Methodology Transfer from Titanium to Zirconium Alloys via Machine Learning: Development of Superior Orthopedic Alloys

Methodology Transfer from Titanium to Zirconium Alloys via Machine Learning: Development of Superior Orthopedic Alloys | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Methodology Transfer from Titanium to Zirconium Alloys via Machine Learning: Development of Superior Orthopedic Alloys S.X. Liang, Z.C. Yin, X.K. Liu, J.S. Zhang, S.Z. Zhang, Y.X. Guo, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9432897/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Some efficient design strategies have been proposed for low-modulus Ti-based alloys, yet these approaches may not be applicable to Zr-based alloys, especially for alloys containing strongly interacting elements. Owing to its favorable biological performance, Zr alloy is regarded as a leading candidate for next-generation orthopedic materials. Here, we present a machine-learning-guided, energy-based design strategy that reliably identifies the low-modulus compositional window in Zr/Ti alloys, including alloy systems with significant elemental interactions. Using this approach, we design a metastable β-type Zr-10Ti-15Nb alloy exhibiting a low Young's modulus of E=52.3±2.8 GPa. Through controlled thermomechanical processing, we produce an optimized specimen with a modulus of E=58.0±2.6 GPa and a yield strength of YS=941±28 MPa, resulting an exciting elastic admissible strain (EAS=YS/E) of 1.62%, surpassing nearly all reported Zr alloys. Combined with its low magnetic susceptibility (MS=141 ppm), this specimen achieves a record critical key metric EAS/MS ratio among permanent implant metallic materials. The alloy also demonstrates superior biocompatibility relative to clinically used titanium alloys. Our findings developed a promising orthopedic candidate material with comprehensively enhanced performance. More importantly, we provide a transferable and generalizable design framework for biomedical alloys to achieve a low Young's modulus and high yield strength. Physical sciences/Materials science/Biomaterials/Implants Physical sciences/Materials science Zirconium alloy Methodology transfer Excellent comprehensive performance Orthopedic alloy Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction The rapid aging of the global population, together with the rising incidence of sports-related injuries, has generated increasing demand for high-performance permanent orthopedic implants. An ideal implant material must concurrently exhibit excellent biocompatibility and mechanical compatibility with the surrounding bone environment 1 . In particular, its elastic modulus should closely approximate that of natural bone to mitigate the “stress shielding” effect 2 . Sufficient strength, especially yield strength, is equally essential to prevent irreversible deformation or even catastrophic fracture under physiological loading. Namely, a high elastic admissible strain ( EAS = YS/E ) is required. Furthermore, magnetic resonance imaging (MRI) has become an increasingly prevalent and indispensable clinical tool. MRI compatibility demands that implant materials possess low magnetic susceptibility ( MS ) to avoid pronounced imaging artifacts, implant displacement, heat generation, and potential tissue damage during scanning. Consequently, the ratio of elastic admissible strain to magnetic susceptibility ( EAS/MS ) has emerged as a key metric for long-term orthopedic applications 3–5 . Commercially pure titanium (CP Ti) and its alloys (e.g., TC4: Ti-6Al-4V) currently dominate clinical practice. However, their elastic modulus (~110 GPa) remains substantially higher than that of human bone (10-30 GPa), and they exhibit high magnetic susceptibility (~195 ppm; SI units are used throughout), which generates pronounced MRI artifacts and may induce implant displacement or tissue injury in strong magnetic fields 6,7 . Compared with titanium, zirconium offers superior biocompatibility 8,9 , markedly lower magnetic susceptibility (~123 ppm) 10,11 , and a lower elastic modulus (~90 GPa). These attributes make zirconium alloys promising candidates for next-generation permanent orthopedic implants 12,13 . Nevertheless, the EAS/MS ratios of existing zirconium alloys remain inadequate for demanding long-term load-bearing applications, thereby hindering their clinical translation. The key to enhancing the EAS/MS ratio lies in reducing the Young’s modulus and increasing the yield strength while preserving low magnetic susceptibility. Metastable β zirconium-based and titanium-based alloys can display substantially reduced elastic modulus 14–16 , underscoring the importance of β-phase stability as a critical design parameter. Conventional composition design strategies rely on empirical descriptors, such as the molybdenum equivalent, the Bo - Md electronic orbital parameters, or the average valence electron number ( e/a ) 14,16,17 . Although effective for Ti alloys containing a single principal element with minor additions, these methods fail to capture the complex electronic interactions in multi-principal-component Zr/Ti alloy systems. For example, in (Zr,Ti)-Mo system, the pronounced disparity in Bo and Md values 13,18 for Mo in body-centered cubic Zr and Ti solutions introduces ambiguity into the averaged parameters and yields unreliable predictions of β-phase stability. Consequently, existing empirical approaches are not readily transferable to unconventional alloy systems featuring strong compositional interactions, revealing a clear methodological gap in the design of metastable β alloys. Here, we address this challenge by introducing a machine-learning-enabled methodology transfer strategy that maps mechanical property targets from titanium to zirconium alloys while explicitly accounting for their intrinsic differences, thereby facilitating the design of low-modulus orthopedic zirconium alloys. This framework circumvents the limitations of traditional empirical rules and enables reliable prediction of low-modulus compositions in chemically complex zirconium alloys. Guided by this approach and combined with targeted microstructural tailoring, we develop a zirconium alloy that exhibits an exceptional combination of properties: a low elastic modulus, simultaneously high yield strength, and a record EAS/MS ratio, all while maintaining outstanding biocompatibility. Beyond delivering a high-performance orthopedic implant material, this work establishes a general design paradigm for multi-component metallic systems in which low modulus and high strength can be achieved concurrently. Results Design Strategy Metallic zirconium exhibits superior biocompatibility relative to titanium, yet premium permanent orthopedic implants remain dominated by titanium and its alloys. This disparity largely reflects the greater maturity of the theoretical framework and processing technologies developed for titanium systems. Zirconium and titanium belong to the same group in the periodic table and share closely related chemical and physical properties, including crystal structures, temperature-driven phase transitions, common β-stabilizing elements (such as Mo, Nb, Ta, Fe, and V), microstructural evolution pathways, and established heat-treatment protocols ( Fig. 1 ). These similarities provide a robust physical basis for transferring alloy design principles and performance targets from titanium to zirconium systems, particularly for developing metastable β alloys with low elastic modulus and high yield strength. Despite these parallels, zirconium and titanium alloys differ intrinsically in atomic size, electronic structure, phase-transition temperature, and the stabilizing efficiency of β-forming elements. To address this challenge, we propose an energy-based composition design strategy that combines methodology transfer from titanium alloys with machine-learning-assisted optimization of intrinsic differences. In this framework ( Fig. 1 ), key thermodynamic and electronic descriptors governing β -phase stability and elastic response are extracted from titanium alloy systems and employed as transferable performance targets ( Extended Data Fig. 1a ). Machine learning is then used to capture the non-linear relationships among composition, phase stability, and elastic modulus in zirconium-based multi-component systems, enabling systematic correction for element-specific differences and interaction effects. Using this method, the composition windows for metastable β Zr/Ti alloys with low elastic modulus were determined as C 500 < C Emin < C 400 ( Fig. 1 ). Here, C 500 and C 400 denote the β -stabilizer contents at which the Gibbs free energies of the α and β phases are equal at 500 K and 400 K, respectively. C Emin is the corresponding content at which the elastic modulus reaches its minimum from experiment results. We apply this strategy to the Zr–Ti–Nb system, where the model predicts a well-defined low-modulus compositional region (predicted CLE region in Fig. 1 ). Given that the Zr-10Ti alloy in the binary Zr-Ti system exhibits a favorable combination of low elastic modulus and high strength 19 , the Zr-10Ti- x Nb system was selected for further investigation. The C 400 and C 500 values for this system are 13.6 wt.% and 16.7 wt.% Nb, respectively ( Extended Data Fig. 2 ). Accordingly, a premium orthopedic zirconium alloy, Zr-10Ti-15Nb (blue star in Extended Data Fig. 1b, hereafter abbreviated ZTN), was developed. Properties The designed Zr-10Ti-15Nb alloy exhibits an exceptional synergy of low Young’s modulus and high yield strength, typical after hot rolling at 525 °C (specimen R525) or solid solution treatment at 850 °C (specimen ST850). Fig. 2 a presents representative stress-strain curves for specimens R525 and ST850. Specimen ST850 possesses the lowest Young's modulus of 52.3±2.8 GPa, along with a high yield strength of 727±17 MPa, an elastic admissible strain of 1.40%, and good ductility of 24.2±2.6%. Relative to ST850, specimen R525 shows a marked increase in yield strength, by nearly 30% to 941±28 MPa, with only a slight increase in modulus to 58.0±2.6 GPa, resulting in an elastic admissible strain of 1.62% that surpasses nearly all Zr alloy systems 20–30 ( Fig. 2 b ). In addition, magnetic susceptibility measurements reveal a relatively low volume magnetic susceptibility of ~141 ppm ( Extended Data Fig. 3 ), which is substantially lower than that of TC4 alloy (~195 ppm). Ultimately, the key metric EAS/MS reaches an impressive value of 115, significantly exceeding the previously highest value of 108 for reported Zr-based and Ti-based alloy systems 20–35 ( Fig. 2 c ), and underscoring the material’s considerable potential for load-bearing bone implant applications 36 . Furthermore, the alloy demonstrates outstanding biological performance. Its relative average cell viability is approximately 91.1%, surpassing that of commercially pure titanium (CP Ti, ~82.5%) and TC4 (~89.4%), both of which are clinical mainstays ( Fig. 2 d, Extended Data Fig. 3 ). This outcome is attributable to the superior biocompatibility of Zr and Nb relative to Ti, Al, V, and other common alloying elements 8 . Long-term in vivo biocompatibility evaluations have already confirmed that Zr-Ti-Nb series alloys exhibit exceptional biocompatibility in both subcutaneous and bone tissues 37 . In summary, the Zr-10Ti-15Nb alloy (specimen R525) exhibits superior comprehensive properties, including a record EAS/MS ratio, outstanding cell viability, ultra-high yield strength, low Young’s modulus, and low magnetic susceptibility, among low-modulus Zr-based and Ti-based alloys ( Fig. 2 e ) . This alloy shows considerable promise as an extraordinary candidate material for orthopedic implants and has been successfully processed into plates ( Fig. 2 f ) and representative components ( Fig. 2 g ) using industrial routes. Microstructure The synergy of low Young’s modulus and ultrahigh yield strength originates from a hierarchical microstructure comprising grains of multiple scales and morphologies. As shown in Fig. 3 a, the EBSD phase distribution map of specimen R525 reveals a dominant β-phase matrix, with a small fraction (~ 6.5%) of α phase distributed among the β grains. TEM analysis further elucidates the microstructural complexity. Numerous lenticular precipitates are are observed within the β matrix ( Fig. 3 b) . The width of these lenticular precipitates ranges from tens of nanometers to approximately 400 nm. The inset selected-area electron diffraction (SAED) pattern in Fig. 3 b and high-resolution TEM (HRTEM) analysis ( Fig. 3 c ) confirm that these lenticular precipitates possess an orthorhombic structure. Their interplanar spacings perfectly match precisely the {211}, {202}, and {213} planes of α″ martensite 38 . These lenticular grains form through the β → α″ martensitic transformation of the relatively stable β phase during rapid cooling 39 . More importantly, numerous dispersed Zr-rich and Nb-poor nanoscale particles, with an average size of only 60.1 nm, are observed in the vicinity of grain boundaries within the β grain interiors ( Fig. 3 d and Fig. 3 e ). This microstructural feature arises from a specific transformation pathway. According to the calculated phase diagram ( Extended Data Fig. 4 ), the BCC-to-HCP transformation of the Zr-10Ti-15Nb alloy initiates at 557 ℃. The β phase undergoes spinodal decomposition over the temperature range of 530 ℃ to 499 ℃. When hot rolling is performed at 525 ℃, the upper bound of the spinodal decomposition range, the supersaturated β phase obtained by quenching from high temperature after solution treatment undergoes incomplete spinodal decomposition. Through the diffusion and expulsion of Nb atoms, two BCC phases of different composition, an Nb-rich phase ( β Nb-rich ) and a Zr-rich phase ( β Zr-rich ), are formed 20,40 . Concurrently, the externally applied load during rolling strongly inhibits precipitate growth 41–43 , yielding dispersed nanoscale β Zr-rich particles. Additionally, equiaxed ultrafine α grains with an average size of 192 nm are dispersed among β grains ( Fig. 3 f ). This microstructural feature results from the combined action of dynamic precipitation and dissolution mechanisms of the α phase during thermal deformation. The conventional Burgers orientation relationship deviates significantly during this dynamic process. When the deformation temperature T is below T β (the completion temperature of α + β → β transformation), dissolution of grain-boundary α phase ( α GB ) occurs, leading to spheroidization of α GB grains until the original β grain boundaries disappear 44 . Discussion To elucidate the intrinsic mechanism by which specimen R525 attains high yield strength while retaining a low Young’s modulus, detailed microstructural analysis was performed on the specimen after tensile fracture. The results indicate that alloy strengthening arises primarily from the potent hindrance to dislocation motion imparted by the combined influence of ultrafine α grains and dispersed nanoscale β Zr-rich particles. Within the β matrix, dense dislocation loops form around the dispersed β Zr-rich precipitates ( Fig. 4 a ). The Orowan loops generated by the strain field of these nanoprecipitates, together with their physical obstruction of dislocation paths, substantially enhance yield strength and hardness 45 . Meanwhile, "dislocation forests" 46 formed by dislocation accumulation are observed between ultrafine α grains ( Fig. 4 b ). The high-density dislocation forests and loops near interfaces confer ultra-high strength through the synergistic effects of dislocation strengthening and grain refinement strengthening 47 . Because these dislocation forests and loops do not alter the phase constitution, phase structure, or β phase stability, the alloy maintains a low elastic modulus. Coordinated deformation among grains spanning multiple size scales further contributes to the strength enhancement 48 . To verify the strengthening contributions of ultrafine α grains and nanoscale β Zr-rich particles, the rolling temperature was increased to 600 ℃ (specimen R600) to completely dissolve the primary α phase while simultaneously avoiding spinodal decomposition. Following deformation and water cooling, only lenticular α″ martensite formed ( Extended Data Figs. 5a and 5b ). Tensile tests reveal a Young’s modulus (60±2.2 GPa) similar to that of HR525, but a markedly reduced yield strength of 740±19 MPa ( Extended Data Fig. 5c ), a value comparable to that of specimen ST850. This finding further proves the crucial strengthening role of ultrafine α grains and dispersed nanoscale β Zr-rich particles in specimen R525 as a representative metastable β alloy. Moreover, α″ martensite contributes to strength and toughness through distinct mechanisms. Nanotwin structures are observed within ultrafine α″ lenticulars with several hundred nanometers in width ( Fig. 4 c ). Similar twinning phenomena in metastable phases have also been reported after thermal deformation of Zr-Nb alloys 49 . The attainment of tensile strengths exceeding 1600 MPa in titanium alloys is fundamentally attributed to the presence of dense, stable, internally twinned nanoprecipitates 50 . Nanotwin structures in Zr-based and Ti-based alloys have been demonstrated to provide substantial strengthening effects 51 . Geometric Phase Analysis (GPA) of the region adjacent the boundary between nanoscale lenticular α″ grains and matrix reveals that, in addition to exhibiting strain comparable to that of the β matrix, high lattice strain exists along the α″/β boundaries ( Fig. 4 d and Fig. 4 e ). This observation indicates that α″ grains not only strengthen the material by increasing the density of α″/β boundaries but also facilitate the accommodation of plastic deformation. The α″ phase promotes to a pronounced strain partitioning effect during tensile deformation, allowing strain to accumulate within the nanoscale α″ grains and thereby preserving the material ductility 52 . To validate the generality of the proposed design strategy for low-modulus metastable β zirconium alloys ( C 500 ≤ C Emin ≤ C 400 ), a series of Zr-15Nb- x Ti ( x = 5, 7.5, 10, 12.5, 15, 17.5, 20, and 30 wt.%) with compositions situated within the predicted CLE region of the Zr-Ti-Nb system ( Extended Data Fig. 6a ) were designed and prepared. Room-temperature tensile results demonstrate that the Young's modulus of the designed alloys first decreases, then increases, and ultimately stabilizes with increasing Ti content ( Extended Data Fig. 6b ). Zr-15Nb- x Ti alloys with Ti contents ranging from 10 to 30 wt.% all exhibit low Young's moduli (< 65 GPa). These results clearly demonstrate that the strong applicability and reliability of the proposed design strategy for predicting properties of complex alloy systems, particularly those containing high concentrations of strongly interacting elements, and provide a broadly applicable tool for the rational design of next-generation orthopedic implant materials. In summary, we have established a composition design strategy for low-modulus metastable β zirconium alloys, defined by C 500 ≤ C Emin ≤ C 400 , through the transfer of well-established methodologies from titanium alloys. The Zr-10Ti-15Nb alloy designed according to this strategy exhibits a Young's modulus as low as 52.3±2.8 GPa. Through the construction of a multi-scale, multi-morphological microstructure, an exceptional synergy of low modulus (58.0±2.6 GPa), ultra-high yield strength (941±28 MPa), and a high elastic admissible strain of 1.62% is realized. Coupled with its low magnetic susceptibility, the specimen achieves a record EAS/MS value of 115 among reported metallic orthopedic materials. These outstanding properties originate from the synergistic strengthening contributions of ultrafine α grains and dispersed nanoscale β Zr-rich particles, which provide potent precipitation strengthening and grain refinement strengthening, together with the deformation twinning effect of ultrafine α″ lenticulars. Biological evaluation confirms its superior biocompatibility relative to CP Ti and TC4. These findings present an ideal material candidate for orthopedic implants capable of mitigating the risks of “stress shielding”, stress concentration cracking, cytotoxicity, and MRI artifacts, while also supplying a powerful design strategy for high-performance medical metallic materials. Methods Machine Learning Methods The machine learning framework integrates compositional descriptors, phase-stability parameters, and elastic property data from zirconium- and titanium-based alloy systems. A total of 356 alloy compositions were collected from literature, experimental measurements, and thermodynamic calculations, covering a broad compositional range of β -stabilizing elements and elastic moduli. Model robustness was further validated by independent experimental synthesis and mechanical testing of newly designed alloys. Compositional descriptors include elemental concentrations, valence electron concentration, atomic size mismatch, electronegativity difference, and mixing enthalpy. Phase-stability descriptors were derived from CALPHAD-based thermodynamic calculations, wherein the Gibbs free energy difference Δ G β→α was computed as a function of composition and temperature. To predict elastic modulus, a neural network was employed. The network consists of an input layer corresponding to the number of compositional and phase-stability descriptors, three hidden layers with 128, 64, and 32 neurons respectively, each followed by ReLU activation, and a single output neuron predicting the elastic modulus. Dropout (rate = 0.2) was applied between hidden layers to mitigate overfitting, and batch normalization was used to stabilize training. Hyperparameters, including learning rate and weight decay, were optimized via five-fold cross-validation, and model performance was evaluated using the coefficient of determination ( R 2 ) and mean absolute error (MAE). To incorporate physical constraints, a critical compositional parameter from metastable β titanium alloys was introduced. The β -stabilizer concentration required to suppress the martensitic transformation, C M , corresponds to Δ G β→α = 0 at a characteristic temperature TM . Since C M is experimentally difficult to determine, it was approximated by C TM from thermodynamic calculations. Based on the physical inference that the composition yielding the minimum elastic modulus ( C Emin ) is close to this critical value, the relationship C Emin ≈ C M ≈ C TM was implemented in the neural network through a physics-guided regularization term. Specifically, the total loss function was defined as: where f θ represents the neural network prediction of elastic modulus. This gradient-based penalty encourages the network to form a local minimum of the predicted elastic modulus near the thermodynamically inferred critical composition, ensuring that low-modulus predictions are physically consistent. This strategy allows the model to capture nonlinear couplings among composition, phase stability, and elastic modulus while guiding exploration of low-modulus β -phase alloy compositions within physically reasonable regions of the high-dimensional compositional space. Phase Diagram Calculation Equilibrium thermodynamic simulations based on the CALPHAD method were conducted to predict and analyze the pseudo-binary phase diagram of the Zr-10Ti- x Nb alloy system and the temperature-dependent phase evolution for the Zr-10Ti-15Nb alloy. Calculations were performed using Thermo-Calc software (version 2024a) with the TCTI5 and TTZR1 thermodynamic databases. The pseudo-binary phase diagram for the Zr-10Ti-xNb system was obtained. Continuous data describing the phase constitution of the Zr-10Ti-15Nb alloy as a function of temperature were extracted and exported. Using the post-processing module, corresponding curves of phase volume fraction versus temperature were generated. Consequently, the regions of different phase constitutions within the system were determined, together with the corresponding alloy compositions and temperature conditions associated with key solid-state phase transformations. Material Preparation Industrial sponge zirconium (Zr+Hf > 99.7 wt.%, Hf = 1.5-2.5 wt.%), pure titanium (99.9 wt.%), and high-purity niobium (99.95 wt.%) were weighed according to the nominal composition Zr-10Ti-15Nb (wt.%) after ultrasonic cleaning and drying. The total mass was 5 kg. The blended raw materials were melted in a vacuum copper crucible suspension furnace under a protective high-purity argon atmosphere following evacuation of the chamber to 10 -3 Pa. The resulting ingot was furnace-cooled to room temperature. The alloy ingot was then subjected to three-stage open-die forging: first at 1000 °C, second at 900 °C, and third at 850 °C. After forging, the surface was turned, ground, and cleaned to obtain plates with dimensions of 50 mm × 20 mm × L (length). The forged plates were cut longitudinally into square bars of 50 mm × 20 mm × 20 mm, which were further processed via either hot rolling or solution treatment. For hot rolling, samples were held at 525 °C or 600 °C for 30 min, followed by multi-pass rolling with a reduction of ~5% per pass. Between passes, samples were returned to the furnace for 5 min. The total rolling reduction was ~80%. After the final pass, samples were immediately water quenched. These specimens were designated R525 and R600 according to their respective rolling temperatures. For solution treatment, cut square bars were heated to 850 °C at 10 °C/min under an argon atmosphere in a vacuum tube furnace, held for 20 min, and then water quenched. These samples were labeled ST850. To verify the generality of the alloy design strategy, additional alloys with nominal compositions Zr-15Nb- x Ti ( x = 5, 7.5, 10, 12.5, 15, 17.5, 20, and 30 wt.%) were prepared. Each alloy weighed 120 g. Melting was performed in an argon-protected vacuum non-consumable arc melting furnace, with each ingot flipped and remelted at least six times to ensure homogeneity. The as-cast ingots were homogenized at 950 °C for 4 h under argon, followed by water quenching, and then hot-rolled at 750 °C using the same rolling procedure described above. All processed samples were ground and cut into appropriate shapes and dimensions for subsequent analyses. Microstructure Characterization The microstructure was systematically characterized using electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM). For EBSD sample preparation, mounted samples were sequentially ground with 400, 800, 1200, 2000, and 5000 grit SiC papers. This was followed by sequential polishing using a 1 μm alumina suspension and a 50 nm silica suspension. Subsequently, the samples were subjected to Ar ion milling in a Leica EM TIC 3X triple-ion-beam mill under the following sequential conditions: 6 kV at 9° for 120 min, follow by 4 kV at 6° for 10 min. After preparation, samples were examined in a scanning electron microscope equipped with an EBSD detector. EBSD analysis was performed at an accelerating voltage of 20 kV and a beam current of approximately 10 nA. The scanning step size was adjusted between 0.05 and 0.5 μm, depending on the grain size of the observed area. For TEM, thin slices (~0.5 mm thick) were cut by wire electrical discharge machining, mechanically ground to below 40 μm, and punched into 3 mm diameter discs. After ultrasonic cleaning in acetone and ethanol, the discs were twin-jet electropolished in a solution of 10% perchloric acid in methanol at temperatures below -20 °C and a voltage of 15.5 V. Samples were then cleaned, dried, and examined using TEM operated at 200 kV. Bright-field and dark-field imaging, along with selected-area electron diffraction were employed for comprehensive microstructural analysis. Mechanical Property Testing Tensile specimens with a gauge length of 18 mm, width of 3 mm, and thickness of 2 mm were machined along the rolling direction via wire cutting. Room-temperature tensile tests were performed on an Instron 5982 mechanical testing system at a strain rate of 5×10 -4 s -1 monitored by a high-precision extensometer with a gauge length of 10 mm. At least three valid tests were conducted for each condition. Biocompatibility Evaluation Cytotoxicity was assessed using human osteosarcoma cells (MG-63) via an extract test. Disc-shaped samples were ultrasonically cleaned in ethanol, sterilized at 121 °C for 20 min in an autoclave, dried, and placed in sterile 15 mL centrifuge tubes. α -Minimum Essential Medium ( α -MEM) supplemented with 10% fetal bovine serum and 1% penicillin-streptomycin was added, and extracts were obtained after 7 days of immersion. Cells were seeded at densities of 2×10 4 cells per well in 24-well plates for fluorescence imaging and 1×10 4 cells per well in 96-well plates for viability assays. After adherence, the culture medium was replaced with the respective alloy extracts. Controls included extracts from commercially pure Ti (CP Ti) and Ti-6Al-4V (TC4), as well as extract-free medium. After 24 h of incubation, the medium was removed and cells were washed with phosphate-buffered saline (PBS). A live/dead double-staining kit (Calcein-AM/PI) was applied to 24-well plates for fluorescence observation. For 96-well plates, cell viability was evaluated using a CCK-8 assay, with absorbance measured at 450 nm using a microplate reader. Each experiment was performed with three independent samples, six biological replicates, and three technical replicates. Magnetic Susceptibility Measurement Samples with dimensions of 2 × 2 × 0.5 mm 3 were prepared by electrical discharge machining, ground to 2000 grit with SiC paper, cleaned, and dried. Magnetization curves (magnetization M in emu/g versus applied magnetic field H in Oe) were measured using a Physical Property Measurement System (MPMS-SQUID, Quantum Design) at 37 °C over a field range of -4 T to 4 T. Declarations Data Availability The data supporting this study are available in the main text. Raw CALPHAD data are protected and are not available due to the restrictions imposed by the Thermo-Calc End User License Agreement (EULA). Additional data are available from the corresponding authors upon request. Source data are provided with this paper. Code availability All code used for analysing the raw data is available upon request from the corresponding authors. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 52125405/52471148/52127808/52071278/U22A20108), Hebei Natural Science Foundation (Grant no. 242Q9906Z), Backbone Talent Program of Hebei Province (Overseas Returnees Platform) (Grant no. A2025009), the Science Research Project of Hebei Education Department (Grant No. KJZX202201), and Just Medical Devices (Tianjin) Co., Ltd. (Grant no. x2026030). Author Contributions Statement Z.C. Y., X.K. L. and S.X. 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Additional Declarations There is NO Competing Interest. Supplementary Files ExtendedDataFig.docx Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9432897","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":624340338,"identity":"d07efa0e-9c5e-429f-8c86-0e338bb4f245","order_by":0,"name":"S.X. Liang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2klEQVRIiWNgGAWjYFAC5oYDQFIOwmEjSgsjWIsxaVpAZGID0VrkZyQ2Hvi5ozZ9w/kzBgwfyg4z8M9uwK/F4MzBhoO9Z47nbriRY8A449xhBok7BwhoYW9sOMDbdgyohceAmbftMIOBRAIBhzUzNhz823Ys3QDoMOa/xGhhON7YcJi3rSbB4ECOATMjMVpAfjks23bAcOaNtIKDPefSeSRuEHLYjOTDH9+21cnznT+88cGPMms5/hmEHAYBhxkUDjAwABEDD1HqgaCOQb6BWLWjYBSMglEw4gAA4HxMM/9OI9gAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0002-6038-139X","institution":"Yanshan University","correspondingAuthor":true,"prefix":"","firstName":"S.X.","middleName":"","lastName":"Liang","suffix":""},{"id":624340339,"identity":"156dac86-37d8-4400-a569-aea86e2a3649","order_by":1,"name":"Z.C. Yin","email":"","orcid":"","institution":"Yanshan University","correspondingAuthor":false,"prefix":"","firstName":"Z.C.","middleName":"","lastName":"Yin","suffix":""},{"id":624340340,"identity":"af47cce3-7b3b-4767-ae0b-7de10d443f43","order_by":2,"name":"X.K. Liu","email":"","orcid":"","institution":"Yanshan University","correspondingAuthor":false,"prefix":"","firstName":"X.K.","middleName":"","lastName":"Liu","suffix":""},{"id":624340341,"identity":"b109eef8-1048-4a9e-aa8f-96e4c78847c5","order_by":3,"name":"J.S. Zhang","email":"","orcid":"","institution":"Yanshan University","correspondingAuthor":false,"prefix":"","firstName":"J.S.","middleName":"","lastName":"Zhang","suffix":""},{"id":624340342,"identity":"b99fb808-4b84-43a1-ac3a-41b3e94f5ef6","order_by":4,"name":"S.Z. Zhang","email":"","orcid":"","institution":"Yanshan University","correspondingAuthor":false,"prefix":"","firstName":"S.Z.","middleName":"","lastName":"Zhang","suffix":""},{"id":624340343,"identity":"59256a61-daad-40e9-a81d-201be5676c58","order_by":5,"name":"Y.X. Guo","email":"","orcid":"","institution":"Yanshan University","correspondingAuthor":false,"prefix":"","firstName":"Y.X.","middleName":"","lastName":"Guo","suffix":""},{"id":624340344,"identity":"87173471-00c3-4142-a5d4-3f4be5ae7ea4","order_by":6,"name":"M.Z. Ma","email":"","orcid":"","institution":"Yanshan University","correspondingAuthor":false,"prefix":"","firstName":"M.Z.","middleName":"","lastName":"Ma","suffix":""},{"id":624340345,"identity":"9e42c0cf-d34e-4738-bf22-c424108263df","order_by":7,"name":"S.D. Feng","email":"","orcid":"","institution":"Yanshan University","correspondingAuthor":false,"prefix":"","firstName":"S.D.","middleName":"","lastName":"Feng","suffix":""},{"id":624340346,"identity":"de38ab93-58fa-4cc0-b56b-bd8676084829","order_by":8,"name":"X.Y. Zhang","email":"","orcid":"","institution":"Yanshan University","correspondingAuthor":false,"prefix":"","firstName":"X.Y.","middleName":"","lastName":"Zhang","suffix":""},{"id":624340347,"identity":"11f4d223-804e-4657-b608-55b2fb495552","order_by":9,"name":"R.P. Liu","email":"","orcid":"","institution":"Yanshan University","correspondingAuthor":false,"prefix":"","firstName":"R.P.","middleName":"","lastName":"Liu","suffix":""}],"badges":[],"createdAt":"2026-04-16 04:15:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9432897/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9432897/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108181422,"identity":"f426c0dc-e32d-4300-bb83-d36377dfc39f","added_by":"auto","created_at":"2026-04-30 08:58:38","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":291322,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMachine-learning-enabled composition design strategy for low-modulus alloys. \u003c/strong\u003eSchematic illustration of the knowledge transfer framework from titanium to zirconium systems. Shared physical principles are leveraged to define transferable descriptors, while machine learning accounts for intrinsic elemental differences and complex interactions in multi-component Zr alloys. A theoretical criterion is obtained to design the composition of Zr alloys with low Young’s modulus. Application of this strategy to the Zr-Ti-Nb system identifies a low-modulus composition window. \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003eT\u003c/em\u003e\u003c/sub\u003e: β stabilizer content at which the Gibbs free energy of the α phase equals that of the β phase at temperature \u003cem\u003eT\u003c/em\u003e K. \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003eEmin\u003c/em\u003e\u003c/sub\u003e: β stabilizer content corresponding to the minimum Young’s modulus. \u003cem\u003eCLE\u003c/em\u003e: composition region of the Zr-Ti-Nb system predicted to exhibit low Young’s modulus.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-9432897/v1/4fd9e00b360ba54f247f6309.png"},{"id":108181647,"identity":"c5593f51-12b5-4f47-b3df-0fa60d19c492","added_by":"auto","created_at":"2026-04-30 08:58:49","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":535728,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eProperties of the Zr-10Ti-15Nb alloy.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e, Stress-strain curves for specimens R525 and ST850. \u003cstrong\u003eb\u003c/strong\u003e, Yield strength versus Young’s modulus for reported Zr alloys. \u003cstrong\u003ec\u003c/strong\u003e, \u003cem\u003eEAS/MS\u003c/em\u003eversus Young’s modulus for reported Zr-based and Ti-based alloy systems. \u003cstrong\u003ed\u003c/strong\u003e, Comparison of cell viability for ZTN (R525), CP Ti and TC4. \u003cstrong\u003ee\u003c/strong\u003e, Comprehensive property of this work (R525) comparison with low-modulus Zr-based and Ti-based alloys (with TC4 shown as a special case). \u003cstrong\u003ef and g\u003c/strong\u003e, ZTN alloy plates and implant prototypes fabricated using industrially relevant routes.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-9432897/v1/c2900b0e15c1b9f1521b44c6.png"},{"id":108076889,"identity":"815027e9-4946-41a4-b612-efb56aa8de36","added_by":"auto","created_at":"2026-04-29 07:05:21","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1177792,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMicrostructure of the Zr-10Ti-15Nb alloy after hot rolling at 525 °C.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e, EBSD phase distribution map. \u003cstrong\u003eb and c\u003c/strong\u003e, TEM bright-field (BF) image with inset SAED pattern and HRTEM image showing lenticular α″ martensite. \u003cstrong\u003ed and e\u003c/strong\u003e TEM BF image with inset SAED pattern and element distribution maps revealing the dispersed nano-sized Zr-rich \u003cem\u003eβ\u003c/em\u003e particles. \u003cstrong\u003ef\u003c/strong\u003e, BF image with inset SAED pattern showing equiaxed ultrafine α grains among β grains.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-9432897/v1/fc265d8c904bfcaeae92cf66.png"},{"id":108182225,"identity":"ef860b49-da2f-4c2f-8956-951bd82143ea","added_by":"auto","created_at":"2026-04-30 08:59:15","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1242727,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMicrostructure of the Zr-10Ti-15Nb alloy (R525) after tensile fracture\u003c/strong\u003e. \u003cstrong\u003ea\u003c/strong\u003e, Dislocation loops accumulated around a representative nano-sized \u003cem\u003eβ\u003c/em\u003e\u003csub\u003eZr-rich\u003c/sub\u003e particle. \u003cstrong\u003eb\u003c/strong\u003e, Dislocations piled up among ultrafine \u003cem\u003eα\u003c/em\u003e grains, forming a dislocation forest. \u003cstrong\u003ec, \u003c/strong\u003eDeformation twins (M: matrix, T: twin,) within ultrafine \u003cem\u003eα″\u003c/em\u003e lenticulars. \u003cstrong\u003ed\u003c/strong\u003e, Deformed \u0026nbsp;nanoscale \u003cem\u003eα″\u003c/em\u003e lenticulars (white arrows). \u003cstrong\u003ee\u003c/strong\u003e, HRTEM image and strain distribution (GPA results) near the boundary between\u0026nbsp; nanoscale \u003cem\u003eα″\u003c/em\u003e lenticular and \u003cem\u003eβ \u003c/em\u003ematrix, obtained from the boxed region in \u003cstrong\u003ed\u003c/strong\u003e.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-9432897/v1/995f9dc42c5f881963627c6d.png"},{"id":108183804,"identity":"0f34135b-0211-4b34-bf25-47a47b16e2d7","added_by":"auto","created_at":"2026-04-30 09:02:51","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3613653,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9432897/v1/1e94ebc0-6429-444b-b719-824875b47921.pdf"},{"id":108076887,"identity":"e5122863-4cbd-4d4d-b9af-245085755f37","added_by":"auto","created_at":"2026-04-29 07:05:20","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":5936909,"visible":true,"origin":"","legend":"","description":"","filename":"ExtendedDataFig.docx","url":"https://assets-eu.researchsquare.com/files/rs-9432897/v1/eb527840a2cd6d69a3227a5a.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Methodology Transfer from Titanium to Zirconium Alloys via Machine Learning: Development of Superior Orthopedic Alloys","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe rapid aging of the global population, together with the rising incidence of sports-related injuries, has generated increasing demand for high-performance permanent orthopedic implants. An ideal implant material must concurrently exhibit excellent biocompatibility and mechanical compatibility with the surrounding bone environment\u003csup\u003e1\u003c/sup\u003e. In particular, its elastic modulus should closely approximate that of natural bone to mitigate the \u0026ldquo;stress shielding\u0026rdquo; effect\u003csup\u003e2\u003c/sup\u003e. Sufficient strength, especially yield strength, is equally essential to prevent irreversible deformation or even catastrophic fracture under physiological loading. Namely, a high elastic admissible strain (\u003cem\u003eEAS = YS/E\u003c/em\u003e) is required. Furthermore, magnetic resonance imaging (MRI) has become an increasingly prevalent and indispensable clinical tool. MRI compatibility demands that implant materials possess low magnetic susceptibility (\u003cem\u003eMS\u003c/em\u003e) to avoid pronounced imaging artifacts, implant displacement, heat generation, and potential tissue damage during scanning. Consequently, the ratio of elastic admissible strain to magnetic susceptibility (\u003cem\u003eEAS/MS\u003c/em\u003e) has emerged as a key metric for long-term orthopedic applications \u003csup\u003e3\u0026ndash;5\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eCommercially pure titanium (CP Ti) and its alloys (e.g., TC4: Ti-6Al-4V) currently dominate clinical practice. However, their elastic modulus (~110 GPa) remains substantially higher than that of human bone (10-30 GPa), and they exhibit high magnetic susceptibility (~195 ppm; SI units are used throughout), which generates pronounced MRI artifacts and may induce implant displacement or tissue injury in strong magnetic fields\u003csup\u003e6,7\u003c/sup\u003e. Compared with titanium, zirconium offers superior biocompatibility \u003csup\u003e8,9\u003c/sup\u003e, markedly lower magnetic susceptibility (~123 ppm) \u003csup\u003e10,11\u003c/sup\u003e, and a lower elastic modulus (~90 GPa). These attributes make zirconium alloys promising candidates for next-generation permanent orthopedic implants\u003csup\u003e12,13\u003c/sup\u003e. Nevertheless, the \u003cem\u003eEAS/MS\u003c/em\u003e ratios of existing zirconium alloys remain inadequate for demanding long-term load-bearing applications, thereby hindering their clinical translation.\u003c/p\u003e\n\u003cp\u003eThe key to enhancing the \u003cem\u003eEAS/MS\u003c/em\u003e ratio lies in reducing the Young\u0026rsquo;s modulus and increasing the yield strength while preserving low magnetic susceptibility. Metastable \u003cem\u003e\u0026beta;\u003c/em\u003e zirconium-based and titanium-based alloys can display substantially reduced elastic modulus\u003csup\u003e14\u0026ndash;16\u003c/sup\u003e, underscoring the importance of \u0026beta;-phase stability as a critical design parameter. Conventional composition design strategies rely on empirical descriptors, such as the molybdenum equivalent, the \u003cem\u003eBo\u003c/em\u003e-\u003cem\u003eMd\u003c/em\u003e electronic orbital parameters, or the average valence electron number (\u003cem\u003ee/a\u003c/em\u003e) \u003csup\u003e14,16,17\u003c/sup\u003e. Although effective for Ti alloys containing a single principal element with minor additions, these methods fail to capture the complex electronic interactions in multi-principal-component Zr/Ti alloy systems. For example, in (Zr,Ti)-Mo system, the pronounced disparity in \u003cem\u003eBo\u003c/em\u003e and \u003cem\u003eMd\u003c/em\u003e values \u003csup\u003e13,18\u003c/sup\u003e for Mo in body-centered cubic Zr and Ti solutions introduces ambiguity into the averaged parameters and yields unreliable predictions of \u0026beta;-phase stability. Consequently, existing empirical approaches are not readily transferable to unconventional alloy systems featuring strong compositional interactions, revealing a clear methodological gap in the design of metastable \u0026beta; alloys.\u003c/p\u003e\n\u003cp\u003eHere, we address this challenge by introducing a machine-learning-enabled methodology transfer strategy that maps mechanical property targets from titanium to zirconium alloys while explicitly accounting for their intrinsic differences, thereby facilitating the design of low-modulus orthopedic zirconium alloys. This framework circumvents the limitations of traditional empirical rules and enables reliable prediction of low-modulus compositions in chemically complex zirconium alloys. Guided by this approach and combined with targeted microstructural tailoring, we develop a zirconium alloy that exhibits an exceptional combination of properties: a low elastic modulus, simultaneously high yield strength, and a record \u003cem\u003eEAS/MS\u003c/em\u003e ratio, all while maintaining outstanding biocompatibility. Beyond delivering a high-performance orthopedic implant material, this work establishes a general design paradigm for multi-component metallic systems in which low modulus and high strength can be achieved concurrently.\u003c/p\u003e"},{"header":"Results","content":"\u003ch3\u003eDesign Strategy\u0026nbsp;\u003c/h3\u003e\n\u003cp\u003eMetallic zirconium exhibits superior biocompatibility relative to titanium, yet premium permanent orthopedic implants remain dominated by titanium and its alloys. This disparity largely reflects the greater maturity of the theoretical framework and processing technologies developed for titanium systems. Zirconium and titanium belong to the same group in the periodic table and share closely related chemical and physical properties, including crystal structures, temperature-driven phase transitions, common \u0026beta;-stabilizing elements (such as Mo, Nb, Ta, Fe, and V), microstructural evolution pathways, and established heat-treatment protocols (\u003cstrong\u003eFig. 1\u003c/strong\u003e). These similarities provide a robust physical basis for transferring alloy design principles and performance targets from titanium to zirconium systems, particularly for developing metastable \u0026beta; alloys with low elastic modulus and high yield strength. Despite these parallels, zirconium and titanium alloys differ intrinsically in atomic size, electronic structure, phase-transition temperature, and the stabilizing efficiency of \u0026beta;-forming elements.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTo address this challenge, we propose an energy-based composition design strategy that combines methodology transfer from titanium alloys with machine-learning-assisted optimization of intrinsic differences. In this framework (\u003cstrong\u003eFig. 1\u003c/strong\u003e), key thermodynamic and electronic descriptors governing \u003cem\u003e\u0026beta;\u003c/em\u003e-phase stability and elastic response are extracted from titanium alloy systems and employed as transferable performance targets (\u003cstrong\u003eExtended Data Fig. 1a\u003c/strong\u003e). Machine learning is then used to capture the non-linear relationships among composition, phase stability, and elastic modulus in zirconium-based multi-component systems, enabling systematic correction for element-specific differences and interaction effects. Using this method, the composition windows for metastable \u0026beta; Zr/Ti alloys with low elastic modulus were determined as \u003cem\u003eC\u003c/em\u003e\u003csub\u003e500\u0026nbsp;\u003c/sub\u003e\u0026lt; \u003cem\u003eC\u003c/em\u003e\u003csub\u003eEmin\u003c/sub\u003e \u0026lt; \u003cem\u003eC\u003c/em\u003e\u003csub\u003e400\u003c/sub\u003e (\u003cstrong\u003eFig. 1\u003c/strong\u003e). Here, \u003cem\u003eC\u003c/em\u003e\u003csub\u003e500\u003c/sub\u003e and \u003cem\u003eC\u003c/em\u003e\u003csub\u003e400\u003c/sub\u003e denote the \u003cem\u003e\u0026beta;\u003c/em\u003e-stabilizer contents at which the Gibbs free energies of the \u003cem\u003e\u0026alpha;\u003c/em\u003e and \u003cem\u003e\u0026beta;\u003c/em\u003e phases are equal at 500 K and 400 K, respectively. \u003cem\u003eC\u003c/em\u003e\u003csub\u003eEmin\u003c/sub\u003e is the corresponding content at which the elastic modulus reaches its minimum from experiment results. We apply this strategy to the Zr\u0026ndash;Ti\u0026ndash;Nb system, where the model predicts a well-defined low-modulus compositional region (predicted \u003cem\u003eCLE\u003c/em\u003e region in\u0026nbsp;\u003cstrong\u003eFig. 1\u003c/strong\u003e).\u0026nbsp;Given that the Zr-10Ti alloy in the binary Zr-Ti system exhibits a favorable combination of low elastic modulus and high strength\u0026nbsp;\u003csup\u003e19\u003c/sup\u003e, the Zr-10Ti-\u003cem\u003ex\u003c/em\u003eNb system was selected for further investigation. The \u003cem\u003eC\u003c/em\u003e\u003csub\u003e400\u003c/sub\u003e and \u003cem\u003eC\u003c/em\u003e\u003csub\u003e500\u003c/sub\u003e values for this system are 13.6 wt.% and 16.7 wt.% Nb, respectively (\u003cstrong\u003eExtended Data Fig. 2\u003c/strong\u003e). Accordingly, a premium orthopedic zirconium alloy, Zr-10Ti-15Nb\u0026nbsp;(blue star in \u003cstrong\u003eExtended Data Fig. 1b,\u0026nbsp;\u003c/strong\u003ehereafter abbreviated ZTN), was developed.\u003c/p\u003e\n\u003ch3\u003eProperties\u003c/h3\u003e\n\u003cp\u003eThe designed Zr-10Ti-15Nb alloy exhibits an exceptional synergy of low Young\u0026rsquo;s modulus and high yield strength, typical after hot rolling at 525 \u0026deg;C (specimen R525) or solid solution treatment at 850 \u0026deg;C (specimen ST850).\u0026nbsp;\u003cstrong\u003eFig. 2\u003c/strong\u003e\u003cstrong\u003ea\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003epresents representative stress-strain curves for specimens R525 and ST850. Specimen ST850 possesses the lowest Young\u0026apos;s modulus of 52.3\u0026plusmn;2.8 GPa, along with a high yield strength of 727\u0026plusmn;17 MPa, an elastic admissible strain of 1.40%, and good ductility of 24.2\u0026plusmn;2.6%. Relative to ST850, specimen R525 shows a marked increase in yield strength, by nearly 30% to 941\u0026plusmn;28 MPa, with only a slight increase in modulus to 58.0\u0026plusmn;2.6 GPa, resulting in an elastic admissible strain of 1.62% that surpasses nearly all Zr alloy systems\u003csup\u003e20\u0026ndash;30\u003c/sup\u003e (\u003cstrong\u003eFig. 2\u003c/strong\u003e\u003cstrong\u003eb\u003c/strong\u003e). In addition, magnetic susceptibility measurements reveal a relatively low volume magnetic susceptibility of ~141 ppm (\u003cstrong\u003eExtended Data Fig. 3\u003c/strong\u003e), which is substantially lower than that of TC4 alloy (~195 ppm). Ultimately, the key metric \u003cem\u003eEAS/MS\u003c/em\u003e reaches an impressive value of 115, significantly exceeding the previously highest value of 108 for reported Zr-based and Ti-based alloy systems\u003csup\u003e20\u0026ndash;35\u003c/sup\u003e (\u003cstrong\u003eFig. 2\u003c/strong\u003e\u003cstrong\u003ec\u003c/strong\u003e), and underscoring the material\u0026rsquo;s considerable potential for load-bearing bone implant applications\u0026nbsp;\u003csup\u003e36\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFurthermore, the alloy demonstrates outstanding biological performance. Its relative average cell viability is approximately 91.1%, surpassing that of commercially pure titanium (CP Ti, ~82.5%) and TC4 (~89.4%), both of which are clinical mainstays (\u003cstrong\u003eFig. 2\u003c/strong\u003e\u003cstrong\u003ed, Extended Data Fig. 3\u003c/strong\u003e). This outcome is attributable to the superior biocompatibility of Zr and Nb relative to Ti, Al, V, and other common alloying elements \u003csup\u003e8\u003c/sup\u003e. Long-term in vivo biocompatibility evaluations have already confirmed that Zr-Ti-Nb series alloys exhibit exceptional biocompatibility in both subcutaneous and bone tissues\u0026nbsp;\u003csup\u003e37\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn summary, the Zr-10Ti-15Nb alloy (specimen R525) exhibits superior comprehensive properties, including a record \u003cem\u003eEAS/MS\u003c/em\u003e ratio, outstanding cell viability, ultra-high yield strength, low Young\u0026rsquo;s modulus, and low magnetic susceptibility, among low-modulus Zr-based and Ti-based alloys (\u003cstrong\u003eFig. 2\u003c/strong\u003e\u003cstrong\u003ee\u003c/strong\u003e)\u003cstrong\u003e.\u0026nbsp;\u003c/strong\u003eThis alloy shows considerable promise as an extraordinary candidate material for orthopedic implants and has been successfully processed into plates (\u003cstrong\u003eFig. 2\u003c/strong\u003e\u003cstrong\u003ef\u003c/strong\u003e) and representative components (\u003cstrong\u003eFig. 2\u003c/strong\u003e\u003cstrong\u003eg\u003c/strong\u003e) using industrial routes.\u0026nbsp;\u003c/p\u003e\n\u003ch3\u003eMicrostructure\u0026nbsp;\u003c/h3\u003e\n\u003cp\u003eThe synergy of low Young\u0026rsquo;s modulus and ultrahigh yield strength originates from a hierarchical microstructure comprising grains of multiple scales and morphologies. As shown in \u003cstrong\u003eFig. 3\u003c/strong\u003e\u003cstrong\u003ea,\u0026nbsp;\u003c/strong\u003ethe EBSD phase distribution map of specimen R525 reveals a dominant \u0026beta;-phase matrix, with a small fraction (~ 6.5%) of \u0026alpha; phase distributed among the \u003cem\u003e\u0026beta;\u003c/em\u003e grains. TEM analysis further elucidates the microstructural complexity. Numerous lenticular precipitates are are observed within the \u0026beta; matrix (\u003cstrong\u003eFig. 3\u003c/strong\u003e\u003cstrong\u003eb)\u003c/strong\u003e. The width of these lenticular precipitates ranges from tens of nanometers to approximately 400 nm. The inset selected-area electron diffraction (SAED) pattern in \u003cstrong\u003eFig. 3\u003c/strong\u003e\u003cstrong\u003eb\u003c/strong\u003e and high-resolution TEM (HRTEM) analysis (\u003cstrong\u003eFig. 3\u003c/strong\u003e\u003cstrong\u003ec\u003c/strong\u003e) confirm that these lenticular precipitates possess an orthorhombic structure. Their interplanar spacings perfectly match precisely the {211}, {202}, and {213} planes of \u003cem\u003e\u0026alpha;\u0026Prime;\u003c/em\u003e martensite \u003csup\u003e38\u003c/sup\u003e. These lenticular grains form through the \u003cem\u003e\u0026beta;\u003c/em\u003e\u0026rarr;\u003cem\u003e\u0026alpha;\u0026Prime;\u0026nbsp;\u003c/em\u003emartensitic transformation of the relatively stable \u003cem\u003e\u0026beta;\u003c/em\u003e phase during rapid cooling \u003csup\u003e39\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eMore importantly, numerous dispersed Zr-rich and Nb-poor nanoscale particles, with an average size of only 60.1 nm, are observed \u0026nbsp;in the vicinity of grain boundaries within the \u0026beta; grain interiors (\u003cstrong\u003eFig. 3\u003c/strong\u003e\u003cstrong\u003ed and\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003eFig. 3\u003c/strong\u003e\u003cstrong\u003ee\u003c/strong\u003e). This microstructural feature arises from a specific transformation pathway. According to the calculated phase diagram (\u003cstrong\u003eExtended Data Fig. 4\u003c/strong\u003e), the BCC-to-HCP transformation of the Zr-10Ti-15Nb alloy initiates at 557 ℃. The \u003cem\u003e\u0026beta;\u003c/em\u003e phase undergoes spinodal decomposition over the temperature range of 530 ℃ to 499 ℃. When hot rolling is performed at 525 ℃, the upper bound of the spinodal decomposition range, the supersaturated \u003cem\u003e\u0026beta;\u003c/em\u003e phase obtained by quenching from high temperature after solution treatment undergoes incomplete spinodal decomposition. Through the diffusion and expulsion of Nb atoms, two BCC phases of different composition, an Nb-rich phase (\u003cem\u003e\u0026beta;\u003c/em\u003e\u003csub\u003eNb-rich\u003c/sub\u003e) and a Zr-rich phase (\u003cem\u003e\u0026beta;\u003c/em\u003e\u003csub\u003eZr-rich\u003c/sub\u003e), are formed \u003csup\u003e20,40\u003c/sup\u003e. Concurrently, the \u0026nbsp;externally applied load during rolling strongly inhibits precipitate growth \u003csup\u003e41\u0026ndash;43\u003c/sup\u003e, yielding dispersed nanoscale \u003cem\u003e\u0026beta;\u003c/em\u003e\u003csub\u003eZr-rich\u0026nbsp;\u003c/sub\u003eparticles.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAdditionally, equiaxed ultrafine \u003cem\u003e\u0026alpha;\u003c/em\u003e grains with an average size of 192 nm are dispersed among \u003cem\u003e\u0026beta;\u003c/em\u003e grains (\u003cstrong\u003eFig. 3\u003c/strong\u003e\u003cstrong\u003ef\u003c/strong\u003e). This microstructural feature results from the combined action of dynamic precipitation and dissolution mechanisms of the \u003cem\u003e\u0026alpha;\u003c/em\u003e phase during thermal deformation. The conventional Burgers orientation relationship deviates significantly during this dynamic process. When the deformation temperature \u003cem\u003eT\u003c/em\u003e is below \u003cem\u003eT\u003csub\u003e\u0026beta;\u003c/sub\u003e\u003c/em\u003e (the completion temperature of \u003cem\u003e\u0026alpha;\u003c/em\u003e+\u003cem\u003e\u0026beta;\u003c/em\u003e \u0026rarr; \u003cem\u003e\u0026beta;\u003c/em\u003e transformation), dissolution of grain-boundary \u003cem\u003e\u0026alpha;\u003c/em\u003e phase (\u003cem\u003e\u0026alpha;\u003c/em\u003e\u003csub\u003eGB\u003c/sub\u003e) occurs, leading to spheroidization of \u003cem\u003e\u0026alpha;\u003c/em\u003e\u003csub\u003eGB\u003c/sub\u003e grains until the original \u003cem\u003e\u0026beta;\u003c/em\u003e grain boundaries disappear \u003csup\u003e44\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eTo elucidate the intrinsic mechanism by which specimen R525 attains high yield strength while retaining a low Young\u0026rsquo;s modulus, detailed microstructural analysis was performed on the specimen after tensile fracture. The results indicate that alloy strengthening arises primarily from the potent hindrance to dislocation motion imparted by the combined influence of ultrafine \u0026alpha; grains and dispersed nanoscale \u003cem\u003e\u0026beta;\u003c/em\u003e\u003csub\u003eZr-rich\u003c/sub\u003e particles. Within the \u003cem\u003e\u0026beta;\u003c/em\u003e matrix, dense dislocation loops form around the dispersed \u003cem\u003e\u0026beta;\u003c/em\u003e\u003csub\u003eZr-rich\u003c/sub\u003e precipitates (\u003cstrong\u003eFig. 4\u003c/strong\u003e\u003cstrong\u003ea\u003c/strong\u003e). The Orowan loops generated by the strain field of these nanoprecipitates, together with their physical obstruction of dislocation paths, substantially enhance yield strength and hardness \u003csup\u003e45\u003c/sup\u003e. Meanwhile, \u0026quot;dislocation forests\u0026quot; \u003csup\u003e46\u003c/sup\u003e formed by dislocation accumulation are observed between ultrafine \u003cem\u003e\u0026alpha;\u003c/em\u003e grains (\u003cstrong\u003eFig. 4\u003c/strong\u003e\u003cstrong\u003eb\u003c/strong\u003e). The high-density dislocation forests and loops near interfaces confer ultra-high strength through the synergistic effects of dislocation strengthening and grain refinement strengthening\u0026nbsp;\u003csup\u003e47\u003c/sup\u003e. Because these dislocation forests and loops do not alter the phase constitution, phase structure, or \u003cem\u003e\u0026beta;\u003c/em\u003e phase stability, the alloy maintains a low elastic modulus. Coordinated deformation among grains spanning multiple size scales further contributes to the strength enhancement\u0026nbsp;\u003csup\u003e48\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTo verify the strengthening contributions of ultrafine \u003cem\u003e\u0026alpha;\u003c/em\u003e grains and \u0026nbsp;nanoscale \u003cem\u003e\u0026beta;\u003c/em\u003e\u003csub\u003eZr-rich\u003c/sub\u003e particles, the rolling temperature was increased to 600 ℃ (specimen R600) to completely dissolve the primary \u003cem\u003e\u0026alpha;\u003c/em\u003e phase while simultaneously avoiding spinodal decomposition. Following deformation and water cooling, only lenticular \u003cem\u003e\u0026alpha;\u0026Prime;\u003c/em\u003e martensite formed (\u003cstrong\u003eExtended Data Figs. 5a and 5b\u003c/strong\u003e). Tensile tests reveal a Young\u0026rsquo;s modulus (60\u0026plusmn;2.2 GPa) similar to that of HR525, but a markedly reduced yield strength of 740\u0026plusmn;19 MPa (\u003cstrong\u003eExtended Data Fig. 5c\u003c/strong\u003e), a value comparable to that of specimen ST850. This finding further proves the crucial strengthening role of ultrafine \u0026alpha; grains and dispersed \u0026nbsp;nanoscale \u003cem\u003e\u0026beta;\u003c/em\u003e\u003csub\u003eZr-rich\u003c/sub\u003e particles in specimen R525 as a representative metastable \u003cem\u003e\u0026beta;\u003c/em\u003e alloy.\u003c/p\u003e\n\u003cp\u003eMoreover, \u003cem\u003e\u0026alpha;\u0026Prime;\u003c/em\u003e martensite contributes to strength and toughness through distinct mechanisms. Nanotwin structures are observed within ultrafine \u003cem\u003e\u0026alpha;\u0026Prime;\u003c/em\u003e lenticulars with several hundred nanometers in width (\u003cstrong\u003eFig. 4\u003c/strong\u003e\u003cstrong\u003ec\u003c/strong\u003e). Similar twinning phenomena in metastable phases have also been reported after thermal deformation of Zr-Nb alloys \u003csup\u003e49\u003c/sup\u003e. The attainment of tensile strengths exceeding 1600 MPa in titanium alloys is fundamentally attributed to the presence of dense, stable, internally twinned nanoprecipitates \u003csup\u003e50\u003c/sup\u003e. Nanotwin structures in Zr-based and Ti-based alloys have been demonstrated to provide substantial strengthening effects\u0026nbsp;\u003csup\u003e51\u003c/sup\u003e. Geometric Phase Analysis (GPA) of the region adjacent the boundary between nanoscale lenticular \u003cem\u003e\u0026alpha;\u0026Prime;\u003c/em\u003e grains and matrix reveals that, in addition to exhibiting strain comparable to that of the \u003cem\u003e\u0026beta;\u003c/em\u003e matrix, high lattice strain exists along the \u003cem\u003e\u0026alpha;\u0026Prime;/\u0026beta;\u003c/em\u003e boundaries (\u003cstrong\u003eFig. 4\u003c/strong\u003e\u003cstrong\u003ed\u003c/strong\u003e and\u0026nbsp;\u003cstrong\u003eFig. 4\u003c/strong\u003e\u003cstrong\u003ee\u003c/strong\u003e). This observation indicates that \u003cem\u003e\u0026alpha;\u0026Prime;\u003c/em\u003e grains not only strengthen the material by increasing the density of \u003cem\u003e\u0026alpha;\u0026Prime;/\u0026beta;\u003c/em\u003e boundaries but also facilitate the accommodation of plastic deformation. The \u003cem\u003e\u0026alpha;\u0026Prime;\u003c/em\u003e phase promotes to a pronounced strain partitioning effect during tensile deformation, allowing strain to accumulate within the \u0026nbsp;nanoscale \u003cem\u003e\u0026alpha;\u0026Prime;\u003c/em\u003e grains and thereby preserving the material ductility\u0026nbsp;\u003csup\u003e52\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTo validate the generality of the proposed design strategy for low-modulus metastable \u0026beta; zirconium alloys (\u003cem\u003eC\u003csub\u003e500\u003c/sub\u003e\u003c/em\u003e \u0026le; \u003cem\u003eC\u003csub\u003eEmin\u003c/sub\u003e\u003c/em\u003e \u0026le; \u003cem\u003eC\u003csub\u003e400\u003c/sub\u003e\u003c/em\u003e), a series of Zr-15Nb-\u003cem\u003ex\u003c/em\u003eTi (\u003cem\u003ex\u003c/em\u003e = 5, 7.5, 10, 12.5, 15, 17.5, 20, and 30 wt.%) with compositions situated within the predicted \u003cem\u003eCLE\u0026nbsp;\u003c/em\u003eregion of the Zr-Ti-Nb system (\u003cstrong\u003eExtended Data Fig. 6a\u003c/strong\u003e) were designed and prepared. Room-temperature tensile results demonstrate that the Young\u0026apos;s modulus of the designed alloys first decreases, then increases, and ultimately stabilizes with increasing Ti content (\u003cstrong\u003eExtended Data Fig. 6b\u003c/strong\u003e). Zr-15Nb-\u003cem\u003ex\u003c/em\u003eTi alloys with Ti contents ranging from 10 to 30 wt.% all exhibit low Young\u0026apos;s moduli (\u0026lt; 65 GPa). These results clearly demonstrate that the strong applicability and reliability of the proposed design strategy for predicting properties of complex alloy systems, particularly those containing high concentrations of strongly interacting elements, and provide a broadly applicable tool for the rational design of next-generation orthopedic implant materials.\u003c/p\u003e\n\u003cp\u003eIn summary, we have established a composition design strategy for low-modulus metastable\u0026nbsp;\u0026beta; zirconium alloys, defined by \u003cem\u003eC\u003csub\u003e500\u003c/sub\u003e \u0026le; C\u003csub\u003eEmin\u003c/sub\u003e \u0026le; C\u003csub\u003e400\u003c/sub\u003e,\u003c/em\u003e through the transfer of well-established methodologies from titanium alloys. The Zr-10Ti-15Nb alloy designed according to this strategy exhibits a Young\u0026apos;s modulus as low as 52.3\u0026plusmn;2.8 GPa. Through the construction of a multi-scale, multi-morphological microstructure, an exceptional synergy of low modulus (58.0\u0026plusmn;2.6 GPa), ultra-high yield strength (941\u0026plusmn;28 MPa), and a high elastic admissible strain of 1.62% is realized. Coupled with its low magnetic susceptibility, the specimen achieves a record EAS/MS value of 115 among reported metallic orthopedic materials. These outstanding properties originate from the synergistic strengthening contributions of ultrafine \u0026alpha; grains and dispersed nanoscale \u003cem\u003e\u0026beta;\u003c/em\u003e\u003csub\u003eZr-rich\u003c/sub\u003e particles, which provide potent precipitation strengthening and grain refinement strengthening, together with the deformation twinning effect of ultrafine \u003cem\u003e\u0026alpha;\u0026Prime;\u003c/em\u003e lenticulars. Biological evaluation confirms its superior biocompatibility relative to CP Ti and TC4. These findings present an ideal material candidate for orthopedic implants capable of mitigating the risks of \u0026ldquo;stress shielding\u0026rdquo;, stress concentration cracking, cytotoxicity, and MRI artifacts, while also supplying a powerful design strategy for high-performance medical metallic materials.\u003c/p\u003e"},{"header":"Methods","content":"\u003ch3\u003eMachine Learning Methods\u003c/h3\u003e\n\u003cp\u003eThe machine learning framework integrates compositional descriptors, phase-stability parameters, and elastic property data from zirconium- and titanium-based alloy systems. A total of 356 alloy compositions were collected from literature, experimental measurements, and thermodynamic calculations, covering a broad compositional range of \u003cem\u003e\u0026beta;\u003c/em\u003e-stabilizing elements and elastic moduli. Model robustness was further validated by independent experimental synthesis and mechanical testing of newly designed alloys. Compositional descriptors include elemental concentrations, valence electron concentration, atomic size mismatch, electronegativity difference, and mixing enthalpy. Phase-stability descriptors were derived from CALPHAD-based thermodynamic calculations, wherein the Gibbs free energy difference \u0026Delta;\u003cem\u003eG\u003csub\u003e\u0026beta;\u0026rarr;\u0026alpha;\u003c/sub\u003e\u003c/em\u003e was computed as a function of composition and temperature. To predict elastic modulus, a neural network was employed. The network consists of an input layer corresponding to the number of compositional and phase-stability descriptors, three hidden layers with 128, 64, and 32 neurons respectively, each followed by ReLU activation, and a single output neuron predicting the elastic modulus. Dropout (rate = 0.2) was applied between hidden layers to mitigate overfitting, and batch normalization was used to stabilize training. Hyperparameters, including learning rate and weight decay, were optimized via five-fold cross-validation, and model performance was evaluated using the coefficient of determination (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e) and mean absolute error (MAE).\u003c/p\u003e\n\u003cp\u003eTo incorporate physical constraints, a critical compositional parameter from metastable \u003cem\u003e\u0026beta;\u003c/em\u003e titanium alloys was introduced. The \u003cem\u003e\u0026beta;\u003c/em\u003e-stabilizer concentration required to suppress the martensitic transformation, \u003cem\u003eC\u003c/em\u003e\u003csub\u003eM\u003c/sub\u003e, corresponds to \u0026Delta;\u003cem\u003eG\u003csub\u003e\u0026beta;\u0026rarr;\u0026alpha;\u003c/sub\u003e\u003c/em\u003e = 0\u0026nbsp;at a characteristic temperature \u003cem\u003eTM\u003c/em\u003e. Since \u003cem\u003eC\u003c/em\u003e\u003csub\u003eM\u003c/sub\u003e is experimentally difficult to determine, it was approximated by \u003cem\u003eC\u003c/em\u003e\u003csub\u003eTM\u003c/sub\u003e from thermodynamic calculations. Based on the physical inference that the composition yielding the minimum elastic modulus (\u003cem\u003eC\u003c/em\u003e\u003csub\u003eEmin\u003c/sub\u003e) is close to this critical value, the relationship \u003cem\u003eC\u003c/em\u003e\u003csub\u003eEmin\u003c/sub\u003e \u0026asymp; \u003cem\u003eC\u003c/em\u003e\u003csub\u003eM\u0026nbsp;\u003c/sub\u003e\u0026asymp; \u003cem\u003eC\u003c/em\u003e\u003csub\u003eTM\u003c/sub\u003e was implemented in the neural network through a physics-guided regularization term. Specifically, the total loss function was defined as:\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"https://myfiles.space/user_files/58895_8739fc6c57c1c19a/58895_custom_files/img1777445468.png\" width=\"336\" height=\"61\"\u003e\u003c/p\u003e\n\u003cp\u003ewhere \u003cem\u003ef\u003c/em\u003e\u003cem\u003e\u003csub\u003e\u0026theta;\u003c/sub\u003e\u003c/em\u003e represents the neural network prediction of elastic modulus. This gradient-based penalty encourages the network to form a local minimum of the predicted elastic modulus near the thermodynamically inferred critical composition, ensuring that low-modulus predictions are physically consistent. This strategy allows the model to capture nonlinear couplings among composition, phase stability, and elastic modulus while guiding exploration of low-modulus \u003cem\u003e\u0026beta;\u003c/em\u003e-phase alloy compositions within physically reasonable regions of the high-dimensional compositional space.\u003c/p\u003e\n\u003ch3\u003ePhase Diagram Calculation\u003c/h3\u003e\n\u003cp\u003eEquilibrium thermodynamic simulations based on the CALPHAD method were conducted to predict and analyze the pseudo-binary phase diagram of the Zr-10Ti-\u003cem\u003ex\u003c/em\u003eNb alloy system and the temperature-dependent phase evolution for the Zr-10Ti-15Nb alloy. Calculations were performed using Thermo-Calc software (version 2024a) with the TCTI5 and TTZR1 thermodynamic databases. The pseudo-binary phase diagram for the Zr-10Ti-xNb system was obtained. Continuous data describing the phase constitution of the Zr-10Ti-15Nb alloy as a function of temperature were extracted and exported. Using the post-processing module, corresponding curves of phase volume fraction versus temperature were generated. Consequently, the regions of different phase constitutions within the system were determined, together with the corresponding alloy compositions and temperature conditions associated with key solid-state phase transformations.\u0026nbsp;\u003c/p\u003e\n\u003ch3\u003eMaterial Preparation\u003c/h3\u003e\n\u003cp\u003eIndustrial sponge zirconium (Zr+Hf \u0026gt; 99.7 wt.%, Hf = 1.5-2.5 wt.%), pure titanium (99.9 wt.%), and high-purity niobium (99.95 wt.%) were weighed according to the nominal composition Zr-10Ti-15Nb (wt.%) after ultrasonic cleaning and drying. The total mass was 5 kg. The blended raw materials were melted in a vacuum copper crucible suspension furnace under a protective high-purity argon atmosphere following evacuation of the chamber to 10\u003csup\u003e-3\u003c/sup\u003e Pa. The resulting ingot was furnace-cooled to room temperature. The alloy ingot was then subjected to three-stage open-die forging: first at 1000 \u0026deg;C, second at 900 \u0026deg;C, and third at 850 \u0026deg;C. After forging, the surface was turned, ground, and cleaned to obtain plates with dimensions of 50 mm \u0026times; 20 mm \u0026times; L (length). The forged plates were cut longitudinally into square bars of 50 mm \u0026times; 20 mm \u0026times; 20 mm, which were further processed via either hot rolling or solution treatment.\u003c/p\u003e\n\u003cp\u003eFor hot rolling, samples were held at 525 \u0026deg;C or 600 \u0026deg;C for 30 min, followed by multi-pass rolling with a reduction of ~5% per pass. Between passes, samples were returned to the furnace for 5 min. The total rolling reduction was ~80%. After the final pass, samples were immediately water quenched. These specimens were designated R525 and R600 according to their respective rolling temperatures. For solution treatment, cut square bars were heated to 850 \u0026deg;C at 10 \u0026deg;C/min under an argon atmosphere in a vacuum tube furnace, held for 20 min, and then water quenched. These samples were labeled ST850.\u003c/p\u003e\n\u003cp\u003eTo verify the generality of the alloy design strategy, additional alloys with nominal compositions Zr-15Nb-\u003cem\u003ex\u003c/em\u003eTi (\u003cem\u003ex\u003c/em\u003e = 5, 7.5, 10, 12.5, 15, 17.5, 20, and 30 wt.%) were prepared. Each alloy weighed 120 g. Melting was performed in an argon-protected vacuum non-consumable arc melting furnace, with each ingot flipped and remelted at least six times to ensure homogeneity. The as-cast ingots were homogenized at 950 \u0026deg;C for 4 h under argon, followed by water quenching, and then hot-rolled at 750 \u0026deg;C using the same rolling procedure described above. All processed samples were ground and cut into appropriate shapes and dimensions for subsequent analyses.\u003c/p\u003e\n\u003ch3\u003eMicrostructure Characterization\u003c/h3\u003e\n\u003cp\u003eThe microstructure was systematically characterized using electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM). For EBSD sample preparation, mounted samples were sequentially ground with 400, 800, 1200, 2000, and 5000 grit SiC papers. This was followed by sequential polishing using a 1 \u0026mu;m alumina suspension and a 50 nm silica suspension. Subsequently, the samples were subjected to Ar ion milling in a Leica EM TIC 3X triple-ion-beam mill under the following sequential conditions: 6 kV at 9\u0026deg; for 120 min, follow by 4 kV at 6\u0026deg; for 10 min. After preparation, samples were examined in a scanning electron microscope equipped with an EBSD detector. EBSD analysis was performed at an accelerating voltage of 20 kV and a beam current of approximately 10 nA. The scanning step size was adjusted between 0.05 and 0.5 \u0026mu;m, depending on the grain size of the observed area. For TEM, thin slices (~0.5 mm thick) were cut by wire electrical discharge machining, mechanically ground to below 40 \u0026mu;m, and punched into 3 mm diameter discs. After ultrasonic cleaning in acetone and ethanol, the discs were twin-jet electropolished in a solution of 10% perchloric acid in methanol at temperatures below -20 \u0026deg;C and a voltage of 15.5 V. Samples were then cleaned, dried, and examined using TEM operated at 200 kV. Bright-field and dark-field imaging, along with selected-area electron diffraction were employed for comprehensive microstructural analysis.\u003c/p\u003e\n\u003ch3\u003eMechanical Property Testing\u003c/h3\u003e\n\u003cp\u003eTensile specimens with a gauge length of 18 mm, width of 3 mm, and thickness of 2 mm were machined along the rolling direction via wire cutting. Room-temperature tensile tests were performed on an Instron 5982 mechanical testing system at a strain rate of 5\u0026times;10\u003csup\u003e-4\u003c/sup\u003e s\u003csup\u003e-1\u003c/sup\u003e monitored by a high-precision extensometer with a gauge length of 10 mm. At least three valid tests were conducted for each condition.\u003c/p\u003e\n\u003ch3\u003eBiocompatibility Evaluation\u003c/h3\u003e\n\u003cp\u003eCytotoxicity was assessed using human osteosarcoma cells (MG-63) via an extract test. Disc-shaped samples were ultrasonically cleaned in ethanol, sterilized at 121 \u0026deg;C for 20 min in an autoclave, dried, and placed in sterile 15 mL centrifuge tubes. \u003cem\u003e\u0026alpha;\u003c/em\u003e-Minimum Essential Medium (\u003cem\u003e\u0026alpha;\u003c/em\u003e-MEM) supplemented with 10% fetal bovine serum and 1% penicillin-streptomycin was added, and extracts were obtained after 7 days of immersion.\u003c/p\u003e\n\u003cp\u003eCells were seeded at densities of 2\u0026times;10\u003csup\u003e4\u003c/sup\u003e cells per well in 24-well plates for fluorescence imaging and 1\u0026times;10\u003csup\u003e4\u003c/sup\u003e cells per well in 96-well plates for viability assays. After adherence, the culture medium was replaced with the respective alloy extracts. Controls included extracts from commercially pure Ti (CP Ti) and Ti-6Al-4V (TC4), as well as extract-free medium. After 24 h of incubation, the medium was removed and cells were washed with phosphate-buffered saline (PBS). A live/dead double-staining kit (Calcein-AM/PI) was applied to 24-well plates for fluorescence observation. For 96-well plates, cell viability was evaluated using a CCK-8 assay, with absorbance measured at 450 nm using a microplate reader. Each experiment was performed with three independent samples, six biological replicates, and three technical replicates.\u003c/p\u003e\n\u003ch3\u003eMagnetic Susceptibility Measurement\u003c/h3\u003e\n\u003cp\u003eSamples with dimensions of 2 \u0026times; 2 \u0026times; 0.5 mm\u003csup\u003e3\u003c/sup\u003e were prepared by electrical discharge machining, ground to 2000 grit with SiC paper, cleaned, and dried. Magnetization curves (magnetization \u003cem\u003eM\u003c/em\u003e in emu/g versus applied magnetic field \u003cem\u003eH\u003c/em\u003e in Oe) were measured using a Physical Property Measurement System (MPMS-SQUID, Quantum Design) at 37 \u0026deg;C over a field range of -4 T to 4 T.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eData Availability\u003c/h2\u003e\n\u003cp\u003eThe data supporting this study are available in the main text. Raw CALPHAD data are protected and are not available due to the restrictions imposed by the Thermo-Calc End User License Agreement (EULA). Additional data are available from the corresponding authors upon request. Source data are provided with this paper.\u003c/p\u003e\n\u003ch2\u003eCode availability\u0026nbsp;\u003c/h2\u003e\n\u003cp\u003eAll code used for analysing the raw data is available upon request from the corresponding authors.\u003c/p\u003e\u003ch2\u003eAcknowledgements\u003c/h2\u003e\n\u003cp\u003eThis work was supported by the National Natural Science Foundation of China (Grant No. 52125405/52471148/52127808/52071278/U22A20108), Hebei Natural Science Foundation (Grant no. 242Q9906Z), Backbone Talent Program of Hebei Province (Overseas Returnees Platform) (Grant no. A2025009), the Science Research Project of Hebei Education Department (Grant No. KJZX202201), and Just Medical Devices (Tianjin) Co., Ltd. (Grant no. x2026030).\u003c/p\u003e\n\u003ch2\u003eAuthor Contributions Statement\u0026nbsp;\u003c/h2\u003e\n\u003cp\u003eZ.C. Y., X.K. L. and S.X. L. conceived the research. J.S. Z., S.Z. Z. and S.X. L.contributed to data analysis. Z.C. Y., X.K. L., S.X. L., Y.X. G., M.Z. M. performed the experiments and analyzed the data. S.D. F., X.Y. Z. and R.P. L. conceived the idea and led the computational modelling. X.Y. Z. and R.P. L. supervised and directed the overall study. Z.C. Y., X.K. L., S.D. F. and S.X. L. wrote the paper with input from all authors.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003eCompeting Interests Statement\u0026nbsp;\u003c/h2\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eBabaei, M. \u003cem\u003eet al.\u003c/em\u003e Metal additive manufacturing of lattice-based orthopedic implants: A comprehensive review of requirements and design strategies. \u003cem\u003eMater. Sci. Eng. R Rep.\u003c/em\u003e \u003cstrong\u003e166\u003c/strong\u003e, 101075 (2025).\u003c/li\u003e\n\u003cli\u003eChmielewska, A. \u0026amp; Dean, D. 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Alloys Compd.\u003c/em\u003e \u003cstrong\u003e920\u003c/strong\u003e, 165563 (2022).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Zirconium alloy, Methodology transfer, Excellent comprehensive performance, Orthopedic alloy","lastPublishedDoi":"10.21203/rs.3.rs-9432897/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9432897/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Some efficient design strategies have been proposed for low-modulus Ti-based alloys, yet these approaches may not be applicable to Zr-based alloys, especially for alloys containing strongly interacting elements. Owing to its favorable biological performance, Zr alloy is regarded as a leading candidate for next-generation orthopedic materials. Here, we present a machine-learning-guided, energy-based design strategy that reliably identifies the low-modulus compositional window in Zr/Ti alloys, including alloy systems with significant elemental interactions. Using this approach, we design a metastable β-type Zr-10Ti-15Nb alloy exhibiting a low Young's modulus of E=52.3±2.8 GPa. Through controlled thermomechanical processing, we produce an optimized specimen with a modulus of E=58.0±2.6 GPa and a yield strength of YS=941±28 MPa, resulting an exciting elastic admissible strain (EAS=YS/E) of 1.62%, surpassing nearly all reported Zr alloys. Combined with its low magnetic susceptibility (MS=141 ppm), this specimen achieves a record critical key metric EAS/MS ratio among permanent implant metallic materials. The alloy also demonstrates superior biocompatibility relative to clinically used titanium alloys. Our findings developed a promising orthopedic candidate material with comprehensively enhanced performance. More importantly, we provide a transferable and generalizable design framework for biomedical alloys to achieve a low Young's modulus and high yield strength.","manuscriptTitle":"Methodology Transfer from Titanium to Zirconium Alloys via Machine Learning: Development of Superior Orthopedic Alloys","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-29 07:05:10","doi":"10.21203/rs.3.rs-9432897/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"0dbec93e-6b3d-4eee-a29f-12891bba53a2","owner":[],"postedDate":"April 29th, 2026","published":true,"recentEditorialEvents":[{"type":"editorInvitedReview","content":"This content is not available.","date":"2026-05-01T13:21:13+00:00","index":1,"fulltext":"This content is not available."}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":66452697,"name":"Physical sciences/Materials science/Biomaterials/Implants"},{"id":66452698,"name":"Physical sciences/Materials science"}],"tags":[],"updatedAt":"2026-04-29T07:05:11+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-29 07:05:10","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9432897","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9432897","identity":"rs-9432897","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}