Photoelectrochemical cathodic protection for metals, leveraging the unique photoelectrochemical properties of TiO₂ semiconductor films, represents an innovative approach to corrosion protection with promising potential. However, pure TiO₂ films exhibit limitations, including low visible light absorption, rapid recombination of photogenerated electrons and holes, and low photoelectric conversion efficiency. To enhance the photoelectrochemical properties of TiO₂ film photoanodes, composite films are essential. In this study, a g-C₃N₄ layer and Ag nanoparticles were sequentially deposited onto an anodized TiO₂ nanotube array film on a Ti foil via simplified chemical vapor deposition and chemical bath deposition, respectively, to enhance the TiO₂ composite film's photoelectrochemical performance for metal cathodic protection applications. The results demonstrated substantial improvements in light absorption and photoelectrochemical performance for the Ag/g-C₃N₄ co-sensitized TiO₂ nanotube composite film compared to the pure TiO₂ nanotube array film. The Ag/g-C₃N₄/TiO₂ composite film's light absorption was extended into the visible light spectrum, enhancing the separation efficiency of photogenerated electrons and holes. Under white light irradiation, the photocurrent density of the composite film in an aqueous solution containing 50% (volume fraction) ethylene glycol and 0.2 mol/L NaOH reached 135 μA/cm², approximately 11 times that of the pure TiO₂ film. Furthermore, when employed as a photoanode, the composite film on the Ti surface reduced the electrode potential of 403 stainless steel in a 0.5 mol/L NaCl solution by 530 mV relative to the steel's free corrosion potential, demonstrating a notably enhanced photoelectrochemical cathodic protection effect.

In the tritium proliferation site of the fusion reactor, the tritium barrier coating can effectively prevent the diffusion of tritium into the cladding structure and avoid the degradation of the material and the loss of tritium resources. However, the performance of existing coatings (such as α-Al₂O₃ and Er₂O₃) in extreme environments such as irradiation is challenged, and high-entropy alloy coatings are considered to be an effective solution. In meeting the aforementioned requirements, (AlCrTaTiZr)N _x coatings were prepared on a Si substrate by magnetron sputtering under different N₂ flows. The crystal structure, microstructure, and elemental content of the coatings were studied by XRD, SEM, and EDS. When no N₂ was introduced, the film was amorphous. By contrast, when N₂ was introduced, the film developed a fcc structure, which was closely combined with the Si substrate, and the coating had good compactness. When the volume flow ratio of N₂ / (Ar + N₂) (R_N) is 15%, the crystallinity of the film was strongest. On the basis of the first principles method combined with the special quasi-random structure, an adsorption model of H₂ molecules on the (001) surface of (AlCrTaTiZr)N was constructed. The hydrogen isotope surface interaction of coatings under service conditions was constructed and studied on the basis of the experiments. First, the adsorption energy of different sites and adsorption modes, as well as the effect of stable adsorption on the mechanical properties of the coating under different H₂ coverages was calculated. Results indicate that the vertical adsorption Hollow sites are stable adsorption sites, and H₂ adsorption on the coating surface is dependent on physical adsorption. H₂ is adsorbed on the Hollow sites composed of CrTaTiZr. After adsorption, the volume modulus (B), shear modulus (G), Young's modulus (E), Poisson's ratio (\nu) and B / G of the coating decreased. From a macroscopic perspective, H₂ adsorption decreases the strength, hardness, and ductility of the coating.

Metastable β-titanium alloys are widely used in advanced biomedical applications because of their high strength and low modulus. Strength improvements in these alloys are mainly achieved through α-phase precipitation. Interestingly, a novel α″ + β dual-phase microstructure has been discovered in a multifunctional Ti2448 alloy after aging treatments, which effectively enhanced the strength while maintaining decent ductility. Since O plays a crucial role in regulating the decomposition and mechanical properties of titanium alloys, understanding its effects on the microstructural evolution and mechanical behavior of Ti2448 alloys is of great importance. However, the effect of O on the decomposition behavior of the Ti2448 alloy remains unclear. To investigate the influence of O content on the microstructure evolution and mechanical properties of the Ti2448 alloy, two Ti2448 alloys with different oxygen contents were selected: low oxygen (LO: 0.08%, mass fraction) and high oxygen (HO: 0.33%, mass fraction). This study employed a two-step heat treatment (annealing at 873/923 K for 10 min, followed by aging at 773 K for 1-4 h) on Ti2448-LO and Ti2448-HO alloys, focusing on the evolution of their microstructure and mechanical properties. Results indicated that O content minimally influenced the phase composition and grain size of the alloys before heat treatment. However, increasing the O content considerably suppressed the double yield phenomenon and enhanced the strength and elastic modulus of the alloy. After the two-step heat treatment, both alloys exhibited the precipitation of dense lamellar phases, resulting in remarkable modulus hardening and aging strengthening. Although the initial thickness of the precipitated phase was relatively unaffected by the O content, its subsequent coarsening behavior during aging was influenced. Under the same heat treatment conditions, the Ti2448-HO alloy exhibited a higher volume fraction of precipitates, leading to stronger modulus hardening and aging strengthening. Consequently, the aged Ti2448-HO alloy exhibited higher elastic modulus and strength than the Ti2448-LO alloy.

Mg alloys with high-strength and long-period stacking ordered (LPSO) phases are promising materials for lightweight structural applications because of their exceptional properties. However, corrosion remains a major challenge that limits their widespread use. The influence of the LPSO phase on the corrosion behavior of these alloys is substantial. On one hand, the microgalvanic effect between the LPSO phase and α-Mg matrix can accelerate corrosion. On the other hand, the LPSO phase may serve as an effective barrier that hinders the spread of corrosion in as-cast Mg alloys. Although the distribution of the LPSO phases considerably influences the corrosion resistance, the relationship between the LPSO phase content and the corrosion resistance remains poorly understood. In this work, a series of as-extruded Mg-xY-yZn-0.1Mn (x = 2, 4, and 8, mass fraction, %; x / y = 2) alloys with varying LPSO contents and morphologies were prepared, and their corrosion resistance were investigated in detail. Microstructural analyses were conducted using OM, SEM, and XRD. Corrosion resistance was evaluated through hydrogen evolution, mass loss, and electrochemical testing. Corrosion morphologies were examined using OM, SEM, confocal laser scanning microscopy (CLSM), while the local corrosion potential was analyzed using scanning Kelvin probe force microscopy (SKPFM). The results showed that the alloys primarily consisted of α-Mg and LPSO phases. The volume fraction of LPSO increased with the elevation of Zn and Y contents, and the morphology of the LPSO phases varied among the alloys. In the Mg-2Y-1Zn-0.1Mn (WZ21M) alloy, which exhibited the lowest Zn and Y contents, the LPSO phases appeared as small blocks. In contrast, the Mg-4Y-2Zn-0.1Mn (WZ42M) alloy, with moderate Zn and Y contents, featured LPSO phases arranged zonally along the extrusion direction. The Mg-8Y-4Zn-0.1Mn (WZ84M) alloy, which exhibited the highest LPSO content, also exhibited a zonal distribution of LPSO phases but with a considerably reduced spacing between adjacent phases. Corrosion tests performed in a 3.5%NaCl (mass fraction) solution revealed that the corrosion resistance decreased in the following order: WZ84M < WZ42M < WZ21M. The WZ21M alloy, exhibited a smoother discharge process and a more negative discharge potential across different current densities, indicating higher corrosion resistance compared to the WZ42M and WZ84M alloys. Conversely, the WZ84M alloy, showed the poorest corrosion resistance due to the pronounced microgalvanic effect between the LPSO phase and α-Mg matrix. The deformed LPSO phases in the as-extruded alloy were less effective in inhibiting corrosion spread. The WZ21M alloy benefited from reduced microgalvanic effects, leading to improved corrosion resistance. Therefore, the corrosion resistance of as-extruded Mg-Y-Zn-Mn alloys is inversely related to the LPSO content, with higher LPSO contents generally resulting in decreased resistance due to intensified microgalvanic effects. Additionally, the morphology of the LPSO phase plays a critical role in determining corrosion resistance.

CrMnFeCoNi high-entropy alloys (HEAs) have attracted considerable attention because of their excellent mechanical properties. Furthermore, these alloys exhibit high energy absorption characteristics under high-strain rate deformation for various deformation modes. The stacking fault energy (SFE) plays a crucial role in improving the deformation modes and mechanical properties. Only few studies have investigated the effect of SFE on the dynamic mechanical properties and deformation mode of CrMnFeCoNi series HEAs. In this work, the effect of SFE on the dynamic mechanical properties and deformation mechanism of CrMnFeCoNi HEAs were investigated through quasi-static and dynamic mechanical tests and microstructural analysis using CrMnFeCoNi (SFE of 35 mJ/m²) and Cr₂₆Mn₂₀Fe₂₀Co₂₀Ni₁₄ (SFE of 23 mJ/m²) HEAs. Results indicate that CrMnFeCoNi and Cr₂₆Mn₂₀Fe₂₀Co₂₀Ni₁₄ HEAs exhibit a strain-rate hardening effect under dynamic deformation. Furthermore, the flow stress, energy absorption ability, and work hardening index increase under static and dynamic conditions with the decrease in SFE. Under quasi-static compression, deformation occurs via dislocation gliding in CrMnFeCoNi, whereas deformation twinning is profound in Cr₂₆Mn₂₀Fe₂₀Co₂₀Ni₁₄ HEA with low SFE; therefore, deformation is dominated by dislocation slip and twinning. The contribution of deformation twinning to the deformation strain increases with the increase in strain rates. In particular, deformation occurs via dislocation gliding and twinning in CrMnFeCoNi HEA. Apart from dislocation slip and twinning, the interaction of twins and the transition from fcc to hcp structures provide additional deformation modes to accommodate the plastic deformation of Cr₂₆Mn₂₀Fe₂₀Co₂₀Ni₁₄ HEA and improve the mechanical properties and energy absorption of these alloys. This work demonstrates that the change in SFE will lead to different deformation modes for accommodating plastic strain, thereby improving the mechanical properties of HEAs.

GH4169 materials are widely used in aerospace, nuclear power, petrochemical, and other industries. However, conventional processing methods fail to meet the demands of high-performance and rapid manufacturing for complex structural parts. Therefore, selective laser melting (SLM) has been adopted as a new rapid manufacturing technology to address these demands. The high-temperature gradient and rapid cooling rate generated during SLM result in a considerably different microstructure in the GH4169 alloy compared with those produced via conventional melting and forging methods. Consequently, heat treatment is an essential post-processing step to enhance the precipitation strengthening of the GH4169 superalloy. Thus, it is critical to examine the microstructure and mechanical properties of the SLM-formed GH4169 alloy after heat treatment. This study focuses on fabricating the GH4169 alloy using SLM technology and investigates the microstructure and mechanical properties of the as-built, directly aged, and solution-aged GH4169 alloy specimens. Results reveal that the as-built structures primarily comprise a γ matrix and Laves phase. After direct aging, the γ′/γ″ phase precipitates within the matrix. After solution aging, the Laves phase completely dissolves. Moreover, the δ phase precipitates with a size of < 1 μm become abundant and uniformly distributed within grains and grain boundaries. Simultaneously, the γ′/γ″ phase precipitate within the matrix, resulting in a more homogeneous distribution. The microhardness, tensile strength, and yield strength at room temperature (25 ^oC) of the SLM GH4169 alloy are 311 HV, 961 MPa, and 649 MPa, respectively. Heat treatment substantially improves the hardness and strength of the material. In the solution-aged state, the microhardness reaches 518 HV, with a tensile strength of 1393 MPa and a yield strength of 1233 MPa at room temperature. Notably, these static mechanical properties surpass those of the corresponding forged materials. The tensile properties at 550, 650, and 750 ^oC indicate that the elevated strength of the heat-treated samples at 650 ^oC complies with relevant forging standards. Owing to the substantial temperature gradient and rapid cooling rate during the SLM forming process, the GH4169 sample exhibits a refined cellular and columnar dendritic structure, small grain size, and high dislocation density. Subsequent heat treatment induces γ′/γ″ phase precipitation, enhancing the mechanical properties of the GH4169 alloy through fine crystal strengthening, dislocation strengthening, and precipitation strengthening.

Ni-based superalloys that are difficult to deform are highly susceptible to cracking during additive manufacturing. Despite their importance, limited research has been conducted on the additive manufacturing of GH4975 superalloy. To address the cracking issues associated with such superalloys, this study focuses on additively manufactured GH4975 superalloy to investigates various crack repair strategies. Experimental approaches, including the addition of TiC heterogeneous nucleating agents to the powder, hot isostatic pressing (HIP), and hot compression, were used to explore effective methods and underlying mechanisms for crack healing. The results show that the calculated mismatch of close-packed planes between TiC and the matrix is 6.0%, with an atomic mismatch of 0.4% in the close-packed direction. Following the addition of nano-TiC particles, the average grain diameter of the GH4975 superalloy decreased from 41.9 μm to 27.2 μm, indicating significant grain refinement; however, the cracks were not effectively eliminated. The HIP repair method further removed some cracks, but microcracks wider than 3 μm remained unhealed. The most effective crack elimination was achieved through hot compression at 1200 °C with a strain rate of 0.1 s^-1 and 30% deformation, which nearly eliminated cracks at the center of the as-printed sample. However, the crack healing ability decreased when hot compression was applied to samples that had already undergone HIP treatment. The main mechanisms of crack healing were identified as matrix plastic flow under external pressure and the diffusion-driven crack filling by Al elements.

With the rapid growth of the international crude oil shipping industry, ensuring the safety of oil tanker transportation has become a critical concern. The cargo oil tank (COT), the primary structure for storing crude oil, is particularly susceptible to corrosion, with the inner bottom plate being a key site for failure and potential oil leakage. Low-alloy corrosion-resistant steel, mandated by the International Maritime Organization as an alternative to traditional anticorrosion coatings, faces challenges in China due to insufficient corrosion resistance, limiting its long-term applicability in COTs. Enhancing the intrinsic properties of ship plate steel while minimizing costs is therefore crucial for improving its corrosion resistance and mechanical performance. In the simulated acidic Cl^- environment of a COT bottom plate, a micro-galvanic couple forms between ferrite and cementite in pearlite, with ferrite acting as the anodic phase and cementite as the cathodic phase. Over time, accumulated cementite thickens on the surface, increasing the anode/cathode area ratio and accelerating the corrosion rate due to intensified micro-galvanic effects. To mitigate this, a deformation spheroidization process was employed to refine the microstructure without additional alloying elements. By optimizing forging and heat treatment parameters, a tempered sorbitic microstructure was achieved in T8 steel. Microstructural evolution was characterized using SEM and EBSD, while mechanical properties were assessed through microhardness testing, tensile experiments, and fracture morphology analysis. Corrosion behavior before and after optimization was examined via mass loss tests, electrochemical analysis, and corrosion product characterization. The results indicate that spheroidization heat treatment enhances the strength, plasticity, and toughness of T8 steel through grain refinement, dislocation strengthening, and dispersion strengthening. The transformation of bulk layered cementite into fine-grained cementite effectively suppresses its accumulation on the surface during corrosion, mitigating the accelerating effect of micro-galvanic corrosion. Consequently, the corrosion resistance of T8 steel in the simulated COT environment was significantly improved. This study demonstrates a cost-effective approach to enhancing both the mechanical properties and corrosion resistance of ship plate steel through microstructural control, offering new insights for the development of corrosion-resistant materials for cargo oil tanks.

Lightweighting for bodies in white has become an important approach for enhancing energy efficiency and reducing emissions within the automotive industry. Among various lightweight materials, high-strength steel has shown considerable potential in terms of cost-effectiveness, safety, and user satisfaction. In particular, Fe-Mn-Al-C twinning-induced plasticity (TWIP) steel, also known as the third generation TWIP steel, has received considerable attention from the automotive industry in recent years owing to its excellent mechanical properties and good formability. During deformation, TWIP steel generates a considerable amount of deformation twinning within its grains, thereby impeding dislocation motion and resulting in high strain hardening rates in TWIP steels. Given that TWIP steels may be subjected to cyclic loading during actual service, the potential for fatigue failure poses a substantial risk during their long-term service, resulting in serious economic losses or human casualties. However, the deformation behavior and microstructure evolution of Fe-Mn-Al-C TWIP steel during low-cycle fatigue remain extensively understudied. Therefore, the study of the fatigue properties of TWIP steels is of considerable importance for their design and application in the automotive industry, warranting increasing attention. Herein, the low-cycle fatigue behaviors of Fe-22Mn-3Al-0.6C steels with different grain sizes were investigated. Steels with grain sizes of 8, 16, and 60 μm were prepared via hot rolling and subsequent heat treatment. After low-cycle fatigue testing, the samples were characterized using SEM equipped with electron channeling contrast imaging components and TEM. The effects of grain size on cyclic stress response, damage mechanisms, and fatigue life of Fe-Mn-Al-C TWIP steel were analyzed. Considering the fatigue damage contributed by strain and stress, the low-cycle fatigue property of TWIP steel was assessed from the perspective of hysteresis energy. Results indicated that the TWIP steel with small grain size (8 μm) exhibited enhanced low-cycle fatigue performance at a small total strain amplitude (Δε / 2 = 0.3%). Conversely, at a large total strain amplitude (Δε / 2 = 1.0%), the TWIP steel with large grain size (60 μm) exhibited enhanced low-cycle fatigue performance. Hysteretic energy model analysis revealed that fatigue damage mechanisms in TWIP steels were dominated by strain damage at large total strain amplitudes, with coarse grains showcasing an improved capacity to accommodate damaged defects. Conversely, at reduced total strain amplitudes, the fatigue mechanism was dominated by stress damage, with fine-grained steels showing enhanced strength and improved resistance against fatigue crack initiation.

High nitrogen austenitic stainless steels have emerged as crucial materials in the steel industry due to their excellent comprehensive properties and their cost-effective and ecofriendly characteristics. However, the yield strength of those alloys at room temperature is limited and fails to meet the requirements for high stress loads. Therefore, high nitrogen austenitic stainless steels having high strength and good ductility are urgently needed. This study focuses on a high nitrogen austenitic stainless steel with a nominal composition of Fe-18.87Cr-10.09Mn-1.12Ni-0.53N-0.18Si-0.04C (mass fraction, %). The steel plate was subjected to cryogenic rolling at the liquid nitrogen temperature with a thickness reduction of 10%, achieving exceptional comprehensive mechanical properties, including a yield strength of 947 MPa, a tensile strength of 1051 MPa, and a uniform elongation of 36%. These results are comparable to the optimal strength and ductility obtained by traditional thermomechanical processes including cold rolling and its subsequent annealing. The substantial enhancement in yield strength, which is 1.86 times than that of the homogenized state, is primarily attributed to the dense dislocation substructures and complex lamellar structures composed of ε-martensite laths, the deformation twins, and local chemical order lath structures introduced during the cryogenic rolling process. The structures induce a synergistic effect of multiple strengthening mechanisms. Moreover, the material maintains good uniform elongation and work hardening ability, which can be attributed to dislocation slip and the significant twinning-induced plasticity effect during plastic deformation. The cryogenic rolling technique demonstrated offers remarkable advantages in cost-savings, process simplification, and efficiency improvement in the preparation and production of the high nitrogen austenitic stainless steel.

Nozzle Ar blowing technology profoundly influences the production and quality of continuous casting slabs. Its primary objectives include minimizing nozzle nodules, eliminating inclusions, and enhancing slab quality. Extensive physical experiments and numerical simulations have been performed to reveal the metallurgical phenomena and principles in continuous casting molds. However, the high costs associated with physical experiments and constraints related to model size and measurement methods hinder the accurate depiction of the actual motion state of high-temperature liquid steel and bubbles. As a result, more researchers are using numerical simulation methods to investigate Ar blowing at the nozzle. The focus of these studies typically involves tracking bubbles' position, velocity, and diameter using the Euler-Lagrange method. Numerous scholars have explored the influence of process parameters such as casting speed and Ar blowing rate on the distribution of Ar bubbles in the mold via numerical simulations. These studies also examine how these parameters affect the capture of Ar bubbles in the solidified shell. However, few scholars have explored the interactions among bubbles, such as collision, coalescence, and fragmentation. Understanding these interactions is crucial for determining bubble distribution, particularly near the mold wall, which significantly impacts the quality of the solidified shell. A collision-polymerization-fragmentation-trapping model has been developed to address this gap and describe bubble behavior. This model aims to effectively manage the movement and distribution of Ar bubbles in the slab mold, enhance the efficiency of inclusion removal by bubbles, and minimize bubble entrapment in the solidified shell. The simulation study examined how casting speed, Ar blowing rate, nozzle angle, and nozzle immersion depth affect the movement of Ar bubbles in a 800 mm × 1300 mm × 230 mm continuous casting mold. The findings underscore the critical role of bubble collision, aggregation, and fragmentation in shaping their size distribution in the mold. Moreover, process parameters substantially influence the spatial distribution of bubbles: larger bubbles tend to accumulate and float up near the nozzle, medium-sized bubbles are located and float up farther from the nozzle, and smaller bubbles predominantly gather and float up near the mold's narrow surfaces. However, some small bubbles have the potential to migrate toward the deeper sections of the mold and become entrapped by the solidified shell, potentially causing defects in the slab quality. The distribution of bubbles is predominantly influenced by the nozzle immersion depth, which affects where bubbles are located in the mold. Meanwhile, the Ar blowing rate and the nozzle angle significantly affect the diameter and number of bubbles in the mold. Additionally, casting speed is crucial in influencing bubble distribution, number, and diameter in the mold. Optimal conditions, such as a casting speed of 1.4 m/min, an Ar blowing rate of 10 L/min, a nozzle angle of -15°, and a nozzle immersion depth of 180 mm, result in a well-dispersed bubble distribution in the mold. This favorable dispersion enhances the effectiveness of inclusion removal, improves the purity of liquid steel, minimizes bubble entrapment by solidified shells, and consequently enhances the overall quality of the slab.

Nickel-based single crystal superalloys are critical materials for manufacturing advanced aircraft engine blades. During operation, microstructural changes in alloys under the applied stress significantly influence their fatigue and creep performances. However, relying solely on experimental methods poses challenges in capturing the dynamic processes by which the applied stress affects the alloy microstructure. Utilizing computational simulations to study the impact of the applied stress on the rafted γ' phase in single crystal superalloys offers distinct advantages. In this study, specific slip systems activated within the γ matrix are identified based on the type of the applied stress and their intrinsic plastic strain is calculated. The simulation models the formation of rafting under the applied stress and investigates the evolution of the microstructure during the rafting process in nickel-based single crystal superalloys. This study focuses on the effect of plastic strain within γ channels on the formation of the rafting morphology during the early stages of creep formation. Plastic strain generated under externally applied tensile stress promotes the preferential growth of γ′ precipitates along specific directions, which is the primary cause of γ′ phase rafting. Moreover, the lattice misfit directly determines the type of rafting (N-type or P-type). The spacing of dislocations at the γ′/γ interfaces, such as along {001} planes, significantly affects the morphology (aspect ratio) of γ′ precipitates but does not influence the growth kinetics or volume of γ′ precipitates at a given time step. In contrast to tensile stress, shear stress induces rafting microstructure coarsening at angles of approximately 30° or 60° relative to the horizontal direction, closely associated with activated slip systems. Additionally, different combinations of slip systems can result in the distortion of γ channels.

Owing to the important role of homogeneous nucleation in grain refinement of rapidly solidified alloys, a detailed molecular dynamics simulation is performed to investigate the incubation of embryos and their evolution into nuclei during the isothermal crystallization of liquid Al droplets. Using the cluster type index method (CTIM) based on Honeycutt-Andersen (H-A) bond-type indices, various fcc critical nuclei formed during isothermal crystallization are distinguished from numerous fcc embryos through reverse tracking of atomic trajectories, relying on the structural heredity of fcc single-crystal clusters. The results show that nuclei first appear in the shell region of Al droplets with a critical size (n_{\mathrm{c}}) ranging from 2 to 100 atoms at an undercooling of ΔT ≈ 0.41T_m (T_m is melting point). Both the steady-state nucleation rate (I₀) and the average critical nucleus size ({\overline{n}}_{\mathrm{c}}) in the shell are higher than those in the core region. Visual analysis of the geometry of critical nuclei reveals that most are non-spherical, and the liquid-solid interface is not a simple fcc-liquid dual-phase configuration, but rather a multi-phase structure involving fcc-liquid and hcp components. Compared with the nucleation in Al bulk, a longer average nucleation incubation time ({\overline{\tau }}_{\mathrm{c}}) of critical nuclei is observed in Al droplets, with {\overline{\tau }}_{\mathrm{c}} in the shell region being longer than that in the core. When {\overline{\tau }}_{\mathrm{c}} is divided into the average incubation time of embryos ({\overline{\tau }}_{\mathrm{e}}) and their average effective growth time ({\overline{\tau }}_{\mathrm{g}}^{\mathrm{e}\mathrm{f}\mathrm{f}}), it is determined that {\overline{\tau }}_{\mathrm{g}}^{\mathrm{e}\mathrm{f}\mathrm{f}} is considerably longer than {\overline{\tau }}_{\mathrm{e}} in both Al droplets and Al bulk. For the four modes of nucleation, i.e., (I) embryo incubation and subsequent effective growth, (II) only effective growth of embryos, (III) direct nucleation after embryo incubation, and (IV) direct transformation from liquid atoms, a tracking analysis of atomic trajectories reveals that few critical nuclei are formed directly from liquid atoms. In contrast, most critical nuclei undergo both embryo incubation and effective growth, and these exhibit the largest {\overline{n}}_{\mathrm{c}}. Moreover, the incubation time ({\tau }_{\mathrm{e}}) of embryos has little effect on {\overline{n}}_{\mathrm{c}} of critical nuclei, whereas a large {\overline{n}}_{\mathrm{c}} typically requires a long effective growth time ({\tau }_{\mathrm{g}}^{\mathrm{e}\mathrm{f}\mathrm{f}}) of embryos during isothermal crystallization.

Gd and its alloys are good magnetic materials, and the addition of the transition metal Co to Gd-Ti alloy can facilitate the formation of thermally stable magnetic compounds. The Gd-Co-Ti alloy exhibits significant potential for the development of magnetic in situ composite materials. However, because of the large positive mixing enthalpy between Gd and Ti, the Gd-Co-Ti alloy is a typical monotectic alloy, exhibiting a miscibility gap in the liquid state. Under the ground gravity conditions, the alloy tends to form a phase-segregated solidification microstructure resulting from liquid-liquid phase transformation. Strong convection in the melt during solidification aggravates this process, rendering it difficult for various influencing factors to interact. However, research on solidification theory for these alloys is limited. Microgravity environments can effectively weaken or even eliminate natural convection in alloy melts, which is beneficial for studying the solidification process and microstructure formation in monotectic alloys. Previous studies have focused on the phase structures, material properties, and thermodynamic behavior of Gd-Co-Ti ternary monotectic alloys. However, research on their solidification process is sparse. In this study, rapid and sub-rapid solidification experiments under drop-tube microgravity conditions were performed using Gd-Co-Ti ternary monotectic alloys. The effects of cooling rates on the solidification microstructure of the alloy were investigated. The resulting samples exhibited a composite microstructure comprising homogeneously dispersed subspherical TiCo-rich particles in the Gd matrix. These particles include: (i) TiCo-rich phase particles formed via liquid-liquid phase transformation, and (ii) TiCo-rich nanoparticles formed through desolventizing precipitation during the cooling process after solidification. To elucidate the microstructure evolution in Gd-Co-Ti alloys solidified under drop-tube conditions, a population dynamics model was established. The model comprehensively considers the thermal and mass transfer characteristics during solidification, as well as the nucleation, growth, and spatial motions of TiCo-rich phase droplets. The algorithm for solving the controlling equations in this model was developed based on the finite volume method. The microstructure formation was simulated, and the results were consistent with the experimental data, thus validating the accuracy of the model. The numerical results demonstrated that the nucleation of the TiCo-rich phase droplets occurred during the liquid-liquid phase transformation under drop-tube microgravity conditions. The number density of these TiCo-rich phase droplets remained unchanged after nucleation, indicating that the Ostwald coarsening of the TiCo-rich droplets was weak during the cooling of the alloy melt. Thus, nucleation and diffusion growth were the primary factors influencing the size of TiCo-rich phase droplets formed during the liquid-liquid phase transformation. With the increase in the sample sizes, the cooling rate of the alloy melt and the number density of the TiCo-rich particles decreased; thus, the average radius of the TiCo-rich particles in the solidification microstructure increased. Furthermore, the maximum nucleation rate (I_DMax) and the number density (N_D) of the TiCo-rich phase droplets/particles exhibited an exponential dependence on the cooling rate ({\dot{T}}_{\mathrm{n}\mathrm{u}\mathrm{c}}) during the nucleation period as per the following expression: I_{\mathrm{D}\mathrm{M}\mathrm{a}\mathrm{x}} = 7.202 × 10^-5{\left({\dot{T}}_{\mathrm{n}\mathrm{u}\mathrm{c}}\right)}^{\mathrm{2.2}} and N_{\mathrm{D}} = 3.385 × 10^-4{\left({\dot{T}}_{\mathrm{n}\mathrm{u}\mathrm{c}}\right)}^{\mathrm{1.3}}.