Hardness Augmentation Engineering of TiFe2 with Doping Design and Single-crystal Realization

Hardness Augmentation Engineering of TiFe2 with Doping Design and Single-crystal Realization | 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 Research Article Hardness Augmentation Engineering of TiFe 2 with Doping Design and Single-crystal Realization Xinyang Tan, Hongxiong Liu, Tingping Hou, Sicong Zhu, Gengping Jiang, and 5 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5457104/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract As a critical reinforcing phase in matrix and coating materials, enhancing the hardness of TiFe 2 significantly improves the upper limits of alloy performance through low-concentration doping. However, the mechanism by which doping alters macroscopic hardness through the disturbance of electronic structure remains unclear. Furthermore, there is a lack of robust experimental evidence to substantiate the hardness enhancements predicted by theoretical calculations. This investigation assessed the strengthening effect of silicon (Si) on the hardness of TiFe 2 through both calculations and experiments. First-principles calculations indicated that Si alloying enhances the structural stability and hardness of TiFe 2 . The mechanisms underlying the notable increase in hardness due to Si were thoroughly investigated from the perspective of bonding characteristics. Si alloying disrupted the original symmetric electronic structure and increased the prevalence of directional covalent bonds. Successful single-crystal preparation experiments confirmed the stability of the doped structure. The results of nano-hardness testing address the deficiency of accurate experimental data on hardness enhancement. This study provides a systematic approach to improving the mechanical properties of TiFe 2 and offers new insights into the development of advanced materials with enhanced hardness. Materials Theory and Modeling Doping design Hardness augmentation engineering Electronic structure modulation TiFe2 Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction The exploration of new materials with exceptional properties is a fundamental pursuit for scientists and engineers. Laves phase-reinforced alloys exhibit high strength and superior hardness, making them valuable for applications in aerospace and automotive industries 1 – 5 . The three crystal structure polytypes of Laves phases (C14, C15, and C36) are formed with AB₂ compositions of various elements, with radius ratios (r A /r B ) ranging from 1.19 to 1.32 6,7 . The comparable simple crystalline structures and versatile combinations of elements enable Laves phases to possess a variety of unique properties, including nanoparticle superlattices 8 , 9 , hydrogen storage 10 – 14 , superconductivity 15 , 16 , and thermostability 17 – 20 . In recent years, an increasing number of researchers have recognized the excellent performance of C14 TiFe 2 as a strengthening phase in coatings and alloy matrices. Previous investigations have shown that FCC high-entropy alloys (HEAs) possess good ductility but limited strength 21 – 24 . To enhance the strength of these materials, researchers have incorporated Ti to form TiFe 2 24,25 . Furthermore, TiFe 2 can improve the wear and oxidation resistance of coatings for structural materials 26 , 27 . These findings highlight the necessity of augmenting the hardness and strength of TiFe 2 to further reinforce both the substrate and the coating. In addition to the close relationship between macroscopic grain size and hardness 28 , the hardness and strength of a unit cell on the nanoscale depend on the nature of its chemical bonding and stability 29 – 33 . Low-content doping can significantly alter properties by modulating the electronic structure without changing the original cell type 34 – 36 . Trial-and-error experimental approaches are costly and time-consuming, while previously reported phase-formation rules are empirical. It is more effective to predict phase stability and microstructure to accelerate the design of Laves phases through a first-principles theoretical approach. Previous studies have not clarified the mechanisms by which doping alters macroscopic hardness through disturbances in the electronic structure. Furthermore, there is a lack of robust experimental evidence to substantiate the hardness enhancements predicted by theoretical calculations. In this work, TiFe 2 was doped with various elements (Co, Mn, Ni, V, Cr, Si, B, S), and it was found that silicon (Si) resulted in the most significant increase in hardness. Finally, in-depth research was conducted on Si-doped TiFe 2 . In this paper, the Ti-Fe-Si ternary alloy system (Ti x Fe 11−x Si, where x = 3 or 4) has been constructed. The structural stability, mechanical properties, and electronic structure of Ti x Fe 11−x Si were calculated, and centimeter-scale single-crystal samples TiFe 2 and Ti 4 Fe 7 Si were prepared experimentally. The elastic modulus and hardness were tested and compared. First, the most stable structure (Ti 4 Fe 7 Si) and the metastable structure (Ti 3 Fe 8 Si) were identified, and the mechanical properties and thermodynamic curves of the most stable structure were calculated. Subsequently, based on the thermodynamic curves, TiFe 2 and Ti 4 Fe 7 Si single-crystals were prepared using the Czochralski method 37 , and their hardness and elastic modulus were examined. The results indicate that the experimental findings are consistent with the theoretical predictions. Finally, the influence of Si alloying on the mechanical properties of TiFe 2 was analyzed from the perspectives of electronic structure and bonding characteristics. Results Model Designs and Screening for Hardness Augmentation The TiFe 2 unit cell model consists of eight Fe atoms located at the 2a and 6h Wyckoff positions (denoted as Fe(2a) and Fe(6h), respectively) and four Ti atoms positioned at the 4f Wyckoff sites (Ti(4f)) (Fig. 1 a). The Fe atoms form corner-sharing tetrahedral units. Figure 1 b illustrates the hourglass-shaped polyhedron formed by Fe atoms, consisting of two centrally symmetric tetrahedra. The Ti atoms are positioned within these polyhedra, each surrounded by three hourglass-shaped polyhedra formed by Fe atoms. The Fe(6h) atoms possess effective magnetic moments aligned along the c-axis 38 , 39 . To identify favorable alloying elements for the TiFe 2 structure, this study selected elements frequently observed in high-entropy alloys. Fe atoms in the TiFe 2 model were sequentially substituted by different elements at the same atomic positions, maintaining an atomic ratio of Ti 4 Fe 7 M (M = Fe, Co, Mn, Ni, V, Cr, Si, B, S). Formation enthalpies ( ΔH ) 40 , 41 , hardness, and elastic moduli of these structures were calculated using first-principles methods, with the results presented in Fig. 1 c. These results indicate that Si has the most favorable overall effect on the TiFe 2 structure. Consequently, Si was selected as the doping element for further calculations and experiments. There are three possible configurations when a Si atom substitutes for Fe(2a), Fe(6h), or Ti(4f) atoms in the formation of the ternary compounds Ti x Fe 11−x Si (x = 3 or 4). The models formed by substituting Si for Fe(2a) and Fe(6h) are denoted as Ti 4 Fe 7 Si-a and Ti 4 Fe 7 Si-h, respectively. Ti 3 Fe 8 Si represents the structure where a Ti atom at the 4f site is replaced by a Si atom. To elucidate the ground-state characteristics of TiFe 2 , Ti 4 Fe 7 Si-a, Ti 4 Fe 7 Si-h, and Ti 3 Fe 8 Si under zero pressure, Table 1 presents the calculated equilibrium lattice parameters, Wyckoff positions, and cell volumes of the fully relaxed structures. The calculated results are consistent with those reported in the literature 39 , 42 , confirming the reliability of the theoretical parameters used in this study. The decrease in cell volume observed in the Si-alloyed samples can be attributed to lattice distortions caused by the substitution of a host atom with a Si atom. Table 1 Calculated and experimental results equilibrium structural parameters Compound Wyckoff position a (Å) c (Å) α , β , γ (˚) V (Å 3 ) ΔH (eV/atom) ΔE (eV/atom) TiFe 2 —— 4.756 7.736 90,90,120 151.57 -7.102 0 —— 4.778 39 7.761 39 —— 4.686 42 7.732 42 Ti 4 Fe 7 Si − a 2a 4.756 7.728 90,90,120 151.42 -8.323 -1.221 Ti 4 Fe 7 Si − h 6h 4.736 7.750 90,90,120 150.76 -8.189 -1.087 Ti 3 Fe 8 Si 4f 4.719 7.663 90,90,120 147.78 -6.852 0.249 The formation enthalpies (ΔH) and reaction energies (ΔE) 43 , 44 were calculated to assess the structural stabilities of TiFe 2 , Ti 4 Fe 7 Si-a, Ti 4 Fe 7 Si-h, and Ti 3 Fe 8 Si ( Section S3 ). A negative reaction energy indicates that the total energy of the products is lower than that of the reactants. As shown in Table 1 , Ti 4 Fe 7 Si-a and Ti 4 Fe 7 Si-h exhibited negative reaction energies, while Ti 3 Fe 8 Si showed a positive reaction energy. Therefore, the substitution of a Si atom in Ti 4 Fe 7 Si-a and Ti 4 Fe 7 Si-h is thermodynamically feasible, resulting in stable products, with reaction energies of -1.221 eV/atom and − 1.087 eV/atom, respectively. In contrast, the substitution of a Si atom in Ti 3 Fe 8 Si is not thermodynamically feasible, as indicated by its positive reaction energy of 0.249 eV/atom. These results suggest that Si atoms preferentially occupy the 2a Wyckoff sites. In summary, the structures of Ti 4 Fe 7 Si-a and Ti 4 Fe 7 Si-h are stable, with Ti 4 Fe 7 Si-a exhibiting the highest stability 45 . Single-crystal Preparation of Ti 4 Fe 7 Si and TiFe 2 To obtain precise data on the effect of element substitution on hardness enhancement, it is essential to use samples of high purity and crystallinity, minimizing the influence of dislocations and grain boundaries. Based on the equilibrium lattice constants of Ti 4 Fe 7 Si-a, a series of lattice constants were further studied in relation to the total energy of Ti 4 Fe 7 Si-a. The relationship between the calculated total energy and volume is depicted in Fig. S4 . This relationship was then used as input data for the Gibbs2 program 46 to determine the thermodynamic parameters of Ti 4 Fe 7 Si-a at elevated temperatures, ranging from 0 K to 2000 K. Figure 1 d illustrates the total energy and volume of the crystalline cells as a function of temperature. The results suggest that the reduction in total energy is primarily due to lattice vibrations, as shown in the Fig.. The temperature range, marked by two dashed lines, is proposed as the optimal range for single-crystal preparation. Based on the results of the theoretical calculations, single-crystal samples of TiFe 2 ( Fig. S3 ) and Ti 4 Fe 7 Si were successfully prepared using the Czochralski method 37 . The equipment employed in the experiment was a four-arc single-crystal growth furnace, and a schematic diagram of the device is presented in Fig. 2 . The preparation process is described in Section S2 . The TiFe 2 and Ti 4 Fe 7 Si crystals produced by this method were cylindrical, with diameters ranging from 0.3 cm to 0.4 cm and lengths of 2 cm. Figure 2 b shows a rod-shaped single-crystal of Ti 4 Fe 7 Si under an optical microscope. The structures and compositions of the samples were subsequently characterized to verify the successful preparation of the single crystals. The X-ray diffraction (XRD) results are shown in Fig. 2 c. It was concluded that the crystalline structure of Ti 4 Fe 7 Si is identical to that of TiFe 2 . Scanning electron microscopy (SEM) was then employed to analyze the microstructure of the samples. As shown in Fig. 2 d, the Ti 4 Fe 7 Si sample exhibited high crystallinity, with no grain boundaries or inclusions. Fig.s 2e-g present the energy dispersive spectroscopy (EDS) mappings for Ti, Fe, and Si, while Fig. 2 h displays the EDS spectra. The distribution of Si was consistent with that of Ti and Fe, and the proportions of the three elements matched the relative mass ratio of Ti 4 Fe 7 Si. Based on the results presented above, it can be concluded that the preparation of the Ti 4 Fe 7 Si single-crystal was successful. Influence of the Hardness Augmentation Methodology on TiFe 2 Mechanical Properties Nano-indentation experiments were conducted to examine the hardness and Young's modulus of single crystals, investigating the effect of Si on the properties of TiFe 2 . The test curves are presented in Fig.s 3a and 3b , while the maximum values are summarized in Fig. 3 c. The average hardness (22.92 GPa) and Young's modulus (334.85 GPa) of Ti 4 Fe 7 Si were significantly higher compared to the hardness (13.99 GPa) and Young's modulus (250.44 GPa) of TiFe 2 , with increases of 63.8% and 33.7%, respectively. Theoretical predictions for the hardness and Young's modulus of TiFe 2 (6.75 GPa; 171.52 GPa), Ti 4 Fe 7 Si-a (10.44 GPa; 201.83 GPa), and Ti 4 Fe 7 Si-h (11.35 GPa; 194.51 GPa) are shown in Fig. 3 c. For comparison, data on intermetallic compounds and wear-resistant alloys were also collected 1 , 44 , 47 – 49 . The hardness and Young's modulus of Ti 4 Fe 7 Si-a and Ti 4 Fe 7 Si-h exceeded those of TiFe 2 . Although numerical deviations existed between theoretical results (calculated under 0 K and 0 Pa) and experimental findings, the overall trend of improvement was consistent. The experimental enhancement of the hardness and Young's modulus of TiFe 2 due to Si doping has thus been theoretically validated. Based on the calculated elastic constants, the bulk modulus ( B ), shear modulus ( G ), Young’s modulus ( E ), and anisotropy ( A U ) were determined using the Voigt-Reuss-Hill approximation ( Section S4 ). The values of these mechanical parameters are presented in Table 2 . Generally, B reflects a structure’s ability to resist volume change under external compression, while G characterizes resistance to shear deformation 50 . The calculated results showed that TiFe 2 had the highest bulk modulus ( \(\:{B}_{H}\) ) value (262.20 GPa), indicating that the structure’s resistance to volume change decreased when Si atoms were substituted into the TiFe 2 crystalline structure. Moreover, the shear modulus ( \(\:{G}_{H}\) ) values for Ti 4 Fe 7 Si-a and Ti 4 Fe 7 Si-h were similar and higher than that of TiFe 2 , whereas Ti 3 Fe 8 Si had the lowest \(\:{G}_{H}\) value (69.56 GPa). These results demonstrate that Si substitution at the 2a and 6h Wyckoff sites enhanced the structure’s resistance to shear strain, while substitution at the 4f Wyckoff site weakened it. The Young’s modulus ( E ) represents the stiffness of a material, with a higher E value indicating greater stiffness 51 . As shown in Table 2 , Ti 4 Fe 7 Si-a exhibited the highest E value (229.27 GPa), closely followed by Ti 4 Fe 7 Si-h (226.34 GPa), while Ti 3 Fe 8 Si had the lowest E value (180.98 GPa). These results suggest that Ti 4 Fe 7 Si-a and Ti 4 Fe 7 Si-h are significantly stiffer than TiFe 2 and Ti 3 Fe 8 Si. The B -to- G ratio is commonly used to evaluate a material's ductility, and Poisson’s ratio (v) is also a standard measure to distinguish between ductility and brittleness. A solid is considered to exhibit metallic ductility if \(\:{B}_{H}/{G}_{H}>1.75\) ( \(\:v>0.26\) ) 52 ; otherwise, it is classified as brittle. As shown in Table 2 , the \(\:{B}_{H}/{G}_{H}\left(v\right)\) ratios for all structures exceeded 1.75 ( \(\:v>\) 0.26), indicating good ductility across all structures. TiFe 2 exhibited the highest ductility, as reflected in its larger \(\:{B}_{H}/{G}_{H}\left(v\right)\) ratio compared to the other structures. Table 2 The bulk modulus B (GPa), shear modulus G (GPa), Young's modulus E (GPa), Poisson's ratio v , Paugh's ratio B/G and anisotropic factors A U of compounds. \(\:\text{S}\text{t}\text{r}\text{u}\text{c}\text{t}\text{u}\text{r}\text{e}\text{s}\) \(\:{B}_{H}\) \(\:{G}_{H}\) \(\:E\) \(\:B/G\) \(\:v\) \(\:{A}^{U}\) Ti 4 Fe 7 Si-a 143.82 89.38 229.27 1.96 0.282 0.257 Ti 4 Fe 7 Si-h 128.80 89.56 226.34 1.78 0.264 0.013 Ti 3 Fe 8 Si 151.41 69.56 180.98 2.17 0.301 0.142 TiFe 2 262.20 72.96 200.32 3.59 0.373 0.011 To explore the anisotropic properties of these materials, the three-dimensional (3D) surface representations of the Young’s moduli for TiFe 2 , Ti 4 Fe 7 Si-a, Ti 4 Fe 7 Si-h, and Ti 3 Fe 8 Si, along with projections of the 3D Young’s moduli on the (100), (010), and (001) planes, are shown in Fig. 3 d-j. The surface representations of the Young’s modulus provide a clearer understanding of a material’s degree of anisotropy across different orientations. A greater deviation of the surface structure from an ideal sphere indicates stronger elastic anisotropy within the unit cell. In this study, it is evident that the Young's moduli of the three Ti-Fe-Si compounds exhibit significant anisotropies, with the order of elastic anisotropy being Ti 4 Fe 7 Si-a > Ti 3 Fe 8 Si > Ti 4 Fe 7 Si-h. Deconstruction of Physical Characteristics of TiFe 2 In this study, the electron density difference distributions have been calculated to gain a deeper understanding of the effect of Si alloying on the structure and properties of TiFe 2 . This density difference is defined as the discrepancy between the electron density of the compound and the sum of the electron densities of the corresponding isolated atoms. Additionally, the total density of states (TDOS) and local density of states (LDOS) have been analyzed to provide more detailed insights into the physical characteristics. In consideration of the magnetic properties of the materials, spin polarization was incorporated during the calculations of the densities of states (DOS). Consequently, the spin-up DOS was found to be asymmetric in relation to the spin-down DOS for both TiFe 2 and all three Ti-Fe-Si ternary compounds. This suggests that these compounds exhibit ferromagnetic characteristics. As illustrated in Fig.s 4h-k , the TDOS near the Fermi level ( E f ) is distinctly non-zero, indicating that these compounds are metallic. It was also observed that when Si occupies a specific lattice site, the LDOS peaks of other atoms at the same type of site decrease in intensity. For instance, the LDOS of the Fe(2a) atom in Ti 4 Fe 7 Si-a is significantly lower than that of the Fe(2a) atoms in Ti 4 Fe 7 Si-h and Ti 3 Fe 8 Si. This trend is also evident for the Fe(6h) and Ti(4f) atoms. Additionally, the spin-down LDOS is lower in intensity compared to the spin-up LDOS ( Fig.s 4l-n ). Although the contribution of the substitutional Si atom to the DOS is negligible, it nonetheless influences the electrical and magnetic properties of the samples. As shown in Fig.s 4a-c , it is clear that some electrons are delocalized and distributed like rivers in the interstitial regions close to the Ti and Fe atoms, implying the existence of metallic and covalent bonding. This result is consistent with the analyses of the DOS. After substituting the original lattice with Si atoms ( Fig.s 4h-k ), it is evident that a portion of the corresponding DOS is positioned at higher energy levels in the conduction band. There is a tendency for hybridization between the orbitals of the Fe (2a) and Fe (6h) atoms in the energy range of approximately − 4 eV to 0 eV, while hybridization between the orbitals of the Fe (6h) and Ti (4f) atoms is apparent in the range of 0 eV to 2 eV (Fig. 4 k). This suggests that the covalent bonds in the compounds primarily originate from the interactions of Fe (6h)-Ti (4f) and Fe (6h)-Fe (2a), which are major contributing factors to the hardness of TiFe 2 53 . Origin of the Hardness Augmenting through Influence of Si Doping on the Bond Strength It is noteworthy that a deep minimum was found in the TDOS near the E f for each of the Ti-Fe-Si compounds. This minimum is referred to as a pseudo gap. Generally, a pseudo gap indicates the presence of strong covalent interactions (i.e., a covalent bond) 54 . A wider pseudo gap corresponds to a stronger covalent bond. Therefore, it can be concluded from the TDOS that the covalent bonds in Ti 4 Fe 7 Si-a and Ti 4 Fe 7 Si-h are stronger than those in Ti 3 Fe 8 Si. Strong covalent bonds typically correlate with a stable structure. In this context, Ti 4 Fe 7 Si-a and Ti 4 Fe 7 Si-h exhibit more stable structures and superior hardness, while Ti 3 Fe 8 Si is the weakest. This conclusion aligns with the formation enthalpies presented in Table 1 . On the other hand, the directional covalent interactions between the Fe(6h) and Ti(4f) atoms resulted in an uneven distribution of bonding forces 55 , 56 , which undoubtedly increased the likelihood of brittle fracture in each of these three compounds along the direction of metallic interactions. This explains the decreased values of σ and B / G for Ti 4 Fe 7 Si-a, Ti 4 Fe 7 Si-h, and Ti 3 Fe 8 Si. In the present study, the Ti 4 Fe 7 Si-a and Ti 4 Fe 7 Si-h materials, with Si atoms substituting the Fe(2a) and Fe(6h) atoms, respectively, exhibited wider pseudo gaps than those in the Ti 3 Fe 8 Si material, which has a Si atom substituting the Ti(4f) atom (Fig. 4 ). In this context, the Ti 4 Fe 7 Si-a and Ti 4 Fe 7 Si-h materials tended to be more brittle than the Ti 3 Fe 8 Si material, consistent with the values of B / G in Table 2 . More specifically, the electron density difference variation diagrams for Fe(6h) to Ti(4f) and Fe(6h) to Fe(2a) are shown in Fig. 4 e-g. The Ti 4 Fe 7 Si-a compound exhibited the strongest covalent bonds between Fe(6h)-Ti(4f) and Fe(6h)-Fe(2a). The covalent bond between Fe(6h) and Fe(2a) in Ti 4 Fe 7 Si-h was nearly as strong as that in the Ti 4 Fe 7 Si-a compound, while the Fe(6h)-Ti(4f) bond was the weakest. Additionally, the Fe(6h)-Ti(4f) bond in Ti 3 Fe 8 Si was slightly stronger than that in Ti 4 Fe 7 Si-h. However, the electron density difference between the Fe(6h) and Fe(2a) atoms was negative. Based on the results presented above, it can be concluded that the covalent interactions between the Fe(2a) and Fe(6h) atoms were significantly enhanced when a Si atom occupied the Fe (2a or 6h) site, but weakened when the Si atom occupied the Ti(4f) site. The degree of weakening of the covalent interactions between the Ti(4f) and Fe(6h) atoms was primarily influenced by the presence of the Si atom at the 6h site. This paper not only provides a theoretical basis for the potential advancements in the physical properties of TiFe 2 and its steel-containing materials but also contributes to the development of other intermetallic compounds. Discussion The structures resulting from the substitution of Fe atoms with Si atoms were found to be more stable than the original structure, with the preferential substitution occurring at the 2a Wyckoff site. The introduction of Si atoms weakened the plasticity of the alloys while enhancing the elastic modulus and hardness. Centimeter-sized single crystals of TiFe 2 and Ti 4 Fe 7 Si were experimentally synthesized, and nano-hardness measurements confirmed the enhancement of hardness and elastic modulus in TiFe 2 due to Si atom substitution. The increases in hardness and Young’s modulus were 63.8% and 33.7%, respectively. Both the original lattice and each of the three silicon alloys exhibited a combination of metallic and covalent bonds, with significant covalent interactions observed between the Fe (6h) and Ti (4f) atoms, as well as between the Fe (6h) and Fe (2a) atoms. The substitution of Si atoms disrupted the original symmetric electronic structure, leading to the strengthening of directional covalent bonds. Methods First-principles calculations The calculations were performed with the first-principles calculations program in the Vienna Ab-initio Simulation Package (VASP), which is based on the basis group of pseudopotential plane waves. Since the valence electron configuration of Fe is 3d 6 4s 2 , the generalized gradient approximation (GGA) was used for the exchange and correlation functions 57 . The GGA based on the Perdew-Burke-Ernzerhof functional 58 , 59 is more accurate than the local density approximation in reflecting the spin polarization 58 . The k-point grid in the Brillouin zone was set to 9 × 9 × 4 in the structural optimization and in the calculations of the mechanical properties. In addition, the cut-off energy of the plane waves was set to 450 eV, and the energy convergence accuracy was set to 10 − 5 eV atom − 1 . In the optimization of the crystalline structures, all structures were allowed to fully relax until the stresses on all atoms were less than 0.02 eV Å −1 . Also, all calculations were performed by using the spin polarization method (spin = 2 in the INCAR file), and the strong magnetism of Fe was used as the initial value of the magnetic moment in the INCAR file (2.0 µ B for Fe). Finally, the elastic constants and moduli were calculated by using the strain-stress method and the Voigt-Reuss-Hill method, respectively 60 . Sample preparation The Czochralski method has in the present study been used to prepare pure TiFe 2 and Ti 4 Fe 7 Si single crystals. A four-arc high-temperature single-crystal growth furnace was then used for this purpose ( Section S2 ). This equipment is very suitable for the growth of intermetallic compounds with active chemical properties and high melting points (usually around 3000 ℃). These compounds include binary and quaternary intermetallic compounds containing rare earth elements (or metallic uranium). High-quality ingredients Ti, Fe, and Si were weighed out in a molar ratio of 1: 1.75: 0.25, arc-melted thrice under argon an atmosphere, utilizing a titanium ingot as an oxygen getter. The polycrystalline samples were then melted in the four-arc furnace to grow the single crystal. Microstructural characterizations The microstructures of these samples were characterized by using field emission scanning electron microscopy (FESEM; Apreo S). Also, the accurate elemental ratios of the single crystals were characterized by using energy dispersive spectroscopy (EDS; Oxford). Furthermore, X-ray diffraction (XRD; SmartLab SE) and four-circle diffractometer used to characterize the crystalline structures and analyze the single-crystal qualities of the samples, respectively. Mechanical tests The hardness and Young’s modulus of TiFe 2 and Ti 4 Fe 7 Si were examined by the Nanoindenter (KLA G200). There are 10 points were randomly selected on the single-crystal for testing using a wedge-shaped indenter in continuous stiffness mode, and the maximum indentation depth is 2 µm. Declarations Data availability All data that support the findings in this paper are available within the article and its Supplementary Information. Acknowledgments This work is supported by the National Natural Science Foundation of China (Nos. 12174296 and U20A20279), Major Program (JD) of Hubei Province (No. 2023BAA019-5), the Science and Technology Program of Guangxi Province (No. AA22068080), the Taishan Industry Leading Talent Project (No. 2020007), the Leading Innovation and Pioneering Team of Zhejiang Province (No. 2021R01020) and the 111 Project (No. D18018). The calculations were carried out at the High-Performance Computing Center of Wuhan University of Science and Technology and National Supercomputer Centre in TianHe1(A). The single-crystal preparation experiments were carried out at the Material Genome Research Platform of the Institute of Physics, Chinese Academy of Sciences. Author contributions X.Y.T. conducted the nano-hardness experiments and wrote the paper. H.X.L. conducted the single-crystal experiments and wrote the paper. 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N., Rao, S., Chaput, K. J. & Woodward, C. Compositional effect on microstructure and properties of NbTiZr-based complex concentrated alloys. Acta Mater. 151 , 201-215 (2018). Li, Y. et al. Theoretical study on the stability, elasticity, hardness and electronic structures of W-C binary compounds. J. Alloys Compd. 502, 28-37 (2010). Li, P., Ma, L., Peng, M., Shu, B. & Duan, Y. Elastic anisotropies and thermal conductivities of WB 2 diborides in different crystal structures: A first-principles calculation. J. Alloys Compd. 747 , 905-915 (2018). Jian, Y. et al. Phase stability, mechanical properties and electronic structures of Ti Al binary compounds by first principles calculations. Mater. Chem. Phys. 221 , 311-321 (2019). Simunek, A. & Vackar, J. Hardness of covalent and ionic crystals: first-principle calculations. Phys. Rev. Lett. 96 , 085501 (2006). Vecchio, K. et al. Fermi energy engineering of enhanced plasticity in high-entropy carbides. Acta Mater. 276 , 120117 (2024). 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Additional Declarations The authors declare no competing interests. Supplementary Files Supplementary2024.11.05.docx SupplementaryInformation-Hardness Augmentation Engineering of TiFe 2 with Doping Design and Single-crystal Realization Cite Share Download PDF Status: Posted 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-5457104","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":378372719,"identity":"5169e002-ac71-4e38-9cd6-0c2a5d99ac27","order_by":0,"name":"Xinyang Tan","email":"","orcid":"","institution":"Wuhan University of Science and Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Xinyang","middleName":"","lastName":"Tan","suffix":""},{"id":378372720,"identity":"3c324d92-d7f0-4d77-a04f-17cd56b01d12","order_by":1,"name":"Hongxiong Liu","email":"","orcid":"","institution":"Chinese Academy of Sciences","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Hongxiong","middleName":"","lastName":"Liu","suffix":""},{"id":378372721,"identity":"dabd8e2c-a107-4740-be5f-3d234245e283","order_by":2,"name":"Tingping Hou","email":"","orcid":"https://orcid.org/0000-0003-3411-5351","institution":"Wuhan University of Science and Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Tingping","middleName":"","lastName":"Hou","suffix":""},{"id":378372722,"identity":"4c98949c-31c8-4a62-8dd1-3dee6c8cf8a6","order_by":3,"name":"Sicong Zhu","email":"","orcid":"","institution":"Wuhan University of Science and Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Sicong","middleName":"","lastName":"Zhu","suffix":""},{"id":378372723,"identity":"d255e1b1-d331-4f7f-9182-04f40cd63884","order_by":4,"name":"Gengping Jiang","email":"","orcid":"","institution":"Wuhan University of Science and Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Gengping","middleName":"","lastName":"Jiang","suffix":""},{"id":378372724,"identity":"4a364b43-673c-45c1-a6fe-4da54d0fc18b","order_by":5,"name":"Dong Zhang","email":"","orcid":"","institution":"Wuhan University of Science and Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Dong","middleName":"","lastName":"Zhang","suffix":""},{"id":378372725,"identity":"e0644a13-5228-4f49-999a-1cdbb8b00bdb","order_by":6,"name":"Junwen Duan","email":"","orcid":"","institution":"Wuhan University of Science and Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Junwen","middleName":"","lastName":"Duan","suffix":""},{"id":378372726,"identity":"db5edf65-b639-4ce6-90ad-50960b917e25","order_by":7,"name":"Xuan Liang","email":"","orcid":"","institution":"Wuhan University of Science and Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Xuan","middleName":"","lastName":"Liang","suffix":""},{"id":378372727,"identity":"e6eb67db-07b6-48eb-8838-30a5384a5fa3","order_by":8,"name":"Kaiming Wu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA40lEQVRIiWNgGAWjYFACNgaGBAYJBgb2BqjAAaK18ICUJhCrBQwkEojUYnAjLfHDwxyLPPnIN2aSP38wyPHdSGD8XIBfy2GJxG0SxYa3c8ykeRIYjCVvJDBLz8CjxexGegNIS+LG2bnbpIEOS9xwI4GNmQe/luYfYC0zz26T/JHAUE+ElrRjYFvmS/BukwA6LMGAkBb7M8/SLEBaNvDkf7bmSZMwnHnmYbM0Pi2S7WnGN39uq0uc334s8eYPGxt5vuPJBz/j0wIHBgfAFDBOGRgbiNHAwCBPpLpRMApGwSgYgQAACwFNumeJxYMAAAAASUVORK5CYII=","orcid":"","institution":"Wuhan University of Science and Technology","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Kaiming","middleName":"","lastName":"Wu","suffix":""},{"id":378372728,"identity":"ee22ce06-9e79-464c-bb08-b8a0231c38b2","order_by":9,"name":"Wuming Liu","email":"","orcid":"","institution":"Chinese Academy of Sciences","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Wuming","middleName":"","lastName":"Liu","suffix":""}],"badges":[],"createdAt":"2024-11-15 02:48:07","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false,"coiExplicitlySet":false},"doi":"10.21203/rs.3.rs-5457104/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5457104/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":69227182,"identity":"fae04a61-a242-4831-99be-b2f4afff7aec","added_by":"auto","created_at":"2024-11-18 08:23:08","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":678583,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ea\u003c/strong\u003e Three possible configurations of the substituting element \u003cem\u003eM\u003c/em\u003e. \u003cstrong\u003eb\u003c/strong\u003e Crystal structure of Laves phase TiFe\u003csub\u003e2\u003c/sub\u003e. \u003cstrong\u003ec\u003c/strong\u003e Hardness, elastic modulus and formation enthalpies of structures with different substitution elements \u003cem\u003eM\u003c/em\u003e. \u003cstrong\u003ed\u003c/strong\u003e The relationship between cell volume and energy with temperature (The illustration shows the contribution of vibration in free energy).\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5457104/v1/f274ccaeaa967571a200c684.png"},{"id":69227184,"identity":"21f88690-7065-4602-b72f-3a299d50872c","added_by":"auto","created_at":"2024-11-18 08:23:08","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":365481,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ea\u003c/strong\u003e Internal structure of the furnace chamber and the process of single-crystal preparation. \u003cstrong\u003eb\u003c/strong\u003e Single-crystal of Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi. \u003cstrong\u003ec \u003c/strong\u003eXRD of Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi. \u003cstrong\u003ed\u003c/strong\u003e SEM image of cross-section. \u003cstrong\u003ee-g\u003c/strong\u003e EDS mapping of Ti, Fe and Si. \u003cstrong\u003eh\u003c/strong\u003e EDS spectra. \u003cstrong\u003ei\u003c/strong\u003e and \u003cstrong\u003ej\u003c/strong\u003e mass percent and atomic percent.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5457104/v1/758a11e2103515e9c8b22266.png"},{"id":69227181,"identity":"4e3aee04-95f6-42a6-af7a-3613a379ad22","added_by":"auto","created_at":"2024-11-18 08:23:07","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":971743,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ea\u003c/strong\u003e Hardness curve of TiFe\u003csub\u003e2\u003c/sub\u003e and Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi. \u003cstrong\u003eb\u003c/strong\u003e Young’s modulus curve of TiFe\u003csub\u003e2\u003c/sub\u003e and Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi. \u003cstrong\u003ec\u003c/strong\u003e The experiment statistics and calculation results about hardness and Young’s modulus of TiFe\u003csub\u003e2\u003c/sub\u003e, Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi and some alloying compounds. \u003cstrong\u003ed-g\u003c/strong\u003e Surface construction of Young’s modulus for TiFe\u003csub\u003e2\u003c/sub\u003e, Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a, Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-h, Ti\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e8\u003c/sub\u003eSi. \u003cstrong\u003eh-j\u003c/strong\u003e Projections of Young’s modulus at the (001), (010) and (100) crystal planes.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5457104/v1/6e296f7e2861da0206c37658.png"},{"id":69227183,"identity":"4f4af059-8098-4036-93c1-f76b570d64cc","added_by":"auto","created_at":"2024-11-18 08:23:08","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1058894,"visible":true,"origin":"","legend":"\u003cp\u003eElectron density difference maps: \u003cstrong\u003ea\u003c/strong\u003e TiFe\u003csub\u003e2\u003c/sub\u003e, \u003cstrong\u003eb\u003c/strong\u003e Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a, \u003cstrong\u003ec\u003c/strong\u003e Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-h, \u003cstrong\u003ed\u003c/strong\u003e Ti\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e8\u003c/sub\u003eSi. \u003cstrong\u003ee\u003c/strong\u003e Electron density difference distribution for Fe (6h) atom with nearest Ti (4f) atom and Fe (2a) atom. The distribution of electron is presented from - 0.01 to 0.01 e/Bohr\u003csup\u003e3\u003c/sup\u003e. \u003cstrong\u003ef\u003c/strong\u003e Electron density difference value curve between Fe (6h) atom and Ti (4f) atom. \u003cstrong\u003eg\u003c/strong\u003e Electron density difference value curve between Fe (6h) atom and Fe (2a) atom. \u003cstrong\u003eh-k\u003c/strong\u003e Calculation of TDOS (black line) and LDOS with different Wyckoff site atoms (Fe (2a), Fe (6h), Ti and Si (2a, 6h, 4f), respectively). The dashed vertical line at 0 eV reflects the Fermi energy level. (\u003cstrong\u003eh\u003c/strong\u003e Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi−a; \u003cstrong\u003ei\u003c/strong\u003e Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi−h; \u003cstrong\u003ej\u003c/strong\u003e Ti\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e8\u003c/sub\u003eSi; \u003cstrong\u003ek\u003c/strong\u003e TiFe\u003csub\u003e2\u003c/sub\u003e). \u003cstrong\u003el\u003c/strong\u003e LDOS of Fe atom at 2a position of three Ti-Fe-Si compounds. \u003cstrong\u003em\u003c/strong\u003e LDOS of Fe atom at 6h position of three Ti-Fe-Si compounds. \u003cstrong\u003en\u003c/strong\u003e LDOS of Ti atom at 4f position of three Ti-Fe-Si compounds.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5457104/v1/fc0de1323180addb0c32f6e8.png"},{"id":69228839,"identity":"565ae532-15e5-44a8-b1c1-203c63123549","added_by":"auto","created_at":"2024-11-18 08:31:10","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3632312,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5457104/v1/0c1404f4-c315-44fa-9d60-da2ce586889b.pdf"},{"id":69227204,"identity":"3ce0f405-4494-43c0-873f-9206795ff07a","added_by":"auto","created_at":"2024-11-18 08:23:10","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":3420603,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSupplementaryInformation-Hardness Augmentation Engineering of TiFe\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e with Doping Design and Single-crystal Realization\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"Supplementary2024.11.05.docx","url":"https://assets-eu.researchsquare.com/files/rs-5457104/v1/11ab0c930065e378efa64bf0.docx"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eHardness Augmentation Engineering of TiFe\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e with Doping Design and Single-crystal Realization\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe exploration of new materials with exceptional properties is a fundamental pursuit for scientists and engineers. Laves phase-reinforced alloys exhibit high strength and superior hardness, making them valuable for applications in aerospace and automotive industries\u003csup\u003e\u003cspan additionalcitationids=\"CR2 CR3 CR4\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. The three crystal structure polytypes of Laves phases (C14, C15, and C36) are formed with AB₂ compositions of various elements, with radius ratios (r\u003csub\u003eA\u003c/sub\u003e/r\u003csub\u003eB\u003c/sub\u003e) ranging from 1.19 to 1.32\u003csup\u003e6,7\u003c/sup\u003e. The comparable simple crystalline structures and versatile combinations of elements enable Laves phases to possess a variety of unique properties, including nanoparticle superlattices\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e,\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e, hydrogen storage\u003csup\u003e\u003cspan additionalcitationids=\"CR11 CR12 CR13\" citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e, superconductivity\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e,\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e, and thermostability\u003csup\u003e\u003cspan additionalcitationids=\"CR18 CR19\" citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eIn recent years, an increasing number of researchers have recognized the excellent performance of C14 TiFe\u003csub\u003e2\u003c/sub\u003e as a strengthening phase in coatings and alloy matrices. Previous investigations have shown that FCC high-entropy alloys (HEAs) possess good ductility but limited strength\u003csup\u003e\u003cspan additionalcitationids=\"CR22 CR23\" citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. To enhance the strength of these materials, researchers have incorporated Ti to form TiFe\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e24,25\u003c/sup\u003e. Furthermore, TiFe\u003csub\u003e2\u003c/sub\u003e can improve the wear and oxidation resistance of coatings for structural materials\u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e,\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e. These findings highlight the necessity of augmenting the hardness and strength of TiFe\u003csub\u003e2\u003c/sub\u003e to further reinforce both the substrate and the coating. In addition to the close relationship between macroscopic grain size and hardness\u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e, the hardness and strength of a unit cell on the nanoscale depend on the nature of its chemical bonding and stability\u003csup\u003e\u003cspan additionalcitationids=\"CR30 CR31 CR32\" citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e. Low-content doping can significantly alter properties by modulating the electronic structure without changing the original cell type\u003csup\u003e\u003cspan additionalcitationids=\"CR35\" citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e. Trial-and-error experimental approaches are costly and time-consuming, while previously reported phase-formation rules are empirical. It is more effective to predict phase stability and microstructure to accelerate the design of Laves phases through a first-principles theoretical approach. Previous studies have not clarified the mechanisms by which doping alters macroscopic hardness through disturbances in the electronic structure. Furthermore, there is a lack of robust experimental evidence to substantiate the hardness enhancements predicted by theoretical calculations. In this work, TiFe\u003csub\u003e2\u003c/sub\u003e was doped with various elements (Co, Mn, Ni, V, Cr, Si, B, S), and it was found that silicon (Si) resulted in the most significant increase in hardness. Finally, in-depth research was conducted on Si-doped TiFe\u003csub\u003e2\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003eIn this paper, the Ti-Fe-Si ternary alloy system (Ti\u003csub\u003ex\u003c/sub\u003eFe\u003csub\u003e11\u0026minus;x\u003c/sub\u003eSi, where x\u0026thinsp;=\u0026thinsp;3 or 4) has been constructed. The structural stability, mechanical properties, and electronic structure of Ti\u003csub\u003ex\u003c/sub\u003eFe\u003csub\u003e11\u0026minus;x\u003c/sub\u003eSi were calculated, and centimeter-scale single-crystal samples TiFe\u003csub\u003e2\u003c/sub\u003e and Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi were prepared experimentally. The elastic modulus and hardness were tested and compared. First, the most stable structure (Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi) and the metastable structure (Ti\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e8\u003c/sub\u003eSi) were identified, and the mechanical properties and thermodynamic curves of the most stable structure were calculated. Subsequently, based on the thermodynamic curves, TiFe\u003csub\u003e2\u003c/sub\u003e and Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi single-crystals were prepared using the Czochralski method\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e, and their hardness and elastic modulus were examined. The results indicate that the experimental findings are consistent with the theoretical predictions. Finally, the influence of Si alloying on the mechanical properties of TiFe\u003csub\u003e2\u003c/sub\u003e was analyzed from the perspectives of electronic structure and bonding characteristics.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eModel Designs and Screening for Hardness Augmentation\u003c/p\u003e \u003cp\u003eThe TiFe\u003csub\u003e2\u003c/sub\u003e unit cell model consists of eight Fe atoms located at the 2a and 6h Wyckoff positions (denoted as Fe(2a) and Fe(6h), respectively) and four Ti atoms positioned at the 4f Wyckoff sites (Ti(4f)) (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea). The Fe atoms form corner-sharing tetrahedral units. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb illustrates the hourglass-shaped polyhedron formed by Fe atoms, consisting of two centrally symmetric tetrahedra. The Ti atoms are positioned within these polyhedra, each surrounded by three hourglass-shaped polyhedra formed by Fe atoms. The Fe(6h) atoms possess effective magnetic moments aligned along the c-axis\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e,\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e. To identify favorable alloying elements for the TiFe\u003csub\u003e2\u003c/sub\u003e structure, this study selected elements frequently observed in high-entropy alloys. Fe atoms in the TiFe\u003csub\u003e2\u003c/sub\u003e model were sequentially substituted by different elements at the same atomic positions, maintaining an atomic ratio of Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eM (M\u0026thinsp;=\u0026thinsp;Fe, Co, Mn, Ni, V, Cr, Si, B, S). Formation enthalpies (\u003cem\u003eΔH\u003c/em\u003e) \u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e,\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e, hardness, and elastic moduli of these structures were calculated using first-principles methods, with the results presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec. These results indicate that Si has the most favorable overall effect on the TiFe\u003csub\u003e2\u003c/sub\u003e structure. Consequently, Si was selected as the doping element for further calculations and experiments.\u003c/p\u003e \u003cp\u003eThere are three possible configurations when a Si atom substitutes for Fe(2a), Fe(6h), or Ti(4f) atoms in the formation of the ternary compounds Ti\u003csub\u003ex\u003c/sub\u003eFe\u003csub\u003e11\u0026minus;x\u003c/sub\u003eSi (x\u0026thinsp;=\u0026thinsp;3 or 4). The models formed by substituting Si for Fe(2a) and Fe(6h) are denoted as Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a and Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-h, respectively. Ti\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e8\u003c/sub\u003eSi represents the structure where a Ti atom at the 4f site is replaced by a Si atom. To elucidate the ground-state characteristics of TiFe\u003csub\u003e2\u003c/sub\u003e, Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a, Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-h, and Ti\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e8\u003c/sub\u003eSi under zero pressure, Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents the calculated equilibrium lattice parameters, Wyckoff positions, and cell volumes of the fully relaxed structures. The calculated results are consistent with those reported in the literature\u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e,\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e, confirming the reliability of the theoretical parameters used in this study. The decrease in cell volume observed in the Si-alloyed samples can be attributed to lattice distortions caused by the substitution of a host atom with a Si atom.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCalculated and experimental results equilibrium structural parameters\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCompound\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWyckoff position\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003ea\u003c/em\u003e (\u0026Aring;)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003ec\u003c/em\u003e (\u0026Aring;)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eα\u003c/em\u003e,\u003cem\u003eβ\u003c/em\u003e,\u003cem\u003eγ\u003c/em\u003e (˚)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003eV\u003c/em\u003e (\u0026Aring;\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003eΔH\u003c/em\u003e\u003c/p\u003e \u003cp\u003e(eV/atom)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003eΔE\u003c/em\u003e\u003c/p\u003e \u003cp\u003e(eV/atom)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eTiFe\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026mdash;\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4.756\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.736\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90,90,120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e151.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-7.102\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026mdash;\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4.778\u003csup\u003e39\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.761\u003csup\u003e39\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026mdash;\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4.686\u003csup\u003e42\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.732\u003csup\u003e42\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTi\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi\u0026thinsp;\u0026minus;\u0026thinsp;a\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2a\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4.756\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.728\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90,90,120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e151.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-8.323\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-1.221\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTi\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi\u0026thinsp;\u0026minus;\u0026thinsp;h\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6h\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4.736\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.750\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90,90,120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e150.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-8.189\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-1.087\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTi\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e8\u003c/sub\u003eSi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4f\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4.719\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.663\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90,90,120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e147.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e-6.852\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.249\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe formation enthalpies (ΔH) and reaction energies (ΔE) \u003csup\u003e\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e,\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e were calculated to assess the structural stabilities of TiFe\u003csub\u003e2\u003c/sub\u003e, Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a, Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-h, and Ti\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e8\u003c/sub\u003eSi (\u003cb\u003eSection S3\u003c/b\u003e). A negative reaction energy indicates that the total energy of the products is lower than that of the reactants. As shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a and Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-h exhibited negative reaction energies, while Ti\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e8\u003c/sub\u003eSi showed a positive reaction energy. Therefore, the substitution of a Si atom in Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a and Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-h is thermodynamically feasible, resulting in stable products, with reaction energies of -1.221\u0026nbsp;eV/atom and \u0026minus;\u0026thinsp;1.087\u0026nbsp;eV/atom, respectively. In contrast, the substitution of a Si atom in Ti\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e8\u003c/sub\u003eSi is not thermodynamically feasible, as indicated by its positive reaction energy of 0.249\u0026nbsp;eV/atom. These results suggest that Si atoms preferentially occupy the 2a Wyckoff sites. In summary, the structures of Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a and Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-h are stable, with Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a exhibiting the highest stability\u003csup\u003e\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eSingle-crystal Preparation of Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi and TiFe\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003cp\u003eTo obtain precise data on the effect of element substitution on hardness enhancement, it is essential to use samples of high purity and crystallinity, minimizing the influence of dislocations and grain boundaries. Based on the equilibrium lattice constants of Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a, a series of lattice constants were further studied in relation to the total energy of Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a. The relationship between the calculated total energy and volume is depicted in \u003cb\u003eFig. S4\u003c/b\u003e. This relationship was then used as input data for the Gibbs2 program\u003csup\u003e\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e to determine the thermodynamic parameters of Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a at elevated temperatures, ranging from 0 K to 2000 K. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ed illustrates the total energy and volume of the crystalline cells as a function of temperature. The results suggest that the reduction in total energy is primarily due to lattice vibrations, as shown in the Fig.. The temperature range, marked by two dashed lines, is proposed as the optimal range for single-crystal preparation.\u003c/p\u003e \u003cp\u003eBased on the results of the theoretical calculations, single-crystal samples of TiFe\u003csub\u003e2\u003c/sub\u003e (\u003cb\u003eFig. S3\u003c/b\u003e) and Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi were successfully prepared using the Czochralski method\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e. The equipment employed in the experiment was a four-arc single-crystal growth furnace, and a schematic diagram of the device is presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The preparation process is described in \u003cb\u003eSection S2\u003c/b\u003e. The TiFe\u003csub\u003e2\u003c/sub\u003e and Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi crystals produced by this method were cylindrical, with diameters ranging from 0.3 cm to 0.4 cm and lengths of 2 cm. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb shows a rod-shaped single-crystal of Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi under an optical microscope.\u003c/p\u003e \u003cp\u003eThe structures and compositions of the samples were subsequently characterized to verify the successful preparation of the single crystals. The X-ray diffraction (XRD) results are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec. It was concluded that the crystalline structure of Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi is identical to that of TiFe\u003csub\u003e2\u003c/sub\u003e. Scanning electron microscopy (SEM) was then employed to analyze the microstructure of the samples. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed, the Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi sample exhibited high crystallinity, with no grain boundaries or inclusions. \u003cb\u003eFig.s 2e-g\u003c/b\u003e present the energy dispersive spectroscopy (EDS) mappings for Ti, Fe, and Si, while Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eh displays the EDS spectra. The distribution of Si was consistent with that of Ti and Fe, and the proportions of the three elements matched the relative mass ratio of Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi. Based on the results presented above, it can be concluded that the preparation of the Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi single-crystal was successful.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eInfluence of the Hardness Augmentation Methodology on TiFe\u003csub\u003e2\u003c/sub\u003e Mechanical Properties\u003c/p\u003e \u003cp\u003eNano-indentation experiments were conducted to examine the hardness and Young's modulus of single crystals, investigating the effect of Si on the properties of TiFe\u003csub\u003e2\u003c/sub\u003e. The test curves are presented in \u003cb\u003eFig.s 3a\u003c/b\u003e and \u003cb\u003e3b\u003c/b\u003e, while the maximum values are summarized in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec. The average hardness (22.92 GPa) and Young's modulus (334.85 GPa) of Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi were significantly higher compared to the hardness (13.99 GPa) and Young's modulus (250.44 GPa) of TiFe\u003csub\u003e2\u003c/sub\u003e, with increases of 63.8% and 33.7%, respectively. Theoretical predictions for the hardness and Young's modulus of TiFe\u003csub\u003e2\u003c/sub\u003e (6.75 GPa; 171.52 GPa), Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a (10.44 GPa; 201.83 GPa), and Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-h (11.35 GPa; 194.51 GPa) are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec. For comparison, data on intermetallic compounds and wear-resistant alloys were also collected\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e,\u003cspan additionalcitationids=\"CR48\" citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e. The hardness and Young's modulus of Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a and Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-h exceeded those of TiFe\u003csub\u003e2\u003c/sub\u003e. Although numerical deviations existed between theoretical results (calculated under 0 K and 0 Pa) and experimental findings, the overall trend of improvement was consistent. The experimental enhancement of the hardness and Young's modulus of TiFe\u003csub\u003e2\u003c/sub\u003e due to Si doping has thus been theoretically validated.\u003c/p\u003e \u003cp\u003eBased on the calculated elastic constants, the bulk modulus (\u003cem\u003eB\u003c/em\u003e), shear modulus (\u003cem\u003eG\u003c/em\u003e), Young\u0026rsquo;s modulus (\u003cem\u003eE\u003c/em\u003e), and anisotropy (\u003cem\u003eA\u003c/em\u003e\u003csup\u003e\u003cem\u003eU\u003c/em\u003e\u003c/sup\u003e) were determined using the Voigt-Reuss-Hill approximation (\u003cb\u003eSection S4\u003c/b\u003e). The values of these mechanical parameters are presented in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Generally, \u003cem\u003eB\u003c/em\u003e reflects a structure\u0026rsquo;s ability to resist volume change under external compression, while \u003cem\u003eG\u003c/em\u003e characterizes resistance to shear deformation\u003csup\u003e\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e. The calculated results showed that TiFe\u003csub\u003e2\u003c/sub\u003e had the highest bulk modulus (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{B}_{H}\\)\u003c/span\u003e\u003c/span\u003e) value (262.20 GPa), indicating that the structure\u0026rsquo;s resistance to volume change decreased when Si atoms were substituted into the TiFe\u003csub\u003e2\u003c/sub\u003e crystalline structure. Moreover, the shear modulus (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{G}_{H}\\)\u003c/span\u003e\u003c/span\u003e) values for Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a and Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-h were similar and higher than that of TiFe\u003csub\u003e2\u003c/sub\u003e, whereas Ti\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e8\u003c/sub\u003eSi had the lowest \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{G}_{H}\\)\u003c/span\u003e\u003c/span\u003e value (69.56 GPa). These results demonstrate that Si substitution at the 2a and 6h Wyckoff sites enhanced the structure\u0026rsquo;s resistance to shear strain, while substitution at the 4f Wyckoff site weakened it.\u003c/p\u003e \u003cp\u003eThe Young\u0026rsquo;s modulus (\u003cem\u003eE\u003c/em\u003e) represents the stiffness of a material, with a higher \u003cem\u003eE\u003c/em\u003e value indicating greater stiffness\u003csup\u003e\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e\u003c/sup\u003e. As shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a exhibited the highest \u003cem\u003eE\u003c/em\u003e value (229.27 GPa), closely followed by Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-h (226.34 GPa), while Ti\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e8\u003c/sub\u003eSi had the lowest \u003cem\u003eE\u003c/em\u003e value (180.98 GPa). These results suggest that Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a and Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-h are significantly stiffer than TiFe\u003csub\u003e2\u003c/sub\u003e and Ti\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e8\u003c/sub\u003eSi. The \u003cem\u003eB\u003c/em\u003e-to-\u003cem\u003eG\u003c/em\u003e ratio is commonly used to evaluate a material's ductility, and Poisson\u0026rsquo;s ratio (v) is also a standard measure to distinguish between ductility and brittleness. A solid is considered to exhibit metallic ductility if \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{B}_{H}/{G}_{H}\u0026gt;1.75\\)\u003c/span\u003e\u003c/span\u003e (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:v\u0026gt;0.26\\)\u003c/span\u003e\u003c/span\u003e) \u003csup\u003e\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e\u003c/sup\u003e; otherwise, it is classified as brittle. As shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{B}_{H}/{G}_{H}\\left(v\\right)\\)\u003c/span\u003e\u003c/span\u003e ratios for all structures exceeded 1.75 (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:v\u0026gt;\\)\u003c/span\u003e\u003c/span\u003e 0.26), indicating good ductility across all structures. TiFe\u003csub\u003e2\u003c/sub\u003e exhibited the highest ductility, as reflected in its larger \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{B}_{H}/{G}_{H}\\left(v\\right)\\)\u003c/span\u003e\u003c/span\u003e ratio compared to the other structures.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe bulk modulus \u003cem\u003eB\u003c/em\u003e (GPa), shear modulus \u003cem\u003eG\u003c/em\u003e (GPa), Young's modulus \u003cem\u003eE\u003c/em\u003e (GPa), Poisson's ratio \u003cem\u003ev\u003c/em\u003e, Paugh's ratio \u003cem\u003eB/G\u003c/em\u003e and anisotropic factors A\u003csup\u003eU\u003c/sup\u003e of compounds.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{S}\\text{t}\\text{r}\\text{u}\\text{c}\\text{t}\\text{u}\\text{r}\\text{e}\\text{s}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{B}_{H}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{G}_{H}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:E\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:B/G\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:v\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{A}^{U}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTi\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e143.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e89.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e229.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.282\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.257\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTi\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-h\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e128.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e89.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e226.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.264\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.013\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTi\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e8\u003c/sub\u003eSi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e151.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e69.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e180.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.301\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.142\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTiFe\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e262.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e72.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e200.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.373\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.011\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo explore the anisotropic properties of these materials, the three-dimensional (3D) surface representations of the Young\u0026rsquo;s moduli for TiFe\u003csub\u003e2\u003c/sub\u003e, Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a, Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-h, and Ti\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e8\u003c/sub\u003eSi, along with projections of the 3D Young\u0026rsquo;s moduli on the (100), (010), and (001) planes, are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed-j. The surface representations of the Young\u0026rsquo;s modulus provide a clearer understanding of a material\u0026rsquo;s degree of anisotropy across different orientations. A greater deviation of the surface structure from an ideal sphere indicates stronger elastic anisotropy within the unit cell. In this study, it is evident that the Young's moduli of the three Ti-Fe-Si compounds exhibit significant anisotropies, with the order of elastic anisotropy being Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a\u0026thinsp;\u0026gt;\u0026thinsp;Ti\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e8\u003c/sub\u003eSi\u0026thinsp;\u0026gt;\u0026thinsp;Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-h.\u003c/p\u003e \u003cp\u003eDeconstruction of Physical Characteristics of TiFe\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003cp\u003eIn this study, the electron density difference distributions have been calculated to gain a deeper understanding of the effect of Si alloying on the structure and properties of TiFe\u003csub\u003e2\u003c/sub\u003e. This density difference is defined as the discrepancy between the electron density of the compound and the sum of the electron densities of the corresponding isolated atoms. Additionally, the total density of states (TDOS) and local density of states (LDOS) have been analyzed to provide more detailed insights into the physical characteristics. In consideration of the magnetic properties of the materials, spin polarization was incorporated during the calculations of the densities of states (DOS). Consequently, the spin-up DOS was found to be asymmetric in relation to the spin-down DOS for both TiFe\u003csub\u003e2\u003c/sub\u003e and all three Ti-Fe-Si ternary compounds.\u003c/p\u003e \u003cp\u003eThis suggests that these compounds exhibit ferromagnetic characteristics. As illustrated in \u003cb\u003eFig.s 4h-k\u003c/b\u003e, the TDOS near the Fermi level (\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e) is distinctly non-zero, indicating that these compounds are metallic. It was also observed that when Si occupies a specific lattice site, the LDOS peaks of other atoms at the same type of site decrease in intensity. For instance, the LDOS of the Fe(2a) atom in Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a is significantly lower than that of the Fe(2a) atoms in Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-h and Ti\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e8\u003c/sub\u003eSi. This trend is also evident for the Fe(6h) and Ti(4f) atoms. Additionally, the spin-down LDOS is lower in intensity compared to the spin-up LDOS (\u003cb\u003eFig.s 4l-n\u003c/b\u003e). Although the contribution of the substitutional Si atom to the DOS is negligible, it nonetheless influences the electrical and magnetic properties of the samples.\u003c/p\u003e \u003cp\u003eAs shown in \u003cb\u003eFig.s 4a-c\u003c/b\u003e, it is clear that some electrons are delocalized and distributed like rivers in the interstitial regions close to the Ti and Fe atoms, implying the existence of metallic and covalent bonding. This result is consistent with the analyses of the DOS. After substituting the original lattice with Si atoms (\u003cb\u003eFig.s 4h-k\u003c/b\u003e), it is evident that a portion of the corresponding DOS is positioned at higher energy levels in the conduction band. There is a tendency for hybridization between the orbitals of the Fe (2a) and Fe (6h) atoms in the energy range of approximately \u0026minus;\u0026thinsp;4 eV to 0 eV, while hybridization between the orbitals of the Fe (6h) and Ti (4f) atoms is apparent in the range of 0 eV to 2 eV (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ek). This suggests that the covalent bonds in the compounds primarily originate from the interactions of Fe (6h)-Ti (4f) and Fe (6h)-Fe (2a), which are major contributing factors to the hardness of TiFe\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e53\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eOrigin of the Hardness Augmenting through Influence of Si Doping on the Bond Strength\u003c/p\u003e \u003cp\u003eIt is noteworthy that a deep minimum was found in the TDOS near the \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e for each of the Ti-Fe-Si compounds. This minimum is referred to as a pseudo gap. Generally, a pseudo gap indicates the presence of strong covalent interactions (i.e., a covalent bond) \u003csup\u003e\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e\u003c/sup\u003e. A wider pseudo gap corresponds to a stronger covalent bond. Therefore, it can be concluded from the TDOS that the covalent bonds in Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a and Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-h are stronger than those in Ti\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e8\u003c/sub\u003eSi. Strong covalent bonds typically correlate with a stable structure. In this context, Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a and Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-h exhibit more stable structures and superior hardness, while Ti\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e8\u003c/sub\u003eSi is the weakest. This conclusion aligns with the formation enthalpies presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eOn the other hand, the directional covalent interactions between the Fe(6h) and Ti(4f) atoms resulted in an uneven distribution of bonding forces\u003csup\u003e\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e,\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e\u003c/sup\u003e, which undoubtedly increased the likelihood of brittle fracture in each of these three compounds along the direction of metallic interactions. This explains the decreased values of σ and \u003cem\u003eB\u003c/em\u003e/\u003cem\u003eG\u003c/em\u003e for Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a, Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-h, and Ti\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e8\u003c/sub\u003eSi. In the present study, the Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a and Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-h materials, with Si atoms substituting the Fe(2a) and Fe(6h) atoms, respectively, exhibited wider pseudo gaps than those in the Ti\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e8\u003c/sub\u003eSi material, which has a Si atom substituting the Ti(4f) atom (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). In this context, the Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a and Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-h materials tended to be more brittle than the Ti\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e8\u003c/sub\u003eSi material, consistent with the values of \u003cem\u003eB\u003c/em\u003e/\u003cem\u003eG\u003c/em\u003e in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eMore specifically, the electron density difference variation diagrams for Fe(6h) to Ti(4f) and Fe(6h) to Fe(2a) are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee-g. The Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a compound exhibited the strongest covalent bonds between Fe(6h)-Ti(4f) and Fe(6h)-Fe(2a). The covalent bond between Fe(6h) and Fe(2a) in Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-h was nearly as strong as that in the Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-a compound, while the Fe(6h)-Ti(4f) bond was the weakest. Additionally, the Fe(6h)-Ti(4f) bond in Ti\u003csub\u003e3\u003c/sub\u003eFe\u003csub\u003e8\u003c/sub\u003eSi was slightly stronger than that in Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi-h. However, the electron density difference between the Fe(6h) and Fe(2a) atoms was negative. Based on the results presented above, it can be concluded that the covalent interactions between the Fe(2a) and Fe(6h) atoms were significantly enhanced when a Si atom occupied the Fe (2a or 6h) site, but weakened when the Si atom occupied the Ti(4f) site. The degree of weakening of the covalent interactions between the Ti(4f) and Fe(6h) atoms was primarily influenced by the presence of the Si atom at the 6h site. This paper not only provides a theoretical basis for the potential advancements in the physical properties of TiFe\u003csub\u003e2\u003c/sub\u003e and its steel-containing materials but also contributes to the development of other intermetallic compounds.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThe structures resulting from the substitution of Fe atoms with Si atoms were found to be more stable than the original structure, with the preferential substitution occurring at the 2a Wyckoff site. The introduction of Si atoms weakened the plasticity of the alloys while enhancing the elastic modulus and hardness. Centimeter-sized single crystals of TiFe\u003csub\u003e2\u003c/sub\u003e and Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi were experimentally synthesized, and nano-hardness measurements confirmed the enhancement of hardness and elastic modulus in TiFe\u003csub\u003e2\u003c/sub\u003e due to Si atom substitution. The increases in hardness and Young\u0026rsquo;s modulus were 63.8% and 33.7%, respectively. Both the original lattice and each of the three silicon alloys exhibited a combination of metallic and covalent bonds, with significant covalent interactions observed between the Fe (6h) and Ti (4f) atoms, as well as between the Fe (6h) and Fe (2a) atoms. The substitution of Si atoms disrupted the original symmetric electronic structure, leading to the strengthening of directional covalent bonds.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003eFirst-principles calculations\u003c/p\u003e \u003cp\u003eThe calculations were performed with the first-principles calculations program in the Vienna Ab-initio Simulation Package (VASP), which is based on the basis group of pseudopotential plane waves. Since the valence electron configuration of Fe is 3d\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e4s\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e, the generalized gradient approximation (GGA) was used for the exchange and correlation functions\u003csup\u003e\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e\u003c/sup\u003e. The GGA based on the Perdew-Burke-Ernzerhof functional\u003csup\u003e\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e,\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e\u003c/sup\u003e is more accurate than the local density approximation in reflecting the spin polarization\u003csup\u003e\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e\u003c/sup\u003e. The k-point grid in the Brillouin zone was set to 9 \u0026times; 9 \u0026times; 4 in the structural optimization and in the calculations of the mechanical properties. In addition, the cut-off energy of the plane waves was set to 450 eV, and the energy convergence accuracy was set to 10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e eV atom\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. In the optimization of the crystalline structures, all structures were allowed to fully relax until the stresses on all atoms were less than 0.02 eV \u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e. Also, all calculations were performed by using the spin polarization method (spin\u0026thinsp;=\u0026thinsp;2 in the INCAR file), and the strong magnetism of Fe was used as the initial value of the magnetic moment in the INCAR file (2.0 \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e for Fe). Finally, the elastic constants and moduli were calculated by using the strain-stress method and the Voigt-Reuss-Hill method, respectively\u003csup\u003e\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e60\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eSample preparation\u003c/p\u003e \u003cp\u003eThe Czochralski method has in the present study been used to prepare pure TiFe\u003csub\u003e2\u003c/sub\u003e and Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi single crystals. A four-arc high-temperature single-crystal growth furnace was then used for this purpose (\u003cb\u003eSection S2\u003c/b\u003e). This equipment is very suitable for the growth of intermetallic compounds with active chemical properties and high melting points (usually around 3000 ℃). These compounds include binary and quaternary intermetallic compounds containing rare earth elements (or metallic uranium). High-quality ingredients Ti, Fe, and Si were weighed out in a molar ratio of 1: 1.75: 0.25, arc-melted thrice under argon an atmosphere, utilizing a titanium ingot as an oxygen getter. The polycrystalline samples were then melted in the four-arc furnace to grow the single crystal.\u003c/p\u003e \u003cp\u003eMicrostructural characterizations\u003c/p\u003e \u003cp\u003eThe microstructures of these samples were characterized by using field emission scanning electron microscopy (FESEM; Apreo S). Also, the accurate elemental ratios of the single crystals were characterized by using energy dispersive spectroscopy (EDS; Oxford). Furthermore, X-ray diffraction (XRD; SmartLab SE) and four-circle diffractometer used to characterize the crystalline structures and analyze the single-crystal qualities of the samples, respectively.\u003c/p\u003e \u003cp\u003eMechanical tests\u003c/p\u003e \u003cp\u003eThe hardness and Young\u0026rsquo;s modulus of TiFe\u003csub\u003e2\u003c/sub\u003e and Ti\u003csub\u003e4\u003c/sub\u003eFe\u003csub\u003e7\u003c/sub\u003eSi were examined by the Nanoindenter (KLA G200). There are 10 points were randomly selected on the single-crystal for testing using a wedge-shaped indenter in continuous stiffness mode, and the maximum indentation depth is 2 \u0026micro;m.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll data that support the findings in this paper are available within the article and its Supplementary Information.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work is supported by the National Natural Science Foundation of China (Nos. 12174296 and U20A20279), Major Program (JD) of Hubei Province (No. 2023BAA019-5), the Science and Technology Program of Guangxi Province (No. AA22068080), the Taishan Industry Leading Talent Project (No. 2020007), the Leading Innovation and Pioneering Team of Zhejiang Province (No. 2021R01020) and the 111 Project (No. D18018). The calculations were carried out at the High-Performance Computing Center of Wuhan University of Science and Technology and National Supercomputer Centre in TianHe1(A). The single-crystal preparation experiments were carried out at the Material Genome Research Platform of the Institute of Physics, Chinese Academy of Sciences.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eX.Y.T. conducted the nano-hardness experiments and wrote the paper. H.X.L. conducted the single-crystal experiments and wrote the paper. X.Y.T., S.C.Z., D.Z., X.L and J.W.D. carried out the DFT calculation and X.Y.T. wrote the paper. T.P.H. conceived this project and wrote the paper. K.M.W. and W.M.L. initiated and supervised the project.\u0026nbsp;All authors contributed to the discussions.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eGuo, Y., Wang, H. \u0026amp; Liu, Q. Microstructure evolution and strengthening mechanism of laser-cladding MoFe\u003csub\u003ex\u003c/sub\u003eCrTiWAlNb refractory high-entropy alloy coatings. J. Alloys Compd. \u003cstrong\u003e834\u003c/strong\u003e, 155147 (2020).\u003c/li\u003e\n \u003cli\u003eMoon, J. et al. Ti-bearing lightweight steel with large high temperature ductility via thermally stable multi-phase microstructure. Mater. Sci. Eng. A. \u003cstrong\u003e808\u003c/strong\u003e, 140954 (2021).\u003c/li\u003e\n \u003cli\u003eRabadia, C. D. et al. Deformation and strength characteristics of Laves phases in titanium alloys. Mater. 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A \u003cstrong\u003e65\u003c/strong\u003e, 6 (1952).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Wuhan University of Science and Technology","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Doping design, Hardness augmentation engineering, Electronic structure modulation, TiFe2","lastPublishedDoi":"10.21203/rs.3.rs-5457104/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5457104/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAs a critical reinforcing phase in matrix and coating materials, enhancing the hardness of TiFe\u003csub\u003e2\u003c/sub\u003e significantly improves the upper limits of alloy performance through low-concentration doping. However, the mechanism by which doping alters macroscopic hardness through the disturbance of electronic structure remains unclear. Furthermore, there is a lack of robust experimental evidence to substantiate the hardness enhancements predicted by theoretical calculations. This investigation assessed the strengthening effect of silicon (Si) on the hardness of TiFe\u003csub\u003e2\u003c/sub\u003e through both calculations and experiments. First-principles calculations indicated that Si alloying enhances the structural stability and hardness of TiFe\u003csub\u003e2\u003c/sub\u003e. The mechanisms underlying the notable increase in hardness due to Si were thoroughly investigated from the perspective of bonding characteristics. Si alloying disrupted the original symmetric electronic structure and increased the prevalence of directional covalent bonds. Successful single-crystal preparation experiments confirmed the stability of the doped structure. The results of nano-hardness testing address the deficiency of accurate experimental data on hardness enhancement. This study provides a systematic approach to improving the mechanical properties of TiFe\u003csub\u003e2\u003c/sub\u003e and offers new insights into the development of advanced materials with enhanced hardness.\u003c/p\u003e","manuscriptTitle":"Hardness Augmentation Engineering of TiFe2 with Doping Design and Single-crystal Realization","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-11-18 08:23:03","doi":"10.21203/rs.3.rs-5457104/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"30e1b144-50ae-48ab-b1ca-6472f6a07f90","owner":[],"postedDate":"November 18th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":40291784,"name":"Materials Theory and Modeling"}],"tags":[],"updatedAt":"2024-11-18T08:23:03+00:00","versionOfRecord":[],"versionCreatedAt":"2024-11-18 08:23:03","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5457104","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5457104","identity":"rs-5457104","version":["v1"]},"buildId":"WrCJVZZCHTDjtuVLN7oU0","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}