運用第一原理計算、古典力場模型及類神經網路勢能探討鉻錳鐵鈷鎳鋁高熵合金及衍生系統的相穩定性及合金設計

本論文透過第一原理配合密度泛函理論(DFT)計算以及古典力場模型，探討CrMnFeCoNi五元高熵合金中空缺缺陷以及少量的Al原子添加對於合金相穩定性以及疊差能的影響。同時也利用類神經網路發展CoCrNi三元合金的力場模型勢能。在第一部分中，大量的DFT計算樣本資料(38262筆)用於建立CoCrNi三元合金的類神經網路勢能(NNPs)，最終30-30-1、40-40-1和50-50-1三種不同結構的NNPs的平均絕對誤差(MAE)分別為26.9、30.9和32.3 meV/atom。從CoCrNi的NNPs訓練及驗證結果可以得知，NNPs的類神經網路架構及大小需要仔細的在計算資源以及類神經複雜度間進行權衡。此外，取樣時需要使用較大的結構進行取樣，以避免因為NNPs的截止距離和週期性邊界造成取樣偏差。第二部分中，使用DFT和古典力場模型探討空缺缺陷對於CrMnFeCoNi的影響。在純面心立方(FCC)的金屬中空缺會使疊差能(SFE)下降，但是在CrMnFeCoNi中空缺卻會使疊差能上升；但是在純FCC金屬以及CrMnFeCoNi中空缺對於疊差滑移障礙(USFE)的影響卻呈現相同的趨勢。因此，單軸壓縮的分子動力學(MD)模擬用於釐清SFE和USFE變化對於機械性質的重要性。而我們的結果顯示，在純FCC金屬和CrMnFeCoNi中，空缺都能夠有效的降低<100>方向的單軸壓縮時的六方最密堆積(HCP)轉變比率以及差排密度。這樣的結果指出，因空缺而造成的USFE變化更能夠有效的影響整體機械性質。在第三部分中，使用DFT研究少量的Al添加對於CrMnFeCoNi五元高熵合金疊差能的影響。在較高Al濃度的情況下，Al濃度的增加會明顯提升合金整體的疊差能。若是少量Al添加的情況下，雖然Al原子的周圍其疊差能依然會因此上升，但是其他較為遠離Al的區域，其疊差能卻會因此下降，甚至低於CrMnFeCoNi中的平均疊差能。因為考慮到Al-Ni是系統中極為穩定的二元對，我們也計算了結構中含有部分Al-Ni聚集的疊差能，結果顯示，部分Al-Ni聚集會使得因Al造成的局域疊差能不均勻分布更加明顯。而在包含不同成分合金的疊差能計算結果中顯示，Ni雖然會明顯提升系統整體的疊差能，但是卻是在高熵合金中扮演穩定FCC相的重要角色，因此可知對於主要為FCC相的高熵合金中Ni是相當關鍵的元素。鍵級和Bader電荷的分析結果指出，少量Al的添加可以使得Al原子周圍局域的電荷和鍵結產生明顯的變化，而其局域的鍵級變化也能夠解釋進一步解釋上文提及之微量Al加入造成的疊差能分布變化。

關鍵字

第一原理計算；古典力場模型；類神經網路勢能；高熵合金

並列摘要

Density functional theory (DFT) and modified embedded atom method (MEAM) are applied in this thesis to investigate the influence of vacancy and the minor addition of Al of CrMnFeCoNi high-entropy alloys (HEAs). Neural network potentials (NNPs) is also applied in this thesis to develop the force field potential for CoCrNi alloy. In the first part, NNPs for CoCrNi ternary alloy system are developed by massive DFT data sampling, which is 38262 samples, and lot of time for training. The final mean absolute errors(MAE) of testing set for the NNPs with 30-30-1, 40-40-1 and 50-50-1 architectures are 26.9, 30.9 and 32.3 meV/atom respectively. The training and validation results indicate that the architecture of the NNPs should be carefully selected to trade off the computational cost and the complexity of functional. Furthermore, to avoid the sampling bias due to the cutoff distance of NNPs and the periodic boundary, the larger size of the strictures in sampling data set is very important. In the second part, DFT and classical model calculations are used to investigate the influence of vacancy for CrMnFeCoNi HEA. The stacking fault energy (SFE) decrease by the vacancies in pure FCC metals, but, in CrMnFeCoNi HEA, the SFE increase by vacancies. However, the effects of vacancy for unstable stacking fault energy(USFE) are same in both pure FCC metals and CrMnFeCoNi HEA. Therefore, uniaxial compress molecular dynamics (MD) simulations with MEAM and EAM potentials are performed to clarify the importance of SFE and USFE for mechanical properties. As a result, the vacancies effectively decrease the HCP-transition percentage and the dislocation density in <100> compress direction in both CrMnFeCoNi and pure Ni, and the decrease of USFE which affected by vacancy is more important for mechanical properties. In the third part, DFT is applied to study the effects of minor addition of Al for CrMnFeCoNi HEA. For higher concentration of Al, the SFE obviously raise for the addition of Al. Considering the minor addition of Al, the SFE near Al atom is same with the SFE in high concentration of Al. However, the SFE of stacking fault which is 3~4 layers apart from Al atom decreases and is even below the average in CrMnFeCoNi. Because of the affinity of Al-Ni pair, the SFE of the structure with partial precipitation of Al-Ni is also calculated, and the partial precipitation of Al-Ni induces the larger difference for SFE. In addition, the results of SFE of the structures with different composition show that Ni can significantly increase the SFE, but Ni can also stabilize FCC phase in HEA. Therefore, Ni is necessary for FCC-based HEA. The Bader charge and bond order analysis indicates that the minor addition of Al significantly changes the local charge distribution and bond strength near Al atom, and the change of bond strength can be used to explain the local SFE distribution for the effect of addition of Al mentioned above.

並列關鍵字

First-principles calculation ； Classical force field modeling ； Artificial neural network potential ； High entropy alloy

參考文獻

Yeh, J. W., Chen, S. K., Lin, S. J., Gan, J. Y., Chin, T. S., Shun, T. T., ... & Chang, S. Y. (2004). Nanostructured high‐entropy alloys with multiple principal elements: novel alloy design concepts and outcomes. Advanced Engineering Materials, 6(5), 299-303..

Google Scholar

Cantor, B., Chang, I. T. H., Knight, P., & Vincent, A. J. B. (2004). Microstructural development in equiatomic multicomponent alloys. Materials Science and Engineering: A, 375, 213-218.