以第一原理計算探討過渡金屬碳化物在體心立方鐵中之界面能、形成能及其成核機制

Abstract

本論文之研究目標為透過第一原理，配合密度泛函理論計算探討過渡金屬碳化析出顆粒和bcc母相鐵之間的接面系統(Fe/Ti1-xMxC,M=Mo,Nb,W)之界面能，以及接面結構形成能，藉此探討Mo和W對於析出強化的影響。本研究建立了16、32以及48顆原子大小之接面系統來模擬析出成長的情況，而濃度選擇為x=0.25,0.5以及0.75。 在本論文第一部份中，研究首先對Fe/(Ti1-xMx)C)進行界面能的計算，我們將其分為化學界面能(Chemical Interface Energy)以及應變界面能(Chemical Interface Energy including Strain Energy )進行探討。在化學界面能的計算中，我們發現Nb、Mo和W的添加皆有助於界面能的降低，但Mo的添加會使界面能下降特別顯著。當我們考慮各二元混合濃度接面系統時，在50%Mo置換的Fe/(Ti0.5Mo0.5)C擁有最低的界面能。我們亦發現W的添加可顯著的降低界面能量，利於析出。除此之外我們並發現化學界面能並非定值，其會隨著接面尺度加大而有降低之趨勢。當考慮應變界面能時，我們發現Fe/(Ti0.5Mo0.5)C接面系統仍具有各混合系統中最低之應變界面能。綜合化學界面能以及應變能的計算，可和實驗上觀測到Ti-Mo一比一混合時會有最強析出強化效果相呼應。 接著我們利用電子性質計算來解釋Mo添加為何能顯著的降低界面能。在能量態密度的計算中我們發現Mo的添加會讓1NN Fe d軌域和接面過渡金屬原子d軌域的交互作用增強，而W的添加也可看到類似效果。在接面結構的電荷轉移分析當中，我們發現TMCs和Fe形成接面結構時，系統電荷將會重新分布:Fe將會失去電子，而這些電子將大量轉移至接面處以及接面碳原子上，在接面系統內形成一Interface Dipole，此偶極矩能幫助穩定接面結構。我們進一步計算這些電荷差異在各系統所造成的Interface Dipole，發現界面能最低的Fe/(Ti0.5Mo0.5)C系統具有最強的Interface Dipole。在W系統中亦可看到Interface Dipole增加的趨勢，但W的添加所能造成的偶極矩效應並不如Mo那麼顯著。綜合此部分電子結構分析我們認為:Mo的添加會使接面系統中的電荷重新分布效應增強，誘發一較強的Interface Dipole使接面系統更加穩定。 在第二部份我們則從熱力學觀點探討接面系統之形成能，我們首先確認接面系統Fe/(Ti1-xMx)C當M原子偏析(Segregation)在接面處會具備最穩定之能量。由形成能計算結果，在Mo添加系統中形成能在35.2%濃度時出現了一個轉折點，我們認為Mo添加系統在35.2%-50% Mo置換區間內利將有最強的析出強化效果，因為在此Ti-Mo混合區間內接面形成能低，且接面形成能隨析出尺寸加大而上升；而在W添加系統中，同樣的轉折點出現在29.2%，因此在29.2%-50%W置換濃度區間會是最佳選擇。本研究進一步探討造成此轉折點的原因，我們認為因為析出成長時因第二元原子分相所造成的能量上升，以及析出加大時穩定接面系統能量下降等因素競爭，是造成在不同濃度下形成能有不同變化的主因。

The aim of this thesis is to reveal the role of Mo addition to the Ti-based steel using first-principles calculations based on density functional theory. In the first part of this thesis, we calculated the chemical interface energy and strain interface energy (chemical interface energy including elastic strain) to investigate the effect of the addition of different composition Mo,W and Nb to the Ti-based interface system Fe/Ti1-xMxC. We built the interface system following Baker-Nutting orientation relationship. Our results of interface enrgy calculation shows that Mo and W addition can significantly decrease interface energy. The Fe/(Ti0.5Mo0.5)C interface system, which has Mo present at interface, has been found to be having the lowest chemical and strain interface energy in all the complex interface system. Furthermore, we found that interface energy isn’t a constant but decreases as particle size increases. We then employed density of state calculation to the different interface systems, the results shows that the interaction between segregated transition metal and its first nearest neighbor Fe has increasedfor the interface system that has the lowest interface energy. Moreover, from the analysis of charge difference calculation, the Mo addition to the interface can cause more ssignificant electron redistribution when the interface formed, and eventually induced stronger interface dipole to help stabilizing the interface. In the second part of the thesis, we investigated the formation energy of the Fe/(Ti1-xMx)C interface system in the viewpoints of thermodynamics. For the dependence of atomic configuration of the TMCs, various stacking sequences have been considered at different composition. We discovered that the complex carbide of (Ti1-xMx)C which has M present at the interface were the most stable. For the Fe/(Ti1-xMox)C precipitation, our results show that there is a turnig point of formation energy at x=0.352 in Fe/Ti1-xMoxC system and x=0.292 for Fe/Ti1-xWxC ststem. Our results suggest that the substitution composition between x=0.352 to x=0.5 can possibly lead to ultimate precipitation hardening enhancement because the formation energy of the interface system in this composition range is low enough for TMC to nucleate,meanwhile, the formation energy increases as precipitation size increases.The results will lead to large amount of extreamly fine precipitations .For the Fe/(Ti1-xWx)C precipitation, our results shows that the substitution composition between x=0.292 to x=0.5 will have same effect.