第一性原理研究反位缺陷对TiAl基合金力学行为的影响
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摘要
采用第一性原理计算方法,计算了二元γ-TiAl基合金的广义层错能(GSFE)随成分的变化,获得了TiAl基合金中孪晶(TW)、普通位错(OD)、超晶格位错(SD_Ⅰ和SD_Ⅱ)等变形模式的形变势垒,分析了在外加应力作用下的变形模式选择,并讨论反位缺陷对二元γ-TiAl基合金塑性的影响。计算结果表明,TiAl反位缺陷能降低以超晶格内禀层错(SISF)为前缘分位错的TW变形模式的势垒,且扩大TW模式开动的剪切应力角度窗口,有利于改善TiAl基合金的塑性。Al_(Ti)反位缺陷则反之。Al_(Ti)反位缺陷降低了以复杂层错(CSF)为前缘分位错的OD和SD_Ⅱ变形模式的滑移势垒(γEB),而且扩大了它们开动的剪切应力角度窗口,可促进OD和SD_Ⅱ的滑移。由于CSF的滑移势垒比SISF高,因此,相较于以SISF为前缘分位错的TW变形模式,OD及SD_Ⅱ滑移对应的强度较高、塑性较差。计算结果较好地说明了Al_(Ti)反位缺陷对TiAl基合金塑性的改善没有TiAl反位缺陷明显的原因。
Microalloying is an effective approach to improve the mechanical properties of TiAl-based alloys which have been applied as high-temperature structure materials. The antisite defects may be regarded as special alloying elements. However, the detailed information about the effect of antisite defects on mechanical behavior(full slip and twinning), which may be described theoretically by generalized stacking fault energy(GSFE), of TiAl-based alloys are scarce. In this work, the composition dependent GSFEs of off-stoichiometric γ-TiAl were calculated by using the first-principles exact muffin-tin orbitals method in combination with coherent potential approximation. With the calculated GSFE, the energy barriers for various deformation modes including twin(TW), ordinary dislocation(OD), and superlattice dislocation(SD_Ⅰ and SD_Ⅱ) were determined. The selection of the deformation mode under external shear stress with various directions was analyzed. The effects of the Ti_(Al) and Al_(Ti) antisite defects on the mechanical properties of γ-TiAl were then discussed. The results showed that the TiAlantisite defect decreases the energy barrier for the TW deformation leading by the superlattice intrinsic stacking fault(SISF) partial dislocation and increases the angle window of the applied shear stress within which TW deformation may be activated. Therefore, TiAl antisite defect is expected to improve the plasticity of γ-TiAl. The effect of Al_(Ti) antisite defect is opposite. The Al_(Ti) antisite defect decreases the energy barriers for the OD and SD_Ⅱ deformations leading by complex stacking fault(CSF) partial dislocation and increases their operating angle window, indicating that Al_(Ti) facilitates the slip of OD and SD_Ⅱ. Considering that the energy barrier for CSF is much higher than that for SISF, the plasticity induced by OD and SD_Ⅱ should be lower than that induced by TW. Calculations in this work explain the experimental finding that Ti_(Al) antisite defect improves the plasticity of γ-TiAl more significantly than Al_(Ti) antisite defect.
Microalloying is an effective approach to improve the mechanical properties of TiAl-based alloys which have been applied as high-temperature structure materials. The antisite defects may be regarded as special alloying elements. However, the detailed information about the effect of antisite defects on mechanical behavior(full slip and twinning), which may be described theoretically by generalized stacking fault energy(GSFE), of TiAl-based alloys are scarce. In this work, the composition dependent GSFEs of off-stoichiometric γ-TiAl were calculated by using the first-principles exact muffin-tin orbitals method in combination with coherent potential approximation. With the calculated GSFE, the energy barriers for various deformation modes including twin(TW), ordinary dislocation(OD), and superlattice dislocation(SD_Ⅰ and SD_Ⅱ) were determined. The selection of the deformation mode under external shear stress with various directions was analyzed. The effects of the Ti_(Al) and Al_(Ti) antisite defects on the mechanical properties of γ-TiAl were then discussed. The results showed that the TiAlantisite defect decreases the energy barrier for the TW deformation leading by the superlattice intrinsic stacking fault(SISF) partial dislocation and increases the angle window of the applied shear stress within which TW deformation may be activated. Therefore, TiAl antisite defect is expected to improve the plasticity of γ-TiAl. The effect of Al_(Ti) antisite defect is opposite. The Al_(Ti) antisite defect decreases the energy barriers for the OD and SD_Ⅱ deformations leading by complex stacking fault(CSF) partial dislocation and increases their operating angle window, indicating that Al_(Ti) facilitates the slip of OD and SD_Ⅱ. Considering that the energy barrier for CSF is much higher than that for SISF, the plasticity induced by OD and SD_Ⅱ should be lower than that induced by TW. Calculations in this work explain the experimental finding that Ti_(Al) antisite defect improves the plasticity of γ-TiAl more significantly than Al_(Ti) antisite defect.
引文
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[16]Joós B,Ren Q,Duesbery M S.Peierls-Nabarro model of dislocations in silicon with generalized stacking-fault restoring forces[J].Phys.Rev.,1994,50B:5890
[17]Jo M,Koo Y M,Lee B J,et al.Theory for plasticity of facecentered cubic metals[J].Proc.Natl.Acad.Sci.USA,2014,111:6560
[18]Van Swygenhoven H,Derlet P M,Fr?seth A G.Stacking fault energies and slip in nanocrystalline metals[J].Nat.Mater.,2004,3:399
[19]Li W,Lu S,Kim D,et al.First-principles prediction of the deformation modes in austenitic Fe-Cr-Ni alloys[J].Appl.Phys.Lett.,2016,108:081903
[20]Wang H Y,Zhang N,Wang C,et al.First-principles study of the generalized stacking fault energy in Mg-3Al-3Sn alloy[J].Scr.Mater.,2011,65:723
[21]Kawabata T,Kanai T,Izumi O.Positive temperature dependence of the yield stress in TiAl L10type superlattice intermetallic compound single crystals at 293-1273 K[J].Acta Metall.,1985,33:1355
[22]Hug G,Loiseau A,Veyssière P.Weak-beam observation of a dissociation transition in TiAl[J].Philos.Mag.,1988,57A:499
[23]Paidar V,Inui H,Kishida K,et al.Dislocation dissociation in TiAl alloys[J].Mater.Sci.Eng.,1997,A233:111
[24]Hug G,Loiseau A,Lasalmonie A.Nature and dissociation of the dislocations in TiAl deformed at room temperature[J].Philos.Mag.,1986,54A:47
[25]Schoeck G,Ehmann J,F?hnle M.Planar dissociations of[101]superdislocations in TiAl:Ab-initio electron theory and generalized peierls-nabarro model[J].Philos.Mag.Lett.,1998,78:289
[26]Grégori F,Veyssière P.Properties of<011]{111}slip in Al-richγ-TiAl I.Dissociation,locking and decomposition of<011]dislocations at room temperature[J].Philos.Mag.,2000,80A:2913
[27]Kumar M,Sriram S,Schwartz A J,et al.Weak-beam analysis of dissociated 1/2(112)superdislocations inγ-TiAl[J].Philos.Mag.Lett.,1999,79:315
[28]Hohenberg P,Kohn W.Inhomogeneous electron gas[J].Phys.Rev.,1964,136:B864
[29]Vitos L.Total-energy method based on the exact muffin-tin orbitals theory[J].Phys.Rev.,2001,64B:014107
[30]Vitos L.Computational Quantum Mechanics for Materials Engineers:The EMTO Method and Applications[M].London:Springer,2007:10
[31]Vitos L,Skriver H L,Johansson B,et al.Application of the exact muffin-tin orbitals theory:The spherical cell approximation[J].Comp.Mater.Sci.,2000,18:24
[32]Kumar V,Andersen O K,Mookerjee A.Lectures on Methods of Electronic Structure Calculations[M].Singapore:World Scientific Publishing Co.Pte.Ltd.,1995:317
[33]Perdew J P,Burke K,Ernzerhof M.Generalized gradient approximation made simple[J].Phys.Rev.Lett.,1996,77:3865
[34]Kresse G,Furthmüller J.Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[J].Phys.Rev.,1996,54B:11169
[35]Kresse G,Hafner J.Ab initio molecular dynamics for open-shell transition metals[J].Phys.Rev.,1993,48B:13115
[36]Kresse G,Furthmüller J.Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set[J].Comp.Mater.Sci.,1996,6:15
[37]Kresse G,Joubert D.From ultrasoft pseudopotentials to the projector augmented-wave method[J].Phys.Rev.,1999,59B:1758
[38]Kibey S,Liu J B,Johnson D D,et al.Predicting twinning stress in fcc metals:Linking twin-energy pathways to twin nucleation[J].Acta Mater.,2007,55:6843
[39]Wen Y F,Sun J.Generalized planar fault energies and mechanical twinning in gamma TiAl alloys[J].Scr.Mater.,2013,68:759
[40]Ehmann J,F?hnle M.Generalized stacking-fault energies for TiAl:Mechanical instability of the(111)antiphase boundary[J].Philos.Mag.,1998,77A:701
[41]Woodward C,Maclaren J M.Planar fault energies and sessile dislocation configurations in substitutionally disordered Ti-Al with Nb and Cr ternary additions[J].Philos.Mag.,1996,74A:337
[42]Zhang W J,Appel F.Effect of Al content and Nb addition on the strength and fault energy of TiAl alloys[J].Mater.Sci.Eng.,2002,A329-331:649
[43]Stucke M A,Vasudevan V K,Dimiduk D M.Deformation behavior of[001]Ti-56Al single crystals[J].Mater.Sci.Eng.,1995,A192-193:111
[2]Appel F,Beaven P A,Wagner R.Deformation processes related to interfacial boundaries in two-phaseγ-titanium aluminides[J].Acta Metall.Mater.,1993,41:1721
[3]Kim Y W.Intermetallic alloys based on gamma titanium aluminide[J].JOM,1989,41(7):24
[4]Lipsitt H A,Shechtman D,Schafrik R E.The deformation and fracture of TiAl at elevated temperatures[J].Metall.Trans.,1975,6A:1991
[5]Appel F,Wagner R.Microstructure and deformation of two-phaseγ-titanium aluminides[J].Mater.Sci.Eng.,1998,R22:187
[6]Parameswaran V R.High temperature aluminides and intermetallics[J].JOM,1992,44(6):41
[7]Tsujimoto T,Hashimoto K,Nobuki M,et al.Structures and properties of an intermetallic compound Ti Al based alloys containing silver[J].Trans.Jpn.Inst.Met.,1986,27:341
[8]Hall E L,Huang S C.Stoichiometry effects:On the deformation of binary Ti Al alloys[J].J.Mater.Res.,1989,4:595
[9]Huang S C,Hall E L.Plastic deformation and fracture of binary TiAl-base alloys[J].Metall.Trans.,1991,22A:427
[10]Darolia R,Lweandowski J J,Liu C T,et al.Structural Intermetallics[M].Warrendale:TMS,1993:143
[11]Appel F,Paul J D H,Oehring M.Gamma Titanium Aluminide Alloys:Science and Technology[M].Singapore:Wiley-VCH Verlag GmbH&Co.KGaA,2011:476
[12]Ji Z W,Lu S,Hu Q M,et al.Mapping deformation mechanisms in lamellar titanium aluminide[J].Acta Mater.,2018,144:835
[13]Vitek V.Structure of dislocation cores in metallic materials and its impact on their plastic behaviour[J].Prog.Mater.Sci.,1992,36:1
[14]Vítek V.Intrinsic stacking faults in body-centred cubic crystals[J].Philos.Mag.,1968,18:773
[15]Hartford J,Von Sydow B,Wahnstr?m G,et al.Peierls barriers and stresses for edge dislocations in Pd and Al calculated from first principles[J].Phys.Rev.,1998,58B:2487
[16]Joós B,Ren Q,Duesbery M S.Peierls-Nabarro model of dislocations in silicon with generalized stacking-fault restoring forces[J].Phys.Rev.,1994,50B:5890
[17]Jo M,Koo Y M,Lee B J,et al.Theory for plasticity of facecentered cubic metals[J].Proc.Natl.Acad.Sci.USA,2014,111:6560
[18]Van Swygenhoven H,Derlet P M,Fr?seth A G.Stacking fault energies and slip in nanocrystalline metals[J].Nat.Mater.,2004,3:399
[19]Li W,Lu S,Kim D,et al.First-principles prediction of the deformation modes in austenitic Fe-Cr-Ni alloys[J].Appl.Phys.Lett.,2016,108:081903
[20]Wang H Y,Zhang N,Wang C,et al.First-principles study of the generalized stacking fault energy in Mg-3Al-3Sn alloy[J].Scr.Mater.,2011,65:723
[21]Kawabata T,Kanai T,Izumi O.Positive temperature dependence of the yield stress in TiAl L10type superlattice intermetallic compound single crystals at 293-1273 K[J].Acta Metall.,1985,33:1355
[22]Hug G,Loiseau A,Veyssière P.Weak-beam observation of a dissociation transition in TiAl[J].Philos.Mag.,1988,57A:499
[23]Paidar V,Inui H,Kishida K,et al.Dislocation dissociation in TiAl alloys[J].Mater.Sci.Eng.,1997,A233:111
[24]Hug G,Loiseau A,Lasalmonie A.Nature and dissociation of the dislocations in TiAl deformed at room temperature[J].Philos.Mag.,1986,54A:47
[25]Schoeck G,Ehmann J,F?hnle M.Planar dissociations of[101]superdislocations in TiAl:Ab-initio electron theory and generalized peierls-nabarro model[J].Philos.Mag.Lett.,1998,78:289
[26]Grégori F,Veyssière P.Properties of<011]{111}slip in Al-richγ-TiAl I.Dissociation,locking and decomposition of<011]dislocations at room temperature[J].Philos.Mag.,2000,80A:2913
[27]Kumar M,Sriram S,Schwartz A J,et al.Weak-beam analysis of dissociated 1/2(112)superdislocations inγ-TiAl[J].Philos.Mag.Lett.,1999,79:315
[28]Hohenberg P,Kohn W.Inhomogeneous electron gas[J].Phys.Rev.,1964,136:B864
[29]Vitos L.Total-energy method based on the exact muffin-tin orbitals theory[J].Phys.Rev.,2001,64B:014107
[30]Vitos L.Computational Quantum Mechanics for Materials Engineers:The EMTO Method and Applications[M].London:Springer,2007:10
[31]Vitos L,Skriver H L,Johansson B,et al.Application of the exact muffin-tin orbitals theory:The spherical cell approximation[J].Comp.Mater.Sci.,2000,18:24
[32]Kumar V,Andersen O K,Mookerjee A.Lectures on Methods of Electronic Structure Calculations[M].Singapore:World Scientific Publishing Co.Pte.Ltd.,1995:317
[33]Perdew J P,Burke K,Ernzerhof M.Generalized gradient approximation made simple[J].Phys.Rev.Lett.,1996,77:3865
[34]Kresse G,Furthmüller J.Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[J].Phys.Rev.,1996,54B:11169
[35]Kresse G,Hafner J.Ab initio molecular dynamics for open-shell transition metals[J].Phys.Rev.,1993,48B:13115
[36]Kresse G,Furthmüller J.Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set[J].Comp.Mater.Sci.,1996,6:15
[37]Kresse G,Joubert D.From ultrasoft pseudopotentials to the projector augmented-wave method[J].Phys.Rev.,1999,59B:1758
[38]Kibey S,Liu J B,Johnson D D,et al.Predicting twinning stress in fcc metals:Linking twin-energy pathways to twin nucleation[J].Acta Mater.,2007,55:6843
[39]Wen Y F,Sun J.Generalized planar fault energies and mechanical twinning in gamma TiAl alloys[J].Scr.Mater.,2013,68:759
[40]Ehmann J,F?hnle M.Generalized stacking-fault energies for TiAl:Mechanical instability of the(111)antiphase boundary[J].Philos.Mag.,1998,77A:701
[41]Woodward C,Maclaren J M.Planar fault energies and sessile dislocation configurations in substitutionally disordered Ti-Al with Nb and Cr ternary additions[J].Philos.Mag.,1996,74A:337
[42]Zhang W J,Appel F.Effect of Al content and Nb addition on the strength and fault energy of TiAl alloys[J].Mater.Sci.Eng.,2002,A329-331:649
[43]Stucke M A,Vasudevan V K,Dimiduk D M.Deformation behavior of[001]Ti-56Al single crystals[J].Mater.Sci.Eng.,1995,A192-193:111