to characterize plastic anisotropy for different loading directions) and the visco-plastic self-consistent (VPSC) polycrystal plasticity simulations on a model alloy system. Two limiting conditions were examined, i.e. unrecrystallized and fully recrystallized conditions. The results of electron backscatter diffraction (EBSD) characterization show that there is a significant through thickness variation in texture for both cases. However, the implications of the texture gradient on the macroscopic plastic response were relatively minor for the unrecrystallized case but quite significant for the recrystallized case. This was manifested as a strong difference in the contraction of the surface layer compared to the centre of the extrudate, particularly in the case of tests at 45° and 90° to the extrusion direction. This was rationalized in terms of the differences in texture between the surface and the centre using VPSC simulations. Finally, it was proposed that this effect will be explored in future work as it may have important implications on the surface stress state which could affect damage initiation, growth and coalescence, particularly in bending situations.

The Enhancement of Hydrogen Oxidation Activity and the Optimization of Alloy Composition in PdRu Nanoparticle Catalysts

Fuel cells are believed as promising power sources with many advantages including their high efficiency and environment-friendliness. Proton exchange membrane fuel cells (PEMFCs), of which usage can be expected as power sources as automobiles and so on, have yet several problems to resolve for the commercialization. Among them, the high price due to the scarcity of Pt, which is used as anode and cathode catalysts, is one of the most serious issues. Pd is a natural choice to replace Pt because the hydrogen oxidation reaction (HOR) activity of Pd is the next to that of Pt, and Pd is at least fifty times more abundant on earth than Pt. Pd is a more attractive substitute for Pt because of its higher intrinsic CO tolerance than Pt, especially as HOR catalysts for PEMFC where the tolerance of CO, a major impurity of hydrogen fuel, is crucial. Although Pd has comparable HOR activity to Pt, the exclusive use of Pd as anode catalysts of PEMFC has not been satisfactory for the replacement of Pt. We confirmed in our previous report (K. Kwon et al., Catal Today, 232 (2014) 175) that the insufficient HOR activity of Pd could be supplemented by coupling with other elements or compounds such as Ru and tungsten oxide. To investigate the effect of alloying with Ru thoroughly, the calculation of hydrogen binding energy was performed on the basis of spin polarized density functional theory. Pure Pd(001) and Ru(001), Pd monolayer on Ru, and Pd bilayer on Ru are considered as model systems in the calculation. Strain and ligand effects are only applicable to bimetallic models (Pd monolayer on Ru and Pd bilayer on Ru). The negative sign of strain and ligand effects stands for a decrease in binding energy for PdRu alloy. Meanwhile, instead of making an effort to turn the model alloy systems into nanoparticles of Pd mono/bilayer on Ru, which would not be realistic in a few nm dimension, the actual confirmation of HOR enhancement at the level of half cell and PEMFC single cell was obtained by fabricating homogeneous PdRu alloy nanoparticles on carbon support. PdRu nanoparticles of different Pd:Ru atomic ratios of 1:0, 9:1, 1:9, and 0:1 were characterized with TEM and XRD, and compared with a commercial state-of-the-art Pt-based anode catalyst (PtRu1.5/C) in electrochemical experiments. The PdRu9 catalyst shows the highest HOR activity among the PdRu samples, which is comparable to the PtRu catalyst, even though the respective Pd and Ru have lower activity than PtRu. The highest HOR activity of the Ru-richest PdRu nanoparticles could be in line with the highest HOR activity of the Ru-richest PdRu model system (Pd monolayer on Ru).

Testing Numerical Modeling of Phase Coarsening by Microgravity Experiments

Quantitative understanding of the morphological evolution that occurs during phase coarsening is crucial for optimization of processing procedures to control the final structure and properties of multiphase materials. Generally, ground-based experimental studies of phase coarsening in solids are limited to model alloy systems. Data from microgravity experiments on phase coarsening in Sn-Pb solid–liquid mixtures, executed on the International Space Station, are archived in NASA’s Physical Sciences Informatics (PSI) system. In such microgravity experiments, it is expected that the rate of sedimentation will be greatly reduced compared with terrestrial conditions, allowing the kinetics of phase coarsening to be followed more carefully and accurately. In this work we tested existing numerical models of phase coarsening using NASA’s PSI microgravity data. Specially, we compared the microstructures derived from phase-field and multiparticle diffusion simulations with those observed in microgravity experiments.

Microstructures and Grain Refinement of Additive-Manufactured Ti-xW Alloys

It is necessary to better understand the composition–processing–microstructure relationships that exist for materials produced by additive manufacturing. To this end, Laser Engineered Net Shaping (LENS™), a type of additive manufacturing, was used to produce a compositionally graded titanium binary model alloy system (Ti-xW specimen (0 ≤ x ≤ 30 wt pct), so that relationships could be made between composition, processing, and the prior beta grain size. Importantly, the thermophysical properties of the Ti-xW, specifically its supercooling parameter (P) and growth restriction factor (Q), are such that grain refinement is expected and was observed. The systematic, combinatorial study of this binary system provides an opportunity to assess the mechanisms by which grain refinement occurs in Ti-based alloys in general, and for additive manufacturing in particular. The operating mechanisms that govern the relationship between composition and grain size are interpreted using a model originally developed for aluminum and magnesium alloys and subsequently applied for titanium alloys. The prior beta grain factor observed and the interpretations of their correlations indicate that tungsten is a good grain refiner and such models are valid to explain the grain-refinement process. By extension, other binary elements or higher order alloy systems with similar thermophysical properties should exhibit similar grain refinement.