Mg-Al-Ca合金中二元Laves相的电子结构和力学性能
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摘要
采用基于密度泛函理论的第一性原理方法,研究了Mg—Al-Ca合金中AB_2型二元Laves相(如CaMg_2,CaAl_2和MgAl_2)在不同形态结构(C14,C15和C36)下的晶体结构、电子结构和力学性能.计算所得的晶格常数与实验数据吻合很好.形成能与相关能的计算表明C15-CaAl_2 Laves相具有很好的合金化能力和结构稳定性.态密度和电荷密度的计算从微观上进一步分析了C15-CaAl_2具有很好的合金化能力和稳定性的根源.弹性常数的计算和力学性能的分析表明C14-MgAAl_2具有很好的延展性,C15-MgAAl_2具有很好的塑性.
In this paper,we have carried out first-principles theoretical calculations to investigate the electronic structure and mechanical properties of the AB_2 type binary Laves phase in Mg-Al-Ca alloy, including C14-,C15- and C36- structure for CaMg_2,CaAl_2 and MgAl_2,respectively.The optimized structural parameters were in very good agreement with the experimental values.The calculated heat of formation and cohesive energy showed that the C15 -CaAl_2 Laves phase was of the strongest alloying ability and structural stability.The electronic density of states(DOS) and charge density distribution were given to reveal the micro-mechanism of the good alloying ability and stability of C15-CaAl_2.The elastic parameters were calculated and the mechanical properties were analyzed.It was shown that C14- MgAl_2 is of the best ductility and C15-MgAl_2 is of the best plasticity in the investigated binary alloys.
In this paper,we have carried out first-principles theoretical calculations to investigate the electronic structure and mechanical properties of the AB_2 type binary Laves phase in Mg-Al-Ca alloy, including C14-,C15- and C36- structure for CaMg_2,CaAl_2 and MgAl_2,respectively.The optimized structural parameters were in very good agreement with the experimental values.The calculated heat of formation and cohesive energy showed that the C15 -CaAl_2 Laves phase was of the strongest alloying ability and structural stability.The electronic density of states(DOS) and charge density distribution were given to reveal the micro-mechanism of the good alloying ability and stability of C15-CaAl_2.The elastic parameters were calculated and the mechanical properties were analyzed.It was shown that C14- MgAl_2 is of the best ductility and C15-MgAl_2 is of the best plasticity in the investigated binary alloys.
引文
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[47]Karki B B,Ackland G J,Crain J.Elastic instabilities in crystals from ab initio stress-strain relations [J].J.Phys.:Condens.Matter,1997,9:8579
[48]Chung D H.First pressure derivatives of polycrystalline elastic moduli:Their relation to single-crystal acoustic data and thermodynamic relations[J].J. Appl.Phys.,1967,38:5104
[49]Cline C F,Dunegan H L,Henderson G W.Elastic constants of hexagonal BeO,ZnS,and CdSe[J]. J.Appl.Phys.,1967,38:1944
[50]Mayer B,Anton H,Bott E,et al.Ab-initio calculation of the elastic constants and thermal expansion coefficients of Laves phases[J].Intermetallics, 2003,11:23
[51]Pugh S F.Relations between the elastic moduli and the plastic properties of polycrystalline pure metals [J].Phil.Mag.,1954,459;823
[52]Sumer A,Smith J F.Single crystalline elastic constants of MgZn_2[J].J.Appl.Phys.,1962,33: 2283
[53]Mattesini M,Ahuja R,Johansson B.Cubic Hf_3N_4 and Zr_3N_4:a class of hard materials[J].Phys. Rev.B,2003,68:184108
[2]Miyashita Y,Sajuri Z B,Umehara T,et al.Magnesium -proceedings of the 6~(th) international conference. Fatigue life prediction of magnesium alloys for structural applications[C].Wileg-VCH Verlag GmbH & Co.KGaA,Weinheim,Germany,2004
[3]Schumann S,Friedrich H.Current and future use of magnesium in the automobile industry[J].Mater. Sci.Forum,2003,419-422:51
[4]Mordike B L,Kainer K U.Proceedings of the magnesium alloys and their applications[M].Germany: Werkstoff-Information sgesellschaft,Frankfurt,, 1998,pp.286-293.
[5]Kainer K U(Ed.).Magnesium alloys and technol [M].Wiley-VCH Verlag GmbH &.Co.KGaA, Weinheim,Germany,2003,pp.198-203
[6]Aroule P.IMA-55.A global vision for magnesium [M].Washington D C.:International Magnesium Association,1998
[7]Nie J F.Preface to viewpoint sets on phase transformations and deformation in magnesium alloys[J], Scripta Mat.,2003,48:81
[8]Mordike B L,Ebert T.Magnesium:properties-applications -potential[J].Mater.Sci.Eng.A,2001, 302:37
[9]Fan J F,Yang G C,Xie H,et al.Surface oxidation behavior of Mg-Y-Ce alloys at high temperature[J], Metall.Mater.Trans.A,2005,36:235
[10]Li Z J,Gu X N,Lou S Q,et al.The development of binary Mg-Ca alloys for use as biodegradable materials within bone[J].Biomaterials,2008,29: 1329
[11]Raghavan V.Al-Ca-Mg(Aluminum-Calcium-Magnesium) [J],J.Phase Equilib.Diff.,2007,28: 450
[12]Hirai K,Somekawa H,Takigawa Y,et al.Effects of Ca and Sr addition on mechanical properties of a cast AZ91 magnesium alloy at room and elevated temperature[J].Mater.Sci.Eng.A,2005,403: 276
[13]Zhou D W,Liu J S,Peng P,et al.A first-principles study on the structural stability of Al_2Ca, Al_4Ca and Mg_2Ca phases[J].Mater.Lett.,2008, 62:206
[14]Suzuki A,Saddock N D,Jones J W,et al.Structure and transition of eutectic(Mg,Al)_2Ca Laves phase in a die-cast Mg-Al- Ca base alloy[J]. Scr.Mat.,2004,51:1005
[15]Suzuki A,Saddock N D,Jones J W,et al.Solidification paths and eutectic intermetallic phases in Mg -Al-Ca ternary alloys[J].Acta Mat.,2005,53: 2823
[16]Zhou D W,Peng P,Liu J S,et al.First-principles study on structural stability of 3d transition metal alloying magnesium hydride[J].Trans.Nonferrous Met.Soc.China,2006,16:23
[17]Tsushio Y,Akiba E.Hydrogenation properties of Mg-based Laves phase alloys[J].J.Alloys Compd.,1998,269:219
[18]Hanada N,Orimo S,Fujii H.Hydriding properties of ordered-/disordered-Mg-based ternary Laves phase structures[J].J.Alloys Compd.,2003, 356-357:429
[19]Yuan G Y,Liu Y,Ding W J,et al.Effects of extrusion on the microstructure and mechanical properties of Mg-Zn-Gd alloy reinforced with quasi-crystalline particles[J].Mater.Sci.Eng.A,2008, 474:348
[20]Liu Y,Yuan G Y,Ding WJ,el al.Deformation behavior of Mg-Zn-Gd-based alloys reinforced with quasicrystal and Laves phases at elevated temperatures [J].J.Alloys Compd.,2007,427- 160
[21]Terashita N,Kobayashi K,Sasai T,et al.Structural and hydriding properties of(Mg_(1-x)Ca_x ) Ni_2 Laves phase alloys[J].J.Alloys Compd.,2001, 327:275
[22]Yamada H,Shimizu H.Magnetic states of MgCo_2 and CaCo_2 with the cubic and hexagonal Laves phase structures[J].J.Alloys Compd.,2005,388:15
[23]Yao Q,Sun J,Zhang Y,et el.First-principles studies of ternary site occupancy in the C15 NbCr_2 Laves phase [J].Acta Mater.,2006,54:3585
[24]Aono K,Orimo S,Fujii H.Structural and hydriding properties of MgYNi_4:a new intermetallic compound with C156-type Laves phase structure [J].J.Alloys Compd.,2000,309:L1
[25]Zhong Y,Ozturk K,Sofo J O,et al.Contribution of first-principles energetics to the Ca—Mg thermodynamic modeling[J].J.Alloys Compd.,2006, 420:98
[26]Zhong Y,Liu J,Witt R A,et al.Al_2(Mg,Ca) phases in Mg-Al-Ca ternary system:first-principles prediction and experimental identification[J]. Scripta Mater.2006,55:573
[27]Zhong Y,Yang M,Liu Z K.Contribution of firstprinciples energetics to Al-Mg thermodynamic modeling [J].CALPHAD,2005,29:303
[28]Mayer B,Anton H,Boot E,et al.Ab-initio calculation of the elastic constants and thermal expansion coefficients of Laves phases[J].Internetallics, 2003,11- 23
[29]Westbrook J H,WestbrookFleischeir R L.Intermetallic compounds:principle and practice,Vol. I(Chapter 9)[M].London:John Wiley and Sons,1995- 195.
[30]Fast L,Wills J M,Johansson B,etal.Elastic constants of hexagonal transition metals:theory[J]. Phys.Rev.B,1995,51:17431
[31]Kresse G,Joubert D.From ultra-soft pseudo-potentials to the projector augmented-wave method[J]. Phys.Rev.B,1999,59- 1758
[32]Perdew J P,Zunger A.Self-interaction correction to density-functional approximations for many-electron systems[J].Phys.Rev.B,1981,23:5048
[33]Langreth D C,Perdew J P.Theory of nonuniform electronic system I:analysis of the gradient approximation and a generalization th at works[J].Phys. Rev.B,1980,21:5469
[34]Perdew J P.Density-functional approximation for the correlation energy of the inhomogeneous electron gas[J].Phys.Rev.B,1986,33:8822
[35]Perdew J P,Wang Y.Accurate and simple analytic representation of the electron-gas correlation energy [J].Phys.Rev.B,1992,45:13244
[36]Payne M C,Teter M P,Allan DC,et al.Iterative minimization techniques for ab initio total-energy calculations:molecular dynamics and conjugate gradients [J].Rev.Mod.Phys.,1992,64:1045
[37]Fu C L,Wang X D,Ye Y Y,et al.Phase stability, bonding mechanism,and elastic constants of Mo_5Si_3 by first-principles calculation[J].Intermetallics, 1999,7:179
[38]Nylen J,Garcia F J,Mosel B D,et al.Structural relationships,phase stability and bonding of compounds PdSn_n(n = 2,3,4)[J].Solid State Sci., 2004,6:147
[39]Ormeci A,Chu F,Wills J M.Total-energy study of electronic structure and mechanical behavior of C15 Laves phase[J].Phys.Rev.B,1996,54:12753
[40]Hill R.The elastic behaviour of a crystalline aggregate [J].Proc.Phys.Soc.A,1952,65:349
[41]Jiang C,Sordelet D J,Gleeson B.Site preference of ternary alloying elements in Ni_3Al:a first-principles study[J].Acta Mater.,2006,54:1147
[42]Ravindran P,Vajeeston P,Vidya R,etal.Detailed electronic structure studies on superconducting MgB_2 and related compounds[J].Phys.Rev.B, 2001,64:224509
[43]Beckstein O,Klepeis J E,Hart G L W,et al. First-principles elastic constants and electronic structure ofα-Pt_2Si and PtSi[J].Phys.Rev.B, 2001,63:134112
[44]Born M,Huang K.Dynamical theory of crystal lattices[M].Oxford:Oxford University Press, 1956
[45]Wang J,Yip S,Phillpot S R,et al.Crystal insta- bilities at finite strain[J].Phys.Rev.Lett., 1993,71:4182
[46]Wang J,Li J,Yip S,et al.Mechanical instabilities of homogeneous crystals[J].Phys.Rev.B,1995, 52:12627
[47]Karki B B,Ackland G J,Crain J.Elastic instabilities in crystals from ab initio stress-strain relations [J].J.Phys.:Condens.Matter,1997,9:8579
[48]Chung D H.First pressure derivatives of polycrystalline elastic moduli:Their relation to single-crystal acoustic data and thermodynamic relations[J].J. Appl.Phys.,1967,38:5104
[49]Cline C F,Dunegan H L,Henderson G W.Elastic constants of hexagonal BeO,ZnS,and CdSe[J]. J.Appl.Phys.,1967,38:1944
[50]Mayer B,Anton H,Bott E,et al.Ab-initio calculation of the elastic constants and thermal expansion coefficients of Laves phases[J].Intermetallics, 2003,11:23
[51]Pugh S F.Relations between the elastic moduli and the plastic properties of polycrystalline pure metals [J].Phil.Mag.,1954,459;823
[52]Sumer A,Smith J F.Single crystalline elastic constants of MgZn_2[J].J.Appl.Phys.,1962,33: 2283
[53]Mattesini M,Ahuja R,Johansson B.Cubic Hf_3N_4 and Zr_3N_4:a class of hard materials[J].Phys. Rev.B,2003,68:184108