基于团簇的多元相成分设计方法: 基于团簇的多元相成分设计方法: 化学势均衡理论在非晶合金材料成分化学势均衡理论在非晶合金材料成分 设计中的应用设计中的应用 董闯董闯 大连理工大学三束材料改性国家重点实验室大连理工大学三束材料改性国家重点实验室 成分敏感成分敏感 多组元合金相成分设计多组元合金相成分设计 多组元体系多组元体系 定量判据定量判据 难难 微观计算和模拟微观计算和模拟 计算量大，且难应用于 复杂体系 计算量大，且难应用于 复杂体系 Phase diagram: phase vs composition 100 90 80 70 60 50 40 30 20 10 100 90 80 70 60 50 40 30 20 10 100908070605040302010 B AC AuBvCw System subsystem relationship AxBy 相图：宏观信息相图：宏观信息 三元以上相图信息少三元以上相图信息少 Al-based QCs Bulk metallic glasses Hydrogen storage alloys e/a-constant cluster line Ra-constant Thin film materials Unified equi- potential rule Quasicrystals are intermetallic compounds An Al-Cu-Fe icosahedral phase grain with the football shape Icosahedral point group Intermetallic with specific composition Al62.5Cu24.5Fe13 Ordered solid Electronic phase e/a=1.86 Al-Cu-Fe-Cr for Dong, Perrot, Dubois, Belin, Mater. Sci. Forum 1994 QC-forming systems e/a-constant line e/a = Ci*(e/a)I (e/a)Al = 3, (e/a)Cu = 1, (e/a)Fe = -2 准晶成分规律准晶成分规律 Tsai, Inoue e/a1.5; Ra Ni3Zr7 Cu-Zr-based BMGs Cu-Zr: H -23 KJ/mol 1) Easy glass forming. 2) Many phases (clusters abundant). 3) Alloying with third elements leads to high GFAs. ZrCu E Tx/Tm Activation energies for crystallization ( E) reach peak values at cluster compositions. Buschow K H L. J Phys. F: Met. Phys., 1984; 14: 593 Cu9Zr4 Cu5Zr8Cu8Zr5Cu6Zr5Cu5Zr6 Cu60Zr40 Cu64Zr36 Cu50Zr50 Cu46Zr54 Cu64.5Zr35.5 special BMG compositions Xu et al, Acta Mater. 2004 Wang et al, Appl. Phys. Lett. 2004 Inoue et al, JIM 2004 Tang et al, Chin. Phys. Lett. 2004 2 mm (max) glass forming range Cu Zr 3mm BMG-forming zone in Zr-Al-Cu 0.00.20.40.60.81.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Al Cu Zr Eutectic eutectics GFA (Tg/Tm and E) increases with increasing e/a Cu5Zr8 Cu5Zr6 Cu6Zr5 Cu8Zr5 Cu9Zr4 Cu58.1Zr35.9Al6 0mm 15mm 4mm Cu55Zr40Al5 Reference cluster Inoue et al, Mater. Sci. Eng. 1994 Schumacher et al, J. Appl.Phys. 1994 Inoue et al, JIM, 2002 Xu et al, Phys. Rev. Lett. 2004 Wang et al, Acta Mater. 2005 3mm BMG-forming zone in Zr-Al-Cu 0.00.20.40.60.81.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Al Cu Zr Eutectics Cu5Zr6 Cu6Zr5 Cu8Zr5 Cu39.7Zr47.1Al13.2 Cu58.1Zr35.9Al6 Cluster Ra Cu8Zr5 e/a = 1.48 Ra-constant line Ra:average atomic radius Ra Cu5Zr6 e/a = 1.5 ico-Cu8Zr5from Cu8Zr3phase deep eutectic point Cu8Zr3phase = (R0/1-R*)/R*= 0.4% topologically dense packing Cu8Zr5 0.00.20.40.60.81.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 M Cu Zr ECu61.8Zr38.2 Cu8Zr5 Cu-Zr-M 体系体系 M=Nb, Sn, Mo, Si, V, Ag, Al, Ti Cu8Zr5-M Cu64Zr36=(Cu8Zr5)1Cu1 Cu64Zr36-M Xia et al. Appl. Phys. Lett., 2006, 88:1.Xia et al. Appl. Phys. Lett., 2006, 88:1. Cluster + glue atom (Cluster + glue atom) + minor alloying element Cluster + glue atom Proof for Cu8Zr5 Our new BMGs: Zr-(Al, Ti)-(Ni, Co) Cu-Zr-M (Nb, Sn, Ag, Al, Ti) (Ce, Sm,Y)-Al-(Ni,Co) (Fe,Co)-based Appl. Phys. Lett. 2006 Mater Sci & Eng. R 2004 Acta Mater. 2003 1. 量化的成分设计。量化的成分设计。 2.联系微观团簇结构和宏观相图特征。联系微观团簇结构和宏观相图特征。 3. 连接亚组元体系和多组元体系。连接亚组元体系和多组元体系。 成分判据特征成分判据特征 Some physics 由Sanderson电负性均衡原理： Electronegativity Equalization Principle (EEM) Upon molecule formation, the electronegativities of all the constituent atoms of a molecule become equal R.T. Sanderson, Science, 121, 207 (1955) Quantum mechanical proof ABAB A0 B0 BA + R.G. Parr et al, J.Chem.Phys., 68, 3801 (1978) A= B= AB 由密度泛函理论，有： +=+=drrVrrFrVrVrTrE HKeene )()()()()()()( )( )( rV r F ?F HK += 化学势 W. Kohn, L.J. Sham, Phys. Rev. A, 140, 1133 (1965) ),(VNEE = 基于密度泛函理论Parr给出化学势与电负性的关系： = = = VV r E N E ) )( ()( R. G. Parr et al., J. Chem. Phys. 68, 3801(1978) Heats of Formation of Transition-Metal Alloys This Letter proposes a scheme for obtaining the d- electron energy-band parameters to be used in a simple analytic model of the alloy heat of formation, H. The scheme employs, as an intermediate step, the equalization of the local chemical potentials of the two sites. Calculations for 3d, 4d, and 5d metal alloys yield H in accord with experimental trends, but, unlike earlier estimates, with d charge transfer in the direction indicated by experiment. R. E. Watson Phys. Rev. Lett. 43, 11301134 (1979) Formation of an electric dipole at metal- semiconductor interfaces A recent theory showed that the polarization of the chemical bonds at metal semiconductor interfaces could quantitatively account for the experimentally observed strength of Fermi level pinning on different semiconductors, without regard to the actual distribution of gap states. The method used in this theory, the electrochemical potential equalization method hitherto employed only in molecular physics, and its limitations are here discussed in detail, especially in the context of application to solid interfaces. Similarities and differences between this theory and the metal induced gap state theory are also discussed. Raymond T. Tung Phys. Rev. B 64, 205310 (2001) 服从费米服从费米-狄拉克分布规律的理想电子气体的化学势为：狄拉克分布规律的理想电子气体的化学势为： 2 1() 12