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Ferrite (α-Fe), as a fundamental phase of steel materials, plays a decisive role in determining their macroscopic mechanical behaviors through its microscopic properties, particularly in engineering applications involving resistance to plastic deformation and fracture, fatigue resistance, wear resistance, and low-temperature toughness. Therefore, alloying elements are commonly introduced to improve the performance of steel via mechanisms such as grain refinement strengthening and precipitation strengthening. However, in these strengthening mechanisms, the effects of doped alloying elements on the stability, electronic structure, and mechanical properties of ferrite itself have not been thoroughly investigated. In this study, orthogonal experimental design and first-principles calculations are employed to investigate the effects of ternary alloy doping with M (Mn, Ti, Mo) on the stabilities, electronic structures, and mechanical properties of a ferrite-based supercell model Fe16-x-y-zMnxTiyMoz (x, y, or z = 0, 1, or 2), aiming to provide both theoretical insight and experimental reference for improving the comprehensive performance of ferrite-based steels by modifying the properties of the matrix phase. The results of the formation enthalpy (Hform) calculations indicate that all solid solutions have negative formation enthalpies, suggesting that they can form spontaneously. Among them, Ti doping is the most favorable for solid solution formation, followed by Mn, with Mo being the least favorable. The Fe13Ti1Mo2 configuration is the easiest to form spontaneously. The cohesive energy (Ecoh) results demonstrate that all solid solutions exhibit structural stabilities. Fe13Ti1Mo2 has the largest (most negative) cohesive energy of –477.96 eV, indicating that it possesses the highest structural stability. The contribution of Mo doping to stability enhancement is the greatest, followed by Ti, while the influence of Mn is the smallest. Electronic structure calculations reveal that M doping consistently reduces the density of states (DOS) at the Fermi level for Fe16-x-y-zMnxTiyMoz. The lowest DOS at the Fermi level is found to be 4.294 in Fe13Ti1Mo2, indicating enhanced hybridization and overlap between Mn 3d, Ti 3d, Mo 4d, and Fe 3d states. This strong hybridization leads to a decrease in the Fermi level and contributes to the high stability of the Fe13Ti1Mo2 phase. Mechanical property calculations indicate that M doping reduces the Young’s modulus (E) and Vickers hardness (HV) of the solid solutions. However, the K values (K = GH/BH) are all greater than 1.75, and Poisson’s ratios (ν) exceed 0.26, implying that while stiffness and hardness decrease, the ductility of the materials is improved. This study provides valuable guidance for designing ductile and tough ferrite-based steel materials.
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Keywords:
- ferrite (α-Fe) /
- Mn /
- Ti /
- Mo doping /
- first-principles calculations /
- mechanical properties
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图 1 Fe16-x-y-zMnxTiyMoz超胞模型 (a) Fe16; (b) Fe13Ti2Mo1; (c) Fe13Ti1Mo2; (d) Fe13Mn1Ti2; (e) Fe13Mn1Ti1Mo1; (f) Fe13Mn1Mo2; (g) Fe13Mn2Ti1; (h) Fe13Mn2Mo1; (i) Fe10Mn2Ti2Mo2
Figure 1. Supercell model of Fe16-x-y-zMnxTiyMoz: (a) Fe16; (b) Fe13Ti2Mo1; (c) Fe13Ti1Mo2; (d) Fe13Mn1Ti2; (e) Fe13Mn1Ti1Mo1; (f) Fe13Mn1Mo2; (g) Fe13Mn2Ti1; (h) Fe13Mn2Mo1; (i) Fe10Mn2Ti2Mo2.
图 2 态密度图和分波态密度图 (a) Fe16; (b) Fe13Ti2Mo1; (c) Fe10Mn2Ti2Mo2; (d) Fe13Ti1Mo2; (e) Fe13Mn1Ti1Mo1; (f) Fe13Mn1Ti2
Figure 2. Density of states and partial density of states plots: (a) Fe16; (b) Fe13Ti2Mo1; (c) Fe10Mn2Ti2Mo2; (d) Fe13Ti1Mo2; (e) Fe13Mn1Ti1Mo1; (f) Fe13Mn1Ti2.
图 3 差分电荷密度图 (a) Fe16; (b) Fe13Ti2Mo1; (c) Fe10Mn2Ti2Mo2; (d) Fe13Ti1Mo2; (e) Fe13Mn1Ti1Mo1; (f) Fe13Mn1Ti2
Figure 3. Differential charge density diagram: (a) Fe16; (b) Fe13Ti2Mo1; (c) Fe10Mn2Ti2Mo2; (d) Fe13Ti1Mo2; (e) Fe13Mn1Ti1Mo1; (f) Fe13Mn1Ti2.
表 1 M掺杂α-Fe的正交试验设计及原子百分比
Table 1. Orthogonal experimental design and atomic percentage content of M-doped α-Fe.
超胞 元素M原子百分比/% Mn Ti Mo Fe16 0 0 0 Fe13Ti2Mo1 0 12.5 6.25 Fe13Ti1Mo2 0 6.25 12.5 Fe13Mn1Ti2 6.25 12.5 0 Fe13Mn1Ti1Mo1 6.25 6.25 6.25 Fe13Mn1Mo2 6.25 0 12.5 Fe13Mn2Ti1 12.5 6.25 0 Fe13Mn2Mo1 12.5 0 6.25 Fe10Mn2Ti2Mo2 12.5 12.5 12.5 
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表 2 Fe16-x-y-zMnxTiyMoz的ε, Hform和Ecoh的计算值
Table 2. Calculated values of ε, Hform and Ecoh for Fe16-x-y-zMnxTiyMoz.
超胞 晶胞体积 ε/% Hform
/(kJ·mol–1)Ecoh
/(kJ·mol–1)Fe16 178.79 — –7.51 –449.39 Fe13Ti2Mo1 190.51 6.56 –16.52 –477.95 Fe13Ti1Mo2 190.70 6.66 –10.73 –477.96 Fe13Mn1Ti2 185.61 3.81 –15.48 –460.85 Fe13Mn1Ti1Mo1 187.73 5.00 –10.40 –461.58 Fe13Mn1Mo2 188.92 5.67 –5.37 –462.35 Fe13Mn2Ti1 182.89 2.29 –9.53 –444.06 Fe13Mn2Mo1 184.48 3.18 –4.58 –445.51 Fe10Mn2Ti2Mo2 194.98 9.06 –12.97 –473.45
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表 3 Fe16-x-y-zMnxTiyMoz的ε, Hform和Ecoh的正交试验分析
Table 3. Orthogonal test analysis of ε, Hform and Ecoh of Fe16-x-y-zMnxTiyMoz.
指标 ε/% Hform/(kJ·mol–1) Ecoh/(kJ·mol–1) Mn Ti Mo Mn Ti Mo Mn Ti Mo K0 13.22 8.85 6.1 –34.76 –17.46 –32.53 –1405.30 –1357.24 –1354.30 K1 14.48 13.95 14.47 –31.25 –30.66 –31.50 –1384.78 –1383.60 –1385.04 K2 14.53 19.43 21.39 –27.08 –44.97 –29.07 –1363.02 –1412.25 –1413.76 R 1.31 10.58 15.29 7.68 27.51 3.46 42.28 55.01 59.46 Ranking Mo＞Ti＞Mn Ti＞Mn＞Mo Mo＞Ti＞Mn
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表 4 Fe16-x-y-zMnxTiyMoz的独立弹性常数和力学稳定性
Table 4. Independent elastic constants and mechanical stability of Fe16-x-y-zMnxTiyMoz.
试样 C11 C12 C44 C11-C12 C11+2C12 Fe16 296.273 159.033 126.763 137.240 614.339 Fe13Ti2Mo1 292.506 158.281 117.403 134.225 609.068 Fe13Mn2Ti2Mo2 293.869 148.470 116.251 145.399 590.809 Fe13Ti1Mo2 210.409 103.675 92.415 106.734 417.759 Fe13Mn1Ti1Mo1 291.402 158.680 123.704 132.722 608.762 Fe13Mn1Ti2 275.790 150.536 112.712 125.254 576.862
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表 5 Fe16-x-y-zMnxTiyMoz的力学性能参数
Table 5. Mechanical property parameters of Fe16-x-y-zMnxTiyMoz.
超胞 B/GPa G/GPa E/GPa K v HV BV BR BH GV GR GH Fe16 204.779 204.779 204.779 103.506 94.675 99.091 255.983 2.067 0.292 13.737 Fe13Ti2Mo1 210.383 210.383 210.383 103.675 92.403 98.039 254.573 2.146 0.298 13.206 Fe10Mn2Ti2Mo2 196.401 196.401 196.401 98.830 91.632 95.231 245.942 2.062 0.291 13.272 Fe13Ti1Mo2 202.961 202.961 202.961 97.287 90.163 93.725 243.667 2.165 0.300 12.496 Fe13Mn1Ti1Mo1 202.921 202.921 202.921 100.767 91.929 96.348 249.548 2.106 0.295 13.168 Fe13Mn1Ti2 192.287 192.287 192.287 92.678 85.395 89.036 231.393 2.159 0.299 11.933
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