高巍,謝飛

(河北大學(xué)質(zhì)量技術(shù)監(jiān)督學(xué)院,河北保定 071000)

第一性原理計(jì)算Fcc-Cr1-xSixN的調(diào)幅分解

高巍,謝飛

(河北大學(xué)質(zhì)量技術(shù)監(jiān)督學(xué)院,河北保定 071000)

基于通過(guò)第一性原理計(jì)算方法,計(jì)算了三元固溶體Fcc-Cr1-xSixN總能,在此基礎(chǔ)上計(jì)算了其分離能和調(diào)幅分解線.結(jié)果說(shuō)明,Fcc-Cr1-xSixN是亞穩(wěn)相,能夠經(jīng)調(diào)幅分解機(jī)制分解為Fcc-CrN和Fcc-SiN.組元相形成的應(yīng)變能小于分離能,不會(huì)抑制Fcc-Cr1-xSixN的調(diào)幅分解.Fcc-Cr1-xSixN的Si含量為滲透閾值時(shí),不會(huì)發(fā)生調(diào)幅分解.Fcc-Cr1-xSixN可能經(jīng)調(diào)幅分解生成Fcc-SiN.

超硬薄膜;調(diào)幅分解;第一性原理

近年來(lái)納米復(fù)合超硬薄膜材料得到了廣泛研究,特別是在TiN薄膜上加入Si元素后形成的Ti-Si-N薄膜倍受關(guān)注[1-3].目前,開(kāi)發(fā)新型材料仍然是此類(lèi)超硬材料的研究重點(diǎn)內(nèi)容之一.Cr-Si-N薄膜作為一種很有希望的納米復(fù)合超硬薄膜候選材料,得到了很多關(guān)注.近來(lái)已有研究者用不同方法制備了Cr-Si-N薄膜,并且獲得了滿意的硬度[4-5].

在已經(jīng)得到研究的Ti-Si-N和Ti-B-N納米復(fù)合超硬薄膜系統(tǒng)中,固溶體相均具備調(diào)幅分解機(jī)制[6-8],從而保證了薄膜制備過(guò)程中TiN相和SiNy相(或BN相)自動(dòng)分離,形成明銳界面,這對(duì)于此類(lèi)納米復(fù)合超硬薄膜系統(tǒng)獲得超硬度起著重要作用[6-9].所以,Fcc-Cr1-xSixN固溶體是否具備調(diào)幅分解機(jī)制令研究者感興趣.但是,由于實(shí)驗(yàn)困難,Cr-Si-N系統(tǒng)的相圖不夠完備,目前仍缺乏關(guān)于Cr-Si-N系統(tǒng)的調(diào)幅分解機(jī)制的認(rèn)識(shí).另一方面,第一性原理計(jì)算作為有效的計(jì)算實(shí)驗(yàn)手段,已經(jīng)對(duì)Ti-A l-N[10-12],Cr-A l-N[13-14],Cr-A l-N[15],Ti-Si-N[6-7],Ti-B-N[8]薄膜系統(tǒng)的調(diào)幅分解特性作出了預(yù)測(cè)和比較.所以應(yīng)用第一性原理計(jì)算方法對(duì)Fcc-Cr1-xSixN固溶體的調(diào)幅分解機(jī)制進(jìn)行預(yù)測(cè)是合理的.

本文基于熱力學(xué)計(jì)算模型,使用第一性原理平面波贗勢(shì)計(jì)算方法計(jì)算了Fcc-Cr1-xSixN固溶體的調(diào)幅分解機(jī)制,得到的計(jì)算結(jié)果能為今后關(guān)于Cr-Si-N薄膜的研究打下理論基礎(chǔ).

1 計(jì)算模型和方法

Fcc-Cr1-xSixN由8個(gè)原子組成的晶胞周期排列形成.x=0時(shí)(Fcc-CrN)為理想立方結(jié)構(gòu)CrN晶體,屬于FM-3M空間群,α=β=γ=90°,晶格常數(shù)a=b=c=0.46 nm,晶胞內(nèi)包含4個(gè)Cr原子和4個(gè)N原子,非對(duì)稱(chēng)原子分?jǐn)?shù)坐標(biāo)為Cr(0,0,0),N(0.5,0.5,0.5).x=0.25,0.5,0.75時(shí)可以視為CrN的8原子晶胞中分別有1,2,3個(gè)Cr原子由Si原子替代.x=1時(shí)(Fcc-SiN)可以視為CrN晶胞中全部Cr原子由Si原子替代.Fcc-Cr1-xSixN的晶體結(jié)構(gòu)如圖1所示.

圖1 Fcc-Cr1-x Si x N的晶體結(jié)構(gòu)Fig.1 Crystal structures of Fcc-Cr1-x Si x N

計(jì)算時(shí)交換關(guān)聯(lián)能采用廣義梯度近似(GGA)下的PBE96.布里淵區(qū)的求和采用線性四面體積分法,在倒空間用四面體方法對(duì)布里淵區(qū)中的64個(gè)點(diǎn)積分.計(jì)算中使用的Cr,Si和N原子的原子球半徑分別為2,2和1.6.

2 計(jì)算結(jié)果和討論

2.1 分離能

分離能ΔH定義為

式中E(Fcc-Cr1-xSixN),E(Fcc-CrN),E(Fcc-SiN)分別為經(jīng)第一性原理計(jì)算得到的Cr1-xSixN,Fcc-CrN, Fcc-SiN的總能量.分離能為正值,說(shuō)明Fcc-Cr1-xSixN的能量大于Fcc-CrN和Fcc-SiN混合態(tài)的能量,Fcc-Cr1-xSixN具有相分解的趨勢(shì),并且分離能越大,相分解的趨勢(shì)越明顯;分離能為負(fù)值,表明固溶體相Fcc-Cr1-xSixN不會(huì)相分解.

圖2為Fcc-Cr1-xSixN的分離能,圖中分離能恒為正值,說(shuō)明Fcc-Cr1-xSixN是亞穩(wěn)相,具有分解為Fcc-CrN和Fcc-SiN的趨勢(shì).圖2中Fcc-Cr1-xSixN的分離能曲線表現(xiàn)出不對(duì)稱(chēng)性,偏向了x較大一側(cè),最大值出現(xiàn)在x=0.66處,說(shuō)明在混溶過(guò)程中,和Fcc-SiN溶入Fcc-CrN相比,Fcc-CrN溶入Fcc-SiN更為不易(即相分解趨勢(shì)更明顯).

2.2 調(diào)幅分解線

將Fcc-Cr1-xSixN系統(tǒng)視為由Fcc-CrN和Fcc-SiN組成的偽二元合金系統(tǒng),其混合自由能ΔG定義為[12]

式中R為氣體常數(shù);T為熱力學(xué)溫度.根據(jù)熱力學(xué)原理,固溶體發(fā)生調(diào)幅分解的臨界條件為d2ΔG/dx2= 0[13].按照臨界條件可以做出調(diào)幅分解線.Fcc-Cr1-xSixN滿足的成分和溫度條件位于調(diào)幅分解線包容區(qū)域內(nèi),能夠發(fā)生調(diào)幅分解;位于調(diào)幅分解線外,能夠保持固溶體結(jié)構(gòu)或以形核-長(zhǎng)大的方式進(jìn)行相分解.

圖3給出了Fcc-Cr1-xSixN的調(diào)幅分解線(圖中實(shí)線).圖中最高溫度為2 750 K,出現(xiàn)在x=0.73處,說(shuō)明調(diào)幅分解線也具有不對(duì)稱(chēng)性,這是由分離能的不對(duì)稱(chēng)性決定的.圖中1 000 K溫度(典型沉積溫度)所對(duì)應(yīng)的調(diào)幅分解范圍是x=0.42～0.96(如箭頭所示).溫度低于500 K時(shí),對(duì)應(yīng)的調(diào)幅分解范圍是x=0.4～0.98.這些結(jié)果說(shuō)明,在較大成分和溫度范圍內(nèi),Fcc-Cr1-xSixN符合調(diào)幅分解的熱力學(xué)條件.

納米復(fù)合薄膜產(chǎn)生超硬度的一個(gè)條件是包裹納米晶相的非晶相具有單原子層厚度[9],以細(xì)化晶粒,減小應(yīng)變能或抑制裂紋缺陷.滿足此條件時(shí),Si的質(zhì)量分?jǐn)?shù)為6%～12%(x=0.12～0.24),稱(chēng)為滲透閾值[16].圖3中,溫度為1 000 K時(shí),滲透閾值已經(jīng)位于調(diào)幅分解線之外(如粗虛線所示),這說(shuō)明Si含量為滲透閾值時(shí), Fcc-Cr1-xSixN可能不會(huì)發(fā)生調(diào)幅分解.

2.3 應(yīng)變能

彈性應(yīng)變能Es定義為

式中S為分解相CrN和Fcc-SiN之間的界面面積,Y為單位界面面積上應(yīng)變能,定義為[7]

式中G為CrN的彈性模量,v為泊松比,t為晶粒尺寸,ε為CrN和Fcc-SiN之間的晶格錯(cuò)配度.式(3)適用于晶格錯(cuò)配度比較小的情況,由于CrN和Fcc-SiN的晶格錯(cuò)配度達(dá)到了4%,所以按照式(3)計(jì)算得到的彈性應(yīng)變能應(yīng)該看作CrN和Fcc-SiN之間的應(yīng)變能的上限值.

若分解相的彈性應(yīng)變能小于分離能,調(diào)幅分解才能發(fā)生.圖4給出了Fcc-Cr1-xSixN的彈性應(yīng)變能和分離能的比較結(jié)果,可以看到,彈性應(yīng)變能遠(yuǎn)小于分離能,不會(huì)抑制Fcc-Cr1-xSixN的調(diào)幅分解.

2.4 晶格常數(shù)

Fcc-SiN是亞穩(wěn)相,傾向于轉(zhuǎn)變?yōu)楦€(wěn)定的β-Si3N4.在Fcc-Cr1-xSixN相分解時(shí),如果形成β-Si3N4的相變阻力較大,Fcc-SiN可能作為共格亞穩(wěn)新相出現(xiàn).如果形成β-Si3N4的相變阻力較小,Fcc-SiN可能直接轉(zhuǎn)變?yōu)棣?Si3N4,抑制調(diào)幅分解.下面從晶格常數(shù)的角度對(duì)此做一分析.圖5給出了計(jì)算得到的Fcc-Cr1-xSixN的晶格常數(shù),其中Fcc-CrN和Fcc-SiN的晶格常數(shù)分別為0.406 nm和0.42 nm,單原子占據(jù)的晶胞體積分別為8.37×10-3nm3和9.26×10-3nm3.另外,計(jì)算得到了β-Si3N4的晶格常數(shù)a=0.754 nm,c=0.287 nm,單原子占據(jù)的晶胞體積為11.65×10-3nm3.根據(jù)以上結(jié)果,CrN和Fcc-SiN的晶胞體積差異為10.6%, CrN和β-Si3N4的晶胞體積差異為28%.可以看到,形成β-Si3N4將造成較大的晶胞體積差異,具有較大相變阻力.所以Fcc-Cr1-xSixN可能經(jīng)調(diào)幅分解生成Fcc-SiN.

3 結(jié)論

使用第一性原理計(jì)算方法,計(jì)算了Fcc-Cr1-xSixN固溶體的分離能、調(diào)幅分解曲線、應(yīng)變能和晶格常數(shù),獲得以下主要結(jié)論:1)Fcc-Cr1-xSixN是亞穩(wěn)相,具有分解為Fcc-CrN和Fcc-SiN的趨勢(shì).2)在較大成分和溫度范圍內(nèi),Fcc-Cr1-xSixN符合調(diào)幅分解的熱力學(xué)條件.3)Fcc-Cr1-xSixN的Si含量為滲透閾值時(shí),可能不會(huì)發(fā)生調(diào)幅分解.4)Fcc-Cr1-xSixN分解相的彈性應(yīng)變能小于分離能,不會(huì)抑制Fcc-Cr1-xSixN的調(diào)幅分解. 5)Fcc-Cr1-xSixN可能經(jīng)調(diào)幅分解生成Fcc-SiN.

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First Principles on Spinodal Decomposition of Fcc-Cr1-xSixN

GAO Wei,XIE Fei
(College of Quality and Technical Supervision,Hebei University,Baoding 071000,China)

Total energies of ternary solution Fcc-Cr1-xSixN phase were calculated by first p rincip le method,and de-mixing energy and spinodal curve of Fcc-Cr1-xSixN phase were calculated.The results showed that Fcc-Cr1-xSixN is metastable and ap t to decompose to Fcc-CrN and Fcc-SiN via spinodal decomposition.The strain energy between the constituent phases was smaller than the de-mixing energy, w hich couldn’t hinder the spinodal decomposition.Spinodal decomposition could not p roceed for Si composition of Fcc-Cr1-xSixN identical to the percolation threshold.Fcc-Cr1-xSixN and decompose to Fcc-SiN via the coherent spinodal decomposition.

superhard film s;spinodal decomposition;first p rincip le

TB 453

A

1000-1565(2010)05-0508-04

2010-03-22

河北省教育廳科研計(jì)劃項(xiàng)目(z2008304)

高巍(1980—),男,河北保定人,河北大學(xué)助教.

(責(zé)任編輯:孟素蘭)