Two-phase Region Research Articles

Phase equilibria of the Nb–Si-Gd ternary system at 1273 K

The phase equilibria of the Nb–Si-Gd ternary system at 1273 K in all the composition ranges were investigated by X-ray diffraction (XRD), electron probe microanalysis (EPMA), and Scanning electron microscopy (SEM) equipped with Energy dispersive spectroscopy (EDS). The isothermal section comprises 12 single-phase regions, 22 two-phase regions, and 11 three-phase regions. The existing of Nb3Si phase was confirmed at 1273 K by couple diffusion. A new ternary compound Gd2Nb3Si4 was discovered and its crystal structure was analyzed by the Rietveld method with Rwp = 2.11%, Rp = 1.54%, Rexp = 0.75%. It belongs to the space group P41212 (No.92) with the lattice parameter a = b = 6.99048 Å, c = 12.94393 Å, α = β = γ = 90°.

Influence of heat flux profile on two-phase flow instability in parallel channels of helical coil once-through steam generator

To enhance the heat transfer capability, the helical coil once-through steam generator (HCOTSG) has been widely utilized in the small modular reactor (SMR). There are hundreds of parallel helical channels in the HCOTSG, and the coolant undergoes the phase change from subcooled liquid to superheated vapor in the helical tube. The flow oscillation between parallel channels may be triggered during the phase change. In present study, the two-phase flow instability is investigated with different heat flux profiles under many operating conditions. The thermal–hydraulic model for parallel channels of HCOTSG is established based on our previous work, while the local heat transfer phenomenon such as subcooled boiling, critical heat flux, and wall conduction are considered in detail. The heat flux profile along the tube is ascertained by the steady-state analysis of HCOTSG under different operating conditions and applied to the outside surface of the helical channel. The heat flux value is increased step by step to trigger the out-of-phase oscillation between parallel helical channels. The thermal–hydraulic model and analysis method are validated against experimental results. The characteristics of flow instability in the helical channel are also analyzed. It is observed that the delay effect causing the flow instability is more obvious if the void fraction exceeds 0.7 in the starting stage. Then the boundary of flow instability is compared under different heat flux profiles for various operating conditions of HCOTSG. The results suggest that the distribution of heat flux in the two-phase region plays a more significant role in the occurrence of flow instability in the parallel helical channel system. The thermal–hydraulic characteristics during flow instability are governed by the combined effects of void propagation and delayed feedback in the system. In conclusion, the thermal–hydraulic condition of HCOTSG undergoes the unstable region to achieve the normal operating point, which can be avoided by adjusting the operating parameters.

Achieving enhanced strength retention at elevated temperatures in ultrafine-fibrous interconnected Al–Ce–Ni eutectic alloy solidified under super-gravity field

Super-gravity field was reported to strongly intensify the buoyancy-driven flow of liquid during solidification, affecting the solute convection and morphology of eutectic structure in binary alloys. In ternary eutectic alloys, certain two-phase regions with a coarse structure can usually be detected concurrently along with three-phase eutectics, leading to the formation of heterogeneous structure with limited ductility. Currently, Al–Ce–Ni ternary eutectic alloy was chosen as a modal system, which was reported for the first time to be solidified under super-gravity field with high volume fraction of three-phase eutectics. Meanwhile, the formation of ultrafine-fibrous interconnected Al11Ce3–Al3Ni eutectic clusters with more “chains” and higher spatial connectivity was detected mainly due to the relatively higher nucleation rate. The high volume fraction and refinement of interconnected Al11Ce3–Al3Ni eutectic clusters with excellent thermal stability could contribute to enhancement of ductility and tensile strength at elevated-temperature. Interestingly, the strength retention at 300 °C and 400 °C were able to reach up to ∼68.1 % and ∼33.2 %, respectively.

NUMERICAL SIMULATION OF ENERGY-EFFICIENT SOLUTIONS OF THE ARC FURNACE STEEL MELTING BATH

Numerical modeling of hydrodynamics and heat and mass transfer in the arc furnace (EAF) steel melting bath under pneumatic stirring conditions demonstrates that the introduction of a «deep» bath with a form factor (ratio of diameter to depth) of 2.5 against the traditional 5.0 provides an energy-efficient bubbling mode of purging at higher inert gas flowrate. An increase in the diameter of the porous plug and the volume of the two-phase region in the "deep" bath allows in 150-ton EAF to increase the mixing power and the coefficient of convective heat transfer in liquid steel by 2-2.2 and 1.4 times on average, respectively. In the context of the «flat bath» process, it is shown the possibility of intensifying the convective melting of scrap in the bath by 24% in average and, thus, increasing productivity and, accordingly, improving the energy efficiency of the EAF.

Dynamic Response of Phase Change Heat Exchange Unit with Layered Porous Media for Pulsed Electronic Equipment

Effective heat dissipation challenges transient high-power electronic devices in hypersonic vehicle cabins. This study introduces a Phase Change Heat Exchange Unit with Layered Porous Media (PCHEU–LPM) employing pulsed heat flow at the top and forced convection at the bottom. The primary aim was a comparative parametric study analyzing the thermal response of the heating surface under pulsed heat flow conditions. The geometric model was generated using electron microscopy images of manufactured objects and the numerical model was established based on the enthalpy–porosity method. Numerical simulations explored amplitude and frequency effects on pulsed thermal excitation, evaluating temperature and phase fields. A comprehensive time-frequency transformation assessed the temperature response. The results indicated an initial decrease and subsequent increase in interface temperature fluctuation with pulse heat flux amplitude growth. Temperature field uniformity correlated with natural convection strength in two-phase and liquid-phase regions. At mid and low frequencies, the phase change process increasingly suppressed interface temperature fluctuations. Optimal pulse thermal excitation selection was crucial for minimizing temperature fluctuations while maintaining the interface temperature within the expected phase transition range. In conclusion, a novel design concept is posited herein, aiming to enhance surface temperature uniformity and broaden the applicability of electronic devices through the manipulation of porosity rates.

Hot deformation behaviors and microstructure evolution of a supersaturated nickel-based superalloy

The hot deformation behaviors and microstructure evolution of a supersaturated Ni-based superalloy GH4742 were investigated by isothermal compression tests. The deformation temperature range encompassed γ' sub-solvus (1000–1075 °C) and super-solvus (1100–1150 °C), with strain rates ranging from 0.001 s−1 to 1 s−1. Separate Arrhenius-type constitutive equations were established considering the re-precipitation of the γ' phase. The correlation coefficient between the calculated stresses and the experimental data was as high as 0.997, which indicated that the rheological behaviors of the material during hot deformation processes could be accurately analyzed by the constitutive relationship. Additionally, the activation energies for the γ + γ' two-phase region and the γ single region were calculated to be 949.08 kJ.mol−1 and 437.66 kJ.mol−1, respectively. Microstructural analysis revealed that the partial dynamic recrystallisation (DRX) occurred in the γ' sub-solvus regime whereas the full DRX occurred in the γ' super-solvus regime. The low DRX fractions in the γ' sub-solvus regime were attributed to the presence of near-spherical re-precipitated γ' phase, which effectively suppresses the nucleation and growth of new grains. The deformed grains were oriented in the <101> direction parallel to the compression direction. Meanwhile, the non-monotonic relationship between the degrees of DRX and strain rate was observed due to the adiabatic temperature rise. The retarding effects of solute elements on the grain growth in the γ' super-solvus regime were determined by comparing the recrystallized grain sizes from theoretical analysis and experiment values. This work can provide guidance for understanding the deformation behaviors of the alloy and achieving desired microstructures.

Linear stability analysis of a solidification process with convection in a bounded region of space

The morphological/dynamic instability of crystallization process in a bounded region in the presence of intense convection in liquid is studied. The paper considers a linear theory of morphological instability with a flat solid-liquid interface on the example of molten metal and magma. The mathematical model includes heat transfer equations and convective type boundary conditions at the interface. The equations for perturbations of the temperature field and interfacial boundary are found, allowing to obtain the dispersion relation. Its analysis has shown the existence of morphological instability of the flat interfacial boundary for a wide range of wavenumbers. Dynamic perturbations (perturbations of the quasi-stationary crystallization velocity) were also analyzed and two solutions for the perturbation frequency were obtained. One of them is stable and the other one is unstable. The system selects one of them depending on the action of convection. The result of morphological and dynamic instability is the appearance of a two-phase region in front of a flat solid-liquid interface. Therefore, the paper also considers the dynamic instability of stationary crystallization with a two-phase region replaced by a discontinuity surface. In this case, the dynamic instability was also found for a wide range of crystallization velocities.

Establishing theoretical foundations for predicting the structural and morphological characteristics of diffusion-welded joints of the beryllium–copper composite

The paper presents the results of theoretical and experimental studies regarding the quality of diffusion welding of the beryllium–copper composite. Numerical investigations of the parameters of heterodiffusion of diffusants and the thickness of the Be–Cu pair welded joint under varying temperature-time conditions were conducted. The analytical examinations revealed that the thickness of the diffusion weld at the Be–Cu joint varies between 26 and 345 µm, with the temperature increasing from 800 to 1000 °C and the holding time ranging from 20 to 120 min. The calculated layer thickness during the diffusion welding of a Be–Cu pair at 800 °C for 2 h is 65 µm, with 15 µm on the beryllium side and 50 µm on the copper side. Notably, a CuBe3 intermetallic compound zone can form in the diffusion weld, which should be considered an adverse factor that reduces the mechanical properties. To theoretically substantiate the modification of the structure and properties of the diffusion zone, a numerical study of welding was carried out using a 10 μm thick nickel foil spacer, which is readily soluble in beryllium. It was demonstrated that after exposure to temperature-time conditions at 900 °C for 20 min, a 50 µm wide diffusion-bonded joint is formed. Its structure includes two single-phase zones of solid solutions based on copper and beryllium, as well as two two-phase regions consisting of solid solutions hardened with intermetallic compounds. Since the weld lacks structural zones consisting solely of intermetallic compounds (unlike when welding the Be–Cu diffusion pair), there are grounds to anticipate a reduction in the embrittling effect on the weld. The results obtained from the analytical studies can serve as the foundation for a theoretical prediction method for assessing the quality of diffusion welding of the beryllium–copper composite.

Effect of Ce content on the microstructure and TiN precipitation behaviour of high-titanium steel during slow cooling solidification

ABSTRACT This study used high-temperature melting experiments, optical microscopy, and scanning electron microscopy to investigate the effects of various Ce contents (0 wt.%~0.0165 wt.%) on the microstructure and TiN precipitation behavior in high-titanium steel during slow cooling solidification. The findings show that the microstructure of the solidified steel in each experiment are equiaxed grains at a cooling rate of 0.17 ℃/s. TiN mainly precipitates in the Liquid + δ two-phase region in this experimental steel. CeAlO3 and Ce2O2S precipitate before TiN, and their small lattice misfit with TiN (7.55% and 7.90%, respectively) are the primary cause of their propensity to act as the cores of TiN heterogeneous nucleation. The TiN area density in each experimental steel increases from 38.6 no./mm2 → 61.4 no./mm2 → 89.3 no./mm2 → 105.8 no./mm2 when the Ce content in the steel rises from 0 wt.% → 0.0015 wt.% → 0.0058 wt.% → 0.0165 wt.%.

Damage evolution mechanism around AlN non-metallic inclusions in Fe-8.5Mn–3Al-0.2C lightweight medium-Mn steel during warm forming

Based on the tensile test in two-phase region, the damage evolution mechanism around AlN non-metallic inclusions in Fe-8.5Mn–3Al-0.2C lightweight medium-Mn steel during warm forming was elucidated. The findings indicate that voids primarily originate from the bonding interfaces between AlN non-metallic inclusions and ferrite. According to the numerical simulation results, strain eventually concentrates at the bonding interface where the AlN inclusion is connected to the high-strain ferrite in the direction parallel to the load, which is in good agreement with the experimental results. TEM analysis reveals the semi-coherent interface between AlN and austenite as well as the incoherent interface between AlN and ferrite. The incoherent interface between AlN and ferrite exhibits higher interfacial energy and worse mechanical stability, accelerating the separation of the bonding interface between AlN and ferrite.

ENERGY EFFICIENT SOLUTIONS FOR STEEL REFINING IN FOUNDRY CLASS ELECTRIC ARC FURNACE

Analysis of recent research and publications. The technological period in foundry class electric arc furnaces (EAF) is usually long term, is determined by desulfurization of steel and accompanied by significant energy loss through emissive surface of shallow steelmaking bath. Known mathematical models of Sulphur removal do not take into attention the impact of hydrodynamics factors due to deepening of the steelmaking bath of the same volume. Purpose. The task is to show feasibility of energy savings in foundry class EAF due to implementation of “deep” bath with forced pneumatic mixing. Method. Numerical modeling of sulfur removal in the steelmaking bath under conditions of forced pneumatic mixing. Research findings. Mathematical model takes into account removal of sulfur on interfacial surface of thin steel film, covering gas bubbles, geometry of bath and two-phase region, hydrodynamics, coalescence of bubbles. Simulation showed that in a “deep” bath, having shape factor (diameter to depth ratio) 2.5, rate of desulfurization, increases up to 5-6.7 times compared with a standard not forcibly stirred bath with shape factor 4.5, due to amplification of mass transfer in two-phase region and film desulfurization, reaching at least 23-28 % in overall process. Rise of porous plug radius contributes to increase sulfur removal velocity due to enlargement of threshold flowrates, corresponding to transition bubble - jet mode and bath "breakdown” mode. Effect of bath deepening in overall improvement of desulfurization kinetics is on average 23%. Practical significance. The obtained results allow to expect a shortening of the technological period due to increase of sulfur removal processes by an average of 1.5 times. Taking into account the share of the technological period in the total duration of melting on average 25-30%, the reduction of melting time will be 8-10%, and the saving of electricity, with an average specific consumption in small-capacity arc furnaces of 850 kWh/t, is expected to be 60-70 kWh per ton of crude steel.

Li4GeO4-Li2CaGeО4 phase equilibria and Li2+xCa1-xGeO4 solid solutions

Detailed studies of the Li4GeО4-Li2CaGeО4 system by solid-phase syntheses of various compositions from pure Li4GeО4 to pure Li2CaGeО4 in the temperature range from 25 to 1125 °C is investigated for a first time. Solid state synthesis powders are characterized by X-ray and DSC/TG methods. Concentration and temperature two-phase regions of Li4GeО4 and Li2CaGeО4 as well as two-phase regions of Li2CaGeО4 and Li2+2xCa1-xGeO4 are established. Region of pure Li2+2xCa1-xGeO4 solid solution are detected too and it structure is investigated. Being structural analog to Li2+2xZn1-xGeO4 and Li2+2xMg1-xGeO4, Li2+2xCa1-xGeO4 has own specific local environment of the metal ions. The obtained results are compared with those for Li4GeО4-Li2ZnGeО4 system and for Li2+2xZn1-xGeO4 solid solution. The differences of the phase diagrams and structural features of the solid solutions are discussed.

Solidification Behavior and Microstructure Evolution in Dissimilar Electron Beam Welds Between Commercially Pure Iron and Nickel

Electron beam welding processes have highly accurate control of both spatial and temporal heating profiles which provide unique capabilities in dissimilar metals joining. In this work, electron beam welds were made between commercially pure nickel and iron to determine the effect of fusion zone composition on solidification behavior and microstructure evolution. The weld was made with a beam deflected in a circular pattern to enable joining and promote mixing. The beam traveled at a shallow angle of approximately 1 deg to the joint interface starting in the nickel and finishing in the iron. The shallow angle created a weld with a composition gradient along its 110 mm length. The solidification behavior and final weld microstructure were characterized using both light optical microscopy and scanning electron microscopy. Electron backscatter diffraction was used to determine the phase fractions in the fusion zone. A change in solidification mode from face-centered cubic austenite to body-centered cubic ferrite was observed as a function of fusion zone composition. Weld cross-sections containing 65.5 wt pct Fe and 76.9 wt pct Fe had a two-phase fcc + bcc microstructure. Using the compositions and phase fractions, the two-phase region was estimated to be between 56.4 and 79.7 wt pct Fe. Martensite was observed in cross-sections containing between 76.9 wt pct Fe and 98.1 wt pct Fe, which was confirmed using hardness measurements.

Tailoring texture in a near-α titanium alloy: Insights from strain paths and cooling rate influences

By elucidating the progressive relationship from the rolling stress state to the activation of slip systems and then to lattice rotation, this paper clarifies the influence mechanism of strain paths on the evolution of α-phase texture in near-α titanium alloys. The distinct rolling textures obtained further provide a robust foundation for investigating whether the competition between different α-phase textures changes with varying cooling rates during β→α phase transformation. In this study, initial Ti65 alloy sheets underwent rolling using three different strain paths (UDR/CDR/MSCR), resulting in the production of three foils characterized by distinct textures. Compressive stress during rolling promotes the activation of basal and pyramidal-II slipping, leading to the formation of a TD-split basal texture in α-phase. Tensile stress during rolling promotes the activation of prismatic slipping, ultimately resulting in a [10 1‾ 0]//RD (in the case of UDR) or [21‾1‾ 0]//RD (in the case of CDR) texture. Variations in stress states along different strain paths led to differences in the global Schmid factor distribution of α-phase for slip systems, ultimately resulting in diverse texture evolution. Subsequently, foil samples underwent two-phase region heat treatments, followed by furnace cooling and air cooling. After furnace cooling, the strength of the transverse texture increased in each type of foils. Conversely, after air cooling, no specific α-phase texture consistently exhibited an increasing trend in the three foils.

FORMATION OF TWO-PHASE ZONES DURING INTERNAL OXIDATION OF BINARY ALLOYS

In the paper the formation patterns of two-phase regions during the internal oxidation process in low-alloyed binary alloys is studied. The goal of the research is the creation of a mathematical model for the internal oxidation process, which is to describe the kinetics of formation and evolution of internal oxidation zones, the study of the patterns governing the two-phase zone formation during internal oxidation, the study of the space-time dynamics of the structural parameters of the two-phase area, namely the number of the oxide particles, their average radius and the phase volume, at different stages of the internal oxidation zone evolution. The two-phase process of diffusion saturation with light components applied to binary alloys is analyzed theoretically. The conditions for formation of disperse oxide particles are formulated. A mathematical model for the formation of two-phase areas as well as the numerical solution for the system of equations describing the kinet- ics of formation and evolution of the two-phase area for different values of the process parameters is proposed. The modeling and experiments demonstrate that the distribution of structural parameters of the two-phase area has complex, non-monotonous nature. The influence of the main parameters of the process on the kinetics of the formation of the two-phase area in a lightly-alloyed binary nickel-based alloy plate is also determined. All stages of the plate’s oxidation process are studied – from the inception of the particles to the coalescence of second-stage particles. The results of the work could be used for developing new technologies in thermal and chemical-thermal treatments for disperse strengthening of materials using internal oxidation, as a physical basis for seeking ways of providing certain distributions of the internal oxidation zone structural parameters, which are required to give the al- loy a necessary set of physical and mechanical properties. The comparison of the modeling and experimental results shows a good correlation, which allows them to be recommended for developing new technologies in disperse strengthening, new heat-resistant steels, disperse-strengthened magnetic materials and electrotechnical alloys.

Green Extraction Strategy Using Bio-Based Aqueous Biphasic Systems for Polyphenol Valorization from Grape By-Product.

Polyphenols are natural compounds with enhanced antioxidant properties. They are present in relatively high concentrations in fruit/vegetable by-products. Therefore, there is a need for the development of efficient and cost-effective methods for the separation and purification of these valuable compounds. Traditional extraction with organic solvents needs to be switched to novel methods that are more efficient, with reduced extraction times and low consumption of organic solvents. Aiming at developing sustainable processes for the separation and purification of phenolic compounds, we used three model compounds, namely resveratrol, quercetin, and gallic acid, to investigate ionic liquid-based aqueous biphasic systems (IL-ABSs) formed by cholinium-based IL in combination with polypropylene glycol with a molecular mass of 400 g/mol (PPG400). The ABS composition in the two-phase region was selected according to a previously determined phase diagram. Extraction studies indicated the preferential partition of resveratrol and quercetin toward the hydrophobic PPG-rich phase that is mainly dominated by its hydrophobic nature and the strong salting-out effect of ILs. On the other hand, due to its considerably hydrophilic nature, gallic acid preferentially migrates toward the IL phase. The achieved results from grape stem extract demonstrated high extraction efficiencies of cholinium dihydrogen phosphate (~99% for resveratrol for the PPG phase and 78% for gallic acid for the IL phase), with considerable selectivity, demonstrating promising outcomes for potential applications.

Study on heat transfer enhancement of spray cooling with bionic vein channel structured surface

Inspired by the fluid transportation capabilities of leaf vein structures in nature, a novel approach is proposed to enhance spray cooling heat transfer performance through improving liquid film distribution. In this study, a leaf vein channel structure was laser etched onto a heat exchange surface and a non-contact open spray cooling test platform based on the principle of induction hea ting was established. The spray cooling heat transfer performance of the enhanced surfaces with identical leaf vein channel shapes but varying channel depths was investigated under different flow rates. The results indicate that, across all tested flow rate conditions, the spray cooling heat transfer performance of the leaf vein channel surpasses that of the smooth surface. Notably, within the two-phase region, an observed 50 % increase in heat flux density highlights significant enhancement effects provided by the leaf vein channels. Furthermore, research findings suggest that for leaf vein channel depths <0.5 mm, greater depth corresponds to improved enhanced heat transfer effects during spray cooling processes. Utilizing high-speed camera technology throughout our investigation allowed us to capture distinct liquid motion phenom ena known as “liquid columns” occurring at the center of each leaf vein channel. These liquid columns exhibit changes in shape and motion mode corresponding to variations in surface temperature.

Microstructural characteristics and recrystallization mechanism of Ti-6.5Al–2Zr–1Mo–1V alloy during two-stage hot deformation

In this study, we investigated the two-stage deformation behavior of near α Ti-6.5Al–2Zr–1Mo–1V alloy at various temperatures (915 °C, 950 °C, 1020 °C) and strain rates (0.01 s−1, 0.1 s−1). The alloy underwent differing holding periods (500s, 1000s) between deformation stages. The results demonstrated an increase in flow stress with decreasing deformation temperature and increasing strain rate. Work hardening of flow stress was observed during the two-stage thermomechanical processing within the α+β two-phase region. Microstructural evolution was characterized by the formation of α lamellar kink bands, the separation and migration of grain boundaries, and grain spheroidization. An increase in deformation temperature and a decrease in strain rate enhanced grain refinement, accelerated structural evolution, and intensified the degree of spheroidization. Dynamic recrystallization (DRX) was more prevalent at higher temperatures and lower strain rates, as the critical nucleation rate for DRX was more readily achieved. The increased interval between thermomechanical processing stages led to a transition from low-angle to high-angle grain boundaries, and a reduction in dislocation density due to static recovery occurred during the holding period. At 915 °C, hot deformation induced the formation of {10-10} twinning, altering grain orientation and reducing stress. The Schmid factor for {10-10}<1120> slip was higher at lower temperatures, which reduced the critical resolved shear stress necessary for yielding in the α phase of the Ti-6.5Al–2Zr–1Mo–1V alloy, thereby facilitating further plastic deformation.

Wetting of L10 twin and antiphase boundaries by nanometer-scale L12 in Fe-Pd alloys

This paper reports microstructure associated with the L10 and L12 two-phase coexistence region in magnetic Fe-Pd alloys and analyzes the observed complex nanometer scale wetting layer structures. Fe - 61.8 at% Pd samples were continuously cooled from the disordered A1 phase through the eutectoid isotherm and aged at 650 °C for various times. X-ray diffraction reveals that the samples first order to L12 then transform to L10-dominant L10 + L12 two-phase mixture. It is shown that L10 forms {110} polytwin microstructure with straight {11¯0} antiphase boundaries (APBs), where L12 exists as nanometer-scale wetting layers along the twin boundaries and APBs. The variant selection for L12/L10 wetting layers is discussed, and evidence of closed/open APB structures is shown with high-resolution transmission electron microscopy.

The isothermal section of the phase diagram of Gd-Mn-Ga (≤50 at.%Ga) ternary system at 873K

The phase diagram of the Gd-Mn-Ga ternary system is a very important tool for the exploration and development of rare earth Heusler alloys with excellent physical properties, such as magnetic properties, half-metallic properties, ferromagnetic shape memory effect, magnetocaloric effect, ect. In this study, the alloy samples were prepared using a vacuum arc melting furnace, and the 873 K isothermal section of the Gd-Mn-Ga (≤50 at.%Ga) ternary alloy phase diagram was determined by using X-ray diffraction (XRD), scanning electron microscopy (SEM), and energy spectrometry (EDS). The isothermal section consists of 22 single-phase regions, 44 two-phase regions, and 23 three-phase regions with the presence of 6 ternary compounds, GdMnGa, Gd2MnGa6, Gd2Mn15Ga2, Gd2Mn11Ga6, GdMn0.56Ga1.44, and GdMn0.37Ga1.63. The solid solubility ranges of Ga in β-Mn and Gd2Mn15Ga2 are 5.0–18.1 at.%Ga and 10.5–25.0 at.% Ga. The maximum solid solubility of Ga in α-Mn, GdMn12, and Gd6Mn23 are 2.0, 2.7, and 7.3 at.% Ga, respectively. The maximum solid solubility of Mn in GdGa2 is determined to be 13.1 at.% Mn.