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如何有效预测高熵合金的稳态结构, 是开展研究其物理及化学等性能的基础. 以FeCuCrMnMo合金为例, 在有限晶胞尺寸内, 采用蒙特卡洛结合密度泛函理论杂化计算方法(Monte Carlo/density functional theory, MC/DFT)预测高熵合金的平衡态结构. 与准随机近似方法(special quasirandom structures, SQS)不同, 该方法不再追求高熵合金结构的理想随机状态, 而是充分考虑合金中原子尺寸、混合焓、原子间相互作用等物理因素. 通过第一性原理计算体系能量来实现, 使得蒙特卡洛(Monte Carlo, MC)方法保证结构在原子交换过程中体系能量逐渐收敛于平衡态. 最终预测得到的平衡态结构出现Cu原子的短程有序现象(short range order, SRO)与实验上合金中的Cu偏析现象相一致. 相较于由SQS方法获得的随机状态, 该SRO结构在能量上更加稳定. 同时本文对稳态结构通过序参数及径向分布函数进行表征, 并对SRO现象的出现进行物理解释, 进一步揭示了SRO的出现对高熵合金结构性质的影响.The prediction of stable state of high-entropy alloys (HEAs) is crucial to obtain fundamental insight to the excellent properties of HEAs. Taking a FeCuCrMnMo alloy as a case study, we combined Monte Carlo (MC) method with the density functional thoery (DFT) calculations (MC/DFT) to predict the equilibrium structure of high-entropy alloys in a finite unit cell. Instead of approaching the ideal random state obtained from special quasi-random approximation (SQS) method, physical factors such as atomic size, mixing enthalpy of atomic pairs, and interatomic interactions in the alloy are fully considered and implemented in our simulation by MC/DFT calculations. MC codes ensure the energy convergence of the system to the equilibrium state through the atom exchange process. The equilibrium structures exhibit Cu-rich short-range orders (SRO), which is consistent with the observation in experiments. Comparing with ideal random state structure, SRO structure is more stable in energy, and more closely packed in atomic arrangement. Moreover, the analyses of order parameters and radial distribution functions (RDFs) are performed to character the structure of high-entropy alloy. The order parameter of Cu-Cu atomic pair reaches to –0.53 in the SRO equilibrium structure, which indicates that Cu-rich regions appear in the alloy. The RDFs show that the atomic distance distribution of the SRO structure is between 2.25 Å to 2.7 Å, which is smaller than the range of 2.16 Å to 2.84 Å in the SQS structure, indicating that the lattice distortions is relatively small in the SRO structure after structural optimization. The appearing of SRO phenomena is attributed to the inherent characteristics of atoms, including (i) atomic size, (ii) interatomic mixing enthalpy and (iii) the interaction of atoms. Atomic sizes in the FeCuCrMnMo alloy are in the order of Fe (11.78) < Cu (11.81) < Cr (11.97) < Mn (14.38) < Mo (15.58), in unit of Å 3/atom. The relatively large sizes of Mn and Mo atoms should disadvantage the pairing of Mo-Mo and Mn-Mn. The mixing enthalpy of Cu with other atoms are all positive values, indicating that Cu is not favor of pairing other elements and precipitate itself. The analyses of density of state (DOS) and Crystal Orbital Hamilton Population (COHP) also support the results. The reason is exactly attributed to the inactive valence electrons of Cu. Furthermore, the effect of SRO on the magnetic and mechanical properties are investigated. The existence of SRO decreases the mean value of magnetic moment, and results in an increase of elastic moduli ( B, Gand E) and a decrease in the ductility and anisotropy properties.
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金属 磁性 晶格 内聚能/eV 体积/Å3 晶格常数 a(理论值) a0(实验值) HEA-SRO FM BCC –8.13 12.15 2.896 2.878[7] NM BCC –8.12 12.05 2.889 FM FCC –8.08 12.31 3.666 HEA-SQS FM BCC –8.09 12.53 2.926 Fe FM BCC –8.32 11.78 2.832 2.834[22] Cu NM FCC –3.72 11.81 3.636 3.615[23] Cr AFM BCC –9.51 11.97 2.835 2.882[23] Mn FM BCC –8.29 14.38 3.080 3.080[23] Mo NM BCC –10.95 15.58 3.148 3.147[23] 混合焓 Cr Mn Mo Fe Cu 12 4 19 13 Cr 2 0 –1 Mn 5 0 Mo –2 原子对 Cu-Fe Cu-Mn Cu-Mo Cu-Cr Cu-Cu ICOHP –0.54 –0.59 –0.88 –0.66 –0.39 原子对 Fe-Cr Fe-Mo Mn-Mo Cr-Mo Cr-Mn ICOHP –1.45 –1.68 –1.72 –1.78 –1.61 结构 C11 C12 C44 B BEOS G E ν G/B AZ SRO 263.4 187.5 100.5 212.8 188.7 88.2 232.5 0.318 2.415 2.65 SQS 156.1 139.3 85.1 144.9 154.4 43.4 118.4 0.364 3.323 10.1 -
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